Nucleation and Growth of Epithelial Cell Clusters

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Nucleation and Growth of Epithelial Cell Clusters
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english
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Suaris, Melanie G
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University of Florida
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Master's ( M.S.)
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University of Florida
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Biomedical Engineering
Committee Chair:
Angelini, Thomas Ettor
Committee Members:
Dobson, Jon P
Carney, Paul Richard
Ormerod, Brandi K

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cell -- migration
Biomedical Engineering -- Dissertations, Academic -- UF
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Biomedical Engineering thesis, M.S.
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Abstract:
Cells move in condensed groups during major steps of development, re-epithelialization during later stages of wound healing, and cancer. However, cell populations are sparse in many biological contexts and processes. In an injury, for example, during the proliferation phase of wound healing, granulation tissue is produced by fibroblasts and is sparsely populated by many cell types. To comprehend these processes, an understanding of the transition between sparse populations and dense populations is necessary. Current understanding comes from confluent sheets or “scratch tests.” Little information is available on the transition between the gas-like free space state to the fluid-like continuum state. This understanding would help engineer tissues and understand cancer and fibroblasts. Here we study the density dependent motion of cells on a surface. We start with a sub-confluent population and observe collective cell motion as the layer transitions from a dispersed distribution to a highly condensed monolayer. We find that this transition is similar to the gas to fluid phase transition process where density rises, velocity drops and slow cells form clusters. We also observe a critical cluster size, a growing correlation length that diverges with increasing cell density, and a migration velocity that appears to diverge negatively with increasing cell density.
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by Melanie G Suaris.
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Thesis (M.S.)--University of Florida, 2013.
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Adviser: Angelini, Thomas Ettor.
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1 NUCLEATION AND GROWTH OF EPITHELIAL CELL CLUSTERS By MELANIE GENNA SUARIS A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2013

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2 2013 Melanie Suaris

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3 To my parents, Wimal and Elita, Julian, and Jeremy for their support

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4 ACKNOWLEDGMENTS I owe my deepest gratitude to my advisor Dr.Thomas Angelini, whose guidance and support helped me develop a deep understanding of cell mechanics and dynamics necessary to complete this thesis. Special thanks to Jolie Breaux and Steven Zehnder and all other members of the Bio and Soft Matter Laboratory in the Department of Mechanical Engineering. Finally, a sincere thank you to the University of Florida Division of Sponsored Research Opportunity Fund, grant number GM03038, by which this work is supported.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................. 4 LIST OF FIGURES .......................................................................................................... 6 ABSTRACT ..................................................................................................................... 7 CHAPTER 1 OVERVIEW OF CELL DYNAMICS ........................................................................... 9 Motivation ................................................................................................................. 9 Hypothesis ................................................................................................................ 9 Introduction ............................................................................................................. 10 Cell Migra tion .......................................................................................................... 10 Single Cell Migration ........................................................................................ 10 Collective Cell Migration ................................................................................... 14 2 MET HODS .............................................................................................................. 26 Cell Culture and Preparation of Sample .................................................................. 26 Microscopy and Image Analysis ............................................................................. 26 3 RESULTS ............................................................................................................... 27 Cell Density and Migration Speed ........................................................................... 27 Nucleation and Growth of Cell Clusters .................................................................. 29 Scaling of Average Cluster Size and Average Migration Speed ............................. 30 4 DISCUSSION ......................................................................................................... 42 5 FUTURE PL ANS AND FINAL REMARKS .............................................................. 43 LIST OF REFERENCES ............................................................................................... 45 BIOGRAPHICAL SKETCH ............................................................................................ 47

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6 LIST OF FIGURES Figure p age 1 1 Illustration of increased F actin concentration ................................................... 18 1 2 Illustration of protrusive machinery .................................................................... 18 1 3 Illustration of Elastic Brownian Ratchet Model ................................................... 19 1 4 Illustration of general principles involving cell mig ration .................................... 20 1 5 St ructure of Myosin II protein ............................................................................. 21 1 6 Illustration of integrin recycling .......................................................................... 22 1 7 Electron micrograph of adherens junction ......................................................... 23 1 8 Stereoimage of desmosome .............................................................................. 24 1 9 Epithelial to Mesenchymal Transition (EMT) ..................................................... 25 3 1 Estimation of cell density over time ................................................................... 32 3 2 Cell migration fields as a function of time .......................................................... 33 3 3 False color intensity map of all speed histograms ............................................ 33 3 4 Normalized speed histogram for three time points ........................................... 34 3 5 Average speed of cells as a function of time is a linear relationship. ................. 34 3 6 Average cell speed as a function of density is diverging. ................................. 35 3 7 Binary 2D speed map of low migration speed clusters as they populate a surface ................................................................................................................ 36 3 8 Average cluster size of growing and transient clusters as a function of time. .... 37 3 9 Cluster size versus speed scales l ike a power law ........................................... 38 3 10 Divergent like behvaior of cluster size and speed ............................................. 39 3 11 Power law relationship between cluster size and reduced density ................... 40 3 12 Power law relationship between speed and reducted density .......................... 41 5 1 Phase diagram for cell dynamics ...................................................................... 44

