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PAGE 1 DEVELOPMENT OF HIGHACCURA CY VIDEO MICROSCOPYBASED SUBCELLULAR TRACKNG IN CHARA CTERIZING CELLULAR DYNAMIC PROCESSES By PEIHSUN WU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORID A IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010 1 PAGE 2 2010 PeiHsun Wu 2 PAGE 3 To my wife and my family 3 PAGE 4 ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Y iider Tseng, for his guidance and support. He has consistently provided me with va luable professional and personal advice and has always guided me to work successfully. I deeply appreciate all the opportunities he has offered to me. I am also thankful fo r my graduate study committee members, Dr. Richard Dickinson, Dr. Tanmay Lele, and Dr. Edward Chan for their valuable experience and expertise that has helped me to finish my work. I would like to express my special than ks to all of my group members for their great assistance in many ways, Dr. Hengy i Xiao, Wei Cheng, ShenHsiu Hung, Sinan Dag, and Patrick Burney. Many thanks also go to James Hinnant, and Dennis Vince for their help in equipment maintenance. Spec ial thanks to Mr. Stephen Hugo Arce for helping to prepare my dissertation. Finally, I want to thank my wife, YunTing Hung, my par ents, and my other family members for their love and gr eat support in these years. This dissertation could not have been acco mplished without the help of so many. I truly appreciate everyone. 4 PAGE 5 TABLE OF CONTENTS page ACKNOWLEDG MENTS .................................................................................................. 4LIST OF TABLES ............................................................................................................ 8LIST OF FI GURES .......................................................................................................... 9LIST OF ABBR EVIATION S ........................................................................................... 11ABSTRACT ................................................................................................................... 12CHAPTER 1 INTRODUC TION .................................................................................................... 141.1 Motiva tion ......................................................................................................... 141.1.1 VideoBased Particle Tracki ng and Mean Square Dis placement ............ 141.1.2 ElectronMult iplying CCD ........................................................................ 151.1.3 Optimum Estimate of the True Trajectory among Nois e .......................... 161.1.4 Nuclear Architectu re and Gene R egulati on ............................................. 181.2 Study Ou tline .................................................................................................... 192 A METHOD TO ACHIEVE HIGH ACCURACY MICRO RHEOLOGY ...................... 212.1 Backgr ound ....................................................................................................... 212.2 Material and Methods ....................................................................................... 232.2.1 Preparation of Glycerol Sa mples with Embedded Fluorescent Particle s ........................................................................................................ 232.2.2 Microscope and CCD Ac quisition S ystem ............................................... 232.2.3 Particle Tracking Algor ithm ...................................................................... 242.2.4 Mean Square Di splacement .................................................................... 252.2.5 Extracting the Noise Amplit ude and Estimating the Mean Signal Intensit y ......................................................................................................... 252.2.6 Monte Carlo Simulati on ........................................................................... 262.2.7 Rheom eter ............................................................................................... 282.2.8 Intracellular Particle Tra cking and Cytoplas mic Rheol ogy ....................... 282.3 Results .............................................................................................................. 292.3.1 Light Source Affe cts the MSD Values...................................................... 292.3.2 Interplay of Several Fact ors Determines the Static Error ......................... 312.3.3 Direct ParameterMapping can be used to Accurately Estimate the Static E rror .................................................................................................... 332.3.4 Procedure Verification using in vitro and in situ Experimental Systems .. 352.3 Discuss ion ........................................................................................................ 372.4 Conclu sion ........................................................................................................ 39 5 PAGE 6 3 A GENERAL METHOD FOR IMPROVING SPATIAL RESOLUTION BY OPTIMIZATION OF ELECTRON MU LTIPLICATION IN CCD IMAGING ................ 473.1 Backgr ound ....................................................................................................... 473.2 Methods and Results ........................................................................................ 493.2.1 The EM Gain can Influenc e Quantitative Im age Analysi s ........................ 493.2.2 EM Gain Char acterizati on ....................................................................... 503.2.3 The Signal to Noise Ratio (SNR) can be used to Optimize the EM Gain Se tting .................................................................................................. 543.2.4. EM Gain Effects on MultiPixel A nalysis ................................................. 553.2.4.1 Optimal EM Gain De pends on the Size and Background Intensity of t he Object ............................................................................. 573.2.4.2 Particle Tracki ng Experiments Verify the EM Gain Effect on Image Anal ysis ....................................................................................... 583.3 Discuss ion ........................................................................................................ 593.3.1. The Working Range and E ffectiveness of EM Gain................................ 593.3.2 Analysis of the Estimat ed Values in th is Stud y ........................................ 603.3.3 Assessment of EM Gain in Subcel lular Particle Tracking Experiments ... 603.3.4 Application of Proper EM Gain to Biophysical Measurements beyond Particle Tr acking ........................................................................................... 613.5 Conclu sion ........................................................................................................ 634 ANALYSIS OF VIDEOBASED MICROSCOPIC PARTICLE TRAJECTORIES USING KALMAN FILTERIN G ................................................................................. 704.1 Backgr ound ....................................................................................................... 704.2 Theory of Kalman Filtering in Particle Tracking ................................................ 724.2.1 The Parameters of the Kalman F ilter Related to a Particle Tracking Trajecto ry ...................................................................................................... 724.2.2 The Kalman Filter Gain is Determined by the Ratio Q / R but not Q or R .. 754.2.3 MSD Estimates from a Filtered Traj ectory are Equal to the True State ... 774.3 Materials and Methods ...................................................................................... 784.3.1 Application of the Kalman Filt er to Simulated Trajectori es ...................... 784.3.2 Microscopic Particle Tracking System ..................................................... 794.3.3 Particle Tracking Experim ents in Glycero l Soluti ons ............................... 794.3.4 Particle Tracking Experimen ts in Gliding Mo tility A ssays ........................ 794.4 Results .............................................................................................................. 804.6 Discuss ion ........................................................................................................ 864.7 Conclu sion ........................................................................................................ 895 CHARACTERIZATION OF THE NAC1 NUCLEAR BODY DYNAMICS AND CHROMATIN ASSOCI ATION ................................................................................. 965.1 Backgr ound ....................................................................................................... 965.2 Methods and Results ........................................................................................ 985.2.1 Characterization of NAC1 NB in nucleus ................................................ 985.2.2 Typical Motion of NAC1 NB in Nu cleus ................................................ 100 6 PAGE 7 5.2.3 NAC1 NB Dynamics Relates to the Chromatin Architecture and ATP Level ........................................................................................................... 1035.3 Discussion and C onclusion ............................................................................. 1076 CONCLUSION S ................................................................................................... 1166.1 Accurate MSD Estimation in VideoBased Tracking ....................................... 1166.2 Optimizing Image Acquisition .......................................................................... 1166.3 Optimum Estimatation of Bi ophysical Pro perties ............................................ 1176.4 Dynamics of Nuclear Organelles Asso ciated with Chromati n Structure .......... 117LIST OF REFE RENCES ............................................................................................. 119BIOGRAPHICAL SK ETCH .......................................................................................... 128 7 PAGE 8 LIST OF TABLES Table page 31 List of sections contain The values of the effective EM gain (k), excess factor .. 6432 List of sections contain The values of the effective EM gain (k), excess factor (F), intensity offset ( ), and relative working range at several EM gain settings estimated for ex perimental system. ....................................................... 64offsetI 8 PAGE 9 LIST OF FIGURES Figure page 21 The mean square displacement (MSD) is correlated to the peak intensity (I ) of microspheres tracked by a chargecoupled device (CCD) camera.. ............... 4122 Static error (2 2) can be estimated using si mulated Gaussian beads. ............... 4223 The method to relate extracted st atic error from simulated beads to experimental microsphere images is demons trated. ......................................... 4324 A Gaussian bead with the parameter s determined by the mapping procedure in this paper can represent t he experimental mi crosphere. ................................ 4425 Static error can be corrected for the MSD of microspheres embedded in glycerol .. ............................................................................................................. 4526 Static error can be corrected for the MSD of 100nm carboxylated polystyrene particles embedded in MC3T 3E1 fibroblast cells under redfluorescenc e.. ..................................................................................................... 4631 EM gain causes contradictory effect s on the spatial resolution of protein clusters .............................................................................................................. 6532 EM gain parameters are determined experimentally ......................................... 6633 The optimal setting of the EM gain depends on the intensity of the signal.. ....... 6734 The relation of the k and S is affected by .. ................................................. 68peakI35 The EM gain performance in parti cle tracking depends on experimental condition s. .......................................................................................................... 6936 Plot of 1000, S vs. 0, S .......................................................................................... 6941 Schematic illustration of the principle of Kalman filter in estimating the accurate trajectory in a ce llular dynamic process. .............................................. 9042 Estimation of the true trajectory from positioning errors using Kalman filter. ...... 9143 Schematic illustration of the procedure of implementin g Kalman filter into a microscopic particle tracking system to improve the spatia l resolution ............... 9244 Characterization of the performance of Kalman filter on estimating particle tracking trajec tories ........................................................................................... 9345 Improving the positioning error of parti cle tracking in glyc erol solution. .............. 94 9 PAGE 10 46 Improving the positioning error of par ticle tracking in gliding motility assays using Kalman filter ............................................................................................. 9551 Fixed and stain images s how the location of NAC1 NB in a nucle us.. ............ 10952 Dynamics structure of NAC1 NBs was analyzed by Fluorescence recovery after Photobl eaching.. ....................................................................................... 11053 Characterize the NAC1 NB dyna mics from their MS D response .. ................... 11154 A vector map shows the NB Movement over three different time scale, 0.1s, 1s and 5s (from top to bottom). ......................................................................... 11255 Reconstructed NA C1 NB im age. ..................................................................... 11256 NAC1 NB mobility is a ssociated with it s size ................................................... 11357 Drug treatment affects NAC1 NB kinet ics.. ..................................................... 11458 MSD plots show the NAC1 NB dynamics over time in response to drug treatment.. ........................................................................................................ 115 10 PAGE 11 LIST OF ABBREVIATIONS ActD Actinomycin D ACF Auto correlation function CCD Chargecoupled device EMCCD Electronmultiplication CCD ICCD Intensified CCD LatB Lactrunculin B MSD Mean square displacement MT Microtubule NB Nuclear body NOC Nocodazole PMT Photonmultiplication tube ROI Region of interest SNR Signal noise ratio 11 PAGE 12 Abstract of Dissertation Pr esented to the Graduate School of the University of Florida in Partial Fulf illment of the Requirements for t he Degree of Doctor of Philosophy DEVELOPMENT OF HIGHACCURA CY VIDEO MICROSCOPYBASED SUBCELLULAR TRACKING IN CHARACTERIZING CELLULAR DYNAMIC PROCESSES By PeiHsun Wu May 2010 Chair: Yiider Tseng Major: Chemical Engineering Videobased particle tracking monitors the microscopic movement of labeled biomolecules, subcellular organelles and fluo rescent probes within a complex cellular environment. Measurements obtained by this technique, mainly the mean square displacement (MSD) of the tracers, enable us to extract the dynamic information of subcellular processes and the intracellular mechanical properties. However, MSD measurements are highly suscept ible to static error introduced by noise in the image acquisition process that leads to an incorrect positioning of the particle. An approach that greatly increases the accuracy of MSD measurements is developed herein by combining experimental data with Monte Carlo simulations. In addition, the trajectories obtained from videobased particle tracking can pr ovide insight into transient subcellular transportation such as endocytosis. In this work it is shown that the Kalman filter, a robust algorithm to estimate the stat e of a linear dynamic system from noisy measurements, can be applied to particle tr acking to dramatically reduce positioning error while retaining the intrinsic fluctuations of a cellular dynamic process. Hence, the Kalman filter can serve as a powerful tool to infer a trajectory of ultrahigh fidelity from 12 PAGE 13 13 noisy images, revealing the details of dynamic cellular processes. Finally, the short time dynamics of NAC1 nuclear bodies (NB) are measured to study their interactions with chromatin since the chromatin architecture is suspected to be highly associated with gene regulation. I demonstrat e that the dynamics of NA C1 NBs are determined by these associations with chromatin as well as the organization of the chromatin structure through the utilization of t he developed high accuracy particle tracking analysis method. PAGE 14 CHAPTER 1 INTRODUCTION 1.1 Motivation 1.1.1 VideoBased Particle Tracking and Mean Square Displacement Videobased particle tracking monitors the re altime motion of tracer particles. The mean square displacement (MSD ) of these tracer particles may be used to interpret cellular biophysical properties, including t he diffusivities of lipid membrane and transmembrane proteins 1, 2, intracellular mechanics3, 4 and the dynamics of chromatin and nuclear bodies 410. However, as more confined spaces are probed with higher temporal resolution, the ability of particle tracking to perform with consistent accuracy is diminished by an inherent measurement error 11, 12. For example, when imaging with a chargecoupled device (CCD) camera, the noise can fluctuate between individual pixels within tracking frames causing a positioning error. This error will propagate as static error to affect the accuracy of MSD analys is because the MSD is calculated from a particles displacement 1214. The characteristics of static error have been previously discussed from a theoretical perspective 1113. Webbs group investigated the magnitude of positioning error as a function of the number of detec ted photons and the spot size, demonstrating that the most reliable results stem from brighter, welldefined particles 13. In their studies, a formula was derived to calculate t he spatial resolution. This formula enables a quick estimation of the spatial resolution with approximately 70% accuracy when compared to their own experimental resu lts from tracking immobilized particles 13. The resolution of tracking is related to the appearance of particles in images, which is determined by factors including focal plan e position and the morphology of a tracer. 14 PAGE 15 Even while tracking the same size of beads, the static error of each probe in an image will be different as a result of their zdistance to the focal plane. Therefore, a method to precisely extract static error for each tracked particle in situ will greatly advance this technique, providing a way to estimate a mo re accurate MSD by the removal of the static error individually. In chapter 2, a new approach is developed to accurately quantify static error. Using a Monte Carlo approach incorporated with experimental imaging noise, the resolution of each individual tracer is succe ssfully estimated. An advantage of this strategy is that it solely relies on exper imental outcomes, bypassing the details of complicated tracking algorithms and the various hardware specifications of tracking systems 12, 13, 15. More importantly, this method signifi cantly improves the resolution of particle tracking experiments, greatly reducin g ambiguities and potential errors in the interpretation of experiments. 1.1.2 ElectronMultiplying CCD In modern microscopic systems, t he most common and economical device adopted as a photon detector is the chargecoupled device (CCD) camera, which can simultaneously sense the intensit y profile of light emitted fr om objects within the visual field of the microscope using more than one m illion parallel arrays. With this device, cell images with detailed information can be c aptured and later analyzed. However, the performance of the CCD camera drops qui ckly with a decreasing of photon signal 16, and, as a consequence, significantly reduces the accuracy of low intensity subcellular measurements in a condition such as single molecule fluorescence imaging. Through the use of much more expensive avalanche photodiode detectors (APD) or photomultiplier tubes (PMT) 17, 18 to acquire images, the resolution of low intensity 15 PAGE 16 measurements can be greatly improved; however, these types of detectors do not have large numbers of individual sensing units in contrast with the parallel array of the CCD camera. When acquiring information from the vi sual field of the microscope, an APD or a PMT sensor uses a scanning mode, whic h is usually much slower than the CCD camera. Hence, if the spatial resolution of low intensity images in a CCD camera can be improved, the CCD camera becomes the best c hoice of camera due to its accessibility and high acquisition rate. Several intensityenhanced techniques have been developed to obtain high contrast images from low intensity signals su ch as intensified CCD (ICCD) and electron multiplying CCD (EMCCD) 16. The new generation of EMCCD camera has outperformed the ICCD and become a popular c hoice for imaging the dynamics of single molecules in cells 19, 20. EMCCD utilizes several specialized extended serial registers on the CCD chip to apply a high vo ltage and produce multiplying gain through the process of impact ionization in silicon 21. This capability to elevate the photongenerated signal above the readout noise of the device even at high frame rates has made it possible to meet the need for ultralowlight imaging applic ations without the use of external image intensifiers. In C hapter 3, a general qua ntitative method is developed for optimizing the EMCCD performance in the m easurement of biophysical parameters including the si ngle particle tracking. 