# Catalyst.jl API

## Reaction Network Generation and Representation

Catalyst provides the @reaction_network macro for generating a complete network, stored as a ReactionSystem, which in turn is composed of Reactions. ReactionSystems can be converted to other ModelingToolkit.AbstractSystems, including a ModelingToolkit.ODESystem, ModelingToolkit.SDESystem, or ModelingToolkit.JumpSystem.

An empty network can be generated using @reaction_network with no arguments (or one argument to name the system), or the make_empty_network function. These can then be extended programmatically using addspecies!, addparam!, and addreaction!.

It is important to note for @reaction_network that any variable not declared to be a parameter after end will be treated as a chemical species of the system. i.e. in

rn = @reaction_network begin
k*X, Y --> W
end k

X, Y and W will all be classified as chemical species.

The ReactionSystem generated by the @reaction_network macro is a ModelingToolkit.AbstractSystem that symbolically represents a system of chemical reactions. In some cases it can be convenient to bypass the macro and directly generate a collection of Reactions and a corresponding ReactionSystem encapsulating them. Below we illustrate with a simple SIR example how a system can be directly constructed, and demonstrate how to then generate from the ReactionSystem and solve corresponding chemical reaction ODE models, chemical Langevin equation SDE models, and stochastic chemical kinetics jump process models.

using Catalyst, OrdinaryDiffEq, StochasticDiffEq, JumpProcesses
@parameters β γ t
@variables S(t) I(t) R(t)

rxs = [Reaction(β, [S,I], [I], [1,1], [2])
Reaction(γ, [I], [R])]
@named rs = ReactionSystem(rxs, t)

u₀map    = [S => 999.0, I => 1.0, R => 0.0]
parammap = [β => 1/10000, γ => 0.01]
tspan    = (0.0, 250.0)

# solve as ODEs
odesys = convert(ODESystem, rs)
oprob = ODEProblem(odesys, u₀map, tspan, parammap)
sol = solve(oprob, Tsit5())

# solve as SDEs
sdesys = convert(SDESystem, rs)
sprob = SDEProblem(sdesys, u₀map, tspan, parammap)
sol = solve(sprob, EM(), dt=.01)

# solve as jump process
jumpsys = convert(JumpSystem, rs)
u₀map    = [S => 999, I => 1, R => 0]
dprob = DiscreteProblem(jumpsys, u₀map, tspan, parammap)
jprob = JumpProblem(jumpsys, dprob, Direct())
sol = solve(jprob, SSAStepper())
Catalyst.@reaction_networkMacro
@reaction_network

Generates a ReactionSystem that encodes a chemical reaction network.

See The Reaction DSL documentation for details on parameters to the macro.

Examples:

# a basic SIR model, with name SIR
sir_model = @reaction_network SIR begin
c1, s + i --> 2i
c2, i --> r
end c1 c2

# a basic SIR model, with random generated name
sir_model = @reaction_network begin
c1, s + i --> 2i
c2, i --> r
end c1 c2

# an empty network with name empty
emptyrn = @reaction_network empty

# an empty network with random generated name
emptyrn = @reaction_network
source
Catalyst.@reactionMacro
@reaction

Generates a single Reaction object.

Examples:

rx = @reaction k*v, A + B --> C + D

# is equivalent to
@parameters k v
@variables t A(t) B(t) C(t) D(t)
rx == Reaction(k*v, [A,B], [C,D])

Here k and v will be parameters and A, B, C and D will be variables. Interpolation of existing parameters/variables also works