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7 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science NUCLEATION AND GROWTH OF EPITHELIAL CELL CLUSTERS By Melanie Suaris May 2013 Chair: Thomas Angelini Major: Biomedical Engineering Cells move in co ndensed groups during major steps of development, reepitheli alization during lat er stages of wound healing, and cancer. However, cell populations are sparse in many biological contexts and processes. In an injury, for example, during t he proliferation phase of wound healing, granulation tissue is produced by fibroblasts and is sparsely populated by many cell types. To comprehend these processes, an understanding of the transition between sparse popul ations and dense populations is necessary. Current unders tanding comes from confluent sheets or scratch tests. Little information is availabl e on the transition between the g as like free space state to the fl uid like continuum state. This understanding would help engineer ti ssues and understand cancer and fib roblasts. Here we study the density dependent motion of cells on a surface. We start with a subconfluent po pulation and observe collective cell motion as the layer transitions from a dispersed distribution to a highly condensed monolayer. We find that this transition is similar to the gas to fluid phase transition process where density rises, velocity drops and slow cells form clusters. We also observe a c ritical cluster size, a growing correlation length that diverges with

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8 increasing cell density, and a migration velocity that appears to diverge negatively with increasing cell density.

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9 CHAPTER 1 OVERVIEW OF CELL DYNAMICS Motivation Over the last several decades, there has been an emphasis on cell migration (both single and collective) at a molecular level, but there is no consistent group of studies that focus on the mechanical forces that drive this phenomenon. The following study will bridge this gap by investigating the physical driving forces that control cell transitions from a nonconfluent to a densely packed monolayer. This will be done by using time lapse microscopy to observe epithelial cells during this transition over a period of three days and determining what critical parameters control single cell and collective cell migration and perhaps of fer a way on how to control these factors for future implications in wound healing and cancer research. Hypothesis As cells move from an uncondensed and sparsely seeded state to a highly condensed monolayer, it is hypothesized that the migration speed of cells will also decrease. However, we also observed that regions of slow migration speed contained groups of cells that maintained their cell cell adhesions, while regions with fast migration speeds had groups of cells with lower lifespans this brought about the hypothesis that there are two different types of cluster systems during this transition, fast and slow moving clusters. With further analysis, it was shown that cluster size and speed both show strong divergences, and cluster size versus speed s cales like a power law leading to the final hypothesis that cluster size versus density, and speed versus density also scales like a power law.

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10 Introduction Research in cell migration has a rich history due to its role in different forms of cancer metastasis, wound healing, and embryogenesis ( 1 3 ) An understanding of the biophysical and biological principles essential to life is vital for developing effect ive therapies to serious medical conditions. In recent years, research in this field has allowed us to learn about the different states that exist as cells populate a surface, but the physical and dynamic characteristics of the cells during these transitions remain a mystery. In this study we observed the migratory behaviors of cells as they populate a surface moving from being dispersed throughout the field of view to a highly condensed monolayer. The following sections will cover current literature on c ell migration. Cell Migration Extensive research has been conducted to monitor the chemical and mechanical characteristics of single cells, however living organisms are more than a compilation of single cells organisms are comprised of groups of cells that behave differently than their single cell counterparts. Results of cell migration studies may also vary between in vivo and in vitro studies, and whether a 2D or three dimensional (3D) substrate/scaffold is used. The following information describes g eneralizations of cell migration across different cell types. Single Cell Migration Migration is a biological process that involves a cascade of events: cell polarization, cell membrane protrusion, substrate adhesion and traction, and then cell translocation ( 1 )

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11 The first step in the cell migration cycle is polarization. This is when clear front and back sides of a cell become distinguishable and are triggered by an environmental cue from the extracellular matrix (ECM) or electric fields ( 1 4 5 ) Two major regulators of polarity in cells are filamentous actin (F actin) and the cell division control protein 42 (Cdc42). In animal cells, F actin is a building block used to make higher order structures such as lamellipodia (cross linked sheets of actin filament).and filopodia (thin, long, ropelike bundles which serve as the sensors to the cell). It is present in different stages of cell migration and can also be seen in other critical cellular processes, like glucose signaling and cell division. Asymmetry of a cell during migration is partly due to an increased concentration of F actin at the front of the cell which has a role in cell membrane extension. A fluorescent stain image illustrating the increased F actin concentration can be seen in Figure 11.The protein Cdc42, has an increased concentration at the front of migrating cells similar to F actin. It is able to influence the position of the Golgi Apparatus in front of the nucleus, which increases delivery of vesicles to the leading side of the cell, leading to increased microtubule organization essential for protrusion ( 5 6 ) When Cdc42 is not expressed, cells are unable to become polarized and instead become large and round ( 7 ) After the cells have achieved spatial asymmetry, cell membrane extensions, due to actin polymerization, are formed in the direction of cell migration and serve as protrusive machinery. Lamellipodia and filopodia are more concentrated at the front of the cell which aid in pulling the cell forward. An illustration of these protrusive elements can be seen in Figure 12. The force exerted by the previously mentioned machinery must be greater than the contractile force made between the cell and the substrate in

