Molecular Dynamic Simulations of Raft Formation and Fullerene Transport in Lipid Membranes

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Molecular Dynamic Simulations of Raft Formation and Fullerene Transport in Lipid Membranes
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english
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Narra, Tarun
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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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Chemical Engineering
Committee Chair:
Kopelevich, Dmitry I
Committee Members:
Chauhan, Anuj

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coarsegrainedmoleculardynamics -- fullerene -- lipidrafts -- moleculardynamicssimulation -- transport
Chemical Engineering -- Dissertations, Academic -- UF
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Chemical Engineering thesis, M.S.
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Abstract:
Cell membranes are known to contain many types of lipids which can form domains resulting in lateral structural heterogeneity. The lipid domains which are tightly packed and more ordered than their surroundings are called rafts.Understanding the aggregation of lipids into rafts is crucial in biological applications.In this study we have used coarse grained molecular dynamic simulations to explore two mechanisms of raft formations, namely ion crossbridging and cholesterol induced raft formation. For exploring the former, we considered an anionic surfactant, a neutral surfactant and artificial lipids with varying number of charges. We observed that the tendency towards the aggregate formation is determined by the number of charged beads in lipid head groups. Specifically, artificial lipids with three negatively charged beads in the head groups aggregate due to calcium ion cross bridging. On the other hand, the surfactants and lipids which have only one charged head group bead did not show aggregation. The other mechanism was explored using ternary mixture of cholesterol, saturated and unsaturated lipids which is known to form liquid ordered(Lo) and liquid disordered(Ld)phases. We also investigated effects of the membrane composition and structure on transport across the membranes. To this end, free energy profiles of the transport of model hydrophobic fullerene nanoparticle across the Lo and Ld phases were reported. Our results show that fullerene encounters a large energy barrier while entering the Lo phase due to tight packing of lipids and cholesterol. No significant energy barrier was observed for transport into the Ld phase.
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by Tarun Narra.
Thesis:
Thesis (M.S.)--University of Florida, 2013.
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Adviser: Kopelevich, Dmitry I.
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RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2013-11-30

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1 M OLECULAR DYNAMIC SIMULATIONS OF RAFT FORMATION AND FULLERENE TRANSPORT IN LIPID MEMBRANE S By TARUN NARRA A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS F OR TH E DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2013

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2 2013 Tarun Narra

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3 To my mom, dad and sister

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4 ACKNOWLEDGMENTS I sincerely thank my research advisor Prof. Dmitry Kopelevich for his consta nt support and encouragement throughout my research work. His guidance enabled me to develop an understanding of molecular dynamics simulatio n. His valuable inputs brought i n great value to this work. I thank Prof. Anuj Chuahan for his suggestions. I than k Dr.Yong Nam Ahn of our research group for his help and suggestions during my research which help ed me to learn the simulation software.

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5 TABLE OF CONTENTS page ACKNO WLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 ABSTRACT ................................ ................................ ................................ ..................... 9 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 11 1.1 Background ................................ ................................ ................................ ....... 11 1.2 Thesis Outl ine ................................ ................................ ................................ ... 13 2 METHODS ................................ ................................ ................................ .............. 14 2.1 Molecular Dynamics Simulations ................................ ................................ ...... 14 2.1.1 Energy Minimization ................................ ................................ ................ 15 2.1.2 Temperature Coupling ................................ ................................ ............. 16 2.1.2.1 Berendsen temperature coupling ................................ ................... 16 2.1.2.2 Nose Hoover temperature coupling ................................ ............... 17 2.1.3 Pressure Coupling ................................ ................................ ................... 18 2.1.3.1 Berendsen pressure coupling ................................ ........................ 18 2.1.3.2 Parrinello Rahman pressure coupling ................................ ............ 19 2.1.4 Calculation of Instantaneous Temperature and Pressure ........................ 19 2.2 Coarse Grained Molecular Dynamics ................................ ............................... 20 2.3 Stochastic Model for Nanoparticle Transport ................................ .................... 25 3 RAFT FORMATION ................................ ................................ ................................ 27 3.1 Stability of Surfactant Aggregates in Lipid Membranes ................................ ..... 27 3.1.1 Background ................................ ................................ ............................. 27 3.1.2 Simulation Details ................................ ................................ .................... 27 3.1.3 Results ................................ ................................ ................................ .... 28 3.2 Phase Separation of Lipids Due to Cross B ridging by Calcium Ions ................. 30 3.2.1 Background ................................ ................................ ............................. 30 3.2.2 Model and Simulation Details ................................ ................................ .. 31 3.2.3 Results ................................ ................................ ................................ .... 32 3.3 Phase Segregations in Tertiary Lipid Mixtures : Effect of Cholesterol .............. 34 3.3.1 Background ................................ ................................ ............................. 34 3.3.2 Model and Simulation Details ................................ ................................ .. 34 3.3.3 Observations ................................ ................................ ........................... 36

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6 4 TRANSPORT OF FULLERENE NANOPARTICLE INTO LIPID MEMBRANE ........ 38 4.1 Background ................................ ................................ ................................ ....... 38 4.2 Model and Simulation Details ................................ ................................ ........... 38 4.3 Results ................................ ................................ ................................ .............. 39 LIST OF REFERENCES ................................ ................................ ............................... 42 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 45

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7 LIST OF TABLES Table page 3 1 Details of the systems considered in simulation of aggregate formation due to salt bridges. ................................ ................................ ................................ ........ 31

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8 LIST OF FIGURES Figure page 2 1 Coarse grained models including corresponding atomistic str uctures ............... 24 3 1 Initial condition s for MD simulations for exploring stability of pre assembled surfactact agg regate ................................ ................................ ........................... 29 3 2 Results of MD simulations showing dispersion of SDS aggregate throughout the diC 16 PC lipid bilayer ................................ ................................ .................... 29 3 3 Worm li ke micelles with aggregation of Q type lipids ................................ .......... 33 3 4 Bilayer system containing Q type and N type lipids ................................ ....... 33 3 5 Distribution of components of bilayer at 323K ................................ ................... 35 3 6 Distribution of components of bilayer at 2 95 K ................................ ................... 36 4 1 Free energy profiles for the transp ort of the model fullerene nanoparticle across the L o and L d lipid phases ................................ ................................ ....... 40