@parameters k b
@variables t A(t)
ex = k*A^2 + t
rx = @reaction b*$ex*$A, $A --> C Notes: • Any symbols arising in the rate expression that aren't interpolated are treated as parameters. In the reaction part (α*A + B --> C + D), coefficients are treated as parameters, e.g. α, and rightmost symbols as species, e.g. A,B,C,D. • Works with any single arrow types supported by @reaction_network. • Interpolation of Julia variables into the macro works similar to the @reaction_network macro. See The Reaction DSL tutorial for more details. source Catalyst.ReactionType struct Reaction{S, T} One chemical reaction. Fields • rate The rate function (excluding mass action terms). • substrates Reaction substrates. • products Reaction products. • substoich The stoichiometric coefficients of the reactants. • prodstoich The stoichiometric coefficients of the products. • netstoich The net stoichiometric coefficients of all species changed by the reaction. • only_use_rate false (default) if rate should be multiplied by mass action terms to give the rate law. true if rate represents the full reaction rate law. Examples using Catalyst @parameters k[1:20] @variables t A(t) B(t) C(t) D(t) rxs = [Reaction(k[1], nothing, [A]), # 0 -> A Reaction(k[2], [B], nothing), # B -> 0 Reaction(k[3],[A],[C]), # A -> C Reaction(k[4], [C], [A,B]), # C -> A + B Reaction(k[5], [C], [A], [1], [2]), # C -> A + A Reaction(k[6], [A,B], [C]), # A + B -> C Reaction(k[7], [B], [A], [2], [1]), # 2B -> A Reaction(k[8], [A,B], [A,C]), # A + B -> A + C Reaction(k[9], [A,B], [C,D]), # A + B -> C + D Reaction(k[10], [A], [C,D], [2], [1,1]), # 2A -> C + D Reaction(k[11], [A], [A,B], [2], [1,1]), # 2A -> A + B Reaction(k[12], [A,B,C], [C,D], [1,3,4], [2, 3]), # A+3B+4C -> 2C + 3D Reaction(k[13], [A,B], nothing, [3,1], nothing), # 3A+B -> 0 Reaction(k[14], nothing, [A], nothing, [2]), # 0 -> 2A Reaction(k[15]*A/(2+A), [A], nothing; only_use_rate=true), # A -> 0 with custom rate Reaction(k[16], [A], [B]; only_use_rate=true), # A -> B with custom rate. Reaction(k[17]*A*exp(B), [C], [D], [2], [1]), # 2C -> D with non constant rate. Reaction(k[18]*B, nothing, [B], nothing, [2]), # 0 -> 2B with non constant rate. Reaction(k[19]*t, [A], [B]), # A -> B with non constant rate. Reaction(k[20]*t*A, [B,C], [D],[2,1],[2]) # 2A +B -> 2C with non constant rate. ] Notes: • nothing can be used to indicate a reaction that has no reactants or no products. In this case the corresponding stoichiometry vector should also be set to nothing. • The three-argument form assumes all reactant and product stoichiometric coefficients are one. source Catalyst.ReactionSystemType struct ReactionSystem{U<:Union{Nothing, ModelingToolkit.AbstractSystem}, V<:Catalyst.NetworkProperties} <: AbstractTimeDependentSystem A system of chemical reactions. Fields • eqs The reactions defining the system. • iv Independent variable (usually time). • states Dependent (state) variables representing amount of each species. Must not contain the independent variable. • ps Parameter variables. Must not contain the independent variable. • var_to_name Maps Symbol to corresponding variable. • observed Equations for observed variables. • name The name of the system • systems Internal sub-systems • defaults The default values to use when initial conditions and/or parameters are not supplied in ODEProblem. • connection_type Type of the system • constraints Non-Reaction equations that further constrain the system • networkproperties NetworkProperties object that can be filled in by API functions. INTERNAL – not considered part of the public API. • combinatoric_ratelaws Sets whether to use combinatoric scalings in rate laws. true by default. Example Continuing from the example in the Reaction definition: # simple constructor that infers species and parameters @named rs = ReactionSystem(rxs, t) # allows specification of species and parameters @named rs = ReactionSystem(rxs, t, [A,B,C,D], k) Keyword Arguments: • observed::Vector{Equation}, equations specifying observed variables. • systems::Vector{AbstractSystems}, vector of sub-systems. Can be ReactionSystems, ODESystems, or NonlinearSystems. • name::Symbol, the name of the system (must be provided, or @named must be used). • defaults::Dict, a dictionary mapping parameters to their default values and species to their default initial values. • checks = true, boolean for whether to check units. • constraints = nothing, a NonlinearSystem or ODESystem of coupled constraint equations. • networkproperties = NetworkProperties(), cache for network properties calculated via API functions. • combinatoric_ratelaws = true, sets the default value of combinatoric_ratelaws used in calls to convert or calling various problem types with the ReactionSystem. • balanced_bc_check = true, sets whether to check that BC species appearing in reactions are balanced (i.e appear as both a substrate and a product with the same stoichiometry). Notes: • ReactionSystems currently do rudimentary unit checking, requiring that all species have the same units, and all reactions have rate laws with units of (species units) / (time units). Unit checking can be disabled by passing the keyword argument checks=false. source ## ModelingToolkit and Catalyst Accessor Functions A ReactionSystem is an instance of a ModelingToolkit.AbstractTimeDependentSystem, and has a number of fields that can be accessed using the Catalyst API and the ModelingToolkit.jl Abstract System Interface. Below we overview these components. There are three basic sets of convenience accessors that will return information either from a top-level system, the top-level system and all sub-systems that are also ReactionSystems (i.e. the full reaction-network), or the top-level system, all subs-systems, and all constraint systems (i.e. the full model). To retrieve info from just a base ReactionSystem rn, ignoring sub-systems of rn, one can use the ModelingToolkit accessors (these provide direct access to the corresponding internal fields of the ReactionSystem) • get_states(rn) is a vector that collects all the species