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12 order for the cell to move forward. To combat the opposing force, the binding and cross linking of filaments are increased in the lamellipodia and filopodia. Actin polymerization can occur via severing or uncapping of already existing filaments but the major contributor to actin is the addition of globul ar actin (G actin) monomers to an F actin growth site. The addition induces the formation of F actin filaments ( 1 8 ) Polymerization of the cell membrane that results in moving the cell forward can be described using the Elastic Brownian Ratchet Model, seen in Figure 13 ( 9 ) The actin fiber (red rope structure) bends constantly due to changes in thermal energy. When bent away from the surface, monomer units are added (pink) which results in a force propelling the cell forward as the actin straightens ( 9 10) Once the lamellipodia and filopodia have extended toward cell migration, adhesions between the cell front and the substrate must be produced to maintain integrity, while the adhesions at the back of the cell get released to decrease tension. The major family responsible for adhesion between the cell and the ECM are called integrins, which are heterodimeric glycoproteins capable of forming receptors and adhesion between the cytoskeleton of the acti n and ECM molecules. They are also responsible for adhesion between cells and are recycled in lamellipodium. Integrins can be considered to be the feet of a cell since it is the direct connection that the cell has with the ECM, and controls whether or not the cell moves forward. An illustration of the role of integrins in cell migration can be seen in Figure 14. Integrins serve a crucial role in cancer metastasis. When cells mutate and begin expressing a metastatic phenotype, both integrin expression and binding affinity to ECM molecules increases ( 11 ) The increased adhesion allows for the cancerous cells to

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13 become more migratory and invasive. In addition, the increased concentration of integrins encourages cell survival by preventing anoikis ( cell death due to the failure of a cell to anchor itself onto the ECM) ( 12) Migration speed depends on the stiffness and level of cell adhesion to the substr ate. Myosin based motors are essential for both detachment and translocation of a cell. The motor protein, myosin II, is a cell locomotion protein that converts adenosine triphosphate (ATP) chemical energy into mechanical energy, and is also involved in pr otein transport and mitosis ( 13 ) It is comprised of a heavy chain pair, motor domain and an essential and regulatory light chain, which provide the structural integrity (Figure 1 4). This motor protein, although found throughout the cell, is more concentrated at the back of the cell when polarized. It has an important role in the di sassembly of adhesions between the cell and the ECM by applying direct physical stress ( 14 ) Myosin II is activated via phosphorylation of the regulatory light chain creating a contraction which pulls on actin filament s that are adhered to the ECM through integrin receptors. Eventually the bond severs and results in a decreased tension at the back side of the cell leading to faster cell migration. Although membrane extension and rear release are separate events, the speed of migration is dependent more heavily on tension release at the back of the cell instead of the forces of protrusion at the front of the cell. It was previously observed that amoebae deficient of myosin II in the cell rear crawled more slowly than the wild type, but when the deficiency was in the front of the cell, the migration speed difference from the wild type was negligible ( 15) The final step in the cell migration cycle is the creation and recycling of integrins after the cell releases its rear As previously descr ibed, the myosin II motor protein uses

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14 mechanical stress to rip the cell from the ECM leaving behind integrins. The integrin molecules that remain on the cell after the myosin II protein rips the cell from its adhesions to the ECM, endocytosis regulat ed by GTPase Rab21 proteins occurs ( 16) and the integrins are used again at the front of the cell. Figure 16 illustrates how ripped integrins from the back of a migrating cell makes its way to the front of the cell through recycling. Cell migration begins with the polarization of the cell, followed by membrane extensions to bring the cell forward, increased adhesion to the ECM through integrin receptors at the front of the cell, decreased traction forces due to ripping, and finally cell rear release and recycling of integrin. Single cell migration has been studied extensively in the past, but only recently has collective cell migration come to the forefront. In order to have a full appreciation of the story of cell migration, it is essential to know how biological and mechanical processes differ between single cell and collective cell migration. Collective Cell Migration Collective cell migration is defined as the movement of two or more cells while maintaining cell cell adhesions. These cell cluster migrations occur during different stages of development and also in adult organisms. For example, during morphogenesis, the sprouting of collective cell migrati on helps to create the tracheal system used for breathing, and in wound healing, keratinocytes migrate laterally across the surface of the wound ( 3 17, 18) Collective cell migration increases tissue integrity, the ability to influence immobile cells to migrate, and neighboring cell interactions, which can influence the overall distribution and shape of the tissue ( 1 ) Similar to single cell migration, the

