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Quantitative analysis of retrovirus-mediated gene transfer into mammalian cells Tayi, Venkata Siva Ganesh 2010

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Quantitative Analysis of Retrovirus-mediated Gene Transfer into Mammalian Cells by  Venkata Siva Ganesh Tayi B.Tech., Jawaharlal Nehru Technological University, India, 2000 M.Tech., Indian Institute of Technology Kanpur, India, 2002 M.A.Sc., University of Toronto, Canada, 2003  A thesis submitted in partial fulfillment of the requirements for the degree of  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Chemical and Biological Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) September 2010 © Venkata Siva Ganesh Tayi, 2010  Abst ract Recombinant retroviruses (gammaretro-, lenti- and foamy-viral vectors) are used for gene therapy as well as for scientific research because of their ability to provide relatively stable gene transfer and expression.  The process of retrovirus-mediated gene transfer into mammalian cells  involves a series of transduction events that take place sequentially. A mathematical model for the retroviral transduction process was developed that incorporates the important extracellular and intracellular rate-limiting steps.  The mathematical model was validated with experimental data  obtained using gibbon ape leukemia virus envelope pseudotyped retroviral vectors and K562 target cells.  The model predictions of transduction efficiency and integrated virus copy number were  generally in good agreement with measured results acquired for both static and centrifugation-based gene transfer protocols. However, a deviation between the model calculations and the experimental transduction efficiency data was observed for centrifugation at high vector-to-cell ratios. To address this limitation, believed to be caused by the saturation of binding sites on the cell surface, a detailed experimental investigation of the binding and entry kinetics of retroviruses was performed. With the help of a mathematical representation for retroviral binding to, dissociation from and entry into mammalian cells, the kinetic rate constants for these three steps were experimentally quantified. The model was modified to incorporate these more complex kinetic steps and was shown to provide even better predictions of the experimental transduction results for the full range of vector-to-cell ratios investigated. The modified model was then used to optimize various retroviral transduction process parameters. Studies of the extracellular transport of viral vectors provided the optimal range of centrifugal forces needed to obtain the maximum transduction efficiency. Based on a simulated performance comparison of the three different types of recombinant retroviruses, lentiviral vectors were found to be very efficient for targeting hematopoietic stem cells. The mathematical model was able to provide a set of conditions where retroviral transduction protocols should yield high transduction efficiencies while maintaining the viral copy number in a lower, more desirable range.  ii  Preface This thesis is based on work carried out with the objective of quantitatively optimizing the retrovirus-mediated gene transfer into mammalian cells. The work was performed under the supervision of Dr. James Piret of the Michael Smith Laboratories and Dr. Bruce Bowen of the Department of Chemical and Biological Engineering, University of British Columbia. This thesis was completed with the valuable guidance and editing assistance provided by my two supervisors. All the experimental work was performed in the Michael Smith Laboratories at the University of British Columbia with the appropriate biohazard approval certificate (Protocol # B09-0105). A version of the material in Chapter 2 was published in the journal of Biotechnology and Bioengineering in January 2010. The work in Chapter 3 and Chapter 4 will soon be submitted to relevant journals. The following is the current list of publications resulting from this work:  Tayi VS, Bowen BD, Piret JM. 2010. Mathematical model of the rate-limiting steps for retrovirus-mediated gene transfer into mammalian cells. Biotechnology and Bioengineering 105(1):195-209.  iii  Cont e nts Abstract ..................................................................................................................................... ii Preface ......................................................................................................................................iii Contents .................................................................................................................................... iv List of tables ............................................................................................................................. vi List of figures........................................................................................................................... vii Nomenclature .........................................................................................................................xiii Acknowledgements ................................................................................................................ xvi 1. Introduction and literature review.................................................................................... 1 1.1 Retroviruses and development of retroviral vectors ....................................................... 2 1.2 Production and stability of retroviral vectors ................................................................ 3 1.3 Gene transfer using retroviral vectors ............................................................................ 5 1.4 Mathematical modeling of retroviral gene transfer ..................................................... 18 1.5 Thesis objectives .......................................................................................................... 21 2. Mathematical of model for retroviral gene transfer ..................................................... 23 2.1 Mathematical model ..................................................................................................... 25 2.2 Materials and methods .................................................................................................. 33 2.3 Results........................................................................................................................... 38 2.4 Discussion ..................................................................................................................... 50 3. Kinetics and mechanism of retroviral binding and entry ............................................. 60 3.1 Materials and methods .................................................................................................. 62 3.2 Results........................................................................................................................... 67 3.3 Discussion ..................................................................................................................... 82  iv  4. Quantitative analysis of retroviral transduction steps .................................................... 89 4.1 Mathematical model ..................................................................................................... 91 4.2 Materials and methods .................................................................................................. 93 4.3 Results........................................................................................................................... 93 4.4 Discussion ................................................................................................................... 116 5. Conclusions and future directions ................................................................................... 123 5.1 Conclusions................................................................................................................. 123 5.2 Future directions ......................................................................................................... 126 References .............................................................................................................................. 129 Appendix I: Computer Program for mathematical model ............................................... 147 Appendix II: Biohazard approval certificate ..................................................................... 150  v  List of tables Table 1.1: Retroviral envelope glycoproteins, targeted receptors and their entry pathways ... 12 Table 2.1: Estimated kinetic parameters of the model............................................................. 55 Table 4.1: Model equations for retroviral gene transfer process ............................................. 93 Table 4.2: Values of the kinetic parameters in the model ....................................................... 94 Table 4.3: Model parameters for gammaretro-, lenti- and foamy-viral vectors .................... 109  vi  List of figures Figure 1.1: Schematic view of the protocols for transduction of mammalian cells with retroviral vectors: (A) transduction under standard gravity, and transduction by enhancing the settling velocity of retroviral vectors using (B) spinoculation, (C) Magnatofection and (D) complexation of retroviral vectors with high density cationic polymers ................................... 6 Figure 1.2: Schematic view of the transduction pathways for the three types of retroviral vectors. (1) Reversable binding to the cell surface; (2) Interaction with receptors and movement to the entry points; (3) Receptor mediated uptake by the cell (for gammaretrovirus and foamy virus by endocytosis, for lentivirus by fusion of membranes on the cell surface); (4) Transport of retroviral vectors close to the microtube network and uncoating of matrix proteins; (5) Reverse transcription of retroviral genome for gammaretrovirus and lentivirus; (6) Transport to the microtubule organization centres along microtubules; (7) Transport into the nucleus (for gammaretrovirus and foamy virus during mitosis, for lentivirus active transport through nuclear pore); and (8) Integration of retroviral genome into the cell chromosome. ............................................................................................................................... 9 Figure 2.1: A-Schematic view of the retroviral transduction process in which mammalian cells are incubated with a medium containing retroviral vectors in a tissue culture dish. BOverview of the steps of the retroviral vector transduction process. (1) Binding of retrovirus to cell surface receptor. (2) Receptor-mediated release of viral capsid into cell cytoplasm. (3) Reverse transcription of retroviral RNA to form DNA (for oncovirus and lentivirus). (4) Transport of viral DNA along microtubule (MT) to the microtubule organizing center (MOC). (5) Degradation of retroviral vector by host cell restriction factors, if present. (6a) Import of the retroviral DNA into nucleus when nucleus membrane disassembles during mitosis (for oncovirus and foamy virus). (6b) Import of retroviral DNA into the nucleus by active transport through nuclear membrane (for lentivirus). (7) Integration of retroviral DNA into the cellular chromosome .............................................................................................................................. 26 Figure 2.2: Decay and binding kinetics of retroviral vectors. MSCV-GALVenv vectors were incubated at 37oC without () or with () K562 cells and, at the indicated time points, the activity of the remaining viral vectors in the extracellular medium was determined. The decay and binding rate constants were obtained by fitting equation (2.22) to the experimental data (solid lines). The error bars represent the standard deviations of two independent experiments .................................................................................................................................................. 40 Figure 2.3: Intracellular degradation kinetics of retroviral vectors. Serum-starved K562 cells were exposed to a pulse of retroviral vectors and then transferred back to a serum-free medium. At the indicated time points, K562 cells were transferred to a serum-containing medium to initiate the transduction of the remaining intracellular vector intermediates and the GFP+ cells were analyzed after 96 h. The y axis represents the % GFP+ cells at time t relative to GFP+ cells at time t = 0. The complete transduction model () was fitted to the experimental data () in order to estimate the intracellular degradation rate. Model simulations obtained with intracellular degradation half-lives of 20.8 h (----) and 6.2 h ( − ⋅ − ) vii  are also presented. The error bars represent the standard deviations of two independent experiments ............................................................................................................................... 42 Figure 2.4: Dynamics of retrovirus trafficking from cytoplasm into the nucleus. K562 cells were exposed to VCM for 30 min to deliver vectors into the cell cytoplasm and, at the indicated time points, the %Transduced cells was measured using flow cytometry. To estimate the cytoplasmic trafficking time, τ, the mathematical model () was then fitted to the experimental data (). The error bars represent the standard deviations of two independent experiments ............................................................................................................................... 44 Figure 2.5: Time course profile of the transduction of K562 cells. The cells were exposed to viral vectors for the indicated time points, transferred to fresh medium, cultured for 72 h and then analyzed for %Transduced cells. The predictions of the mathematical model () were fitted to the experimental data () to estimate the concentration of viral vectors at t = 0. The error bars represent standard deviations of two independent experiments ............................... 46 Figure 2.6: Transduction efficiency for K562 cells as a function of viral vector dosage. K562 cells were contacted with VCM at the indicated vector-to-cell ratios either at static gravity () or under centrifugation at 2000g () for 6 h. The solid lines represent the model predictions under the same conditions. For the centrifugation case, the model was also used to predict the transduction results that would have been obtained if δ2 = 1 (----) (i.e., all intracellular vectors are retained by only one daughter cell during cell division) or δ2 = e − ( nv −1) ( −⋅ − ) (i.e., at least one viral vector is retained by each daughter cell when more than one intracellular vector is present during division). The error bars represent standard deviations of two independent experiments each replicated twice ............................................................................................ 47 Figure 2.7: Mean copy number as a function of transduction efficiency. The experimental data () were obtained using real-time PCR. The solid line represents model predictions of the average integrated copy number of the transduced cells .................................................... 49 Figure 2.8: Sensitivity analysis of the kinetic parameters of the model. The y axis represents the percent change in gene transfer efficiency relative to a 10% percent increase in each of the following model parameters: extracellular degradation rate (kde), binding rate (Kb), intracellular degradation rate (kdi), cytoplasmic trafficking time (τ), and nuclear import rate (kn). Two values of kdi were investigated corresponding to cases where the vector intermediates that form in the cell cytoplasm are fairly stable with kdi = 0.0012 h–1 (black bars) and relatively unstable with kdi = 0.107 h–1 (gray bars). The other parameters used in the analysis were: g′ = 1×g, tf = 24 h ............................................................................................. 57 Figure 3.1: Binding of retroviral vectors on the cell surface is dependent on the dose of protamine sulfate. MSCV-GALVenv retroviral vectors were contacted with RAT-1 cells for 30 min at 1000g and 17oC in the presence of different concentrations of protamine sulfate as indicated. Then, the VCM was removed, the cells were washed and fresh medium was added. The cells were incubated at 37oC for 2 h, then trypsinized and seeded at low density. They were then incubated for an additional 48 h, after which they were analyzed for GFP+ cells. The error bars indicate the standard deviations of four replicates from two independent experiments ............................................................................................................................... 68 viii  Figure 3.2: Protamine sulfate assists the irreversible binding of retroviral vectors to the cell surface. MSCV-GALVenv retroviral vectors were contacted with RAT-1 cells for 30 min at o 1000g and 17 C in the absence () or presence () of 10 µg/mL protamine sulfate. The VCM was removed, the cells were washed and fresh medium was added. The cells were o incubated at 37 C and, at the indicated time points, the medium above the cells was collected and assayed for titer. The error bars indicate the standard deviations of four replicates from two independent experiments ................................................................................................... 69 Figure 3.3: The entry of retroviral vectors is not affected by the presence of the optimum concentration of protamine sulfate. MSCV-GALVenv retroviral vectors were contacted with o RAT-1 cells for 30 min at 1000g and 17 C in the absence () or presence ( ) of 10 µg/mL protamine sulfate. The VCM was removed, the cells were washed and media with different o concentrations of protamine sulfate were added. The cells were incubated at 37 C for 2 h, then trypsinized and seeded at low density. The cells were then cultured for 48 h, after which they were analyzed for GFP+ cells. The error bars indicate the standard deviations of four replicates from two independent experiments. The asterisks indicate a p value of less than 0.05 based on Student’s t-test ........................................................................................................... 70 Figure 3.4: Effect of citrate buffer and trypsin on the inactivation of GALVenv retroviral vectors. MSCV-GALVenv vectors were contacted with RAT-1 cells for 30 min at 2000g and o 17 C. The VCM was removed, and then the cells in some wells were washed and treated with o citrate buffer for 2 min. The cells in other wells were treated with trypsin at 37 C for 10 min and then were immediately seeded at low density. Control samples were mock-treated with medium. The medium in the remaining plates was replaced and the cells were incubated at o 37 C for 2 h, then trypsinized and seeded at low density. All cells were incubated for 48 h, after which they were analyzed for GFP+ cells. The ordinate axis represents the % GFP+ cells relative to that of the control. The error bars indicate the standard deviations of four replicates from two independent experiments. The asterisks indicate a p value of less than 0.05 w.r.t. control based on Dunnett’s method .......................................................................................... 72 Figure 3.5: Dissociation and entry kinetics of GALVenv retroviral vectors on RAT-1 cells. MSCV-GALVenv retroviral vectors were contacted with RAT-1 cells for 30 min at 1000g and o 17 C in the absence () or presence ( ) of 10 µg/mL protamine sulfate. The VCM was removed, the cells were washed and fresh medium was added. The cells were incubated at o 37 C and, at the indicated time points, were trypsinized and seeded at low density. All cells were cultured for 48 h to later estimate the GFP+ cells. The error bars indicate the standard deviations of four replicates from two independent experiments. The lines represent the best fit of Equation (3.5) to the data with k-b = 0 () and k-b ≠ 0 (----) ............................................... 74 Figure 3.6: Ammonium chloride inhibits the infectious entry of GALVenv retroviral vector. MSCV-GALVenv retroviral vectors were contacted with RAT-1 cells for 30 min at 1000g and 17ºC. The VCM was removed, the cells were washed and media with different concentrations of NH4Cl were added. The cells were incubated at 37ºC for 1 h, then trypsinized and seeded at low density. The cells were then incubated for 48 h, after which they were analyzed for GFP+ cells (gray bars, normalized to the no added ammonium chloride control). The effect of ix  ammonium chloride on the growth of the cells was determined from the fold increase in cell number during the 48 h incubation after the treatment ().The error bars indicate the standard deviations of four replicates from two independent experiments ............................................. 76 Figure 3.7: Viral degradation rate was not affected by the presence of ammonium chloride. MSCV-GALVenv retroviral vectors were incubated for different times in media without () or o with () 100 mM NH4Cl at 37 C. The incubated virus samples were then assayed for titer by o adding them to RAT-1 cells and centrifuging at 2000g and 17 C and later replacing the medium. The error bars indicate the standard deviations of four replicates from two independent experiments .......................................................................................................... 77 Figure 3.8: Low pH treatment does not facilitate the entry of GALVenv retroviral vectors. MSCV-GALVenv retroviral vectors were bound to tissue culture dishes with (black bars) or without (gray bars) RAT-1 cells by centrifuging with VCM containing 10 µg/mL protamine o sulfate at 1000g and 17 C for 30 min. The VCM was removed and treated with media having the indicated pH values for 2 min. All the plates were washed and RAT-1 cells were seeded in the treated dishes without cells. After fresh medium was added to the wells containing cells, o the latter were incubated at 37 C for 1 h and then trypsinized and seeded at low density. All the samples were incubated for 48 h, after which they were analyzed for GFP+ cells. The data were normalized to the results obtained from the wells that were treated for 2 min with the medium at pH 7.4. The error bars indicate the standard deviations of four replicates from two independent experiments .......................................................................................................... 79 Figure 3.9: Chlorpromazine does not affect the infectivity of GALVenv retroviral vectors. RAT-1 cells were incubated with media containing indicated concentrations of chlorpromazine at 37oC for 30 min. Later the medium was replaced by VCM with corresponding concentrations of chlorpromazine and centrifuged at 37oC and 1000g for 30 min. Then the cells were washed, trypsinized and seeded at low density. The cells were cultured for 48 h to analyze for GFP+ cells. The error bars indicate the standard deviations of four replicates from two independent experiments .................................................................. 80 Figure 3.10: GALVenv retroviral vector entry was inhibited by extracting cholesterol from cell membranes. RAT-1 cells were incubated with media containing 10 mM MBCD or no MBCD (control) and then infected with GALVenv retroviral vectors under centrifugation at 1000g. The VCM was removed and the plates were washed. One set of control samples was treated with MBCD medium for 30 min after infection. All the cells were then trypsinized and seeded at low density. The cells were cultured for 48 h and analyzed for GFP+ cells. The ordinate axis represents the % GFP+ cells relative to control. The error bars indicate the standard deviations of four replicates from two independent experiments. The asterisks indicate a p value of less than 0.05 w.r.t. control based on Dunnetts’s method ....................... 82 Figure 4.1: (A) Transduction efficiency as a function of vector-to-cell ratio and (B) mean number of integrated viral copies per transduced cell as a function of transduction efficiency. Experimental data were obtained as described in Section 2.3 and the solid lines represent the predictions of the model presented in Table 4.1 ....................................................................... 96  x  Figure 4.2: The effect of the height of the VCM on transduction efficiency. A constant number of K562 cells was suspended in different volumes of VCM, containing either 9.24×106 () or 2.36×106 () vectors/cm3, to obtain different VCM heights. Each suspension was then centrifuged at 2000g for 6h. The solid lines represent the predictions of the model presented in Table 4.1. The error bars indicate the standard deviations of four replicates from two independent experiments ................................................................................................... 97 Figure 4.3: The effect of centrifugal force (or settling velocity of vectors) on transduction efficiency (A) and the exposure time of VCM to target cells needed to reach 95% vector depletion (B). The simulations were carried out for the transduction of cells with the height of VCM equal to 2 (- ⋅⋅ -), 5 (----) and 10 mm () using the kinetic parameters in Table 4.2...... 99 Figure 4.4: The effect of kinetic rate constants: extracellular decay (A), binding (B), dissociation (C) and entry (D) on the transduction efficiency () and the time of exposure to VCM to obtain maximum transduction efficiency (----) at an initial vector-to-cell ratio of 1 and a centrifugal force of 1000g ............................................................................................. 101 Figure 4.5: The effect of extracellular kinetic rate constants: decay (A), binding (B), dissociation (C) and entry (D) on the transduction efficiency as a function of the initial vectorto-cell ratio. The simulations were performed for the case where transduction was carried out under centrifugation at 1000g for 4 h using the parameters in Table 4.2, except where individual extracellular parameter were changed according to the table below: Curve  A: kde (h-1)  B: kb (cm3/cell-h)  C: k-b (h-1)  D: ke (h-1)  - ⋅⋅ 0.1386 5 x 10-9 5.0 0.5 -8 ---0.0139 5 x 10 0.5 1.0 0.0014 5 x 10-7 0.05 5.0  ................................................................................................................................................ 103 Figure 4.6: The effect of intracellular decay half-life on transduction efficiency as a function of vector-to-cell ratio under centrifugation conditions. The simulations were carried out at a centrifugal force of 1000g for 4 h using vector intracellular half-lives of 6.2 h (- ⋅⋅ -), 20.8 h (----) and 600 h (). The remaining parameters were at their default values as listed in Table 4.2 ........................................................................................................................................... 105 Figure 4.7: The effect of the cytoplasm-trafficking time on the transduction efficiency as a function of vector-to-cell ratio in the absence (A) or presence (B) of the intracellular degradation of retroviral vectors. The simulations were carried for transduction with VCM having different initial concentrations under centrifugation at 1000g for 4 h using different cytoplasm trafficking times of 1 h (), 10 h (----) and 20 h (- ⋅⋅ -) for intracellular half-lives of 600 h (A) and 6.2 h (B). The remaining parameters were at their default values as listed in Table 4.2 ................................................................................................................................. 106 Figure 4.8: The effect of the rate of nuclear transport of PIC on the transduction efficiency as a function of vector-to-cell ratio in the absence (A) or presence (B) of the intracellular degradation of retroviral vectors. The simulations were carried out for different initial concentrations of VCM under centrifugation at 1000g for 4 h using different nuclear entry xi  rates of 0.067 h-1 (- ⋅⋅ -), 0.134 h-1 (----) and 0.667 h-1 () for intracellular half-lives of 600 h (A) and 6.2 h (B). The remaining parameters were at their default values as listed in Table 4.2 ........................................................................................................................................... 107 Figure 4.9: The transduction efficiency of gammaretro- (), lenti- (----) and foamy- (- ⋅⋅ -) viral vectors as a function of the doubling time of target cells in the absence (A) or presence (B) of intracellular degradation of viral vectors at a centrifugal force of 1000g and a VCM exposure time of 4 h ............................................................................................................... 110 Figure 4.10: The transduction efficiency of gammaretro- (), lenti- (----) and foamy- (- ⋅⋅ -) viral vectors as a function of the cytoplasm trafficking time in the absence (A) or presence (B) of intracellular degradation of vectors at a centrifugal force of 1000g and a VCM exposure time of 4 h ............................................................................................................................... 112 Figure 4.11: The average number of integrated copies per transduced cell as a function of %Transduced cells for gammaretro- (), lenti- (----) and foamy- (- ⋅⋅ -) viral vectors. The simulations were performed using the parameters in Table 4.3 and by varying the vector-tocell ratios in order to obtain the range of transduction efficiencies shown in the figure ........ 115 Figure 4.12: The effect of the intracellular degradation rate on the relationship between the transduction efficiency and the integrated viral copy number for gammaretro- (), lenti- (----) and foamy- (- ⋅⋅ -) viral vectors. The simulations were performed using the parameters in Table 4.3 and by varying the vector-to-cell ratios to obtain the number of viral copies at a transduction efficiency of 50% for the three retroviral vector systems .................................. 