defined within rn. • get_ps(rn) is a vector that collects all the parameters defined within reactions in rn. • get_eqs(rn) is a vector that collects all the Reactions defined within rn. • get_iv(rn) is the independent variable used in the system (usually t to represent time). • get_systems(rn) is a vector of all sub-systems of rn. • get_defaults(rn) is a dictionary of all the default values for parameters and species in rn. These are complemented by the Catalyst accessor • Catalyst.get_constraints(sys) is the constraint system of rn. If none is defined will return nothing. The preceding accessors do not allocate, directly accessing internal fields of the ReactionSystem. To retrieve information from the full reaction network represented by a system rn, which corresponds to information within both rn and all sub-systems of type ReactionSystem, one can call: • species(rn) is a vector collecting all the chemical species within the system and any sub-systems that are also ReactionSystems. • reactionparams(rn) is a vector of all the parameters within the system and any sub-systems that are also ReactionSystems. These include all parameters that appear within some Reaction. • reactions(rn) is a vector of all the Reactions within the system and any sub-systems that are also ReactionSystems. These accessors will allocate unless there are no subsystems. In the latter case they are equivalent to the corresponding get_* functions. Finally, as some sub-systems may be other system types, for example specifying algebraic constraints with a NonlinearSystem, it can also be convenient to collect all state variables (e.g. species and algebraic variables) and such. The following ModelingToolkit functions provide this information • ModelingToolkit.states(rn) returns all species and variables across the system, all sub-systems, and all constraint systems. • ModelingToolkit.parameters(rn) returns all parameters across the system, all sub-systems, and all constraint systems. • ModelingToolkit.equations(rn) returns all Reactions and all Equations defined across the system, all sub-systems, and all constraint systems. states and parameters should be assumed to always allocate, while equations will allocate unless there are no subsystems or constraint systems. In the latter case equations is equivalent to get_eqs. Below we list the remainder of the Catalyst API accessor functions mentioned above. ## Basic System Properties See Programmatic Construction of Symbolic Reaction Systems for examples and ModelingToolkit and Catalyst Accessor Functions for more details on the basic accessor functions. Catalyst.speciesFunction species(network) Given a ReactionSystem, return a vector of all species defined in the system and any subsystems that are of type ReactionSystem. To get the variables in the system and all subsystems, including non-ReactionSystem subsystems, uses states(network). Notes: • If ModelingToolkit.get_systems(network) is non-empty will allocate. source Catalyst.reactionparamsFunction reactionparams(network) Given a ReactionSystem, return a vector of all parameters defined within the system and any subsystems that are of type ReactionSystem. To get the parameters in the system and all subsystems, including non-ReactionSystem subsystems, use parameters(network). Notes: • If ModelingToolkit.get_systems(network) is non-empty will allocate. source Catalyst.isbcFunction Catalyst.isbc(s) Tests if the given symbolic variable corresponds to a boundary condition species. source ## Basic Reaction Properties Catalyst.ismassactionFunction ismassaction(rx, rs; rxvars = get_variables(rx.rate), haveivdep = any(var -> isequal(get_iv(rs),var), rxvars), stateset = Set(states(rs))) True if a given reaction is of mass action form, i.e. rx.rate does not depend on any chemical species that correspond to states of the system, and does not depend explicitly on the independent variable (usually time). Arguments • rx, the Reaction. • rs, a ReactionSystem containing the reaction. • Optional: rxvars, Variables which are not in rxvars are ignored as possible dependencies. • Optional: haveivdep, true if the Reaction rate field explicitly depends on the independent variable. • Optional: stateset, set of states which if the rxvars are within mean rx is non-mass action. Notes: • Non-integer stoichiometry is treated as non-mass action. This includes symbolic variables/terms or floating point numbers for stoichiometric coefficients. source Catalyst.dependentsFunction dependents(rx, network) Given a Reaction and a ReactionSystem, return a vector of the non-constant species the reaction rate law depends on. e.g., for k*W, 2X + 3Y --> 5Z + W the returned vector would be [W(t),X(t),Y(t)]. Notes: • Allocates • Does not check for dependents within any subsystems. • Constant species are not considered dependents since they are internally treated as parameters. source Catalyst.substoichmatFunction substoichmat(rn; sparse=false) Returns the substrate stoichiometry matrix,$S$, with$S_{i j}$the stoichiometric coefficient of the ith substrate within the jth reaction. Note: • Set sparse=true for a sparse matrix representation • Note that constant species are not considered substrates, but just components that modify the associated rate law. source Catalyst.prodstoichmatFunction prodstoichmat(rn; sparse=false) Returns the product stoichiometry matrix,$P$, with$P_{i j}$the stoichiometric coefficient of the ith product within the jth reaction. Note: • Set sparse=true for a sparse matrix representation • Note that constant species are not treated as products, but just components that modify the associated rate law. source Catalyst.netstoichmatFunction netstoichmat(rn, sparse=false) Returns the net stoichiometry matrix,$N$, with$N_{i j}$the net stoichiometric coefficient of the ith species within the jth reaction. Notes: • Set sparse=true for a sparse matrix representation • Caches the matrix internally within rn so subsequent calls are fast. • Note that constant species are not treated as reactants, but just components that modify the associated rate law. As such they do not contribute to the net stoichiometry matrix. source ## Functions to Extend or Modify a Network ReactionSystems can be programmatically extended using addspecies!, addparam!, addreaction!, @add_reactions, or composed using ModelingToolkit.extend and ModelingToolkit.compose. Catalyst.addspecies!Function addspecies!