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15 collective cell migration is a direct result of a polarization of a group of cells. This polarity is induced by an environmental trigger, such as fibroblast growth factor (FGF) or vascular endothelial growth factor (VEGF). In order for a clus ter of cells to migrate, protrusions (extensions of cellular membranes from the leading edge) must also be created that extend outward towards the environmental stimulus. Like lamellipodia and filopodia in single cell migration, these structures are created from the leading edge cells as a result of actin polymerization and they connect the plasma membrane to the ECM. Adhesion between the substrate and the actin cytoskeleton through the use of integrins is also an essential step for collective cell migration. Other types of cell cell interactions adherens junctions, desmosomes, tight junctions, and gap junctions are not seen in single cell migration ( 3 ) Adherens junctions are strong cell cell adhesions that form bridges between the actin cytoskeletons of adjacent cells and are mediated by calcium dependent E cadherins, which is a type of transmembrane protein found along cell cell interfaces. An electron micrograph of an adherens junction is produc ed by passing an electron beam through the sample can be seen in Figure 17. Contrast in electron microscopy is generated by electron density measured after the beam has passed through the sample. Tight junctions are the closest cell interactions in nature and are highly ion selective. They form at the apical surface of the cell creating a barrier exterior to the basolateral surface of the cell resulting in zero net movement of membrane proteins ( 19)

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16 Desmosome are cell cell interactions common among epithelial cells. They are primarily seen along the lateral membrane, displayed as patches, which bind intermediate filaments with the plasma m embrane, as seen in Figure 18. When cells lose desmosome adhesion it leads to a process known as the epithelial to mesenchymal transition (EMT). EMT occurs when a polarized cell begins changing phenotype and losing cell cell junctions. The underlying basement membrane deteriorates which allows for the cell to travel through the lymphatic system to a new destination. A major difference between gap junctions and the previously mentioned cell cell interactions is that the two neighboring cells are not actuall y attached in a gap junction, providing a direct channel that connects the interior contents of adjacent cells to each other allowing for free passage of ions. Obtaining a deeper understanding of how cells multiply (uncontrolled mitosis) and metastasize ( travel to other parts of the body) is a potential key that may lead to more successful therapeutics. Research has shown that one malignant cell detachment from the primary tumor site is sufficient for traveling and recolonization of a new tissue system. Th is is known as the epithelial to mesenchymal transition (EMT). A mesenchymal cell is a type of undifferentiated stem cell. The mesenchymal to epithelial transition (MET) during cancer progression (Figure 19) is when the undifferentiated cancer cell adopts once again the epithelial phenotype and begins metastasizing and forming new tumors. It is also possible for incompleteEMT to occur in advanced types of cancers. This occurs when the cancerous cells adopt the mesenchymal phenotype while maintaining some epithelial cell features such as cell cell junctions ( 20) Adopting

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17 the mesenchymal phenotype keeps a small cluster of cells together rather than having single cells leave the primary tumor. When a single cancer cell detaches from the tumor, apoptosi s may occur as a result of the unfavorable environmental conditions surrounding cell. However, in collective cancer cell migration, the cells on the edges of the cluster, buffer most of the harmful environmental mechanisms, allowing for the cell at the center of the cluster to move through the blood stream unaffected ( 3 20) This allows the cluster to survive until it reaches the final destination and create a new tumor. When cells move from an un condensed to a confluent (highly dense) monolayer there are kinetic changes observed ( 2 ) At low densities the cell population is disordered and as they continue to multiply and eventually attach to neighboring cells they transition from a gas like state to one that is more ordered. The behaviors of cells contribute to their overall collective motion and are dependent on the cell cell adhesions the stronger the adhesion the more coordinated and mechanically coupled the adjacent cells become. In other words, with increased density, free motion of individual cells becomes restricted by neighboring cells forcing the group of cells to move together.

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18 Figure 1 1 Illustration of increased F actin concentration at front of migrating cell. Increased actin polymerization allows for the distinction between a clear front and rear of a cell. The front of the cell is the side of the cell that leads cell migration and is the site of the formation of protrusiv e elements ( 21) Figure 1 2 Illustration of protrusive machinery, lamellipodia and filopodia, in a migrating cell. These elements are created due to actin polymerization at the leading edge of a cell and form adhesions to the substrate which help the cell propel forward. ( 22)

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19 Figure 1 3 Illustration of Elastic Brownian Ratchet Model which explains the forces that contribute to cell movement. The red wire represents actin filam ents and over time, actin monomers are added to the end of these filaments, as represented by the wire shaded pink (in step 1). Since the actin fiber is elastic, as it exhibits Brownian Motion, this is when actin monomers are added (step 2). When the newly elongated fiber goes back to its original position, it propels the cell forward (step 3). ( 9 )

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20 Figure 1 4 Illustration of general principles involving cell migration in the direction of net force, filopodia and lamellipodia are formed at the leading edge, and integrins (as represented by the 3 parallel lines) are the feet of the cell that serve as the contact point between the cell and the substratum ( 1 )

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21 Figure 1 5 a) Structure of Myosin II protein essential for cell migration is seen in it is made of an essential light chain which makes up the motor, a r egulatory light chain, and nonhelical tail which make up the heavy chain. b) direction of actin filaments with respect to myosin II protein. The motor puts physical stress on the adhesions formed my integrins at the rear end of cells which results in a r ipping of the cell from the substrate, which decreases tension and allows for the cell to propel forward. ( 13)

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22 Figure 1 6 Illustration of integrin recycling following integrin ripping due to myosin motor induced stress. Integrins that are no longer adhered to the substrate can move along the edge of a cell and come back into the cell by way of endocytosis. They are then reprocessed and are sent to the front of the cell to form adhesions with the protrusive elements. ( 1 )

