Mathematical modelling of a suspension culture microenvironment

MATHEMATICAL MODELLING OF A SUSPENSION CULTURE MICROENVIRONMENT ASHRAY RAMACHANDRAN (BSCEE, Purdue University, West Lafayette) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF SCIENCE NUS GRADUATE PROGRAMME IN BIOENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2010 Abstract The aim of this work is to create a computer model for in-vitro cellular growth of neural cells The identification of Neural Stem Cells (NSCs) began with the initial work on neural progenitors isolated from the adult rat brain in the sixties This was followed by work done on the embryonic mammalian central nervous system (CNS) where distinct pools of neural cells were identified as having stem cell properties Further work was done to identify NSC in the subependymal region and in the hippocampus dentate gyrus (DG), where they divide to generate progenitors Subsequently, NSCs were cultured in-vitro as floating suspensions called neurospheres Neurosphere culture is plagued with variances in neurosphere numbers and cellular expansion rates This has made it difficult to benchmark the culture conditions that promote cellular proliferation We present a neurosphere formation model that incorporates experimental data about paracrine factor stimulation in a 20000 cells/ml, N2 supplemented medium Factor transport is modelled as a three dimensional isotropic diffusion event Diffusion coefficients are adapted from the diffusion coefficients of similar sized molecules in the rat brain tissue The cellular response is modelled as a factor concentration dependent response The cellular doubling time is set at 20hrs when the conditions are ideal for division Cellular proliferation is based on a 0.1% subset that is predetermined to form neurospheres and a further 1.3% of cells that are dependent on a critical cell surface factor concentration threshold that ensures geometric expansion rates through cellular doubling The model’s predictions match the experimental data for neurosphere cell numbers at both high (200000 cells/ml) and low densities (2000 cells/ml) The model forms a framework to build upon for the simulation of a suspension culture that can be used to investigate other aggregate suspension cultures ii Acknowledgements I would like to thank my parents who supported me through these four years and provide me with timely advice and motivation when I needed it I would also like to thank Anju for advising me and encouraging me when i needed it the most I joined Graduate Programme in Bioengineering with a group of enthusiastic colleagues Chee Tiong, Vinayak, Rong Bin, Kalyan, Lei Yang to mention a few They were an amazing group of people to work and study with My two supervisors Dr Martin Lindsay Buist and Dr Sohail Ahmed were pillars of my scientific endeavour without whom I would not have achieved any of this They were always there for me providing scientific guidance and much needed counselling every step of the way They encouraged me when I did well and were critical when I was going astray thus providing constant feedback to my best I here acknowledge members of both labs who treated me like one among their family and provided support, encouragement and companionship through these years I would like to specially thank Dr Yu Fenggang from whom I learnt about cell culture and factor production in neurospheres and Dr David Nickerson for his advice and insights in CMISS programming I would like to thank Huiting, Huimin and Mike Yu whom I worked with on the neurosphere project I thank NUS, IMCB, IMB and A-STAR for the financial support as well as providing me a platform to my scientific work for the last few years iii Contents Abstract ii Acknowledgements iii List of Tables vii List of Figures viii List of Symbols xi List of Abbreviations xv Chapter Introduction 1.1 The definition, identification and importance of neural stem cells 1.2 The neurosphere model for cell expansion 1.3 Hypotheses and aims 1.4 Thesis overview Chapter Literature review 2.1 Biology review 2.1.1 Conditioned medium and neural stem cells 2.1.2 Neurosphere culture of neural stem cells 2.1.3 The importance of a cellular niche for maintenance of NSC 10 2.1.4 Current hurdles associated with the propagation and analysis of NSC 10 2.1.5 The clonal analysis assay for neural stem cells and its limitations 11 2.2 Modelling review 12 2.2.1 Characterization of diffusion based factor concentration profiles 12 2.2.2 Mathematical models for diffusion 13 Chapter Experimental methodology 15 3.1 Isolation and culture of neural cells 15 3.2 Neurosphere survival assay 15 3.3 Protein purification 15 3.4 Molecular mass spectrometric analysis 16 3.5 Neurosphere