116  xii  Nomenclature Cb  Concentration of target cells with bound virus on their surface, cells/cm2  Cc  Concentration of target cells carrying at least one virus in their cytoplasm, cells/cm2  Cf  Concentration of target cells free of viruses, cells/cm2  Ci  Concentration of target cells with at least one integrated virus, cells/cm2  Ct  Total target cell concentration on culture surface, cells/cm2  Ct,max Maximum (i.e., confluent) target cell concentration on culture surface, cells/cm2 dv  Diameter of retrovirus, cm  Dv  Diffusivity of retrovirus, cm2/h  F0EGFP Fluorescence value of amplified EGFP sequence at cycle 0  F0ERV 3 Fluorescence value of amplified ERV3 sequence at cycle 0 f(k)  Fraction of cells that have k viruses in their cytoplasm  g  Gravitational force constant, cm/h2  g’  Gravitational force applied during transduction process, cm/h2  h  Height of virus-containing medium (VCM), cm  k  Number of viruses in cell cytoplasm  kB  Boltzman constant, cm2·g/h2·K  kb  Rate constant for binding of vector to cell surface, cm3/cell·h  Kb  Equilibrium rate constant for binding of vector to cell surface, cm3/cell·h  k-b  Rate constant for dissociation of vector from the cell surface, h–1  kde  Rate constant for extra-cellular decay of retroviruses, h–1  kdi  Rate constant for intracellular decay of retroviruses, h–1  ke  Rate constant for entry of retrovirus into cell cytoplasm, h–1 xiii  kn  Rate constant for transport of retroviral vector into the nucleus, h–1  nv  Average number of vectors inside virus-carrying cells free of integrated viruses, vectors/cell  p(k)  Probability of a cell carrying k viruses in its cytoplasm becoming virus-free during division  rc  Radius of target cell, cm  t  Time of exposure of cells to VCM, h  tf  Final time of exposure of cells to VCM, h  td  Doubling time of target cells, h  T  Temperature of medium containing retroviral vectors, K  u  Settling velocity of retroviral vector, cm/h  Vm  Concentration of viral vectors in the medium, vectors/cm3  Vc  Concentration of viral vectors in the cytoplasm of cells, vectors/cm2  Vf  Concentration of viral vectors in the cytoplasm of cells free of integrated viruses, vectors/cm2  Vi  Concentration of viral vectors integrated in cells’ genome, vectors/cm2  [VC] Concentration of virus-cell complexes, Xavg  Average target cell concentration used to estimate the binding rate constant, cells/cm3  z  Elevation above the target cells, cm  δ1  Fraction of virus-carrying cells that become virus-free due to intracellular degradation of virus  δ2  Fraction of virus-carrying cells that become virus-free due to cell division  η  Viscosity of medium containing retroviral vectors, g/cm·h  λ  Fraction of transduced cells in DNA extracted sample xiv  µ  Growth rate of target cells, h–1  ρm  Density of medium containing retroviral vectors, g/cm3  ρv  Density of retroviral vector, g/cm3  τ  Trafficking time of retroviral vector in host cell cytoplasm, h  xv  Ac kno wledge men ts I owe my sincere gratitude to my supervisors, Professor Bruce Bowen and Professor James Piret, for giving me the opportunity to work on this project.  Their continued  encouragement and valuable guidance during the research work and helpful suggestions throughout the thesis/manuscripts writing period is greatly appreciated. It has been the most exciting and rewarding phase of my career so far and, indeed, it has been a great pleasure and privilege to have worked with them. I thank my supervisory committee members, Dr. Eric Lagally and Dr. Fabio Rossi, for their feedback and suggestions on this work.  Funding from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canadian Institutes of Health Research (CIHR) through the Collaborative Health Research Projects Program was gratefully appreciated. The support from Stem Cell Technologies, Vancouver in the form of reagents and media was also highly valuable. Finally, I wish to acknowledge the University of British Columbia who provided partial financial support through a University Graduate Fellowship.  I am indebted to my many student colleagues for providing a stimulating and enjoyable environment in which to learn and grow. I am especially grateful to Pascal Beauchesne and Chris Sherwood for helping me to learn mammalian cell culture techniques during my initial period in the lab. The endless discussions with Pascal about our related research projects were always very helpful.  I am forever grateful to my wife Parimala for her understanding, endless patience and encouragement when it was most required. The encouragement and support from my wife, parents, sisters and in-laws has been a powerful source of inspiration and energy. xvi  1. Introduction and literature review Gene transfer into mammalian cells is an invaluable tool used to investigate the molecular mechanisms underlying diverse biological functions. Engineered gene transfer vector systems have enabled structure/function studies of selected mammalian gene expression products. Physical, chemical or viral-based delivery methods are used to greatly increase the normally low efficiency of naked DNA transfer into mammalian cells. Viruses are obligatory parasites that have evolved with elaborate mechanisms to invade and efficiently utilize the host cell machinery. They are natural gene transfer vehicles that carry the genetic information required for their replication in the host cell. Hence, virus-based vectors are very efficient in transferring genes into the cell compared to physical- or chemical-based DNA transfer schemes. Furthermore, some viral vectors (e.g. retroviral vectors) provide stable and longterm expression of a transgene by integrating their genomes into the host cells’ genomes. Retroviral vectors are prominently used for scientific research as well as clinicallyrelevant applications of gene transfer into mammalian cells, especially when stable and efficient integration of a transgene is required to pass on this genetic information to the cells’ progeny. Tracking of a cell type by stably inserting a marker gene in the cells’ genomes is one of the common applications of retroviral gene transfer in basic scientific research. Gene therapy is considered to be the ultimate clinically-relevant application of gene transfer. The basic science of gene therapy is to deliver a defined DNA sequence into specific cells of a patient either to replace a defective gene (for monogenic disorders), or to introduce a new gene for additional function (to treat cancer) or to prevent a disease (as a vaccine). Retroviral vectors are the second most widely used gene transfer vehicles in gene therapy clinical trials.  1  Retrovirus-mediated gene transfer into mammalian cells involves mass transport of vectors to the vicinity of a target cell and a series of extracellular and intracellular kinetic steps which lead to integration of the viral transgene into the host genome. The following sections present a brief literature review about the development, production and stability of retroviral vectors, as well as a thorough review of the mass transport and kinetic steps involved in the retroviral gene transfer process vectors and the available mathematical models for at least portions of this process. This chapter will then conclude with the thesis objectives and an outline of the work done to achieve these objectives.  1.1 Retroviruses and development of retroviral vectors The family of retroviruses is divided into the orthoretrovirus and spumaretrovirus subfamilies (Coffin et al. 1997). The well-known recombinant retroviruses that are used for gene transfer/gene therapy purposes are derived from gammaretroviruses or lentiviruses, both in the orthoretrovirus subfamily. The foamy virus, which is increasingly being investigated as another option, belongs to the spumaretrovirus subfamily. Retroviruses are enveloped RNA viruses, which convert their RNA genome into double-stranded DNA by reverse transcription inside the infected cells, with the exception of foamy viruses for which the reverse transcription occurs in the cells that produce the virus. Gammaretroviruses and lentiviruses consist of two identical copies of single-stranded RNA (typically 7-10 kb), while foamy viruses contain double-stranded DNA up to 13 kb. These genomic components, along with reverse transcriptase and integrase enzymes, are enclosed in a shell made of capsid proteins. Some lentiviruses are packaged with additional protein components inside the capsid (e.g., for HIV-1: vif, vpr, vpu, tat, rev and nef). The capsid shell is covered by a lipid membrane that is overlaid on a support made of matrix proteins. The lipid membrane is studded with envelope glycoproteins which mediate the attachment of the retrovirus to a specific membrane receptor 2  on the host cell surface followed by the release of the viral core into the cytoplasm. Hence, the envelope protein type determines the host range (or tropism) of the retroviral vectors. Gammaretroviruses served as a model for constructing the first engineered viral gene transfer vector (Mann et al. 1983). Normally, retroviruses replicate by cellular mechanisms since they integrate their genome into the host cell chromosome. The genome of a retroviral vector is made replication defective by replacing the protein coding sequences in the wild-type retroviral genome with the gene of interest (Miller 1990). Retroviral vectors are produced by helper cells, also called packaging cells.  The helper cells are obtained by transfecting  mammalian cells with plasmids that encode the necessary components for packaging the retroviral vectors. The present generation packaging cells are engineered to encode: (1) the replication-defective retroviral genome, (2) the gag and pol proteins, and (3) the envelope proteins from three separate cassettes of plasmids to avoid the production of replicationcompetent retroviral vectors. Self-inactivating (SIN) retroviral vectors, which are obtained by deleting the U3 (promoter/enhancer) region of the viral LTR, provide additional safety by eliminating the production of replication-competent vectors.  1.2 Production and stability of retroviral vectors The packaging cell lines for the production of gammaretroviral vectors were initially constructed based on mouse NIH-3T3 cell lines (Miller 1990). The presence of retroviral sequences in mouse cells could potentially result in the generation of replication-competent vectors.  Hence, interest has been focused on packaging cells based on other cell lines  especially of human origin (Davis et al. 1997; Patrick et al. 1999; Rigg et al. 1996). Also, the requirement for the scale-up production of retroviral vectors led to the development of suspension cell-based packaging cell lines (Chan et al. 2001; Ghani et al. 2007; Pizzato et al. 2001b). The stoichiometry of the three plasmids that are transfected into packaging cells to 3  produce retroviral vectors was found to have a strong influence on the titers (Yap et al. 2000). SIN retroviral vectors are difficult to produce at high titers because of deletions to their promoter and enhancer regions.  However, great progress has recently been made in  generating packaging cell lines for the production of safe and efficient retroviral vectors of all three types at high titers (Loew et al. 2009; Throm et al. 2009; Wiktorowicz et al. 2009). The titers of retroviral vectors during production are strongly influenced by their limited stability. Gammaretroviral vectors decay exponentially as a function of time with half-lives at 37oC reported to be in the range of 4-9 h (Chuck et al. 1996; Higashikawa and Chang 2001; Kaptein et al. 1997; Le Doux et al. 1999; Lee et al. 1998). The lenti- and foamy-viral vectors also are reported to decay with half-lives in the range of 4-9 h (Higashikawa and Chang 2001; Li et al. 2002b; Strang et al. 2004). Due to the short half-life of these vectors, the optimum harvest time after medium exchange was found to be 8-24 h for many packaging cell lines (Reeves et al. 2000). The inactivation phenomenon of retroviral vectors not only influences the titers but also the gene transfer efficiency. The thermal stability of retroviral vectors was found to be inversely proportional to the cholesterol level in their lipid membranes, which in turn depends on the type of producer cells and the temperature of production (Beer et al. 2003). A 10% reduction in the cholesterol content and a 90% enhancement of the half-life of retroviral vectors were obtained by increasing the osmolality of the medium from 335 to 450 mOsm/kg (Coroadinha et al. 2006a; Coroadinha et al. 2006b).  From these investigations, it was  speculated that excess cholesterol alters the structure of the membrane, making it more sensitive to environmental attack (Beer et al. 2003; Carmo et al. 2006). The loss of both gammaretrovirus and lentivirus infectivity was found to correlate with the loss of their ability to undergo the reverse transcription process (Carmo et al. 2009; Carmo et al. 2008). This may 4  be due to the loss of reverse transcriptase enzyme activity and/or the degradation of RNA by the reverse transcriptase (Casali et al. 2008). However, these findings could not explain the similarly rapid degradation of foamy-viral vectors, since they do not depend on reverse transcription after being produced by the packaging cells.  1.3 Gene transfer using retroviral vectors The process of retrovirus-mediated gene transfer involves several steps in series that are required to ensure successful transduction. The mechanistic steps of retroviral vector transfer from the extracellular environment to the nucleus of the target cell and the various physico-chemical and biological means used to overcome the rate-limiting barriers are discussed below. 1.3.1 Cell-retrovirus contact: Retroviruses have diameters in the range of 100-120 nm and are approximately spherical in shape. Their densities are reported to be in the range of 1.161.18 g/cm3 (Cimarelli et al. 2000; Fassati and Goff 1999; Loh and Matsuura 1981). Assuming a retrovirus to be a solid spherical colloidal particle with a diameter of ~110 nm and a density of ~1.17 g/cm3, the Stokes settling velocity and Stokes-Einstein diffusivity at 37oC can be calculated to be ~1.2 nm/s and ~2.4 x 10-4 cm2/h, respectively. Since retroviral vectors decay with an average half-life of ~6 h at 37oC, the mean distance that they can travel by diffusion during this period is only ~500 µm with a mean diffusive velocity of ~25 nm/s. Hence, the movement of such particles in a stationary medium is primarily governed by random Brownian motion (Figure 1.1(A)). The probability of a retroviral vector contacting the target cell in an active form will strongly depend on its position relative to the target cell at the beginning of the transduction process. The transduction efficiency of target cells placed on top of virus-producing cells was found to be much higher than that obtained by incubating the cells in a virus containing medium from the same producer cells, further illustrating that the 5  (A)  Retroviral vector  (B)  Mammalian cell  (C)  Magnetic nanoparticle  (D)  High density cationic polymer  Magnet  Figure 1.1: Schematic view of the protocols for transduction of mammalian cells with retroviral vectors: (A) transduction under standard gravity, or transduction by enhancing the settling velocity of retroviral vectors using (B) spinoculation, (C) magnetofection and (D) complexation of retroviral vectors with high density cationic polymers.  6  transduction is limited by the decay of these vectors during handling and storage (Bodine et al. 1991). This limitation in ex vivo processing can be overcome by driving the viral particles to the surface of the target cells through physical and chemical approaches. Enhancement of settling velocity: Centrifugation of cells with the vector-containing medium (spinoculation) results in increased sedimentation velocities and increased concentrations in the vicinity of the target cells (Figure 1.1(B)). A 4- to 18-fold increase in transduction efficiency with centrifugation at 32oC, depending on the titer and type of retroviral vectors, was reported (Bunnell et al. 1995; Kotani et al. 1994).  The impact of parameters like  temperature, speed and frequency of centrifugation has been investigated in an attempt to optimize the transduction of hematopoietic stem cells and T-lymphocytes (Ayuk et al. 1999; Bahnson et al. 1995; Lamana et al. 2001; Quintas-Cardama et al. 2007). Spinoculation is a widely used method for scientific and clinically-relevant retroviral transduction of hematopoietic stem cells and lymphocytes (Bunnell et al. 1995; Millington et al. 2009; Sanyal and Schuening 1999; Tonks et al. 2005; Yang et al. 2008). Magnetofection was also reported to be an attractive approach to enhance transduction (Figure 1.1(C)).  In this case, the  retroviral vectors are associated with magnetic nanoparticles and are driven towards the target cells by a magnetic field (Haim et al. 2005; Scherer et al. 2002). A 20-fold enhancement in transduction by magnetofection relative to that obtained using polybrene was reported (Scherer et al. 2002). It was also reported that charged polymers of high molecular weight and charged polymer complexes can enhance transduction by aggregating the virus particles and hence increasing their sedimentation velocity (Figure 1.1(D)) (Davis et al. 2004; Le Doux et al. 2001). Induction of medium flow: The limitation due to the low Brownian diffusion coefficients of retroviral vectors can be overcome by adding a convective component to the mass transfer 7  (Chuck et al. 1996). For example, (Chuck and Palsson 1996a) produced a relative motion between the vector-containing medium and the cells by causing the medium to flow through a layer of cells placed on a micro-filtration membrane.  However, the enhancement in  transduction was also found to be dependent on the virus adsorption characteristics of the membrane (Chuck and Palsson 1996b). A 2- to 4-fold enhancement of transduction efficiency was obtained in the presence of an acoustic standing wave field thought to be due to the micro-streaming of the virus-containing medium between nodal planes containing the cells (Lee and Peng 2005; Lee et al. 2005). Acoustic micro-streaming is a circular motion of fluid between pressure node planes that could increase the virus-cell encounter frequency. 1.3.2 Binding to cell surface: The transduction steps followed by the retroviral vectors are presented in Figure 1.2. Retroviral vectors and cells have surfaces that bear net negative charges. When a viral particle reaches the surface of a target cell, it encounters energy barriers imposed by electrostatic repulsion, steric-hindrance and hydration forces. Retroviral vectors with either non-specific envelope proteins or with no envelope proteins were bound to cells at the same rate as vectors with cell receptor-specific proteins, indicating that a receptorenvelope interaction is not required for initial binding (Pizzato et al. 2001a; Pizzato et al. 1999). This initial adsorption is likely mediated by abundant cellular surface components, such as glycosaminoglycans or proteoglycans, and not by the relatively few specific vector receptors. Also, retroviral vectors are packaged with heparan sulfate proteoglycans in their membrane (Kureishy et al. 2006; Lei et al. 2002). The initial binding of the amphotropic murine leukemia virus to TE671 cells was shown to be mediated by virus-associated heparan sulfate proteoglycans rather than by envelope glycoproteins (Kureishy et al. 2006). Various cationic polymers can enhance the transduction efficiency 2- to 40-fold by neutralizing the charge on the membranes and thus overcoming the electrostatic repulsion 8  Lentivirus  Gammaretrovirus  Foamy virus  1 2 2  2 3 4  5  3  4  5  3  6  4  6  7  7  Cytoplasm 8  8 Nucleus  Figure 1.2: Schematic view of the transduction pathways for the three types of retroviral vectors. (1) Reversible binding to the cell surface; (2) Interaction with receptors and movement to the entry points; (3) Receptor-mediated uptake by the cell (for gammaretrovirus and foamy virus by endocytosis, for lentivirus by fusion of membranes on the cell surface); (4) Transport of retroviral vectors to the vicinity of the microtubule network and uncoating of matrix proteins; (5) Reverse transcription of retroviral genome for gammaretrovirus and lentivirus; (6) Transport to the microtubule organization centres along microtubules; (7) Transport into the nucleus (for gammaretrovirus and foamy virus during mitosis, for lentivirus active transport through nuclear pores); and (8) Integration of retroviral genome into the cell chromosome. 9  between the virus and the cell (Cornetta and Anderson 1989; Davis et al. 2004; Landazuri and Le Doux 2004). An optimum concentration of 5-12 µg/mL of these cationic polymers has been suggested to maximize transduction (Cornetta and Anderson 1989; Seitz et al. 1998). However, this optimum concentration depends on the concentration of anionic species, especially from the medium serum (Andreadis and Palsson 1997; Davis et al. 2004). The adsorption of these retroviral vectors onto the surface of target cells in the presence of polybrene was found to be an irreversible process (Davis et al. 2002). This irreversible binding of retroviral vectors to the target cell surface in the presence of cationic polymers is mediated by viral-membrane associated heparan sulfate (Lei et al. 2002). A major improvement in retroviral gene transfer protocols came when the fibronectin fragment CH-296 was introduced as a significant enhancer of retroviral vector transduction of hematopoietic stem cells (Hanenberg et al. 1996). The colocalization of retroviral vectors and target cells occurs through irreversible binding of the retroviral vectors to fibronectin-coated dishes, mediated by viral-membrane associated heparan sulfate (Lei et al. 2002). The presence of fibronectin was also found to preserve the repopulating potential of hematopoietic stem cells, possibly by engaging cell surface receptors (Dao et al. 1998). The recombinant CH-296, also called Retronectin®, has become an attractive additive to enhance retroviral vector transduction and has been used in many scientific and clinically-relevant retroviral gene transfer protocols. Cationic lipids (e.g., Lipofectamine and Lipofectin) can enhance the retroviral gene transfer efficiency by 10- to 100-fold depending on the type of lipids and the vector-cell system, reaching up to ~95% transduction (Hodgson and Solaiman 1996; Martin et al. 1999; Porter et al. 1998; Song et al. 2000; Themis et al. 1998). It was demonstrated that the main mechanisms are the formation of virus-liposome complexes, and enhancement of the flux of 10  viruses delivered to the cell surface by the cationic lipids modulating the repulsive charge force shield between the viruses and the cells. Cationic lipid-mediated retroviral gene transfer can be enhanced a further 2- to 4-fold when used in combination with physical means such as centrifugation or the flow-through process to increase the delivery of virus-liposome complexes to the surfaces of the target cells (Liu et al. 2000; Swaney et al. 1997). 1.3.3 Receptor-mediated entry into the cell cytoplasm: Though the initial binding of a retrovirus to a target cell surface occurs independently of the envelope glycoproteins, the interaction of the envelope proteins with their specific receptors on the cell surface is absolutely necessary to initiate the infection process. The expression of retroviral-specific receptors and hence the entry of these vectors was verified to be independent of the cell cycle (Goulaouic et al. 1994). The list of receptors specific to a retroviral envelope glycoprotein is presented in Table 1.1. Various retroviral vectors have been successfully pseudotyped with other envelope glycoproteins for more efficient transduction. A remarkable example is that retroviral vectors pseudotyped with a glycoprotein of the vesicular stomatitis virus (VSV-G) consistently provide high transduction efficiency since they directly target the phospholipid components of the cell membrane without the need for a receptor. Though pseudotyping of foamy-viral vectors with other envelopes has been unsuccessful (Pietschmann et al. 1999), it may not be essential since these vectors already exhibit broad target tropism (Russell and Miller 1996). Chimeric envelope proteins of the foamy virus have been successfully used to pseudotype murine leukemia viral vectors (Lindemann et al. 1997). However, knowledge about how these retroviruses behave and interact with their specific receptors on the cell surface is limited. Disruption of the actin cytoskeleton blocked the infection process of MLV following its binding to the cell surface indicating that the actin network is involved in the post-binding events, probably the clustering of receptors near the bound retrovirus (Kizhatil 11  and Albritton 1997). The recruitment of co-receptors for HIV-1 subsequent to its binding to the CD4 receptor was also found to be mediated by the actin network of the host cell (Iyengar et al. 1998).  High resolution microscopy visualization of retroviral vectors on live cell  surfaces revealed that the vectors with VSV-G, MLV or HIV-1 envelopes exhibit actinTable 1.1: Retroviral envelope glycoproteins, targeted receptors and their entry pathways. Virus  Receptor(s)  Entry mechanism  Moloney Murine Leukemia Virus (MMLV)  MCAT-1  pH-independent endocytosis  Amphotropic Murine Leukemia Virus (AMLV)  Pit-2  pH-independent endocytosis  Gibbon Ape Leukemia Virus (GALV)  Pit-1  ?  10A1 Murine Leukemia Virus (10A1-MLV)  Pit-1 or Pit-2  ?  Human Immunodeficiency Virus type-1 (HIV-1)  CD4 (primary) CXCR4 or CCR5 (secondary)  Fusion on cell surface  Human Foamy Virus (HFV)  ?  pH-dependent endocytosis  Vesicular Stomatitis Virus# (VSV)  Believed to bind directly to phospholipid components  pH-dependent endocytosis  #  Not a retrovirus but retroviral vectors are pseudotyped with its envelope  dependent directed movement, mediated by myosin-II, towards the hotspots of entry (Lehmann et al. 2005). Recruitment of receptors for MLV and HIV-1 or clathrin for VSV-G may occur prior to or during this movement. In the next step, the surface glycoprotein subunit interacts with the specific receptor on the target cell through a receptor binding domain (RBD) and induces conformal changes 12  mediated by the transmembrane portion of the envelope protein. This results in the exposure of the retroviral vector fusion peptide to the target cell lipid bilayer, leading to the fusion of their membranes. The fusion may occur directly at the cell surface or after internalization within endosomes. The retroviral vectors that fuse directly to the cell surface have to cross the dense actin network, whereas endocytosis can naturally bypass this actin network barrier. HIV-1 fuses directly at the cell surface (Mcclure et al. 1988) utilizing its Nef (negative regulatory factor) to cross the actin network barrier by remodeling the actin filaments (Campbell et al. 2004). This pH-dependent endocytosis process involves the endocytic vesicle internalization of the virus, and then acidification of the endocytic vesicles leads to fusion of the viral membrane with the endosomal membrane and release of the viral core into the cytoplasm.  Retroviral vectors with the VSV-G envelope enter into the cells through a  clathrin-mediated endocytic process (Sun et al. 2005; White et al. 1981). Foamy viruses were also found to utilize a pH-dependent endocytic pathway to gain entry into the cytoplasm but by a different mechanism than VSV-G (Picard-Maureau et al. 2003). The insensitivity to lysosomotropic agents towards infection of several gammaretroviruses in earlier studies suggested that they enter by direct fusion on the plasma membrane (Mcclure et al. 1990). However, accumulating evidence indicates that murine leukemia retroviruses utilize these pHindependent endocytosis pathways mediated by lipid-raft micro-domains (Beer et al. 2005; Lee et al. 1999). This is consistent with the fact that gammaretroviruses lack Nef to cross the actin network barrier. However, it was reported that the entry of MoMLV was by a pHdependent endocytosis process into NIH-3T3 cells and by a pH-independent process into RatXC sarcoma cells, suggesting that cell-specific components can play a role in determining the type of entry (Kizhatil and Albritton 1997).  13  1.3.4 Trafficking inside the cytoplasm: Once inside the cytoplasm, retroviral cores utilize actin and microtubule networks to reach the microtubule organizing centre (MTOC), also called the centrosome, where nuclear entry is initiated. Live microscopy images revealed a short-range transport of HIV-1 cores along the cell periphery indicating that they utilize the actin cytoskeleton to move closer to a microtubule (Bukrinskaya et al. 1998; McDonald et al. 2002). On the other hand, retroviruses that bypass the actin network by the endocytic route may interact with microtubules through cellular proteins. This is supported by the finding that IQGAP1, a microtubule interacting protein, appears to bind with the matrix of the MLV core and contribute to productive infections (Leung et al. 2006). It has been shown that HIV-1 and foamy-virus cores utilize dynein and dynactin motor proteins to move along the microtubule and reach the MTOC (McDonald et al. 2002; Petit et al. 2003; Saib et al. 1997). The reverse transcription of gammaretroviral and lentiviral RNA can occur prior to or during trafficking along the microtubules. The viral components that are released into the cell cytoplasm arrange into a structure, commonly referred to as the reverse transcription complex (RTC). Analysis of cytoplasmic extracts of MLV and HIV-1 vectors revealed at least two RTC species with different densities, of which only the one with the highest density is competent for reverse transcription while the others may be intermediate or defective species (Fassati and Goff 1999; Fassati and Goff 2001). The reverse transcription of retroviral RNA is completely blocked in quiescent cells (G0 phase) indicating that the synthesis of viral DNA occurs only during an active cell cycle (Goulaouic et al. 1994; Harel et al. 1981; Varmus et al. 1977). Synthesized retroviral DNA was found in all the cells arrested at different points of their normal cell cycle thus confirming that the reverse transcription of retroviral RNA can occur in all phases of the cell cycle (Roe et al. 1993). The availability of cellular nucleotides rather than the arrest point in the host cell 14  cycle is thought to be the key factor controlling the reverse transcription of viral RNA (Goulaouic et al. 1994). This is supported by the observation that medium supplementation with nucleosides of G0-resting lymphocytes resulted in the production of reverse transcribed gammaretroviral or lentiviral DNA (Korin and Zack 1999; Pieroni et al. 1999). MLV and HIV-1 full-length reverse-transcribed DNA molecules were found to appear in cytoplasmic extracts at 7 h after vector entry (Fassati and Goff 1999; Fassati and Goff 2001). This is in agreement with the reported retroviral vector reverse transcription within 6-12 h, depending on the availability of nucleotides (Coffin et al. 1997). Gammaretroviral and lentiviral vectors are packaged with two identical copies of RNA. But one RNA copy was found to be sufficient for the synthesis of one proviral DNA (Jones et al. 1994). Also, only one DNA copy is produced even though these vectors contain two RNA copies (Hu and Temin 1990; Panganiban and Fiore 1988). 