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23 Figure 1 7 Electron micrograph of adherens junction which holds epithelial cells together and create thin bands or patches between the cells. This type of cell cell interaction is se en in collective cell migration and helps prevent cells from detaching from one another. ( 23)

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24 Figure 1 8 Stereoimage of desmosome which is a patch that connects the cytoplasm of two cells to each other. This type of interaction is seen in collective cell migration and help prevent cells from moving as individuals. ( 24)

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25 Figure 1 9 Epithelial to Mesenchymal Transition (EMT) as it relates to cancer progression is seen here. This is when a cell, or a group of cells, abandon traditi onal epithelial characteristics and adopt a mesenchymal phenotype, allowing them to detach from the primary tumor site. They are then able to travel through blood vessels and the lymphatic system until they reach a new site, and then begin to proliferate and form a new tumor. When they attach to a new site, and go back to adopting an epithelial phenotype, this is known as the Mesenchymal to Epithelial Transition (MET). ( 25)

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26 CHAPTER 2 METHODS Cell Culture and Preparation of Sample MadinDarby canine kidney (MDCK) cells were cultured in Dulbeccos Modified Eagle Medium (DMEM) with 5% Fetal Bovine Serum (FBS) and 1% Penicillin Streptomycin (PenStrep). An island of cells was created by depositing 1 microliter of cell culture media containing approximately 500 cells at the center of a collagen coated glass bottom dish obtained by Pyrex. The sample was then left at room temperature for 20 minutes in order to let the cells form adhesions to the collagen coated petri dish. Afterwards the dish was filled with approximately 5 mL of cell culture media and placed in an incubator where it was maintained at 37oC and 5% CO2 for two hours. Microscopy and Image Analysis The island of cells was imaged using a fully automated and environmentally controlled livecell microscope in bright field every minute until the field of view was filled with enough cells to make a confluent monolayer. One in focus and one out of focus image were taken in order to differentiate cell clusters from areas void of cells. This was done because out of focus images are enhanced when imaging above the cell layer. Velocity fields were computed using a particle image velocimetry (PIV) technique and a speed histogram was generated for every time point for each substrate. Average cell size was estimated by manually counting, in 200 minute intervals, the number of cells in a several different area.

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27 CHA PTER 3 RESULTS Cell Density and Migration Speed Over a period of approximately three days, cells were observed as they migrate, proliferate, and populate a surface moving from a sparse cell population to a condense monolayer. In order to study these transitions, cell density was calculated manually in 200 minute intervals. Several different sections of the field of view were chosen and the number of cells in a given area was counted, providing the appropriate information to calculate cell density. An average of the different densities for the same time point was calculated. Figure 31 shows a scatter plot of the measured cell densities over time. In order to estimate the density of every frame, a smoothing spline fit was used, which is a method of fitting a smooth curve to noisy data. Particle Image Velocimetry (PIV) is an optical method that calculates velocity fields for a particular domain using software to determine how speed during collective cell migration differs from single cell migration. Figure 3 2 shows the velocity fields at three different time points. The first time point (Figure 32a) shows the cells sparsely seeded throughout the field of view the cells are larger, trying to seek out neighbors and form cell cell adhesions. From the first time point, the next two images (Figure 32b and Figure 32c) show the cells as they fill the entire surface to form a confluent monolayer. As the layer transitions from having several small clusters to one large cluster, the average cell begin to decreas e in size and the migration speeds also decrease (Figure 32e, Figure 3 2f).The corresponding migration speeds (Figure 32d) are high (as can be seen by the increase in vector length) since the cells are in a gas like state. The cells at the last time poi nt are so densely packed that their migration velocity fields show them not to be

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28 moving at all, inferring that cells may transition into another class as a function of cell dynamics. At each time point, the velocity vector magnitudes obtained from the P IV software analysis are combined in order to create a speed histogram which shows the distribution of migration speeds over time. Each histogram was normalized, illustrating a probability density function (with an integral over the entire area equal to one) and computed using a bin size of .46 m hr1. An arrangement of all speed histograms at each time point was arranged to create a 2D false color intensity map (Figure 33), which makes otherwise black, white, and grey images easier to understand. The map ranges from red (most intense) to blue (least intense). Figure 33 illustrates how the peak of the speed histogram shifts to a slower cell migration speed and narrows over time. The narrow peaks seen at later time points in comparison to broad peaks s een at the beginning of the experiments show that, as a cell cluster grows to form a densely packed, confluent monolayer, the distribution of speeds becomes homogenous because each cell is affected and moves like neighboring cells. In the case of later tim e points, the cells all have a lower average cell migration speed due to the increase in density. Figure 34 depicts this relationship with three histograms displayed at different time points showing the peak becoming narrower and shifting towards a slower speed with time. The peak of each speed histogram for each time point was denoted as the average mig r ation speed for that particular time. This was done instead of calculating the overall mean of the distribution which can bias the average due to skewed d istributions. Figure 35 is a plot of these histogram peaks as a function of time, showing that average speed did decrease with time, going from approximately 14 m hr-