survival and proliferation assay 16 3.6 Neurosphere size assay 17 3.7 Conditioned medium protein reconstitution 17 3.8 Sandwich assay 18 Chapter Experimental Results 20 4.1 Neurospheres secrete factors that enhance their survival 20 4.2 Neurospheres secrete factors that affect their growth 21 iv 4.3 Cell seeding density affects the lag time for neurosphere growth when aggregation is minimized 22 4.4 Purification and characterization of factors in CM 24 4.5 Apolipoprotein E (ApoE) and Chondroitin Sulphate Proteoglycan (CSPG) provide the survival stimulus for NSCs 27 4.6 CytC stimulates growth of neurospheres in a dose dependent manner 29 4.7 Cell aggregation 30 4.7.1 Neurosphere initiation and growth in bulk culture 30 4.7.2 Clonal cultures proliferate with far lower efficiency than bulk cultures at 20000 cells/ml 31 4.7.3 Aggregation based bulk cultures reproducibly produce neurospheres of a similar size 32 Chapter Computational methodology 35 5.1 Derivation of cellular production rates 35 5.2 Cellular factor production and diffusion 36 5.2.1 Diffusion and binding coefficients 39 5.2.2 Factor binding to the cell surface 39 5.3 Cellular states and transition between states 41 5.4 Cellular arrangement in concentric shells 42 5.4.1 Neurosphere factor production and diffusion 43 5.4.2 Effect of tortuosity on diffusion coefficients in neurospheres 43 5.4.3 Boundary conditions 44 5.4.4 Neural cell aggregation coefficients in bulk culture 46 Chapter Computational Results 48 6.1 The factor based growth threshold 48 6.2 The factor based neurosphere initiation threshold 49 6.3 Aggregation coefficients for neural cells 50 6.4 Testing the aggregate doubling rate at differing cell densities 51 6.5 Verifying the factor concentration near the cell surface by setting the cells as non dividing constant point sources 52 6.6 Utilizing the factor based threshold to predict the growth at 200000 cells/ml and 2000 cells/ml without aggregation 53 6.7 Cell density affects ApoE distribution more than CSPG 55 6.8 Paracrine factor contribution to the neighboring cells and conditioned medium 57 6.9 Diffusion profile across the cell filled shells as the shells fill up with cells 58 6.10 Diffusion profile across shell and as shells to fill up with cells sequentially as the neurosphere is formed 59 v 6.11 Factor concentration profile at 1.5 days and at the end of the culture 60 Chapter Discussion 62 Chapter Conclusion and further recommendations 68 Appendix 70 A Shelldatastep120.exnode for 20000 cells/ml 70 B Shelldatastep108.exnode for 20000 cells/ml 75 C Shelldatastep75.exnode for 200000 cells/ml 78 D Shelldatastep505.exnode for 2000 cells/ml 80 References 87 vi List of Tables Table 1, Peptide sequences detected using mass spectrometry 27 Table 2, Neurosphere size in a clonal culture 32 vii List of Figures Figure In-vitro neural cell culture system Figure Cell culture passaging timeline Figure Neurospheres after days of culture photographed with 17 a 10x objective on a Leica microscope Figure A schematic of the arrangement used for sandwich cultures 18 Figure Neurosphere survival stimulation by conditioned medium 21 Figure Neurosphere growth stimulation by conditioned medium 22 Figure Growth at 200,000 cells/ml on a sandwich culture 23 Figure Growth at 20,000 cells/ml on a sandwich culture 24 Figure Protein fractionation and concentration 25 Figure 10 Survival stimulation by conditioned medium fractions 26 Figure 11 Reconstitution of survival factors to prove their role 28 Figure 12 CytC stimulation at high cell density 29 Figure 13 Dose dependent response of neurospheres to CytC 30 Figure 14 Neurosphere size distribution at high cell plating density 31 Figure 15 Average neurosphere size at high plating density 32 Figure 16 Average neurosphere size at low plating density 33 Figure 17 Neurosphere numbers at low and high density 34 Figure 18 Model execution flowchart 37 viii Figure 19 Factor complex schematic for neural cell stimulation 40 Figure 20 Three state model for cellular expansion 41 Figure 21 The neurosphere structure model 42 Figure 22 Aggregation based doubling at 20 cells/µl seeding density 52 Figure 23 Cell surface concentration of ApoE and 53 DSD-1-proteoglycan (CSPG) at uniform plating density of 20000 cells/ml with no aggregation and cell division until 36 hours Figure 24 Cell surface concentration of ApoE and 54 DSD-1-proteoglycan (CSPG) at uniform plating density of 200,000 cells/ml with no aggregation Figure 25 Cell surface concentration of ApoE and 54 DSD-1-proteoglycan (CSPG) at uniform plating density of 2000 cells/ml with no aggregation Figure 26 Factor concentration profile radially away from the cells 56 after 36 hours at plating density of 2000 cells/ml