Mathematical model of the rate-limiting steps for retrovirus-mediated gene transfer into mammalian cells.

A quantitative understanding of the process of retrovirus-mediated gene transfer into mammalian cells should assist the design and optimization of transduction protocols. We present a mathematical model of the process that incorporates the essential rate-limiting transduction steps including diffusion, convection and decay of viral vectors, their binding at the cell surface and entry into the cell cytoplasm, reverse transcription of uncoated RNA to form DNA intermediates, transport of the latter through the cytosol to the cell nucleus and, finally, nuclear import and integration of the delivered DNA into the target cell genome. Cell and virus population balances are used to account for the kinetics of multiple vector infections which influence the transduction efficiency and govern the integrated copy number. The mathematical model is validated using gibbon ape leukemia virus envelope pseudotyped retroviral vectors and K562 target cells. Viral intermediate complexes derived from the internalized retroviral vectors are found to remain stable inside the K562 cells and the cytoplasmic trafficking time is consistent with the time scale for retrovirus uncoating, reverse transcription and transport to the cell nucleus. The model predictions of transduction efficiency and integrated copy number agree well with experimental data for both static (i.e., standard gravity) and centrifugation-based gene transfer protocols. The formulation of the model can also be applied to transduction protocols involving lenti- or foamy-viruses and so should prove to be useful for the optimization of several types of gene transfer processes.

Effect of cell lysates on retroviral transduction efficiency of cells in suspension culture.

Recombinant retroviruses are effective vectors able to integrate transgenes into the target cell's genome to achieve longer-term expression. This study investigates the effect of cell lysis products, a common cell culture by-product, on the transduction of suspension cells by gammaretroviral vectors. Cell lysates derived from human and murine suspension cell lines significantly increased the transduction of human TF-1 and K-562 cell lines by gibbon ape leukemia virus-pseudotyped retroviral vectors without altering tropism. The transduction efficiency of TF-1 cells increased as a function of lysate concentration and decreased with increasing target cell concentrations. This was adequately predicted using a saturation equation based on the lysed-to-target cell concentration ratio, R, where: Fold increase = 1+Fold_(Max) (R/(K_(L)+R)). Lysate completely masked the effects of fibronectin when the two were added in combination. With protamine sulfate, the transduction efficiency was increased by lysate to 58% from 20% for protamine sulfate alone. Overall, the presence of cell lysate significantly influenced the outcome of the transduction process, either alone or in the presence of protamine sulfate or fibronectin.

Cell separator operation within temperature ranges to minimize effects on Chinese hamster ovary cell perfusion culture.

A cell retention device that provides reliable high-separation efficiency with minimal negative effects on the cell culture is essential for robust perfusion culture processes. External separation devices generally expose cells to periodic variations in temperature, most commonly temperatures below 37 degrees C, while the cells are outside the bioreactor. To examine this phenomenon, aliquots of approximately 5% of a CHO cell culture were exposed to 60 s cyclic variations of temperature simulating an acoustic separator environment. It was found that, for average exposure temperatures between 31.5 and 38.5 degrees C, there were no significant impacts on the rates of growth, glucose consumption, or t-PA production, defining an acceptable range of operating temperatures. These results were subsequently confirmed in perfusion culture experiments for average exposure temperatures between 31.6 and 38.1 degrees C. A 2(5-1) central composite factorial design experiment was then performed to systematically evaluate the effects of different operating variables on the inlet and outlet temperatures of a 10L acoustic separator. The power input, ambient temperature, as well as the perfusion and recycle flow rates significantly influenced the temperature, while the cell concentration did not. An empirical model was developed that predicted the temperature changes between the inlet and the outlet of the acoustic separator within +/-0.5 degrees C. A series of perfusion experiments determined the ranges of the significant operational settings that maintained the acoustic separator inlet and outlet temperatures within the acceptable range. For example, these objectives were always met by using the manufacturer-recommended operational settings as long as the recirculation flow rate was maintained above 15 L day(-1) and the ambient temperature was near 22 degrees C.

Optimization of an acoustic cell filter with a novel air-backflush system.

