ReactionSystem

struct Reaction{S, T<:Number}

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 ModelingToolkit
@parameters t k[1:20]
@variables 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.

struct ReactionSystem <: ModelingToolkit.AbstractSystem

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.

• ps

  Parameter variables.

• observed

• name

  The name of the system

• systems

  systems: The internal systems

Example

Continuing from the example in the Reaction definition:

rs = ReactionSystem(rxs, t, [A,B,C,D], k)

oderatelaw(rx; combinatoric_ratelaw=true)

Given a Reaction, return the reaction rate law Operation 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 Operation 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.

jumpratelaw(rx; rxvars=get_variables(rx.rate), combinatoric_ratelaw=true)

Given a Reaction, return the reaction rate law Operation 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 Operation that is returned will be k * binomial(X,2) * binomial(Y,3).

Notes:

• rxvars should give the Variables, i.e. species and parameters, the rate depends on.
• 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.

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.

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

Convert a ReactionSystem to an ODESystem.

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!. If combinatoric_ratelaws=false then the ratelaw is k*S^2, i.e. the scaling factor is ignored.

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

Convert a ReactionSystem to an NonlinearSystem.

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!. If combinatoric_ratelaws=false then the ratelaw is k*S^2, i.e. the scaling factor is ignored.

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

Convert a ReactionSystem to an 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!. If combinatoric_ratelaws=false then the ratelaw is k*S^2, i.e. the scaling factor is ignored.

• noise_scaling=nothing::Union{Vector{Operation},Operation,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, an Operation 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{Operation} 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.

Base.convert(::Type{<:JumpSystem},rs::ReactionSystem; combinatoric_ratelaws=true)

Convert a ReactionSystem to an 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.