Variable-Depth Simulation of Most Permissive Boolean Networks

TL;DR

This paper introduces a variable-depth simulation method for Most Permissive Boolean Networks, enabling better sampling of trajectories and understanding of biological systems' heterogeneity in time and concentration scales.

Contribution

It presents a novel approach to simulate MPBNs with variable permissive depth, capturing heterogeneity and assessing robustness of attractor predictions.

Findings

Depth parametrization helps evaluate robustness of attractor propensities.

Simulation method captures transitions related to biological heterogeneity.

Application to literature models demonstrates practical utility.

Abstract

In systems biology, Boolean networks (BNs) aim at modeling the qualitative dynamics of quantitative biological systems. Contrary to their (a)synchronous interpretations, the Most Permissive (MP) interpretation guarantees capturing all the trajectories of any quantitative system compatible with the BN, without additional parameters. Notably, the MP mode has the ability to capture transitions related to the heterogeneity of time scales and concentration scales in the abstracted quantitative system and which are not captured by asynchronous modes. So far, the analysis of MPBNs has focused on Boolean dynamical properties, such as the existence of particular trajectories or attractors. This paper addresses the sampling of trajectories from MPBNs in order to quantify the propensities of attractors reachable from a given initial BN configuration. The computation of MP transitions from a configuration is performed by iteratively discovering possible state changes. The number of iterations is referred to as the permissive depth, where the first depth corresponds to the asynchronous transitions. This permissive depth reflects the potential concentration and time scales heterogeneity along the abstracted quantitative process. The simulation of MPBNs is illustrated on several models from the literature, on which the depth parametrization can help to assess the robustness of predictions on attractor propensities changes triggered by model perturbations.