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9 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 MOLECULAR DYNAMIC SIMULATIONS OF RAFT FORMATION AND FULLERENE TRANSPORT IN LIPID MEMBRANE S By Tarun Narra May 2013 Chair: Dmitry I,Kopelevich Major: Chemical Engineering C ell membranes are known to contain many types of lipids which can form domains resulting in lateral structural heterogeneity. The lipid domains which are tightly packed and more ordered than thei r surroundings are called rafts Understanding the aggregation of lipids into rafts is crucial in biological a pplications. In this study we have used coarse grained molecular dynamic simulations to explore two mechanisms of raft formation s namely ion crossbridging and cholesterol in duced raft formation For exploring the former we considered an anionic surfactan t, a neutral surfactant and artificial lipids with varying number of charge s We observed that the tendency towards the aggregate formation is determined by the numbe r of charged beads in lipid head groups. Specifically, artificial lipids w ith three negati ve ly charge d beads in the head groups aggregate due to calcium ion cross bridging. On the other hand, t he surfactants and lipids which have only one charged head group bead did no t show aggregation. The other mechanism was explored using ternary mixture of cholesterol, saturated and unsaturated lipids which is known to form liquid ordered ( L o ) and liquid disordered ( L d ) phases We also investigated effects of the membrane composition and structure on

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10 transport across the membranes. To this end, free energy pr ofiles of the transport of model hydrophobic fullerene nanoparticle across the L o and L d phases were reported Our results show that fullerene encounters a large energy barrier while entering the L o phase due to tight packing of lipids and cholesterol No significant energy barrier was observed for transport into the L d phase.

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11 CHAPTER 1 INTRODUCTION 1.1 Background B iological cell membranes are lipid bilayers embedded with proteins. The y serve several functions, including protect ing the cell interior from its environment and controlling transport of molecules in and out of the cell. These membranes are known to contain many types of lipids which can form domains resulting in lateral structural heterogeneity The lipid domains which are tightly packed and m ore ordered than their surroundings are called rafts. The mechanism of the raft formation is still not completely understood. Earlier studies have proposed several mechanisms including electrostatic coupling ( 1 ), inte rfacial energy minimizations (2 ), lipid and cholesterol interactions (3 ) and composition curvature coupling ( 4 ) for explaining the heterogeneity. T he main focus of this thesis is to apply molecular dynamic (MD) simulations to investigate two of the mechanisms of the raft f ormation s in a lipid b ilayer namely by ion cross linking and by cholesterol The first part of the thesis studies the interaction of surfactants in membrane. Surfactants are amphiphilic molecules containing hydrophilic head groups and hydrophobic tail groups. Interactions betwe en the surfactants and the lipid bilayers have been extensively studied due to their importance in drug delivery and food industry. Previous studies have shown that contact of surfactants with a lipid membrane may result in increase of the membrane permeab ility (5)(6) This increase in permeability is often transient ( 7) i.e. the permeability of lipid bilayer eventually decreases healing the bilayer A possible mechanism for the healing may be due to aggregation of surfactants

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12 in the membrane (8 ) Therefor e we have explored the likeliness of aggregation surfactant s in a membrane using MD simulations In the first set of simulation studies, w e have explored the r aft formations in lipid membranes due to the crossbridging by ion s This study was conducted to understand the influence of ions in stabilizing the rafts The presence of cholesterol at biologically relevant concentrations (10 30%) in a lipid membrane consisting of saturated and unsaturated lipids results in the raft formation. I n the next set of sim ulations w e have explored the lipid segregation which occurred due to the presence of cholesterol in a ternary lipid membrane In addition we have explored the transport of nanoparticle across the different phases formed in ternary mixture of saturated, u nsaturated lipids and cholesterol. The nanoparticles are u ltrafine particles that have size in the or der of one billionth of a meter These particles exhibit different size dependent physical and chemical properties from those of their bulk counterparts. R esearch on n ano particles has revolutionized various areas of science and technology They hav e various applications in such fields as medic ine electronics, food packaging, paints, materials, cosmetics and fabrics. Currently more than a thousand commercial products containing nanoparticles are available on the market and more products are being added almost every week Project on Emerging Nanotechnologies ( 9 ) D ue to this rapid increase in number of products containing na noparticles, it is evident that humans and the environment are coming into contact with the manufactured nanoparticles (MNs) either by accident or by intention. It is therefore important to

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13 a nalyze the possibility of any unintended consequences of the se pa r ticles on humans and thei r environment. 1.2 Thesis Outline The thesis is organized as follows: In C hapter 2, the methods of molecular dynamic (MD) simulations are presented. The coarse gained molecular models which are used for extending the time and le ngth scales accessible to the simulation are discussed. Constrained simulations employed in analysis of the fullerene transport are also described. In C hapter 3, analysis of stability of pre assembled surfactant aggregate s i s presented. Then the simulat ions which aimed at understanding the aggregations of the lipids due to crossbridging by calcium ions are presented. Next we report our simulations of domain formation in a mixture containing cholesterol and saturated and unsaturated lipid s. In C hapt er 4, the model and simulation details of transport of the fu llerene nanoparticle across lipid membrane domains is presented and analyzed.

