Backward stochastic differential equation approach to modeling of gene expression

TL;DR

This paper introduces a backward stochastic differential equation (BSDE) approach to model gene expression dynamics, enabling time-reversed analysis of protein levels and providing a new tool for systems biology applications.

Contribution

The paper presents the novel application of BSDEs to model gene expression, allowing inference of prior protein levels from endpoint data, unlike traditional forward SDE methods.

Findings

BSDE method accurately infers prior protein distributions.

Numerical simulations validate the approach against SSA data.

Enables time-reversed biological condition assessment.

Abstract

In this article, we introduce a novel backward method to model stochastic gene expression and protein level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation (BSDE). Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specification of endpoint ("final") conditions, in addition to the model parametrization. To validate our approach we employ Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time reversed simulations, allowing, for example, the assessment of the biological conditions (e.g. protein concentrations) that preceded an experimentally measured event of interest (e.g. mitosis, apoptosis, etc.).