1.3.5 Nuclear transport of pre-integration complex:  The nuclear accumulation of  gammaretro- and foamy-viral pre-integration complexes (PICs) was found to occur only when cells pass through the mitotic phase indicating that the dissolution of the nuclear membrane is required for transport of their PICs into the nucleus (Roe et al. 1993; Trobridge and Russell 2004). On the other hand, passage of cells through the mitotic phase was not found to be essential for the nuclear transport of lentiviral PICs (Lewis and Emerman 1994). It was reported earlier that the presence of nuclear localization signals in lentiviral proteins facilitates the transport of PICs into the nucleus (Bouyac-Bertoia et al. 2001). However, lentiviral vectors with mutations in all the known NLSs are still able to transport PICs into the nucleus of non-dividing cells (Yamashita and Emerman 2005). In addition, though foamy-viral PICs contain at least three proteins with NLSs (Imrich et al. 2000), they cannot cross the nuclear membrane in growth-arrested cells (Trobridge and Russell 2004). These findings suggest that 15  the presence of NLSs in the retroviral components is not sufficient or essential for the transport of their PICs through the nuclear membrane. Lentiviral vectors with MLV capsids were unable to enter into the nucleus of non-dividing cells, indicating that capsid proteins are a dominant factor in the differences between the nuclear transport ability of these vectors (Yamashita and Emerman 2004). The PIC of gammaretroviruses containing synthesized DNA was found to be associated with most of their capsid proteins (Bowerman et al. 1989; Fassati and Goff 1999), unlike lentiviruses that lose their capsid proteins completely after entering the cell (Bukrinsky et al. 1993; Khiytani and Dimmock 2002; Miller et al. 1997). The nuclear transport of the lentiviral DNA in non-dividing lymphocytes proceeded only when these cells were stimulated with cytokines indicating that cellular functions are required for a step preceding the nuclear transport (Korin and Zack 1998; Unutmaz et al. 1999). A recent study suggests that the targeting of incoming viral capsids by cellular restriction factors determines the ability of HIV-1 entry into the nucleus of non-dividing cells (Yamashita and Emerman 2009). These findings indicate that the uncoating of capsid proteins from PICs can be a determining factor for the nuclear transport of retroviral PICs. 1.3.6 Integration of viral genome:  Integration of retroviral DNA into the host cell  chromosomal DNA is an essential step of the retrovirus life cycle. The reverse-transcribed retroviral DNA is a blunt-ended product and is processed by the integrase enzyme by removing the 2 nucleotides at each 3’-end to expose CA dinucleotides (Roth et al. 1989). The DNA integration is carried out by a nucleoprotein complex, in which the processed retroviral DNA ends are stably associated by the integrase (Li et al. 2006; Wei et al. 1997). The integration of processed retroviral DNA occurs in two steps. The first step is the strand transfer, catalyzed by integrase, in which the host DNA is cleaved at a specific site and the processed 3’-ends of retroviral DNA are ligated to the strands on opposite sides of the host 16  DNA (Bushman et al. 1990; Craigie et al. 1990; Engelman et al. 1991; Pahl and Flugel 1993). This step is initiated at a rapid rate immediately upon entry of the retroviral DNA into the nucleus provided that the DNA ends are processed. The second step is the gap repair which involves joining the 5’-ends of the retroviral DNA to the remaining ends of the host chromosomal DNA. A delay of less than 1 h between the joining of the 3’-ends and 5’-ends was observed, indicating that the overall integration is indeed a rapid process (Roe et al. 1997). Though the integration of a retroviral vector into the host genome is a desirable property for long-term stable transgene expression, the integration near proto-oncogenes can result in the transformation of cells by insertional mutagenesis. This has been observed in gene therapy clinical trials as well as laboratory experiments that have caused leukemia (Hacein-Bey-Abina et al. 2003; Li et al. 2002a; Schwarzwaelder et al. 2005). The integration site of retroviral vectors is a determining factor for causing insertional mutagenesis. Murine leukemia viruses tend to integrate near the transcription start regions thus increasing the possibility of activating proto-oncogenes (Wu et al. 2003). Since HIV-1 tends to integrate within active genes, this may alter the function of these genes (Schroder et al. 2002). On the other hand, foamy viruses do not tend to integrate in either transcription start sites or within the genes (Trobridge et al. 2006). Self-inactivating (SIN) retroviral vectors, with deleted promoter and enhancer regions, were designed to avoid generation of replication-competent vectors (Yu et al. 1986). The elimination of promoter and enhancer regions from both LTRs may also provide safer gene transfer for human gene therapy. But, some findings suggest that SIN retroviral vectors are not effective in completely eliminating the activation of oncogenes (Bosticardo et al. 2009). Integration of retroviral DNA at a specific site in the human chromosome is an attractive 17  approach for eliminating the risk of insertional oncogenesis. Recently, retroviral vectors have been designed with sequence-specific DNA-binding proteins for site-specific integration of retroviral DNA (Ciuffi et al. 2006; Ferris et al. 2010; Su et al. 2009). The risk of insertional mutagenesis is greater with increased numbers of integrated vector copies per cell. Thus, the risk of insertional mutagenesis can be increased by attempting to improve the transduction efficiency (Kustikova et al. 2003). The toxicity of multiple vector insertions resulting in the apoptosis of transduced cells at a high dosage of retroviral vectors has also been observed (Arai et al. 1999). On the other hand, there is a need to have a sufficient transduction level to obtain the required protein expression.  1.4 Mathematical modeling of retrovirus-mediated gene transfer There have been relatively few attempts to model the retroviral transduction process. A two-dimensional model for retroviral transduction that includes cell-cycle dynamics but limited extracellular and intracellular kinetics was developed to investigate the effect of intracellular decay on transduction efficiency (Andreadis and Palsson 1996). Their numerical analysis showed that the transduction efficiency increased with an increase of viral titer until a plateau was reached. The maximum transduction efficiency attained was governed by the intracellular half-life of the retroviral vectors. Increasing the rate of viral entry did not increase the maximum transduction efficiency but did allow that maximum value to be obtained with lower virus-to-cell ratios. Simulation of cell synchronization showed that the cell-cycle dependence of retroviral gene transfer was important only when the intracellular half-life was low compared to the doubling time of the target cells. This model was used to design experiments for quantifying the intracellular half-life of retroviral vectors, which, for MoMLV vectors in NIH-3T3 cells, was estimated to be ~6.5 h, similar to the extracellular half-life for this vector (Andreadis et al. 1997). In order to address the relationship between 18  the intracellular kinetics of the retroviral vectors and the cell-cycle dynamics, this model had to be two-dimensional, thus making it computationally intensive. A model for the diffusion of virus particles onto a monolayer of target cells with instantaneous irreversible adsorption (Valentine and Allison 1959), was modified by incorporating the decay kinetics of the retroviral vectors in the extracellular medium (Andreadis et al. 2000). Their simulation results showed that many active viral particles are needed for a single successful gene transfer event because of the decay and low diffusivity of retroviral vectors in the medium. These factors combine to limit the effective height of the virus-containing medium (VCM) above the target cells. Simulation results revealed that there is a critical depth of VCM beyond which the number of adsorbed active viral particles remains relatively unchanged. This critical depth depends on the half-life of the vectors and the transduction time.  Excess volumes of VCM beyond this critical depth can lead to  underestimation of the viral titer (CFU/mL). The measured effect of the volume of VCM on the CFU assay was in good agreement with the model predictions. The model assumed that the surface at the end of the diffusion path (i.e., the bottom of the culture dish) is entirely covered by a monolayer of cells. In conventional transduction protocols, cells are maintained at sub-confluent conditions to allow the growth of cells (i.e., progression through the mitotic phase) as is required for the integration of the viral genome. To address this situation, a model originally designed to determine the flux of current at a stationary disk electrode in an infinite medium (Shoup and Szabo 1982), was applied to this system (Andreadis et al. 2000). The initial concentration of infectious retroviral vectors (infectious vectors/mL) calculated from the model was found to be independent of the target cell number in contrast to the titer (CFU/mL) which is strongly dependent on this number. The relative transduction efficiency, an empirical 19  factor introduced to handle the post-adsorption steps, can be used to compare the efficiency of one cell type relative to others.  The number of adsorbed active viral particles per cell  calculated from the model was found to be more appropriate than the more commonly used measure, multiplicity of infection (MOI). The titer estimated using the model is accurate for each retrovirus-cell system. However, different cell types will have different susceptibilities to different types of retroviral vectors, and thus the MOI estimation of the titer will depend on the cell-retrovirus combination. All of the above models assumed instantaneous adsorption of viruses on the cell surface, which is not the case for retroviral vectors. A model which involves not only diffusion and extracellular deactivation of retroviral vectors but also explicitly includes the adsorption process was introduced by (Kwon and Peng 2002). Integration of experimental data at different polybrene concentrations with the model resulted in a log-log relationship between the adsorption rate constant and the polybrene concentration, while giving the same initial vector concentration for different polybrene concentrations. Also, based on experimental data obtained using different viral suspensions at different decay times, the model yielded different initial concentrations inversely related to the decay times. The model estimated different adsorption rates for vectors bearing different types of envelopes, with the higher value for the VSV-G envelope in agreement with its higher transduction efficiency. By using the same model, it was found that the efficiency of an untreated viral suspension was higher than those of virus-containing media subjected to ultracentrifugation or separation using the sucrose gradient method (Kwon et al. 2003). These results suggested that the loss of envelope proteins in a VCM subjected to either ultracentrifugation or sucrose gradient purification resulted in lower transduction rates. They concluded that the initial infectious retrovirus concentration obtained from this mathematical model is much more 20  appropriate and more accurate than the commonly used titer. The transduction rate constant is a parameter that needs to adapt to the diversity of experimental systems such as different retrovirus-cell combinations, the presence or absence of polycations, and changes that result from the treatment of the viral solution by different concentration and/or purification methods. However, the assumption that the transduction rate constant properly accounts for all processes occurring at the cell surface as well as inside the cell make the model unreliable for accurate estimates of titer.  1.5 Thesis objectives From the above literature review, it is evident that the retrovirus-mediated gene transfer process is a complex biological phenomenon involving the mass transport of vectors in the virus-containing medium and a series of extracellular and intracellular kinetic pathways. Engineering modeling of this complex process can help us obtain a mechanistic understanding of the various sub-processes involved and provide insights for optimizing gene transfer protocols using retroviral vectors. Though there have been a few attempts to model the retrovirus-mediated gene transfer process, the models are generally restricted to extracellular steps and cannot handle the convective mass transport of vectors. However, most of the present-day retroviral transduction protocols utilize some sort of convective approach to enhance the mass transfer of vectors to the vicinity of the target cells. Also, the inclusion in the model of the important intracellular kinetic steps like reverse transcription, uncoating, nuclear transport and intracellular vector degradation may be essential in order to reliably predict the overall effectiveness of gene transfer. In addition, current models have made no attempt to include factors like the entry of multiple vectors into a cell and the sharing of these vectors during division which can influence both the transduction efficiency and the number of integrated viral copies per cell. A robust mathematical model should be able to predict both 21  quantities, as the parameters important to each protocol must be selected not only to maximize the transduction efficiency but also to maintain the copy number in a desirable range. Thus, the model will have its greatest utility only if it is designed to handle all the above-mentioned factors. The overall goal of my thesis is, therefore, to develop a comprehensive and generalized mathematical model of the retrovirus-mediated gene transfer process which is applicable to the complete family of retroviruses. The model should incorporate the convective mass transport of retroviral vectors and include all the essential extracellular and intracellular kinetic steps. Such a model can then be used to identify the rate-limiting factors in the retroviral transduction process and provide a means of testing methods to accelerate these limiting steps. In Chapter 2 which follows, a mathematical model which includes diffusive and convective mass transport as well as all of the essential rate-limiting steps for retroviral gene transfer is developed and experimentally validated. In Chapter 3, the interactions between retroviruses and the target cell surface, including their binding to, dissociation from and entry into a mammalian cell, were investigated. The kinetic rates were quantified and the mechanism of a retroviral entry was investigated. This allowed us to extend the model to include a more elaborate description of these interaction kinetics, and thereby expand its applicability. This modified model was then used in Chapter 4 to investigate the effect of various kinetic and mass transport parameters on gene transfer efficiency and to compare the performances of the three subfamilies of retroviral vectors: namely, the gammaretro-, lenti- and foamy-viral vectors.  Finally, the main conclusions of the thesis are summarized and some  recommendations for future work are made in Chapter 5.  22  2. Mat hemati cal mo del for retroviral gene transfer Recombinant retroviruses have been widely used for scientific research as well as gene therapy purposes because of their relatively stable, chromosomally-integrated gene transfer and expression (Edelstein et al. 2007). However, due to the low diffusivities (~2×10–4 cm2/h) and short half-lives (4-9 h) of retroviral vectors, their ability to transfer, in the active form, from a bulk suspension to the target cell surface is very limited (Chuck et al. 1996; Kaptein et al. 1997; Le Doux et al. 1999). Thus, in conventional protocols where cells at the bottom of a culture dish are exposed to a suspension of retroviruses, essentially only vectors within ~500 µm have the ability to encounter the target cells before they become inactive (Chuck et al. 1996). In addition, the repulsive forces due to the net negative charge on both the retroviral envelope and the target cell membrane result in low binding efficiencies. As a consequence of these limitations, often only a small fraction of target cells can be transduced, especially when there are low titers of the retrovirus. Various improved transduction methods have been developed using several physicochemical approaches. These include enhancement of the settling velocity of retroviral vectors by centrifugation (Bahnson et al. 1995; Kotani et al. 1994), aggregation (Davis et al. 2004) or magnetically controlled attraction (Scherer et al. 2002), convective flow of a virus-containing medium through a membrane supporting cells (Chuck and Palsson 1996a), addition of cationic polymers to increase the binding of viruses to cells (Coelen et al. 1983; Cornetta and Anderson 1989) and colocalization of viruses and cells by precoating surfaces with fibronectin (Hanenberg et al. 1996).  However, increasing the transduction efficiency results in a  corresponding increase in the integrated virus copy number of the transduced cells (Arai et al. 1999; Kustikova et al. 2003; Wahlers et al. 2001). 23  A major problem for gene therapy applications is that retroviral insertional mutagenesis can result in oncogene activation leading to the induction of leukemia (Baum et al. 2003), with the risk increasing as the integrated virus copy number rises (Moolten and Cupples 1992).  Also, increasing the number of retrovirus integrations can enhance the  apoptosis of transduced cells (Arai et al. 1999). Furthermore, high integrated copy numbers of, for instance, a fluorescent reporter gene can influence the outcome of functional studies by elevating transgene expression (Wahlers et al. 2001) and variable transgene copy numbers can complicate the analysis of single cell responses in scientific studies.  Hence, retroviral  transduction methods require optimization not only to maximize the transduction efficiencies but also to deliver a narrow range of integrated copies per cell. A quantitative understanding of the process by which cells are transduced using retroviral vectors should provide insights to assist the optimization of this process. We have improved upon previous mathematical models that focussed on subsets of the overall retroviral transduction process, such as the extracellular transport and binding of viral vectors to target cells (Andreadis et al. 2000; Kwon and Peng 2002), by incorporating the intracellular rate-limiting steps as well as by adding other extracellular aspects. Andreadis et al. (2000) assumed that the binding of retroviral vectors to cells is instantaneous and the process is entirely governed by diffusion, while Kwon and Peng (2002) considered the viruscontaining medium above the cells to be a semi-infinite space. Also, neither of these models accounted for the convection of retroviral vectors that occurs, for example, during centrifugation-based transduction protocols. A mathematical model with limited intracellular kinetics was presented to address the effects of intracellular inactivation of retroviral vectors (Andreadis and Palsson 1996). Structured models have been developed for the infection dynamics of other enveloped viruses like the Semliki Forest virus and baculovirus (Dee et al. 24  1995; Dee and Shuler 1997). Overall, no mathematical model of the retroviral transduction process has been reported that incorporates all of the extra- and intracellular rate-limiting steps. Also, no attempt has been made to quantify the integrated copy number and relate it to the transduction efficiency. The primary focus of this chapter, therefore, is to develop and test a generalized model for the retroviral transduction process that can predict not only the transduction efficiency but also the integrated copy number. The model applies to the standard geometrical arrangement where a homogeneous layer of cells at the bottom of a culture dish is incubated with an overlying suspension of retroviral vectors treated as uniformly-sized spheres. The model accounts for extracellular viral diffusion and convection, decay and irreversible binding to the cell surface, as well as the essential intracellular steps: intracellular decay, reverse transcription, transport of the preintegration complex to the vicinity of the nucleus, and its import into the nucleus. By using population balances that incorporate the kinetics of multiple viral entries into cells, the model is able to calculate not only the transduction efficiency but also the integrated copy number. The model parameters are determined experimentally and the model is validated with copy number as well as transduction data obtained by means of both static and centrifugation-based transduction protocols.  2.1 Model formulation The model system is shown in Figure 2.1(A). It consists of a layer of target cells, assumed to be from a homogeneous population, lying at the bottom of a culture dish in contact with medium of depth h containing a suspension of retroviruses having an initially uniform concentration. As well as undergoing Brownian diffusion and decay with time, the viral particles are allowed to settle, either under normal gravity (conventional static protocol) or 25  Figure 2.1 A: Schematic view of the retroviral transduction process in which mammalian cells are incubated with a medium containing retroviral vectors in a tissue culture dish. B: Overview of the steps of the retroviral vector transduction process. (1) Binding of retrovirus to cell surface receptor. (2) Receptor-mediated release of viral capsid into cell cytoplasm. (3) Reverse transcription of retroviral RNA to form DNA (for gammaretroviruses and lentiviruses). (4) Transport of viral DNA along microtubule (MT) to the microtubule organizing center (MOC). (5) Degradation of retroviral vector by host cell restriction factors, if present.  (6a) Import of the retroviral DNA into nucleus when nuclear membrane  disassembles during mitosis (for gammaretroviruses and foamy viruses). (6b) Import of retroviral DNA into the nucleus by active transport through nuclear membrane (for lentiviruses). (7) Integration of retroviral DNA into the cellular chromosome.  26  under augmented forces (centrifugation-based protocol) to the cell surface where they irreversibly bind. The retroviral vector bound to a receptor on the cell surface then follows the sequence of steps shown in Figure 2.1(B), as it makes its way through the cell membrane and eventually into the cell nucleus where it integrates with the cell genome. These intracellular steps can vary depending on the type of retrovirus selected to transduce the gene of interest. The mathematical model presented below incorporates the kinetics of the essential ratelimiting steps of the overall process as follows: 2.1.1 Extracellular transport, decay and binding: Assuming there is no hindered diffusion or hindered convection, the rate of change of the concentration of active retroviral vectors in the virus-containing medium, Vm = Vm(t,z), due to mass transport by diffusion and convection, as well as decay in the medium can be represented by ∂Vm ∂Vm ∂ 2Vm +u = Dv − kdeVm ∂t ∂z ∂z 2  (2.1)  where t is time, z is the elevation above the target cells, kde is the decay rate constant of retroviral vectors in the extracellular medium, Dv is their diffusion coefficient, and u is their velocity due to an external force. At the upper surface of the medium (z = h), the net flux of retroviral vectors must be zero, i.e., − Dv  ∂Vm 0. + uVm = ∂z  (2.2)  At the bottom of the culture dish (z = 0), the retroviral vectors are removed from the medium by adsorbing to the target cells. Under these circumstances, the flux of retroviral vectors at the bottom of the culture dish is given by the following equation: − Dv  ∂Vm + uVm = −kbVmCt + k− b [VC ] ∂z  (2.3)  27  where kb and k-b are the binding and dissociation rate constants, respectively, Ct is the total target cell density on the culture surface, which is obtained as the sum of all the cell populations. A retrovirus that transfers to the vicinity of a cell can bind non-specifically to the cell surface through a reversible physical bond until it interacts with a specific receptor where it binds irreversibly (Figure 2.1(B), step 1). At least for the moderate values of viral titer considered here, the number of sites for initial binding of viruses on cell surface to form viruscell complexes is not limiting. Assuming that the bound viruses decay at the same rate as free viruses suspended in the medium, the rate of change in the concentration of virus-cell complexes, [VC], is given by d [VC ] = kbVmCt − k− b [VC ] − ke [VC ] − kde [VC ] dt  (2.4)  where ke is the entry rate of vectors into the cells. Assuming quasi-stady state of the processes occurring on the cells’ surface, i.e.  d [VC ] ≈ 0 , the boundary condition in equation (2.3) can be dt  reformulated as  − Dv  ∂Vm + uVm = − K bVmCt ∂z  (2.5)  where Kb is the net binding and entry rate constant given as follows: Kb =  kb  k− b  1 +   ( ke + kde )   (2.6)  The time-dependent population balance of target cells that remain free of viruses is given by dC f dt  = − K bC f Vm (t , 0) + δ1kdi Cc + δ 2 µ Cc + µ C f  (2.7)  28  where Cf is the concentration of virus-free cells on the culture dish surface, Cc is the concentration of virus-carrying cells that have at least one virus in their cytoplasm, kdi is the rate constant for intracellular degradation of retroviral vectors, δ1 is the fraction of singlevirus-carrying cells (these become virus-free cells when the viral genome decays), δ2 is the fraction of virus-carrying cells that become virus-free during cell division (since all the internalized viruses in the cytoplasm may be retained by only one daughter cell during division), and µ is the growth rate of the target cells. 2.1.2 Internalization and intracellular trafficking: The retrovirus bound to the cell surface receptor releases the viral core into the cell cytoplasm either by endocytosis or by membrane fusion (Figure 2.1(B), step 2). This internalization of the viral core is a rapid process which is completed in 30-60 min (Kolokoltsov and Davey 2004; Narayan et al. 2003) and, hence, is not considered to be rate limiting. Once in the cytoplasm, the viral core undergoes a structural rearrangement to convert its RNA to DNA through a reverse transcription process mediated by the reverse transcriptase enzyme (Figure 2.1(B), step 3). One retroviral RNA is sufficient for the synthesis of one proviral DNA (Jones et al. 1994), and only one DNA copy is produced from the two copies of retroviral RNA contained in each retrovirus (Hu and Temin 1990; Panganiban and Fiore 1988).  The pre-integration complex (PIC) is then transported by  cellular cargo proteins along the microtubules to the nuclear membrane (McDonald et al. 2002) (Figure 2.1(B), step 4). Since the release of the viral core into the cell cytoplasm is not a rate-limiting step, the rate of change of the viral vectors inside the cytoplasm of the total cell population is given by dVc = K bCtVm (t , 0) − kdiVc − knVc (t −τ ) dt  (2.8)  29  where Vc is the concentration of the viral vectors inside the cytoplasm of all cells, kn is the rate constant for nuclear import of the PIC and τ is the mean trafficking time of a virus in the cell cytoplasm which includes the times for reverse transcription and transport to the vicinity of the nucleus. It is only those viral vectors that have completed reverse transcription and have been transported to the vicinity of the nucleus that are ready to be imported. Hence, the superscript in the last term of equation (2.8) denotes that Vc is to be evaluated at τ h prior to the current time t. The population balance for the corresponding target cells which carry at least one viral genome inside their cytoplasm is given by the following equation: dCc = K bC f Vm (t , 0) − δ1kdi Cc + (1 − δ 2 ) µ Cc − knCc (t −τ ) . dt  (2.9)  At any given time, a cell can have more than one viral genome inside its cytoplasm, since the target cells are susceptible to multiple infections. To avoid the complexity of writing a separate balance for each cell population having a different number of viral vectors, the model has been simplified by using only a single population of virus-carrying (but unintegrated) cells which have an average number of viruses, nv, in their cytoplasm. The Poisson distribution has long been used to predict the fraction of cells infected with a given number of viruses at different multiplicities of infection (Fields et al. 2007). The population distribution of viruscarrying cells bearing different numbers of non-integrated vectors can be represented by the Poisson equation. The fraction of virus-carrying cells that contain k vectors inside their cytoplasm is therefore calculated as: f (k ) =  (nv − 1) k −1 e − ( nv −1) (k − 1)!  (2.10)  where the average number of viruses inside the virus-carrying cells, nv, is obtained from 30  nv =  Vf Cc  .  (2.11)  Equation (2.10) has been modified to yield f(k) = 1 when k = nv = 1. In equation (2.11), Vf represents the concentration of non-integrated viruses inside the virus-carrying cells only, and is given by dV f dt  = K b (C f + Cc )Vm (t , 0) − kdiV f − kn nv Cc(t −τ ) .  (2.12)  The last term of equation (2.12) accounts for not only the nuclear import of viral vectors that are ready to integrate but also the depletion of viral vectors that are retained in the cytoplasm of virus-carrying cells when they become virus-integrated cells. Because the interaction of viruses with cells occurs by chance, even in the presence of a limiting number of viruses per cell, a small fraction of cells are always infected by more than one virus and thus the parameter nv is always >1. The parameter δ1 represents the fraction of virus-carrying cells with only one virus inside their cytoplasm and is obtained from equation (2.10) by setting k = 1, i.e.,  δ1 = e − ( n −1) . v  (2.13)  During the division of a cell that contains k viruses inside its cytoplasm, the probability that one of the daughter cells becomes a virus-free cell is given by p (k ) = 21− k .  (2.14)  For example, if k = 3, cell division leads to eight possible vector distributions between daughter cells [1×(3-0), 3×(2-1), 3×(1-2) and 1×(0-3)], yielding p(3) = 2/23 = 2–2.  The  parameter δ2 can then be obtained as the summation of all the fractions of virus-carrying cells  31  given by equation (2.10), multiplied by their probability of becoming virus-free given by equation (2.114), i.e., = δ2  ∞  ∑ f (k ) × p(k ) .  (2.15)  k =1  For moderate values of nv, terms with k > 5*nv decay rapidly and do not contribute significantly to the summation and hence the nearest integer value of 5*nv is used as the upper limit for k in equation (2.15). 