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14 CHAPTER 2 METHODS 2.1 M olecular Dynamics Simulations Molecular dynamic (MD) simulations have become one of the prin cipal tools for pro viding detailed information on n anoscale systems. This information in general cannot be easily obtained through macroscopic experiments due to the small time and length scale s of the processes. They also act as a com plementary tool for v erifying experimental results or to test theoretical predictions. MD simulation s dynamic behavior of microscopic sy stems The forces ( F i ) acting on the particle i of mass m i will move it to new positions by sol ving F i = (2.1) Where F i is the negative partial derivative of the potential function V(r 1, r r N ), with respect to the particle position( r i ). F i = (2.2 ) In our MD simul ations we have used Verlet leap frog algorithm ( 1 0 ) for obtaining the evolution of coordinates a nd velocities of the particles. The leap frog algorithm use s the p article positions r i at time t and velocities v i at time t to compute the positions and velocities at next timestep (2.3 ) (2.4 )

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15 For MD simulations, we need the initial positions and velocities of all the parti cles present in the system. T he velocities of particles are generate d from the Maxwell velocity distribution. (2.5) Here f v is probability density of velocity, k is Boltzmann constant, T is temperature and v x ,v y, v z are the vel ocity components The particles that are to be simulated are usually contained in a re ctangular box. E dge effects in a finite system are reduced by periodic boundary conditions (PBC). The PBC ensure that a molecule leaving from one side of the box re enters the box on the opposite side. Any simulation study typically consists of three steps. The first step is energy minimization Two MD simulation runs are then carried out. The first MD simulation run known as equilibration run, uses strong temperature and/or pressure coupling for relaxing the system and to stabilize desired ensemble (NVT, NPT, etc.) properties. A production MD s imulation is then carried out using weak temperature and/or pressure coupling. The data collected from the production MD simulation is used in the analysis. 2.1.1 Energy M inimization If the initial positions of the particles contain overlapping atoms, MD simulations will fail due to very large forces. These forces need to be minimized before we perform MD simulations. In the current work w e have used the steepest descent method for minimizing energy of our initial systems. The steepest descent is a quick a nd simple method to reduce the energy of the system. However its convergence near the local minimum can be very slow.

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16 The steepest descent algorithm takes a step in the direction of the force. The se steps move the system downhill alo ng the potential energy landscape (2.6) Here vector r represents a vector of all 3 N coordinates. F n is the force and h n is maximum displacement If the (n+1)th step decreases the potential energy ( i.e., V n+ 1 < V n ) the new positions are accepted and the displacement magnitude is increased h n+1 = 1.2h n Otherwise the new positions are rejected and the displacement magnitude is decreased h n = 0.2h n 2.1.2 Temperature Coupling All our simulations are performe d in the NPT ensemble. To simulate constant temperatures in the simulations we have employed Berendsen temperature coupling scheme ( 1 1 ) in the equilibration MD run and Nose Hoover temperature coupling scheme ( 1 2, 1 3) in the production MD run. 2.1.2.1 Berend sen t emperature coupling The Berendsen algorithm is a strong coupling to a heat bath at a constant temperature T 0. The temperature deviations from the value of T 0 are corrected using (2.7) The relaxation time is (2.8) Here C v represents heat capacity of the system, N F is number of degrees of freedom and is temper ature coupling time constant that we specify.

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17 For maintaining the constant temperature, heat flow in or out of the system is control l ed by scaling the velocities of each particle with a time dependent factor after sufficient number of time steps n TC is given as (2.9) This algorithm however fails to generate good canonical ensemble as it suppresses the fluctuations of kinetic energy. It generates errors which scale with 1/number of particles in the systems. However, t his algorithm is extremely efficien t for relaxing the system to a target temperature. Hence this algorithm is used for the equilibration st age of our simulations. 2.1.2.2 Nose Hoover temperature coupling This coupling scheme was first proposed by Nose and later modified by Hoover. The Hamiltonian of the system is extended by using a n additional degree of freedom for representing the thermal bath. The algorithm uses the following equations of motion for the particles: (2.10) T he equation of motion for the heat bath degree of freedom is (2.11) Here i s the momentum corresponding to Q is known as the ma s s parameter of the thermal bath given by:

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18 (2.12) Here is chosen to be 4 5 times l arger than relaxation time 2.1.3 Pressure Coupling In our simulations we have con trolled the pressure using Berendsen pressure coupling ( 1 1) for equilibration MD simulations and by Parinello Rahman pressure coupling ( 14,1 5) in the pr oduction MD simulations In our membrane simulations, we have used semi isotropic pressure coupling to maintain zero surface tension of the membrane. 2.1.3.1 Berendsen pressure coupling Similar ly to Berendsen temperature coupling, deviations of pressure fr om the set values are corrected acco rding to the following equation: (2.1 3 ) This is accomplished by rescaling the particle coordinates and box vectors every n PC steps with a scaling a matrix given by: (2.1 4 ) Here P oij and P ij are elements of reference pressure matrix P 0 and i nstantaneous pressure matrix P respectively This algorithm is used in our equilibration simulations. This strong coupling s cheme does not simulate true constant pressure ensembles but is efficient at bring ing our system to the given pressure.

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19 2.1.3.2 Parrinello Rahman pressure coupling We have used Parrinello Rahman pressure coupling in the production MD simulations. This method is similar to Nose Hoover temperature coupling and in theory yields true constant pressure ensemble. In this algorithm, evolution of the box size obeys the following (2.15 ) Here b is a matrix containing the box vectors (i.e. vectors defining the size and shape of the simulation box) V is the volume of the box, W is a matrix determi ning the coupling strengt h and is given by ( 2.16 ) Here L is the largest box matrix element The equations of motion for the particles are (2.17 ) w here M is the friction coefficient given by (2.18 ) 2.1.4 Calculation of Instantaneous Temperature and Pressure Both the temperature and pressure schemes require calculation of instantaneous temperature and pressure. Temperature of an N particle system is given by (2.19 )

