Modeling of Chemical Reaction Networks using Catalyst.jl

Catalyst.jl is a modeling package for analysis and high performance simulation of chemical reaction networks (CRNs). It defines symbolic representations for CRNs, which can be created programmatically or specified via a domain specific language. Catalyst provides tooling to analyze models, and to translate CRNs to ModelingToolkit-based ODE, SDE, and jump process models. In this workshop we will overview how to generate, analyze, and efficiently solve such models across a variety of applications.

Workshop Pluto notebooks will be available at https://github.com/TorkelE/JuliaCon2022_Catalyst_Workshop

At the highest level, Catalyst models can be specified via a domain-specific language (DSL), where they can be concisely written as a list of chemical reactions. Such models are converted into a Symbolics.jl-based intermediate representation (IR), represented as a ModelingToolkit.jl AbstractSystem. This IR acts as a common target for many tools within SciML, enabling them to be applied to Catalyst-based models. Symbolic models can also be directly constructed using the symbolic IR, allowing programmatic construction of CRNs or extensions of DSL-defined CRNs.

In this workshop, we will demonstrate how to generate CRN models through the Catalyst DSL and programmatically via the IR. Catalyst features such as custom rate laws, component-based modeling, and parametric stoichiometry will be explored to demonstrate the breadth of models supported by Catalyst. We will then illustrate how such models can be translated to other symbolic Modelingtoolkit-based mathematical representations, and simulated with SciML tooling. Such representations include deterministic ODE models (based on reaction rate equations), stochastic SDE models (based on chemical Langevin equations), and stochastic jump process models (based on the chemical master equation and Gillespie's method). For each of these representations, the DifferentialEquations.jl package provides a variety of solvers that can accurately and efficiently simulate the model's dynamics. We will also demonstrate further tools for analysis of CRN-based models, including methods for parameter fitting, network analysis, calculation of steady states, and bifurcation analysis (through the BifurcationKit.jl package).

To help users with real-world applicability, we will demonstrate how to appropriately use the Catalyst and SciML tooling to scale simulations to tens of thousands of reactions in ways that exploit sparsity, giving easy access to methodologies which outperform competitor packages by orders of magnitude in performance. Aspects such as parallelization of simulations, automatic differentiation usage (in model calibration), and more will be discussed throughout the various topics to give users a complete view of how Catalyst.jl can impact their modeling workflows.