Increasing worldwide demand for mammalian cell production capacity will likely be partially satisfied by a greater use of higher volumetric productivity perfusion processes. An important additional component of any perfusion system is the cell retention device that can be based on filtration, sedimentation, and/or acoustic technologies. A common concern with these systems is that pumping and transient exposure to suboptimal medium conditions may damage the cells or influence the product quality. A novel air-backflush mode of operating an acoustic cell separator was developed in which an injection of bioreactor air downstream of the separator periodically returned the captured cells to the reactor, allowing separation to resume within 20 s. This mode of operation eliminated the need to pump the cells and allows the selection of a residence time in the separator depending on the sensitivity of the cell line. The air-backflush mode of operating a 10L acoustic separator was systematically tested at 10(7) cells/mL to define reliable ranges of operation. Consistent separation performance was obtained for wide ranges of cooling airflow rates from 0 to 15 L/min and for backflush frequencies between 10 and 40 h(-1). The separator performance was optimized at a perfusion rate of 10 L/day to obtain a maximum separation efficiency of 92 +/- 0.3%. This was achieved by increasing the power setting to 8 W and using duty cycle stop and run times of 4.5 and 45 s, respectively. Acoustic cell separation with air backflush was successfully applied over a 110 day CHO cell perfusion culture at 10(7) cells/mL and 95% viability.

Basal medium composition and serum or serum replacement concentration influences on the maintenance of murine embryonic stem cells.

The expansion of stem cell numbers while retaining their developmental properties is a bioprocess challenge. We compared the growth rates and embryoid body (EB) formation yields of R1 and EFC murine embryonic stem cells (mESC) cultured in two basal media (DMEM or DMEM:F12) with additions of 1.7-15% fetal bovine serum (FBS) or serum replacer (KOSR). Whereas the basal medium or KOSR dose did not have a significant effect on growth rate for either cell line, increasing doses of KOSR had a significant negative effect on the EB yield of EFC cells. Use of DMEM:F12 and increasing doses of FBS independently and significantly increased the growth rate for both cell lines. DMEM:F12 also significantly increased EB yields for both cell lines. The results show that use of DMEM:F12 and several-fold lower than conventional concentrations of KOSR can efficiently support maintenance of mESC and that KOSR should be dose as well as lot optimized.

Optimizing the rotor design for controlled-shear affinity filtration using computational fluid dynamics.

Controlled shear affinity filtration (CSAF) is a novel integrated processing technology that positions a rotor directly above an affinity membrane chromatography column to permit protein capture and purification directly from cell culture. The conical rotor is intended to provide a uniform and tunable shear stress at the membrane surface that inhibits membrane fouling and cell cake formation by providing a hydrodynamic force away from and a drag force parallel to the membrane surface. Computational fluid dynamics (CFD) simulations are used to show that the rotor in the original CSAF device (Vogel et al., 2002) does not provide uniform shear stress at the membrane surface. This results in the need to operate the system at unnecessarily high rotor speeds to reach a required shear stress of at least 0.17 Pa at every radial position of the membrane surface, compromising the scale-up of the technology. Results from CFD simulations are compared with particle image velocimetry (PIV) experiments and a numerical solution for low Reynolds number conditions to confirm that our CFD model accurately describes the hydrodynamics in the rotor chamber of the CSAF device over a range of rotor velocities, filtrate fluxes, and (both laminar and turbulent) retentate flows. CFD simulations were then carried out in combination with a root-finding method to optimize the shape of the CSAF rotor. The optimized rotor geometry produces a nearly constant shear stress of 0.17 Pa at a rotational velocity of 250 rpm, 60% lower than the original CSAF design. This permits the optimized CSAF device to be scaled up to a maximum rotor diameter 2.5 times larger than is permissible in the original device, thereby providing more than a sixfold increase in volumetric throughput.

Characterization and optimization of acoustic filter performance by experimental design methodology.