(network::ReactionSystem, s::Symbolic; disablechecks=false) Given a ReactionSystem, add the species corresponding to the variable s to the network (if it is not already defined). Returns the integer id of the species within the system. Notes: • disablechecks will disable checking for whether the passed in variable is already defined, which is useful when adding many new variables to the system. Do not disable checks unless you are sure the passed in variable is a new variable, as this will potentially leave the system in an undefined state. source addspecies!(network::ReactionSystem, s::Num; disablechecks=false) Given a ReactionSystem, add the species corresponding to the variable s to the network (if it is not already defined). Returns the integer id of the species within the system. • disablechecks will disable checking for whether the passed in variable is already defined, which is useful when adding many new variables to the system. Do not disable checks unless you are sure the passed in variable is a new variable, as this will potentially leave the system in an undefined state. source Catalyst.addparam!Function addparam!(network::ReactionSystem, p::Symbolic; disablechecks=false) Given a ReactionSystem, add the parameter corresponding to the variable p to the network (if it is not already defined). Returns the integer id of the parameter within the system. • disablechecks will disable checking for whether the passed in variable is already defined, which is useful when adding many new variables to the system. Do not disable checks unless you are sure the passed in variable is a new variable, as this will potentially leave the system in an undefined state. source addparam!(network::ReactionSystem, p::Num; disablechecks=false) Given a ReactionSystem, add the parameter corresponding to the variable p to the network (if it is not already defined). Returns the integer id of the parameter within the system. • disablechecks will disable checking for whether the passed in variable is already defined, which is useful when adding many new variables to the system. Do not disable checks unless you are sure the passed in variable is a new variable, as this will potentially leave the system in an undefined state. source Catalyst.setdefaults!Function setdefaults!(rn, newdefs) Sets the default (initial) values of parameters and species in the ReactionSystem, rn. For example, sir = @reaction_network SIR begin β, S + I --> 2I ν, I --> R end β ν setdefaults!(sir, [:S => 999.0, :I => 1.0, :R => 1.0, :β => 1e-4, :ν => .01]) # or @parameter β ν @variables t S(t) I(t) R(t) setdefaults!(sir, [S => 999.0, I => 1.0, R => 0.0, β => 1e-4, ν => .01]) gives initial/default values to each of S, I and β Notes: • Can not be used to set default values for species, variables or parameters of subsystems or constraint systems. Either set defaults for those systems directly, or flatten to collate them into one system before setting defaults. • Defaults can be specified in any iterable container of symbols to value pairs or symbolics to value pairs. source ModelingToolkit.extendFunction ModelingToolkit.extend(sys::Union{NonlinearSystem,ODESystem}, rs::ReactionSystem; name::Symbol=nameof(sys)) Extends the indicated ReactionSystem with a ModelingToolkit.NonlinearSystem or ModelingToolkit.ODESystem, which will be stored internally as constraint equations. Notes: • Returns a new ReactionSystem and does not modify rs. • By default, the new ReactionSystem will have the same name as sys. source ModelingToolkit.extend(sys::ReactionSystem, rs::ReactionSystem; name::Symbol=nameof(sys)) Extends the indicated ReactionSystem with another ReactionSystem. Similar to calling merge! except constraint systems are allowed (and will also be merged together). Notes: • Returns a new ReactionSystem and does not modify rs. • By default, the new ReactionSystem will have the same name as sys. source extend(sys::ModelingToolkit.AbstractSystem, basesys::ModelingToolkit.AbstractSystem; name) -> ReactionSystem  extend the basesys with sys, the resulting system would inherit sys's name by default. ModelingToolkit.composeFunction compose(sys, systems; name)  compose multiple systems together. The resulting system would inherit the first system's name. ModelingToolkit.flattenFunction Catalyst.flatten(rs::ReactionSystem) Merges all subsystems of the given ReactionSystem up into rs. Notes: • Returns a new ReactionSystem that represents the flattened system. • All Reactions within subsystems are namespaced and merged into the list of Reactions of rs. The merged list is then available as reactions(rs) or get_eqs(rs). • All algebraic equations are merged into a NonlinearSystem or ODESystem stored as get_constraints(rs). If get_constraints !== nothing then the algebraic equations are merged with the current constraints in a system of the same type as the current constraints, otherwise the new constraint system is an ODESystem. • Currently only ReactionSystems, NonlinearSystems and ODESystems are supported as sub-systems when flattening. • rs.networkproperties is reset upon flattening. • The default value of combinatoric_ratelaws will be the logical or of all ReactionSystems. source Base.merge!Method merge!