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https://github.com/SciML/Catalyst.jl

Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.
https://github.com/SciML/Catalyst.jl

biology chemical-reactions differential-equations dsl gillespie-algorithm julia ode rate-laws reaction-network scientific-machine-learning sciml sde simulation systems-biology systems-biology-simulation

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Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.

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README 

        
# Catalyst.jl



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[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://docs.sciml.ai/Catalyst/stable/)

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Catalyst.jl is a symbolic modeling package for analysis and high performance

simulation of chemical reaction networks. Catalyst defines symbolic

[`ReactionSystem`](https://docs.sciml.ai/Catalyst/stable/catalyst_functionality/programmatic_CRN_construction/)s,

which can be created programmatically or easily

specified using Catalyst's domain specific language (DSL). Leveraging

[ModelingToolkit](https://github.com/SciML/ModelingToolkit.jl) and

[Symbolics.jl](https://github.com/JuliaSymbolics/Symbolics.jl), Catalyst enables

large-scale simulations through auto-vectorization and parallelism. Symbolic

`ReactionSystem`s can be used to generate ModelingToolkit-based models, allowing

the easy simulation and parameter estimation of mass action ODE models, Chemical

Langevin SDE models, stochastic chemical kinetics jump process models, and more.

Generated models can be used with solvers throughout the broader

[SciML](https://sciml.ai) ecosystem, including higher level SciML packages (e.g.

for sensitivity analysis, parameter estimation, machine learning applications,

etc).



## Breaking changes and new features



**NOTE:** version 14 is a breaking release, prompted by the release of ModelingToolkit.jl version 9. This caused several breaking changes in how Catalyst models are represented and interfaced with.



Breaking changes and new functionality are summarized in the

[HISTORY.md](HISTORY.md) file.



## Tutorials and documentation



The latest tutorials and information on using the package are available in the [stable

documentation](https://docs.sciml.ai/Catalyst/stable/). The [in-development

documentation](https://docs.sciml.ai/Catalyst/dev/) describes unreleased features in

the current master branch.



Several Youtube video tutorials and overviews are also available, but note these use older 

Catalyst versions with slightly different notation (for example, in building reaction networks):

- From JuliaCon 2023: A short 15 minute overview of Catalyst as of version 13 is

available in the talk [Catalyst.jl, Modeling Chemical Reaction Networks](https://www.youtube.com/watch?v=yreW94n98eM&ab_channel=TheJuliaProgrammingLanguage).

- From JuliaCon 2022: A three hour tutorial workshop overviewing how to use

  Catalyst and its more advanced features as of version 12.1. [Workshop

  video](https://youtu.be/tVfxT09AtWQ), [Workshop Pluto.jl

  Notebooks](https://github.com/SciML/JuliaCon2022_Catalyst_Workshop). 

- From SIAM CSE 2021: A short 15 minute overview of Catalyst as of version 6 is

available in the talk [Modeling Biochemical Systems with

Catalyst.jl](https://www.youtube.com/watch?v=5p1PJE5A5Jw).

- From JuliaCon 2018: A short 13 minute overview of Catalyst when it was known

  as DiffEqBiological in older versions is available in the talk [Efficient

  Modelling of Biochemical Reaction

  Networks](https://www.youtube.com/watch?v=s1e72k5XD6s)



Finally, an overview of the package and its features (as of version 13) can also be found in its corresponding research paper, [Catalyst: Fast and flexible modeling of reaction networks](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011530).



## Features



- A DSL provides a simple and readable format for manually specifying chemical

  reactions.

- Catalyst `ReactionSystem`s provide a symbolic representation of reaction networks,

  built on [ModelingToolkit.jl](https://docs.sciml.ai/ModelingToolkit/stable/) and

  [Symbolics.jl](https://docs.sciml.ai/Symbolics/stable/).

- Non-integer (e.g. `Float64`) stoichiometric coefficients are supported for generating

  ODE models, and symbolic expressions for stoichiometric coefficients are supported for

  all system types.

- The [Catalyst.jl API](http://docs.sciml.ai/Catalyst/stable/api/catalyst_api) provides functionality for extending networks,

  building networks programmatically, network analysis, and for composing multiple

  networks together.

- `ReactionSystem`s generated by the DSL can be converted to a variety of

  `ModelingToolkit.AbstractSystem`s, including symbolic ODE, SDE and jump process

  representations.

- Coupled differential and algebraic constraint equations can be included in

  Catalyst models, and are incorporated during conversion to ODEs or steady

  state equations.

- Conservation laws can be detected and applied to reduce system sizes, and generate

  non-singular Jacobians, during conversion to ODEs, SDEs, and steady state equations.

- By leveraging ModelingToolkit, users have a variety of options for generating

  optimized system representations to use in solvers. These include construction

  of dense or sparse Jacobians, multithreading or parallelization of generated

  derivative functions, automatic classification of reactions into optimized

  jump types for Gillespie type simulations, automatic construction of

  dependency graphs for jump systems, and more.

- Generated systems can be solved using any

  [DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/stable/)

  ODE/SDE/jump solver, and can be used within `EnsembleProblem`s for carrying

  out parallelized parameter sweeps and statistical sampling. Plot recipes

  are available for visualizing the solutions.

