A differentiable Gillespie algorithm for simulating chemical kinetics, parameter estimation, and designing synthetic biological circuits

TL;DR

This paper introduces a differentiable version of the Gillespie algorithm that enables gradient-based parameter estimation and network design in stochastic chemical kinetics, facilitating applications in synthetic biology.

Contribution

The paper presents the first fully differentiable Gillespie algorithm, allowing for efficient parameter learning and network design using deep learning techniques.

Findings

Successfully learned kinetic parameters from experimental data.

Designed promoter architectures with specific input-output behaviors.

Demonstrated utility in stochastic gene expression modeling.

Abstract

The Gillespie algorithm is commonly used to simulate and analyze complex chemical reaction networks. Here, we leverage recent breakthroughs in deep learning to develop a fully differentiable variant of the Gillespie algorithm. The differentiable Gillespie algorithm (DGA) approximates discontinuous operations in the exact Gillespie algorithm using smooth functions, allowing for the calculation of gradients using backpropagation. The DGA can be used to quickly and accurately learn kinetic parameters using gradient descent and design biochemical networks with desired properties. As an illustration, we apply the DGA to study stochastic models of gene promoters. We show that the DGA can be used to: (i) successfully learn kinetic parameters from experimental measurements of mRNA expression levels from two distinct $\textit{E. coli}$ promoters and (ii) design nonequilibrium promoter architectures with desired input-output relationships. These examples illustrate the utility of the DGA for analyzing stochastic chemical kinetics, including a wide variety of problems of interest to synthetic and systems biology.