(network1::ReactionSystem, network2::ReactionSystem) Merge network2 into network1. Notes: • Duplicate reactions between the two networks are not filtered out. • Reactions are not deepcopied to minimize allocations, so both networks will share underlying data arrays. • Subsystems are not deepcopied between the two networks and will hence be shared. • Returns network1. • combinatoric_ratelaws is the value of network1. source ## Network Analysis and Representations Note, currently API functions for network analysis and conservation law analysis do not work with constant species (currently only generated by SBMLToolkit). Catalyst.conservationlawsFunction conservationlaws(netstoichmat::AbstractMatrix)::Matrix Given the net stoichiometry matrix of a reaction system, computes a matrix of conservation laws, each represented as a row in the output. source conservationlaws(rs::ReactionSystem) Return the conservation law matrix of the given ReactionSystem, calculating it if it is not already stored within the system, or returning an alias to it. Notes: • The first time being called it is calculated and cached in rn, subsequent calls should be fast. source Catalyst.conservedequationsFunction conservedequations(rn::ReactionSystem) Calculate symbolic equations from conservation laws, writing dependent variables as functions of independent variables and the conservation law constants. Notes: • Caches the resulting equations in rn, so will be fast on subsequent calls. Examples: rn = @reaction_network begin k, A + B --> C k2, C --> A + B end k k2 conservedequations(rn) gives 2-element Vector{Equation}: B(t) ~ A(t) + _ConLaw[1] C(t) ~ _ConLaw[2] - A(t) source Catalyst.conservationlaw_constantsFunction conservationlaw_constants(rn::ReactionSystem) Calculate symbolic equations from conservation laws, writing the conservation law constants in terms of the dependent and independent variables. Notes: • Caches the resulting equations in rn, so will be fast on subsequent calls. Examples: rn = @reaction_network begin k, A + B --> C k2, C --> A + B end k k2 conservationlaw_constants(rn) gives 2-element Vector{Equation}: _ConLaw[1] ~ B(t) - A(t) _ConLaw[2] ~ A(t) + C(t) source Catalyst.ReactionComplexElementType struct ReactionComplexElement{T} One reaction complex element Fields • speciesid The integer id of the species representing this element. • speciesstoich The stoichiometric coefficient of this species. source Catalyst.ReactionComplexType struct ReactionComplex{V<:Integer} <: AbstractArray{Catalyst.ReactionComplexElement{V<:Integer}, 1} One reaction complex. Fields • speciesids The integer ids of all species participating in this complex. • speciesstoichs The stoichiometric coefficients of all species participating in this complex. source Catalyst.reactioncomplexmapFunction reactioncomplexmap(rn::ReactionSystem) Find each ReactionComplex within the specified system, constructing a mapping from the complex to vectors that indicate which reactions it appears in as substrates and products. Notes: • Each ReactionComplex is mapped to a vector of pairs, with each pair having the form reactionidx => ± 1, where -1 indicates the complex appears as a substrate and +1 as a product in the reaction with integer label reactionidx. • Constant species are ignored as part of a complex. i.e. if species A is constant then the reaction A + B --> C + D is considered to consist of the complexes B and C + D. Likewise A --> B would be treated as the same as 0 --> B. source Catalyst.reactioncomplexesFunction reactioncomplexes(network::ReactionSystem; sparse=false) Calculate the reaction complexes and complex incidence matrix for the given ReactionSystem. Notes: • returns a pair of a vector of ReactionComplexs and the complex incidence matrix. • An empty ReactionComplex denotes the null (∅) state (from reactions like ∅ -> A or A -> ∅). • Constant species are ignored in generating a reaction complex. i.e. if A is constant then A –> B consists of the complexes ∅ and B. • The complex incidence matrix,$B$, is number of complexes by number of reactions with $$$B_{i j} = \begin{cases} -1, &\text{if the i'th complex is the substrate of the j'th reaction},\\ 1, &\text{if the i'th complex is the product of the j'th reaction},\\ 0, &\text{otherwise.} \end{cases}$$$ • Set sparse=true for a sparse matrix representation of the incidence matrix source Catalyst.complexstoichmatFunction complexstoichmat(network::ReactionSystem; sparse=false) Given a ReactionSystem and vector of reaction complexes, return a matrix with positive entries of size number of species by number of complexes, where the non-zero positive entries in the kth column denote stoichiometric coefficients of the species participating in the kth reaction complex. Notes: • Set sparse=true for a sparse matrix representation source Catalyst.complexoutgoingmatFunction complexoutgoingmat(network::ReactionSystem; sparse=false) Given a ReactionSystem and complex incidence matrix,$B$, return a matrix of size num of complexes by num of reactions that identifies substrate complexes. Notes: • The complex outgoing matrix,$\Delta$, is defined by $$$\Delta_{i j} = \begin{cases} = 0, &\text{if } B_{i j} = 1, \\ = B_{i j}, &\text{otherwise.} \end{cases}$$$ • Set sparse=true for a sparse matrix representation source Catalyst.incidencematgraphFunction incidencematgraph(rn::ReactionSystem) Construct a directed simple graph where nodes correspond to reaction complexes and directed edges to reactions converting between two complexes. Notes: • Requires the incidencemat to already be cached in rn by a previous call to reactioncomplexes. For example, sir = @reaction_network SIR begin β, S + I --> 2I ν, I --> R end β ν complexes,incidencemat = reactioncomplexes(sir) incidencematgraph(sir) source Catalyst.linkageclassesFunction linkageclasses(rn::ReactionSystem) Given the incidence graph of a reaction network, return a vector of the connected components of the graph (i.e. sub-groups of reaction complexes that are connected in the incidence graph). Notes: • Requires the incidencemat to already be cached in rn by a previous call to reactioncomplexes. For example, sir = @reaction_network SIR begin β, S + I --> 2I ν, I --> R end β ν complexes,incidencemat = reactioncomplexes(sir) linkageclasses(sir) gives 2-element Vector{Vector{Int64}}: [1, 2] [3, 4] source Catalyst.deficiencyFunction deficiency(rn::ReactionSystem) Calculate the deficiency of a reaction network. Here the deficiency,$\delta$, of a network with$n$reaction complexes,$\ell$linkage classes and a rank$s\$ stoichiometric matrix is

