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.