Figure 27 Factor concentration profile radially away from the cells 56 after 36 hours at plating density of 20000 cells/ml with no cell division Figure 28 Factor concentration profile radially away from the cells 57 after 36 hours at plating density of 200,000 cells/ml Figure 29 Outermost shell concentration at uniform plating 58 density of 20000 cells/ml with no aggregation ix Figure 30 Diffusion profile across the cell filled shells 59 at uniform plating density of 20000 cells/ml with no aggregation Figure 31 Diffusion profile across shell as shells to fill up 60 with cells sequentially at uniform plating density of 20000 cells/ml with no aggregation Figure 32 Factor concentration profile at 1.5 days and at the end 61 of the culture at uniform plating density of 20000 cells/ml with no aggregation x [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: 3.320887088776 0.005352483131 0.000949569687 15 3.310440778732 2.008807897568 2.014088392258 0.069305613637 3.307982921600 0.005279130302 0.000945207255 16 3.306981801987 1.997717738152 2.012912273407 0.069251738489 3.297606945038 0.005220243242 0.000941703678 17 3.304224729538 1.988877773285 2.011974811554 0.069208830595 3.289336204529 0.005173423328 0.000938916521 18 3.302062511444 1.981945276260 2.011239767075 0.069175221026 3.282850265503 0.005136835855 0.000936732686 19 3.300412178040 1.976653337479 2.010678529739 0.069149613380 3.277899265289 0.005109054502 0.000935065735 20 3.299207925797 1.972791552544 2.010269165039 0.069130979478 3.274286508560 0.005088878796 0.000933849311 21 3.298397064209 1.970191478729 2.009993553162 0.069118499756 3.271853923798 0.005075294524 0.000933030329 22 3.297937154770 77 [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: 1.968716859818 2.009837388992 0.069111421704 3.270474433899 0.005067589693 0.000932565832 23 3.297796249390 1.968256115913 2.009788513184 0.069109201431 3.270044088364 0.005065181758 0.000932420662 C Shelldatastep75.exnode for 200000 cells/ml At timepoint of 5.98 hours of culture with seeding density of 200000 cells/ml Cells are allowed to divide Shell represents the cell surface and the subsequent shells are concentric shells The numbers represent the concentrations of factors in units of nM SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: 8.199587821960 11.578420639038 4.269687175751 0.146261677146 13.286610603333 0.098026990891 0.006543144118 6.877903461456 6.611503601074 3.890233278275 0.128443777561 8.772233009338 0.045480147004 0.004985524807 6.259671211243 4.624104499817 3.679447650909 0.119488924742 6.917551040649 0.025802081451 0.003799360013 6.092041492462 4.085248947144 78 [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: 3.622293233871 0.117060840130 6.414664268494 0.020492505282 0.003475107253 6.010548591614 3.823306560516 3.594506740570 0.115880407393 6.170188426971 0.017925625667 0.003317717928 5.964130401611 3.674090147018 3.578678131104 0.115208014846 6.030935287476 0.016471715644 0.003228212474 5.935765266418 3.582892894745 3.569004058838 0.114797100425 5.945841312408 0.015587801114 0.003173594130 5.918158531189 3.526268720627 3.562997341156 0.114542007446 5.893023014069 0.015041611157 0.003139733803 5.907662868500 3.492494583130 3.559414625168 0.114389911294 5.861537456512 0.014717139304 0.003119561821 10 5.902250766754 3.475067138672 3.557566165924 0.114311456680 5.845302104950 0.014550205320 0.003109162906 11 5.900706768036 3.470094203949 3.557039022446 0.114288993180 5.840666294098 0.014502567239 0.003106191754 79 D Shelldatastep505.exnode for 2000 cells/ml At timepoint of days of culture with seeding density of 2000 cells/ml Cells are allowed to divide Shell represents the cell surface and the subsequent shells are concentric shells The numbers represent the concentrations of factors in units of nM SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: 3.886023044586 9.382192611694 1.658640980721 0.062086433172 9.259891510010 0.038940377533 0.001160450280 2.564085245132 4.414473056793 1.279101014137 0.044264882803 4.744749069214 0.011349785142 0.000566896109 1.944516539574 2.422777175903 1.067860245705 0.035290725529 2.886036634445 0.005740852095 0.000342317537 1.774564862251 1.876459240913 1.009915113449 0.032829053700 2.376172542572 0.004210866988 0.000280910288 1.689610958099 1.603384494781 0.980949461460 0.031598530710 2.121297121048 0.003446258139 0.000250218174 1.638661980629 1.439620614052 0.963577449322 0.030860541388 80 [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: 1.968432307243 0.002987780375 0.000231812475 1.604720354080 1.330528855324 0.952003955841 0.030368886888 1.866595506668 0.002682427177 0.000219552661 1.580501437187 1.252688288689 0.943745195866 0.030018053949 1.793930411339 