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20 The instantaneous pressure tensor P is calculated from the difference in the kinetic energy E KE and the virial P (2.20 ) (2.21 ) Here r ij is vector connecting the j th particle with the nearest image of the i th particle F ij is the force exerted by the j th particle on the i th part icle and represents direct product of two vectors. 2.2 Coarse Grained Molecular Dynamics Presently, molecular dynamics simulations on the atomic scale are limited to simulation times of less than 1 s due to the limitations of comp uter power. One of the possible ways to extend time scales accessible to the molecular dynamics simulations is to use less precise models such as coarse grained molecular dynamic (CGMD) simulations. up of atoms. This grouping of atoms helps one reduce the number of degrees of freedom and thus extend the time and length scales accessible to the simulations. For our studies we use the MARTINI CG MD model proposed by Marrink et a l (1 6) The MARTINI CG MD mo del generally uses 4:1 mapping scheme i.e o n average four heavy atoms are represented as one standard spherical bead. For representation of the underlying atomistic structure, the following four bead types are introduced: C(apolar), P(polar), N(non polar) and Q(charged). Apart from the 4:1 mapping scheme for standard beads, CGMD also uses 2 3:1 mapping scheme to represent ring compounds. Each bead type has several

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21 subtype s. For example, subtypes of 0, d, a and da indicate hydrogen bonding capabilities: 0(n o hydrogen bonding capabilities), d (some hydrogen donor capabilities), a (hydrogen acceptor capabilities) and da (both donor and acceptor capabilities) and subtypes of 1,2,3,4,5 indicate the polarity of the bead : 5 is more than 1. The masses of most beads are set to 72 atomic mass units The interactions between the CG beads i and j not connected by a chemical bond are described using the Lennard Jones(LJ) potential, (2.22) Her e is the LJ diameter is the depth of the potential well and i, j represent types of beads. The value of is 0.47 nm for most of the standard particles. The value for standard beads is varied from 5.6 KJ/mol for strongly attractive to 2.0 KJ/mol for nearly repulsive interactions. For the interaction between beads representing a ring structure, the value of is changed to 0.43 nm and the values of are reduced to 75% of the standard bead values. T he electrostatic interaction energy of N particles and their periodic images is (2.23) Here and is the permittivity of the medium and are the charges on i th and j th bead respectively, is the index vector of the s imulation box, is the real distance between the charges, the asterisk indicate that the terms with i=j are omitted when

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22 Ewald summation is an elegant method to calculate long range interactions as it converts the single slowly converging sum in Eq.2.23 i nto two quickly converging terms and a constant term. In this technique, the summation is divided into short range and long range parts which are evaluated in real and reciprocal (Fourier) spaces, respectively. (2.24) (2.25) (2.26) (2.27) The parameter determines the relative weight of th e direct and reciprocal sums. m = (m x m y m z ). The term V 0 removes the interaction of the particle with itself contained in reciprocal sum. Small vibrations of the bond length and angles are approximated by harmonic potentials. (2.28 ) (2.29 ) Here and are the equilibrium bond lengths and bond angl es and, are the force constants. All our simulations were performed using software GROMACS ( 2 1).

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23 The CG models and the corresponding atomic structures of the considered species are shown in F ig ure 2.1 Every fou r water molecules in the system were modeled as one single P type bead. The membrane bilayers are modeled using saturated dipalmitoyl phosphatidylcholine (diC 16 PC) lipids, unsaturated dilinoleyl phosphatidylcholine (diC 18:2 PC) lipids and cholesterol. The diC 16 PC, diC 18:2 PC and cholesterol CG models were developed by Marrink et al (17)(18) The diC 16 PC and diC 18:2 PC lipid molecule consist a hydrophilic head group, an ester backbone, and two hydrophobic tails. The zwitterionic head group of these li pids consists of choline (modeled as Q0 bead with positive charge) and a phosphate group (modeled as Qa bead with negative charge). The ester backbone of lipids is modeled as two Na beads. The two hydrophobic tails are modeled as two chains, each containin g four C beads. The only difference between the models of diC 16 PC and diC 18:2 PC is the double bonds in the tails of diC 18:2 PC. The polar head group of cholesterol was modeled as a P bead. The sterol body was modeled by using a ring of five C beads. The hydrophobic tail was modeled as a chain of two C beads. In addition, we introduced several artificial lipids in order to investigate effects of the lipid structure on the raf t formation. B y replacing zwitterionic head group of diC 16 PC with a negatively c harged head group we have prepared an artificial lipid which we call as E type lipid Specifically, w e replaced the positive charge of the Q0 bead by a negative charge of the same magnitude and removed the charge from the Qa bead.

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24 A B C D E F G H Figure 2 1. Coarse grained models including corresp onding atomistic structures of A ) Water B) diC 16 PC C ) diC 18:2 PC D ) cholesterol E ) SDS F) Tridecanoic acid G ) Q type lipid H) Fullerene nanoparticle

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25 Q type lipid s were defined as lipids consisting of hydrophilic head group, an ester backbone and two hydrophobic chains. The head group is composed of a chain of beads containing a polar P4 bead and three charged Qa beads. The ester bone is modeled as two Na beads. The hydrophobic tails are modeled as two chains, with four C beads in one chain and five C beads in other In addition, we introduced N type lipid which is similar to the Q type lipid and was obtained by replacing the charged Qa beads of the Q type lipid with Na beads. In order to investigate effects of electrostatics on the surfactant membrane interactions, Sodium Dodecyl S ulfate ( SDS) a nd Tridecanoic acid were considered The SDS was modeled using a neg atively charged Qa bead for representing sulfate group and three C beads to rep resent the tail. The Tridecanoic Acid surfactant is similar to SDS; here the charged Qa bead is replaced by a P bead. The motivation for considering these two surfactants was to investigate electrostatic effects of interactions with membrane. The CG model for fullerene C 60 et al (19) The C 60 is modeled by placing 20 evenly spaced C beads on a sphere of diameter ~1.1nm. A 3:1 mapping is employed here. To preserve the shape of fullerene, the bond lengths and angles between C beads were constrained 2.3 Stochastic Model for Nanoparticle Transport The time scale s of transport of molecules and nanoparticle s across lipid membrane are to o large for direct MD simulations. The transport rates are therefore calculated by using an indirect method known as potential of mean force (PMF) method. The C 60 transport across lipid bilayer was assumed to be des cribed by the Langevin equation(20)

