Main API

mutable struct DelayJumpSet{T1, T2, T3<:Function}

A delay jump set that consists of five inputs, namely delay_trigger, delay_interrupt, delay_complete, delay_trigger_set and delay_interrupt_set. One only need to specify the first three inputs and the rest two can be automatically generated.

Fields

• delay_trigger: reactions in the Markovian part that trigger the change of the state of the delay channels or/and the state of the reactants upon initiation.

• delay_complete: reactions in the Markovian part that change the state of the delay channels or/and the state of the reactants in the middle of on-going delay reactions.

• delay_interrupt: reactions that are initiated by delay trigger reactions and change the state of the delay channels or/and the state of the reactants upon completion.

• delay_trigger_set: collection of indices of reactions that can interrupt the delay reactions. of delay_trigger.

• delay_interrupt_set: collection of indices of delay_interrupt.

Notes

• delay_trigger::Dict{Int,T}: reactions in the Markovian part that trigger the change of the state of the delay channels or/and the state of the reactants upon initiation.

  • Keys: Indices of reactions defined in the Markovian part that can trigger the delay reactions;
  • Values: value type T can be either
    • Function: a function that decides how to update the delay channel and/or the state of the reactants. For example, one can define

      delay_trigger_affect! = function(integrator, rng)
          append!(integrator.de_chan[1], rand(rng))
          integrator.u[2] +=1
      end

      which means adding a random number (with a given random seed rng) in (0,1) to the first delay channel, and adding 1 individual to the second species.
    • Vector{Pair{Int,T2}} where T2<:Union{Real, Vector{Real}} a pair type is a simplified update function for only changing the delay channel (which will render better performance). For example, setting delay_trigger_affect! = [1=>τ] is equivalent to

      delay_trigger_affect! = function(integrator, rng)
          append!(integrator.de_chan[1], τ)
      end

• delay_interrupt::Dict{Int,Function}: reactions in the Markovian part that change the state of the delay channels or/and the state of the reactants in the middle of on-going delay reactions.

  • Keys: Indices of reactions defined in the Markovian part that can interrupt the delay reactions;
  • Values: value type T can be an update function of Function type that decides how to update the delay channel or the state of the reactants.

• delay_complete::Dict{Int,T}: reactions that are initiated by delay trigger reactions and change the state of the delay channels or/and the state of the reactants upon completion.

  • Keys: Indices of the delay channel;
  • Values: value type T can be either an update function of Function type or a Vector{Pair{Int,Int}} type that decides how to update the delay channel or the state of the reactants upon completion

• delay_trigger_set::Vector{Int}: collection of indices of reactions that can trigger the delay reaction.

• delay_interrupt_set::Vector{Int}: collection of indices of reactions that can interrupt the delay reactions.

We take this model for example.

# Take the following example
# C: 0 --> X_A
# γ: X_A --> 0
# β: X_A -->  X_I, which triggers  X_I ==> 0 after time τ
# γ: X_I -->0

# the 3rd reaction will trigger a delay reaction
delay_trigger_affect! = function (integrator, rng)
  append!(integrator.de_chan[1], τ)
end
# this is equivalent to
# delay_trigger = Dict(3=>[1=>τ])
delay_trigger = Dict(3=>delay_trigger_affect!)

# the 1st delay reaction will cause the 2nd species of molecule to degrade
delay_complete = Dict(1=>[2=>-1])


# the 4th reaction will interrupt the delay reactions
delay_interrupt_affect! = function (integrator, rng)
   i = rand(rng, 1:length(integrator.de_chan[1]))
   deleteat!(integrator.de_chan[1],i)
end
delay_interrupt = Dict(4=>delay_interrupt_affect!)


delaysets = DelayJumpSet(delay_trigger,delay_complete,delay_interrupt)

function DelayJumpProblem(prob::DiscreteProblem, aggregator::AbstractDelayAggregatorAlgorithm, jumps::JumpSet, delayjumpset::DelayJumpSet, de_chan0)

Fields

• prob::DiscreteProblem

  A discrete problem defined by the initial values.

• aggregator::AbstractDelayAggregatorAlgorithm

  A given algorithm to solve the DelaySSA problem.

• jumps::JumpSet

  A jumpset containing the information of Markovian part.

• delayjumpset::DelayJumpSet

  A delay jumpset containing the information of Non-Markovian part.

• de_chan0::Vector{Vector{T}}

  The initial condition of the delay channel.

function DelayJumpProblem(js::JumpSystem, prob, aggregator, delayjumpset, de_chan0; kwargs...)

Fields

• js::JumpSystem

  A jump system containing the information of Markovian part, defined by Catalyst.

  • prob::DiscreteProblem

  A discrete problem defined by the initial values.

• aggregator::AbstractDelayAggregatorAlgorithm

  A given algorithm to solve the DelaySSA problem.

• delayjumpset::DelayJumpSet

  A delay jumpset containing the information of Non-Markovian part.

• de_chan0::Vector{Vector{T}}

  The initial condition of the delay channel.

abstract type AbstractDelayAggregatorAlgorithm

An abstract type that contains delay stochastic simulation algorithms:

• DelayDirect
• DelayRejection
• DelayMNRM
• DelayDirectCR
• DelayCoevolve

struct DelayDirect <: DelaySSAToolkit.AbstractDelayAggregatorAlgorithm

Delay Direct Method from Xiaodong Cai, "Exact stochastic simulation of coupled chemical reactions with delays", The Journal of Chemical Physics 126, 124108(2007).

struct DelayRejection <: DelaySSAToolkit.AbstractDelayAggregatorAlgorithm

Delay Rejection Method from Barrio, Manuel, Kevin Burrage, André Leier, and Tianhai Tian. "Oscillatory regulation of Hes1: discrete stochastic delay modelling and simulation." PLoS computational biology 2, no. 9 (2006): e117..

struct DelayMNRM <: DelaySSAToolkit.AbstractDelayAggregatorAlgorithm

A modifed version of the Delay Next Reaction Method from David F. Anderson, "A modified Next Reaction Method for simulating chemical systems with time dependent propensities and delays", The Journal of Chemical Physics 128, 109903(2008).

struct DelayDirectCR <: DelaySSAToolkit.AbstractDelayAggregatorAlgorithm

A modifed Composition-Rejection Direct Method with delays (DelayDirectCR), implementation combining features from the original article and from the code in JumpProcesses package: DirectCR : A constant-time kinetic Monte Carlo algorithm for simulation of large biochemical reaction networks, by A. Slepoy, A.P. Thompson and S.J. Plimpton, J. Chem. Phys, 128, 205101 (2008). and Efficient Formulations for Exact Stochastic Simulation of Chemical Systems, by S. Mauch and M. Stalzer, ACM Trans. Comp. Biol. and Bioinf., 8, No. 1, 27-35 (2010).