1.1.3 Optimum Estimate of the True Trajectory among Noise Cellular and subcellular dynamics control cell physiology 22, 23. These dynamic processes include not only protein diffusi on and transport but also the motion of intracellular organelles 22, 24. The invasion process of bacteria into the intracellular regions of mammalian cells has also been disco vered to involve in the intracellular 16 PAGE 17 dynamics of the host cells 25. Therefore, the dynamic proce sses play a critical role in understanding the molecular mechanisms of a subcellular event and should not be ignored. The most direct way to study a ce llular dynamic process is to monitor the motion of the observed object, and to further correlate this physical motion to the biochemical functions of the composed biomol ecules of the objec t. For example, the analysis of the step size of the motor pr oteindriven transport cargoes led to the understanding of how the motor proteins function 2629. The connection between the bacteria motion and the function of the bacterial protein, ActA, elucidates how bacteria move inside the host 30, 31. In these studies, particle tracking serves as the most direct technique for studying the real time movement of objects in live cells. Particle tracking has been applied to study various subcellular events, such as the genomic dynamics 32, viral infection 33, 34, cellular endocytosis 35, membrane protein trafficking 36, and cargo transport 37. Besides the studies of dynamic events in a live cell, particle tracking is also applicable to probe the mechanical properties of the intracellular region of the live cells via particle tracking microrheology 38, which analyzes the dynamic fluctuation of disp lacement of an inert particle embedded in the cytoplasmic region of a live cell. Thr ough the microrheology theorem 39, 40, the rheological parameters of a cell, such as creep complia nce, elastic modulus, and viscous modulus, can be explored 38, 41. Compared to other existing techniques, such as atomic force microscopy, intracellular microrheology intr oduces minimal perturbation to acquire the physical properties of the intr acellular region of the cells. Using this technique, the mechanical properties of various cell lines under different extracellular stimuli (chemical 41 and mechanical 42) and microenvironmental topolog y (twodimensional vs. three17 PAGE 18 dimensional 43) have been probed. The motion from objects can contribute valuable insights into many biological events, and the accuracy of trajec tory from particle tracking is critically important for the effectiveness of those studies. In the system and control field, the theory to estimate an appr opriate state of a dynamic system from noisy meas urements is wellestablished. In particular, the Kalman filter algorithm provides t he optimal state estimate for linear dynamic systems in the presence of Gaussian noise generated from measurements. The Ka lman filter has been successfully applied to wide variety in engineering and science fields 44, 45, And the potential use of a Kalman filt er to study cell motion has been mentioned in the past 46. In Chapter 4, I explore in detail the application of the Kalman filter algorithm to improve the estimation of the particle trajectory obtai ned from a microscopic particle tracking experiment. 1.1.4 Nuclear Architectur e and Gene Regulation The accomplishments of several genome proj ects provide great insights into the genomics and nuclear architecture 4749. However, the regulatory mechanism of a gene is not solely determined by the genome sequence 4951. For example, the DNAprotein complex, chromatin, can pack into multip le levels of condensed states through DNAassociated proteins, which are believed to be associated with the gene regulation 50, 52. In addition, the cell nucleus also features se veral distinct architectures and functional compartments, including the nucleoli, PML bodies, Cajal bodies, nuclear speckles and lamina 5355. Since the transcription process requires a protein complex to interact to the gene 56, the gene expression is determined by the accessibility of the genetic materials to the transcriptional protei n complexes, which may be associated to the changes of nuclear architecture. 18 PAGE 19 It has been reported that the development of cancer cells are also associated with nuclear architecture changes 57. The evolution of cancer ce lls is a multistep process and it has been shown that an alteration in gene expression plays a central role 58. Epigenetics hypothesizes that t he alteration in gene expression of cancer cells may be mediated without mutations in the primary DNA sequence of a gene 59. Together, the nuclear architecture change might also be associated with tumorigenesis. Currently, much of the structural information of nuc lear organization is based on the analysis of fluorescent labeling in fixed cells 50. However, the real time response of the chromatin structure is not well understood due to experimental difficu lty. In Chapter 5, the dynamics of a newly discovered nuclear bod y (NB), which contains a cancer cell associated protein NAC1, is studied in live cells by utilizing single particle tracking. This chapter provides intranuclear dynamics information, determined by the association between chromatin and the NAC1 prot eincontaining NB (NAC1 NB). 1.2 Study Outline This dissertation includes four research topics, which are described in detail from chapter 2 to 5, respectively. In this chapt er (chapter 1), I have ex plained the rationale for studying these topics. In C hapter 2, the foundati on for describing how to extract the positioning error from image analysis in later chapters is introduced. In chapter 3, the method to quantitatively determine the optimum settings of elec tron multiplication from a chargecoupled device for particle tracking is addressed. In chapter 4, I develop a method using the Kalman filter, a recursive algorithm used successfully in systems and control theories, to estimate a highresolution trajectory when tr acking under the optical limitations. In chapter 5, the investigation of the real time movement of NAC1 nuclear 19 PAGE 20 20 bodies in living cells is presented, based on the developed methods described in prior chapters. Finally, the last chapter (chapt er 6) concludes this dissertation. PAGE 21 CHAPTER 2 A METHOD TO ACHIEVE HIGH ACCURACY MICRORHEOLOGY 2.1 Background Videobased particle tracking monitors the re altime motion of tracer particles. The mean square displacement (MSD ) of these tracer particles may be used to interpret cellular biophysical properties, including t he diffusivities of lipid membrane and transmembrane proteins 1, 2, intracellular mechanics3, 4 and the dynamics of chromatin and nuclear bodies 410. However, as more confined spaces are probed with higher temporal resolution, the ability of particle tracking to perform with consistent accuracy is diminished by the inher ent measurement error 11, 12. For example, w hen imaging with a chargecoupled device (CCD) camera, the noise can fluctuate between individual pixels within tracking frames causing a positioning error. This error will propagate as static error to affect the accuracy of MSD analys is because the MSD is calculated from a particles displacement 1214. The characteristics of static error have been previously discussed from a theoretical perspective 1113. Webbs group investigated the magnitude of positioning error as a function of the number of detec ted photons and the spot size, demonstrating that the most reliable results stem from brighter, welldefined particles 13. In their studies, a formula was derived to calculate t he spatial resolution. This formula enables a quick estimation of the spatial resolution with approximately 70% accuracy when compared to their own experimental resu lts from tracking immobilized particles 13. Later, Savin and Doyle also develo ped a theoretical model to de scribe the static error based on a signalindependent Gaussian noise. Their work suggested that more accurate MSDs could be obtained by directly subtracting the extracted static error from 21 PAGE 22 experimental MSD results 12. These works approximated the static error in tracking systems, demonstrating the crit ical importance of correcti ng a potentially significant bias. However, a method to precisely extract static error from individual experimental systems is not currently known, and the accuracy of the MSD information used to decipher the biophysical properties of cellular systems has thus been limited. Herein, a new method is developed to accurately quantify static error. Using a Monte Carlo approach over a statistically m eaningful number of tr ials, the standard deviation (the spatial resolution, ) of the tracked positions of a static particle in an image was used as a quantitative meas urement of the static error (2 2) 1214. In this way, the dependence of static error on a particles signal intens ity, background intensity, radius, and center position within a pixel wa s individually quantified. Simulated images constructed from these controlling parameters were empirically mapped to experimental images so that the static error extracted fr om simulations could be applied to correct the MSD of actual experiments. An advantage of this strategy is that it solely relies on experimental outcomes, bypassing the details of complicated tracking algorithms and the various hardware specific ations of tracking systems 12, 13, 15. More importantly, this method significantly improves the resolution of particle tracking experiments, greatly reducing ambiguities and potential errors in the interpretation of experiments. The effectiveness of this approach was succe ssfully tested by tracking particles in glycerol. Rheological measurements using th is novel approach compare very well with conventional macroscopic rheologic al measurements. Creep compliance measurements of the cytoplasmi c region of serumstarved MC3T3E1 fibroblasts using this method revealed a greater degree of fr ee diffusion in a shorter time scale than 22 PAGE 23 originally observed. Thus, this correction enhances our capacity to assess accurate MSD and offers a powerful approach for the signi ficant advancement of particle tracking techniques used for the studies of cellular dynamics and microrheology. 2.2 Material and Methods 2.2.1 Preparation of Glycer ol Samples with Embedded Fluorescent Particles Glycerol samples with suspended 100nm carboxylated polystyrene fluorophores (Invitrogen, Carlsbad, CA) were made by well mixing with ethanol at a 1/1000 volumeratio on a center area of a glass bottom dish (MatTek, Ashland, MA). Slides for tracking immobile particles were prepared by air dr ying the mixture onto a glass coverslip. The coverslip was mounted onto a glass s lide with a drop of FluoromountG (SouthernBiotech, Birmingham, AL) and allowed to dry for 4 hrs before being sealed with nail polish. 2.2.2 Microscope and CCD Acquisition System A Nikon TE 2000E inverted microscope equipped with a 60 oilimmersion, N.A. 1.4 objective lens (Nikon, Melville, NY) and a Cascade 1k camera (Roper scientific, Tucson, AZ) was used to acquire the time c ourse images of fluorescent particles for each sample. UVvisible light from XCite 120 PC (EXFO, Mississauga, Ontario, Canada) incorporated with a G2E/C filter (528553/590630 excitation/emission, Nikon) was used to excite the particl es. Three by three binning, which increased the increment of pixel size three times to 390 nm, and region of interest control were used to increase the frame rate to 30 frames per second (fps) and enhance the signaltonoise ratio (SNR). Onchip multiplication gain functionalit y of the CCD was activated to effectively reduce the CCD readout noise and further enhance the SNR. Video was captured at 30 23 PAGE 24 fps over the course of 21.5 sec, allowing 1. 5 sec for the frame ra te to stabilize after initiation and 20 sec for a single particle tracking realization. 2.2.3 Particle Tracking Algorithm Tracking images not only cont ain the signals from the obj ects that were being analyzed, but also the systems inherent noise and background signals. To distinguish the object signals from the noise and backg round, the images needed to be filtered to reduce the noise and to subtract the background. In this study, a Gaussian kernel filter 15 was selected to process the images. Many f ilters are designed for this purpose, such as an Airy disk 2 for the pointspread function; however a Gaussian kernel filter is mathematically more tractable and shows an insignificant difference in practice. In this study, MSD obtained by three pos itioning algorithms, centroid, Gaussianfitting, and cross correlation (COR), have been crosscompared for fixed particles (Presumably the true MSD is equal to zero). The results suggest ed that the position determined by the Gaussianfitting algorithm possessed the smallest static error because it generated the lowest MSD values for fixed particles. Moreover, the Gaussianfitting algorithm not only yields an estimated particle position but also a peak intensity and radius, which can further be utilized in this simulation approach for predicting the static error (see the M onte Carlo simulation section below). Thereafter, the filtered images were subjecte d to direct Gaussian curve fitting, as it had shown that this was the pr eferred method for particle localization in comparison to the Centroid and CrossCorrelation methods 14. Direct Gaussian curve fitting utilizes a least squares algorithm on the logarithmic 2dimensional Gau ssian distributi on formula, 2 2 2'2 )'()'( )'log(),(loga y x pR y x IyxI (21) 24 PAGE 25 to fit the particle intensity on the filtered images and to locate the particle position from the local maximum intensity pixel and its adjacent four pixels 14. In the equation, Ip represents the pixel in tensity of an image and the fitted parameters I Ra x and y represent the particle peak intensity, parti cle image radius, and cent er position of the particle in xand ydirection, respectively. 2.2.4 Mean Square Displacement Captured videos of fluctuating microspher es were analyzed by custom particle tracking routines incorporated into MATL AB (The MathWorks, Inc., Natick, MA). Individual timeaveraged MSDs ar e expressed by the formula, r2 xt xt2 yt yt2 (22) where x(t) and y(t) are the time dependent coordinates of a nanoparticle in the xand ydirections, t is the elapsed time, is the time lag, and t he brackets represent time averaging 60. 2.2.5 Extracting the Noise Amplitude and Estimating the Mean Signal Intensity Various combined sources of noise c an occur in a CCD camera. The dominant varieties of noise are shot noise, readout noise, and background noise from outoffocus particles 12, 61. Under a uniform light source, each s ensing unit (i.e., a pixel) should receive the same quantity of photons to be c onverted to the digital intensity output IP. However, the fixed pattern noise suggested t hat each pixel unit inherently possesses an incomparable random bias in photon measurement 61. The mean signal intensity (IPS) of the whole image can be estimated from t he mean intensity over all pixels (IP). To eliminate the bias caused by fixed pattern noise, intensity subtraction between two frames with the same amplit ude of illumination power is us ed. Therefore, the standard 25 PAGE 26 deviation (STD) of pixel intensity (IP) can mathematically repr esent the noise amplitude (IPN). IPN STD ( I P 1 I P 2) 2 (23) To estimate the background intensity (IB) from an experim ental CCD image with fluorescent particles present, the same method described in the previous paragraph was applied but using only the particlesignalfree region in stead of the entire image. The particle signal region was found by looking for a difference larger than one between two convolved images, i.e., Gaus sian kernel of half width (1 pxl) and Gaussian kernel of consistent size (2w+1, 7 pxl) 12. Therefore, the region wher e the signal difference was less than one was selected for further background intensity analysis. 2.2.6 Monte Carlo Simulation Gaussian particles were simulated in the central area of a zerointensity, 31 pixel 31 pixel zone image. A twodimensional Gaussian distribution was used to describe the intensity profile of a simulated Gaussian bead. A noise free Gaussian particle (IP) can be expressed as IP( x y ) I exp( ( x x)2 ( y y)22 Ra 2 ) IB, (24) where IP(x, y) is the pixel intensity value at the x, y position of an image, I represents the peak intensity, x and y are the subpixel location of Gaussian particle in xand ydirection respectively, and Ra indicates the apparent radius of particle intensity profile. Further, homogenous background intensity (IB) is added to each pixel in order to mimic real imaging. The IP intensity array represents t he simulated noise free image. Based on the experimental noise extracted from the microscopic tracking system used, 26 PAGE 27 the IPN of each pixel is correlated with its IPS, the individual pixel signal intensity (see Fig. 21D). Therefore, simulated images (IMG) that mimic real imaging conditions can be represented by IMG ( x y ) [ IP( x y )] StoN ( IP( x y )) R 0 1 (25) In the preceding function, StoN repres ents the empirically measured correlation between IPS and IPN (in the case herein, it is a 4t h order polynomial; see Fig 21C). R(0,1) represents a normally distribut ed random number with zero mean and unit variance. Here a Gaussian noise was used to represent the system noise over the full intensity spectrum. The noise sources in a pixel of CCD are mainly dominated by readout and photon shot noise. The noise intens ity histogram of the CCD camera of the experimental system displayed a Gaussian distribution throughout the entire CCD signal sensing range from 1300 arbitrary units (A U) to 65535 AU. The Rsquared value from fitting a Gaussian distribution to the entire spectrum of IPS in the experiment was always higher than 0.98, suggesting t hat the use of a Gaussian random number in the Monte Carlo simulation to represent IPS could be justified. This is in agreement with previous independent studies, which dem onstrated that the combined noises, including shot noise, dark noise and readout noise, show a Gau ssian distribution for a high influx of photons 13, 61. The simulated image was further processed through the particletracking algorithm to estimate the simulated particles position. Six hundred trials were tested for each condition in order to estimate the uncertainty in positioning and the relative error for this estimation was found to be below 3%. The position error (p) is defined as the distance between the true position and the position estima ted by the tracking algorithm. Spatial 27 PAGE 28 resolution ( ), and hence static error (2 2), is estimated from t he summation of standard deviation in the xand ydirections. 2.2.7 Rheometer Conventional rheology studies on the glycerol samples were conducted using an ARG2 stresscontrolled softwareoperated rheometer (TA Instruments, New Castle, DE). Glycerol was loaded into a 60 mm cone andplate sampler module (cone angle = 1 ). To determine the viscoelasti c properties of glycerol, t he sample was subjected to 0.05% sinusoidal shear strains with the frequ ency gradually increasing from 0.01 to 50 Hz (frequency sweep test) under isothermal conditions (23 C). 2.2.8 Intracellular Particle Tr acking and Cytoplasmic Rheology MC3T3E1 (Riken Cell Bank, To kyo, Japan) were cultured in MEM supplemented with 10% fetal bovine serum (FBS, Hyclone, Logan, UT), 100 IU/ml penicillin and 100 g/ml streptomycin and maintained at 37 C in a humidified, 5% CO2 environment. Cells were passed every 34 days and seeded (approximately 1 104 cells/ml) onto 10cm cell culture dishes. Before particle tracking ex periments, MC3T3E1 cells were plated on 35mm cell culture dishes and subjected to ba llistic injection of 100nm carboxylated polystyrene fluorophores (Invitro gen) using a Biolistic PDS1000/HE particledelivery system (BioRad, Hercules, CA). In the balli stic injection process, nanoparticles were placed on macrocarriers and allowed to dry for 2 hrs. A ruptur e disk with 1800psi rupture pressure were used in conjunction with a hepta adapter 3. After injection, cells were plated again using MEM supplemented with 5% F BS on dishes coated with 20 g/ml fibronectin (EMD Chemicals, Gibbstown NJ). Culture medium was replaced the 28 PAGE 29 next day with serumfree MEM. Cells were serumstarved for 48 hrs prior to the particle tracking experiments. After the particle tracking experiment, the MSD of each pr obed nanosphere was directly related to the local creep compliance 62 of the cytoplasm, ( ), by () 3 a 2 kBT r2 (26) The creep compliance (expressed in units of cm2/dyne, the inverse of a modulus) describes the local deformation of the cyt oplasm induced by the thermally excited displacements of the nanoparticles. If the cytoplasm around a nanosphere has fluidlike behavior (e.g. glycerol), then the creep complia nce increases continuously and linearly with time, with a slope that is invers ely proportional to the shear viscosity, ( ) = / If the cytoplasm has local solidlike behavior (e .g. a gel), then the creep compliance is a constant with a value inversely proporti onal to the elasticity of the gel, ( ) = 1/G0. The local frequencydependent viscoelastic parameters of the cytoplasm, G'( ) and G''( ) (both expressed in units of dyne/cm2, a force per unit area) were computed in a straightforward manner from the MSD 4. The elastic modulus, G', and viscous modulus, G'', describe the propensity of a complex fluid to resist elastically and to flow under mechanical stress, respectively. 