2.1.3 Nuclear import and integration: The PIC of the retrovirus enters into the nucleus by a distinct mechanism that depends on the type of retrovirus involved in the transduction process. Oncoviruses and foamy viruses require cell division for the transport of their PIC into the nucleus (Figure 2.1(B), step 6a).  During the mitotic phase, the nuclear membrane is  disassembled thereby facilitating the entry of the viral genome (Roe et al. 1993).  For  lentiviruses, because of their small size and/or the presence of nuclear localization signals (Lewis and Emerman 1994), the PIC does not require cell division in order to cross the nuclear membrane barrier (Figure 2.1(B), step 6). Once the viral genome is imported into the nucleus, the integration with the cell chromosome occurs within 1 h (Figure 2.1(B), step 7) and hence can be considered an instantaneous process (Lee and Coffin 1991; Roe et al. 1997). It has been observed that, for HIV-1 retroviruses, only a fraction of the DNA copies imported into the nucleus integrate into the chromosome, especially when the number of copies is large (Barbosa et al. 1994; Bell et al. 2001). Assuming that integration is not affected by the number of viral vectors imported into the nucleus, the rate of change in the concentration of viral genomes integrated into the cell chromosome, Vi, is given by dVi = knVc( t −τ ) + µVi . dt  (2.16)  32  The integrated retrovirus is replicated during subsequent cell cycles as represented by the last term in the above equation. The corresponding population balance of target cells with at least one integrated virus in their chromosome, Ci, is given by dCi = knCc( t −τ ) + µ Ci . dt  (2.17)  The above equations are solved numerically subject to the following initial conditions: = Vm (0, z ) Vm= V= V= Vi ,0 ,0 ; V f (0) f ,0 ; Vc (0) c ,0 ; Vi (0) = C f (0) C= C= Ci ,0 f ,0 ; Cc (0) c ,0 ; Ci (0)  .  (2.18)  In order to compare the model predictions with the experimental data for transduction efficiency and integrated copy number per transduced cell, the transduction efficiency is given by % Transduced cells =  Ci ×100 Ct  (2.19)  where the total target cell concentration, Ct, is Ct = C f + Cc + Ci  (2.20)  and the integrated copy number is obtained as:  Integrated copy no./transduced cell=  Vi . Ci  (2.21)  2.2 Materials and methods 2.2.1 Cell cultures: K562 (Human myeloid leukemia) cells were obtained from the ATCC repository.  RAT1 and PG13 cells were gifts from Dr. Connie Eaves of the Terry Fox  Laboratory (TFL), Vancouver, Canada. All the cell types were maintained in Dulbecco’s Modified Eagle’s Medium (DMEM) supplemented with 10% Fetal Bovine Serum (FBS).  33  2.2.2 Retroviral vector production: PG13 cells were engineered in the TFL to produce a murine stem cell virus with a gibbon ape leukemia virus envelope, termed the MSCVGALVenv retroviral vector. Briefly, retroviral vector packaging cells (PG13), based on the gibbon ape leukemia virus envelope and the murine leukemia virus gag and pol proteins (Miller et al. 1991), were transfected with a murine stem cell virus-based vector for retroviral RNA, containing a gene for the enhanced green fluorescent protein (EGFP) (Hennemann et al. 1999). For the production of vectors, these cells were cultured in 875 cm2 roller bottles with 250 mL medium, with the latter being replaced by fresh medium when the cells reached ~95% confluence. Retroviral vectors were harvested for 24 h and the medium was collected and filtered through a 0.45 µm filter to remove cells and debris. The virus-containing medium (VCM) was stored in aliquots at –70oC for later use. 2.2.3 Virus decay and binding: Decay and binding experiments were carried out in 25 mL shake flasks (Corning, Lowell, USA) at 37oC and 130 rpm in a Minitron shaker-incubator (Infors, Bottmingen, Switzerland). Binding of viruses to the hydrophobic surface of the shake flasks was negligible. For the decay experiments, the VCM was incubated in a shake flask and, at different time points, a sample of VCM was collected and stored at 4oC to later estimate the titer. For the binding experiments, mid-exponential K562 cells were centrifuged at 100g for 15 min and resuspended in diluted VCM at a final concentration of 9.8×105 cells/mL. Then the mixture was incubated and, at indicated time points, a 2.5 mL sample of the mixture was collected. The cell concentration was measured to allow calculation of the average value during the experiment, and the remaining sample was centrifuged at 100g for 15 min to collect the supernatant. The supernatant was stored at 4oC for determination of the titer of the remaining vectors at a later time. The viral titers of the collected samples were estimated by infecting RAT1 cells seeded at ~5000 cells/cm2 in 24-well tissue culture plates 34  (Sarsted, Montreal, Canada) the previous day. The samples of VCM from the decay and binding experiments were diluted by half with fresh medium and added to the pre-seeded plates. The plates were centrifuged at 1000g and 37oC for 2 h to infect the cells with the vectors and later the cells from the 24-well plates were seeded into 6-well plates and incubated for 72 h. At this time, the percentage of GFP+ cells was measured using flow cytometry. 2.2.4 Intracellular decay of retroviral vectors:  Exponentially-growing K562 cells were  centrifuged at 100g for 30 min, resuspended in serum-free DMEM, and then incubated for 24 h. These cells were transduced by centrifuging with serum-free VCM at 1000g and 37oC for 30 min and then transferring the cells to serum-free DMEM. At different time points, the infected cells were transferred to DMEM+10%FBS to stimulate the growth of the surviving cells. The cells were then cultured for 96 h, after which the percentage of GFP+ cells was determined. 2.2.5 Intracellular viral trafficking: Mid-exponential K562 cells were centrifuged at 100g for 15 min and resuspended in VCM. Then the mixture was centrifuged in a T-25 flask (Sarsted, Montreal, Canada) at 1000g and 37oC for 30 min. The cells were separated from the VCM by centrifugation and then resuspended in fresh medium at a final concentration of 1.2×105 cells/mL. At different time points as indicated, a sample of the solution was taken and analyzed for GFP+ cells using flow cytometry. 2.2.6 Transduction: Measurements of the transduction efficiency of K562 cells at different VCM exposure times were carried out using 35×10 mm tissue culture dishes (Sarstedt). Exponentially growing K562 cells were centrifuged at 100g for 15 min and resuspended in ¼diluted VCM to a final concentration of ~5×105 cells/mL. 1.7 mL of this suspension were transferred to each tissue culture plate (equivalent to a 2 mm height of VCM) and incubated at 35  37oC and 5% CO2. At the indicated time points, the cells in the plates were transferred from the VCM into the growth medium and were incubated at 37oC and 5% CO2 for 72 h, at which time the %GFP+ cells was analyzed using flow cytometry. Transduction with different virus doses was carried out in 24-well tissue culture plates. Different concentrations of VCM were made by serially diluting the stock VCM with medium and these VCM solutions were added to K562 cells to a final concentration of ~5×105 cells/mL. 400 µL of these suspensions (equivalent to a 2 mm height of VCM) were added to the wells of the 24-well plates in duplicate. The transduction under static gravity was carried out by incubating the plates at 37oC and 5% CO2 in an incubator for 6 h. For transduction under centrifugation conditions, the head space of the plates was replaced with 5% CO2 air and sealed to maintain pH and osmolality. The plates were centrifuged at 2000g and 37oC for 6 h. Then the cells were separated from the VCM and incubated in fresh medium for 72 h prior to analyzing for GFP+ cells using flow cytometry. 2.2.7 Measuring transduction efficiency: The transduction efficiency was determined by measuring GFP+ target cells using a FACScalibur cytometer (BD Biosciences, San Jose, USA) equipped with a 488 nm argon-ion laser for excitation. The EGFP intensity of the cells was measured on fluorescent channel 1 equipped with a 530/30 nm filter while their viability was measured on fluorescent channel 3 equipped with a 585/42 nm filter for propidium iodide staining. 1 mL of medium containing transduced cells was transferred to a FACS tube and propidium iodide solution was added to a final concentration of 5 µg/mL. The samples were analyzed using the FACScalibur and the %Transduced cells was estimated by measuring the percentage of GFP+ cells excluding the nonviable cells. The viability of cells in the samples was always >98%.  36  2.2.8 Measuring vector copy number:  Samples of transduced K562 cells with various  transduction efficiencies were cultured for two weeks and genomic DNA from ~106 transduced K562 cells in each sample was extracted using the GenEluteTM mammalian genomic DNA miniprep kit (Sigma-Aldrich, St. Louis, USA). The extracted DNA was used to amplify a sequence in the EGFP gene of the integrated viral DNA and a sequence in the ERV3 gene of the cellular DNA using real-time PCR with SybergreenTM technology. The forward primer egfpF (5’-AGAACGGCATCAAGGTGAAC-3’) and the reverse primer egfpR (5’-TCAGGTAGTGGTTGTCG-3’) were used to amplify a 135 bp sequence in the EGFP gene, while the forward primer erv3F (5’-CATGGGAAGCAAGGGAACTAATG-3’) and the reverse primer erv3R (5’-CCCAGCGAGCAATACAGAATTT-3’) were used to amplify a sequence of the same length in ERV3. The following relationship was used to quantify the average integrated copy number in the transduced K562 cells: Mean copy number =  F0EGFP 2 F0ERV 3λ  (2.22)  where F0EGFP and F0ERV 3 are fluorescence values (arbitrary units) at cycle 0 (initial fluorescence) for the amplified EGFP and ERV3 genes, respectively, and λ is the fraction of transduced cells in the sample from which the genomic DNA was extracted. 2.2.9 Numerical methods: The partial differential equation (2.1) is converted into a set of ordinary differential equations (ODEs) by discretizing in the z direction using the exponential differencing scheme, which was developed to reduce false diffusion error in convectiondiffusion problems (Patankar 1980).  The exponential interpolation function is the exact  solution for the corresponding one-dimensional steady-state convection-diffusion problem. Therefore, it provides better accuracy than other methods especially when the Peclet number is high. The set of ordinary differential equations along with the other ODEs (equations (7)-(9), 37  (12), (16) and (17)) were solved using a fourth-order Runge-Kutta method in MATLAB. For the estimation of the model parameters: intracellular degradation rate constant (kdi), cytoplasm trafficking time (τ) and initial concentration of active vectors (Vm,0), the numerical solution was fitted to selected experimental data using the Levenberg-Marquardt method of leastsquares minimization.  2.3 Results 2.3.1 Physical properties of retroviral vectors: Viral vectors in the medium harvested from the PG13 packaging cells were examined under a transmission electron microscope. The retroviruses were approximately spherical, and had an average diameter of 115 nm. The diffusion coefficient of the vectors was estimated from the Stokes-Einstein equation: Dv =  k BT 3πη d v  (2.23)  where kB is the Boltzmann constant, T is the absolute temperature, η is the viscosity of the medium, and dv is the diameter of the retrovirus. Based on the average diameter, the diffusion coefficient of these retroviral vectors at 37oC is 1.98×10–4 cm2/h, a value which is in the range reported for other retroviruses (Andreadis et al. 2000). The velocity, u, in equation (2.1) was calculated as the Stokes settling velocity: u=  g ' ( ρv − ρ m )dv 2 18η  (2.24)  where g’ is the gravitational force to which the retroviral vectors were subjected during a static (g’ = g) or centrifugation-based (g’ >> g) transduction process, ρm is the density of the medium, and ρv is the density of the retroviruses. The retrovirus density is 1.16 g/cm3 (Fassati and Goff  38  1999). The following parameters were also used: T = 310 K, ρm = 1.01 g/cm3, and η = 25.6 g/cm·h. 2.3.2 Decay rate and net binding rate of retroviral vectors: The rates at which the active retroviral vectors decay in the medium and bind to the target cells were estimated by measuring the decrease of the active virus concentration in the absence and in the presence, respectively, of target cells. VCM was incubated either without or with target cells and, at different times, the VCM was sampled and assayed for the remaining active viruses. The rate of change of the active vector concentration in the well-stirred mixture with time relative to its initial value is mathematically represented by Vm − ( K X + k )t = e b avg de Vm ,0  (2.25)  where Xavg is the average target cell concentration during the incubation period. The rate of depletion of active retroviruses in the absence of target cells gives the extracellular decay rate while the depletion rate in the presence of target cells is due to the combined effects of decay and uptake by cells due to binding and entry into the cells. By fitting equation (2.25) to the two sets of data shown on Figure 2.2, the decay rate constant, with Xavg = 0, was estimated to be 0.112 h–1 (half-life = 6.2 h) and, with Xavg = 1.19×106 cells/cm3, the binding rate constant was 3.38×10–8 cm3/cell·h. The diffusion-limited, maximum binding rate constant can be calculated from the Smoluchowski equation, Kb,max = 4πDvrc, assuming that the reaction rate between the cell with radius rc, and the virus with diffusivity Dv, is instantaneous (Smoluchowski 1917). Thus, the diffusion-limited binding rate constant for MSCV-GALVenv vectors to K562 cells with rc = 8.5 µm is 2×10–6 cm3/cell·h. When the viral receptors do not cover the entire cell surface, the diffusion-limited binding rate is given by Kb,r = Kb,maxN·r/(πrc+N·r), where N is the number of receptors and r is the radius of the receptor 39  % of added vectors  100 80 60 40 20 10 8 0  2  4  6 8 Time, h  10  12  14  Figure 2.2: Decay and binding kinetics of retroviral vectors. MSCV-GALVenv vectors were incubated at 37oC without () or with () K562 cells and, at the indicated time points, the activity of the remaining viral vectors in the extracellular medium was determined. The decay and binding rate constants were obtained by fitting equation (2.22) to the experimental data (solid lines). The error bars represent the standard deviations of two independent experiments.  40  (Berg and Purcell 1977). The number of receptors for retroviruses on a cell surface generally ranges from 103 to 106. Assuming r = 25 Ao, the diffusion-limited binding rate, Kb,r ≅ 0.11.0·Kb,max, and the experimentally measured binding rate constant is, therefore, 1.6-16% of the diffusion-limited value. Hence, the binding of MSCV-GALVenv viruses to K562 cells is reaction limited similar to what has been observed for other retrovirus/cell systems. 2.3.3 Intracellular vector degradation rate: The fate of MSCV-GALVenv retroviral vectors inside K562 cells was investigated. When cells are subjected to serum starvation, they are arrested in the G0/G1 phase, and the retroviral vectors that have entered into their cytoplasm remain as intermediates that undergo only partial reverse transcription (Chen and Temin 1982; O'Brien et al. 1994). The rate of change in the transduction of these growth-arrested cells was determined by exposing them to a pulse of viruses and then stimulating their growth by adding serum at different time points. The transduction efficiencies relative to the value obtained at the initial time point (i.e., t = 0) are presented in Figure 2.3. The observed lag time in the growth of serum-starved K562 cells after transferring them into a complete growth medium was found to be ~12 h. By assuming that reverse transcription and transport to the nuclear membrane were completed within this lag time and that the intracellular degradation rate was constant, the transduction model developed above was fitted to the data shown in Figure 2.3 by varying the intracellular decay rate constant, kdi, the only remaining unknown parameter. In this way, the best-fit value of kdi was estimated to be 0.0012 h−1, yielding a half-life of retroviral vectors inside K562 cells of ~600 h. This long half-life implies that the retroviral vectors remain as essentially stable intermediates in the cell cytoplasm. However, we cannot exclude the possibility of degradation beyond the 26 h of the experiment. For actively replicating K562 cells with a doubling time of 20.8 h, any degradation beyond 26 h is not a limiting factor since the DNA from each internalized gammaretrovirus should integrate into 41  % Intracellular viral vectors  100 80 60 40 20 0  0  5  10 15 20 Time of transfer, h  25  Figure 2.3: Intracellular degradation kinetics of retroviral vectors. Serum-starved K562 cells were exposed to a pulse of retroviral vectors and then transferred back to a serum-free medium. At the indicated time points, K562 cells were transferred to a serum-containing medium to initiate the transduction of the remaining intracellular vector intermediates and the GFP+ cells were analyzed after 96 h. The y axis represents the % GFP+ cells at time t relative to GFP+ cells at time t = 0.  The complete transduction model () was fitted to the  experimental data () in order to estimate the intracellular degradation rate.  Model  simulations obtained with intracellular degradation half-lives of 20.8 h (----) and 6.2 h ( − ⋅ − ) are also presented. The error bars represent the standard deviations of two independent experiments.  42  the cell chromosome during the next cell division. For comparison, the simulated transduction efficiency results obtained with an internal decay half-life equivalent to the external half-life (6.2 h) or the doubling time of the cells (20.8 h) are also presented in Figure 2.3. 2.3.4 Trafficking inside the cytoplasm: Following its entry into the cell, each retrovirus spends time in the cell cytoplasm for uncoating, reverse transcription and transport to the vicinity of the nucleus.  The greatest proportion of this time is needed for the reverse  transcription of retroviral RNA to DNA which requires 8-12 h (Coffin et al. 1997). The total time required from initial retrovirus entry into the cell cytoplasm until the PIC reaches the vicinity of the nucleus is represented by the delay time, τ, in the model. The nuclear import of a gammaretrovirus depends on the rate of cell division since, for these viruses, nuclear import of viral DNA can occur only during the mitotic phase at the end of the cell cycle. So, the average time for half the number of viral vectors to be imported into the nucleus is half of the doubling time of the K562 cells. The nuclear import rate constant for gammaretroviruses can therefore be calculated as = kn  ln 2 = 0.067 h -1 (td / 2)  (2.26)  where td (= 20.8 h) is the doubling time of K562 cells. Assuming that the lag time for the onset of expression from the integrated viral genome is negligible compared to the time spent by a virus in the cytoplasm, the cytoplasmic trafficking time was estimated from the time course increase in GFP+ cells when K562 target cells were exposed to a pulse of retroviruses (Figure 2.4). The cytoplasmic trafficking time, τ, estimated by fitting the model to these experimental data was found to be 11.2 h. At least 7 h is required for the positive strand retrovirus DNA to appear during the reverse transcription of a retroviral vector (Fassati and Goff 1999). Also, a lag time of 5.2 h between the syntheses of early and late DNA during 43  % Transduced cells (Relative to maximum)  1.0 0.8 0.6 0.4 0.2 0.0 0  20  40 60 Time, h  80  100  Figure 2.4: Dynamics of retrovirus trafficking from cytoplasm into the nucleus. K562 cells were exposed to VCM for 30 min to deliver vectors into the cell cytoplasm and, at the indicated time points, the %Transduced cells was measured using flow cytometry.  To  estimate the cytoplasmic trafficking time, τ, the mathematical model () was then fitted to the experimental data ().  The error bars represent the standard deviations of two  independent experiments.  44  reverse transcription has been observed (Lim et al. 2004). Based on these time scales, the estimated cytoplasmic trafficking time of 11.2 h is reasonable especially since it also includes the times for uncoating and rearranging the viral core before reverse transcription, and transporting the PIC to the vicinity of nucleus afterwards. 2.3.5 Quantification of retroviral vector titer: There is no direct experimental method to quantify the initial infectious retrovirus concentration, Vm,0.  The traditional way of  quantifying the titer is to determine the number of colonies formed by the cells containing integrated viruses when target cells at the bottom of a culture dish are exposed to a thin layer of VCM for a specified period and then cultured in fresh medium.  A more accurate  quantification was obtained by fitting a simple external diffusion model (Andreadis et al. 2000; Kwon et al. 2003) to experimental transduction results. Our current model can quantify the concentration of active vectors even more accurately because it incorporates intracellular kinetics in addition to the extracellular processes. Here, the infectious retrovirus concentration in the VCM was estimated by fitting the current model to the experimental transduction data shown in Figure 2.5. For transduction under static gravity conditions (i.e., g’ = 1×g), it was found that the cells settled to the bottom of the culture dish and migrated towards the centre to form a closely-packed monolayer. Hence, Ct in the boundary condition equation (2.5) is replaced with the constant maximum target cell density, Ct,max. For K562 cells with a diameter of ~17 µm, Ct,max = 4.4×105 cells/cm2. The following initial conditions from the experiment were used to solve the model equations: V= Vm ,0 ;= V f (0) 0; = ; Vc (0) 0;= Vi (0) 0 m (0, z )  . (2.27) C f (0) = 1.12 ×105 cells/cm 2 ; Cc (0) = 0; Ci (0) = 0  For this experiment, the initial active retrovirus concentration, Vm,0, was found to be 2.31×106 vectors/cm3.  The VCM used had been diluted by a factor of 4; so the active vector 45  % Transduced cells  10 8 6 4 2 0 0  5  10 15 Time, h  20  25  Figure 2.5: Time course profile of the transduction of K562 cells. The cells were exposed to viral vectors for the indicated time points, transferred to fresh medium, cultured for 72 h and then analyzed for %Transduced cells. The predictions of the mathematical model () were fitted to the experimental data () to estimate the concentration of viral vectors at t = 0. The error bars represent standard deviations of two independent experiments.  46  % Transduced cells  100 80 60 40 20 0 0  5  10 Vectors/Cell  15  Figure 2.6: Transduction efficiency for K562 cells as a function of viral vector dosage. K562 cells were contacted with VCM at the indicated vector-to-cell ratios either at static gravity () or under centrifugation at 2000g () for 6 h. The solid lines represent the model predictions under the same conditions. For the centrifugation case, the model was also used to predict the transduction results that would have been obtained if δ2 = 1 (----) (i.e., all intracellular vectors are retained by only one daughter cell during cell division) or δ2 =  e − ( nv −1) ( − ⋅ − ) (i.e., at least one viral vector is retained by each daughter cell when more than one intracellular vector is present during division). The error bars represent standard deviations of two independent experiments each replicated twice.  47  concentration of the stock VCM solution was 9.24×106 active vectors/cm3. The model takes into account only the integrated and expressing viral copies.  Thus, the model may  underestimate the actual titer if the integrated vectors cannot express EGFP. 2.3.6 Effect of vector-to-cell ratio on transduction efficiency: The influence of the vector-tocell ratio on the transduction efficiency of K562 cells was investigated and compared with the model predictions. The vector-to-cell ratio here represents the number of active viral vectors per cell at the start of the transduction process. The K562 cells were transduced using vectorto-cell ratios ranging from 0.5 to 17 at two different gravitational forces (1×g and 2000×g) and the results are presented in Figure 2.6. The initial concentrations of active vectors were obtained by serially diluting the stock VCM whose titer was determined in the previous section. At static gravity conditions (i.e., g’ = 1×g), the transduction efficiencies varied linearly with vector-to-cell ratio and the model predictions (solid line) were in good agreement with the experimental results. At g’ = 2000×g, enhancements of 35- to 4.5-fold in transduction efficiency compared to the values at 1×g were obtained as the vector-to-cell ratio ranged from 0.5 to 17. The model predictions (solid line) for this case were also in good agreement with the experimental data (with a slight deviation at high vector-to-cell ratios), showing a sharp increase in transduction efficiency at low ratios and saturation at high values. 2.3.7 Transduction efficiency and integrated copy number: The model can predict the integrated virus copy number per transduced cell along with the transduction efficiency. The model was used to simulate experimental copy number data, obtained by employing PCR to amplify sequences of selected genes in both the retroviral and target cell DNA. These data are plotted in Figure 2.7 as a function of transduction efficiency. Once again, a satisfactory validation of the model is obtained, as it provides a good representation of the relationship 48  Mean copy no./transduced cell  5 4 3 2 1 0 0  20  40 60 80 % Transduced cells  100  Figure 2.7: Mean copy number as a function of transduction efficiency. The experimental data () were obtained using real-time PCR. The solid line represents model predictions of the average integrated copy number of the transduced cells.  49  between the copy number and the transduction efficiency. As Figure 2.7 shows, the increase in the integrated copy number was less than the proportional increase in transduction efficiency up to ~60%. Beyond a transduction efficiency of 60%, the integrated copy number increased in an exponential fashion. These results indicate that transduction efficiencies obtained via a single exposure to VCM should be limited to <60% if it is desirable to obtain a mean integrated copy number per cell of <2.  2.4 Discussion We have developed a mathematical model for retrovirus-mediated gene transfer. The model differs from other mathematical descriptions of retroviral transduction in that it considers all of the rate-limiting steps involved in the delivery of the retroviral genome into the target cell nucleus. By considering only a single population of virus-carrying cells with an average number of viruses in their cytoplasm and representing the distribution of viruses within these cells by a modified Poisson equation, a simplified and efficient model having a minimum number of virus and cell population balances was obtained. This approach allows the inclusion of multiple vector infection kinetics and, hence, yields a correlation between the transduction efficiency and the mean copy number, both of which need to be optimized to allow the best use of available vectors. The binding of MSCV-GALVenv retroviral vectors to K562 cells was found to be a reaction-limited step in the transduction process. It has also been reported that the binding of viruses to target cells is a reaction-limited process for other transduction systems (Dee and Shuler 1997; Le Doux 1998).  The maximum binding rate arises when every  collision of a virus with the cell surface results in irreversible binding. However, the initial viral attachment occurs non-specifically by a combination of electrostatic and van der Waals 50  forces and, hence, the bond is weak and reversible, resulting in the equilibrium detachment of some of the bound viruses. It is only after the retrovirus and the specific receptor come into contact - by the movement of one or the other along the cell surface - that irreversible binding, leading to virus internalization, can take place. Since this overall binding process, represented in the model by the binding rate constant, Kb, is the rate-limiting step in the delivery of vectors from the VCM into the cell cytoplasm, increasing Kb can lead to an enhancement in the transduction efficiency. An increase in the binding rate can be obtained, for example, by the addition of polycations, which have been shown to enhance the transduction of retroviruses by reducing the non-specific repulsive interaction between the net negatively-charged vectors and cells (Davis et al. 2004). The measured intracellular half-life of MSCV-GALVenv retroviral vectors indicates that they remain as stable intermediates in the cytoplasm of K562 cells for at least 26 h. If the serum-starved target cells are infected with retroviruses, an intermediate complex forms due to partial reverse transcription of the retroviral RNA and reverse transcription can be completed at later times if the growth of the cells is stimulated with serum (Chen and Temin 1982; Fritsch and Temin 1977; Harel et al. 1981; Springett et al. 1989; Varmus et al. 1977). The intermediates of some retroviruses in serum-starved stationary cells were reported to remain as stable intermediates (Fritsch and Temin 1977; Harel et al. 1981; Varmus et al. 1977) while the intermediates of other retroviruses were found to be labile and did not yield infections up to the levels obtained in replicating cells upon mitogenic stimulation with serum (Chen and Temin 1982; Springett et al. 1989). Also, the intermediates of an amphotropic retroviral vector was found to be labile in stationary T-lymphocytes but stable in stationary fibroblasts (Springett et al. 1989). The intracellular stability of vectors/complexes might depend on factors like the stability of the reverse transcriptase or integrase enzymes or the presence of 51  host restriction factors in a specific target cell environment. Certain target cells contain genes that generate restriction proteins (e.g., APOBEC, TRIM5α, Fv1) which can block retrovirus transduction events in the cytoplasm by degrading essential retroviral components (Wolf and Goff 2008). Hence, the intracellular degradation of retroviral vectors likely depends on the specific cell-retrovirus system.  