Modeling HIV-1 dynamics and fitness in cell culture across scales

A common approach to understand and analyze complex biological systems is to describe the dynamics in terms of a system of ordinary differential equations (ODE) depending on numerous biologically meaningful and descriptive parameters that are estimated using observed data. The ODE models are often based on the implicit assumption of well-mixed dynamics, i.e., the delay of interaction due to spatial distribution is not included in the model. In this article, we address the question how the heterogeneity of the underlying system affects the estimated parameter values of the ODE model, and on the other hand, what information about the microscopic system can be drawn from these values. The system we are considering is a pairwise growth competition assay used to quantify ex vivo replicative fitness of different HIV-1 isolates. To overcome the lack of ground truth, we generate data using a detailed microscopic spatially distributed hybrid stochastic-deterministic (HSD) infection model in which the dynamics is controlled by parameters directly related to cell level infection, virus production processes, and diffusion of virus particles. The synthetic data sets are then analyzed using an ODE based well-mixed model, in which the corresponding macroscopic parameter distributions are estimated using Markov chain Monte Carlo (MCMC) methods. This approach provides a comprehensive picture of the statistical dependencies of the model parameter across different scales.