2.3 Results 2.3.1 Light Source Affects the MSD Values The consistency of a purely homogeneous medium should be reflected by an identical MSD value for each tracked particle at any given time lag. This was not observed for glycerol, which had a distri bution of MSDs inconsistent with a homogeneous medium, especially at shorter time lags (Fig. 21A). Analysis of this 29 PAGE 30 discrepancy revealed a correlation between MSD ( = 33 msec) and the peak intensity for individual microspheres (Fig. 21B). Emission outside of the microscopes focal plane or interference from other randomly distributed particles obstructing the light path may affect the light intensity emitted from a microsphere to the photon detector, causing a distribution of peak intensity within a samp le. Additionally, the digitization of photon signals by the detector introduces shot noise and may also involve other types of noise 61. The presence of this combined noise could introduce significant bias in image analysis, making it essential to correct MSD va lues in particle tracking experiments. Subsequently, it was invest igated whether the error re vealed by the variation in MSD directly stems from the intensity fluct uations of the overall recorded signal. This was accomplished by extracting the signal and noise information from individual pixels throughout the whole image. Different pixels do not generate purely random noise under the same projected light due to noise inherent to the measurement device such as dark current variation and fixed pattern noise 61, which are consistently associated with an individual pixel and independent of outside signals. To eliminate this bias from each pixel, one reference image was set as a standard, and a successive image with the same illumination was then subtra cted from the reference image 61. This procedure resulted in an evenweight (one bit of data per pixel) array with nonbiased random noise. The random noise had an approximate G aussian distribution and zero mean (consistently biased noise and the background intensity are filtered by the reference image subtraction). Therefor e, the intensity of homogene ous light emitted from a halogen bulb can be determined by the mean pixel intensity (IPS) for pixels over the whole image, and a distribution profile of random noise corre sponding to the illumination 30 PAGE 31 source can be determined to obtain the mean random noise intensity (IPN) (see materials and methods). Using the above method, images of water were taken under a homogeneous field of collimated light from a halogen bulb, either with or without a 590nm cutoff (red) filter in the light path, or with various concentrations of rhodamine Blabelled dextran with a red filter, to extract the IPS and the IPN particular to the microscope being used. Using a CCD camera, a consistent correlation between IPS and IPN emerged from each of the three different experimental settings, over the full working range of light intensity (Fig. 21C). Therefore, the correlation between IPS and IPN suggests that a tracking system could possess a digital output signal depe ndent noise, which cannot be simply expressed by only shot noise (IPN = IPS 1/2) 14, Gaussian noise (IPN = N, where N is a constant) 12, nor a combination of both (IPN = IPS 1/2 + N) 13. Consequently, this information was used to effectively estimate the SNR (IPS / IPN) for pixels over the full spectrum of IPS (Fig. 21D). These data further revealed that varying light intensity drastically affects the SNR for the camera readout, with brighter particles yielding better spatial resolutions. Furthermore, because the settings of a CCD camera (such as the gain in onchip mult iplication) can alter the correlation between IPS and IPN, the method demonstrated here offers a generic procedure to easily extract the SNR profile from any CCD came rabased tracking system for static error determination. 2.3.2 Interplay of Several Factors Determines the Static Error The SNR determined for the tracking system was then applied to create simulated images, which were used as a basis for investigating the conditions governing IPS fluctuations and the degree of particle posit ioning bias. A Gaussianshaped simulated bead was constructed (see materials and met hods), which had a defined peak intensity 31 PAGE 32 (I), radius (Ra) and subpixel location ( x = y = 0 for the center of the pixel), with a homogeneous background intensity (IB). Once the bead parameters were assigned, the appropriate level of random noise was added to individual pixels in the simulated image based on the established SNR (Fig. 21D). Subsequently, t he simulated image containing the system noise was added to t he particle tracking algorithm to determine the experimental tracked position of t he bead. These images were reconstructed multiple times to represent separate tracki ng trials under the giv en initial parameters, and the spatial resolution (i.e. standard deviati on of the positioning distribution) of the bead was obtained after conducting a statistically meaningful number of such trials (Fig. 22A). Using this Monte Carlo approach, an investigation was conducted of the relationship between the peak intensity of par ticles (I) and the resulting positioning distributions. Trials for three diffe rent Gaussian bead peak intensities ( x = y = 0, Ra = 0.54 and I = 5,000, 10,000 and 50,000, res pectively) with a uniform background intensity (IB = 3,000) suggested that the positioning error is related to the peak intensities (Fig. 22B, left). In addition, the br ighter peak intensities resulted in a tighter distribution of tracked positions and a smaller positioning e rror (Fig. 22B, right). Since the spatial resolution ( ) can be quantitatively linked to the static error (2 2) 1214, the brighter peak intensities directly translate to a diminished static error. Moreover, static error vs. the peak intensity was plotted fo r Gaussian beads having three sets of IB and Ra values to demonstrate the dependence of stat ic error on these additional parameters (Fig. 22C). In each case, the static error always decreased incrementally with Gaussian bead peak intensity. 32 PAGE 33 The final Gaussian bead parameter that c ould have an effect on the static error profile was the subpixel lo cation. Under a uniform IB, Gaussian beads with a fixed I and Ra were assigned different subpixel locations, i.e., ( x, y) = (0, 0), (0.25, 0.25) and (0.5, 0.5), where i = 0 corresponded to the pixel center and i = 0.5 corresponded to the pixel edge, respectively. The static erro r extracted from the se t centered within the pixel was used as a reference to observe devi ations in the error distribution at other bead locations. Monte Carlo simulations su ggested a trend of increasing error as Gaussian beads move closer to the pixel edge (Fig. 22D). To further understand this trend, the evaluation of subpi xilation effects on the static error was repeated throughout a whole pixel quadrant (since there is symmetr y about the pixel center in both the xand yaxis). It was found that the subpixel positio n can augment static error up to 1.5 fold (from ~ 6 103 m2 to ~ 9 103 m2) for a single set of a ssigned bead parameters (Fig. 22E). Thus, the subpixel localization of t he bead center also contributes to the static error, revealing that severa l bead parameters collectively contribute to the propagation of such error. 2.3.3 Direct ParameterMappi ng can be used to Accurate ly Estimate the Static Error Although the static error extr acted from the Monte Carlo trials is affected by the individual manipulation of peak intensity, radius, subpixel location and background intensity values, these paramet ers may not be independent or constant throughout an actual experiment. As particles move out fr om the focal plane, th eir projected image will simultaneously appear to have a larger radius and dimmer peak intensity than if they were in focus 63. The background intensity also changes for different microscopic and environmental conditions. Furthermore, some microenvironments constrain particles so 33 PAGE 34 that the total displace ment of a particle during short l ag times can be less than the pixel size (i.e., a particle embedded in highly viscous and/or highly elastic media). In this case, subpixel localization of t he particle will be a dominant fact or for static error in the tracking analysis. Therefore, the accurate representation of ex perimental particles necessitates a case by case assignment of the proper Gaussi an bead parameters to validate the Monte Carlo approac h of extracting the spatial resolution using simulated images. Particle tracking algorithms independently process microspheres in the acquired images and produce a set of experimental parameters, (Ra I x and y ) to describe each tracked microsphere. However, these parameters cannot represent the true characteristics of particles because they have been processed by convolution of the tracking algorithm, and cannot be directly used to extract the static error by Monte Carlo simulation. A novel mapping procedure has been developed to estimate the true parameters (Ra, I, x and y) of the original microsphere fr om the convolved images of the nonlinear algorithm tracking analysis (Fig. 23A). During this process, the addition of extracted system noise to the simulat ed images was omitted in order to avoid generating additional variation in the im age data that would only corrupt the comparisons. The mapping begins by assuming that t he absolute position of a simulated Gaussian bead, ( x, y), is the same as the experi mentally tracked positions, ( x y ). This assumption has previously been evaluat ed with the conclusion th at the pixelization effects can only generate up to 0.02 pixels of error 12. Several simulated Gaussian bead images generated by a series of Ra values (from 0.38 to 1.80 pixels) and different peak 34 PAGE 35 and background intensities were subjected to the tracking algorithm to retrieve the corresponding apparent radii (Ra ). A scatter plot of Ra to Ra fit by a 4thorder polynomial with perfect regression (R2 = 1) (Fig. 23B) is evidenc e that the correlation of Ra and Ra depends only on the tracking algorith m and is independent of the peak intensity of the Gaussian bead and the background pixel intens ity. Having accounted for all other Gaussian bead parameters, the rela tionship between I and I was uncovered using a linear curve fitting (Fig. 23C). T he entire mapping procedure was repeated for a range of Gaussian bead paramet er configurations until a clear link between simulated and experimental tracking images was evident. Th rough this simple process, any typical microsphere experimental image can be prec isely simulated by a corresponding Gaussian bead image (Fig. 24). The mapped values of the pixel intensity in a 3 pixel 3 pixel region are comparable between the simulated bead and the experimentally tracked microsphere. This resu lt demonstrates that the corre lations determined by this procedure can be used to define experimenta lly relevant Gaussian beads to determine static error. 2.3.4 Procedure Verification using in vitro and in situ Experimental Systems The accuracy of the mapping procedure was verified by imaging static particles. Several microspheres were immobilized onto a coverslip and their MSDs were tracked. Immobilized microspheres should exhibit approximately no movement, and the detected MSD values are expected to represent the static error. The mapping procedure was applied to estimate the static error from the experimental images. Comparing the experimental static error of each microsphere to its peak int ensity revealed that static 35 PAGE 36 error invariably reduces when the peak int ensity of the corres ponding microsphere increases (Fig. 25A). Using the Monte Carlo simulation trials, the static error (2 2) was extracted and correlated to the experimental stat ic error in a loglog plot showing that the simulated static error is in agreement with the experimental results (MSD), having a strong linear correlation (R2 = 0.99) (Fig. 25B). This strong correlation confirms that the Monte Carlo simulation approach explained herein can successfully estimate realtime static error. MSD data from a standard tracking analysis in glycerol was corrected using this technique by directly subtract ing the estimated static erro r value. Comparison between the raw and corrected results under low (25%) and high (100%) illumination suggests that the correction produce sign ificantly more precise results, reflecting the true nature of the homogeneous Newtonian fl uid (Fig. 25C). When the generalized StokesEinstein Relation was used to convert the MSDs to the viscous modulus, it was found that the values are underestimated in the raw MSDs of low illumination, but are accurate when the MSDs are calibrated or are obtained fr om high illumination experiments (Fig. 25D). This provides another validation of the fact that static e rror is important in tracking experiments, and should be elim inated using the correction algorithm (Fig. 25E). Further investigations demonstrated t he use of the correction technique for tracking particles inside cells and calculating the creep compliance from the MSD data. Onehundrednm diameter, carb oxylated fluorescent microspheres were ballistically bombarded into the cytoplasm of a MC3T3E1 fibroblasts culture. After serumstarving for 48 hrs, the majority of par ticles were evenly distributed into the cytoplasmic region of the cells (Fig. 26A). In co mparison with a standard cell cult ure, serumstarved cells lack 36 PAGE 37 massive actincytoskeletal structures in most of their cytoplasmic region 64, and in this cytoskeletaldepleted zone, particles are permi tted to exhibit a rela tively greater degree of free diffusion. Yet, the time scaling profile of the raw MSDs obtained from particle tracking indicate that almost all such par ticles in the cytoplasmic region move subdiffusively (Fig. 26B). In contrast, the corrected MSD values obtained by the approach herein suggest that these parti cles are less subdiffusive (Fig. 26C). This analysis strongly advocates the necessity of eliminating static error from MSD measurements for correctly probing the cellular biophysical properties using particle tracking. 2.3 Discussion MSD inaccuracy due to static error is ubiquitous in CCD camerabased particle tracking systems. However, t he complex interplay between mu ltiple tracking parameters had precluded the development of a practical method to mi nimize the errors. The correction approach explained herein significantly minimizes static error. This approach circumvents the complication of direct static error calculat ion by employing a simulationbased method to correct experimental par ticle tracking measurements. This considerably enhances the accuracy of the MSD and improves the subsequent estimation of diffusivity as well as rheological properties. Tracking of particles in a homogenous glycero l solution resulted in a wider MSD distribution at short lag times with decreasing light source int ensity. This result indicates that static error can significantly bi as the MSD profile, potentially causing a misinterpretation of the underlying physical properties 11. Static error in the tracking system used herein can be es timated to be between ~ 2 105 m2 and ~ 103 m2 by tracking immobilized microspheres, suggesting that measured MSD values within this 37 PAGE 38 range are clearly unreliable. Ho wever, elimination of this static error allows for an accurate MSD measurement with a resolution of ~ 106 m2 from a sufficiently bright particle. In the simulation approach, the simulat ed Gaussian bead has a single point position expressing the peak intensity, which is an appropriate model to match with the Gaussian fit algorithm. The parti cle diameter used in this st udy was 100 nm while many in vitro studies have applied particles of a larger size for tracking. Compared to larger particles, the 100nm particle is more suitable to be considered as a point light source. Meanwhile, my unpublished data suggested that the estimated static error is comparable to the measured MSD obtained from fixed 1micron particles. In essence, this method can be applied to the current particle tracking experim ents regardless of the particle size. However, there are some additional advantages to the use of 100 nm particles that were chosen for this work. Light scattering by tracking particles can directly affect the background signal in a tracking video while simultaneously deplet ing the detectable peak intensity within the exposure time. Thes e effects can have a detrimental outcome on the proper estimation of MSD. Based on the Mie theory, the main parameter to consider in elastic light scatteri ng is the size parameter, x = 2 R/ where is the wavelength and R is the radius of the particle. The wavelengt h of the light used in the videobased particletracking ex periment ranges between ~ 400 to 700 nm. Therefore, the 100nm size particle has an x ~ 0.5, in wh ich the extinction coefficient is negligible and light scattering effects are minimized. M eanwhile, Rayleigh scattering will not affect the particle tracking results unless the size of the particle is reduced to ~ 10 nm. 38 PAGE 39 For a 1micron particle, the size parame ter of light scattering is approximately equal to 5 and the extinction coefficient appr oaches the maximum value. Therefore, light absorbance by 1micron particles is i nevitable. Nevertheless, the emitted signal from an 1micron particle is much higher t han the detectable threshold (SNR is much greater compared to the 100nm particle). The larger particle should have much smaller static error. However, when the particle size increases from 100 nm, the extinction coefficient consequently increases as well, which would generate heat and increase the temperature to the microenvir onment. Therefore, heat effe cts on the experiments would need to be assessed. To ensure that the discrepancy of MSD values of 100 nm particles embedded in glycerol was not an effect of heat generated from different power settings of the light source, particletracking was repeated successi vely three times on a sample at full power of light intensity. In th is case, the sample was exposed to constant light for more than 1 minute. The three tracking results were carefully compared to evaluate whether the MSD values shift toward higher or lowe r values. The result showed that there was no heat accumulation which would affect a change in the MSD (data not shown). The short lagtime MSD values for the first 5sec period and the last 5sec period in the same experiment were also evaluated to ex amine the transient he at buildup and it was concluded that the difference of MSD values were not caused by the heat effect for the 100nm particles. 2.4 Conclusion In summary, this correction technique is not limited to the particular system used herein, but is broadly applicable to any tracking system. The tr ansition to another system requires simple steps of determini ng the correlation between the pixel signal 39 PAGE 40 and noise, and appropriately selecting correct tracking parameters. By closely following the methodology described herein, static error can be significantly e liminated, leading to a greater clarity when interpreting the MSD va lues from a particle tracking experiment. 40 PAGE 41 104 50 100 150 1,500 65,535 104 101 102 103 no filter red filter dextranred 1,500 65,535 102 103 104 103 5x103 101 100 103 102 B A DMSD ( m2) (s) MSD 33ms( m2)I (au) 25% illumination 100% illumination IPS (au)IPN(au)y = 0.40x4+6.73x342.20x2+1.18x1.21, R2=0.99SNRIPS (au)C Figure 21. The mean square displacement (MSD) is correlated to the peak intensity (I ) of microspheres tracked by a chargecoupled device (CCD) camera. ( A ) A MSD vs. time lag plot of microspher es (n = 47) embedded in glycerol shows the presence of MSD variation in a homogeneous aqueous solution (arrow head). The particle tracking experiments we re conducted at a time resolution of 33 ms with using 25% of full power of illumination. ( B ) A logarithm plot of MSD ( = 33 ms) vs. peak intensity of microspheres (n= 53) embedded in glycerol under 25% ( ) and 100% ( ) power of illumination suggests a relationship between increasing peak intensity and decreasing MSD value. The error bar shows the mean and standard deviation of the MSD ( = 33 ms). ( C ) Digital intensity signal (IPS) and noise (IPN) values are extracted from uniform light sources: the head light without a filter ( ), the head light with a red filter (+), and the UVvisible light with a red filter at different concentration of Rhodamine Btagged 70 kD Dextran ( ). The IPSIPN relationship is expressed by a 4th order polynomial fit. ( D ) Signalnoiseratio (SNR) vs. digital signal intensity may be dete rmined by the curve fitting described in panel 1 C to wellestimate the SNR as a func tion of the digita l signal strength ranging between saturated signal (65535 ar bitrary units; i.e., au) and dark current (~ 1500 au). 41 PAGE 42 0.2 0 0.2 0.2 0 0.2 104 105 104 102 IB=3,000, Ra=0.54 IB=8,000, Ra=0.54 IB=8,000, Ra=1.28 0.5 0 0.5 0 0 50 100 0 50 100 0 0.1 0.2 0 50 100 Gaussian particle imageA 1pxl1pxl: Quadrant subpixel region0.5 0.5 y (pxl) y (pxl) Static Error( m2)I (au)Static Error( m2) Count p(pxl) x (pxl) Repeat 600XAdd Noise Positioning resolution Track particle Mimic real imaging conditions 0 0.1 0.2 100 0 100 200 0 0.1 0.2 100 0 100 200 x (pxl)y (pxl)0.5 p(pxl)Count x (pxl) I=5,000, Ra=0.54, IB=3,000BC D E 0 0 6 7 8 9 x 103 Figure 22. Static error (2 2) can be estimated using simulated Gaussian beads. ( A ) A flow diagram demonstrates how to esti mate static error by Monte Carlo simulation. (B ) Distribution patterns of tra cked positions were generated by running 600 independent trials incorporating pixel noise into simulated images using three different intensitie s of Gaussian beads (I = 5,000 ( ), 10,000 (+), and 50,000 ( )) with x = y = 0, Ra = 0.54 and IB = 3,000 (left panel). Three histograms in the right panel indicate the distribution of the experimental position error, p (the displacement between the experimental center and the assigned center). Beads possessing a higher intensity generate smaller experimental errors with sharper distributions. ( C ) Static error vs. the assigned peak intensity (I) is plotted fo r the three different Gaussian beads. ( D ) Left: The distribution of the tracked center afte r six hundred simulations for Gaussian beads initially in three s ubpixel locations within the lowerleft pixel quadrant ((0, 0), (0. 25, 0.25) and (0.5, 0.5 )) is shown. Right: A histogram of 6,000 positioning error si mulations for Gaussian beads located at the pixel center was set as a reference for offcenter beads, and differences in count of the tracked displacements suggest that the subpixel location of a microsphere affects the size of its positioning error. ( E ) The intensity diagram illustrates the corre lation between static error and the Gaussian particle subpixel location at a resolution of 0.01 pixels. The intensity bar indicates the range of positioning error. 42 PAGE 43 A Monte Carlo Simulation Mapping Gaussian Bead Experimental particle image ( IB, I, x, y, Ra ) Static errorTracking ( IB, I' x', y', Ra' ) Gaussian particle image (noise free) Gaussian fit Sets of parameters ( IB, I, x, y, Ra ) Corresponding (IB, I' x', y', Ra' ) ** Indicate the initiation of process Filter image by convolution Build up correlation Tracking 0 1 2 3 x 104 2 2.5 3 3.5 4 x 10 4 B=2,000, Ra=0 B=8,000, Ra=0 B=8,000, Ra=0 B=8,000, Ra=0 I'(au)I (au) Ra=0.70, IB=8,000 Ra=0.70, IB=3,000 Ra=0.38, IB=8,000 Ra=1.28, IB=8,000BC 1.4 1.6 1.8 2 0 0.5 1 1.5 2 A=30000 B=8000 A=10000 B=3000 Ra' (pxl)Ra (pxl) I=30,000, IB=8,000 I=10,000, IB=3,000 y=1.58x4 + 11.86x3 33.39x2+ 42.48x 20.37Figure 23. The method to relate extract ed static error from simulated beads to experimental microsphere images is demonstrated. ( A ) The left flow chart demonstrates the process of estimating static error from raw particle image. The process retrieves tracked paramet ers from a raw image, maps the adequate parameters to simulate experimental images with the complementary Gaussian particle, and applies Monte Carlo simulation to estimate the static error. The right flow chart shows the procedure used to map parameters for simulated Gaussian be ads to match experimental tracked parameters. (B ) A 4th order polyn omial equation can be adopted to describe the relationship between the radius of the simulated Gaussian bead, Ra, and the radius of tracked microsphere, Ra with perfect fitting (R2 = 1). This result is independent of the peak intensity, I, and background intensity, IB. ( C ) The Gaussian bead peak intensity (I) vs. the experimental peak intensity (I ), plotted for three different Gaussian bead radii, showing a linear correlation between I and I The plot also suggests that the correlation is independent of the pixel background since lines are overlaid at the same Ra despite having pixel backgrounds that are set differently. 