However, we cannot rule out the possibility that the  intracellular degradation rates in actively replicating cells might be different than in stationary cells. Andreadis et al. (1997) developed a method to quantify the intracellular stability of retroviral vectors in actively replicating cells without synchronization and estimated the intracellular half-life of MoMLV vectors inside NIH-3T3 cells to be 6.5 h. This method may be useful to better quantify the intracellular half-life of our retroviral vectors, since the serum starvation experiment indicated that intracellular degradation was non-negligible. Once the retrovirus is delivered into the cell cytoplasm, uncoating and rearrangement of the retroviral genome occurs to initiate reverse transcription.  The PIC after reverse  transcription is transported along microtubules to the microtubule organizing center. The estimated trafficking time for this overall process was found to be 11.2 h. The major portion of this time is expected to be due to the reverse transcription process that can require 8-12 h when the available nucleotides are not limiting. The reverse transcription of retroviral RNA can be completely blocked in quiescent cells (G0 phase) indicating that the synthesis of viral DNA occurs only during an active cell cycle (Goulaouic et al. 1994; Harel et al. 1981; Varmus et al. 1977). It has been found that reverse transcription can occur in any phase of the cell cycle but only in actively replicating cells (Roe et al. 1993). The availability of cellular nucleotides in the host cell is the key factor which controls the reverse transcription of retroviral RNA (Goulaouic et al. 1994). The time for reverse transcription likely remains  52  constant in actively replicating cells but is longer in slowly growing cells like hematopoetic stem cells. The initial concentration of infectious retroviral vectors in the VCM was estimated by fitting the model to the experimental data. There is no direct experimental method to quantify the retroviral vector concentration accurately. The titration method, which is performed by overlaying a thin layer of diluted VCM onto target cells contained in a culture plate and counting the number of cells infected, is the standard means of estimating the concentration of infectious units in a VCM sample. The titer determined by this method can vary depending on the experimental conditions such as target cell number, target cell type, use of polycations, height of VCM, and exposure time. Mathematical models that account for these extracellular variations have been used in the past to quantify the viral titer by comparing their predictions with experimental transduction data (Andreadis et al. 2000; Kwon et al. 2003). In addition to these extracellular factors, intracellular factors such as intracellular degradation of vectors, cytoplasmic trafficking time, doubling time of target cells and sharing of vectors between daughter cells also have an impact on the quantification of titer. The concentrations estimated by the current model account for these intracellular events in addition to the extracellular factors and, therefore, it is capable of estimating the titer more accurately than previous gene transfer models. The initial concentrations of the stock VCM estimated from the data of Figure 2.5 by using the assumptions of Andreadis et al. (2000) and Kwon and Peng (2003) are 3.03×106 and 4.32×106 vectors/cm3, respectively. The model of Andreadis et al. (2000) does incorporate an efficiency factor to account for extracellular binding and all the intracellular transduction steps. However, this factor can only be determined experimentally with reference to a cell line in which all these steps proceed with 100% efficiency. Because they lack explicit intracellular rate-limiting steps as well as any description of cell dynamics in their 53  formulations, both models significantly underestimate the value of vectors/cm3 obtained by the current model.  Vm,0 = 9.28×106  Note that these models would have  underestimated the initial concentration even further if significant intracellular vector degradation had occurred. Under static gravity (1×g) conditions, the settling velocity of the retroviruses used here is 5.47×10-4 cm/h according to equation (2.25). Under these circumstances, the mass transport of viral vectors to the target cells is essentially governed by diffusion. The transduction efficiencies under 1×g conditions were low since the cells at the bottom of the culture dish had access to only a limited number of viral vectors due to their low diffusivity and short decay half-life. Centrifugation has been widely used to enhance retroviral gene transfer, presumably by increasing the convective component in equation (2.1) (Bahnson et al. 1995; QuintasCardama et al. 2007). When subjected to a centrifugal force of 2000×g, the settling velocity of our viral vectors increases to 1.1 cm/h, which greatly enhances their rate of mass transfer to the bottom of the culture dish. This provides an increased concentration of vectors accessible to the target cells located there and, hence, results in an increased flux of viruses entering into the cells. Centrifugation, therefore, does not enhance transduction by increasing the surface area of the target cells (i.e., by flattening) nor by increasing the fusion efficiency, as has been suggested by others (O'Doherty et al. 2000). When the convective mass transport of vectors in the model is represented by the Stokes settling velocity, the model predictions of transduction enhancement by centrifugation agreed well with the experimental data.  The use of  centrifugation also allowed us to validate the model over a large variation of vector-to-cell ratios yielding a wide range of transduction efficiencies. The small deviations observed at high vector-to-cell ratios for this case might be the due to the saturation of binding sites on the cell surface, given the greatly increased local VCM concentrations that occur under these 54  circumstances. Though the deviations are acceptable for the current experimental conditions, an improved model should account for the saturation binding that occurs when the binding sites on the target cells become a limiting factor. The number of viral vectors delivered inside the virus-carrying cells plays an important role in determining both the transduction efficiency and the integrated copy number. By considering only the average number of viruses per cell, it became possible for the model to efficiently predict both of these outcomes, using a minimal number of virus and cell population balances.  The parameter δ2, obtained by employing the Poisson equation to  represent the distribution of vectors between virus-carrying cells, yielded good agreement between the model predictions and the experimental data, as can be seen in Figures 2.6 and 2.7. This parameter value provides results that lie between those predicted using two extreme values of δ2. When it is assumed that all the viruses inside the cell are retained by only one of the dividing cells (i.e., δ2 = 1), the simulated transduction results are low and show a saturation behavior when compared to the experimental data (Figure 2.6). When it is assumed that at least one viral vector is retained by each daughter cell when more than one intracellular vector is present during division (i.e., δ 2 = e − ( nv −1) ), the model over-predicted the experimental transduction efficiencies, especially at vector-to-cell ratios >3. These results demonstrate that, even when several viruses are present in the cell cytoplasm, there is still a reasonable probability of obtaining a virus-free cell during mitosis, because of the lack of equal sharing between the two daughter cells. As a consequence, the model predicted a limited transduction efficiency (i.e., ~90%) even when the vector-to-cell ratio was increased to 17. A sensitivity analysis of the model was performed by artificially raising by 10% each of the parameter values shown in Table 2.1 while keeping all of the other parameter values 55  constant. Two different intracellular degradation rates were investigated: kdi = 0.0012 h–1 (Table 2.1) representing the case where a fairly stable intermediate forms in the target cell  Table 2.1: Estimated kinetic parameters of the model Parameter  Value  Extracellular decay rate constant, kde  0.112 h–1  Binding rate constant, Kb  3.38×10-8 cm3/cell·h  Intracellular decay rate constant, kdi  0.0012 h–1  Cytoplasmic trafficking time, τ  11.2 h  Nuclear import rate constant, kn  0.067 h–1  Growth rate of target cells, µ  0.033 h−1  cytoplasm, and kdi = 0.107 h–1 (Andreadis et al. 1997) where intracellular degradation is increased, such as by the presence of host cell restriction factors. The results are shown in Figure 2.8. The sensitivity on the y–axis represents the percent change in the gene transfer efficiency relative to the percent increase in the parameter value, where, for the purposes of this analysis, the gene transfer efficiency is defined as % Gene transfer =  (Vi / Ct ) ×100  (V  m ,0 × h / Ct ,0 )  (2.28)  where Ct,0 = Cf,0 is the total target cell concentration at t = 0. The analysis shows that increasing the extracellular decay rate has a significantly negative impact on the gene transfer process. The gene transfer efficiency can be enhanced substantially by increasing the half-life of the retroviruses in the extracellular medium, for 56  1.2  Sensitivity  0.8 0.4 0.0  kde  kdi Kb  τ kn  -0.4 -0.8 -1.2 Model parameters  Figure 2.8:  Sensitivity analysis of the kinetic parameters of the model.  The y axis  represents the percent change in gene transfer efficiency relative to a 10% percent increase in each of the following model parameters: extracellular degradation rate (kde), binding rate (Kb), intracellular degradation rate (kdi), cytoplasmic trafficking time (τ), and nuclear import rate (kn). Two values of kdi were investigated corresponding to cases where the vector intermediates that form in the cell cytoplasm are fairly stable with kdi = 0.0012 h–1 (black bars) and relatively unstable with kdi = 0.107 h–1 (gray bars). The other parameters used in the analysis were: g′ = 1×g, tf = 24 h.  57  example, by optimizing environmental conditions like temperature and osmolality during their production. It has been reported that the half-life of MoMLV vectors can be doubled by increasing the osmolality of the production medium from 335 to 450 mOsm/kg (Coroadinha et al. 2006b). If such an increase could be obtained with the MSCV-GALVenv retroviral vectors used in our experiments, the model predicts that the gene transfer efficiency would be enhanced by ~60-100% depending on the intracellular degradation rate. The other parameters that have a significant effect on the gene transfer efficiency are the cytoplasmic trafficking time and the nuclear import rate, especially when the intracellular degradation of vectors takes place fairly rapidly. Most of the cytoplasmic trafficking time is taken up by the reverse transcription process, whose duration depends to a large extent on the host cell nucleotide content. The cytoplasmic trafficking time can be much longer when slowly growing cells like hematopoietic stem cells are targeted. For example, when τ is twice the value in Table 1, the transduction efficiency is reduced by 20% if the vectors are stable and 50% if the vectors degrade inside the cell.  On the other hand, foamy-viral vectors need less cytoplasmic  trafficking time as the reverse transcription process is not required for transduction (Rethwilm 2007). The nuclear import rate of onco- and foamy-viral vectors depend on the doubling time of the target cells and, hence, it is expected that the transduction efficiency would be considerably lowered if such viruses were used to infect slowly growing cells like hematopoietic stem cells, especially if the viruses degrade rapidly in the cytoplasm. For example, according to the model, if kn were reduced to half of its Table 1 value, then the transduction efficiency would fall by 40-70% depending on the vector’s intracellular degradation rate. In the case of lentiviruses, nuclear import can occur at any stage of the cell cycle and is therefore independent of the doubling time of the target cells. The nuclear import rate constant for the HIV-1 lentivirus is ~0.17 h–1 (Barbosa et al. 1994), which is ~2.6 times 58  the value of kn estimated for the MSCV-GALVenv gammaretroviral vector based on the doubling time of K562 cells. This suggests that when targeting hematopoietic stem cells with a doubling time of >40 h, the nuclear import rate for onco- and foamy-viral vectors becomes very low and lentiviral vectors become the superior choice for enhancing gene transfer effectiveness, provided that the reverse transcription process occurs efficiently.  59  3. Kinetics and mechanism of retroviral bindi ng and entry The entry of retroviral vectors into cells normally depends on nonspecific cell surface binding before interaction with a specific cell surface receptor leads to fusion of the viral and cellular membranes, and then viral core release into the cell cytoplasm. Understanding the mechanisms by which retroviral particles bind and enter into mammalian cells is necessary for efficient and controlled gene delivery. When a retroviral vector comes sufficiently close to the target cell surface, it binds to the cell membrane independent of the nature of the viral envelope protein (Pizzato et al. 2001a; Pizzato et al. 1999). For example, the initial binding of the amphotropic murine leukemia virus to TE671 cells is mediated by virus-associated heparan sulfate proteoglycans acquired from the viral producer cells (Kureishy et al. 2006). Such initial binding events can be enhanced by the use of various cationic agents (Davis et al. 2002; Katakura et al. 2004) which modulate the charge of both the cellular and viral membranes (Davis et al. 2004). However, the infectious release of the viral core into the cell cytoplasm requires the interaction of the bound virus envelope with specific cell surface receptors.  A bound  retrovirus was shown to undergo actin-driven lateral movement on the cell surface in a random fashion until interaction with specific receptors takes place, and then an organized movement to hot-spots that facilitate entry (Lehmann et al. 2005). The viral envelope protein mediates both receptor specificity and membrane fusion. The interaction of a virus with a single specific receptor often results in low affinity binding, while interaction with multiple receptors can provide irreversible binding and facilitates recruitment of endocytic structures and/or fusion activation (Marsh and Helenius 2006; Pelkmans 2005). The surface unit (SU) portion 60  of the viral envelope protein is responsible for binding with the specific cell surface receptor while the transmembrane (TM) portion is responsible for the fusion of the cellular and viral membranes through a fusion peptide. Viruses enter cells either by direct fusion with the cell surface or by an endocytic process. The insensitivity to lysosomotropic agents of some retroviruses in early studies suggested that plasma membrane fusion is the more dominant mechanism (Mcclure et al. 1988; Mcclure et al. 1990; Stein et al. 1987). However, there is accumulating evidence that receptor-mediated endocytosis may be the only effective cell entry pathway for retroviruses (Beer et al. 2005; Lee et al. 1999; Miyauchi et al. 2009). A well-studied endocytosis process mediated by clathrin-coated vesicles involves the acidification of endocytic vesicles resulting in conformal changes to the viral envelope protein leading to fusion with the cellular membrane. Clathrin-mediated endocytosis is favored by most non-retroviruses (Marsh and Helenius 2006; Sun et al. 2005; White et al. 1981) and some retroviruses [e.g., avian leukosis virus (Mothes et al. 2000), mouse mammary tumor virus (Redmond et al. 1984), equine infectious anemia virus (Brindley and Maury 2005), foamy virus (Picard-Maureau et al. 2003) and Jaagsiekte sheep retrovirus (Bertrand et al. 2008)]. Endocytosis via clathrin-coated pits had been thought to be the only endocytic pathway that was exploited by viruses entering into the host cell. However, more recent advances have confirmed the presence of non-clathrin endocytic pathways in mammalian cells (Kirkham and Parton 2005).  Several viruses  including murine leukemia retroviruses were found to utilize pH-independent endocytosis pathways that were instead mediated by lipid-raft microdomains (Beer et al. 2005; Lee et al. 1999; Marsh and Helenius 2006). Gibbon ape leukemia virus envelope psuedotyped (GALVenv) retroviral vectors have been a popular choice for targeting hematopoietic cells (Gaspar et al. 2004; Lemoine et al. 61  2004) because of their efficient transduction compared to vectors with other envelopes (Relander et al. 2002b). GALV utilizes the Pit-1 receptor, a multiple membrane-spanning type III sodium-dependent phosphate transporter, highly expressed in bone marrow (Kavanaugh et al. 1994). However, the actual route of entry utilized by GALV vectors has not been reported. Also, there are only few reported investigations of the quantitative kinetic behavior of viral interactions on cell surface during binding and subsequent entry into the cell cytoplasm (Lim et al. 2004; Yu et al. 1995). A quantitative analysis of these interactions should determine the rate-limiting steps and suggest strategies to accelerate these steps. In this article, we have investigated the pathway utilized and analyzed the quantitative kinetic behavior of GALVenvelope retroviral entry into RAT-1 mammalian cells.  3.1 Materials and Methods 3.1.1 Mathematical representation of kinetic steps: At low vector-to-cell ratios (i.e. < 1), the kinetics of the virus interaction with the cells can be represented by the following schematic: kb ke  → Cb  V + C f ← → Cc k− b  where V is a viral vector, Cf is a virus-free cell, Cb is a cell with a bound virus and Cc is a cell with an internalized virus. kb, k–b, and ke are the binding rate constant, the dissociation rate constant and the entry rate constant, respectively. Consider the condition where viruses have already been bound to the surface of the cells and no viruses are present in the medium. Under these circumstances, the viruses can either enter into the cells or dissociate from the cell surfaces and become resuspended in the medium. It is assumed that rebinding of these dissociated viruses is negligible because the high concentration gradient away from the cell surface (i.e., kb = 0). Thus, the dynamic cell population balances can be represented by the following equations: 62  dC f = k− bCb + kdmCb dt  (3.1)  dCb = −k− bCb − keCb − kdeCb dt  (3.2)  dCc = keCb dt  (3.3)  where kde is the extracellular decay rate constant for retroviral vectors. The bound viruses can be assumed to decay at the same rate as free viruses suspended in the medium. It is assumed that these retroviral vectors are stable inside the cell cytoplasm as was found in chapter 2. Based on the analytical solutions of the above population balances, the transduction efficiency as a function of time is given by = η (t )  (η b0 / 2)  (1 − e    k− b + kde 1 +  ke    − ( kde + k− b + ke ) t  )  (3.4)  where η(t) is the %Transduced cells at time t and η b0 is the % of cells with a bound virus on their surface at time t = 0. 3.1.2 Reagents: Protamine sulfate, ammonium chloride, chlorpromazine (CPZ) and methylbeta-cyclodextrin (MBCD) were purchased from Sigma Aldrich (St. Louis, MO). Dulbecco’s Modified Eagle’s medium (DMEM) and fetal bovine serum (FBS) were purchased from Invitrogen (Carlsbad, CA). 3.1.3 Cell culture and retroviral vectors: RAT-1 and retrovirus packaging (PG-13) cells were gifts from Dr. Connie Eaves of the Terry Fox Laboratory (TFL), Vancouver, Canada. All cells were cultured in DMEM supplemented with 10% FBS. The PG-13 cells were engineered at the TFL to produce retroviral vectors with murine stem cell virus-based viral RNA containing EGFP, murine leukemia virus gag and pol proteins, and a gibbon ape leukemia virus envelope (Hennemann et al. 1999; Miller et al. 1991); here referred to as MSCV63  GALVenv vectors. For the production of these viral vectors, the PG-13 cells were cultured in 1750 cm2 roller bottles. 250 mL medium were replaced by fresh medium when the cells reached ~95% confluence. The retroviral vectors were harvested for 24 h and passed through a 0.45 µm filter to remove cells and debris. The virus-containing medium (VCM) was stored in aliquots at –70oC for later use. 3.1.4 Vector binding efficiency: RAT-1 cells were seeded in 24-well tissue culture plates (Sarstedt, Montreal, Canada) at ~5000 cells/cm2 and cultured at 37oC for 48 h to form confluent monolayers. The medium was then replaced by VCM with different concentrations of protamine sulfate and centrifuged at 1000g and 17oC for 30 min to eliminate diffusion limitations. After centrifugation, the VCM from each well was removed, washed once with DMEM and replaced with fresh medium. The plates were incubated at 37oC for 2 h and then the cells were trypsinized and seeded at low density (2000 cells/cm2) in 6-well plates (Sarstedt, Montreal, Canada). These cells were cultured for 48 h and then analyzed for %GFP+ cells using flow cytometry. 3.1.5 Retroviral vector dissociation dynamics: RAT-1 cells were seeded in tissue culture dishes (Sarstedt) at ~5000 cells/cm2. At 48 h the medium was replaced by VCM with either 0 or 10 µg/mL protamine sulfate. The plates were centrifuged at 1000g and 17oC for 30 min. Then they were washed once with DMEM, fresh medium was added and the cells were incubated at 37oC. At the indicated time points, the medium above the monolayer of cells was collected and stored at 4oC until an estimation of the infectious viral vectors could be made. 3.1.6 Protamine sulfate effect on entry dynamics: In a 24-well tissue culture plate with a confluent monolayer of RAT-1 cells, the medium was replaced with VCM containing 0 or 10 µg/mL of protamine sulfate. Both sets of wells were then centrifuged at 1000g and 17oC for 64  30 min. The plate was washed once with DMEM and fresh medium containing different concentrations of protamine sulfate was added to duplicate wells in each set. The plates were incubated at 37oC for 2 h and then the cells were trypsinized and seeded at low density in 6well plates to later analyze for GFP+ cells using flow cytometry. 3.1.7 Virus inactivation: The media in tissue culture dishes with confluent monolayers of RAT-1 cells were replaced with VCM and centrifuged at 1000g and 17oC for 30 min. The dishes were washed once with DMEM and one set of dishes was treated with trypsin for 10 min at 37oC and then seeded at low density in culture medium. The medium in another set of dishes was replaced with citrate buffer (40 mM citric acid, 135 mM NaCl, 10 mM KCl, pH 3.0), incubated for 2 min and washed with DMEM, then replaced with fresh medium. The control samples were mock-treated with DMEM. The control and citrate-buffer-treated dishes were incubated at 37oC for 2 h and then trypsinized and seeded at low density in 6-well plates. These cells were cultured for 48 h and then analyzed for %GFP+ cells using flow cytometry. 3.1.8 Entry and dissociation kinetic rates: The media in one set of dishes with confluent RAT-1 cells cultured for 48 h were replaced with VCM or VCM containing 10 µg/mL protamine sulfate. All the dishes were centrifuged at 1000g and 17oC for 30 min. Then the plates were washed once with DMEM and incubated at 37oC after adding the culture medium. At the indicated time points, a pair of plates from both sets was removed from the incubator and trypsinized immediately to inactivate surface-bound vectors. Then the cells were seeded at the low density of 2000 cells/cm2 in 6-well plates to later estimate the %GFP+ cells using flow cytometry. 3.1.9 Viral entry in the presence of NH4Cl: The medium in each well of a 24-well tissue culture plate, each having a confluent monolayer of RAT-1 cells, was replaced with VCM and 65  centrifuged at 1000g and 17oC for 30 min. The plates were washed once with DMEM and fresh medium containing different concentrations of ammonium chloride was added to each well. The plates were incubated at 37oC for 1 h and then the cells were trypsinized and seeded at a low density in 6-well plates. At 48 h, the cell density in each plate was measured and analyzed for GFP+ cells using flow cytometry. 3.1.10 NH4Cl effect on viral decay: The viral vectors in the media containing 0 or 100 mM ammonium chloride (both adjusted to pH 7.4) were incubated at 37oC and the infectivity of the viral vectors in both media at different time points was determined. At each time point, samples of VCM were stored on ice. All of these virus-containing samples were added to plates seeded with RAT-1 cells and centrifuged at 1000g and 17oC for 1 h. Then the VCM was replaced with fresh medium and the viral vectors were allowed to infect the cells at 37oC. The cells were cultured for 48 h to analyze for GFP+ cells using flow cytometry. 3.1.11 Acidic-medium treatment of bound viruses:  A 24-well tissue culture plate with  confluent monolayers of RAT-1 cells and another plate without cells were centrifuged with o  VCM containing 10 µg/mL protamine sulfate at 1000g and 17 C for 30 min. The VCM was removed and duplicate wells in each plate were treated with media having different pH values (7.4, 7, 6, 5 and 4) for 2 min. All the wells were washed with DMEM and those without cells were seeded with RAT-1 cells. Fresh medium was added to the treated wells with cells, which o  were subsequently incubated at 37 C for 1 h and then trypsinized and seeded at low density. The cells were cultured for 48 h and then analyzed for GFP+ cells using flow cytometry. 3.1.12 Virus infection with chlorpromazine: Tissue culture plates seeded with RAT-1 cells were incubated with media containing 0, 10, 25 and 50 µM CPZ at 37oC for 30 min. The medium was replaced with VCM containing corresponding concentrations of CPZ and the 66  plates were centrifuged at 37oC and 1000g for 30 min. After the VCM was removed, the cells were washed with DMEM and then cultured in fresh medium for 48 h to analyze for GFP+ cells. 3.1.13 Virus infection of methyl-beta-cyclodextrin-treated cells: Media containing 0 or 10 mM MBCD were added to a set of wells containing RAT-1 cells and incubated at 37oC for 30 min to extract cholesterol from their surface. Then all the wells were washed with DMEM, VCM was added and the plates were centrifuged at 1000g and 37oC for 30 min.  The  supernatant from the wells was removed, washed with DMEM and incubated in the culture medium for a further 30 min in the incubator. Then, infected control samples were incubated with media containing 0 or 10 mM MBCD at 37oC for 30 min. Finally, all the samples were washed with DMEM and cultured in fresh medium for 48 h to analyze for GFP+ cells. 3.1.14 Measuring transduction efficiency: The transduction efficiency was determined by measuring GFP+ target cells using a FACScalibur cytometer (BD Biosciences, San Jose CA) equipped with a 488 nm argon-ion laser for excitation. The EGFP intensity of the cells was measured on fluorescent channel 1 using a 530/30 nm filter while their viability was measured on fluorescent channel 3 with a 585/42 nm filter for propidium iodide staining (5 µg/mL). The samples were analyzed using the FACScalibur and the %Transduced cells was estimated by measuring the percentage of GFP+ cells, excluding the nonviable cells. The viability was always >99%.  3.2 Results 3.2.1 Binding efficiency of retroviral vectors:  The efficiency of the initial binding of  retroviral vectors to target cells in the absence and presence of a cationic polymer was investigated. RAT-1 cells were contacted under low-speed centrifugation at 1000g and 17oC 67  with a suspension of MSCV-GALVenv vectors containing different concentrations of protamine sulfate.  After VCM removal and incubation at 37oC, the %Transduced cells  provides a measure of the retroviral vector binding efficiency at different concentrations of protamine sulfate (Figure 3.1). As the concentration of protamine sulfate was augmented, the binding efficiency initially increased, yielding a maximum 5-fold enhancement in transduction at 10 µg/mL, and then decreased. There was no observed toxicity to cells due to their exposure to these concentrations of protamine sulfate for this time period. 3.2.2 Retroviral vector dissociation from the cell surface: The low transduction efficiency in the absence of protamine sulfate is either due to the binding of a small number of vectors to the cell surface and/or the dissociation of these bound vectors from the cell surface. To investigate the dissociation phenomenon, the MSCV-GALVenv retroviral vectors were allowed to bind to the surface of RAT-1 cells in the absence or presence of 10 µg/mL protamine sulfate, and then the titer of viral vectors that were released from the cell surface into a virusfree medium was measured. The ordinate scale in Figure 3.2 represents the percentage of vectors desorbed at time, t, relative to the total number bound at t = 0. As can be seen from the figure, in the case where the vectors were adsorbed in the absence of protamine sulfate, 60% of the bound retroviruses dissociated from the cell surface within 2 h, indicating that the adsorption process was readily reversed. Over the same period of time, only about 5% of the vectors bound in the presence of protamine sulfate subsequently desorbed, indicating that cationic polymers can cause essentially irreversible binding of retroviruses to the cell surface. 3.2.3 Influence of protamine sulfate on the post-binding events: To investigate the influence of protamine sulfate on post-binding events, retroviral vectors were bound in the absence or presence of 10 µg/mL protamine sulfate and the effect of protamine sulfate concentration in subsequent, virus-free media was examined (Figure 3.3). For the case of vectors adsorbed 68  Figure 3.1: Binding of retroviral vectors on the cell surface is dependent on the dose of protamine sulfate. MSCV-GALVenv retroviral vectors were contacted with RAT-1 cells for 30 min at 1000g and 17oC in the presence of different concentrations of protamine sulfate as indicated. Then, the VCM was removed, the cells were washed and fresh medium was added. The cells were incubated at 37oC for 2 h, then trypsinized and seeded at low density. They were then incubated for an additional 48 h, after which they were analyzed for GFP+ cells. The error bars indicate the standard deviations of four replicates from two independent experiments.  69  Figure 3.2: Protamine sulfate assists the irreversible binding of retroviral vectors to the cell surface. MSCV-GALVenv retroviral vectors were contacted with RAT-1 cells for 30 min at o  1000g and 17 C in the absence () or presence () of 10 µg/mL protamine sulfate. The VCM was removed, the cells were washed and fresh medium was added. The cells were o  incubated at 37 C and, at the indicated time points, the medium above the cells was collected and assayed for titer. The error bars indicate the standard deviations of four replicates from two independent experiments.  