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29 1 to 4 m hr1. Interestingly, average speed did not follow the same linear relationship with increased cell density. At a density around 2,000 cells mm2, the average speed dramatically decreases, exhibiting a divergent behavior and indicating an upper limit, or critical density, during collective cell migration (Figure 36). Nucleation and Growth of Cell Clusters At low densities, the surface of the sample is populated by small clusters that grow into one large cluster as density increases with time. The cell layer is divided into two populations fast and slow moving clusters. The slow moving clusters take up approximately 10% of the surface at low densities, and gradually increase to 90% as density increases. In order to differentiate between a fast and slow moving cluster of cells, a cutoff speed was applied to all frames. This cutoff was determined by calculating the average cell migration speed at a point where 90% of the surface was covered with cells; this gives us the speed of the average slow moving cluster this cutoff is approximately 15.5 m hr1. A binary 2D speed map is shown in Figure 37 with the applied cutoff speed and cluster of cells defined as regions in the binary speed map that are connected in both space and time. All areas highlighted in red represent slow moving clusters. Figures 16ac show the slow, growing clusters at low densities migrating and proliferating over time to establish one large slow moving cluster. For the duration of the experiment, many fast and slow moving clusters had a short life time as a result of the cells detaching from one another due to forces pulling the cluster in opposite directions. At the same time, other cells were able to exist permanently and continue to grow until a condensed phase was created. The average sizes of these growing clusters and transient clusters over time were measured and are plotted in Figure 38. The area of the short lived transient clusters was observed to be

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30 less than approximately 5,000 m2, and growing clusters grew indefinitely with an area greater. This established a critical cluster size, which was deter mined to be approximately 10 cells. If a cluster was below this threshold, it was unstable and would not persist or grow to become a part of the confluent monolayer, but if the average area of the cluster was greater that the critical cluster size, it woul d continue to grow until the surface became a condensed monolayer. The relationship between the average areas of the growing cluster size versus speed is shown to scale like a power law with an exponent of .2 (Figure 39) with a clear decrease in speed as the cluster size increases. Scaling of Average Cluster Size and Average Migration Speed The power law relationship, seen in Figure 39, between average cluster size and speed gave rise to the hypothesis that these two parameters, each plotted against cell density, will follow the same relationship. Determining whether these factors follow a scaling law is important because the divergent behavior further suggests that a critical point, whether for cluster size or cell density, is established. The first step was to make two separate plots of cluster size versus cell density, and average speed versus cell density (Figure 310). They both exhibited divergent like behavior; with cluster size increasing with cell density, and speed decreasing with cell densit y. But when scaled on a logarithmic axis, the relationship between cluster size and cell density was not linear, indicating that it does not follow a power law but rather behaves like a polynomial. A reduced density was calculated in order to fit a power law relationship. Reduced density was calculated using equation (31) where is the reduced density and is the critical density. :

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31 = (3 1) This value for reduced density was then fitted with the average cluster size in the following scaling law equation (3 2) with as the average c luster size, is the critical amplitude, and p1 is the critical exponent. = ( ) ( ) (3 2) We found that the critical density according to this power law was, = 2499 +/ 9 mm2, critical amplitude = 4370 +/ 460 mm2 and a critical exponent p1 = 1.01 +/ .02 The cluster size versus reduced density that scales like a power law can be seen in Figure 311. Applying a reduced density to fit a scaling law was used with average cell migration speed by the following equat ion (3 3) : = ( ) ( ) (3 3) The critical density calculated was similar to the one calculated with cell cluster size, = 2507 +/ 3 mm2. It was also found that = 14.17 +/ .07 m hr1, and p2 = .214 +/ .002. The power law relationshi p between average speed and reduced density can be seen in Figure 312.

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32 Figure 3 1 Cell density as the layer transitioned from a sparse to a highly dense monolayer was calculated by manually counting cells within a given area at several different points at for every 200 frames. A smooth fitting spline was applied to this data in order to estimate the cell density at every time point for a period of 72 hours.

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33 Figure 3 2 a c) show the layer at three different time points (t = 0, 1.5, 3 days ) and d f) show their corresponding velocity field vectors long vectors represent fast moving cells, and short vectors are slow moving. These speed maps were obtained by using particle image velocimetry (PIV). As time goes on, the field of view becomes densely packed with cells, and the velocity fields also become slower. (Scalebars = 200 m) Figure 3 3 Speed histograms were calculated for each time point, and Figure 11a is a false color intensity map for every time point. The peaks of the histograms b ecome narrower and shift to the left as time persists, showing that the migration speeds become more homogenous over time and those speeds are slowing down.

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34 Figure 3 4 Speed histograms for three different time points were normalized and plotted here, f urther showing how the peaks shift to the left over time, and become narrower over time. Figure 3 5 Speed of a particular time point was determined by using the peak of each speed histogram rather taking an average over the entire curve, this was done because the peak represents the speed of the majority of the cells and including other speeds would introduce bias. When plotting speed versus time, a linear relationship is seen scaling like a power law which is indicative of a phase transition.

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35 Figur e 3 6 Speed plotted against cell density shows a strong divergence, which leads to the hypothesis that perhaps there is an upper limit to cell density.

