Catalyst: Fast and flexible modeling of reaction networks

Abstract

We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high performance simulation of chemical reaction networks (CRNs). 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 reaction networks; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for use in numerical solvers. Currently Catalyst supports conversion to symbolic discrete stochastic chemical kinetics (jump process), chemical Langevin (stochastic differential equation), and mass-action reaction rate equation (ordinary differential equation) models. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in a broad variety of numerical solvers. The performance of the numerical solvers Catalyst targets is illustrated across a variety of reaction networks by benchmarking stochastic simulation algorithm and ODE solver performance. We demonstrate the extendability and composability of Catalyst by highlighting both how it can compose with a variety of Julia libraries, and how existing open source projects have extended the intermediate representation. These benchmarks demonstrate significant performance improvements compared to several popular reaction network simulators.

Julia for biologists

“…In Julia, using the package Catalyst.jl 39 , this model can be written directly in terms of its reactions, with the corresponding rates. Source code is human readable and differs minimally from the conventional chemical reaction systems shown in Fig.…”

Approximating solutions of the Chemical Master equation using neural networks

“…Gradients of the loss function were computed directly by Flux using the built-in Zygote.jl automatic differentiation system ( Innes et al., 2019 ). The training datasets were constructed by defining chemical reaction networks via Catalyst.jl ( Loman et al., 2022 ) and simulating them using DifferentialEquations.jl ( Rackauckas and Nie. 2017 ) (SSA) and FiniteStateProjection.jl (FSP).…”

“…(2017) Flux.jl v0.13.3 https://github.com/FluxML/Flux.jl Innes (2018) Zygote.jl v0.6.4 https://github.com/FluxML/Zygote.jl Innes et al. (2019) Catalyst.jl v10.8.0 https://github.com/SciML/Catalyst.jl Loman et al. (2022) DifferentialEquations.jl v7.1.0 https://github.com/SciML/DifferentialEquations.jl Rackauckas and Nie (2017) FiniteStateProjection.jl v0.2.0 https://github.com/kaandocal/FiniteStateProjection.jl BlackBoxOptim.jl v0.6.1 https://github.com/robertfeldt/BlackBoxOptim.jl …”

“…Gradients of the loss function were computed directly by Flux using the built-in Zygote.jl automatic differentiation system (Innes et al, 2019). The training datasets were constructed by defining chemical reaction networks via Catalyst.jl (Loman et al, 2022)…”

Plant organellar RNA maturation

“…Partially edited mRNAs do not appear to be excluded from ribosomes (reviewed in Zoschke and Bock 2018 ), and in mutants lacking specific editing factors, the unedited transcripts are translated normally, giving rise to defective proteins. Yet in wild-type plants there is no evidence of any complete translation products being produced from unedited or partially edited transcripts ( Lu and Hanson 1994 ). Either any such products are rapidly degraded, or the editing factors themselves prevent complete translation of unedited mRNA by remaining bound until editing is complete.…”