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26 (2.30 ) Here is the friction coefficient m is mass of particle, G is the free energy, z is the direction of transport and (z, t) is random force. In our system, the lipid bilayer is parallel to the xy plane. The distance between the centers of mass of nanoparticle and lipid membranes are constrained at different distances along the z axis by applying constrained force (F). The nanoparticle was free to move in the x and y direction s The average of the constrained force is directly related to PMF. (2. 31 )

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27 CHAPTER 3 RAFT FORMATION 3.1 Stability of Surfactant Aggregates i n Lipid Membranes 3.1.1 Background The surfactants on contact with lipid membrane get adsorbed in the exposed lipid membrane leaflet. This adsorption of surfactant increases the pressure in the leaflet leading to increased permeability ( 22 ). This increase in permeability is often transient (7) i.e. the permeability of lipid bilayer ev entually decreases The decrease in permeability is called as healing. A hypothesis for explaining the healing of the bilayer s tates that healing may be due to jumping of surfactant molecules between the outer and inner layers of the bilayer and/or aggrega tion of surfactant molecules ( 8 ) In this section we present our MD simulations for investigate the possibility of surfactant aggregation in the diC 16 PC membrane. To this end, we consider stability of preassembled surf actant aggregates in a bilaye r. 3.1. 2 S imulation D etails An initial system containing preassembled surfactant aggregate was created. The aggregate was then surrounded by a lipid bilayer. In our system, we have used SDS Tridecanoic Acid and diC 16 PC coarse graine d models as described in S ect ion 2. 2. Initially, we arranged 628 SDS molecules in a circular bilayer structure to represent an aggregate as shown in Fig ure 3.1 The aggregate contains equal number of surfactant molecules in each layer. The distance between the Qa beads of SDS molecu les across the bilayer was varied in order to investigate the dependency of aggregate stability on its thickness Two distances 4.36nm and 2.6nm were considered for this purpose. Th e distance of

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28 4.36nm was considered for making SDS aggregate thickness near ly equal to that of the diC 16 PC bilayer and distance of 2.6nm was considered as it is nearly equal to the diameter of a SDS micelle. The horizontal spacing bet ween SDS molecules was 0.5 nm This distance is greater than the was chosen to avoid an overlap between the molecules. The surfactant aggregate was then surrounded by diC 16 PC bilayer, water and sodium ions. A ll lipid molecules overlapping with the surfactant molecules were removed. We added 628 Na+ ions to neutralize t he system. The resultant system consists of 628 molecules of SDS, 1957 molecules of diC 16 PC 628 Na+ ions and 36294 beads of water in a box with dimensions 27 nm x 27 nm x 1 1 nm An energy minimization is performed using the steepest descent algorithm. The s ystem is then equilibrated for 200ns at 323 K temperature and 1 bar pressure allowing some of the lipids in the bilayer to relax while positions of SDS molecules are restrained The resultant system i s shown in F ig ure 3.1. The position restraint on the SD S molecules was then removed and a production MD simulation was performed using both long range and sho rt range electrostatic s. In order to understand the contribution of el ectrostatic interactions for stabilizing our surfactant aggregate we repeate d the simulations for a system i n which the anionic SDS surfactant s were replaced by neutral Tridecanoic Acid surfactant s. 3.1.3 Results The surfactant aggregates are observed to be unstable. They disperse throughout the lipid bilayer in few nanoseconds of rem oval of the position restraint. For the short range electrostatic model, the SDS aggregate with the initial thickness of 4.36 nm dispersed throughout the membrane within 90 ns as shown in F igure 3. 2 In the

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29 case of long range electrostatics, some of the SD S molecules were observed to desorb from the bilayer. This behavior is most probably due to increased attraction of SDS by Na+ ions which pulled them out of the bilayer. The remaining SDS molecules dispersed throughout the bilayer within 80 ns. A B F igure 3 1. Initial conditions for MD simulations for exploring stability of pre assembled surfactact aggregate A ) Pre assembled SDS aggregate B ) diC 16 PC lipid bilayer containing a pre assembled SDS aggregate Figure 3 2 Results of MD simulations showi ng dispersion of SDS aggregate throughout the diC 16 PC lipid bilayer In the simulations with the SDS aggregate of initial thickness of 2.6nm, we observed that the SDS aggregate dispersed in membrane in 85 ns. The Tridecanoic

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30 Acid aggregate with thickness of 4.36nm dispersed throughout the membrane within 70 ns. The difference between these times is too small to perform meaningful co mparison between the systems The dispersion of surfactant molecules in all our simulations suggests that the considered surf actants do not form aggregates in diC 16 PC bilayer. 3.2 P hase Separation of Lipids Due t o Cross B ridging by Calcium Ions 3.2.1 Background L ipids in the membranes are known to aggregate into domains of different composition resulting in heterogeneity of the bilayer. Many m echanisms as stated in Chapter 1 are proposed for explaining the aggregation of lipids. I n contrast to our observations reported in the S ection 3.1 Pantano et al (2 3 ) observed raft formation of surfactant molecules. Their modeled system consists of surfactants which mimic charged and neutral surfactants called C and N type surfactants, respectively. The C and N type surfactant is modeled using 5 hydrophilic and 7 hydrophobic beads to represent the hydrophilic and hydrophobic parts of surf actants. In C type surfactants, three head group beads were modified to mimic cha rged beads. Cross linker ion like particles which mimic calcium were added to the system. The size of crosslinker ion and its interaction strength with the charged group mimic king beads of the C type surfactants was varied to drive the segregation. It is important to note that the beads mimicking the charges did not in clude real charges. The simulations resulted in formation of d omains composed of C type surfactants and Calcium ions. In our study, we are investigating raft formation using artificial lipid molecules which are similar to the surfactant molecules used by Pantano et al. However our study greatly differs from Pantano as in our simulations, we have used explicit charg es for

