Reconstruction of Multimodal Distributions for Hybrid Moment-based Chemical Kinetics, Supporting Information

TL;DR

This paper compares two moment-based methods, MM and MCM, for reconstructing multimodal distributions in biochemical networks, finding MCM more accurate especially with conditional distributions.

Contribution

It introduces a maximum entropy approach to reconstruct distributions from moments and compares the effectiveness of MM and MCM in modeling multimodal biochemical distributions.

Findings

MCM better captures multimodal distributions.

Conditional moments improve reconstruction accuracy.

Maximum entropy effectively reconstructs distributions from moments.

Abstract

The stochastic dynamics of biochemical reaction networks can be accurately described by discrete-state Markov processes where each chemical reaction corresponds to a state transition of the process. Due to the largeness problem of the state space, analysis techniques based on an exploration of the state space are often not feasible and the integration of the moments of the underlying probability distribution has become a very popular alternative. In this paper the focus is on a comparison of reconstructed distributions from their moments obtained by two different moment-based analysis methods, the method of moments (MM) and the method of conditional moments (MCM). We use the maximum entropy principle to derive a distribution that fits best to a given sequence of (conditional) moments. For the two gene regulatory networks that we consider we find that the MCM approach is more suitable to describe multimodal distributions and that the reconstruction is more accurate if conditional distributions are considered.