Simulating quantitative cellular responses using asynchronous threshold Boolean network ensembles

With increasing knowledge about the potential mechanisms underlying cellular functions, it is becoming feasible to predict the response of biological systems to genetic and environmental perturbations. Due to the lack of homogeneity in living tissues it is difficult to estimate the physiological effect of chemicals, including potential toxicity. Here we investigate a biologically motivated model for estimating tissue level responses by aggregating the behavior of a cell population. We assume that the molecular state of individual cells is independently governed by discrete non-deterministic signaling mechanisms. This results in noisy but highly reproducible aggregate level responses that are consistent with experimental data.

We developed an asynchronous threshold Boolean network simulation algorithm to model signal transduction in a single cell, and then used an ensemble of these models to estimate the aggregate response across a cell population. Using published data, we derived a putative crosstalk network involving growth factors and cytokines - i.e., Epidermal Growth Factor, Insulin, Insulin like Growth Factor Type 1, and Tumor Necrosis Factor α - to describe early signaling events in cell proliferation signal transduction. Reproducibility of the modeling technique across ensembles of Boolean networks representing cell populations is investigated. Furthermore, we compare our simulation results to experimental observations of hepatocytes reported in the literature.

A systematic analysis of the results following differential stimulation of this model by growth factors and cytokines suggests that: (a) using Boolean network ensembles with asynchronous updating provides biologically plausible noisy individual cellular responses with reproducible mean behavior for large cell populations, and (b) with sufficient data our model can estimate the response to different concentrations of extracellular ligands. Our results suggest that this approach is both quantitative, allowing statistical verification and calibration, and extensible, allowing modification and revision as guided by experimental evidence. The simulation methodology is part of the US EPA Virtual Liver, which is investigating the effects of everyday contaminants on living tissues. Future models will incorporate additional crosstalk surrounding proliferation as well as the putative effects of xenobiotics on these signaling cascades within hepatocytes.