70  Figure 3.3: The entry of retroviral vectors is not affected by the presence of the optimum concentration of protamine sulfate. MSCV-GALVenv retroviral vectors were contacted with o  RAT-1 cells for 30 min at 1000g and 17 C in the absence () or presence ( ) of 10 µg/mL protamine sulfate. The VCM was removed, the cells were washed and media with different o  concentrations of protamine sulfate were added. The cells were incubated at 37 C for 2 h, then trypsinized and seeded at low density. The cells were then cultured for 48 h, after which they were analyzed for GFP+ cells. The error bars indicate the standard deviations of four replicates from two independent experiments. The asterisks indicate a p value of less than 0.05 based on the Student’s t-test.  71  without protamine sulfate, there was a concentration-dependent enhancement in the number of transduced cells up to 10 µg/mL protamine sulfate, as was observed in the case of initial binding (Figure 3.1). These results indicate that the dissociation of reversibly-bound vectors is significantly reduced in the presence of protamine sulfate. On the other hand, in the case where the viral vectors were irreversibly bound in the presence of 10 µg/mL protamine sulfate, protamine sulfate in the virus-free medium had no significant influence on entry events up to ~20 µg/mL, whereas beyond this concentration, it reduced virus entry into the cells. 3.2.4 Quantification of virus dissociation and entry rates: To examine and quantify the virus entry rate, it is necessary to inactivate vectors that have been previously adsorbed onto the cell surface. A short period (~2 min) of treatment with citrate buffer (pH 3.0) has been used to inactivate surface-bound retroviruses, including the Moloney murine leukemia virus (MMLV) (Katen et al. 2001; Kizhatil and Albritton 1997), the amphotropic-MLV (Katen et al. 2001), as well as the avian sarcoma and leukosis virus (ASLV) (Narayan et al. 2003). There were also studies that used trypsin to inactivate murine leukemia viruses (Andersen and Nexo 1983; Portis et al. 1985). We tested the effectiveness of both citrate buffer and trypsin inactivation of MSCV-GALVenv viruses bound to the RAT-1 cell surface. Unlike the other retroviruses, MSCV-GALVenv vectors were found to be resistant to citrate buffer and, in fact, the treatment resulted in an enhancement of transduction (Figure 3.4). On the other hand, incubation of cells with trypsin at 37oC for 10 min was effective in removing bound viruses from the cell surface.  Hence, in the subsequent experiments, only trypsin was used to inactivate the  surface-bound MSCV-GALVenv vectors. (For the case of MMLV, in agreement with the literature, both the citrate buffer and trypsin were able to detach >98% of the surface-bound viruses, data not shown).  72  Figure 3.4: Effect of citrate buffer and trypsin on the inactivation of GALVenv retroviral vectors. MSCV-GALVenv vectors were contacted with RAT-1 cells for 30 min at 2000g and o  17 C. The VCM was removed, and then the cells in some wells were washed and treated o  with citrate buffer for 2 min. The cells in other wells were treated with trypsin at 37 C for 10 min and then were immediately seeded at low density. Control samples were mock-treated with medium.  The medium in the remaining plates was replaced and the cells were o  incubated at 37 C for 2 h, then trypsinized and seeded at low density. All cells were incubated for 48 h, after which they were analyzed for GFP+ cells. The ordinate axis represents the % GFP+ cells relative to that of the control. The error bars indicate the standard deviations of four replicates from two independent experiments. The asterisks indicate a p value of less than 0.05 with respect to control based on Dunnett’s method. 73  To quantify the kinetic rates of entry and dissociation of retroviruses, a mathematical representation of the dynamic behavior of viral vectors on the cell surface was developed and is described in the Materials and Methods section. The kinetic rates of interest were obtained by fitting the analytical solution of the model equations to experimental transduction data. To quantify the entry rate, MSCV-GALVenv vectors in VCM containing 10 µg/mL protamine sulfate were irreversibly bound to RAT-1 cells and, at different time points, the vectors remaining on the cell surface were inactivated by trypsin treatment. Since k–b = 0 in this case and kde = 0.112 h-1 (estimated in section 2.3.2), fitting equation (3.4) to the transduction data as shown in Figure 3.5 yields the entry rate constant, ke. The entry rate constant estimated in this manner was found to be 1.09±0.05 h-1, which implies that half of the irreversibly bound vectors enter into the cell cytoplasm in 38 min. This value is close to the rate constant of 1.04 h-1 reported for MMLV entry into 293-HEK cells (Kolokoltsov and Davey 2004). When the vectors are bound to the cell surface without protamine sulfate, both entry and dissociation of vectors occur and the dynamics is a result of the net effect. The dissociation rate constant obtained by using this second set of data along with the value of ke = 1.09 h-1 determined above was found to be 1.28±0.08 h-1, again indicating a fairly rapid process with a half-time of 33 min. 3.2.5. Infection of MSCV-GALVenv in the presence of NH4Cl: When viruses enter cells via endocytic vesicles, it is expected that lysosomotropic agents in the extracellular medium should influence the vesicle trafficking process.  The lysosomotropic agent ammonium  chloride is a weak base that selectively accumulates in the endosomes and raises their pH by acting as a proton sink, thus preventing the fusion events of acid-dependent viruses. NH4Cl at a concentration of 50 mM has been shown to completely inhibit the entry of several  74  Figure 3.5: Dissociation and entry kinetics of GALVenv retroviral vectors on RAT-1 cells. MSCV-GALVenv retroviral vectors were contacted with RAT-1 cells for 30 min at 1000g and o  17 C in the absence () or presence () of 10 µg/mL protamine sulfate. The VCM was removed, the cells were washed and fresh medium was added. The cells were incubated at o  37 C and, at the indicated time points, were trypsinized and seeded at low density. All cells were cultured for 48 h to later estimate the GFP+ cells. The error bars indicate the standard deviations of two replicates. The lines represent the best fits of equation (5) to the data with k-b = 0 () and k-b ≠ 0 (----).  75  pseudotyped acid-dependent viruses (Brindley and Maury 2005; Diaz-Griffero et al. 2002; Picard-Maureau et al. 2003). However, it has also been shown that ammonium chloride can partially inhibit the trafficking of viruses that utilize pH-independent endocytosis processes (Katen et al. 2001). To investigate the role played by endocytic vesicles in the internalization of retroviruses with the GALV envelope, the vectors were initially bound to the cells and then allowed to enter in the presence of media with different concentrations of NH4Cl. As shown in Figure 3.6, the number of transduced cells was inhibited by NH4Cl in a dose-dependent manner indicating that the virus utilizes an endocytic pathway for entry into the cells. However, the inhibition was only partial compared to the ability of 50 mM NH4Cl to completely inhibit clathrin-mediated endocytic entry. The viability and growth of the cells were not affected by 1 h exposures to these concentrations of ammonium chloride. To determine if the reduction in the transduction could be due to an increase in the degradation rate of retroviruses in the presence of ammonium chloride, the stability of the viral vectors in the absence and presence of NH4Cl was examined.  Viruses in media  containing either 0 or 100 mM added NH4Cl were incubated at 37ºC and the infectivity of the viral vectors was determined at different time points. There was no observed difference in the degradation rate of viral vectors in the presence or absence of ammonium chloride (Figure 3.7). The half-life of the viral vectors for both cases was ~6 h which is consistent with the reported half-lives of other retroviral vectors. Hence, the reduction in the infectivity of retroviruses in the presence of NH4Cl was not due to its direct influence on vector stability. 3.2.6 Low pH treatment of bound MSCV-GALVenv vectors on cells: Viruses utilize the endocytic pathway, especially the clathrin-mediated endocytic pathway, because of the requirement of an acidic pH environment to trigger the fusion events that subsequently release the viral genome into the cytoplasm. The fusion of some low-pH dependent viruses with the 76  Figure 3.6: Ammonium chloride inhibits the infectious entry of GALVenv retroviral vectors. MSCV-GALVenv retroviral vectors were contacted with RAT-1 cells for 30 min at 1000g and 17ºC.  The VCM was removed, the cells were washed and media with different  concentrations of NH4Cl were added.  The cells were incubated at 37ºC for 1 h, then  trypsinized and seeded at low density. The cells were then incubated for 48 h, after which they were analyzed for GFP+ cells (gray bars, normalized to the control with no added ammonium chloride). The effect of ammonium chloride on the growth of the cells was determined from the fold increase in cell number during the 48 h incubation after the treatment (). The error bars indicate the standard deviations of four replicates from two independent experiments.  77  Figure 3.7: Viral degradation rate was not affected by the presence of ammonium chloride. MSCV-GALVenv retroviral vectors were incubated for different times in media without () or with () 100 mM NH4Cl at 37oC. The incubated virus samples were then assayed for o  titer by adding them to RAT-1 cells and centrifuging at 2000g and 17 C and later replacing the medium. The error bars indicate the standard deviations of four replicates from two independent experiments.  78  cell membrane can be initiated by exposing the surface bound virions to a low pH medium (Brindley and Maury 2005). MSCV-GALVenv vectors were initially bound to a monolayer of RAT-1 cells by centrifugation. The cells were then exposed for 2 min to media with lower pH levels and then were incubated for 1 h in a medium at pH 7.4. The resulting normalized infectivities are presented in Figure 3.8. The treatment of cells with a low pH medium did not enhance transduction by increasing the number of vectors that fuse with the cells before they detach from the cell surface. This indicates that a low pH does not trigger the fusion events of the GALV envelope protein with the cell membrane. 3.2.7 Investigation of the type of endocytic pathway utilized by MSCV-GALVenv: Chlorpromazine, an amphiphilic drug, disrupts clathrin-mediated uptake by causing the clathrin-coated vesicles to assemble on endosomes rather than on the cell surface (Wang et al. 1993). Thus, chlorpromazine, at concentrations up to 50 µM, is widely used to block the internalization of viruses that utilize clathrin-coated vesicles for endocytosis (Blanchard et al. 2006; Diaz-Griffero et al. 2002). We further investigated the role of clathrin-coated vesicles in the endocytosis of MSCV-GALVenv vectors by infecting the cells in the presence of various concentrations of chlorpromazine (Figure 3.9).  The presence of chlorpromazine did not  inhibit the transduction of MSCV-GALVenv vectors indicating that they do not use clathrincoated vesicles to gain entry into the cell cytoplasm. Recently, clathrin-independent endocytic pathways have been identified which are pHindependent and insensitive to inhibition by lysomotrophic agents (Mayor and Pagano 2007). These endocytosic processes, however, are highly dependent on the presence of lipid-rafts which are ordered microdomains of glycosphingolipids and sterols. Caveolae are specialized, lipid-rafts enriched, flask-shaped vesicles that are stabilized by cholesterol-binding integral membrane proteins called caveolins. Cholesterol is the major component of these caveolae 79  Figure 3.8: Low pH treatment does not facilitate the entry of GALVenv retroviral vectors. MSCV-GALVenv retroviral vectors were bound to tissue culture dishes with (black bars) or without (gray bars) RAT-1 cells by centrifuging with VCM containing 10 µg/mL protamine o  sulfate at 1000g and 17 C for 30 min. The VCM was removed and treated with media having the indicated pH values for 2 min. All the plates were washed and RAT-1 cells were seeded in the treated dishes without cells. After fresh medium was added to the wells o  containing cells, the latter were incubated at 37 C for 1 h and then trypsinized and seeded at low density. All the samples were incubated for 48 h, after which they were analyzed for GFP+ cells. The data were normalized to the results obtained from the wells that were treated for 2 min with the medium at pH 7.4. The error bars indicate the standard deviations of four replicates from two independent experiments.  80  Figure 3.9: Chlorpromazine does not affect the infectivity of GALVenv retroviral vectors. RAT-1 cells were incubated with media containing indicated concentrations of chlorpromazine at 37oC for 30 min.  Later, the medium was replaced by VCM with  corresponding concentrations of chlorpromazine and centrifuged at 37oC and 1000g for 30 min. Then the cells were washed, trypsinized and seeded at low density. The cells were cultured for 48 h to analyze for GFP+ cells. The error bars indicate the standard deviations of four replicates from two independent experiments.  81  and the extraction of cholesterol from the cell surface leads to disruption of these microdomains and release of associated proteins and receptors (Ilangumaran and Hoessli 1998).  Methyl-β-cyclodextrin (MBCD) at 10 mM was effectively used to extract the  cholesterol from cell surfaces to inhibit infection by viruses that employ lipid-raft caveolae endocytosis for entry (Beer et al. 2005; Lu and Silver 2000; Wang et al. 2008). We tested the influence of cholesterol extraction from the cell surface on the entry of GALVenv retroviruses. MBCD at 10 mM was used to extract the cholesterol from RAT-1 cells and the infectivity of MSCV-GALVenv viruses with these cells was compared with that of untreated cells. The extraction of cholesterol resulted in a 70% reduction of the number of infected cells relative to the untreated cells (Figure 3.10). The treatment of cells with MBCD after virus entry yielded a negligible reduction in the number of transduced cells (Figure 3.10), indicating that the extraction of cholesterol does not affect the post-entry events of the viruses already in the cytoplasm. These results demonstrate that MSCV-GALVenv vectors utilize lipid-raft/caveolaemediated endocytosis similar to the internalization mechanism of murine leukemia retroviruses (Beer et al. 2005; Lee et al. 1999).  3.3 Discussion Binding and subsequent entry are essential replication steps for retroviruses to successfully produce infection.  Virus binding leading to cell entry involves several  intermediate steps including (i) binding of the retrovirus to the cell surface, (ii) interaction of the retrovirus with single or multiple cognate receptors to activate fusion or endocytosis, and (iii) release of viral genomic components into the cell cytoplasm through fusion with the cell surface or by an endocytosis pathway (Haywood, 1994). We have investigated the behavior of GALVenv retroviral vectors on the RAT-1 cell surface to quantify the previously unreported 82  Figure 3.10: GALVenv retroviral vector entry was inhibited by extracting cholesterol from cell membranes. RAT-1 cells were incubated with media containing 10 mM MBCD or no MBCD (control) and then infected with GALVenv retroviral vectors under centrifugation at 1000g. The VCM was removed and the plates were washed. One set of control samples was treated with MBCD medium for 30 min after infection. All the cells were then trypsinized and seeded at low density. The cells were cultured for 48 h and analyzed for GFP+ cells. The ordinate axis represents the % GFP+ cells relative to control. The error bars indicate the standard deviations of four replicates from two independent experiments. The asterisks indicate a p value of less than 0.05 with respect to control based on Dunnett’s method.  83  kinetics of the binding and internalization processes and to elucidate the mechanism of entry into the cell cytoplasm. The initial binding of the MMLV retrovirus is mediated by the membrane polysaccharide, heparan sulfate, which it acquires from its packaging cell (Kureishy et al. 2006). Since our retrovirus was produced from a NIH-3T3-based cell line (Miller et al. 1991), its membrane can also be expected to contain heparan sulfate. Because most virus and cell membranes are covered with negatively-charged components, including heparan sulfate domains, initial binding in the absence of cationic polymers is mediated by a weak van der Waal’s interaction. Our results demonstrate that the initial binding of GALV to the RAT-1 cell surface is minimal and weak, with rapid dissociation from the cell surface. This initial binding can be enhanced by the addition of cationic polymers which act as charge modulation agents between the virus and the cell surface (Davis et al. 2004). We have utilized protamine sulfate, a low molecular weight (~5 kDa) cationic polymer, to investigate the kinetic behavior of this retrovirus on the RAT-1 cell surface. It has been reported that cationic polymers with molecular weights less than 15 kDa do not contribute to virus aggregation (Davis et al. 2004). Our binding experiments showed a maximum of 5-fold enhancement in the number of bound retroviral vectors in the presence of the optimum 10 µg/mL protamine sulfate concentration. Though the number of viral vectors that bind in the absence of protamine sulfate is more than half the number of those bound in the presence of the optimum concentration, the greater (net 5-fold) difference in the delivered viral vectors is the result of dissociation of the viruses from the cell surface. At low concentrations, up to 10 µg/mL, protamine sulfate adsorbs either to the retrovirus particle or to the cell surface (including to the heparan sulfate domain since protamine has high affinity to this molecule), and this assists the binding of the retrovirus to the oppositely-charged portion of the cell 84  surface through electrostatic interaction. The adsorption of the cationic species occurs in a rapid and saturable manner (Davis et al. 2004). In the presence of excess protamine sulfate, the cationic polymer adsorbs to both the virus and the cell surface, resulting in a net positive charge on both surfaces and, hence, a reduction in the available oppositely-charged binding sites between the virus and the cell. As a consequence, viral binding decreases and the number of viral vectors delivered into the cells is reduced. Our experiments also demonstrate that the dissociation of retroviral vectors from the cell surface is negligible if they are bound in the presence of the optimum (i.e., 10 µg/mL) concentration of protamine sulfate, indicating that the binding is irreversible when it occurs through electrostatic interaction. It was also found that the retroviral vectors bound initially by weak van der Waal’s interactions can easily dissociate from the cell surface but rebind strongly if protamine sulfate is present in the medium at the optimal concentration. The role of cationic polymers in the binding process has been well documented in the literature, but its effect on post-binding events has never before been reported. We have investigated the effect of protamine sulfate on the post-binding events to accurately quantify the entry rate. The presence of excess protamine sulfate in the medium, beyond 20 µg/mL, appears to affect the entry kinetics of GALV into the cell cytoplasm. The retrovirus, once it gains access to the cell surface, initiates the entry process through interaction with specific receptors. It may be that the presence of excess cationic polymers interferes with the ability of the surface-bound virus to further interact with these essential receptors. Thus, it may be that when the protamine sulfate concentration is higher, i.e., >20 µg/mL, both the binding and entry processes are adversely affected, thereby reducing the net transduction efficiency. From these findings, it is known that 10 µg/mL of protamine sulfate in the medium facilitates the irreversible binding of a maximum number of retroviruses to the cell surface and 85  does not influence the post-binding events that lead to entry into the cytoplasm. We have employed this concentration to quantify the entry rate of MSCV-GALVenv vectors irreversibly bound on the cell surface. In the absence of protamine sulfate, however, the dynamics of the disappearance of surface bound viruses from the cell surface is the result of both entry and dissociation; thus making it possible, by difference, to determine the dissociation rate. These kinetic rates were quantified with the aid of a mathematical description of these phenomena given in Section 3.1.1. The entry kinetics was found to be rapid with a rate constant of 1.12 h1  and the dissociation rate is equally rapid with a rate constant of 1.33 h-1. These rates  demonstrate that, even though internalization is a rapid process, more than half of the retroviral vectors bound in the absence of cationic polymers dissociate from the cell surface before they can enter, indicating that dissociation is a significant rate-limiting step in the overall retroviral transduction process. The half-time of retroviral entry (37 min) is relatively long compared to the half-times of viruses that utilize clathrin-mediated endocytic entry (≤ 10 min) (Johannsdottir et al. 2009; Kielian et al. 1986). Retroviral vectors employ either direct fusion of their membranes with those of the cells or an endocytosis mechanism to gain entry into the cytoplasm. We have therefore investigated the pathway utilized by GALVenv retroviral vectors to enter RAT-1 cells. First, we found that the presence of ammonium chloride during entry reduced the infection rate of GALVenv retroviral vectors in these cells, suggesting that this virus is internalized via an endocytic process. The entry of acid-dependent viruses by clathrin-mediated endocytosis can be inhibited by more than 90% in the presence of only 50 mM ammonium chloride (Bertrand et al. 2008; Brindley and Maury 2005; Picard-Maureau et al. 2003). However, in the case of GALVenv retroviruses, the inhibition at this concentration was only partial which is similar to the behavior observed for murine leukemia viruses (Bertrand et al. 2008; Katen et al. 2001; 86  Picard-Maureau et al. 2003).  In addition to blocking the acidification of endosomes,  lysosomotropic agents are reported to arrest the transport of vesicles through the endocytic pathway without significantly affecting the internalization of endocytic vesicles from the cell surface (Clague et al. 1994; Vanweert et al. 1995). Although ammonium chloride specifically inhibits pH-dependent clathrin-mediated endocytosis, the partial inhibition might be a result of an arrest in the progression of other endocytic pathways. Also, the inhibition is linear with the ammonium chloride concentration in the medium during the entry process, indicating possible roles for the arresting time and the degradation rate of viral vectors. The larger the amount of ammonium chloride in the medium taken up by the endocytic vesicles along with the virus, the more is the time needed for it to diffuse out and resume endocytic trafficking. However, these retroviruses are labile, with a short half-life of ~6 h, and the inhibition may simply reflect the loss of infectivity of the viruses before the trafficking process is resumed. In addition, a low pH medium did not facilitate infection, suggesting that a low pH is not needed for fusion. However, we cannot exclude the possibility of blocks that, in the presence of acid treatment, are cell-type specific (Marsh and Bron 1997).  Nonetheless, the treatment of cells with  chlorpromazine, which has been shown to inhibit the internalization of viruses that require low pH for fusion, confirms that clathrin-coated vesicles are not involved in the uptake of GALVenv viral vectors. On the other hand, the extraction of cholesterol from the cell surfaces markedly reduced the infection of these cells with GALVenv retroviral vectors.  Though  extraction of cholesterol can affect clathrin-coated vesicles, the results indicating that these vesicles don’t play a role in the infection process suggest the possibility of an alternative endocytic route for entry. Consistent with recent findings for amp-MLV (Beer et al. 2005) and eco-MLV (Lee et al. 1999; Lu and Silver 2000), the most likely alternative is the endocytic pathway mediated by lipid rafts/caveolae. It is not surprising that viruses would 87  exploit such endocytosis pathways considering their many advantages, including the organized trafficking of vectors through the crowded cytoplasm to specific destinations, especially sites that are closer to the nucleus. The entry of a retrovirus into a mammalian cell depends on the location and strength of the initial binding of the virus to the cell. A retrovirus that binds weakly to the cell is believed to undergo two-dimensional surfing on the cell surface until it encounters specific receptors with which it may interact to form a strong bond and initiate entry. However, if vectors were initially bound irreversibly on the cell surface then such lateral movement would not be possible. The interaction with the receptors takes place either by the clustering of lipid-rafts containing receptors to form coated-pits (with or without caveolin) via multivalent binding of these viral envelope proteins to the receptors, or by coated pit formation underneath the virus through signaling induced by the bound vector (Pelkmans 2005). It is now well known that some non-enveloped viruses upon binding induce cell signaling for entry through endocytosis, e.g., Simian Virus 40 through lipid-raft/caveolae (Pelkmans et al. 2002) and adenovirus through clathrin-mediated endocytosis (Nemerow and Stewart 1999). Whether retroviruses induce cell signaling for endocytic entry is still a question to be explored in detail. Our experiments suggest that retroviruses with the GALV envelope utilize non-clathrin cholesterol-rich endocytic vesicles for entry into RAT-1 cells. Investigating the roles played by dynamin and caveolins in the endocytosis process could provide further evidence about the specific endocytosis mechanism exploited by these retroviruses to gain entry into the cell cytoplasm.  88  4. Qua ntitative ana lysis of retroviral transduction steps Retroviral vectors are powerful tools for carrying out gene transfer into mammalian cells because of their ability to permanently integrate their genome into the target cell chromosome for stable and long-term expression of transgenes. The family of retroviruses is divided into the orthoretrovirus and spumaretrovirus subfamilies. Gammaretroviruses and lentiviruses  belong  to  the  orthoretrovirus  subfamily  while  foamy  viruses  are  spumaretroviruses. A gammaretrovirus served as a model for the construction of the first artificial viral gene transfer vehicle and gammaretroviral vectors have been the ones most commonly used for gene therapy clinical trials to date (Edelstein et al. 2007; Mann et al. 1983). However, there is a decreasing interest in these vectors because of their potential drawbacks, such as insertional mutagenesis and an inability to transduce quiescent cells (Hacein-Bey-Abina et al. 2003; Howe et al. 2008).  The ability of lentiviral vectors to  transduce non-dividing cells makes them attractive for high efficiency gene transfer into hematopoietic stem cells and lymphocytes (Akkina et al. 1996; Naldini et al. 1996). However, the pathogenic nature of lentiviruses has raised questions concerning their applicability to clinical settings. Nonetheless, developments in constructing self-inactivating lentiviral vectors for safe gene transfer has led to the recent approval of some clinical trials using these vectors (Escors and Breckpot 2010). On the other hand, the development of foamy-viral vectors is increasingly important because of their non-pathogenic nature and lower preference for integrating near oncogenes (Hill et al. 1999). Also, efforts are currently underway to develop next-generation retroviral vectors capable of site-specific integration in the human genome by incorporating DNA fusion protein domains into the integrase (Ferris et al. 2010; Su et al. 2009). 89  The efficiency of retrovirus-mediated gene transfer is governed by a series of extraand intracellular kinetic steps, including the extracellular mass transport of retroviral vectors in the virus-containing medium (VCM).  Among the methods used to accelerate the  extracellular transport of retroviral vectors to the vicinity of the target cells, the centrifugation of the cells with VCM (spinoculation) is the one most widely employed for scientific and clinically-relevant retroviral transduction studies (Bunnell et al. 1995; Millington et al. 2009; Sanyal and Schuening 1999; Tonks et al. 2005; Yang et al. 2008). Once the retroviral vectors approach the target cell, a series of major kinetic steps (binding to the target cell, receptormediated entry, uncoating and reverse transcription, transport of DNA into the nucleus and integration of the retroviral DNA into the cell chromosome) has to occur successfully for the retroviral genome to be incorporated into the target cell chromosome. A limitation in any of these steps can reduce the overall gene transfer rate and various approaches have been suggested to diminish these limitations. For example, several cationic agents have been promoted for enhancing the irreversible binding of the retroviral vectors to the cell surface through shielding of the repulsive forces that exist between the overall negatively-charged retrovirus and target cell (Davis et al. 2004; Hanenberg et al. 1996; Hodgson and Solaiman 1996). Also, spinoculation along with cationic agents has been suggested to ensure enhanced contact of the retroviral vectors and target cells (Costello et al. 2000; Swaney et al. 1997; Tonks et al. 2005). However, the net delivery of retroviral genomes into the cells’ cytoplasm is often limited by the receptor-mediated entry process. Enhancement in the entry step can be obtained by pseudotyping the retroviral vectors with envelope proteins that target the most abundant receptors on the cell surface (Gallardo et al. 1997; Relander et al. 2002b). For delivered vectors, the efficiency of the various intracellular events is dependent on the retrovirus type and the cell-cycle status. Though the majority of the kinetic pathways are 90  similar for all three types of retroviral vectors, they differ in two important intracellular steps. Most retroviruses, by nature, complete their reverse transcription after entering into the target cell (Coffin et al. 1997).  