- [Symbolics.jl](https://github.com/JuliaSymbolics/Symbolics.jl) symbolic

  expressions and Julia `Expr`s can be obtained for all rate laws and functions

  determining the deterministic and stochastic terms within resulting ODE, SDE

  or jump models.

- [Latexify](https://korsbo.github.io/Latexify.jl/stable/) can be used to generate

  LaTeX expressions corresponding to generated mathematical models or the

  underlying set of reactions.

- [Graphviz](https://graphviz.org/) can be used to generate and visualize

  reaction network graphs. (Reusing the Graphviz interface created in

  [Catlab.jl](https://algebraicjulia.github.io/Catlab.jl/stable/).)



## Packages supporting Catalyst

- Catalyst [`ReactionSystem`](@ref)s can be imported from SBML files via

  [SBMLToolkit.jl](https://github.com/SciML/SBMLToolkit.jl), and from BioNetGen .net

  files and various stoichiometric matrix network representations using

  [ReactionNetworkImporters.jl](https://github.com/SciML/ReactionNetworkImporters.jl).

- [MomentClosure.jl](https://github.com/augustinas1/MomentClosure.jl) allows

  generation of symbolic ModelingToolkit `ODESystem`s, representing moment

  closure approximations to moments of the Chemical Master Equation, from

  reaction networks defined in Catalyst.

- [FiniteStateProjection.jl](https://github.com/kaandocal/FiniteStateProjection.jl)

  allows the construction and numerical solution of Chemical Master Equation

  models from reaction networks defined in Catalyst.

- [DelaySSAToolkit.jl](https://github.com/palmtree2013/DelaySSAToolkit.jl) can

  augment Catalyst reaction network models with delays, and can simulate the

  resulting stochastic chemical kinetics with delays models.

- [BondGraphs.jl](https://github.com/jedforrest/BondGraphs.jl) a package for

  constructing and analyzing bond graphs models, which can take Catalyst models as input.

- [PEtab.jl](https://github.com/sebapersson/PEtab.jl) a package that implements the PEtab format for fitting reaction network ODEs to data. Input can be provided either as SBML files or as Catalyst `ReactionSystem`s.



## Illustrative examples

#### Gillespie simulations of Michaelis-Menten enzyme kinetics



```julia

using Catalyst, Plots, JumpProcesses

rs = @reaction_network begin

  c1, S + E --> SE

  c2, SE --> S + E

  c3, SE --> P + E

end

p  = (:c1 => 0.00166, :c2 => 0.0001, :c3 => 0.1)

tspan = (0., 100.)

u0 = [:S => 301, :E => 100, :SE => 0, :P => 0]



# solve JumpProblem

dprob = DiscreteProblem(rs, u0, tspan, p)

jprob = JumpProblem(rs, dprob, Direct())

jsol = solve(jprob, SSAStepper())

plot(jsol; lw = 2, title = "Gillespie: Michaelis-Menten Enzyme Kinetics")

```



![](https://user-images.githubusercontent.com/1814174/87864114-3bf9dd00-c932-11ea-83a0-58f38aee8bfb.png)



#### Adaptive time stepping SDEs for a birth-death process



```julia

using Catalyst, Plots, StochasticDiffEq

rs = @reaction_network begin

  c1, X --> 2X

  c2, X --> 0

  c3, 0 --> X

end

p     = (:c1 => 1.0, :c2 => 2.0, :c3 => 50.)

tspan = (0.,10.)

u0    = [:X => 5.]

sprob = SDEProblem(rs, u0, tspan, p)

ssol  = solve(sprob, LambaEM(), reltol=1e-3)

plot(ssol; lw = 2, title = "Adaptive SDE: Birth-Death Process")

```



![](https://user-images.githubusercontent.com/1814174/87864113-3bf9dd00-c932-11ea-8275-f903eef90b91.png)



## Getting help

Catalyst developers are active on the [Julia

Discourse](https://discourse.julialang.org/), the [Julia Slack](https://julialang.slack.com) channels \#sciml-bridged and \#sciml-sysbio, and the [Julia Zulip sciml-bridged channel](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged).

For bugs or feature requests [open an issue](https://github.com/SciML/Catalyst.jl/issues).



## Supporting and citing Catalyst.jl

The software in this ecosystem was developed as part of academic research. If you would like to help support it,

please star the repository as such metrics may help us secure funding in the future. If you use Catalyst as part

of your research, teaching, or other activities, we would be grateful if you could cite our work:

```

@article{CatalystPLOSCompBio2023,

    doi = {10.1371/journal.pcbi.1011530},

    author = {Loman, Torkel E. AND Ma, Yingbo AND Ilin, Vasily AND Gowda, Shashi AND Korsbo, Niklas AND Yewale, Nikhil AND Rackauckas, Chris AND Isaacson, Samuel A.},

    journal = {PLOS Computational Biology},

    publisher = {Public Library of Science},

    title = {Catalyst: Fast and flexible modeling of reaction networks},

    year = {2023},

    month = {10},

    volume = {19},

    url = {https://doi.org/10.1371/journal.pcbi.1011530},

    pages = {1-19},

    number = {10},

}

```