43 PAGE 44 1 1.5 2 2.5 3 x 104 Intensity around peak ( 104 au) 1.001.210.99 2.603.401.00 1.531.380.89 1.281.430.98 2.462.931.13 1.461.741.04 Figure 24. A Gaussian bead with the parameters determined by the mapping procedure in this paper can represent the experimental microsphere. The experimental (Left) and si mulated (Right) data is in agreement, as evident in their images and the pixel intensity of the 3x3 area surrounding the brightest pixel. 44 PAGE 45 105 104 103 102 105 104 103 102 log (y) =1.05 log(x)0.17 R2=0.99 50 100 150 200 250 102 103 104 105 104 103 102 A B E C DG (dyne/cm2)MSD 33ms( m2)Static Error( m2) MSD 33ms( m2)I'(au) 0.04 0.04 0.1 0.10.040.10.040.1 103104 s1 s2 s3 s4MSD ( m2) (s) Raw MSD ( 25% illumination) Cal MSD ( 25% illumination) Raw MSD ( 100% illumination) Cal MSD ( 100% illumination) MSDmeasurement Figure 25. Static error can be corrected for the MSD of micr ospheres embedded in glycerol. ( A ) A sample of fixed microspheres is used to verify the estimated static error from simulations by repr esenting the tracked MSD values as the spatial error generated from the experimental system. ( B ) The logarithm of experimental static error (MSD at 33 ms) and the corresponding estimated simulated static error strongl y correlate with a linear fit, R2 = 0.99. (C ) Raw MSD data from particle tracking under 25% power of illumination (n = 47) exhibits a degree of heterogeneity in the data, but raw MSD data (n = 53) and its corrected MSD both obtained under 100 % power of illumination share a similar scale and trend as the corrected MSD from low illumination (25%). ( D ) The mean viscous modulus, G'', of glycerol is estimated at time lags of 33 ms from the raw and corrected MSD va lues at 25% and 100 % power of illumination, respectively. The dashed line indicates the viscous modulus measured by a conventional rheometer and the star denotes the significantly lower G'' of the raw MSD at 25 % power of illumination using a twotailed ttests with P < 0.05. ( E ) The illustration explains how errors generated from the experimental system can affect the MS D result in the cases of glycerol: Measured MSD is the culmination of system MSD and static error. MSDsystem+ Static error (2 2)= log ( )log (MSD) = 33 msec 45 PAGE 46 46 102 101 100 101 106 104 102 100 102 101 100 101 106 104 102 100 ABC (sec)MSD ( m2) (sec)MSD ( m2) Figure 26. Static error can be corrected for the MSD of 100nm carboxylated polystyrene particles embedded in MC3T 3E1 fibroblast cells under redfluorescence. ( A ) An image acquired from the CCDcamera. Square dots indicate the positions of micr ospheres within the frame. ( B ) A MSD vs. time lag plot extracted from the cellular syst em (80 particles in 7 cells) implies subdiffusive particle motion at shorter lag times, indicating a range of local microenvironments that the micr ospheres are encountering. ( C ) Using the developed method to subtract out the estimated static error in the system revealed a new MSD profile, which imp lies more diffusive particle motion throughout the cellular environment at short lag times. PAGE 47 CHAPTER 3 A GENERAL METHOD FOR IMPROVING SPAT IAL RESOLUTION BY OPTIMIZATION OF ELECTRON MULTIPLI CATION IN CCD IMAGING 3.1 Background Singlecell biophysical assays that quantify size 65, morphology 66 and movement 67, 68 of subcellular components c an provide great insight into macromolecular function and effectively bridge the biological activiti es at the cellular and the molecular scale together 69. However, given the heter ogeneous nature of the cell structure, single cell measurements need to be performed with hi gh resolution to produce accurate and statistically meaningful data 41, 70. The most straightforwar d way to conduct such measurements is through the analysis of indi vidual images or a stack of images acquired with highresolution microscopy 38, 69, 71. Therefore, the success of these types of measurements relies on the capability of the camera to obtain high quality cell images. In modern microscopi c systems, the most comm on device adopted as a photon detector is the chargecoupled device ( CCD) camera, which can simultaneously use more than one million parallel arrays to sense t he intensity profile of light emitted from objects within the visual field of the microscope. With this device, cell images with detailed information can be c aptured and later analyzed. Yet, the performance of the CCD camera deteriorates with decreasing light intensity from the sample 16, and this significantly reduces the accuracy of low intensity subcellular measurements, such as in si ngle molecule fluorescence imaging. This problem can be solved by acquiring im ages on much more expensive avalanche photodiode detectors (APD) or photomultiplier tubes (PMT) 17, 18. These types of detectors do not have large numbers of indivi dual sensing units like the parallel array of the CCD camera. When acquiring information from the visual field of the microscope, an 47 PAGE 48 APD or a PMT sensor needs to use a scanni ng mode, which is usually much slower than the CCD camera. Therefore, if the spatial resolution of low intensity images in a CCD camera can be improved, the CCD camera becomes the best choice due to its accessibility and high acquisition rate. Several intensityenhanced techniques have been developed to obtain high contrast images from low intensity signals su ch as intensified CCD (ICCD) and electron multiplying CCD (EMCCD) 16. After the backilluminated EMCCD camera was introduced, the sensitivity of EMCCD has outperformed the ICCD and the EMCCD has become a popular choice for imaging the dy namics of single molecules in cells 19, 20. EMCCD utilizes several specialized extended serial registers on the CCD chip to apply a high voltage and produce multip lying gain through the process of impact ionization in silicon 21. This capability to elevate the photongenerated signal above the readout noise of the device even at high frame rates has made it possible to meet the need for ultralowlight imaging applicat ions without the use of ex ternal image intensifiers 72. While the EMCCD camera is certainly pr omising for single particle tracking, a quantitative evaluation of the influence of EM gain on spatial resolution has not been performed. Therefore, Equations to relate the nominal EM gain with image intensity and the variance of image intensit y are derived. These equations were fit to experimental data to estimate the relevant image par ameters. Quantitativ e mappings were used along with a Monte Carlo procedure to calcul ate the dependence of signal to noise ratio (SNR) and spatial positioning error on EM gain. The EMCCD performance to achieve the best spatial resolution and SNR for particle tracking by this approach is successfully optimized. Through this specific exampl e, we have created a general method, 48 PAGE 49 applicable to other types of CCD cameras, whic h can optimize electron multiplication for subcellular imaging, and prov ide a quantitative gui deline to improve the accuracy of subcellular biophysical assays. 3.2 Methods and Results 3.2.1 The EM Gain can Influen ce Quantitative Image Analysis EM gain is an analog signal multiplication feature that multip lies an electronic signal by applying high voltage across several CCD registers before readout 21. The EM gain setting of the EMCCD camera aims to improve the contrast of the image. Image analysis uses intensity profiles of a group of specif ic pixels that describe an object. The intensity relations between the adjacent pixels are important for reliable tracking of a single particle. However, t he EM gain function does not amplify the SNR equally for objects with different intensities 73. This suggests that there may be an optimal EM gain setting for achieving the best spatial resolution. To investigate this in more detail, tw o types of cellular bodies were probed to determine if the EM gain could preserve or c onsistently improve the spatial resolution of positioning. Cytoplasmic mRNA processing bodies (also called Pbodies or GWbodies), labeled by GFPAgo2 74 through transfection, and nuclear promyelocytic leukemia (PML) bodies, labeled by YFPSumo1 (A ddgene Inc., Cambridge, MA), were videotracked without EM gain or with EM gain = 2000 in a fixed NIH 3T3 fibroblast using a TE 2000 microscope (Nikon, Melville, NY), equipped with a Cascade:1K EMCCD camera (Roper Scientific, Tucson, AZ) and a NA 1.45, oilimmersion 60 objective lens (Nikon). For a specific type of EMCCD camera, the EM gain is an arbitrary number correlated to the applied voltage on the CCD registers. The range for our CCD EM gain setting is between 0 and 4095. Through proper assignment of the region of interest (ROI) a high 49 PAGE 50 temporal resolution (30 Hz) can be achieved. In our case, the binning feature in the CCD camera is set as 3 3, resulting in a pixel size of 390 nm. Under these two EM settings, 300 experimental images repeatedly acquired from the same sample were used to assess the variance of positioning via particle tracking 75. In brief, the raw images were subjected to a Gaussian kernel filter 76, 77 to reduce background noise before being fed into the 2Dparticle tracking algorithm. The algorithm determined the particles positions by leastsquare fitting their logarithmic in tensities in the 3 3 binning area directly into a Gaussian curve: 2 )()( )log(),(log2 2 2 a y x PR y x IyxI (31) where the fitted peak intensity determines the particles subpixel position, (x ,y ), within the central pixel of t he binning area (the origin, (0, 0), is set to the center of the pixel). In Eq. (31), represents the pixel intensit y of a particle and the fitted parameters, PI I aR x and y represent the particles peak intensity, apparent radius, and the position in the xand ydirection of a Cartesian plane, respectively. These results indicate that the positioning erro r strongly depends on the EM gain setting in a manner that depended on the intens ity of the tracked object (Fig. 31). Choosing an EM gain of 2000 increased the positioning error by as much as 48% (subcellular body #6) and decreased it by 44% (subcellular body #3). 3.2.2 EM Gain Ch aracterization The above result suggested t hat an optimal EM gain setting might exist to achieve the minimal positioning error in particle tracking. Thus, a method to characterize the EM gain performance is developed. Previously, we established a method to estimate the 50 PAGE 51 positioning error of particle tracking in an ac quired image using Monte Carlo simulation. This method requires the information of a pixe ls SNR profile over the whole intensity range. A quantitative mapping between the int ensitydependent SNR and the EM gain is derived as discussed below. This discussion will define many variables that are summarized in Table 1 for reference. The derivation accounted for the conversi on of incident photons into final pixel intensity (Fig. 32A). Consider N P as the average number of ph otons per pixel that are incident on the CCD camera coming from the observed object. photons give rise to electrons. In addition, electrons, dark current, are generated over time by thermal energy within the CCD camera, which are independent of the incident light on the detector 78. Next, a fixed value of EM gain, k, which depends on the applied voltage 21, amplifies the electrons by a multiplication factor, This multiplied electron signal is ultimately sent to the analogdigital converter that converts electron signals to an intensity count by a factor, with an offset, to give the final average digital intensity per pixel, The described signal processing in an EMCCD camera can be mathematically represented as: PNPENDEADCNGkEMG,k,offsetIkoutI, ) (, koffset ADC kEM DE PE koutIGGNNI (32) Because the magnitude of dark current elec trons increases with the exposure time 79, the effect of dark current electrons can be mitigated by decreasing the exposure time of the analyzed image. However, as seen in Eq. (32), the signal from dark current is multiplied by the effective EM gain, ; hence, its effect on the magnitude of the output cannot be omitted at high k. Since the value does not change with the kEMG, koffsetI, 51 PAGE 52 binning setting of the CCD camera, which can boost the dark current signal several times depending on the integrated pixels, the level of binning is adjusted without incident light and used li near fitting to obtain the in Eq. (32). koffsetI,At ground state (k = 0), Eq. (32) can be rearranged as: ). /() () (0, 0, 0, ADC EM offset out DE PEGGIINN (33) Substituting Eq. (33 ) into Eq. (32) with G = 1, we get the following relation between the output intensity unde r electron multiplication ( ) and that in the ground state ( ): 0, EM koutI,Iout ,0 .0, 0, offset kEM koffset outkEM koutIGIIGI (34) We acquired images at varying light source intensities at a fixed k, and measured average per pixel (for 100,000 pixels) co rresponding to the different light intensities. These experiments were repeated fo r identical light source intensities at k = 0. This resulted in a series of data points ( ) corresponding to different light source intensities that were plotted for k values varying from 1000 to 4000 (Fig. 32B). As seen in Fig. 32B, the saturates at high light source intensities. Since Eq. (34) only represents the relation between and before becomes saturated, this equation is used to fit unsaturated data points, which fit the data smoothly. Thus, the values of were estimated at different values of k and tabulated in Table 31. Notably, the relationship between the effective gain and k is not linear based on these trends. koutI, 0, outIkoutI, kout ,GkoutI, 0, outI IkoutI, kEMG, kEM 52 PAGE 53 We next derived a quantitative relation between the variance in the measured intensity and effective EM gain To do this, we accounted for noise propagation in the conv ersion process of photons to the variance in the final First, photon shot noise and dark current noise occur when photons are detected in each pixel, and their variances are equal to the signal magnitude 78. This variance is given by koutI,EMGPNkoutI, DEN PE DE PENNN ) var(PS2G2 kF. Electron multiplication further increases the variance by In addition, the EM amplification process introduces an accumulated variance ( ; where is called the excess factor) into the signal, which is generated from all the register steps 21. Finally, the analog to digital converter converts the electronic signal to an output intensity count by t he multiplication factor, also generating an additional signal in dependent readout variance, This leaves a total pixel intensity variance, 2 kEMkFADCG2 Rout k 2, described by: ) (22 2 2 2 Rk ADC kEM DE PE koutFGGNN (35) Substituting the intensity count fo r the electronic signal, we get: .2 22 2 k ADC kEM koffset Rk ADC kEM koutkoutFGGIFGGI (36) In the above equation, the value of is already known from the previous measurements and fitting. We next measured as half of the variance of the pixel intensities in the image obt ained from two repeated image subtractions (we accounted first for pattern noise, which is systematic variation in pixel intensities). Eq. (36) was fit to the measured values of and at k = 0 where = 1; this allowed for the estimation of as 1.75 au per electron. This value was not expected to change as a kEMG, k ,2 kout2 koutoutI0FADCG 53 PAGE 54 function of k; therefor e, it is assumed constant for fi tting Eq. (36) to the data at nonzero values of k (Fig. 32C). This a llowed us to estimate the excess factor, kFIn the high intensity region, the vari ance obtained by experiments was smaller than that of the theoretically estimated value. This is presumably a result of image saturation. The theoretical calculation does not take the saturation into account; hence, the estimated variance can represent the total shot noise and readout noise at high incident photon levels. In a real case, a signal with intensity higher than the maximum pixel output can cause the pixel to only export that maximum output va lue, giving rise to a signal loss. Thus, the mean and variance of the output intensity count will be underestimated as the intensity count approaches saturation. 3.2.3 The Signal to Noise Ra tio (SNR) can be used to Optimize the EM Gain Setting One can also easily derive the SNR at various incident photon magnitudes as: .) ) ((22 2 2 Rk ADC kEM DE PE ADC kEM PEFGGNNGGNSNR (37) With short acquisition times, the dark electron effect can be neglected. The value can be calculated by Eq. (32) using the value of Therefore, we can estimate the theoretical SNR for different at a given EMsetting from Eq. (37) since all parameters in this equation are known (Tabl e 31). As a result, the theoretical SNR for k = 2000 can be calculated over whole work ing range of light int ensity. Meanwhile, this value can also be obtained from the value of NPEkoutI, 2000INPE2000, 2000, ,/) (out offset outI where and 2000, outI2000, out can be measured experimentally. A comparison (Fig. 33A) shows that the experiments were in very good agr eement with the theoretical estimates. 54 PAGE 55 This allowed us to estimate the SNR res ponse for different EM gain settings from Eq. (37) at varying magnitudes of intensity. Comparison for the same amount of light intensity (i.e. ) but at different k values (Fig. 33B) indicates that changing the EM gain setting can result in different SNR va lues under identical illumination. At higher incident photon levels, SNR can be simplified to 0, outI kPEFN / by neglecting the readout noise in Eq. (37). Hence, no single EM gain achieved the best performance as predicted by the minimization of the excess factor (Fig. 33B), but at lower increasing k enhances the SNR (Fig. 33B inse t). The improvement of the SNR at low plateaus when k is above 2000 for the ex perimental imaging system, and the SNR crossover takes place around = 1800 au (Fig. 33C). PNPN0, outI3.2.4. EM Gain Effects on MultiPixel Analysis The above study revealed the capability of EM gain to improve the SNR at the single pixel level when the intensity of incident light is low, but that it has the opposite effect when the light intensity is high. The extent to which this can influence spatial resolution during particle tracking where mult iple groups of pixels are analyzed is unclear. The different pixels may possess vari ous intensities, and the EM process could introduce spatially varying error in the analysi s. We therefore dete rmined the effect of EM gain on the positioning error (S ; or spatial resolution) of particle positioning of a 100nm particle using a Monte Ca rlo method published previously 75. A Gaussian particle with a fixed radius was assigned different peak intensities sequentially to mimic real system conditions. Furthermore, proper magnitudes of random noise corresponding to the noise prof ile of the assigned signal intensity under the specified EM gain condition, were added to each pixel in the simulation 75. Fixed 55 PAGE 56 pattern noise in our CCD camera has a mi nimal effect on particle resolution as demonstrated from Monte Carlo simulations ( data not shown). Theref ore, this type of noise was omitted from further simulations while identifying the S of a particle. The extracted S values correspond to varying particle peak intensities ( denotes the peak intensity at k = 0, see Fig. 34A), s howing that EM gain can significantly improve peakIS by more than 10 fold when the of the object is lower than 100 au. This EM gain effect decreases gradually an d eventually reverses at high ( 2000 au). For example, a Gaussian particle with of 15,000 au possesses 2.3 times smaller S at k = 0 than at k = 2000. Saturation of a pixel can occur when the of a Gaussian particle is high, and this caused a fluc tuating and irregular correlation between peakIpeakIpeakIpeakI S and in the simulation results. IpeakTo understand the above phenomenon in more detail, we estimated the critical value ( ), which is the intersection point of the S curves in Fig. 34A at k = 0 and another EM gain setting k (Fig. 34B). Due to the adverse effect of EM gain on S in object positioning at high intensity le vels, the figure suggests a boundary (the k curve) to separate the regions between where EM gain activation is beneficial for object positioning and where it is not. The profile also sets a quan titative standard for applying adequate EM gain. It is import ant to note that increasin g the EM gain reduces the working range of photon acquisiti on and therefore leads to a smaller working range of values. peakIpeakIkCI, kCI, 56 PAGE 57 3.2.4.1 Optimal EM Gain Depends on the Size and Background Intensity of the Object The above study suggests that the value depends on k and can help determine whether EM gain should be applied to improve the resolution of a quantitative biophysical assay probing an object with known To explore whether other physical parameters of the object also affect the value in particle tracking, the simulated Gaussian particle was used as an ideal and simplified model for mimicking cellular components. Different leve ls of background signal ( ) were assigned to the simulation to examine how changes with The results showed that an increase in leads to a decrease in and when the exceeds 900 au, both the and drop approximately to zero (Fig. 35A ). Therefore, hi gh background images reduce the advantage of EM gain activation. kCI, kCI, peakIIBG BGIBGkCI, CIIBGICIk 1000, CI2000,We next evaluated the effects of par ticle size and subpixel location on Gaussian particles with different sizes or subpixel locations were used again as a simplified model. The simulat ed results suggested that the and values drop quickly