Foamy viruses are unique among retroviruses in that reverse  transcription is mostly completed in the virus-producing cells rather than in the target cells (Moebes et al. 1997; Yu et al. 1996; Yu et al. 1999).  Reverse transcription for  gammaretroviral and lentiviral vectors can be accelerated by supplementing the G0-resting target cells with nucleosides. Another difference between the three retroviral vectors is that the transport of the pre-integration complex (PIC) of gammaretro- and foamy-viral vectors occurs only during the mitotic phase, while the PIC of lentiviruses can enter into the nucleus at any stage in the cell cycle (Lewis and Emerman 1994; Miller et al. 1990; Trobridge and Russell 2004). In this chapter, a modified version of the mathematical model for retroviral gene transfer from Chapter 2 was used to quantitatively analyze the role of the various kinetic and mass transport steps in the retroviral transduction process. The model was used to find the optimum extracellular process conditions for centrifugation by examining the effects of centrifugal force, time of centrifugation as well as the effects of individual extra- and intracellular kinetic parameters on the transduction efficiency. The performances of the three retroviral vectors with respect to transduction efficiency and integrated copy number were also investigated by assigning kinetic parameters based on their differences in transduction pathways.  4.1 Mathematical model The mathematical model for the retroviral transduction process in Chapter 2 was developed assuming that the saturation of binding sites on the cell surface is negligible. However, this assumption is not applicable for all virus and target cell systems. Also, we 91  observed a saturation of the experimental transduction efficiency (Figure 2.6) which showed deviations compared to the model predictions, particularly at high vector-to-cell ratios. Though these deviations are acceptable for the target cell and virus system used to validate the model, the model may fail to predict the behavior of poorly transduced cells with a limited number of virus-binding sites. Hence, the model was modified for the phenomenon that the retroviral vectors only bind to cells with unsaturated virus-binding sites. Thus, the mass flux of retroviral vectors to the bottom of the culture dish (i.e., z = 0) in equation (2.3) can now be written as: −D  ∂Vm + uVm = − kb ( Ct − [VC ]) Vm + k− b [VC ] ∂z  (4.1)  where kb and k-b are the binding and dissociation rate constants, respectively, and Ct is the total target cell density at the bottom of the culture dish. The rate of change in the concentration of virus-cell complexes [VC] is given by d [VC ] =kb ( Ct − [VC ]) Vm − k− b [VC ] − ke [VC ] − kde [VC ] dt  (4.2)  where ke is the rate constant for the entry of retroviral vectors into the cell. Assuming a quasisteady state of the process occurring on the cell surface, i.e.  d [VC ] ≈ 0 , the boundary condition dt  in equation (4.1) can be reformulated as −D  ∂Vm Vm + uVm = − keCt K s + Vm ∂z  (4.3)  where Ks is the saturation constant given by K = s  ke k− b + kdm + ke . = Kb kb  (4.4)  The complete set of model equations with this modification in the virus and target cell population balances is presented in Table 4.1. 92  4.2 Materials and Methods 4.2.1 Transduction with different heights of VCM: The transduction of K562 cells with different heights of VCM containing MSCV-GALVenv retroviral vectors was carried out in 6well tissue culture plates (Sarstedt, Montreal, Canada). Samples with ~7.5×106, ~3.75×105 and ~2×105 target cells in two different concentrations of VCMs were prepared. Then, 1.5, 3.0 and 5.0 mL of these suspensions (equivalent to 1.5, 3.0 and 5.0 mm heights of VCM, respectively) were added to the wells of the 6-well plates in duplicate. The head space of the 6-well plates was replaced with 5% CO2/balance air and sealed to maintain pH and osmolality. The plates were centrifuged at 2000g and 37oC for 6 h. Then the cells were separated from the VCM and incubated in fresh medium for 72 h prior to analyzing for GFP+ cells using flow cytometry (BD Biosciences, San Jose, USA). 4.2.2 Numerical analysis: The partial differential equation (4.5) was converted into a set of ordinary differential equations (ODEs) by discretizing in the z direction using the exponential differencing scheme, which was developed to reduce the false diffusion error in convectiondiffusion problems (Patankar 1980). This set of ordinary differential equations along with the other ODEs (equations (4.8)-(4.13)), were solved using a 4th-order Runge-Kutta method in MATLAB.  4.3 Results 4.3.1 Model validation with experimental data:  The rate constants of MSCV-GALVenv  vectors for the dissociation from and entry into RAT-1 cells were estimated in Chapter 3. Assuming that the rates with which these vectors dissociate from and enter into K562  93  Table 4.1: Model equations for retroviral gene transfer process  Mass transport of retroviral vectors: ∂Vm ∂V ∂ 2Vm + u m = Dv − kdeVm ∂t ∂z ∂z 2 ∂V Vm (t , 0) B.C. 1: − Dv m + uVm = −keCt K s + Vm (t , 0) ∂z ∂V B.C. 2: − Dv m + uVm = 0 ∂z  (4.5) at z = 0  (4.6)  at z = h  (4.7)  Intracellular virus populations: dV f  Vm (t , 0) − kdiV f − kn nv Cc(t −τ ) dt K s + Vm (t , 0) dVc Vm (t , 0) = − kdiVc − knVc (t −τ ) keCt dt K s + Vm (t , 0) dVi = knVc( t −τ ) + µVi dt = ke (C f + Cc )  (4.8) (4.9) (4.10)  Target cell populations: dC f  Vm (t , 0) + δ1kdi Cc + δ 2 µ Cc + µ C f dt K s + Vm (t , 0) dCc Vm (t , 0) = ke C f − δ1kdi Cc + (1 − δ 2 ) µ Cc − knCc (t −τ ) dt K s + Vm (t , 0) dCi = knCc( t −τ ) + µ Ci dt Ct = C f + Cc + Ci = − ke C f  (4.11) (4.12) (4.13) (4.14)  Parameters in equations:  δ1 = = e − ( n −1) ; δ2 v  (nv − 1) k −1 e − ( nv −1) 1− k ×2 ; ∑ (k − 1)! k =1  5×nv  nv =  Vf Cc  (4.15)  Output parameters: % Transduced cells =  Ci ×100 Ct  Integrated copy no./transduced cell=  (4.16)  Vi Ci  (4.17) 94  cells are not significantly different from those determined using RAT-1 cells, the modified model was tested using the experimental data obtained in Chapter 2 (Figures 2.6 and 2.7). The binding rate constant, kb, was derived from the value of the equilibrium binding rate constant, Kb, measured in Chapter 2 using the dissociation and entry rate constants. The values of all the parameters needed to run the model are presented in Table 4.2. The model predictions of the transduction efficiency at vector-to-cell ratios ranging from 0.5 to 17 under static gravity (1g) and centrifugation (2000g) conditions are compared with the corresponding experimental data in Figure 4.1(A). The transduction efficiency predictions obtained using the modified model, which now accounts for the saturation of binding sites, agree even better with the experimental data. The model results thus explain why the transduction efficiency plateaus at lower values when high vector-to-cell ratios are used under centrifugation conditions. The  Table 4.2: Values of the kinetic parameters in the model Parameter  Value  Extracellular decay rate constant, kde  0.112 h–1  Binding rate constant, kb  7.69×10-8 cm3/cell·h  Dissociation rate constant, k-b  1.28 h-1  Entry rate constant, ke  1.09 h-1  Intracellular decay rate constant, kdi  0.0012 h–1  Cytoplasmic trafficking time, τ  11.2 h  Nuclear import rate constant, kn  0.067 h–1  Growth rate of target cells, µ  0.033 h−1  95  predictions of the modified model were also compared with the experimental data showing the relationship between the mean integrated viral copy number and the transduction efficiency (Figure 4.1(B)). Similar to the results obtained with the unmodified model developed in Chapter 2, the predictions are once again in good agreement with the experimental data. However, there was an improvement in that the measured and predicted transduction efficiencies did not increase above 80% (where the mean copy number was ~3) partially because of the saturation of bound viruses at the target cell surface. The model was further tested using experimental transduction data obtained by varying the height of VCM above the target cells under conditions where the number of cells per unit surface area was held constant (Figure 4.2). The model predictions show that, when a centrifugal force of 2000g is applied, the transduction efficiency increases as the VCM height is raised indicating that an increasing number of vectors are delivered to the vicinity of target cells at the bottom of the culture dish. However, this increase in the transduction efficiency with height of VCM plateaued at ~80% when the higher concentration of vectors was used. Overall the model predictions and the corresponding experimental data were again in good agreement, indicating that the modified mathematical model predicts very well the effects of centrifugation on the mass transport of viral vectors. 4.3.2 Extracellular mass transport analysis: The extracellular mass transport of retroviral vectors is governed by their density, size and shape. By assuming that the retroviruses were spheres having a diameter of 115 nm and a density of 1.17 g/cm3, the model was used to investigate the effect on the transduction efficiency of other mass transport parameters such as the settling velocity (centrifugation speed) of the viral vectors, the height of the VCM above the target cells and the time of VCM exposure to the target cells.  96  Figure 4.1: (A) Transduction efficiency as a function of vector-to-cell ratio and (B) mean number of integrated viral copies per transduced cell as a function of transduction efficiency. Experimental data were obtained as described in Section 2.3 and the solid lines represent the predictions of the model presented in Table 4.1. The dashed lines indicate predictions of the model presented in the section 2.1. 97  Figure 4.2: The effect of the height of the VCM on transduction efficiency. A constant number of K562 cells was suspended in different volumes of VCM, containing either 2.36×106 () or 9.24×106 () vectors/cm3, to obtain different VCM heights.  Each  suspension was then centrifuged at 2000g for 6 h. The solid lines represent the predictions of the model presented in Table 4.1. The error bars indicate the standard deviations of four replicates from two independent experiments.  98  4.3.2.1 Settling velocity of viral vectors:  The effect of the vector settling velocity (or  centrifugation speed) on transduction efficiency as a function of VCM height is presented in Figure 4.3(A). The total time of VCM exposure was set as the time until the depletion of 95% of the initial active retroviral vectors from the extracellular medium. The figure shows that increasing the centrifugal force on the vectors results in a corresponding increase in transduction efficiency until a plateau is reached at progressively higher values as the VCM layer becomes thicker. The increase in the height of the VCM for a constant number of cells per unit surface area provides a larger number of available vectors per cell. It should also be noted that a centrifugal force of only 1000g is sufficient, even with a 10 mm height of VCM, to approximately reach the maximum transduction efficiency. This suggests that a medium speed centrifugation at 1000 – 2000g should be adequate to obtain the maximum benefit from a given viral vector suspension. 4.3.2.2 Time of VCM exposure to target cells: The time of VCM exposure until 95% of the active vectors are depleted from the extracellular medium under the conditions in Figure 4.3(A) is presented in Figure 4.3(B). Figure 4.3(B) shows that the exposure time remains essentially constant for gravitational forces up to 10g, then decreases with an increase in the centrifugal force up to 1000g to a minimum value where it remains constant with further increases in the vector settling velocity. Though the times at low settling velocities up to 1000g are different for different heights of VCM, they converge to approximately the same minimum time as the settling velocity is increased beyond 1000g.  This minimum time  corresponds to the time required for the kinetic process involving vector entry into the cytoplasm. Spinoculation provides the condition where the target cells are exposed to thin layer of highly concentrated VCM and hence only reduces the exposure time without affecting the 99  Figure 4.3: The effect of centrifugal force (or settling velocity of vectors) on transduction efficiency (A) and the exposure time of VCM to target cells needed to reach 95% vector depletion (B). The simulations were carried out for the transduction of cells with the height of :  VCM equal to 2 (- -), 5 (----) and 10 mm () using the kinetic parameters in Table 4.2. 100  kinetics. The depletion of active retroviral vectors from the extracellular medium occurs either due to the decay of extracellular viral vectors or due to their delivery into the target cells as governed by their binding, dissociation and entry rates. The influence of these kinetic rates (normalized to the values in Table 4.2) on the transduction efficiency and the required exposure time (until 95% of the active vectors are depleted from the extracellular medium) for an initial vector-to-cell ratio of 1 and centrifugation at 1000g is presented in Figure 4.4. As can be seen from Figure 4.4(A), a 100-fold change in the extracellular half-life resulted in only an approximately 2-fold change of the VCM exposure time although there was a 6-fold change in the transduction efficiency. However, the kinetics of binding, dissociation and entry all have more significant effects on the exposure time required to obtain maximum transduction efficiency. A 100-fold decrease in either the binding or the entry rate or a 100-fold increase in the dissociation rate resulted in 5- to 6-fold increase in the required exposure time. The same change in these kinetic parameters resulted in only an approximately 2-fold change in the transduction efficiency. These results indicate that the exposure time is greatly influenced by the cell surface kinetics of viral vectors. The faster they bind and enter into target cells without dissociation, the lower is the required time of VCM exposure to the target cells and the greater is the transduction efficiency. 4.3.3 Kinetic rates that affect the saturation of transduction efficiency: Retrovirus-mediated gene transfer involves several kinetic steps that occur in series for productive transduction. The mathematical model has been formulated to include all of the essential rate-limiting kinetic steps. Here we investigate the effect of these kinetic rates on the overall transduction efficiency and its saturation below the maximum possible value of 100% as the initial vectorto-cell ratio is changed. The kinetic rate constants from Table 4.2 were used as default values except for the one that is varied. 101  Figure 4.4: The effect of kinetic rate constants: extracellular decay (A), binding (B), dissociation (C) and entry (D) on the transduction efficiency () and the time of exposure to VCM to obtain maximum transduction efficiency (----) at an initial vector-to-cell ratio of 1 and a centrifugal force of 1000g.  102  4.3.3.1 Extracellular kinetic steps: The delivery of retroviral vectors into the cells is governed by four important extracellular kinetic processes: decay, binding, dissociation and receptormediated entry, in addition to the mass transport of retroviral vectors from the VCM to the cell surface. The effects of changes in these kinetic rates on the transduction efficiency as a function of the retrovirus concentration are presented in Figure 4.5. Spinoculation at 1000g for 4 h was used for all the following investigations since they were found to be sufficient to reach maximum transduction efficiency (Figure 4.3). Figure 4.5(A) shows that a 100-fold increase in the vector decay half-life did not result in a significant change in the transduction efficiency as a function of viral vector concentration and did not alter the maximum transduction efficiency. Increasing the binding rate reduced the required number of vectors per cell needed to obtain the same level of transduction efficiency, but also did not change the plateau value of the transduction efficiency (Figure 4.5(B)). As was the case for the binding rate, decreasing the dissociation rate did not affect the maximum attainable transduction efficiency, but did cause a noticeable reduction in the vector-to-cell ratio required for a given transduction efficiency when dissociation was negligible (Figure 4.5(C)). The effect of the rate of entry of bound retroviral vectors into the cell cytoplasm is presented in Figure 4.5(D). As the entry rate constant increases, the maximum attainable transduction efficiency rises to reach a value close to 100%. This indicates that viral entry into the cells is one of the key extracellular kinetic steps that determine the level of saturation of the transduction efficiency, and hence, accelerating this step would provide higher transduction efficiencies. 4.3.3.2 Intracellular kinetic steps: The retroviral genome delivered into the cytoplasm spends a considerable amount of time undergoing the uncoating and reverse transcription processes. During this time, it may be prone to degradation by cellular factors. The influence of the  103  Figure 4.5: The effect of extracellular kinetic rate constants: decay (A), binding (B), dissociation (C) and entry (D) on the transduction efficiency as a function of the initial vector-to-cell ratio. The simulations were performed for the case where transduction was carried out under centrifugation at 1000g for 4 h using the parameters in Table 4.2, except where individual extracellular parameter were changed according to the table below: Curve  A: kde (h-1)  B: kb (cm3/cell-h)  C: k-b (h-1)  D: ke (h-1)  - ⋅⋅ ---  0.1386 0.0139 0.0014  5 x 10-9 5 x 10-8 5 x 10-7  5.0 0.5 0.05  0.5 1.0 5.0  104  intracellular degradation rate on the efficiency of retroviral transduction using the other parameters of the model in Table 4.2 is presented in Figure 4.6. The transduction efficiency increases with an increase in the retrovirus concentration and reaches a plateau at vector/cell ratios exceeding ~10. The plateau value depends on the intracellular degradation rate and increases significantly as the half-life of the viral vectors is raised. Thus, the intracellular decay of viral genomes can restrict the system’s ability to reach a high level of transduction even when an abundance of vectors is supplied. The dynamics of the effects of the cytoplasm trafficking time and the nuclear transport rate on the transduction efficiency also depends on the intracellular degradation of retroviral genomes. The effect of the cytoplasm-trafficking time is investigated for the case of no degradation (Figure 4.7(A)) and also for the case where intracellular degradation occurs with a half-life of 6 h (Figure 4.7(B)). For both cases, the transduction efficiency increased with increasing vector-to-cell ratio and reached a plateau value that depends on the trafficking time. In the absence of intracellular degradation, an increase in the trafficking time from 1 to 20 h resulted in a decrease of 20% in the transduction efficiency (Figure 4.7(A)). But when the retroviral vectors decay intracellularly with a half-life of 6 h, the same increase in trafficking time yielded a reduction of ~45% in the transduction efficiency. Thus, the presence of intracellular degradation can elevate the reduction in transduction efficiency that occurs with an increase in trafficking time. A similar dependency between the nuclear transport rate of the retroviral PIC and the intracellular half-life was observed. The effect of the nuclear transport rate on transduction efficiency was also investigated for the two cases when intracellular degradation is absent (Figure 4.8(A)) and when it is present (Figure 4.8(B)). A 10-fold enhancement in the nuclear import rate caused a marginal increase of only ~15% in the transduction efficiency when no intracellular decay of retroviral genomes occurs. When 105  Figure 4.6: The effect of intracellular decay half-life on transduction efficiency as a function of vector-to-cell ratio under centrifugation conditions.  The simulations were  carried out at a centrifugal force of 1000g for 4 h using vector intracellular half-lives of 6.2 h (- ⋅⋅ -), 20.8 h (----) and 600 h (). The remaining parameters were at their default values as listed in Table 4.2.  106  Figure 4.7: The effect of the cytoplasm-trafficking time on the transduction efficiency as a function of vector-to-cell ratio in the absence (A) or presence (B) of the intracellular degradation of retroviral vectors. The simulations were carried out for transduction with VCM having different initial concentrations under centrifugation at 1000g for 4 h using different cytoplasm trafficking times of 1 :  h (), 10 h (----) and 20 h (- - ) for intracellular half-lives of 600 h (A) and 6.2 h (B). The remaining parameters were at their default 107  values as listed in Table 4.2.  Figure 4.8: The effect of the rate of nuclear transport of PIC on the transduction efficiency as a function of vector-to-cell ratio in the absence (A) or presence (B) of the intracellular degradation of retroviral vectors. The simulations were carried out for different initial :  concentrations of VCM under centrifugation at 1000g for 4 h using different nuclear entry rates of 0.067 h-1 (- -), 0.134 h-1 (----) and 0.667 h-1 () for intracellular half-lives of 600 h (A) and 6.2 h (B). The remaining parameters were at their default values as listed in 108  Table 4.2.  intracellular degradation takes place with a half-life of 6 h, the same enhancement in the nuclear import rate resulted in an increase of ~35% in the transduction efficiency. This indicates that, to achieve high transduction efficiency, retroviral vectors need to be transported into the nucleus at a rapid rate, especially when intracellular degradation factors are present in the target cell. 4.3.4 Performance of gammaretro-, lenti- and foamy-viral vectors: Gammaretro-, lenti- and foamy-viral vectors are the favored vehicles for obtaining chromosomally-integrated gene transfer with long-term expression of the transgene. These retroviruses all have diameters ranging from 100 to 120 nm and have shapes that are approximately spherical. Their densities are reported to be in the range of 1.16-1.18 g/cm3 (Cimarelli et al. 2000; Fassati and Goff 1999; Loh and Matsuura 1981). A diameter of 115 nm and density of 1.17 g/cm3 were selected as common representative values for all three vectors. Pseudotyping foamy-viral vectors with other envelope proteins were not successful but foamy-viral envelope proteins were successfully used to pseudotype gammaretroviral and lentiviral vectors.  Retroviral  vectors with foamy-viral envelopes utilize a clathrin-mediated endocytosis process for entry and this is a rapid process with an entry half-time of ~10 min. To ensure a similar efficiency of entry into the target cell cytoplasm, we have assumed that all the three retroviral vectors have been pseudotyped with foamy-viral envelopes.  Compared to gammaretroviral and  lentiviral vectors, foamy-viral vectors spend considerably less time in the cytoplasm before they are ready to be transported into the nucleus since the latter do not need to undergo reverse transcription. Hence, an approximate time of 1 h was assigned as the cytoplasm trafficking time of foamy-viral vectors. Gammaretro- and foamy-viral vectors depend on the doubling time of the target cells for entry into the nucleus, whereas lentiviral vectors enter by active transport through the nuclear membrane pores in addition to the entry during cell division. 109  The rate of nuclear entry by active transport through nuclear pores for the HIV-1 retrovirus was reported to be 0.17 h-1 and, hence, this value is used for lentiviral vectors, while the nuclear entry rate constant for gammaretro- and foamy-viral vectors is calculated based on the doubling time of the target cells.  The performance of the three retroviral vectors was  investigated by using kinetic parameters based on these assumptions and whose default values are listed in Table 4.3.  Table 4.3: Model parameters for gammaretro-, lenti- and foamy-viral vectors  #  Parameter  gammaretroviral vector  lentiviral vector  foamy-viral vector  kde (h-1)  0.112  0.112  0.112  Kb (cm3/cell.h)  5.0×10-8  5.0×10-8  5.0×10-8  ke (h-1)  4.0  4.0  4.0  kdi (h-1)  0.0012 or 0.112  0.0012 or 0.112  0.0012 or 0.112  τ (h)  10  10  1.0  kn (h-1)  2*ln(2)/td  2*ln(2)/td+0.17#  2*ln(2)/td  0.17 h-1 is the value for the rate of active transport of HIV-1 DNA into the nucleus (Barbosa et al. 1994).  4.3.4.1 Doubling time of target cells: The doubling time of the target cells can vary depending on their type as well as the number and types of cytokines used in the culture. Here we investigate, for the three vectors, the relationship between the transduction efficiency and the cell doubling time in the absence and presence of intracellular degradation. When the vectors remain stable in the cytoplasm of the target cells, the transduction efficiency increased with an increase in the doubling time for both the gammaretroviral and lentiviral vectors and eventually reached a constant value (Figure 4.9(A)). The low transduction efficiency in rapidly dividing cells was due to the dilution of vectors during the time they spent for reverse 110  :  Figure 4.9: The transduction efficiency of gammaretro- (), lenti- (----) and foamy- (- -) viral vectors as a function of the doubling time of target cells in the absence (A) or presence (B) of intracellular degradation of viral vectors at a centrifugal force of 1000g and a VCM exposure time of 4 h.  111  transcription and uncoating.  This was unlike the transduction efficiency of foamy-viral  vectors that were independent of the doubling time of the target cells since they spend negligible time for reverse transcription and uncoating. However, in the presence of intracellular degradation, the transduction efficiency of both gammaretro- and foamy-viral vectors decreased with an increase in the target cell doubling time (Figure 4.9(B)). But the lentiviral vectors had the same increased performance with an increase in the doubling time due to their different cell-cycle independent entry into the nucleus as compared to gammaretro- and foamy-viral vectors.  This indicates that lentiviral vectors may be the  superior choice for efficient gene transfer into target cells with longer doubling times, especially when the intracellular degradation of retroviral genomes is significant.  The  following investigations were performed assuming that human hematopoietic stem cells are the target and using the reported doubling time of 55 h when they are expanded with chromatin modifying agents to retain their repopulating potential (Araki et al. 2007). 4.3.4.2 Cytoplasm trafficking time: The cytoplasm-trafficking time is dependent upon the efficiency of uncoating and/or reverse transcription of retroviral vectors inside the cytoplasm. The effect on the transduction efficiency of changes in the cytoplasm-trafficking time (7 – 55 h for gammaretroviral and lentiviral vectors and 1 − 55 h for foamy-viral vectors) in the absence and presence of intracellular vector degradation is presented in Figures 4.10(A) and 4.10(B), respectively.  Increasing the trafficking time resulted in decreased transduction  efficiency, with lentiviral vectors yielding the highest efficiency for both cases. The higher performance of lentiviral vectors is due to their entry into the nucleus at a faster rate compared to the other two viral vectors.  The transduction efficiency results were similar for the  gammaretro- and foamy-viral vectors since the only difference between them is the cytoplasm trafficking time. In the absence of intracellular vector decay, the transduction efficiency 112  :  Figure 4.10: The transduction efficiency of gammaretro- (), lenti- (----) and foamy- (- -) viral vectors as a function of the cytoplasm trafficking time in the absence (A) or presence (B) of intracellular degradation of vectors at a centrifugal force of 1000g and a VCM exposure time of 4 h.  113  decreased linearly with an increase in trafficking time for all three vectors, and the difference in performance between the lentiviruses and the other two vectors remained essentially constant over the independent variable range tested. The longer trafficking time resulted in the dilution of intracellular viral vectors amongst the dividing cells before they permanently integrate into each daughter cell’s chromosome, and caused a decrease in the transduction efficiency. On the other hand, when intracellular viral decay is present, the transduction efficiency of all three retroviral vectors decreased exponentially with an increase in trafficking time. Though the lentiviral vectors gave superior performance at low trafficking times, at higher values, their transduction efficiencies decreased to levels similar to those obtained for gammaretro- and foamy-viral vectors. This indicates that the processes in the cytoplasm should occur very efficiently if the lentiviral vectors are to perform to their full potential. 4.3.4.3 Integrated copy number as a function of transduction efficiency: The number of integrated copies per cell is an important variable for assessing the risk of genotoxicity due to the altered chromosome of the target cell. As the integrated copy number increases, the risks of insertional mutagenesis and also cell apoptosis rise.  The relationship between the  integrated copy number and the transduction efficiency for the three retroviral vectors is presented in Figure 4.11. The simulations were performed for the case where the vectors are stable inside the cells (as was shown in chapter 2). As was observed in Chapter 2, the integrated copy number increased only slowly with an increase in the transduction efficiency up to ~75%, and then in an almost exponential fashion beyond this value. There was no observable difference in the behavior of gammaretro- and foamy-viral vectors whose copy numbers both increased at a higher rate compared to that of the lentiviral vectors. This indicates that the nuclear import rate plays a more important role than the cytoplasm trafficking time in determining the number of integrated viral copies. 114  Figure 4.11: The average number of integrated copies per transduced cell as a function of %Transduced cells for gammaretro- (), lenti- (----) and foamy- (- ⋅⋅ -) viral vectors. The simulations were performed using the parameters in Table 4.3 and by varying the vector-tocell ratios in order to obtain the range of transduction efficiencies shown in the figure.  115  The effect of the intracellular decay rate constant on the average number of integrated viral copies at 50% transduction efficiency for the three retroviral vectors is presented in Figure 4.12. The presence of intracellular viral degradation resulted in an increased number of integrated viral copies at the same level of transduction efficiency for both the gammaretroand foamy-viral vectors.  