$$$\delta = n - \ell - s$$$

Notes:

• Requires the incidencemat to already be cached in rn by a previous call to reactioncomplexes.

For example,

sir = @reaction_network SIR begin
β, S + I --> 2I
ν, I --> R
end β ν
rcs,incidencemat = reactioncomplexes(sir)
δ = deficiency(sir)
source
Catalyst.subnetworksFunction
subnetworks(rn::ReactionSystem)

Find subnetworks corresponding to each linkage class of the reaction network.

Notes:

• Requires the incidencemat to already be cached in rn by a previous call to reactioncomplexes.

For example,

sir = @reaction_network SIR begin
β, S + I --> 2I
ν, I --> R
end β ν
complexes,incidencemat = reactioncomplexes(sir)
subnetworks(sir)
source
Catalyst.linkagedeficienciesFunction
linkagedeficiencies(network::ReactionSystem)

Calculates the deficiency of each sub-reaction network within network.

Notes:

• Requires the incidencemat to already be cached in rn by a previous call to reactioncomplexes.

For example,

sir = @reaction_network SIR begin
β, S + I --> 2I
ν, I --> R
end β ν
rcs,incidencemat = reactioncomplexes(sir)
linkage_deficiencies = linkagedeficiencies(sir)
source
Catalyst.isreversibleFunction
isreversible(rn::ReactionSystem)

Given a reaction network, returns if the network is reversible or not.

Notes:

• Requires the incidencemat to already be cached in rn by a previous call to reactioncomplexes.

For example,

sir = @reaction_network SIR begin
β, S + I --> 2I
ν, I --> R
end β ν
rcs,incidencemat = reactioncomplexes(sir)
isreversible(sir)
source
Catalyst.isweaklyreversibleFunction
isweaklyreversible(rn::ReactionSystem, subnetworks)

Determine if the reaction network with the given subnetworks is weakly reversible or not.

Notes:

• Requires the incidencemat to already be cached in rn by a previous call to reactioncomplexes.

For example,

sir = @reaction_network SIR begin
β, S + I --> 2I
ν, I --> R
end β ν
rcs,incidencemat = reactioncomplexes(sir)
subnets = subnetworks(rn)
isweaklyreversible(rn, subnets)
source
Catalyst.reset_networkproperties!Function
reset_networkproperties!(rn::ReactionSystem)

Clears the cache of various properties (like the netstoichiometry matrix). Use if such properties need to be recalculated for some reason.

source

## Network Comparison

Base.:==Method
==(rx1::Reaction, rx2::Reaction)

Tests whether two Reactions are identical.

Notes:

• Ignores the order in which stoichiometry components are listed.
• Does not currently simplify rates, so a rate of A^2+2*A+1 would be considered different than (A+1)^2.
source
Catalyst.isequal_ignore_namesFunction
isequal_ignore_names(rn1::ReactionSystem, rn2::ReactionSystem)

Tests whether the underlying species, parameters and reactions are the same in the two ReactionSystems. Ignores the names of the systems in testing equality.