with increasing apparent r adius of an object (Fig. 35B) but the subpixel location of the Gaussian bead does not have a significant effect on the and values (data not shown). In essence, these studi es demonstrate that t he EM gain is most effective in a biophysical assay such as particle tracking and positioning when the object possesses a small radius, low peak intensity, and low background intensity. kCI, 2000, 1000, CICI2000, CICI1000, 57 PAGE 58 3.2.4.2 Particle Tracking Experiments Verify the EM Gain Effect on Image Analysis These simulation results were verifi ed through the tracking of fixed 100nm fluorescent microspheres. The kS based on the positioning error in 600 trials of positioning a fixed microsphere, were determi ned at a fixed EM gain. An x y diagram was used to describe the results (Fig 36). The xaxis represents the 0, S while the yaxis represents the 1000, S In this case, the straight line, x = y, divides the diagram into two regions: above the line, there is a detrimental EM gain effect (i.e., S becomes larger when EM gain is activated) and below the line, there is a beneficial EM gain effect (i.e., S becomes smaller when the EM gain is activated). If the kS value falls on the line, then it means that EM gain has no significant effect on the S Since the concentration of the microspheres can contribute to the a sample with a high concentration of fixed, outoffocus fluorescent microspheres was used to create a high which was 2000 au higher than the dark curr ent under the full powe r of the UV light source. Under such conditions, 35 infocus particles were tracked (shown as hollow squares) to assess their BGIBGI0, S and 1000, S values. In parallel, 43 fixed, fluorescent microspheres were tracked in samples wit h lower particle concentrations and lower excitation light intensity (shown as solid circles), which produced low (= 1200 au, which contains the intrinsic value, see Eq. (32)) and low (lower than 2000 au). Results obtained from thes e experiments confirmed t hat EM gain performance on the BGIk offsetIpeakIS of particletracking experiments depends on and and that EM gain can damage the resolution of experiments at higher BGIpeakIBGI 58 PAGE 59 3.3 Discussion 3.3.1. The Working Range a nd Effectiveness of EM Gain In previous chapter it is demonstrated that accuracy in particlepositioning relies heavily on a high SNR in acquired images 75. Here, we further explored how the EM gain settings in a CCD camera can affect the SNR in acquired images. Modification in an established method 78 quantified the dependence of the SNR values on the EM gain, k, of an EMCCD camera and evaluated to whic h extent the EM gain could affect the outcome of a particle tracking experiment. Af ter comparing the SNR values for different k values over a full range of incident ligh t, I concluded that the EM gain only enhances the SNR of an output signal when the incident light intens ity is lower than a certain critical level (in this case, it is 1900 au as measured at k = 0). When the incident light intensity is higher than that critical level, it will dimini sh the SNR value and damage the fidelity of particle tracking results. I also concluded that the work ing range of a particle tracking experiment is determined by the maximum of a group of tracked particles because the electron multiplicati on of the brightest particle will more quickly result in saturation of the amplified maximum peak intensity ( ), reducing accuracy in particle positioning. The maximum values allowed in our syst em are 12,840, 1,910 and 71 au (using k = 0 as a reference) for k = 2000, 3000 and 4000, respectively. This demonstrates that the worki ng range for EM gain in particl e tracking diminishes quickly with increasing EM gain when k is larger than 2000. peakIoutIpeakIAlthough the maximum pixel in tensity allowed before saturation at k = 2000 is over 10,000 au in our experimental system as suggested in data shown in Fig. 34A, the simulation results suggest that the smaller pos itioning error compared to that at k = 0 for 59 PAGE 60 particle tracking occurs only when the 6000 au. Hence, application of the highest k allowed by the working range will not necessa rily produce the most accurate tracking result. Presumably this is because particle tracking needs to quantitatively analyze the intensity profile over a group of pixels to identify the position or boundary information. Since the SNR of a pixel at different int ensities does not linearly depend on the EM gain setting, the relative intensities among the group of pixels representing the object of interest are quantitatively altered, changing the outcome of their calculated positions. peakI3.3.2 Analysis of the Esti mated Values in this Study In my evaluation, the extraction of the value plays a critical role to determine the excess factor, The range of within a 95% confidence interval was found to be 0.028, representing 3.96 times its st andard deviation. The standard deviation of estimated from this information is 0.007, wh ich is 0.4% of its mean value. This can be quickly verified by calculat ing the standard deviation for using four independent trials, which was found to be less than 0.8%. Therefore, using the extreme values of (2 standard deviations from the mean), we could estimate the range of excess factor, which was found to be within 0.98 ~ 1.02 times its mean value, or approximately within 2% of the mean in all different condit ions. From this analysis, we expect that other parameters that can be deriv ed based on the extracted value will also possess very little deviati on from their mean values. ADCGkFADCGADCGADCGADCGFkADCG3.3.3 Assessment of EM Gain in Sub cellular Particle Tracking Experiments The signal is highly sensitive to the EM gain setting, and the results suggest that the EM gain is not very useful for tracking parti cles that are typically brightly visible and 60 PAGE 61 clearly defined in the image (such as YFPsumo). These imaging experiments provide an example to demonstrate this phenomenon. A PMLnuclear body labeled by YFPsumo has high background intensity, presum ably caused by the freely diffusive YFPsumo molecules in the nucleus 80. This nuclear body also has high intensity and large radius. Therefore, it is not beneficial to track YFPsumo labeled PMLnuclear bodies using an EM gain setting. In contrast, electron multiplication favored the tracking of GWbodies with dimmer intensities and possessing smaller radii. This study provides direct evidence to demonstrate that the EM gain setting of the EMCCD camera can significantly influence the positioning error during subcellular particle tracking. 3.3.4 Application of Proper EM Gain to Biophysical Measurements beyond Particle Tracking Many biophysical studies utilize signals generated from GFP or their derivatives. The applications of GFP in quantitative ce llular biophysics are very powerful but are challenging at low intensitie s. If the GFP molecules emit light with low intensity, the acquired image possesses a low SNR value and the accuracy of the biophysical assay is reduced. On the other hand, if the exposure time is increased, photobleaching effects become unavoidable. In most cases, it is best to minimize the UVlight exposure so a consistent signal output can be maintai ned. Therefore, a proper EM gain setting could greatly improve the accuracy of biophysical assays for lowintensity signals. Electron multiplication can effectively r educe the required image intensity and extend the possible experimental time frame without af fecting spatial resolution. Under optimal EM gain settings, the pixel intensity can be more reliably measured for photon counting histogram analysis 18. In this regard, the EMCCD came ra can be used to improve the detection of molecular fluctuations in microscale volumes and improve the reliability of 61 PAGE 62 fluorescence correlation spectroscopy (FCS) 81 or concentration measurements 20. In these types of studies, the EM gain feature is critical to successfully amplify the photon fluctuation to overcome readout noise sinc e the photon count in the pixel is usually small. In an effort to achieve the highest a ccuracy in microscopybased biophysical measurements, a standard proc edure to analyze the EM gain settings of a CCD camera is developed in this study. These quantitativ e cellular biophysical assays usually focus on imaging subcellular dynam ics. Often, a quantitative m easurement is required, and the accurate positioning of the subcellular object in image analysi s becomes a critical step for the success of the biophysical assa y. The parameters that can affect EM performance include the exposure time of image acquisition (temporal resolution), the background intensity and shape of the probed object. To be applicable to a broad range of experimental situations, this EMCCD charac terization must be available for a variety of particle shapes, sizes and intensities. The method that is provided in this study is theoretically suitable for all types of EM CCD camera. Since the intensified CCD (ICCD) camera has similar signal amplification proc essing (photon signal is enhanced first in a similar way and sensed by CCD chip later) but a different physical mechanism; it is expected that some minor modifications to our method ma y be required to accurately assess the optimal settings for an ICCD came ra. However, further verification is required. Nevertheless, this study prov ides a method to quantitatively choose the appropriate EM gain for maximizing the resolution of biophysical assays. The optimization procedure presented here should greatly im prove the accuracy of such measurements. 62 PAGE 63 3.5 Conclusion The EM gain magnifies the photonsignalinduced electron flow in individual pixels of a CCD camera. A higher EM gain can gener ate more output from the pixel until the pixel reaches its maximum output capacity (saturation). This saturation sets the working range that should be used when am plifying the incident signa l. A quantitative method to assess the outcome after using EM gain and evaluate its effectiveness in a biophysical assay is essential to ensure high resolution in subcellular measurements. Therefore, EM gain effects on simulated Gaussian shaped particles are investigated here to gain an understanding of the optimal EM gain se ttings in cellular particle tracking. This model system is adopted for three purposes. First, particle tracking is a powerful technique in cellular biophysics. Information gained from this approach can have a direct and immediate impact on t he particle tracking community. Second, a Gaussian shaped particle is relatively easy to evaluate. Hence, results obtained from this model can be more easily verified than other models. Last, the evaluation procedure developed by use of this model can be extended as a platform to explore the effectiveness of EM gain on biophysical st udies of cellular components with more complicated features. 63 PAGE 64 Table 31. The values of the effe ctive EM gain (k), excess factor Notation (unit) Description Notation (unit) Description I P (au) Pixel intensity of a particle I (au) Fitted particle's peak intensity R a (px) Fitted particles apparent radius x (px) Fitted particles position in xdirection y (px) Fitted particles position in ydirection N P (photon) Average number of incident photons per pixel on the CCD camera N P E (e) NP photons give rise to photoactivated electrons N D E (e) Dark current electrons k () EM setting parameter for image acquisition GEM k () Electron multiplication gain at EM setting k G AD C (au/e) Analog to digital converter gain PS 2 (e2) Photon shot noise I offset k (au) Pixel intensity offset value at EM setting k I out k (au) Average output digital intensity per pixel at EM setting k F k () Excess factor R 2 (au2) Readout noise out k 2 (au2) Total pixel intensity variance S k (px2) Spatial resolution in particle tracking SNR () Signal to noise ratio I peak (au) Peak intensity of Gaussian particle at k = 0 I C k (au) Critical I peak value at EM setting k I B G (au) Background intensity R a (px) Gaussian particle size Table 32. The values of the effective EM gain (k), excess fa ctor (F), intensity offset ( ), and relative working range at se veral EM gain settings estimated for our system. offsetI offsetIK Effective EM gain ( GEM) Excess factor ( F) (au) Relative working range to zero EM gain (%) 0 1.00 1.00 1095.2 100.0 200 1.31 1.14 1383.1 75.9 500 1.47 1.17 1406.8 67.7 1000 1.90 1.24 1450.0 52.4 1500 2.80 1.29 1499.4 35.5 2000 4.98 1.34 1551.4 19.9 3000 33.41 1.41 1693.6 3.0 4000 878.82 1.38 2998.1 0.1 64 PAGE 65 Figure 31. EM gain causes contradictory ef fects on the spatial resolution of protein clusters. An NIH 3T3 fibroblast expre ssed two different proteins, GFPAgo2 and YFPSumo1, forming two types of protein complexes containing one kind of fusion protein each. These specklelike complexes (n = 6) were tracked to analyze the positioning error after t he cell was fixed by formaldehyde. The analyzed results are listed in the t able beside the image with the object numbers designated in the image. The effects of EM gain (at k = 2000) on the resolution (presented by the variance of tracked positions) was listed as the ratio of the positioning resolution at k = 0 to k = 2000 (far right column). 1 2 3 4 5 6 Obj 1 2 3 4 5 6 3.01 1035.02 1049.77 1051.12 1025.35 1031.68 1032.31 1035.04 1051.74 1041.36 1023.72 1031.14 1031.30 1.00 0.56 0.83 1.44 1.48 ratio positioning resolution ( m2) k = 0 k = 2000 65 PAGE 66 Figure 32. EM gain parameters are determined experimentally. ( A ). Schematic plot of photon conversion and noise propagation in the EMCCD camera. ( B ). Logarithmic plot of intensity count ( ) at different EM gain ( ) versus under varying light intensities. The solid line represents the least squared fitting results to the linear model. Act ual electron multiplication gain can be estimated from the slope of fitted model. ( C ). Scatter plot of 2 versus at k = 0, 1000, 2000, 3000 and 4000 in the logarithmic scale. Linear model fitting results at different EM gain ar e shown as a solid line and agree well with experimental data. R2 > 0.99 for all fitted models. koutI, 0, outIkoutI,, kout Photon sensing Readout ( GADC) Electron multiplication ( GEM)Photon signal processing in EMCCDIncident photons ( NP) Electrons ( NE = NPE + NDE) Amplified electrons ( NEGEM) Intensity count ( NEGEMGADC+ Ioffset) Noise propagation( PS 2) = NPE + NDEPS 2GEM 2F2PS 2GEM 2F2GADC 2+ R 2 105 103 104 105 103104103 104 105 101 102 103 104B CSaturationAIout,k(au)out,k 2(au2) Iout,k(au)Iout,0(au) 66 PAGE 67 SNR SNR SNR 1600 1800 2000 10 14 18 C65,535 103 104 0 20 40 60 80 A65,535 103 104 0 50 100 150 200 110013002 46 8B )au( 2000 out,I )au( 0 out,I )au( 0 out,I Figure 33. The optimal setting of the EM gai n depends on the intensit y of the signal. ( A ) The correlation between SNR and is plotted for k = 2000. The theoretically derived SNR curve (solid line) agrees well wit h experimental data ( ). ( B ) Values of the SNR at different EM gain (k = 0, 1000, 2000, 3000 and 4000) are determined theoretically and plo tted at the same amount of light intensity as At a high incident light intensit y, the highest SNR is at k = 0, and the SNR decreases with increasing k. Inset: the region marked by the dashed box in panel B is shown in mo re detail. The arrow points in the direction of increasing k. ( C ). The SNR crossover between k = 0 and a given k occurs around = 1800 au. koutI, 0, outI I0, out 67 PAGE 68 Figure 34. The relation of the k and S is affected by ( A ) The EM gain setting affects the peakI S dependency on These results show that EM gain effectively improves the `peakIS at low signal intensity, but the effect diminishes with increasing of the objects. After the peakIS at a certain k crosses over that of k = 0 ( ~ 2000 au), a contrary effect occurs. ( B ) The crossover points of the peak intensity at the junction of the pos itioning error curves of nonzero k and at k = 0 () depend on k. The crossover points set an upper bound as the critical points for the highest values at a certain EM gain; at < one can still take the advantage of EM gain to reduce the positioning error in particle tracking ex periments. The error bar is the standard deviation from five indi vidual simulation results. peakIpeakIpeakIkCI, 0 500 1000 1500 2000 5000 7000 9000 B A102 103 104 103 101 101 k = 3000 k)au( peakI 68 PAGE 69 69 Figure 35. The EM gain performance in particle tracking depends on experimental conditions. (A ) Background intensity, affects the significantly. With > ~ 900 au, the EM gain will not improve the S for particle tracking. ( B ). A large apparent radius of particle, Ra, also affects the significantly. Open triangles ( ) and open squares ( ) correspond to k = 1000 and 2000, respectively. BGIkCI, kCI,BGI Figure 36. Plot of 1000, S vs. 0, S Two experimental condi tions were chosen: 35 microspheres at high at 100 % light s ource intensity ( ) and 43 microspheres at low at 25% power of light source intensity ( ). The solid line corresponds to peak peak 1000II, S = 0, S Zero EM gain causes a 23% ( 10%) improvement in positioning error at 100 % light source intensity in which is larger than 10,000 au and background in tensity is ~ 5000 au. On the other hand, EM gain (k = 1000) improved the positioning error by 46% ( 11%) for the particle with small (~ 1000 au) and minimal background ( ~ 0 at 25% light source intensity).peakIpeakIBGI 8000 0 500 1000 0 2000 4000 6000 A B 8000 4000 0.5 0 1 1.5 2 2.5 )au( BGI )au( aR 106 104 102 106 104 102 ) m( 2 0 S PAGE 70 CHAPTER 4 ANALYSIS OF VIDEOBASED MICROSCOPIC PARTICLE TRAJECTORIES USING KALMAN FILTERING 4.1 Background Cellular dynamics controls cell physiology 22, 23. This dynamics process includes not only protein diffusion and transport but al so the intracellular organelles motion 22, 24. Meanwhile, the invasion process of bacteria in the intracellular region of mammalian cells has also been discovered to involve in t he intracellular dynamics of the host cells 25. Therefore, to understand the molecular mechanisms of a subcellular event, the cellular dynamics plays a critical role and cannot be ignored. The most direct way to study a cellular dynamics process is to m onitor the physical motion of the observed object, and to further correlate this motion to the biochemical functions of the composed proteins of the object. For example, the analysis of the st ep size of the cargomotor protein transport led to the understanding of how the motor proteins function 2629. The connection of the bacteria motion to the functi on of bacterial protein, ActA, elucidates how bacteria move inside the intracellular region of the host 30, 31. In these studies, particle tracking serves as the most direct method for studying the real time movement of objects of interest in live cells. Particle tracking has been applied to study various subcellular events, such as genomic dynamics 32, viral infection 33, 34, cellular endocytosis 35, membrane protein trafficking 36, and cargo transport 37. Besides the study of t he dynamic events of a live cell, particle tracking is also applied to probe the mechanical properties of the intracellular region of the live cells through the particle tracking microrheology 38, which analyzes the fluctuations in displacement of an inert particl e embedded in the cytoplasmic region of a live cell at differ ent time lag. Through the microrheology 70 PAGE 71 theorem 39, 40, the rheological properti es of a cell, such as creep compliance, elastic modulus, and viscous modulus, can be explored 38, 41. Compared to other existing techniques, such as atomic force microsc opy, intracellular microrheology imposes a minimized perturbation to acquire the physica l properties of the intracellular region of the cells. Using this technique, the mechanical properties of various cell lines under different extracellular stimuli (chemical 41 and mechanical 42) and microenvironmental topology (twodimensional vs. threedimensional 43) can be probed. Since the particletracking technique can c ontribute valuable insights into many biological events, the accura cy of particle tracking is cr itically important for the effectiveness of those studies. However, in a particle tracking experiment the sensor noise in the image acquisition system is transfo rmed into a positioning error. As a result, the computed particle trajectory is a noisy ve rsion of the true parti cle trajectory. This hinders a deeper analysis of the trajectory aimed at gaining detailed insights into the dynamic processes related to t he observed object (Fig. 41) 76. Accordingly, many advanced instruments were recently developed, which improve the spatial resolution of tracking techniques 19, 20. However, signal filtering and es timation algorithms offer an alternative route to reduci ng the extraneous noise associat ed with particle trajectories. These algorithms can be applied regardless of the underlying instrumentati on, and thus provide a general approach that can effectivel y enhance the spatial resolution of particle tracking. Deriving states of a dynamic system from noisy measurements is a very wellresearched problem in control and estimation theory. In particular, the Kalman filter algorithm provides the optimal state estimate for linear dynamic systems from sensor 71 PAGE 72 measurements in the pres ence of Gaussian noise. The Kalman filter has been successfully applied in a wide variety of situations in engineering and science 44, 45. The potential use of a Kalman f ilter to study cell motion has been mentioned in passing 46. In this paper, we explore in detail the application of the Kalman filter algorithm to improve the estimation of the particle trajectory obtained from a microscopic particle tracking experiment. At first, it is demonstrat ed that the Kalman f ilter can be used to infer intrinsic (noisefree) trajectories. Second, we explai n how the input parameters (the variance of process and measurement noise) necessary for the design of the Kalm an filter can be estimated for a given experimental situation. Third, we discuss the efficacy of Kalman filter in particle tracking. Finally, I examine in vitro particle tracking in glycerol and in a gliding motility assay to validat e the application of the Kalman filter. It is concluded that the Kalman filter can effe ctively eliminate the posit ioning error generated by measurement noise if the noise variance parameters are chosen appropriately. As a result, the accuracy of the trajectory der ived from particle tracking experiments is improved, which can provide the reliable biophysical information critical for the understanding of various biol ogical processes. 