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36 Figure 3 7 The velocity field maps seen in Figure 32m gives rise to the hypothesis that there are two different types of clusters as the layer transitions into a tightly packed monolayer slow and fast moving clusters. a) slow moving clusters at t = 1 hour, b) slow moving clusters at t = 1.5 days, c) slow moving clusters at t = 3 days. A slow mov ing cluster was determined by taking the average speed of a cell at the final time point. This cell migration speed was used as a threshold and a 2D binary map was created. The patches in red show slow moving clusters and with time, these patches grow unt il they create one large slow moving cluster (Scalebars = 330 m)

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37 Figure 3 8 Growing clusters are defined as a group of cells that appear and never disappear, or in other words, they keep growing indefinitely. Transient clusters are defined as clusters that appear and then disappear having a short life time. The average size of these two types of clusters was calculated for each time point and when plotted, a critical cluster size is determined to be approximately 5000 m2.

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38 Figure 3 9 Size of the growing clusters when plotted versus cell migration speed scales like a power law with an exponent of .2. This result leads to the hypothesis that if this relationship scales like a power law, then maybe cluster size versus cell density and speed versus cell density also scales like a power law.

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39 Figure 3 10. From the results in Figure 17, it was hypothesized that cluster size and migration speed versus cell density will scale like a power law. The first step in deter mining this relationship is to plot these relationships unscaled. It shows that both parameters show strong divergences, and a critical density is at approximately the same point 2500 mm2.

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40 Figure 3 11. Reduced density is calculated using predeterm ined equations for scaling analysis and when plotting cluster size versus this reduced density, a power law relationship is observed. The critical amplitude of this relationship is very close to the critical nucleus size previously calculated.

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41 Figur e 3 12. Cell migration speed versus reduced density also shows a power law relationship. The critical amplitude calculated is 14.17 +/ .07 m hr1 which is very close to the speeds of cells at very low densities.

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42 CHAPTER 4 DISCUSSION In this study, collective cell migration was studied as it transitions from a state of sparsely seeded cells to a confluent monolayer. Parameters observed dur ing this transition include a critical cluster size, above which a group of cells will be able to grow indefinitely until they fill a surface, a critical density observed through power law relationships. The critical density observed here was close to the density at the glass transition ( glass = 2800 mm2) This transition occurs when a material slows down in average migration speed and while the viscosity increases in a solidlike state, but still flows over a long period of time ( 2 ) The critical cluster size amplitude, *, and critical speed, v*, are also noted as being very similar to the critical size seen in Figure 17 (which distinguishes a growing cluster from a transient cluster) and the migration speed of cells at low densities, respectively. The information gathered from this data suggests the existence of an upper limit on cell density and a lower limit on c ell or cluster size. Critical exponents from scaling laws are believed to be universal (the exponents will be the same regardless of the chemical or physical composition of a particular transition) and help describe phase transitions. When taking the square root of equation 3, the following equation (4 1) is obtained for correlation length. = ( ) ( / ) (4 1) A diverging correlation length is a phenomenon that is observed in mean field universality classes, and an exponent of 1/2 is similar to the exponent characteristic of the gas to liquid transition.

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43 CHAPTER 5 FUTURE PLANS AND FINAL REMARKS The next step in this collective cell migration research is to determine what dynamic states cells transition between as they populate a surface. Eventually, we will exert substrate stiffness control, which will act as a 2D pressure. It is hypothesized that over a large parameter space, cell density, migration speed, and the varying pressures will give way to a phase diagram for cell dynamics. In Figure 5 1, you will see the preliminary diagram that shows the different densities of cells with varying pressures as they enter three different phases: one uncondensed phase and two different condensed phases. More data points must be collected in order to c omplete the phase diagram. Understanding the transitions seen in this study between an uncondensed to a confluent monolayer has potential applications for biomedical and tissue engineering. ECM based scaffolds have been implanted for regenerative purposes ranging from cartilage to the creation of function new tissue for organs. Prior to implantation, cells of the desired phenotype grow into the scaffold and are expected to proliferate and interact with neighboring affected tissues once inside the body. T his study shows that migration and proliferation are dependent on a critical cluster size as well as the upper limit to cell density. These two parameters may influence the final state of the desired system and should be considered prior to implantation of any scaffold that is dependent on collective cell migration.

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44 Figure 5 1 For future experiments, it is planned to vary a 2dimensional pressure and measure cell density as it moves from an uncondensed to a condensed monolayer, and create a phase diagram for cell dynamics. This 2D pressure will be altered by changing the substrate (PDMS) by which the cells adhere to. Figure 21 shows current results. Three clear phases have been observed, one uncondensed phase and 2 distinct condensed phases. It is hypo thesized that the transitions between these phases are dependent on pressure.