Notes:

• Does not currently simplify rates, so a rate of A^2+2*A+1 would be considered different than (A+1)^2.
• Does not include defaults in determining equality.
source
Base.:==Method
==(rn1::ReactionSystem, rn2::ReactionSystem)

Tests whether the underlying species, parameters and reactions are the same in the two ReactionSystems. Requires the systems to have the same names too.

Notes:

• Does not currently simplify rates, so a rate of A^2+2*A+1 would be considered different than (A+1)^2.
• Does not include defaults in determining equality.
source

## Network Visualization

Latexify can be used to convert networks to LaTeX mhchem equations by

using Latexify
latexify(rn)

If Graphviz is installed and commandline accessible, it can be used to create and save network diagrams using Graph and savegraph.

Catalyst.GraphType
Graph(rn::ReactionSystem)

Converts a ReactionSystem into a Graphviz graph. Reactions correspond to small green circles, and species to blue circles.

Notes:

• Black arrows from species to reactions indicate reactants, and are labelled with their input stoichiometry.
• Black arrows from reactions to species indicate products, and are labelled with their output stoichiometry.
• Red arrows from species to reactions indicate that species is used within the rate expression. For example, in the reaction k*A, B --> C, there would be a red arrow from A to the reaction node. In k*A, A+B --> C, there would be red and black arrows from A to the reaction node.
• Requires the Graphviz jll to be installed, or Graphviz to be installed and commandline accessible.
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Catalyst.complexgraphFunction
complexgraph(rn::ReactionSystem; complexdata=reactioncomplexes(rn))

Creates a Graphviz graph of the ReactionComplexs in rn. Reactions correspond to arrows and reaction complexes to blue circles.

Notes:

• Black arrows from complexes to complexes indicate reactions whose rate is a parameter or a Number. i.e. k, A --> B.
• Red dashed arrows from complexes to complexes indicate reactions whose rate depends on species. i.e. k*C, A --> B for C a species.
• Requires the Graphviz jll to be installed, or Graphviz to be installed and commandline accessible.
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Catalyst.savegraphFunction
savegraph(g::Graph, fname, fmt="png")

Given a Graph generated by Graph, save the graph to the file with name fname and extension fmt.

Notes:

• fmt="png" is the default output format.
• Requires the Graphviz jll to be installed, or Graphviz to be installed and commandline accessible.
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## Rate Laws

As the underlying ReactionSystem is comprised of ModelingToolkit expressions, one can directly access the generated rate laws, and using ModelingToolkit tooling generate functions or Julia Exprs from them.

Catalyst.oderatelawFunction
oderatelaw(rx; combinatoric_ratelaw=true)

Given a Reaction, return the symbolic reaction rate law used in generated ODEs for the reaction. Note, for a reaction defined by

k*X*Y, X+Z --> 2X + Y

the expression that is returned will be k*X(t)^2*Y(t)*Z(t). For a reaction of the form

k, 2X+3Y --> Z

the expression that is returned will be k * (X(t)^2/2) * (Y(t)^3/6).

Notes:

• Allocates
• combinatoric_ratelaw=true uses factorial scaling factors in calculating the rate law, i.e. for 2S -> 0 at rate k the ratelaw would be k*S^2/2!. If combinatoric_ratelaw=false then the ratelaw is k*S^2, i.e. the scaling factor is ignored.
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Catalyst.jumpratelawFunction
jumpratelaw(rx; combinatoric_ratelaw=true)

Given a Reaction, return the symbolic reaction rate law used in generated stochastic chemical kinetics model SSAs for the reaction. Note, for a reaction defined by

k*X*Y, X+Z --> 2X + Y

the expression that is returned will be k*X^2*Y*Z. For a reaction of the form

k, 2X+3Y --> Z

the expression that is returned will be k * binomial(X,2) * binomial(Y,3).

Notes:

• Allocates
• combinatoric_ratelaw=true uses binomials in calculating the rate law, i.e. for 2S -> 0 at rate k the ratelaw would be k*S*(S-1)/2. If combinatoric_ratelaw=false then the ratelaw is k*S*(S-1), i.e. the rate law is not normalized by the scaling factor.
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## Transformations

Base.convertFunction
Base.convert(::Type{<:ODESystem},rs::ReactionSystem)

Convert a ReactionSystem to an ModelingToolkit.ODESystem.

