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: (1) successfully learn kinetic parameters from experimental measurements of mRNA expression levels from two distinct Escherichia coli promoters and (2) 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.

Microbial communities living in the same environment often display alternative stable states, each characterized by a unique composition of species. Understanding the origin and determinants of microbiome multistability has broad implications in environments, human health, and microbiome engineering. However, despite its conceptual importance, how multistability emerges in complex communities remains largely unknown. Here, we focused on the role of horizontal gene transfer (HGT), one important aspect mostly overlooked in previous studies, on the stability landscape of microbial populations. Combining mathematical modeling and numerical simulations, we demonstrate that, when mobile genetic elements (MGEs) only affect bacterial growth rates, increasing HGT rate in general promotes multistability of complex microbiota. We further extend our analysis to scenarios where HGT changes interspecies interactions, microbial communities are subjected to strong environmental selections and microbes live in metacommunities consisting of multiple local habitats. We also discuss the role of different mechanisms, including interspecies interaction strength, the growth rate effects of MGEs, MGE epistasis and microbial death rates in shaping the multistability of microbial communities undergoing HGT. These results reveal how different dynamic processes collectively shape community multistability and diversity. Our results provide key insights for the predictive control and engineering of complex microbiota.