As the intracellular half-life increased, the viral copy number  decreased down to a value of <2 for these two types of retroviral vectors. But, for the lentiviral vectors, the average number of integrated viral copies was always lower than that of the other retroviral vectors, and was not significantly affected by the changes in the intracellular degradation half-life.  4.4 Discussion Centrifugation can be used to enhance the settling velocities of retroviral vectors and drive them to the vicinity of the target cells, thereby resulting in a greater number of vectors accessible to these cells. Our simulation results showed that the maximum transduction efficiencies for a given height and concentration of VCM can be reached at centrifugation speeds as low as 1000-2000g. Increasing the height of the VCM for a constant number of cells per unit surface area provides enhanced transduction efficiency especially when the concentration of retroviral vectors in the VCM is low. Centrifugation of target cells with VCM at room temperature followed by incubation up to 24 h is the standard protocol employed for spinoculation (Sanyal and Schuening 1999; Yang et al. 2008).  Repeated  exposure of hematopoietic stem cells (HSCs) to VCM at different time points is required to transduce all the cells since only a fraction of these cells will be in cell cycle at any given time. Such prolonged exposures of sensitive target cells, especially hematopoietic stem cells, with the added effects of VCM conditioned by packaging cells may result in the alteration of their normal functionality (e.g. loss of stem cell function). On the other hand, purification of the 116  Figure 4.12: The effect of the intracellular degradation rate on the relationship between the transduction efficiency and the integrated viral copy number for gammaretro- (), lenti(----) and foamy- (- ⋅⋅ -) viral vectors. The simulations were performed using the parameters in Table 4.3 and by varying the vector-to-cell ratios to obtain the number of viral copies at a transduction efficiency of 50% for the three retroviral vector systems.  117  retroviruses from conditioned VCM adds steps to the processing and results in substantial losses of active vectors (Rodrigues et al. 2007). Our simulations suggest that the exposure time of target cells to VCM can be reduced to ~5 h by using centrifugation at 1000-2000g and 37oC which is sufficient to deliver most of the vectors to the target cells for a VCM height up to 1 cm. This exposure time can be reduced further by improving the kinetic steps that take place at the cell surface, i.e., by enhancing the binding to, eliminating the dissociation from and accelerating the entry of the retroviral vectors into the target cells (Figures 4.2(B), (C) and (D), respectively). The binding rate of retroviruses to the cell surface can vary depending on the vector and target cell types (Salmons and Gunzburg 1993). Retroviral vectors mainly bind to the most abundant glycosaminoglycans on the cell surface without any need for specific receptors (Kureishy et al. 2006; Pizzato et al. 2001a). Cationic polymers have been shown to enhance this binding step by shielding the repulsive forces between the retroviral vector and target cell membrane and by minimizing the dissociation of bound vectors (Davis et al. 2002; Davis et al. 2004). Hence, the use of cationic agents in combination with methods to enhance the settling velocity is an attractive approach to reduce the time of VCM exposure to the cells. Even when binding is enhanced and dissociation is eliminated, a slower entry rate of vectors into the cells can hamper their overall delivery. The entry rate depends on the type and number of receptors on the cell surface that the retroviral envelope is targeting. Enhancements in transduction efficiency have been obtained by increasing the expression of specific receptors (MacDonald et al. 2000; Relander et al. 2002a). Retroviral vectors pseudotyped with vesicular stomatitis virus G (VSV-G) proteins as their envelope proteins were found to transduce target cells very efficiently (Akkina et al. 1996; Burns et al. 1993). The positive charges of the VSV-G envelope bind with the abundantly available negatively-charged phospholipids in the cell membrane (Carneiro et al. 2002). Also, retroviral vectors with a 118  VSV-G envelope enter into the target cells rapidly using clathrin-mediated endocytosis. These features make VSV-G an attractive alternative envelope protein for pseudotyping retroviral vectors in order to enhance the binding and entry of retroviral vectors into the cells without the need for cationic agents. Retroviral transduction often results in the saturation of the transduction efficiency below 100% depending on the vector-cell system even when highly concentrated VCM is used. Simulations investigating the effects of various kinetics rates on gene transduction indicate that the steps following vector binding can significantly modulate the saturation level achieved.  Enhancing the binding rate or eliminating dissociation does not improve the  saturation limit but does allow this limit to be reached at a lower concentration of retroviral vectors. However, improving the rate of retroviral entry into the cytoplasm makes it possible to raise the transduction plateau to values approaching 100%. Thus, the methods discussed above to enhance the binding and entry rate, and to reduce the dissociation of retroviral vectors can be applied to obtain greater transduction efficiencies at lower vector-to-cell ratios. However, the intracellular kinetic steps need to occur fairly rapidly in order for these improvements in the extracellular methods to achieve their maximum benefit. The degradation of gammaretroviral genomes inside the cytoplasm of target cells has been reported, indicating that these vectors can be labile in the intracellular environment (Andreadis et al. 1997; Patton et al. 2004; Springett et al. 1989). This decay is thought to be due to the degradation of the RNA template by cellular factors or to the instability of the reverse transcriptase or integrase enzymes. Intracellular vector degradation was also found to be dependent on the target cell type (Springett et al. 1989).  In our  simulation studies, an increase in the intracellular vector decay rate reduced the maximum reachable transduction efficiency remarkably even when high concentrations of vectors were provided. Accelerating the intracellular processes that lead to the successful integration of a 119  retroviral genome into the chromosome (i.e., reverse transcription, uncoating and nuclear transport) may be a viable option for rescuing the vectors from intracellular degradation. For example, supplementing nucleosides in the culture medium can accelerate the reverse transcription of retroviral vectors in resting cells and hence reduce the cytoplasm-trafficking time (Goulaouic et al. 1994; Pieroni et al. 1999). The simulations showed that there was an inverse relationship between the trafficking time and the saturation limit of transduction efficiency. A longer trafficking time in the absence of intracellular degradation decreases the transduction efficiency due to the dilution of vectors in the cytoplasm amongst the dividing cells.  However, the maximum transduction efficiency limit underwent a more drastic  reduction when the trafficking time was increased in the presence of intracellular vector decay. Supplementing nucleosides in the culture during transduction is an attractive approach for accelerating the reverse transcription process and allowing it to be completed in the minimum required time (Goulaouic et al. 1994; Pieroni et al. 1999). The transport of a gammaretroviral genome for integration in the target cell nucleus is dependent on the mitotic phase of the target cell cycle. Though a decrease in the doubling time of the target cells can accelerate this step, the use of retroviral genomes that do not require a mitotic phase for integration could be most effective for targeting slowly dividing hematopoietic stem cells or non-dividing lymphocytes. This was attempted by incorporating nuclear localization signals into gammaretroviral vectors, but was unsuccessful in transporting their genomes into cell nuclei independent of the mitotic phase (Deminie and Emerman 1994; Seamon et al. 2002). The capsid proteins are closely associated with the PICs of gammaretroviral vectors (Bowerman et al. 1989; Fassati and Goff 1999) but not with those of lentiviral vectors (Khiytani and Dimmock 2002; Miller et al. 1997). It was reported that the capsid protein is the dominant determinant in retroviral infectivity and it has been hypothesized that the uncoating of capsid proteins from retroviral PICs is an important factor that determines the nuclear import of the vectors genomes 120  (Yamashita and Emerman 2004). Hence, the rate of nuclear transport of gammaretroviral PICs could be enhanced by designing the gammaretroviral vectors with capsid proteins that are recognized and uncoated efficiently by the target cells. The performances of three types of retroviral vectors were compared by assigning kinetic parameters based on differences in their intracellular pathways. Since the effectiveness of these vectors depends on their stability in the cytoplasm of the target cells, their performances for both stable and unstable cases were investigated. Hematopoietic stem cells (HSCs) and lymphocytes are important targets for gene transfer using retroviral vectors. The use of various cytokines in the culture medium can stimulate non-dividing lymphocytes to resume the expression of some additional genes (expression of some proteases) and allow the HSCs to proliferate (Ueda et al. 2000). Also, the addition of chromatin modifying agents along with cytokines has been reported to increase the rate of division of HSCs while retaining their repopulating potential (Araki et al. 2007). By simulating the effects of the doubling times on the transduction efficiency, it was shown (Figure 4.7) that lentiviral vectors provided the highest efficiencies in slowly-growing target cells, especially when the vectors are unstable inside the cell cytoplasm. It should also be noted that lentiviral vectors are the only choice for the efficient transduction of non-dividing lymphocytes. The reverse transcription of the gammaretroviral and lentiviral genomes is inefficient in G0-resting target cells, indicating that the limited availability of nucleotides can prolong the reverse transcription process (O'Brien et al. 1994; Pieroni et al. 1999; Sutton et al. 1999). Even foamy-viral vectors, which enter into the cell with reverse transcribed DNA, were found to remain uncoated in G0-resting cells (Lehmann-Che et al. 2007). These findings suggest that the cytoplasm-trafficking time can be prolonged for all three retroviral vectors if the reverse transcription and/or uncoating do not occur efficiently. According to the simulations, an increase in the trafficking time resulted in a dramatic decrease in the performance of all three vectors especially when the intracellular 121  degradation of retroviral genomes occurs. Supplementing the G0-resting lymphocytes with nucleosides resulted in the production of completely reverse-transcribed lentiviral DNA (Korin and Zack 1999), but the integration of lentiviral vectors proceeded only when these cells also were stimulated with cytokines (Korin and Zack 1998; Unutmaz et al. 1999). This indicates that certain cellular functions are required for the steps following reverse transcription and before nuclear transport, probably the uncoating of the capsid proteins. This is supported by the finding that the uncoating of foamy-viral vectors proceeded only in cells that had been stimulated with cytokines in order to resume the cellular expression of proteases that target the capsid proteins (Lehmann-Che et al. 2007). Cells need to be supplemented with both cytokines and nucleosides to accelerate cytoplasmic processes in gammaretroviral and lentiviral vectors, while cytokines alone are sufficient when foamy-viral vectors are used. The analysis of the relationship between the transduction efficiency and the mean integrated copy number for the three retroviral vectors showed that transduction with lentiviral vectors results in a low number of integrated viral copies per cell, especially at high transduction efficiencies. However, there was no observed difference in this relationship between gammaretro- and foamy-viral vectors.  This indicated that the rate of nuclear  transport, but not the cytoplasm-trafficking time, affects the mean integrated viral copy number. However, this copy number can be further decreased if the intracellular degradation of viral vectors is minimized. Hence, designing retroviral vectors that are capable of active transport through the nuclear membrane as well as resistant to intracellular degradation could provide not only high transduction efficiencies but also lower numbers of integrated viral copies per target cell.  122  5. Conclusions and future directions 5.1 Conclusions A mathematical model was developed for the rate-limiting steps of the mammalian cell retroviral transduction process that includes: (i) the mass transport of vectors by diffusion and convection; (ii) the extracellular decay of viral vectors, their binding at the cell surface and entry into the cell cytoplasm; and (iii) the intracellular reverse transcription of uncoated RNA to form DNA intermediates and transport of the latter through the cytosol to the vicinity of cell nucleus, both accounted for by a cytoplasm trafficking time and, finally, (iv) nuclear import and integration of the delivered DNA into the target cell genome. The model also accounts for the kinetics of multiple vector infections which influences the transduction efficiency and is required to determine the average copy number of the integrated viruses.  The Poisson  equation was used to represent the distribution of vectors between the virus-carrying cells and was employed to determine vector sharing during cell division. The mathematical model is validated using gibbon ape leukemia virus envelope pseudotyped (MSCV-GALVenv) retroviral vectors and K562 target cells. MSCV-GALVenv retroviral vectors were found to decay in the extracellular medium with a half-life of 6.2 h. The estimated rate constant of the net binding of MSCV-GALVenv retroviral vectors at equilibrium indicated it as a reaction-limiting process. Viral intermediate complexes derived from the internalized retroviral vectors are found to remain stable inside K562 cells. The cytoplasmic trafficking time, estimated as 11.2 h, is consistent with the time scale for retrovirus uncoating, reverse transcription and transport to the cell nucleus. The initial concentration of active retroviral vectors in the medium was estimated using the model and the model was successfully validated using transduction data obtained for both static and centrifugation-based gene transfer protocols. The model clearly 123  explained the mechanism of transduction enhancement by the centrifugation-based method. The model incorporates, in a simplified manner, the internal trafficking of retroviruses and provides a basis for designing and optimizing strategies for efficient retroviral gene transfer. Compared to the experimental data, the model slightly overpredicted the transduction efficiency under centrifugation conditions at high vector-to-cell ratios. It was suspected that this deviation might be due to the saturation of binding sites on the cell surface when the local vector concentration reaches sufficiently high values. The inclusion of more complex binding kinetics in the mathematical model in order to address this saturation phenomenon required an experimental investigation of the kinetic behavior of retroviral vectors on the mammalian cell surface. The kinetics and mechanisms of the retroviral binding to, dissociation from and entry into mammalian cells were studied using GALV envelope-pseudotyped retroviral vectors and RAT-1 target cells.  The cationic  polymer, protamine sulfate, was used to assist in differentiating and estimating the retroviral vector kinetics of cell binding, dissociation and cell entry. The retroviruses were bound to the target cells maximally when 10 µg/mL of protamine sulfate was present in the viruscontaining medium. Although only half of this number of vectors bind to the cell surface in the absence of protamine sulfate, rapid dissociation of ~60% of the bound retroviruses from the cell surface resulted in an overall 5-fold reduction in the number of vectors delivered into the cells, compared to the case with the optimum protamine sulfate concentration. The presence of excess protamine sulfate, especially beyond 20 µg/mL, in the virus-containing medium significantly reduced both the binding and cell internalization processes, thus reducing the number of viruses entering the cells’ genomes. The kinetic rates for entry into the cytoplasm and dissociation from the cell surface were quantified using a mathematical model based on cell population balances. The rate constant for entry of irreversibly bound 124  viruses into the cell cytoplasm was estimated to be 1.09 h-1 (t1/2 = 38 min), and the rate of dissociation from the cell surface in the absence of protamine sulfate was found to be rapid with a rate constant of 1.28 h-1 (t1/2 = 33 min). The internalization of retroviruses was not inhibited by chlorpromazine, was partially inhibited in the presence of NH4Cl levels that prevent clathrin-mediated endocytosis, and was significantly inhibited by methyl-βcyclodextrin treatment. These results indicate that retroviral vectors with the GALV envelope utilize non-clathrin, lipid-raft-mediated endocytic vesicles to enter cells. The model was modified by incorporating these more complex binding kinetics in order to address the phenomenon of binding site saturation on the cell surface. The modified model gave improved predictions that agreed very well with the experimental data for centrifugation-based transduction especially at high vector-to-cell ratios, and clearly describes why a saturation plateau in transduction efficiency occurs. The model was used to analyze the roles played by the various kinetic and mass transport steps in the gene transfer process. An analysis of the centrifugation parameters showed that a moderate centrifugal force of 1000– 2000g for 4 h is sufficient to obtain maximal transduction efficiency. However, the minimum time of exposure to VCM could be further reduced by accelerating the irreversible binding and entry rates of the retroviral vectors. An analysis of the various kinetic steps that follow mass transfer to the cell surface showed that vector entry into the cell and subsequent intracellular processes govern the plateau value of the transduction efficiency especially when the intracellular vector decay rate is substantial. The model developed here was also applied, with appropriate changes in kinetic parameters, to explore transduction processes involving other recombinant retroviruses.  Thus, the model was used to compare the performances of  gammaretro-, lenti- and foamy-viral vectors. Lentiviral vectors were found to perform in a superior way when compared to the other two vector systems, especially when the intracellular 125  vector decay rates are substantial. However, some processes in the cytoplasm, such as the reverse transcription and the uncoating of lentiviral vectors, need to occur very efficiently to yield high transduction efficiencies.  Lentiviral vectors were also found to yield lower  integrated viral copies in the target cell chromosome at high transduction efficiencies compared to the other two retroviral systems. The model explains why retroviral vectors that are resistant to intracellular degradation and that enter into the nucleus without depending on cell division yield high transduction efficiencies with a lower range of integrated viral copies.  5.2 Future directions The mathematical model developed for the retrovirus-mediated gene transfer process involves the steps only up to the integration of retroviral vectors. However, the complete optimization of the process depends on the purpose of gene transfer, which, in general, requires quantitative knowledge about the protein expression from the integrated viral vectors. The concentration level of a therapeutic or marker protein produced from integrated genes in the target cells depends on the kinetics of mRNA transcription and translation as well as the protein degradation rate. These aspects could be added to the model given an understanding of the minimum concentration of the protein from the transduced cells that would be required for therapeutic purposes. The latter could then be achieved by modulating the copy number to the desired level while, at the same time, minimizing any genotoxic effects of the transgenes. On the other hand, when gene transfer is to be applied to tracking certain cell phenotypes and their progenies, the expressed marker protein should ideally disappear as the cell changes to another phenotype. This not only depends on the degradation rate of the protein but also the amount of protein expressed from the integrated viral copies. Hence the number of integrated viral copies should be modulated in a narrow range to minimize the carryover effect. The  126  incorporation of the kinetics of protein production and degradation in the mathematical model could help in modulating the copy number to achieve the desired protein levels. Retroviral vectors pseudotyped with the most commonly used envelope proteins generally enter the cell cytoplasm via an endocytic process (clathrin- or caveolae-mediated). Endocytosis is a sequential and organized trafficking process in which endocytic vesicles are released into the cell cytoplasm, followed by the fusion of vesicles with endosomes and later with lysosomes where degradation of the contents in the vesicles occurs. Retroviral vectors entering through endocytic vesicles must escape from these vesicles by fusion with the vesicle membrane before the vesicles meet the lysosomes which cause vector degradation. The efficiency of the retroviral transduction process might be dependent on the rate of the retroviral release into the cytoplasm from the endocytic vesicles compared to the rate of the fusion of vesicles with lysosomes. Visualization through the fluorescent labeling of retroviral vectors together with vesicles, endosomes and lysosomes could provide a better mechanistic understanding of this process. The kinetics of retroviral entry in the model could then be further elaborated to incorporate the kinetics of vesicle trafficking, fusion and release of viral capsids and viral vector degradation in the lysosomes. This could provide a means to improve the rate of retroviral trafficking inside the endocytic vesicles and to decrease the rate of degradation of retroviral vectors in the lysosomes. The mathematical model developed here applies to gene transfer targeting a homogeneous population of cells. But many gene transfer applications involve hematopoietic stem cells (HSCs) which are heterogeneous, in part due to contamination by other cell types. This is caused by the current apparent inability to fully purify hematopoietic stem cell populations.  In addition, HSCs tend to differentiate into other cell types during their  expansion in culture (Ogawa 1993). The gene transfer process requires culturing the target 127  cells during and after exposure to viral vectors and hematopoietic stem cells may differentiate during these steps.  In addition, retroviral vectors are mutagens capable of activating  neighboring oncogenes after integration, resulting in the generation of a leukemia subpopulation in the culture. The model predictions of transduction efficiency will likely deviate greatly from the experimental observations if the current model is applied to transducing HSCs. Mathematical models have been developed to represent the expansion and differentiation of HSCs in culture especially to investigate the occurrence of leukemia (Colijn and Mackey 2005; Roeder and Glauche 2006).  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Proceedings of the National Academy of Sciences of the United States of America 83(10):3194-3198.  146  Appendix I: Computer program for mat hematical mo del The following is the MATLAB code for the retroviral transduction process using the mathematical model presented in Table 4.2. function transduction fid=fopen('output.rtf','w'); % ***************** Properties of target cells **************************** td = 20.8; % Doubling time of target cells, h. mu = log(2)/td; % Growth rate of target cells, 1/h. Cc0 = 1.0e5; % Initial cell density, cells/cm2. % ***************** Experimental parameters ******************************* tf = 6.0; % Final time, h. tinc = 3*td; % Time of incubation, h. Zf = 0.2; % Height of the medium, cm. ng = 2000; % multiplier for gravitational force. g = 981; % Gravitational force, cm/s2 % ***************** Kinetic parameters ************************************ the = 6.2; % Half-life in the medium, h. kde = log(2)/the; % External Deay rate, 1/h. kb = 7.69e-8; % Binding rate constant, cm3/cell.h. kd = 1.28; % Dissocation rate constant, 1/h. ke = 1.09; % Entry rate constant, 1/h. thi = 600; % Internal half-life of retroviral vector, h. kdi = log(2)/thi; % Rate of decay in the cytoplasm, 1/h. kn = 2*mu; % Integration rate constant, 1/h. tau = 11.2; % Cytoplasm trafficking time, h. % ***************** Properties of medium ********************************** Tm = 37; % Temperature of the medium, C. eta = 0.71; % Viscosity of the medium, cP. rowm = 1.01; % Density of the medium, g/cc. % ***************** Properties of Retroviral vectors ********************** dv = 115; % Diameter of retroviral vector, nm. rowv = 1.17; % Density of the retroviral vector, g/cc. vcr=17.1; % Vector-to-cell ratio. Cv0=vcr*Cc0/Zf; % Initial retroviral concentration, vectors/cm3. % ************************************************************************** fprintf(fid,'Doubling time of target cells = %10.5f h \n',td); fprintf(fid,'Extracellular decay rate constant = %10.5f 1/h \n',kde); fprintf(fid,'Binding rate constant = %10.5e cm3/cell.h \n',kb); fprintf(fid,'Dissociation rate constant = %10.5f 1/h \n',kd); fprintf(fid,'Entry rate constant = %10.5f 1/h \n',ke); fprintf(fid,'Intracellular decay rate constant = %10.5f 1/h \n',kdi); fprintf(fid,'Cytoplasmic trafficking time = %10.5f h \n',tau); fprintf(fid,'Nuclear entry rate constant = %10.5f 1/h \n',kn); fprintf(fid,'Centrifugal force = %10.5f g \n',ng); fprintf(fid,'Time of VCM exposure to cells = %10.5f h \n',tf); fprintf(fid,'Target cell density = %10.5e cells/cm2 \n',Cc0); fprintf(fid,'Concentration of viral vectors = %10.5e vectors/cm3 \n',Cv0); % ***************** Computational parameters ****************************** dz = 0.01; % VCM height incriment, cm dt = 0.1; % Time step, h. nz = round(Zf/dz)+1; % Number of points for the VCM height. nte = round(tf/dt)+1; % Number of points for exposure time. nti= round(tinc/dt)+1; % Number of points for incubation time. nt=nte+nti-1; % Number of points for total time. dz=Zf/(nz-1); % Corrected VCM height incriment, cm.  147  dt=(tf+tinc)/(nt-1); % Corrected time step, h. % ************************************************************************* D = 5.25e-5*(Tm+273)/(dv*eta); % Stokes-Einstein's diffusivity. u = 3.6e-9*ng*g*(rowv-rowm)*dv^2/(18*eta); % Stokes' settling velocity. %-------------------------------------------------------------------------Time_tot=zeros(nt); Ctot=zeros(nt); Cs=zeros(nt,7); nvt=zeros(nt); c0(1)=Cc0; c0(2)=1.0e-9; c0(3)=1.0e-9; c0(4)=1.0e-9; c0(5)=1.0e-9; c0(6)=1.0e-9; c0(7)=Cc0; c0(8)=1.0e-9; c0(9:nz+8)=Cv0; Cs(1,:)=c0(1:7); z=((1:nz)-1)*Zf/(nz-1); tm=((1:nti)-1)*dt; Ctot(1)=c0(1)+c0(2)+c0(3); % ************************************************************************* c0(1:8)=c0(1:8)/Cc0; kb=kb*Cc0/Zf; c0(9:nz+8)=c0(9:nz+8)*Zf/Cc0; Cs=Cs/Cc0; dz = dz/Zf; D=D/Zf^2; u=u/Zf; z=z/Zf; nvt(1)=1; Ctot(1)=Ctot(1)/Cc0; % ************************************************************************* for i=2:nte tlim=[(i-2)*dt (i-1)*dt]; [t,c] = ode45(@fcn,tlim,c0); c0=c(end,:); Cv=c0(9:nz+8); ci0=c0(1:7); Cs(i,:)=c0(1:7); Ctot(i)=c0(1)+c0(2)+c0(3); Time_tot(i)=t(end); nvt(i)=c0(4)/c0(2); if(i==nte) jti=round(t(end)/dt)+1; for j=jti+1:nt tspni=[(j-2)*dt (j-1)*dt]; [ti,ci] = ode45(@fcni,tspni,ci0); ci0=ci(end,:); Cs(j,:)=ci(end,:); Ctot(j)=ci0(1)+ci0(2)+ci0(3); Time_tot(j)=ti(end); nvt(j)=ci0(4)/ci0(2); end Ctoti = ci(end,1)+ci(end,2)+ci(end,3); Tran = ci(end,3)*100/Ctoti; Copy = ci(end,6)/ci(end,3); Vint = ci(end,6)/Ctoti; GTE = Vint*100/(Cv0*Zf/Cc0); end end fprintf(fid,' %10.5f %10.5f %10.5f %10.5f \n',vcr,Tran,GTE,Copy); fprintf(' %10.5f %10.5f %10.5f %10.5f \n',vcr,Tran,GTE,Copy); fclose(fid);  function dcdt = fcn(t,c) dcdt = zeros(nz+8,1); Ct=c(1)+c(2)+c(3); pn=u*dz/D; Cvz=c(9:nz+8); Cvm=trapz(z,Cvz); a1 = u*exp(-pn)/(dz*(1-exp(-pn))); a2 = -u*(1+exp(-pn))/(dz*(1-exp(-pn)))-kde; a3 = u/(dz*(1-exp(-pn))); b1 = -2*a1-kde; b2 = 2*a3; b3 = 2*a1; b4 = -2*a3-kde; Kb=kb*ke/(kd+ke+kde); Ks=ke/Kb; VCS=c(9)/(Ks+c(9)); nv=c(4)/c(2); pb1=exp(1-nv); pb2=pb1; if(nv>58) nv=58; end np=round(5*nv); for ip=2:np pb2=pb2+((nv-1)^(ip-1)*exp(1-nv)/factorial(ip-1))*(2^(1-ip)); end tp=t-tau; ctau=c(1:6); if (tau>0) if (tp>=0) st=fix(tp/dt)+1;  148  for ip=1:6 ctau(ip)=Cs(st,ip)+(Cs(st+1,ip)-Cs(st,ip))*(tp-tm(st))/(tm(st+1)-tm(st)); if(ctau(ip)>c(ip)) ctau(ip)=c(ip); end end else ctau=zeros(6); end end dcdt(1) = -ke*c(1)*VCS+pb1*kdi*c(2)+pb2*mu*c(2)+mu*c(1); dcdt(2) = ke*c(1)*VCS-pb1*kdi*c(2)+(1-pb2)*mu*c(2)-kn*ctau(2); dcdt(3) = kn*ctau(2)+mu*c(3); dcdt(4) = ke*(c(1)+c(2))*VCS-kdi*c(4)-kn*ctau(4); dcdt(5) = ke*Ct*VCS-kdi*c(5)-kn*ctau(5); dcdt(6) = kn*ctau(5)+mu*c(6); dcdt(7) = mu*c(7); dcdt(8) = ke*Ct*VCS; dcdt(9) = b1*c(9)+b2*c(10)-2*ke*Ct*VCS/dz; for ip=10:nz+7 dcdt(ip) = a1*c(ip-1)+a2*c(ip)+a3*c(ip+1); end dcdt(nz+8)=b3*c(nz+7)+b4*c(nz+8); end function dcdti = fcni(ti,ci) dcdti=zeros(7,1); nv=ci(4)/ci(2); pb1=exp(1-nv); pb2=pb1; if(nv>58) nv=58; end np=round(5*nv); for ip=2:np pb2=pb2+((nv-1)^(ip-1)*exp(1-nv)/factorial(ip-1))*(2^(1-ip)); end tp=ti-tau; ctau=ci(1:6); if (tau>0) if (tp>=0) st=fix(tp/dt)+1; for ip=1:6 ctau(ip)=Cs(st,ip)+(Cs(st+1,ip)-Cs(st,ip))*(tp-tm(st))/(tm(st+1)-tm(st)); if(ctau(ip)>ci(ip)) ctau(ip)=ci(ip); end end else ctau=zeros(6); end end dcdti(1) = pb1*kdi*ci(2)+pb2*mu*ci(2)+mu*ci(1); dcdti(2) = -pb1*kdi*ci(2)+(1-pb2)*mu*ci(2)-kn*ctau(2); dcdti(3) = kn*ctau(2)+mu*ci(3); dcdti(4) = -kdi*ci(4)-kn*ctau(4); dcdti(5) = -kdi*ci(5)-kn*ctau(5); dcdti(6) = kn*ctau(5)+mu*ci(6); dcdti(7) = mu*ci(7); end end  149  Appendix II: Biohazard approval certificate  150  

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