4.2 Theory of Kalman Filter ing in Particle Tracking 4.2.1 The Parameters of the Kalman Filter Related to a Particle Tracking Trajectory Videobased particle tracking utilizes the visual information in a sequence of captured images to reconstruct the trajecto ries of labeled objects and determine their dynamical properties. The temporal resolution in a particle tracking experiment is determined from the time betw een each frame, represented by t Individual image 72 PAGE 73 frames in the tracking sequence can then be denoted by their respective time step, k and a subscript of k can represent the state of a given variable at time k t Conceptually, the position of a tracked object in a new frame is the result of a combination of active motion and random displacements due to thermal fluctuations that acted on the object over t since its previous position. In biological systems, the heterogeneous presence of obstacles restricts the magnitude of an object's velocity in a manner that intrinsically fluctuates. Thus, the change in position between time steps can be described by a constant directed movement, associated with a fluctuation, as well as the intrinsic thermal fluctuat ions. Using an ensemble fluctuation term, u0w0w k to account for and the thermal fluctuations the conceptual position, w0 x k 1, of a tracked object in a new frame c an be formulated as: k kkwuxx 0 1. (41) This relationship between position, acti ve motion and thermal fluctuations has been previously established in different forms 82, 83. However, during the image acquisition process there is an intrinsic measurement noise, v k that distorts the measured position, z k from its conceptual value as described by: kkkvxz (42) The Kalman filter is a recursive, com putational method to make an estimate of the real state of the position, x kk from these types of noisy observations while preserving their intrinsic fluctuations 84. However, having a better understanding of the parameters that govern the moti on of an object is necessary before describing the major input factors of the Kalman f ilter. The measurement noise, v k is better defined as the positioning error, and is assumed to obey: 73 PAGE 74 v k ~ N ( 0 R k ), (43) where N ( 0,Rk) is the Gaussian distribution functi on describing white noise with a zero mean and a variance of positioning error, R k Similarly, the process noise w k caused by thermal fluctuations is assumed to obey: w k ~ N ( 0 Q k ), (44) where N ( 0 Q k ) is also the Gaussian distribution function with zero mean and variance of thermal fluctuations, Q k In onedimensional Brownian dynamics, Q k 2 D where D is the effective diffusivity of a labeled object and is the diffusion time. If tracking object undergoes pure Brownian motion, the value of is zero, and the value of u0w k only represents the thermal fluctuations. In the case of directed motion, the magnitude of can be experimentally estimated by calculating the average displacement between time steps, i.e., u0u0 zk 1 zk Taking all of this into account, the most important parameters of the Kalman filter are the raw trajectory information and the variance terms Q and R The value of R for a tracked particle can be extracted as previously described 75, but the value of Q must be attained using another method. The mean squared displacement (MSD) of the measured trajectory, z k is calculated as the variance of the measured displacement, and is related to Q and R by 75, 76: S ( var( dz ))S Q 2 R (45) Because noise from image acquisition do es not directly influence the physical system of interest, the value of Q is independent of R and this relationship serves as an explicit method to estimate Q 74 PAGE 75 4.2.2 The Kalman Filter Gain is Determined by the Ratio Q / R but not Q or R The Kalman filter uses a recursive procedur e to estimate the tr ue state of a linear process. It preserves the intrinsic fluctuat ions of the measured obj ect while effectively removing the external noise. Here is a brie f discussion of how to use this method to estimate the true trajectory from a measured trajectory obtained from the videobased particle tracking experiment. In the Cart esian coordinate system, the xand ycomponents of a particle trajectory moving in the xy plane are theoretically independent from one another; therefore, the use of the Kalman filter on a typical videobased particle tracking experiment can be simplified to a onedimensional model of particle motion in each direction. Individual time steps of the Kalman filter process employ two distinct processing phases: predict and update. The elapsed time after onset is represented by k t where k represents the observation ti me step. Any given variable with a subscript, lk, is at time step, k, and in phase, l When l = k 1 the variable is in its prediction phase, and when l = k the variable is in the update phase. Using this format, the positi on at the current time step, x k  k 1, is first predicted by the sum of the previous position, x k 1  k 1, and the displacement, from either the freely diffusive or directed motion of the particle: u0 x k  k 1 x k 1  k 1 u0. (46) Once the position, x k  k 1, is predicted, it is updated to a more accurate current position, x k  k in the update phase. This is achiev ed by adding a correction term that uses an adjustable factor, K k to weigh the difference bet ween the measured position, z k and x k  k 1: x k  k x k  k 1 K k ( z k x k  k 1). (47) 75 PAGE 76 The factor K k is at its optimal value and refe rred to as the Kalman gain when the x k  k reaches the minimal error covariance, Pkk E (( x k  k xk)2) At this minimal value, Kk Pkk 1 Pkk 1 Rk 1, (48) where Pkk1 E (( x k  k1 xk)2) and Rk E (( zk xk)2) are the magnitudes of the error covariance for x k  k 1 and z k respectively 84. The thermal fluctuation, Q k propagates during this recurs ive process; therefore, P k 1k must also be updated at each time step: P k 1  k P k  k Q k (49) In addition, P kk is concurrently updated with x kk in subsequent time steps: P k  k P k  k 1 K k P k  k 1. (410) Substituting Eq. 49 into Eq. 410, the discrete algebraic Riccati equation is obtained: P k 1  k P k  k 1 K k P k  k 1 Q k (411) In the onedimensional particle tracking case, Q k and R k are considered to be independent of k so that the number of variables is significant ly reduced. Therefore, P k  k 1, P k  k and K k can reach their steady state val ues quickly. In a steady state, P k  k 1 and P kk are independent of k, and equal to each other, which can be denoted as P Together, Eq. 48 can be simplified as K = Kk = P ( P + R )1 and be further substituted into the simplified form of Eq. S6, which is expressed as KP = Q Therefore, it yields P2 QP QR 0. (412) Since P is the error covariance, it possesses possess a positive value. Thus, the solution of P in Eq. 412 is 76 PAGE 77 P Q /2 Q2 4 QR /2, (413) which leads to K ( Q / R ) ( Q / R )2 4( Q / R ) 2 ( Q / R ) ( Q / R )2 4( Q / R ) (414) Thus, K is solely determined by the value of Q / R but not the individual Qand Rvalues. 4.2.3 MSD Estimates from a Filtered Trajectory are Equal to the True State When the Kalman filter is at its best performance, i.e., the correct Q / R value has been applied, the MSD value estimated by filtered position c an be expressed as: M S DE[( x k  k x k 1  k 1)2]. (415) The expression of x k  k and x k 1  k 1 in Eq. 410 and Eq. 411, respectively, is subsequently substituted into Eq. 415 and the following equation is obtained: M S D E [( K ( zk x k  k 1) u0)2] E [( K (( zk xk) ( xk x k  k 1)) u0)2]. (416) From Eq. 43 of the main text, we know that z k x k v k we further use x kk 1 to represent ( x k x kk 1 ) and obtain M S D E [( K ( vk x k  k 1) u0)2] K2E [( vk x k  k 1)2] 2 u0KE [( vk x k  k 1)] u0 2. (417) Here, v k and x kk 1 are both random variables with Evk 2 R andE x kk 1 2 Pkk 1 P. Further, v k is not correlated with x kk 1 so E 2 vk x kk 0. Therefore, the M S D can be further simplified to: M S D K2R P u0 2 Q u0 2, (418) where the relation K2R P Q can be obtained from Eqs. 48 and 412. 77 PAGE 78 Analytically, the true MSD at the shortest time lag can be calculated based on the true positions state, x k and Eq. 41 in the main text: MSD E [( xk xk 1)2] E [( wk u0)2] Q u0 2. (419) Therefore, the MSD calc ulated from a filtered trajectory using the correct values of Q and R in Eq. 418 is equal to the true MSD in Eq. 419. 4.3 Materials and Methods 4.3.1 Application of th e Kalman Filter to Simulated Trajectories The trajectory of a labeled object undergoing linear motion (e.g., Brownian motion or active movement containing ther mal fluctuation) can be simulated based on Eq. 41 and 44. The effective diffusivity and temporal resolution applied to the simulation were 0.006 m2 / sec and 0.033 sec, respectively, which were extracted from particle tracking experiments of 100nm micr ospheres in glycerol solution. From these conditions, the variance of a onedimensiona l thermal fluctuation is represented by QT (= 2 0.006 0.033 m2). For the simulation of Browni an motion the velocity of active movement is set to zero. In each simulation, a trajectory contains 1000 time steps; and extrinsic noise with variance, RT, is further added to each step based on Eq. 42 and 43 to mimic the positioning error resulting from the imaging process. The Kalman filter was then applied to t hese simulated noisy trajectories using several values of Q and R to understand the performance of the filter as the input variance terms differed from their true values (here, QT and RT). The accuracy of the filtered trajectory was evaluat ed by calculating the root m ean square error of positions (RMSE) (i.e., x k  k xk2 ). 78 PAGE 79 4.3.2 Microscopic Partic le Tracking System A Cascade:1K EMCCD camera (Roper Scie ntific, Tucson, AZ) mounted on a TE 2000E inverted microscope (Nik on, Melville, NY) with a 60, NA 1.45, oilimmersion objective lens (Nikon) was used to acquire particletracking video for image analysis. The particle tracking experiments were carri ed out by capturing video at a rate of 30 frames per second (fps). Each image sequence is composed of 650 frames. To achieve this high temporal resolution, the region of interest (ROI) function in the camera was activated and the binning was set at 3by3 for the particle tracking in glycerol (390 nm effective pixel size) and 2by2 for the glid ing motility assay (260 nm effective pixel size). 4.3.3 Particle Tracking Experi ments in Glycerol Solutions Carboxylated polystyrene fluorospheres (Invitrogen, Carlsbad, CA) with 100nm diameter in water were diluted into glycerol at 1/1000 volume ratio. A drop of the mixture was placed on the central area of a glass botto m dish (MatTek, Ashland, MA) for videobased particle tracking experiments. The par ticle tracking method was described previously 75. In brief, the background noise of t he raw image stack was reduced using a Gaussian kernel filter 76, 77. Afterward, a 2dimensiona l Gaussian distribution with logarithmic weighting wa s used to leastsquare fit the parti cles intensity distribution in the region contains the pixel possessing the maximum intensity and its four adjacent pixels to determine the particles positions. 4.3.4 Particle Tracking Experime nts in Gliding Motility Assays Kinesin was prepared as previously described 85. Microtubules were prepared by polymerizing 20 g biotinlabeled tubulin (Cytoskelet on Inc., Denver, CO) in 6.5 l growth solution, containing 4 mM MgCl2, 1 mM GTP and 5% (v/v) DMSO in BRB80 79 PAGE 80 buffer (80 mM PIPES, pH 6.9, 1 mM MgCl2, 1 mM EGTA) for 30 min at 37 C. The microtubules were 100fold diluted and stabilized in 10 M Paclitaxel (Sigma, Saint Louis, MO). The experiments were performed in ~100 m high and 1 cm wide flow cells assembled from two cove rslips and doublestick tape 86. First, BRB80 with 0.5 mg/ml casein (Sigma) was injected into the flow cell. After 5 min, it was exchanged with a kinesin solution (BRB80 with 0.5 mg/m l casein, ~10 nM kinesin and 20 M ATP). Five min later, this was exchanged against a motility solution (0.2 mg/ml casein, 20 mM Dglucose, 20 g/ml glucose oxidase, 8 g/ml catalase, 10 mM dithiothreitol and 20 M ATP in BRB80) containing 0.8 g/ml biotinylated microtubules. Five min were allowed for microtubule attachment after which 20 nM Alexa 568labeled streptavidin (Invitrogen) in motility solution was perfused into the flow cell and incubated for 5 min to cover all the biotin sites on the microtubules 87. Finally, after three washes with motility solution, biotinlabeled 40 nm fluorospheres (Invitrogen) at 100 pM concentration in motility solution were introduced into the flow cell and the edges of the flow cell were sealed with Apiezon grease to minimize evaporation. 4.4 Results To explore the application of the Kalman filt er to effectively correct the influence of measurement noise on position estimation in single particletracking experiments, an errorfree Brownian trajectory was simulated to serve as the reference trajectory (Fig. 42 A ). Positioning errors with increasing variance values, denoted as R were individually added to the reference trajectory to derive 4 noisy trajectories (Fig. 42 B ; from the left to the right, R = 0.0004, 0.0011, 0.004 and 0.04, respectively). In these simulated trajectories, the input par ameters, including the R values, were chosen based on typical experimental conditions 75. The Kalman filter was applied to these trajectories and the 80 PAGE 81 root mean square errors (RMSE) of the positions between the estimated trajectories and the errorfree trajectory were determined. The application of the Kalman filter requires two input paramet ers, the variance of thermal fluctuation ( Q ) (from process noise) and the variance of positioning error ( R ) (from measurement noise), which are not known a priori First, identical values for Q and R are chosen to calculate the resulting RMSE values and to determine whet her Kalman filtering could improve the noisy trajectories. The results show that the Kalman filter can reduce the positioning error even if the input parameters are arbitrarily assigned (Fig. 42 C ). However, if the true values of Q and R are utilized (known for the simulation), the positioning error of the noisy trajectories can be further reduced up to ~3 fold (Fig. 42 D ). The evaluation of the Kalman filter was fu rther extended to trajectories describing active motion. Active motion trajectories without (Fig. 42 E ) or with positioning error (Fig. 42 F ; from the left to the right, R = 0.0004, 0.0011, 0.004 and 0.04, respectively) were simulated. Either arbitrary (Fig. 42 G ) or accurate (Fig. 42 H ) Kalman filter input parameters were applied to the no isy trajectories to estimate the true trajectories. Again, the positioning error generated during the acqui sition process was reduced, and the optimal performance of the Kalman filter depended on the correct choice of input parameters. These simulations suggest that the Kalm an filter can effectively eliminate positioning error caused by measurement noi se while retaining the intrinsic thermal fluctuations if the input parameters, Q and R are available. However, the Q and R are two independent unknowns, whose values cannot be directly determined from an acquired image. Previously, a Monte Carlo method that utilizes empirical parameters 81 PAGE 82 obtained from images is develop ed to extract the value of R 75. This value of R is a positioning error that is individually estimated for each of our imaging experiments because R depends strongly on the incident light intensity and parameters of the acquisition system. The value of Q can be determined using the Eq. 45 75, 76. Since S can be obtained from experi ments, the value of Q can be obtained as S 2 R (Fig. 43; please also see Materials and Methods). A potential shortcoming of this method is that errors in the determination of R and S directly affect the accuracy of Q To assess the impact of inaccurate Qand R values in a model system, I tracked freely diffusing 100nm diameter carboxylat ed polystyrene fluorescent particles in glycerol at room temperature and an acquisition frequency of 33 frames per second. These experiments were repeated many times and the value of R was estimated using the Monte Carlo procedure for each experiment 75. Comparing the resulting microrheological measurement of the viscosity of gl ycerol with a conventional rheological measurement va lidated the accuracy of R The standard deviation of R from 20 independent simulations is le ss than 3%, which is a further indication of the precision of this technique. Next, S was calculated as the mean square displacement (MSD) of the particles, and the value of Q for each experiment was obtained by using the relation, Qi = Si 2 Ri, where the subscript i represents an independent tracking experiment. A plot of S and Q against the corresponding R shows that S and R are proportional to each other while Q remains constant throug h different values of R (Fig. 44 A ). This calculated Q value was also in agreement with t he theoretically ca lculated thermal fluctuations at room temperature, QRT ( = 0.8 103 m2) 75. We next determined the mean and the standard deviation of Q within fixed intervals of R (Fig. 44 B ). Although Q 82 PAGE 83 and R are independent, the standard deviation of Q does increase with R Since the experimental values of Q and R can be obtained, we can evaluate the performance of the Kalman filter on measur ed trajectories using the experimentally determined Q and R For the linear dynamic model, it is eas ily shown that the Kalman gain is determined only by the ratio of Q to R and not the individual Qand R values (see Eq. 414). Thus, the performance of Kalman filter ing is described by the plot of RMSE vs. normalized Q / R (= ( Q / R )/(QT/ RT) = (Q / R )/( Q / R )T), where the QT and RT represent the true variances of thermal fluctuation and positioning error in the acquired image, respectively (Fig. 44 C ). As expected, the minimum RMSE value always occurs at normalized Q / R = 1, where the Kalman f ilter utilizes the accurate input ratio for the parameters, Q and R Since the determination of the Q value using the procedure described above has some uncertainty (g reen region: one standard deviation around mean of Q ; red region: two standard deviation s around the mean), the RMSE values obtained using the experimentally determined Q / R tend to be slightly larger than the optimum. These RMSE values can be com pared to the RMSE value at very large normalized Q / R (e.g. 104). In this region, the Ka lman filter assumes minimal measurement noise and places a much gr eater reliance on the measurements by making minimal changes to the measured traj ectory. Therefore, the RMSE values at very large normalized Q / R are representative of t he unfiltered RMSE values. A comparison shows that t he experimentally obtained R and Q values lead the Kalman filter to estimate more accurate trajecto ries with smaller RMSE values when compared to the RMSE values of the original trajectory. 83 PAGE 84 Based on the experimental data, the percentage of RMSE improvement after applying the Kalman filter can be quantified (Fig. 44 D ). Using the mean value of R in each R interval and the corresponding Q at the mean one standard deviation as the input parameters of the Kalm an filter, the RMSE of the f iltered trajectories can be calculated and compared to the minimal RMSE value obtained for Q / R equal to ( Q / R )T. The data ( : left and : right bound in Fig. 4 C ) suggests that within the standard deviation (68.2%) of the Q value, the Kalman filter achieves at least 82% of the maximal reduction in RMSE value. First considering that an accurate estimate of R can be obtained in the experiment usi ng the Monte Carlo simulation technique, secondly that the estimate of Q / R determined in real experiment s has a limited range (e.g., normalized Q / R values vary from ~ 0.79 to 1.16 and ~ 0.63 to 2.3 for R ~ 6 104 and 3.4 103 m2, respectively, in Fig. 4 B ), and finally that the filtered RMSE value for input parameters, Q and R in this limited range is very close to the minimum RMSE value obtained for the optimal Q / R It concludes that the applic ation of the Kalman filter as described can reliably reduce the positio ning error generated in the image acquisition process. To demonstrate the application of the Kalman filter to experimental data of a purely diffusive process, particle tra cking of 100nm carboxylated polystyrene fluorescent microspheres in glycerol was performed and the MSD profiles were calculated from the tracking tr ajectories (see Fig 45). New MSD profiles calculated from the Kalman filtered trajecto ries of the microspheres de monstrated the successful removal of extrinsic nois e by the Kalman filter. 84 PAGE 85 We further applied the Kalman filter to an active transport process by estimating a more accurate trajectory of beads a ttached to a microtubule gliding on surfaceadhered kinesin1 motors (Fig. 46 A ). These position data and the extracted parameters, R and Q from the images were used as input for the Kalman filter, and the estimated trajectory for the microtubule was obtained (Fig. 46 B ). The average distance covered as a function of the time between frames (Fig. 46 C ) and the variance of the fluctuations around this average distance as a function of the time lag (Fig. 46 D ) show the expected linear behavior 82, 88, 89 for the filtered trajectory, while system noise distorts the unfiltered quantities. If the microtubules were st ationary objects, the position variance of the attached beads would not disp lay this linear increase. However, the active movement of the microt ubules during the gliding motilit y assays will directly affect the observed position of the attached beads. In essence, the gliding motion is thought to consist of a movement with constant veloci ty (caused by the active transport by the surfaceadhered motors) superimposed with a di ffusive movement against a high drag caused by protein friction (motor binding events which do not contribute a forward force). Thus, it is the diffusive movement of the microtubules and not of the attached beads that causes the linearly increasing pos itional variance of the beads. Previous studies of gliding cytoskeletal filaments, such as actin f ilaments and microtubules, have also interpreted the increasing positional variance as a result of protein friction 82, 9095. The glycerol and in vitro gliding motility studies show that the Kalman filter can restore particle trajectories fr om diffusive as well as acti ve transport, providing a more accurate picture of the underly ing dynamics. To further ve rify the results from the motility studies, an independent method to correct for trajectory error was performed 85 PAGE 86 and compared to the Kalman filtered MSD va lues and the raw data. The MSD profiles from the two different met hods shared an approximate 5fold decrease in MSD value from the raw data and were in good agreement when directly overlaid (Fig. 46 E ). Another way to verify the success of Kalman filtering is to analyze the autocorrelation function (ACF) of the innovation residual of the Kalman filter ( z k x k ; observed position predicted position). Theoretically, the i nnovation residue should be Gaussian white noise; hence, the signature of its ACF will be i ndependent of time lag, which is demonstrated by a value of unity at 0 and a va lue of 0 for all other time lag (Fig. 46 F ) 96. Through these separate analyses of the Kalman filtering of the gliding motility assay, which are independent of the st ochastic model used, I can solidly conclude that the Kalman filter can be succe ssfully applied to this in vitro system. 