Computational modeling approaches to the dynamics of oncolytic viruses

Abstract

Replicating oncolytic viruses represent a promising treatment approach against cancer, specifically targeting the tumor cells. Significant progress has been made through experimental and clinical studies. Besides these approaches, however, mathematical models can be useful when analyzing the dynamics of virus spread through tumors, because the interactions between a growing tumor and a replicating virus are complex and nonlinear, making them difficult to understand by experimentation alone. Mathematical models have provided significant biological insight into the field of virus dynamics, and similar approaches can be adopted to study oncolytic viruses. The review discusses this approach and highlights some of the challenges that need to be overcome in order to build mathematical and computation models that are clinically predictive. WIREs Syst Biol Med 2016, 8:242-252. doi: 10.1002/wsbm.1332 For further resources related to this article, please visit the WIREs website.

Figure 1

Simulation of therapy using a replicating virus, model (1). The virus is administered once, as indicated by the arrow. Shading indicates the phase of the dynamics following administration of the virus. (i) Use of a weakly cytopathic virus results in sustained cancer remission. (ii) Use of a more cytopathic virus results in long term persistence of the cancer and the virus.

Figure 2

Infection terms and model predictions. Single-round virus infection experiments were performed. Different doses of the virus were used to infect the target cell population, and the number of productively infected cells was determined by fluorescence after one round of replication. Mathematical models were fit to the data from experiments with 50,000 target cells, and the curves for experiments with higher target cell numbers was then predicted by the model. (a) Infection term βxy. The model over-predicts the experimental curves. (b) infection term (1+ɛ)βxy/(x+ɛ). The model accurately predicts the data. (c) Infection term (1+α)βv(1 ′ e^′αS)/α. The model accurately predicts the data.

Figure 3

Fitting mathematic models to data. 549 human lung cancer nude xenografts were infected with the adenovirus Ad309, and tumor volume was recorded over time. Different mathematical models were fitted to these data, including two models from the “slow” category, and one model from the “fast” category (see text). (a) Model fits to the data, dynamics are shown for the duration of the experiment. (b) Parameterized model simulated for a longer period of time, beyond the time frame of the experiment.

Figure 4

Experimental outcomes of spatial virus spread and model fitting. (a) A “ring structure” can develop where the virus population expands as a growing ring. The model can accurately describe the time evolution of cells and qualitatively reproduces the spatial structure. (b) The other spatial pattern is the disperse pattern. Again, the model can accurately describe the time evolution of cells and qualitatively reproduces the spatial structure. In the predicted time series, the black line is the predicted number of cells, and the upper and lower grey lines represent standard deviations. In the spatial plots, the upper panels are experimental data where infected cells are shown by green fluorescence. The lower panels are computer simulations based on the estimated parameters, where green represents uninfected cells, red infected cells, and grey empty space.