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45 LIST OF REFERENCES 1. Lauffenburger DA & Horwitz AF (1996) Cell migration: A physically integrated molecular process. (Translated from English) Cell 84(3):359 369 (in English). 2. Angelini TE et al. (2011) Glass like dynamics of collective cell migration. (Translated from eng) Proc Natl Acad Sci U S A 108(12):47144719 (in eng). 3. Ilina O & Friedl P (2009) Mechanisms of collective cell migration at a g lance. (Translated from English) Journal of Cell Science 122(18):32033208 (in English). 4. Petrie RJ, Doyle AD, & Yamada KM (2009) Random versus directionally persistent cell migration. (Translated from eng) Nat Rev Mol Cell Biol 10(8):538549 (in eng). 5. Ridley AJ et al. (2003) Cell migration: integrating signals from front to back. (Translated from eng) Science 302(5651):17041709 (in eng). 6. EtienneManneville S (2004) Cdc42--the centre of polarity. (Translated from eng) J Cell Sci 117(Pt 8):12911300 (in eng). 7. Adams AE, Johnson DI, Longnecker RM, Sloat BF, & Pringle JR (1990) CDC42 and CDC43, two additional genes involved in budding and the establishment of cell polarity in the yeast Saccharomyces cerevisiae. (Translated from eng) J Cell Biol 111(1):131142 (in eng). 8. Fechheimer M & Zigmond SH (1993) Focusing on unpolymerized actin. (Translated from eng) J Cell Biol 123(1):15 (in eng). 9. Kaksonen M, Toret CP, & Drubin DG (2006) Harnessing actin dynamics for clathrin mediated endocytosis. (Translated from eng) Nat Rev Mol Cell Biol 7(6):404414 (in eng). 10. Ananthakrishnan R & Ehrlicher A (2007) The forces behind cell movement. (Translated from eng) Int J Biol Sci 3(5):303317 (in eng). 11. Hood JD & Cheresh DA (2002) Role of integrins i n cell invasion and migration. (Translated from eng) Nat Rev Cancer 2(2):91 100 (in eng). 12. Stupack DG & Cheresh DA (2002) Get a ligand, get a life: integrins, signaling and cell survival. (Translated from eng) J Cell Sci 115(Pt 19):37293738 (in eng). 13. Clark K, Langeslag M, Figdor CG, & van Leeuwen FN (2007) Myosin II and mechanotransduction: a balancing act. (Translated from eng) Trends Cell Biol 17(4):178186 (in eng).

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46 14. Jay PY, Pham PA, Wong SA, & Elson EL (1995) A mechanical function of myosin II in cell motility. (Translated from eng) J Cell Sci 108 ( Pt 1):387393 (in eng). 15. Wessels D et al. (1988) Cell motility and chemotaxis in Dictyostelium amebae lacking myosin heavy chain. (Translated from eng) Dev Biol 128(1):164177 (in eng). 16. Pellinen T et al. (2008) Integrin trafficking regulated by Rab21 is necessary for cytokinesis. (Translated from eng) Dev Cell 15(3):371385 (in eng). 17. Rorth P (2009) Collective cell migration. (Translated from eng) Annu Rev Cell Dev Biol 25:407 429 (i n eng). 18. Shaw TJ & Martin P (2009) Wound repair at a glance. (Translated from English) Journal of Cell Science 122(18):32093213 (in English). 19. Shin K, Fogg VC, & Margolis B (2006) Tight junctions and cell polarity. (Translated from eng) Annu Rev C ell Dev Biol 22:207235 (in eng). 20. Christiansen JJ & Rajasekaran AK (2006) Reassessing epithelial to mesenchymal transition as a prerequisite for carcinoma invasion and metastasis. (Translated from eng) Cancer Res 66(17):83198326 (in eng). 21. Coates TD, Watts RG, Hartman R, & Howard TH (1992) Relationship of F actin distribution to development of polar shape in human polymorphonuclear neutrophils. (Translated from eng) J Cell Biol 117(4):765774 (in eng). 22. Mattila PK & Lappalainen P (2008) Filopodia: molecular architecture and cellular functions. (Translated from eng) Nat Rev Mol Cell Biol 9(6):446454 (in eng). 23. Harris TJ & Tepass U (2010) Adherens junctions: from molecules to morphogenesis. (Translated from eng) Nat Rev Mol Cell Biol 11(7):502514 (in eng). 24. Culkins CC & Setzer SV (2007) Spotting desmosomes: the first 100 years. (Translated from eng) J Invest Dermatol 127(E1):E23 (in eng). 25. Kalluri R & Weinberg RA (2009) The basics of epithelial mesenchymal transition. (Translated fr om eng) J Clin Invest 119(6):14201428 (in eng).

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47 BIOGRAPHICAL SKETCH Melanie Suaris obtained her Bachelor of Science at the University of Miami in 2011, with a major in biomedical engineering while on a premedicine track. During her time in Miami, sh e worked as an undergraduate researcher at BioTissue, Inc. under the direction of Dr.Scheffer Tseng, where she completed her independent thesis entitled Amniotic Membrane Transplantation for Ocular Surface Reconstruction. Upon graduation, Melanie moved t o Gainesville, Florida where she became a graduate student in the Department of Biomedical Engineering. During her time at the University of Florida, Melanie conducted research at the Bio and Soft Matter Laboratory in the Department of Mechanical Engineeri ng under the direction of Principal Investigator, Dr. Thomas Angelini. Melanie graduated with her Masters Degree in May 2013 and was accepted to medical school where she will obtain her MD.