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31 driving the segregation of lipids due to crosslinking by calcium ions which acts as crossb ridges This results in a more realistic representation of electrostatic forces in our system. 3.2.2 Model and Simulation D etails We considered t hree models systems: a mixture of diC 16 PC and Q type lipids, a mixture of Q type lipids and N type lipids and a mixture of diC 16 PC and E type lipid. The models of diC 16 PC, Q type N type and E type lipids were described in Section 2.2 The system compositions and s imulation details are summarized in Table 3 1. Table 3 1. De tails of the systems considered in simulation of aggregate formation due to salt bridges System Composition Duration of simulation Box size Simulation parameters Initial conditions System 1 160 0 diC 16 PC lipids, 1600 E type lipids, 49200 water beads and 800 Ca2+ ions. 400ns 31nm x 31nm x 10nm Long range electrostatics. Temperature =323 K. Pressure =1 bar Bilayer of diC 16 PC lipids and 1600 E type lipids surrounded by water and calcium ions. Sy stem 2 196 diC 16 PC lipids, 196 Q type lipids, 6174 water beads and 294 Ca 2+ ions and 6174 beads of water 200ns 11nm x 12nm x 9nm Long range electrostatics. Temperature =323 K. Pressure =1 bar Randomly dispersed lipids and ions in water System 3 838 mo lecules of N type lipid, 246 molecules of Q type lipid, 369 Ca2+ ions and 13924 representing water 200ns 14nm x 14nm x 14nm Long range electrostatics. Temperature =323 K. Pressure = 1 bar L ipids are arranged in form of bilayer by placing lipids apart by 0.5 nm

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32 A system containing diC 16 PC and E type lipids was considered to analyze if the Ca 2+ ions can cross link lipids and drive the aggregation of lipids having only one charged bead in a head group For creating the initial bilayer system, half of the lipid s in a self assembled diC 16 PC bilayer system were replaced by E type lipids. Our second system initially contains a random mixture Q type lipids and diC 16 PC A Q type lipid contains 3 charged beads in head group for driving the aggregation by electrosta tic coupling with Ca2+ ions. In our third system, we create d a bilayer containing Q type and N type lipids. These lipids contain equal number of beads for representing the head and tail groups. This system was considered to explore the influence of headgr oup length of neutral lipids on the aggregation. 3.2.3 Results No segregation of lipids has occurred in the S ystem 1. The random initial mixtures of Systems 2 and 3 self assembled into worm like micelles and bilayer like structures shown in Fig ure 3.3 and 3.4 respectively. We note that an equilibrium self assembled structure in System 3 is likely to be a bilayer. The defects of the bilayer like structures formed in our simulation are likely due to a large size of the simulation box. It is likely that a pe rfect bilayer can be obtained by performing self assembly simulations in a system of a smaller size or by simulating the system for a very long period of time. The high number of Ca2+ ions near the head groups of Q type lipids suggests that lipid segregati on takes place due to the crosslinking of Q type lipids by Ca2+ ions. This segregation of Q type lipid molecules is in agreement with the study of Pantono el at. However the segregation of the lipids was not observed when the lipids have only

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33 single charge d head groups indicating that the aggregation occurs only for lipids with several charged groups in their head groups. Fig ure 3 3 .Worm like micelles with aggregation of Q type lipids Fig ure 3 4 B ilayer sys tem containing Q type and N type lipids. Note: The Q type lipid aggregation can be observed.

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34 3.3 Phase Segregations i n Tertiary Lipid Mixtures : Effect of Cholesterol 3.3.1 Background In the S ection 3.2, we have considered the aggregation of artificial lipids due to crosslinking by ions. Here, we turn to a widely known natural lipid segregation mechanism which occurs due to the presence of cholesterol. The biological membranes separate in to various domains including the liquid ordered (L o ) and liquid disordered ( L d ) phases. This segregation takes place in the presence of cholesterol at biologically relevant concentrations ( 10 30%). The L o phase is enriched with cholesterol and saturated lipids and the L d phase is mostly composed of unsaturated lipids. L ipid bilayers generally exist as either disordered liquid crystalline or ordered gel phases The liquid ordered phase L o is perceived as an intermediate phase between the liquid crystalline and gel phases. Many theories are p roposed to explain formation of the L o phases. One of the hypotheses is that cholesterol i nteract ing with saturated lipids increase s the degree of orientation order of membrane leading to a tight er packing. This hypothesis was confirmed by simulations of Risselada el at( 2 4 ) The goal of the current study is to understand the segregation and prepare samples of different membrane phases to be used in analysis of transport of fullerene across these phases. 3.3.2 Model and Simulation D etails In this system the saturated and unsaturated lipids in a biomembrane were modeled using diC 16 PC and diC 18:2 PC respectively. According to the simulatio ns carried by Risselada el at(24 ), an initial system of diC 16 PC/diC 18:2 PC/cholesterol molecules in the ratio of 0.48:0.28:0.3 have separated in to two equilibrium phases.

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35 These phases were called Lo and Ld phase with compositions of diC 16 PC/diC 18:2 PC/cholesterol in the ratio 0.61:0.01:0.37 and 0.08:0.75:0.17, respectively. A bilayer structure was obtained by Risselada el at (24 ) and posted in w ebsite (25) The system consists of 828 diC 16 PC molecules 540 diC 18:2 PC molecules 576 cholesterol molecules and 12600 water beads To this system, 45345 additional water beads were added and the resulting box size was 22 nm x 22 nm x 18 nm MD simulation is performed for 200ns at a temperature of 323 K to melt the ordered phase. This is follow ed by a n MD simulation for 1000ns at 295K. A B C Figure 3 5 Distribution of components of bilayer at 323K A) The cholesterol distribution in the bilayer at 323K B) The corresponding distribution of lipids in the bilayer. C) The Color co ding of cholesterol and lipids

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36 3.3.3 Observations At 323K, the ordered phase melted dissolving the ph ase boundary as shown in Figure.3.5 The system shown in Figure 3.5 did not reach the steady state. The lipids are expected to mix completely and result in a homogeneous phase upon simulating the system for a longer period of time at 323K R educ ing the tem perature of the system to 295 K leads to phase separation as shown in F ig ure 3. 6 The figures show that the degree of separation in the ternary mixtures of diC 16 PC, diC 18:2 PC and cholesterol is temperature dependent. A B C Figure 3 6 Distribution of components of bilayer at 295 K A) The cholesterol distribution in the bilayer B) The corresponding distribution of lipids in the bilayer. C) T he Cross sectional view of the bilayer. Note that the cholesterol has shown preference towards the diC 16 PC molecules.