Keyword args and default values:

• combinatoric_ratelaws=true uses factorial scaling factors in calculating the rate law, i.e. for 2S -> 0 at rate k the ratelaw would be k*S^2/2!. Set combinatoric_ratelaws=false for a ratelaw of k*S^2, i.e. the scaling factor is ignored. Defaults to the value given when the ReactionSystem was constructed (which itself defaults to true).
• remove_conserved=false, if set to true will calculate conservation laws of the underlying set of reactions (ignoring constraint equations), and then apply them to reduce the number of equations.
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Base.convert(::Type{<:NonlinearSystem},rs::ReactionSystem)

Convert a ReactionSystem to an ModelingToolkit.NonlinearSystem.

Keyword args and default values:

• combinatoric_ratelaws=true uses factorial scaling factors in calculating the rate law, i.e. for 2S -> 0 at rate k the ratelaw would be k*S^2/2!. Set combinatoric_ratelaws=false for a ratelaw of k*S^2, i.e. the scaling factor is ignored. Defaults to the value given when the ReactionSystem was constructed (which itself defaults to true).
• remove_conserved=false, if set to true will calculate conservation laws of the underlying set of reactions (ignoring constraint equations), and then apply them to reduce the number of equations.
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Base.convert(::Type{<:SDESystem},rs::ReactionSystem)

Convert a ReactionSystem to an ModelingToolkit.SDESystem.

Notes:

• combinatoric_ratelaws=true uses factorial scaling factors in calculating the rate law, i.e. for 2S -> 0 at rate k the ratelaw would be k*S^2/2!. Set combinatoric_ratelaws=false for a ratelaw of k*S^2, i.e. the scaling factor is ignored. Defaults to the value given when the ReactionSystem was constructed (which itself defaults to true).
• noise_scaling=nothing::Union{Vector{Num},Num,Nothing} allows for linear scaling of the noise in the chemical Langevin equations. If nothing is given, the default value as in Gillespie 2000 is used. Alternatively, a Num can be given, this is added as a parameter to the system (at the end of the parameter array). All noise terms are linearly scaled with this value. The parameter may be one already declared in the ReactionSystem. Finally, a Vector{Num} can be provided (the length must be equal to the number of reactions). Here the noise for each reaction is scaled by the corresponding parameter in the input vector. This input may contain repeat parameters.
• remove_conserved=false, if set to true will calculate conservation laws of the underlying set of reactions (ignoring constraint equations), and then apply them to reduce the number of equations.
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Base.convert(::Type{<:JumpSystem},rs::ReactionSystem; combinatoric_ratelaws=true)

Convert a ReactionSystem to an ModelingToolkit.JumpSystem.

Notes:

• combinatoric_ratelaws=true uses binomials in calculating the rate law, i.e. for 2S -> 0 at rate k the ratelaw would be k*S*(S-1)/2. If combinatoric_ratelaws=false then the ratelaw is k*S*(S-1), i.e. the rate law is not normalized by the scaling factor. Defaults to the value given when the ReactionSystem was constructed (which itself defaults to true).
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ModelingToolkit.structural_simplifyFunction
structural_simplify(sys)
structural_simplify(sys, io; simplify, kwargs...)


Structurally simplify algebraic equations in a system and compute the topological sort of the observed equations. When simplify=true, the simplify function will be applied during the tearing process. It also takes kwargs allow_symbolic=false and allow_parameter=true which limits the coefficient types during tearing.

The optional argument io may take a tuple (inputs, outputs). This will convert all inputs to parameters and allow them to be unconnected, i.e., simplification will allow models where n_states = n_equations - n_inputs.

## Unit Validation

ModelingToolkit.validateMethod
validate(rx::Reaction; info::String = "")

Check that all substrates and products within the given Reaction have the same units, and that the units of the reaction's rate expression are internally consistent (i.e. if the rate involves sums, each term in the sum has the same units).

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## Utility Functions

Catalyst.symmap_to_varmapFunction
symmap_to_varmap(sys, symmap)

Given a system and map of Symbols to values, generates a map from corresponding symbolic variables/parameters to the values that can be used to pass initial conditions and parameter mappings.

For example,

sir = @reaction_network sir begin
β, S + I --> 2I
ν, I --> R
end β ν
subsys = @reaction_network subsys begin
k, A --> B
end k
@named sys = compose(sir, [subsys])

gives

Model sys with 3 equations
States (5):
S(t)
I(t)
R(t)
subsys₊A(t)
subsys₊B(t)
Parameters (3):
β
ν
subsys₊k

to specify initial condition and parameter mappings from symbols we can use

symmap = [:S => 1.0, :I => 1.0, :R => 1.0, :subsys₊A => 1.0, :subsys₊B => 1.0]
u0map  = symmap_to_varmap(sys, symmap)
pmap   = symmap_to_varmap(sys, [:β => 1.0, :ν => 1.0, :subsys₊k => 1.0])

u0map and pmap can then be used as input to various problem types.

Notes:

• Any Symbol, sym, within symmap must be a valid field of sys. i.e. sys.sym must be defined.
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