0.002464624820 0.000210805360 1.562362909317 1.194391369820 0.937559366226 0.029755283147 1.739508628845 0.002301586792 0.000204254597 10 1.548281073570 1.149134278297 0.932756483555 0.029551265761 1.697258830070 0.002175098052 0.000199169444 11 1.537041902542 1.113014459610 0.928922593594 0.029388416559 1.663538217545 0.002074215328 0.000195111323 12 1.527872800827 1.083548784256 0.925794363022 0.029255544767 1.636028647423 0.001991907833 0.000191801111 13 1.520258665085 1.059079051018 0.923196136951 0.029145192355 1.613184690475 0.001923553180 0.000189052778 14 1.513842821121 81 [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: 1.038459539413 0.921006262302 0.029052188620 1.593936324120 0.001865974860 0.000186737496 15 1.508370637894 1.020871758461 0.919137954712 0.028972849250 1.577519416809 0.001816883567 0.000184763281 16 1.503655433655 1.005715608597 0.917527556419 0.028904467821 1.563373446465 0.001774600823 0.000183062642 17 1.499557018280 0.992540717125 0.916127204895 0.028845012188 1.551078319550 0.001737867366 0.000181584983 18 1.495968341827 0.981003165245 0.914900481701 0.028792934492 1.540312409401 0.001705720555 0.000180291609 19 1.492805957794 0.970835089684 0.913818955421 0.028747025877 1.530825853348 0.001677411725 0.000179152397 20 1.490004062653 0.961820483208 0.912860095501 0.028706334531 1.522421240807 0.001652349485 0.000178143615 21 1.487510204315 0.953790187836 0.912006080151 0.028670096770 1.514940738678 0.001630060957 82 [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: 0.000177246242 22 1.485281705856 0.946607589722 0.911242365837 0.028637697920 1.508256554604 0.001610163483 0.000176444897 23 1.483283758163 0.940162420273 0.910557031631 0.028608629480 1.502264022827 0.001592343673 0.000175727007 24 1.481487512589 0.934362411499 0.909940242767 0.028582477942 1.496876835823 0.001576342736 0.000175082139 25 1.479868888855 0.929130554199 0.909383893013 0.028558893129 1.492022991180 0.001561945188 0.000174501634 26 1.478407859802 0.924402177334 0.908881008625 0.028537586331 1.487641930580 0.001548969653 0.000173978216 27 1.477087259293 0.920122623444 0.908425867558 0.028518306091 1.483682394028 0.001537263161 0.000173505730 28 1.475892543793 0.916245341301 0.908013522625 0.028500845656 1.480100989342 0.001526694861 0.000173078923 29 1.474811315536 0.912730395794 0.907639622688 83 [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: 0.028485022485 1.476860284805 0.001517152996 0.000172693297 30 1.473832845688 0.909543275833 0.907300591469 0.028470681980 1.473924994469 0.001508540940 0.000172344968 31 1.472946524620 0.906654238701 0.906993269920 0.028457690030 1.471264481544 0.001500775339 0.000172030574 32 1.472143769264 0.904037177563 0.906714856625 0.028445923701 1.468854784966 0.001493783202 0.000171747190 33 1.471417665482 0.901669502258 0.906462907791 0.028435278684 1.466675043106 0.001487500966 0.000171492255 34 1.470762014389 0.899531066418 0.906235396862 0.028425667435 1.464706778526 0.001481872518 0.000171263528 35 1.470171332359 0.897604405880 0.906030297279 0.028417009860 1.462933540344 0.001476848382 0.000171059030 36 1.469640970230 0.895873785019 0.905846118927 0.028409233317 1.461341142654 0.001472358825 0.000170876199 37 84 [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: 1.469166636467 0.894325375557 0.905681371689 0.028402278200 1.459916830063 0.001468342845 0.000170712650 38 1.468744277954 0.892946779728 0.905534684658 0.028396088630 1.458648920059 0.001464768313 0.000170567073 39 1.468370795250 0.891726970673 0.905404984951 0.028390612453 1.457527518272 0.001461606356 0.000170438318 40 1.468042850494 0.890655934811 0.905291080475 0.028385808691 1.456543326378 0.001458831364 0.000170325337 41 1.467757940292 0.889724731445 0.905192196369 0.028381632641 1.455688238144 0.001456420054 0.000170227169 42 1.467513442039 0.888925313950 0.905107319355 0.028378050774 1.454954624176 0.001454351470 0.000170142957 43 1.467307329178 0.888250410557 0.905035734177 0.028375029564 1.454335808754 0.001452606521 0.000170071915 44 1.467137336731 0.887694001198 0.904976665974 0.028372537345 1.453825712204 85 [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: SHELL: [APOE ]: [CSPG ]: [CYTC ]: [GF ]: [TensC ]: [ApoEPG]: [CYTGF ]: 0.001451167976 0.000170013343 45 1.467001676559 0.887250125408 0.904929578304 0.028370549902 1.453418731689 0.001450020238 0.000169966617 46 1.466898798943 0.886913180351 0.904893875122 0.028369041160 1.453109741211 0.001449149102 0.000169931140 47 1.466827154160 0.886678159237 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of neural precursors Brain Res, 2006 1107(1): p 8296 Robert, M.B and N.L Matthew, eds Physiology 4th edition ed 1998, Mosby page 7, right column, diffusion coefficient 91 [...]