4.6 Discussion The application of the Kalm an filter to biological systems will encounter several challenges that must be overcome. Subc ellular dynamics are often complicated and effective models that can faithfully describe them are usually unava ilable. Many factors such as the thermal fluctuations, the steric effects from heterogeneous cellular architecture and the dynamics of the cytoskeleton reorgani zation contribute to the complexity of the dynamic movement of a mi cronor submicronsca led tracer inside a living cell. Therefor e, the first step to using a Kalman f ilter for this type of approach is to determine the appropriate stochastic model describing the motion of a subcellular object. Such a model would highly depend on se veral factors such as diffusivity, cell cycle stage, microenvironmental conditions and composition. If the model justifies the application of a linear filt er, the Kalman filter can be applied using the same 86 PAGE 87 methodology as the in vitro systems discussed in this work. With the correct stochastic model in place, the Kalman f ilter could become a powerful tool to reduce measurement noise and reveal the realtime dynamic interactions between a particle and its microenvironment. Another challenge facing the application of the Kalman f ilter to intracellular dynamics is the presence of photobleaching e ffects or big movements out of the focal plane in particle tracking experiments. Fo r typical particles like quantum dots and 100nm diameter fluorescence microspheres, which possess Q / R values within the range studied here, the variance of the positioning error ( R ) is assumed to be unchanged during the observation period in these in vitro studies. However, these conditions may not be fulfilled when studying the dynamics of a single molecule in living cells at 30 fps due to the large mobility of the probing mole cule. The reported diffusivity of GFP in cytoplasm is 20 m2/s and the focal depth ~ 1m. Thus, the time required for the GFP to diffuse out of the focal plane is ~ 0.05 s (~ L2/D). In that case, the R value would be a function of the molecular position in the zdirection and change dramatically if the temporal resolution is not correspondingly higher than 30 fp s. Photobleaching effects would also change the R value because the decreasing intensity causes a gradual increase in positioning error. As the temporal resoluti on is increased to offset movements out of the focal plane, the acquired images would be correspondingly dimmer unless the light source intensity wa s increased, which would further aggravate photobleaching problems. This tradeoff between temporal and spatia l resolution has limited the ability to further explore the cellular dynamic process of subcellular components and intracellular 87 PAGE 88 microrheology 38, 42, 43, 64, 97. Videobased microscopy studi es have provided a qualitative understanding of this issue 98, but an optimal balance of temporal and spatial resolution has not yet been fully developed. Recent dev elopments in photon detection techniques allow us to track object movem ent with high temporal resolution 99, which would help to compensate for movements out of the focal plane. As these types of techniques develop and a more comprehensive knowledge of spatiotemporal resolution emerges, problems associated with photobleaching effect s and movements out of the focal plane can be overcome. High temporal resolution c ould then be utilized in a particle tracking experiment at the expense of some degree of spatial resolution that could later be restored analytically by proper use of the Kalman filter, increasing the capacity to identify and quantitatively characterize subtle intracellular motion. I characterized the performance of the Kalman filter in estimating the native trajectory of particles diffusing within a gl ycerol solution and the transport process of microtubules in vitro I demonstrate that the Kalman filter is an effective tool to eliminate positioning error incorporated into the real trajectory during image acquisition while preserving the inherent therma l fluctuations, and that the success of the Kalman filter depends on the correct setting for the parameter describing Q / R Kalman filtering can preserve the native fluctuations while remo ving the measurement no ise; hence it greatly enhances the reliability of an estimated trajectory. I have shown that the value of R in a particle tracking experiment can be extracted using a Monte Carlo simulation technique 75. The extracted value of R is highly reproducible and successfully corrects the static error of noisy MSD curves. Furthermore, by using the values of Q and R extracted from experim ents, the individual 88 PAGE 89 trajectory resulting from the Kalman filter is optimized. The reliability of Kalman filter in predicting the trajectory can be assessed by the RMSE computation, which is compared to a simulated, true trajectory. The trajectory estimation from the Ka lman filter using the extracted values of Q and R can lead to a significant reduction of the RMSE value, close to the minimal value achievable with exact knowledge of Q and R At this minimum, the estimated trajectory carries a MSD equal to the MS D obtained from the true trajectory which can be proved mathematica lly as well (see sect ion 4.2). Therefore, it is concluded that Kalman filter can effectively impr ove the videobased particletracking trajectory in the in vitro systems examined. 4.7 Conclusion In summary, the purpose of this study is to take a first step and introduce the application of the Kalm an filter to biology and biophysics The Kalman filter has evolved since its initial development in to an extremely powerful tool used in many applications, even in the analysis of the stock market 44. This work suggests t hat the Kalman filtering approach can be utilized for the investigation of the in vitro systems studied here and in vivo systems in the future under careful consideration of its limitations. 89 PAGE 90 Figure 41. Schematic illustra tion of the principle of Kalm an filter in estimating the accurate trajectory in a cellular dynamic process The relation between adjacent steps of a trajectory is xk+1 = xk + uk + wk, where the occurring displacements before the next monitored time for the particle in xk position are determined by its projective movement displacement, uk, and a random movement generated by t hermal fluctuation, wk. Here, the subscript k represents the kth step of the tracking trajecto ry. In tracking experiments, the real particle position, xk+1, is recorded as zk+1 due to the positioning error. The Kalman filter is an established algorithm to restore the correct trajectory for a linear process. Experimental observation Real position (Hidden) Observation time period Kalman filter Kalman prediction Real trajectory (not available) noise noise Observed trajectory kkx),( ) ( 1 111 1 11 1RQfK xzKxx uxxk kkkkkkkk kkkkk kxkzkzkx1 kz1 kxkukw1 ku1 kw 90 PAGE 91 Q = 4 04R = QR = 2.7 Q R = 10 QR = 100QARRMSE = 0.0279RMSE = 0.0470RMSE = 0.0916RMSE = 0.2868 Free diffusion Active motionC RMSE = 0.0231RMSE = 0.0335RMSE = 0.0655RMSE = 0.2034Kalman Filter ( Qi= Ri= Q ) Kalman Filter ( Qi= Q ; Ri= R )DRMSE = 0.0217RMSE = 0.0323RMSE = 0.0461RMSE = 0.0848 RMSE = 0.0292RMSE = 0.0497RMSE = 0.0979RMSE = 0.2997EF Kalman Filter ( Qi= Ri= Q )RMSE = 0.0235RMSE = 0.0361RMSE = 0.0663RMSE = 0.1985G Kalman Filter ( Qi= Q ; Ri= R )RMSE = 0.0233RMSE = 0.0332RMSE = 0.0509RMSE = 0.0970H Figure 42. Estimation of the tr ue trajectory from positioning errors using Kalman filter ( A ) A simulated Brownian motion trajecto ry is represented without positioning error. (B ) Increasing degrees (fro m left to right) of posit ioning error (quantified by its variance R ) are added to the simulated trajectory. Higher R values yield noisier trajectories. ( C ) The Kalman filter removes some extrinsic noise under an arbitrary setting of the input parameters Ri and Qi, e.g. Qi = Ri = Q where Q is the thermal fluctuation variance. ( D ) The Kalman filter restores the noisy trajectories if the correct Qand R value are used as input parameters Qi and Ri. ( E ) A simulated active motion trajecto ry is represented without positioning error. (F ) Increasing degrees of positioning error are added to the active motion trajectory. ( G ) The Kalman filter improves the noisy trajectories under the setting Q = R ( H ) The Kalman filter restores the noisy trajectories under the correct Q and R setting. 91 PAGE 92 Q = Si2 R Kalman filter ( fn ( Q, R ) ) var ( dp ) Mapping Gaussian bead signature ( IBG, Ipeak, ra,x,y) Construct mimic GB image Add imaging noise, repeat trackingImplementing Kalman filter to obtain the resolution beyond optical limitation Observed bead sequential frames S Figure 43. Schematic illustration of the procedure of implem enting Kalman filter into a microscopic particle tracking system to improve the spatial resolution The acquired images are used to extract t he parameters to simulate Gaussian particle, which is applied to the particletracking algorithm to determine the variance of positioning error ( R ). The R value and corresponding Q value, determining by the MSD of the tracking trajectory and R value, then be used as the input parameters for Kalman filt er to restore the true trajectory. RRaw image Filtered trajectory observed trajectory tracking 92 PAGE 93 Figure 44. Characterization of the performanc e of Kalman filter on estimating particle tracking trajectories ( A ) The variance of thermal fluctuation ( Q ) can be extracted from the variance of displacement ( S ) and the variance of positioning error ( R ) using the relationship, Q = S 2 R. The mean of Q is estimated for different intervals of R with an interval size of 0.4 103 m2. The error bar represents the standard deviation of Q The resolution of Q decreases with increasing of R Inset: The trajectories contain 504 data points from particle tracking in glycerol described in the methods section. ( B ) Kalman filter performance is determined by the accurate Q / R value. Using the experimental R values and their corresponding ranges of Q value in simulations, the root mean square e rror (RMSE) of the Kalman filterestimating trajectories, compared to t he simulated true trajectory, can be obtained. The green and red region represents the RMSE value for Q value within one (green) or two (red) standard deviations of the mean. ( C ) The performance of the Kalman filter in esti mating the true trajectory measured by the RMSE reduction relative to the maximal RMSE reduction achieved for Q / R = ( Q / R )T. At the minimal RMSE value, t he estimating trajectory carries a MSD value equal to the true trajectory (see supporting material). The filtered trajectory is identical to the unfiltered tr ajectory if there is no positioning error ( R = 0) or if no improvement has been achi eved which occurs in for very large normalized Q / R Thus, the RMSE value at large Q / R represents the original RMSE value of the track ed trajectory. The maximu m improvement of the RMSE value thus is equal to the diffe rence between the RMSE value at large Q / R and the minimal RMSE value in the RMSEQ / R curve. 0 2 4 6 x10 3 0 1 2 3 4 5 x 103 R (m2) Q (m2)03B A 0 2 4 6 x10 3 0 0.005 0.01 0.015 S ( = MSDexp)R (m2)S or Q (m2)Q 03 0 2 4 6 x10 3 80 85 90 95 100 CR (m2)Performance (%) 03104 102 100 102 1011040.80 0.31 0.15 ( Q / R )true=( Q / R ) / ( Q / R )trueRMSE 0.1 0.05 0.021.33 93 PAGE 94 Figure 45. Improving the positioning error of particle tracking in glycerol solution ( A ) The MSD curves were obtained by parti cle tracking of 100nm carboxylated polystyrene fluorescent microspheres in glycerol, 31 microspheres were tracked. ( B ) The MSD curves were calculated from the filtered trajectories. Insets in ( A ) and ( B ) represent one of the traj ectories before and after application of the Kalman f ilter, respectively. Results from tracking a 20nm biotinylated nanosphere attached to a micr otubule in a gliding motility assay at 30 fps. 101 100 103 102 101 AB 101 100 103 102101 Time lag (s)MSD m2 Time lag (s)MSD m2 94 PAGE 95 95 Figure 46. Improving the positioning error of particle tracking in gliding motility assays using Kalman filter ( A ) Images of a gliding motility assa y. Images from left to right represent the microtubule, the nanosphere at 0 sec and the nanosphere at time 15.6 sec, respectively. The arrow indicates the initial position of the nanosphere, which is moving with a microtubule. ( B ) Observed trajectory (left) and filtered trajectory (right) of this nanosphere during the observation time period (15.6 sec). Scale bar: 200 nm. ( C ) Average of nanosphere displacem ent as a function of time interval. Removal of noise reduces the displacement at small time intervals of the filtered trajectory ( ) relative to the raw trajectory ( ), as expected for movement with constant velocity. ( D ) Variance of nanosphere displacement as a function of time interval for the filtered ( ) and raw ( ) trajectory. Removal of measurem ent noise yields the expected linear function starting at the origin and enables a correct estimate of the motional diffusion coefficient. (E ) MSD from the different particl e trajectories for different time lag is plotted. The value of the observed MSD (dashed line) is roughly 5 fold hi gher in comparison to MSD values with static error removed (solid line) and MSD values calculated from the Kalman filtered trajectory ( ). ( F ) The innovation residual of the Kalman filter ( z k x k or the difference between observed and predicted positions) is theoretically Gaussi an white noise. The autocorrelation function (ACF) of innovation resi dual is plotted against different time lag. Accordingly, the ACF is indep endent of lag time, which is a feature of Gaussian white noise. 0 100 200 300 400 500 0 0.5 1 102 101 100 104 103 102 101 0 0.2 0.4 0.6 0 1 2 3 x 104 Time lag (s)variance(d) m2 0 sec 15.6 sec Time lag (s) PAGE 96 CHAPTER 5 CHARACTERIZATION OF THE NAC1 NUCLEAR BODY DYNAMICS AND CHROMATIN ASSOCIATION 5.1 Background In this chapter, the methods described in the prior chapters are further used to study intranuclear dynamics. The cell nucleus plays a central role in mediating cell function through gene regulation. Thanks to the completion of the human genome project, the full sequence of t he human genome has been unveiled 47. However, it remains unclear how highly dynamic cell physiology can be governed strictly by gene regulation 50, 56. Variation of gene expression profiles in different types of cells and diseases suggests that a complicated system s hould exist in the nucleus to regulate the genome function 100, 101, and that dynamic changes in nuclear organization and architecture may play a key role in gene expression 48. The evolution of a cancer cell involv es a complicated, multistep process containing many unident ified factors that ma y alter gene expression 101, 102. The detailed mechanism of gene regulation remains unknown; nevertheless, the alteration of nuclear architecture has been observed in the progression of cancer cells 59, 101. Hence, the changes in nuclear architecture might deter mine the gene accessibilit y of transcription factors 52 as a means to mediat e gene transcription and prom ote cancer development. Presently, ovarian cancer is one of the most lethal gynecolog ical malignant diseases in the United States. In the tumorigenesis of ovarian cancer, the nucleus accumbens1 (NAC1) protein has been recently ident ified as one of the upregulated genes 103. NAC1 is located in the nucleus and it forms hom odimers via the BTB/POZ domain, which is reported to be an essential pr ocess for tumor cell growth104. The overexpression of NAC1 is tightly associated with the development of chemoresistance in ovarian cancer 96 PAGE 97 cells 105, 106. Interestingly, high expres AC1 causes the formation of distinct, dense bodylike stru from chromatin, the nucleus possesses many other organelles s clear speckles, Cajal bodies and PML ne re ewly ly the dy is disrupted and the expre that the h ing sion level of N ctures in the nucleus 104. Aside uch as nucl eoli, nu bodies 50, 53. These known nuclear bodies are believed to be associated with ge regulation that governs important cell functions 49, 55, 107. For instance, Cajal bodies a associated with RNA synthesis and RNP assembly 49. Thus, it is probable that the n discovered NAC1 NB is also involved with the genome regulati on in the nucleus. Recently, two downstream transcriptional targets of NAC1 have been identified: Gadd45gammainteracting protein 1 (Gadd45gip1) and Gadd45gamma. They are each associated with the Gadd45 pathway and their expression is downregulated by NAC1 106. When a dominantnegative form of the NAC1 protein containing on BTB/POZ domain is introduced into cells, the nuclear bo ssion of both Gadd45gip1 and Gadd45gamma increases. This indicates intact structure of NAC1 NB is involved in the regulation of transcr iption as well. Yet, the detailed mechanism of NAC1 NBcont rolled gene transcription regulation is still unknown. This knowledge about the nuclear body is mainly available through the characterization of its com ponents at the protein level 50. However, the real time interactions of the intact nuclear body with chromatin are not well understood. For example, it is known in det ail that the PML NB is disr upted in acute promyelocytic leukemia (APL) blasts as a consequence of the dominantnegative action of the PMLRAR fusion protein over PML NB through dire ct physical interactions. The oncogenic PMLRAR protein, which induces APL, is generat ed by te fusion of the gene encod 97 PAGE 98 PML protein and the gene encodi ng retinoic acid receptor When the PML NB is to be reformed, resulting from treatment with retinoic acid, the aberrant phenotype can be reversed 108. However, the true func tion of the PML NB in t he nucleus still remains as an open question. In this study, the short time dynamics of NAC1 NB is examined by directly tracking the NAC1 NB movement to characterize their interaction with chromatin. While examining the short time dynamics of NB, the limited photon integrating able time is imp ion, ion, and cytoskeleton disruption. e ortant to consider. An adequate spatia l resolution remains necessary to avoid tracking with great amount of error that could bias measurements and lead to misinterpretation of the results. Through careful application of the method described in the prior chapters, trustworthy NB dynamics can be acquired. In this work, confocal microscopy is used to examine the struct ure of NAC1 NB and its location in the nucleus. The movement of NB is measured for characterizing their mobility at short time scales. Finally, drug treatments are appli ed to examine the change in NAC1NB dynamics in response to different cellular pertu rbations, including tran scription inhibit ATP reduct 5.2 Methods and Results 5.2.1 Characterization of NAC1 NB in nucleus Since NAC1 NB was a newly discovered nu clear structure, we first studied th nuclear location of NAC1 NB. RK3E cells stably expressing the GFPNAC1 were stained by propidium iodide (PI; Sigma, St. Louis, MO) to label the chromatin region. Confocal microscopy (EZC1, Nikon, Melville NY) was used to acquire images using 30m pinhole to achieve better localization of NAC1 NB in the chromatin cluster. The 98 PAGE 99 images from the stainednuclei show that the NAC1 NB is s patially excluded from the DNA dense regions (Fig. 51). This result i ndicates that NAC1 NB s are located in the interchromatin compartments, where most nucleus organelles, including PML and Caja bodies, are located. However, unlike PML prot eins that form a ringlike structure in the PML body, the NAC1 proteins have a mo re homogeneous distribution in NAC1 N Throug l B 107. h observing the cell in interphase, it is found that NAC1 NBs possess differ evealed The ens ity. The intensity of the ROI at different onset time after the photobleac urther normalized (denoted eaching (denoted as Iprior and Ibleach respe ent sizes. This result was supported by previous electron microscopy study, which showed that the size of NAC1 was di stributed in the range of 0.2 1.8 um 104. A sequential observation for a 24hour period on the same batch of cells further r that the size of the NAC1 NBs correspondently grows with the progression of cell cycle until mitosis, in which the NBs dissolve (data not shown). The kinetics of the NAC1 NB was assessed by fluorescence recovery after bleaching (FRAP). The pinhole size of the confocal module was set to the maximum (150 m) to minimize the outoffocus effect fr om the zdirection mo vement of NB bleaching of the NAC1 NB was operated on a region of interest (ROI) with 1 m 1 m squared size to document the recovery of int hing (denoted as IROI) was f as I) by the intensity prior to and right after photobl ctively) as: ) /() ('bleach prior bleach ROIIIIII (5 FRAP analysis showed that the recovery of NAC1 NB intensity reaches ~50% after few minutes (Fig. 52). This recove ry rate was similar to both PML and Cajal bodies, suggesting that NAC1 NBs possess a similar assembly kinetics as PML and 1) 99 PAGE 100 Cajal bodies 107. In addition, NAC1 NBs presumably possessed a stable core structure judging from the 50% of immob ile fraction that wont be repl aced by fluorescent form of NAC1 after Photobleaching. 