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37 In the C hapter 4 we investigate nanoparticle transport across the L o and L d phases are modeled as a ternary mixture of diC 16 PC, diC 18:2 PC and cholesterol On the basis the composition obtained by Risselada el at(2 4 ) for L o and L d phases, we have prepared two bilayer systems. T he bilayer system with 264 diC 16 PC molecules, 5 diC 18:2 PC molecules, 160 cholesterol molecules and 10586 beads o f water is prepared to represent L o phase. Our L d phase is represented by a bilayer containing 264 diC 18:2 PC molecules, 60 cholesterol molecules, 28 diC 16 PC molecules and 10586 beads of water

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38 C HAPTER 4 TRANSPORT OF FULLERENE NANOPARTICLE INTO LIPID MEMBRANE 4.1 Background Understanding permeation of nanoparticle s into the cell membrane has great importance in nanotoxicology research. In our work we have focused on a transport of a hydrophobic fullerene nanoparticle across th e membrane The f ullerene nanoparticles are composed of carbon atoms hold promise in the areas of drug delivery, antimicrobial therapy (2 6 ), diagnostic imaging and cancer research ( 2 7 ). However, both the pristine and functionalized fullerenes have been sho wn to exhibit toxicity ( 2 8 ). One of the possible toxicity mechanisms is generation of reactive oxygen species (ROS) c ausing lipid peroxidation and cell death ( 2 9 ). Besides this mechanism nanoparticles can also damage the integrity of membranes by physical mechanisms. Most of earlier molecular dynamics studies of the transport of fullerene nanoparticles into the lipid membranes have been performed for sing le component lipid membranes ( 19 30 3 1 ). These studies have shown that fullerenes can enter the lipid me mbrane with ease and stay in the membran e for a very long time It is thus possible that this long residence of nanoparticles in membranes leads to membrane destabilization. The goal of C hapter 4 is to explore effect of the membrane composition on nanopart icle transport across membranes Specifically, we analyzed the transport of fullerene across the liquid ordered and liquid disordered phases of membranes composed of saturated and unsaturated lipids and cholesterol. 4.2 Model and Simulation Details The mo dels of the liquid ordered (Lo) and liquid disordered (Ld) phases of a lipid bilayer were created using diC 16 PC, diC 18:2 PC and cholesterol as described in S ection 2.2.

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39 The two bilayer systems were equilibrated for 200ns at a temperature of 295 K and pr essure of 1 bar. A model C 60 was then introduced into the systems An energy minimization simulation is preformed followed by a MD equilibration simulation of the system for 100ns. The free energy profiles for the transport of the model fullerene nanopart icle across the L o and L d lipid phases are obtained using the constrained simulations described in S ection 2.3. In this method we constrain the distance between the center of masses of C 60 and lipid bilayer at different positions along the z direction (rec all that the bilayer is parallel is parallel to the x y plane). The initial conditions for the constrained simulations were obtained by application of an artificial force to pull C 60 through a bilayer at a rate of 0.0001 nm/ps. The pulling simulations yiel ded systems with distances between the centers of mass of C 60 and membrane varying from 0.2 nm to 6 nm. Constraining the distance between the centers of mass, we performed production MD simulations for 400ns using the time step of 0.01 ps to obtain the fre e energy profile. 4.3 R esu lts The obtained free energy profiles for the transport of C60 into the membrane phases are shown in the F igure 4 1 The free energy profiles for the fullerene nanoparticle transport across the L o and L d phases show a great quali tative difference. The profiles indicate that in both phases the fullerene present in water is attracted towards the bilayer center This is due to hydrophobic attraction between the hydrophobic fullerene and hydrophobic tails of the lipids

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40 Figure 4 1 Free energy profile s for the transport of the model fullerene nanoparticle across the L o and L d lipid phases In L d phase, the fullerene i s shown to easily enter the bilayer with negligible resistance. The hydrophilic head groups of the lipids do not provi de any observable resistance to the transport. This is due to the similarity between interactions of fullerene with hydrophilic head groups and water. Upon entering the membrane, fullerene continues to experience hydrophobic attractions which move it to th e center of the membrane. The energy profile for the Ld phase is similar to the previous simulations studies (19, 30 3 1 ) and indicates that the fullerene can easily enter the membrane

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41 On the other hand, in the L o phase t he fullerene experiences a high ener gy barrier of height ~20 KJ/mol at the entrance This energy barrier is likely due to the tight packing of the lipids and cholesterol in the Lo phase. Upon the entry of nanoparticle into the b ilayer, the free energy increas es gradually which is likely due to the increase in density of cholesterol ring s The free energy profile then decreases as the fullerene moves towards the center of the bilayer due to the hydrophobic attraction by tail groups and also due to a decreased thickness of the cholesterol ring s T he computed free energy profiles indicate that the C60 nanoparticles are more likely to be present in the L d phase of the membrane as the L o phase provides a larger resistance to their entry.