... distances and have an effect on distant cells The distribution of chemotactic agents for axon guidance was studied and subsequently mathematically modelled based on a linear diffusion model [68-70] Furthermore the extrasynaptic transport of glutamate molecules was studied and the structural constraints of the extracellular space was found to affect the binding and 12 receptor activation of glutamate... gives an overview of the previous work done on neural stem cells and the factors that affect neural stem cell survival and proliferation In Section 2.2, the background studies on mathematical modelling of diffusion of factors, modelling of tortuosity due to extra cellular geometry and imaging studies of long range profiles of morphogens are highlighted Chapter 3 details the materials and methods that... were carried out to culture neural cells in-vitro and to identify and qualify the effects of paracrine factors in the in-vitro neural cell culture Chapter 4 details the biological experiments done to identify the paracrine factors and their roles in cellular expansion Chapter 5 details the computational approach used to model the growth and survival stimulus of aggregates in a suspension culture Chapter... embryonic and adult brain [1, 2, 4, 12-14] and have great potential as cell therapy for CNS diseases such as Parkinson’s disease, Alzheimers, Multiple Sclerosis and recovery from the damage caused by a stroke [15] A number of studies have suggested that NSCs may aid in CNS repair by acting as support cells rather than through cell replacement [16] NSCs can be harvested from brain tissue and expanded in-vitro... relative similarity in the size and shape of embryoid bodies and neurospheres, the work indicates that diffusion based models can be used to analyze the profile of autocrine/paracrine survival and proliferation promoting factors in an in-vitro cultured neurosphere niche Work has been done on diffusion of epidermal growth factor in the extracellular volume of the rat brain [66] EGF was tagged in the rat... to the relatively low abundance of neural stem cells and lack of specific markers NSCs have traditionally been characterized based on their functional properties These properties consist of 1) the ability to generate cell aggregates called neurospheres after repeated dissociation, called self renewal; and 2) the ability of single NSCs to form neurospheres that can produce all primary neural cell types... The medium was found to spread evenly throughout the surface of the coverslip The arrangement was placed in a 10 cm diameter NUNC culture dish The procedure was repeated a total of 3 more times so as to fully utilize the culture dish Each coverslip (sandwich) was then overlaid with 0.5 ml of GM Care was taken to ensure that the arrangement was kept stable and that the medium stayed on top of the coverslip... independently to an external signal [88, 89] Although all of these works stand in isolation, a comprehensive model that tries to explain the cellular response to paracrine survival factors in an in-vitro suspension culture that can be readily studied and tested under laboratory conditions has yet to be developed 14 Chapter 3 Experimental methodology 3.1 Isolation and culture of neural cells Murine neural cells... 20ng/ml of EGF From the second day of plating, the cultures started to form free floating neurospheres Cells were passaged every 7 days by mechanical dissociation and reseeding 3.2 Neurosphere survival assay Neurosphere survival is a measure of a single cell’s ability to initiate the formation of a neurosphere in a culture Neurospheres were allowed to grow at at a single cell seeding density of 10 cells/ml... culture of neurospheres at normal plating density (as per isolation and culture of neural cells, see above) The medium was centrifuged to remove cells and debris and passed through a 30 kDa ultra-filtration column to obtain a 10/35-fold concentrated residue, collected as residue 1 The filtrate was passed through a 3 kDa ultra filtration column to obtain a 10/14-fold concentrated 15 residue collected as ... expansion Chapter details the computational approach used to model the growth and survival stimulus of aggregates in a suspension culture Chapter details the parameterization of the constants... molecules was studied and the structural constraints of the extracellular space was found to affect the binding and 12 receptor activation of glutamate receptors [71] A more detailed mathematical model... This allowed for the analysis of global concentration profiles of diffusible factors and the study of cellular pattern formation in both the transition and steady state phases As cells are rarely