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Overview

BioSimulator.jl simulates stochastic dynamical systems using Markov chain theory. Because transition probabilities are usually unavailable and infinitesimal generators are often impractical, we provide a few modeling objects to represent a chain. Two cases are handled: well-mixed and lattice-based systems. Here the term "well-mixed" is taken to mean that the underlying space for a chain concerns discrete quantities and/or vectors (non-spatial), whereas lattice-based systems model configurations of interacting particles (spatial).

Well-Mixed Systems

A Network object summarizes interactions between populations. Each Species participates in at least one Reaction. For example, the following code defines a birth-death-immigration process in BioSimulator.jl's modeling language:

# initialize
network = Network("BDI")

# species definitions; add components with <=
network <= Species("X", 5)

# reaction definitions
network <= Reaction("birth", 2.0, "X --> X + X")
network <= Reaction("death", 1.0, "X --> 0")
network <= Reaction("immigration", 0.5, "0 --> X")

Interface

BioSimulator.Network — Type
Network(id)

Construct an empty Network representing a system of interacting particles. A particle is represented by a Species, and an interaction is represented by a Reaction.

Add a Species or Reaction using <=:

m <= Species("X", 100)
m <= Reaction("birth", 2.0, "X --> X + X")
BioSimulator.Species — Type
Species(id, [value=0])

Define a Species with a name and initial population value.

BioSimulator.Reaction — Type
Reaction(name, rate, formula)

Define a Reaction with a name, a stochastic rate constant, and a formula.

The formula should use Species from a Network. Multiple reactants are separated by a + symbol; similarly for products. Reactants and products are separated by a --> symbol. Refer to the examples below:

Examples

Reaction("birth", 1.0, "X --> X + X")   # equiv. X --> 2*X
Reaction("death", 0.5, "X --> 0")       # no products
Reaction("immigration", 0.5, "0 --> X") # no reactants

Lattice/Cellular Automata

Interacting Particle Systems (IPSs) are defined using the @def_reactions macro. The syntax resembles chemical reaction notation but the + symbol implies directionality; for example:

interactions = @def_reactions begin
    X + 0 --> 0 + X, α
    X + Y --> Z + 0, β
    Z --> 0, α
end α β

The first interaction reads as "X moves to an empty site" (swapping locations). The second is taken to mean "X interacts with an adjacent Y to form Z at the same location as X, with Y being consumed in the process". However, this construction not contain any spatial information. You can specify a topology using @enumerate_with_sclass:

model = @enumerate_with_sclass interactions VonNeumann() 2

This command "compiles" a 2-D version of the IPS in which interactions are between nearest-neighbors along cardinal directions. Initial conditions are specified with a Lattice object:

state = Lattice(coordinates, ...)