Acoustic cell filters operate at high separation efficiencies with minimal fouling and have provided a practical alternative for up to 200 L/d perfusion cultures. However, the operation of cell retention systems depends on several settings that should be adjusted depending on the cell concentration and perfusion rate. The impact of operating variables on the separation efficiency performance of a 10-L acoustic separator was characterized using a factorial design of experiments. For the recirculation mode of separator operation, bioreactor cell concentration, perfusion rate, power input, stop time and recirculation ratio were studied using a fractional factorial 2(5-1) design, augmented with axial and center point runs. One complete replicate of the experiment was carried out, consisting of 32 more runs, at 8 runs per day. Separation efficiency was the primary response and it was fitted by a second-order model using restricted maximum likelihood estimation. By backward elimination, the model equation for both experiments was reduced to 14 significant terms. The response surface model for the separation efficiency was tested using additional independent data to check the accuracy of its predictions, to explore robust operation ranges and to optimize separator performance. A recirculation ratio of 1.5 and a stop time of 2 s improved the separator performance over a wide range of separator operation. At power input of 5 W the broad range of robust high SE performance (95% or higher) was raised to over 8 L/d. The reproducible model testing results over a total period of 3 months illustrate both the stable separator performance and the applicability of the model developed to long-term perfusion cultures.

Mathematical model of renal elimination of fluid and small ions during hyper- and hypovolemic conditions.

This study is concerned with the formulation of a 'kidney module' linked to the plasma compartment of a larger mathematical model previously developed. Combined, these models can be used to predict, amongst other things, fluid and small ion excretion rates by the kidney; information that should prove useful in evaluating values and trends related to whole-body fluid balance for different clinical conditions to establish fluid administration protocols and for educational purposes. The renal module assumes first-order, negative-feedback responses of the kidney to changes in plasma volume and/or plasma sodium content from their normal physiological set points. Direct hormonal influences are not explicitly formulated in this empiric model. The model also considers that the renal excretion rates of small ions other than sodium are proportional to the excretion rate of sodium. As part of the model development two aspects are emphasized (1): the estimation of parameters related to the renal elimination of fluid and small ions, and (2) model validation via comparisons between the model predictions and selected experimental data. For validation, model predictions of the renal dynamics are compared with new experimental data for two cases: plasma overload resulting from external fluid infusion (e.g. infusions of iso-osmolar solutions and/or hypertonic/hyperoncotic saline solutions), and untreated hypo volemic conditions that result from the external loss of blood. The present study demonstrates that the empiric kidney module presented above can provide good short-term predictions with respect to all renal outputs considered here. Physiological implications of the model are also presented.

Empirical models of the proliferative response of cytokine-dependent hematopoietic cell lines.

There is an expanding need for predictive mathematical models to accelerate the optimization of cell therapy culture processes. Here we demonstrate the ability of simple mathematical models to describe quantitatively the cytokine growth-rate dependence of two human hematopoietic cell lines, TF-1 and MO7e. These cells are immortal but depend on either interleukin-3 (IL-3) or granulocyte-macrophage colony stimulating factor (GM-CSF) for their continued survival and maximal proliferation. They are also responsive to interleukin-6 (IL-6) and exhibit saturation kinetics when these cytokines are limiting. A Monod-type relationship consistently failed to fit measured cytokine dose-proliferation response curves while a Hill-type relationship showed a good fit. Cytokine interactions were first modeled by modifying the Hill-function to include an interaction parameter, gamma. This model did not indicate either synergistic or even additive effects between IL-3 and GM-CSF. Based on the reported competition between IL-3 and GM-CSF for their common receptor (beta(c)) subunit, a competitive model was also developed. This model had no new parameters beyond those obtained from single cytokine cultures and provided improved prediction of the growth rates for both cell lines exposed to combinations of IL-3 and GM-CSF over a wide range of concentrations. As expected, the competitive model failed to fit the data for IL-6 in combination with either IL-3 or GM-CSF, since IL-6 signaling does not involve the beta(c) chain of the IL-3/GM-CSF receptors. Interestingly, the cell-specific rates of GM-CSF uptake and cell proliferation were found to be uncoupled processes. Taken together, these results illustrate the utility of appropriately designed empirical models to describe the proliferative responses of hematopoietic cells to cytokine stimulation.