Catalyst: Fast and flexible modeling of reaction networks.

We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high-performance simulation of chemical reaction networks (CRNs). Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. Through comprehensive benchmarks, we demonstrate that Catalyst simulation runtimes are often one to two orders of magnitude faster than other popular tools. More broadly, Catalyst acts as both a domain-specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying CRNs; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for numerical solvers. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in numerical solvers. Finally, we demonstrate Catalyst's broad extensibility and composability by highlighting how it can compose with a variety of Julia libraries, and how existing open-source biological modeling projects have extended its intermediate representation.

The σB alternative sigma factor circuit modulates noise to generate different types of pulsing dynamics.

Single-cell approaches are revealing a high degree of heterogeneity, or noise, in gene expression in isogenic bacteria. How gene circuits modulate this noise in gene expression to generate robust output dynamics is unclear. Here we use the Bacillus subtilis alternative sigma factor σB as a model system for understanding the role of noise in generating circuit output dynamics. σB controls the general stress response in B. subtilis and is activated by a range of energy and environmental stresses. Recent single-cell studies have revealed that the circuit can generate two distinct outputs, stochastic pulsing and a single pulse response, but the conditions under which each response is generated are under debate. We implement a stochastic mathematical model of the σB circuit to investigate this and find that the system's core circuit can generate both response types. This is despite one response (stochastic pulsing) being stochastic in nature, and the other (single response pulse) being deterministic. We demonstrate that the main determinant for whichever response is generated is the degree with which the input pathway activates the core circuit, although the noise properties of the input pathway also biases the system towards one or the other type of output. Thus, our work shows how stochastic modelling can reveal the mechanisms behind non-intuitive gene circuit output dynamics.

Tunable phenotypic variability through an autoregulatory alternative sigma factor circuit.

Genetically identical individuals in bacterial populations can display significant phenotypic variability. This variability can be functional, for example by allowing a fraction of stress prepared cells to survive an otherwise lethal stress. The optimal fraction of stress prepared cells depends on environmental conditions. However, how bacterial populations modulate their level of phenotypic variability remains unclear. Here we show that the alternative sigma factor σV circuit in Bacillus subtilis generates functional phenotypic variability that can be tuned by stress level, environmental history and genetic perturbations. Using single-cell time-lapse microscopy and microfluidics, we find the fraction of cells that immediately activate σV under lysozyme stress depends on stress level and on a transcriptional memory of previous stress. Iteration between model and experiment reveals that this tunability can be explained by the autoregulatory feedback structure of the sigV operon. As predicted by the model, genetic perturbations to the operon also modulate the response variability. The conserved sigma-anti-sigma autoregulation motif is thus a simple mechanism for bacterial populations to modulate their heterogeneity based on their environment.