Simulating heterogeneous populations using Boolean models

Brian C. Ross, Mayla Boguslav, Holly Weeks, James C. Costello

Certain biological processes, such as the development of cancer and immune activation, can be controlled by rare cellular events that are difficult to capture computationally through simulations of individual cells. Information about such rare events can be gleaned from an attractor analysis, for which a variety of methods exist (in particular for Boolean models). However, explicitly simulating a defined mixed population of cells in a way that tracks even the rarest subpopulations remains an open challenge. Here we show that when cellular states are described using a Boolean network model, one can exactly simulate the dynamics of non-interacting, highly heterogeneous populations directly, without having to model the various subpopulations. This strategy captures even the rarest outcomes of the model with no sampling error. Our method can incorporate heterogeneity in both cell state and, by augmenting the model, the underlying rules of the network as well (e.g., introducing loss-of-function genetic alterations). We demonstrate our method by using it to simulate a heterogeneous population of Boolean networks modeling the T-cell receptor, spanning ∼ 1020 distinct cellular states and mutational profiles. We have developed a method for using Boolean models to perform a population-level simulation, in which the population consists of non-interacting individuals existing in different states. This approach can be used even when there are far too many distinct subpopulations to model individually.