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4 2 LIST OF REFERENCES 1. May, S. 2009. Trans mono layer coupling of fluid domains in li pid bilayers. Soft Matter 5, 3148 3156 2. Collins, M. D. 2008. Interleaflet coupling mechanisms in bilayers of lipids and cholesterol Biophys. J. 94, L32 L34. 3. McMullen, T., R. Lewis and R. McElhaney 2004. Cholest erol phospholipid interactions, the liquid ordered phase and lipid rafts in model and biological membranes. Curr. Opin. Colloid Interface Sci. 8, 459 468. 4. Leibler, S. and D. Andelman 1987. Ordered and curved meso structures in membranes and amphiphilic films. Journal De Physique. 48, 2013 2018. 5. Xia, W. and H. Onyuksel 2000. Mechanistic studies on surfactant induced membrane permeability enhancement Pharm. Res. 17, 612 618. 6. Groot, R. and K. Rabone 2001. Mesoscopic simulation of cell membrane damage morphology change and rupture by nonionic surfactants. Biophys. J. 81, 725 736. 7. Lesieur, S., C. Grabielle Madelmont, C. Menager, V. Cabuil, D. Dadhi, P. Pierrot and K. Edwards 2003. Evidence of surfactant induced formation of transient pores in lipid bilayers by using magnetic fluid loaded liposomes. J. Am. Chem. Soc. 125, 5266 5267 8. Gupta, C., A.K. Daechsel and A. Chauhan 2011. Interaction of ionic surfactants with cornea mimicking anionic liposomes. Langmuir. 27, 10840 10846. 9. The Woodrow Wilson 2011 http://www.nanotechproject.org/news/archive/9231 Accessed 2013 F EB 10. Verlet, L. 1967. Computer experiments on classical flui ds .I. thermodynamical properties of lennard jones molecules. Physical Review. 159, 98 &. 11. Berendsen, H., J. Postma, W. Vangunsteren, A. Dinola and J. Haak 1984. Molecular dynamics with coupling to an external bath. J. Chem. Phys. 81, 3684 3690. 12. Nos e, S. 1984. A molecular dynamics method for simulations in the canonical ensemble. Mol. Phys. 52, 255 268. 13. Hoover, W. 1985. Canonical dynamics equilibrium phase space distributions. Phys. Rev. A. 31, 1695 1697

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43 14. Parrinello, M. and A. Rahman 1981 Polymorphic transitions in single crystals a new molecular dynamics method. J. Appl. Phys. 52, 7182 7190. 15. Nose S. and M. Klein 1983. Constant pressure molecular dynamics for molecular systems. Mol. Phys. 50, 1055 1076 16. Marrink, S. J., H.J. Riss elada, S. Yefimov, D.P. Tieleman and A.H. de Vries 2007. The MARTINI force field: Coarse grained model for biomolecular simulations. J Phys Chem B. 111, 7812 7824 17. Marrink, S. J., A.H. de Vries, T.A. Harroun, J. Katsaras and S.R. Wassall 2008. Cholester ol shows preference for the interior of polyunsaturated lipid. J. Am. Chem. Soc. 130, 10 +. 18. Marrink, S., A. de Vries and A. Mark 2004. Coarse grained model for semiquantitative lipid simulations. J Phys Chem B. 108, 750 760. 19. D'Rozario, R. S. G., C .L. Wee, E.J. Wallace and M.S.P. Sansom 2009. The interaction of C 60 and its derivatives with a lipid bilayer via molecular dynamics simulations. Nanotechnology. 20, 115102. 20. Gardiner, C. W. 2004 Handbook of Stochastic Methods for Physics, Chemistry a nd the Natural Sciences. 3rd Ed Springer 21. Van der Spoel, D., E. Lindahl, B. Hess, G. Groenhof, A. Mark and H. Berendsen 2005. GROMACS: Fast, flexible, and free. J. Comput. Chem. 26, 1701 1718. 22. Heerklotz, H. and J. Seelig 2007. Leakage and lysis o f lipid membranes induced by the lipopeptide surfactin. Eur. Biophys. J. Biophys. Lett. 36, 305 314 2 3 Pantano, D. A., P.B. Moore, M.L. Klein and D.E. Discher 2011. Raft registration across bilayers in a molecularly detailed model. Soft Matter. 7, 8182 8 191. 24 Risselada, H. J. and S.J. Marrink 2008. The molecular face of lipid rafts in model membranes. Proc. Natl. Acad. Sci. U. S. A. 105, 17367 17372. 25. Risselada, H. J. and S.J. Marrink 2008. The molecular face of lipid rafts in model membranes http://md.chem.rug.nl/cgmartini/images/applications/bichol/raft.gro Last accessed 2013 JAN 2 6 Tegos, G., T. Demidova, D. Arcila Lopez, H. Lee, T. Wharton, H. Gali and M. Hamblin 2005. Cationic fullerenes are effective and selective antimicrobial photosensitizers. Chem. Biol. 12, 1127 1135.

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44 2 7 Chen, Z., R. Mao and Y. Liu 2012. Fullerenes for cancer diagnosis and therapy: Preparation, biological and clinical perspectives. Curr. Drug Metab. 13, 1 035 1045 2 8 Oberdorster, E. 2004. Manufactured nanomaterials (fullerenes, C 60) induce oxidative stress in the brain of juvenile largemouth bass. Environ. Health Perspect. 112, 1058 1062. 2 9 Trpkovic, A., B. Todorovic Markovic an d V. Trajkovic 2012. Toxicity of pristine versus functionalized fullerenes: Mechanisms of cell damage and the role of oxidative stress. Arch. Toxicol. 86, 1809 1827. 30 Kopelevich, D. I., J. Bonzongo, R. A. Tasseff, J. Gao, Y. Ban and G. Bitton.2008; 2008 .Potential toxicity of fullerenes and molecular modeling of their transport across lipid membranes; In Nanoscience and nanotechnology, John Wiley & Sons, Inc., 233 260. 3 1 Baowan, D., B.J. Cox and J.M. Hill 2012. Instability of C 60 fullerene interacting w ith lipid bilayer. J. Mol. Model. 18, 549 557.

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45 BIOGRAPHICAL SKETCH Tarun Narra received a Bachelor of Technology degree in Chemical Engineering from Osmania University, Hyderabad, India in 2011. He received his Master of Science degree in chemical e ngineering from U niversity of Florida in May 2013 During his masters, he worked under the supervision of Prof. Dmitry I Kopelevich.