Chemostats.jl

Chemostats.jl is a package to efficiently simulate cell populations in Julia, featuring state-of-the-art algorithms that estimate population dynamics at sub-exponential cost. It is compatible with the SciML ecosystem, including DifferentialEquations.jl, ModelingToolkit.jl and Catalyst.jl

This package is experimental - any feedback is appreciated (either by email or by opening an issue).

Example

(This does not quite work yet...)

using Catalyst
using Chemostats
using JumpProcesses
using CairoMakie

# Define a reaction network in which ribosomes are produced in a volume-dependent manner
# Time is measured in units
rn = @reaction_network begin
    @species R(t) = 0.
    @variables V(t) = V_d / 2
    @parameters σ = 10. λ = 1. V_d = 2.

    σ * V(t), 0 --> R

    @equations begin
        D(V) ~ λ * R
    end
end 

# A cell divides once it doubles its initial volume. Implemented with a callback.
cb_div = Chemostats.DivideCallback(rn, rn.V ~ rn.V_d)

# This function determines what offspring a dividing cell produces.
function divide(int)
    rand() < 0.1 && return nothing      # Die with probability 1/10

    # Create two cells with half the volume and (roughly) half the ribosomes
    # The model parameters are inherited from the parent cell
    cell_1 = (u0 = (V = int[:V] / 2, R = rand(Binomial(Int(int[:R]), 0.5))), p=nothing)
    cell_2 = (u0 = (V = int[:V] / 2, R = int[:R] - cell_1.u0.R), p=nothing)
    
    cell_1, cell_2
end

prob = ODEProblem(rn, [], (0., 1.); callbacks=cb_div) # tspan here does not matter
cells = DECell[ DECell(prob, divide) ]
chem = Chemostat(cells)

# Simulate population for a day
Chemostats.simulate!(chem, 24 * 60, Chemostats.Strict(10); saveat=0:10:100.)

# The full population would require simulating a lot of cells!
est_Λ(chem)

plot(chem)

See also

Chemostats.jl is designed for efficient estimation of growth rates in cell population models. If simple population simulations are required (corresponding to the Direct algorithm), the following packages may be relevant:

• Agents.jl: A Julia framework for agent-based modelling.
• AgentBasedModeling.jl: A flexible framework built directly on top of Catalyst.

References

• Giardinà, Kurchan, Peliti. "Direct evaluation of large-deviation functions," Phys. Rev. Lett. 96(12), 2006
• Lecomte & Tailleur. "A numerical approach to large deviations in continuous time," J. Stat. Mech.: Theory Exp. 2007(3), 2007

Acknowledgments

• Thanks to Chris Rackaukas, Aayush Sabharwal, Sam Isaacson, and the SciML community for their help and support (and their work on the SciML ecosystem!).