5.2.2 Typical Motion of NAC1 NB in Nucleus The dynamics of NAC1 NB were studied by single particle tracking method with the e xperimental setup described in section 4.3.2. To minimi ze the effect of dynamic error, the exposure time was reduc ed to 6 ms. The static error (s) of each measured MSD was estimated using method described in chapter 2. Further, to exclude the unreliable data, in which the resolution is insuffi cient to estimate stat ic error, a threshold for the signaltonoise ratio (SNR) was c hosen to be 0.2. The SNR was determined by following equation, ssMSD/) (exp ( This threshold value was selected based on t he minimum resolution t hat the static err can still be successfully estimated. The MSD values of the tracked NAC1 NBs obtained from only xor ydirection were similar, suggesting that NAC1 NBs have isotropic motion in xy plane. Therefore, the 2dimensional MSD profiles in xy plane were analyzed in different time lags from 168 NAC1 NBs in 21 cells and plotted in the l ogarithmic scale in Fig. 53A. The results showed NAC1 NB undergoes a subdiffusive mo 52) or tion in short time intervals (time lag ( ) < 0.3s), wherthe subdiffusive motion coeff motio 0.3e icient ( d (MSD)/ d ) is less than 0.6. The n became more free diffusive ( =1) if the probing time lag increased. The distribution of the motion coefficient at three different time l ag intervals, 0.1s 0.3s 1s and 1s5s, showed an average coefficient of 0.5, 0.58 and 0.96, respectively (Fig. 5 100 PAGE 101 3B). At large time lag ( > 5s), some MSDs show the trend of directed motion (which has the signature, > 1). The arrows, indicating the displacement at large time lag ( = 5s), implied that the NBs have cons istently synchronized movements in a nucleus (Fig. 54). ent, indicating by the motion coeff e NBs urement, the correlated coefficient (ij 2 PAGE 102 the NAC1 NB movement was mainly dominat ed by its interaction with the surrounding chromatin. The size distribution of the NAC1 NB in the nucleus had been addressed in section 5.2.1. Here, I further examined the role of size on NB mobility. The rela of NBs was estimated from a sequential zstack of fluorescent images, captured righ after particle tracking of the same NBs. In general, an image in which the object of interest has the brightest intensity in a stack of sequential zdimensional scan was the image taken closest to the focal plane. Thus, an image having the brightest NB of interest in the sequential Z tive size t dimensional sca n was chosen to measure the size of the spec ge g s in the posit z = 0.5) (Fig. 56B). In other words, NAC1 NBs with a larger size usually possessed ific NB by a 2D Gaussian fit (Eq. 31). Even though sizes determined by this method could not represent the true size of i ndividual NBs, the size of an NB estimated from this method was used to establish the re lative difference in size when compared to other NBs. Crosscomparing t he estimated size of NB by this method with the 3D ima from confocal microscopy further supports the eligibility of this method (Fig. 55). Durin the required time period, which is ~20 sec, to scan and acquire sequential image zdirection, the distance an NAC1 NB can move was less than 300nm. Hence, the ion of a NB being monitored in tracking experiment can directly correspond to the sequential images and the relative size of the NB can be assessed. From the above measurements, the scatter plot of the NB size vs. MSD value at a lag time of 0.1 sec indicat ed that these two variables are negatively correlated with a correlation coefficient () equal to 0.6 (Fig. 56A). A similar analysis also suggested that the MSD slope negatively co rrelates with the MSD value at a lag time of 0.1 sec ( 102 PAGE 103 smaller MSDs and lesser subdiffusive effects in the short time lag. This correlation was not found in long time lag presumably because their motion is dominated by the bulk nucle was TP nd (ActD), which binds n the ActD. Since ActD is known as a transcrip tion inhibitor that can bind to the active sites of chromatin to prevent the elongation of mRNA, it was reasonable to assume that us convective motion. The correlation between a NBs mobility and its location also examined and no significant direct iondependence was found on the monitored plane (data no shown). This result suggest ed that the NAC1 NB s in a nucleus are enclosed by a uniform architecture within the interchromatin region. 5.2.3 NAC1 NB Dynamics Relates to the Chromatin Architecture and ATP Level It is known that the ATP is required to maintain the chromatin structure, and in ATP deficient cells, the chroma tin is condensed and less dynamic 5. Thus I further studied the dynamics of NAC1 NB in the nuc leus with the depletion of ATP. The A level in a cell was reduced by the addition of the cellular respiration inhibitor, sodium azide (10mM), alone with the glycolysis inhibi tor, 2deoxy glucose (6mM) for 1hr. The morphology of NAC1 NB did not significantly alter after drug treatment. However, the values of the effective diffusivity (Deff MSD/4 ) of NAC1 NB at 0.1s time lag increased ~3.5 times (Fig. 57A). Howe ver, the ATP depletion did not change the subdiffusive state of NAC1 NB. This result suggested that the association between NAC1 NB a chromatin, which potentially causes the s ubdiffusive effect, is not ATPdependent. Furthermore, when cells were treated with 1ug/ml Actinomycin D to DNA by intercalation109, it had the opposite effect on the Deff of the NAC1 NB, which reduced ~ 2 fold 30mins a fter the treatment (Fig. 57A). After 1hr, only less tha 5% of NBs had a movement amplitude that was above the detection limitation (<5nm). This suggested the chromatin structure su rrounding the NAC1 NB was responsive to 103 PAGE 104 the mechanical properties of t he DNA string were enhanced by t he intercalation effect of ActD. The mechanical changes of chromatin c ould contribute to the loss of the mobilit of NAC1 NB after treatment. Mo reover, this result could also lead to the hypothesis that the NAC1 NBs are located in a gene rich region. Unlike ActD, another DNA binding molecule Hoechst 33342 (1mg/ml) that binds to the DNA AT grooves had little effec the mobility of NAC1 after 1hr incubation (Fig. 57B). Hence, this res y t on ult indicated that dyna was f the a either the AT groove binding dye had littl e effect on the chromatin mechanics and mics, or the effect will not c hange the mobility of NAC1 NB. Whether the intact cytoskeleton structure could affect the dynamics of NAC1 also studied. Microtubule (MT ) and actin were disrupted by nocodazole (NOC) (1uM, 30min) and latrunculin B (Lat B) (100nM, 30min), respectively. MT Disruption did not alter the Deff of NAC1 NB. However, the latruncul in B treatment resulted in actin depolymerization and gave rise to a rounded cell shape. As a result, the Deff value of NAC1 NB in short time lag ( = 0.1 s) increased ~2 times (Fig. 57B). This result suggested that the integrity of actin cytoskeleton can a ffect the NAC1 NB dynamics directly or through the dynamics of chroma tin. Since it is known that the actin cytoskeleton physically links to nucleus to maintain the nucleus integrity, disruption o ctin cytoskeleton could potentially affect the stability of the nuclear structure as suggested by the increase of NAC1 NB mobility after actin disruption. Another possible mechanism for the LatB treat ment to affect the NAC1 NB motion was through the disruption of nuclear acti n, which potentially has a role in maintaining the nucleoskeleton or mediating intranuclear transcription. 104 PAGE 105 The NAC1 NBs motion coefficient, at short time lag (0 .1 0.3s) was also measured before and after different drug treat ments (Fig. 57C). The ActD and LatB treatments were found to signi ficantly increase subdiffusivity and the motion coefficient dropped ~50% and ~60%, respectively, after the treatment. Yet, these two drugs possessed opposite effects on the mobility of NAC1 NB. This result suggested that ActD and LatB treatments affect the chromatinNAC1 NB in teraction through different mechanisms. Hypothetically, ActD treatment could stiffen the chromatin that is associated with NAC1. Henc e, the NAC1 NB motion was well confined in the stiffer chrom s his f usion me ovement as motion of NAC1 NBs was subdiffusive regardless of the time lag range (from 33ms to 10s) (Fig. 58A). This atin environment, which lowers the moti on coefficient to a more subdiffusive state. In contrast, Lat B treatment increased the mobility of the NAC1 NB (as the value of MSD increased) but decrease the motion coefficient. The possible explanation for t phenomenon was that the chromatinNAC1 NB interaction was reduced through nucleoskeleton disruption. The other possibili ty was that the disruption of the actin cytoskeleton increases the diffusivity of the whole nucleus, which also makes the mobility of all the NBs incr ease. Yet, the rounded nucleus c ould decrease the space o interchromatin in the xy plane and cause the NAC1 NB to quickly reach a diff barrier (or corral) within the observing time lag. The changes of diffusion patterns of NAC1 NB over time in response to drug treatments were characterized from their relation between MS D and lag time (Fig. 58). In a normal untreated cell, the NAC1 NB showed a subdiffusi ve behavior in short ti lag ( ~0.5) and gradually became diffusive and eventually had directed m mentioned in previous section. After AT P depletion, the 105 PAGE 106 indica ng nt from e reased the MSD values of NAC1 NB over he otion ted that the directed mo vement of the nucleus is no longer dominant in the lo time lag, considering the ~0.5 subdiffusive coefficient at lager time lag and the less synchronized NB movement in 10s (Fig. 58A, inset ). This further suggested that the directional movement of t he nucleus requires ATP. In ActD treated cells, NAC1 NBs show ed a strong subdiffusive response ( <0.25) over short time lag ( < 0.2 s) and dramatically progressed to directed motion (Fig. 58B). Hence, after 0.2 sec the MSD is dominated by the di rected moveme bulk nucleus with higher magnitude compari ng the state before treatment. The 10 sec displacements of NAC1 NBs showed the augmented degree of directional motion, which was consistent with the MSD result (Fig. 58A, inset ). Binding the DNA by H33342 did not substant ially affect the diffusion behavior of NAC1 NB, but the magnitudes of the directed motion lowered ~5 times, which is estimated from the MSD values at time lag = 10 sec (Fig. 58C). Since a prolonged exposure to H33342 can cause cell death, this result suggested cells respond to th H33342 profoundly, and the change in the nucleus mobility may act as a significant marker to address the cell death. The disruption of the actin cytoskeleton inc all observed time lag (Fig. 58D). Ho wever, it was specul ated that multiple mechanisms could be involved in this phenomenon. In short time lag, the MSD increase could be possibly caused from the reduction of the chromatinNAC1 NB interaction as previous discussed. As the time lag incr eased, disruption by the actin cytoskeleton seemingly became more prominent because t he nucleus more easily moved within t cytoplasm due to the loss of anchorage to the actin cytoskeleton. Thus, the bulk m 106 PAGE 107 of the nucleus would cause a larger degree of movement of the NAC1 NBs and this would explain the increased MS D over long lag time. Meanwhile, disruption of NOC (Fig. 58E) did not show a significant change in MSD, suggesting that the nuclear bod dynamics and nucleus movement in the observa tion y time period is less sensitive to the MT. B tracking at the short time as s over the local motion of NAC1 NBs. NAC1 ar. 5.3 Discussion and Conclusion In this chapter, I studied the dynami cs of the oncogenic NAC1 NBs to gain insights for chromatinNAC1N B interaction. The results suggested that the NAC1 NBs are located in chromatinpoor regions or in the interchromatin area of the nucleus. ChromatinNAC1 NB interactions can be probed by NAC1 N lag (0.10.3 sec). NAC1 NB movement in longer time lag is more complicated since the bulk movement of the nucleus becomes a dominant factor for NAC1 NB motion. The MSD of NAC1 NB in short ti me lag suggesteda subdiffusive motion ( ~0.5), suggesting the chromatinNAC1 NB in teraction can affect the motion of NAC1 NBs. The subdiffusive pattern of NAC1 NB becomes weak with increasing time lag the bulk motion of the nucleus take Drug treatment experiments suggested that the mobility of NAC1 NB is governed by many factors, including the ATP level, t he chromatin structure, the chromatinNB interaction, and the integrity of the cytoskeleton. However, even thought the data supported that the chromatinNAC1 NB intera ction plays an important role in the NAC1 dynamics, the association of chromatin and NAC1 NB to gene regulation is uncle Incorporating protein modification into this type approach could potentially yield more insight into this question. 107 PAGE 108 The dynamic study of nuclear organelles implies a poten tial method to probe the chromatin architecture. However, nuclear or ganelles may not be ideal targets since th chemical properties and reactivity to chromatin may be mediated by several factors thereby complicating the mobility of nucl ear organelles. To better characterize chrom eir atin dynamics, it is desirable to bypass chemical interaction effects. This can be achieved by using an inert sed to estimate the mech the a tracer, and mi crorheology may be u anical properties of a nucleus. Though parti cles can be directly injected into nucleus by microinjection, the nucleus may be damaged, which is difficult to identify. MX1 protein possesses a nucleuslocating sequence and forms nuclear bodies with crystallike structur e inside the nucleus5. A MX1 protein mediated marker may offer a way to better examine the chromatin architecture. 108 PAGE 109 Figure 51. Fix and stain images show the location of NAC1 NB in a nucleus. Confocal ained Chromatin ( B ), and the 1 NB is located in chromatinpoor regions. ( D ) A cartoon demonstrates the NAC1 NB location in the nucleus. 2um GFP NAC 1 PI Chromosome territory Chromosome territory regionAB C DInterchromatin sections of GFP labeled NAC1 NB ( A ), PI st overlayed images ( C ) showing that the NAC109 PAGE 110 Figure 52. Dynamics structur e of NAC1 NBs was analyzed by Fluorescence recovery after Photobleaching. ( A ) NAC1 NBs is bleached and its fluorescent Intensity in a 1um *1um region of interest spot is measured over 400s. The thick blue line shows the mean of the recovery curve. ( B ) A control experiment shows no significant amount of fluorescence bleaching during the observation time period. The red line indicates the mean of intensity value over time. 0 100 200 300 400 0 0.5 1 0 100 200 300 400 0.5 0.75 1 1.25 1.5 Time (s)ROI intensityTime (s)ROI intensityN=29 N=21AB 110 PAGE 111 102 101 100 101 104 103 102 101 Time lag (s)MSD m221 Cells with168 NBs 0 0.5 1 1.5 2 0 0.2 0.4 0 0.5 1 1.5 2 0 0.2 0.4 0.2 Characterization of NAC1 NB dynamics from their MSD responses. (A ) MSD result of NAC1 NB (N=168) from 21 cells were plotted against the time lag. The yellow dashed line represents the mean value of MSD and t Figure 53 he black line indicates an MSD slope of 0.5. ( B ) Histogram of subdiffusion coefficient ( ) over different time lag ranges (from top to bottom, 0.10.3s, 0.31s, 15s) showing how the mean and distribution of increase with time lag. 0 0.5 1 1.5 2 0 0.1 = 0.1 0.3 s = 0.3 1 s = 1 5 sOccurrence (%)A B 111 PAGE 112 Figure 54 Figure 55. Reconstructed NAC1 NB image (l eft) where the NB size represent the estimate of NAC1 NBs size from wide fi led zstack images. The result agrees with the zprojection image from confocal microscopy (right). A vector map shows the NB Move ment over three diffe rent time scales, 0.1s, 1s and 5s (from t op to bottom). Synchronized NB movement is found in the same nucleus. Enclosed dash lines indicate the location of the nucleus. = 0.1s = 1s = 5s 112 PAGE 113 Figure 56. NAC1 NB mobility is associated with its size (A ) A scatter plot of MSD values at 0.33s and their slopes show that they are negatively correlated with a correlation coefficient of 0.6. (N=82). (B ) MSD values are also negatively correlated with size. (correlation coefficient = 0.5) 0 0.5 1 105 104 103 102 slopeMSD0.33(um2) 0 1 2 3 105 104 103 102 MSD0.33(um2)Ra (px)AB 113 PAGE 114 Figure 57. Drug treatment a ffects NAC1 NB kinetics. ( A ) Effective diffusivity (MSD/4) of NAC1 NB at 0.1s increases after ATP depletion but decreases in ActD treatment. The blue lines sketch the distri bution of effective diffusivity in the control condition. ( B ) A bar plot shows the change of effective diffusivity after different drug treatments. The change in effective diffusivity is normalized to the control. (C) A bar plot shows the subdiffusion coefficient change. The value is normalized by its subdiffusivity prior to treatment. Error bars represent the standard error of the mean. 0 0.5 1 1.5 4 3 2 1 0 0.1 0.2 4 3 2 1 0 0.1 0.2 4 3 2 1 0 0.1 0.2 Log Deff( m2)Occurrence (%)Control ATP deplete ActD 4Normalized Deff( m2/s) 0 1 3 2poABst/ preC 114 PAGE 115 Figure 58. MSD plots show the NAC1 NB dynamics over time in response to drug treatment. MSDs of NAC1 NBs prior to (yellow) and after treatment (blue) with ATP depletion( A ), ActD(B ), H33342( C ), latrunculin B ( D ) and nocodazole ( E ). Black bar indicate the slope of 0.5 and 1. Inset images in (A C ) show the typical movement of NB over 10 seconds after treatment. Error bars represent the standard error of the mean. 102 101 100 101 104 103 102 101 102 101 100 101 104 103 102 101 102 101 100 101 104 103 102 101 102 101 100 101 104 103 102 101 102 101 100 101 104 103 102 101 Time lag (s)MSD m2Time lag (s)MSD m2Time lag (s)MSD m2Time lag (s)MSD m2Time lag (s)MSD m2ActD ATP() H33342 Actin () MT () AB C DE 115 PAGE 116 CHAPTER 6 CONCLUSIONS 6.1 Accurate MSD Estimation in VideoBased Tracking MSD inaccuracy due to static error is ubiquitous in CCD camerabased particle tracking systems. However, t he complex interplay between mu ltiple tracking parameters had precluded the development of a practical method to mi nimize the errors. The correction approach explained herein significantly minimizes static error. This approach circumvents the complication of direct static error calculat ion by employing a simulationbased method to correct experimental par ticle tracking measurements. This considerably enhances the accuracy of the MSD and improves the subsequent estimation of diffusivity as well as rheologica l properties. This correction technique is not system. T correlation tracking parameters. By clos ely following the can be significantly eliminated, leading to a greater clarity when interpreting the MSD values from a particle tracking experiment. In conclusion, this method greatly advances the application of single particle tracking in practice. 6.2 Optimizing Image Acquisition By thoroughly deciphering the photon s ensing mechanism of the EMCCD camera, I am able to successfully characterize the performance of this type of photon detector. Due to the various applications of an EMCCD camera in addition to particle tracking, specific settings may be us ed to fulfill different demands. With an understanding of the performance of this photon detector, t he resolution of imagebased limited to the particular system used herein, but is broadly applicable to any tracking he transition to another system requires simple steps of determining the between the pixel signal and noi se, and appropriately selecting correct methodology de scribed herein, static error 116 PAGE 117 biophysical methods can be assessed Carlo method to find the optimum settings for subsequent experiments. The estimation of biophysical properties is always affected by noise that deviates observations from their true value. Obtain ing an image using the optimum resolution decreases, but does not remove the noise from the image. Thus, biophysical properties estimated from images are consequently de viated from the true state. With an understanding of the noise withi n the measurement systems, I learn the effect of this noise on the resolution of biophysical property estimation by using a Monte Carlo method. This method is flexible and can be adapted to be suitable even when the image contains heterogeneous intensity values. The knowledge of the variation in real biophysical property estimations empowers us to make an optimum estimation from the observed set of noisy data. In this work, t he observed noisy trajectory serves as an example to demonstrate that with the adequate model and estimate of position variation, the root mean square error of estimated positions can be significantly decreased. In another words, the resolution of a measured trajectory can increase by roughly three times. This method is very ef fective and I believe it can be further applied to the estimation of many other cellular properties. 6.4 Dy One popular scheme for the func tion of nuclear organelles is that they are involved in gene expression regulation by acting as a nuclear hub for protein storage. In this dissertation, I have examined the dynamics of a newly discovered nucleus body, NAC1 NB, and have found that its dynamics are st rongly related to the surrounding chromatin structure. These studies furt her show that the dynamics of NAC1 NB are related to by the Monte 6.3 Optimum Estimatation of Biophysical Properties namics of Nuclear Organelles A ssociated with Chromatin Structure 117 PAGE 118 various factors, including NB size, the associ ation to chromatin, chromatin structure, and the cytoskeleton. Different drug treatme nts to the nucleus can induce different modulated effec C1 NB. My results ics ts, which can be successfully assessed by the MSD of NA indicate that the NAC1 NB is asso ciated with chromatin in the interchromatin space. Through this investigation, I propose an alternative view of how the NB dynam can contribute to gene expression regulation. 118 PAGE 119 (Un)confined diffusion of CD59 in t he plasma membrane determined by high(2007). 2. Saxton, M.J. & Jacobson, K. Singlepart LIST OF REFERENCES 1. Wieser, S., Moertelmaier, M., Fuer tbauer, E., Stockinger, H. & Schutz, G.J. resolution single molecule microscopy. 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He is an author or coauthor of mo re than 4 papers published in peerreviewed journals. grew up mostly in Kaohsiung, graduating fr om Kaohsiung Senior High School in 1 ned his B.S. in Chemical Engineering f in 2003. From 2003 to 2004, he served as soldier in Taiwan Army and until 2005 h w In 128 