Catalyst.jl for Reaction Network Modeling

Catalyst.jl is a symbolic modeling package for analysis and high performance simulation of chemical reaction networks. Catalyst defines symbolic ReactionSystems, which can be created programmatically or easily specified using Catalyst's domain specific language (DSL). Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst enables large-scale simulations through auto-vectorization and parallelism. Symbolic ReactionSystems 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 ecosystem, including higher level SciML packages (e.g. for sensitivity analysis, parameter estimation, machine learning applications, etc).


  • A DSL provides a simple and readable format for manually specifying chemical reactions.
  • Catalyst ReactionSystems provide a symbolic representation of reaction networks, built on ModelingToolkit.jl and Symbolics.jl.
  • 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 provides functionality for extending networks, building networks programmatically, network analysis, and for composing multiple networks together.
  • ReactionSystems generated by the DSL can be converted to a variety of ModelingToolkit.AbstractSystems, 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 ODE/SDE/jump solver, and can be used within EnsembleProblems for carrying out parallelized parameter sweeps and statistical sampling. Plot recipes are available for visualizing the solutions.
  • Symbolics.jl symbolic expressions and Julia Exprs can be obtained for all rate laws and functions determining the deterministic and stochastic terms within resulting ODE, SDE or jump models.
  • Latexify can be used to generate LaTeX expressions corresponding to generated mathematical models or the underlying set of reactions.
  • Graphviz can be used to generate and visualize reaction network graphs. (Reusing the Graphviz interface created in Catlab.jl.)

Packages Supporting Catalyst

  • Catalyst ReactionSystems can be imported from SBML files via SBMLToolkit.jl, and from BioNetGen .net files and various stoichiometric matrix network representations using ReactionNetworkImporters.jl.
  • MomentClosure.jl allows generation of symbolic ModelingToolkit ODESystems, representing moment closure approximations to moments of the Chemical Master Equation, from reaction networks defined in Catalyst.
  • FiniteStateProjection.jl allows the construction and numerical solution of Chemical Master Equation models from reaction networks defined in Catalyst.
  • DelaySSAToolkit.jl can augment Catalyst reaction network models with delays, and can simulate the resulting stochastic chemical kinetics with delays models.
  • BondGraphs.jl a package for constructing and analyzing bond graphs models, which can take Catalyst models as input.
  • 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 ReactionSystems.


Catalyst can be installed through the Julia package manager:

using Pkg

To solve Catalyst models and visualize solutions, it is also recommended to install DifferentialEquations.jl and Plots.jl


Illustrative Example

Here is a simple example of generating, visualizing and solving an SIR ODE model. We first define the SIR reaction model using Catalyst

using Catalyst
rn = @reaction_network begin
    α, S + I --> 2I
    β, I --> R

\[ \begin{align*} \mathrm{S} + \mathrm{I} &\xrightarrow{\alpha} 2 \mathrm{I} \\ \mathrm{I} &\xrightarrow{\beta} \mathrm{R} \end{align*} \]

Assuming Graphviz and is installed and command line accessible, the network can be visualized using the Graph command


which in Jupyter notebooks will give the figure

SIR Network Graph

To generate and solve a mass action ODE version of the model we use

using DifferentialEquations
p     = [:α => .1/1000, :β => .01]
tspan = (0.0,250.0)
u0    = [:S => 999.0, :I => 1.0, :R => 0.0]
op    = ODEProblem(rn, u0, tspan, p)
sol   = solve(op, Tsit5())       # use Tsit5 ODE solver

which we can plot as

using Plots
plot(sol, lw=2)

Getting Help

Catalyst developers are active on the Julia Discourse, and the Julia Slack's #sciml-bridged and #sciml-sysbio channels. For bugs or feature requests open an issue.

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:

    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 = {},
    pages = {1-19},
    number = {10},


The documentation of this SciML package was built using these direct dependencies,
Status `~/.julia/packages/Catalyst/quz1b/docs/Project.toml`
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Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`
and using this machine and Julia version.
Julia Version 1.9.2
Commit e4ee485e909 (2023-07-05 09:39 UTC)
Platform Info:
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⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.8.7+0
  [7e76a0d4] Libglvnd_jll v1.6.0+0
  [7add5ba3] Libgpg_error_jll v1.42.0+0
  [94ce4f54] Libiconv_jll v1.17.0+0
  [4b2f31a3] Libmount_jll v2.35.0+0
  [89763e89] Libtiff_jll v4.5.1+1
  [38a345b3] Libuuid_jll v2.36.0+0
  [856f044c] MKL_jll v2023.2.0+0
  [2ce0c516] MPC_jll v1.2.1+0
  [e7412a2a] Ogg_jll v1.3.5+1
⌅ [656ef2d0] OpenBLAS32_jll v0.3.21+0
  [458c3c95] OpenSSL_jll v3.0.12+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.2+0
  [30392449] Pixman_jll v0.42.2+0
  [c0090381] Qt6Base_jll v6.5.3+0
  [f50d1b31] Rmath_jll v0.4.0+0
⌅ [fb77eaff] Sundials_jll v5.2.1+0
⌅ [3428059b] SymEngine_jll v0.9.0+1
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+1
  [2381bf8a] Wayland_protocols_jll v1.25.0+0
  [02c8fc9c] XML2_jll v2.11.5+0
  [aed1982a] XSLT_jll v1.1.34+0
  [ffd25f8a] XZ_jll v5.4.4+0
  [f67eecfb] Xorg_libICE_jll v1.0.10+1
  [c834827a] Xorg_libSM_jll v1.2.3+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.11+0
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.4+0
  [1082639a] Xorg_libXext_jll v1.3.4+4
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.10+4
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.15.0+0
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.0+0
  [3161d3a3] Zstd_jll v1.5.5+0
  [35ca27e7] eudev_jll v3.2.9+0
  [214eeab7] fzf_jll v0.35.1+0
  [1a1c6b14] gperf_jll v3.1.1+0
  [a4ae2306] libaom_jll v3.4.0+0
  [0ac62f75] libass_jll v0.15.1+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.2+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.38+0
  [f27f6e37] libvorbis_jll v1.3.7+1
  [009596ad] mtdev_jll v1.1.6+0
  [1270edf5] x264_jll v2021.5.5+0
  [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+1
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.3
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.9.2
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays
  [10745b16] Statistics v1.9.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.0.5+0
  [781609d7] GMP_jll v6.2.1+2
  [deac9b47] LibCURL_jll v7.84.0+0
  [29816b5a] LibSSH2_jll v1.10.2+0
  [3a97d323] MPFR_jll v4.1.1+4
  [c8ffd9c3] MbedTLS_jll v2.28.2+0
  [14a3606d] MozillaCACerts_jll v2022.10.11
  [4536629a] OpenBLAS_jll v0.3.21+4
  [05823500] OpenLibm_jll v0.8.1+0
  [efcefdf7] PCRE2_jll v10.42.0+0
  [bea87d4a] SuiteSparse_jll v5.10.1+6
  [83775a58] Zlib_jll v1.2.13+0
  [8e850b90] libblastrampoline_jll v5.8.0+0
  [8e850ede] nghttp2_jll v1.48.0+0
  [3f19e933] p7zip_jll v17.4.0+0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`
You can also download the manifest file and the project file.