Interpretation of morphogen gradients by a bistable circuit

Running the Simulation and Bifurcation Analysis

The parametrised differential equation model used to describe the genetic circuit is defined by the rates and jacobian functions in models/protected-degradation.jl. The parameters are contained in a dictionary θ which is then unpacked by symbol name in the two functions. Changing the model requires changing θ, rates and jacobian.

The initial conditions u0 and other simulation parameters such as t_final can be changed in the simulation script main.jl. The DifferentialEquations.jl library is used to simulate the model. This is followed by bifurcation analysis for 15 frames of the entire length of the simulation. The bifurcation algorithm parameters are contained in get_bifurcations in lib/bifurcations.jl

Running main.jl will produce an animation, the layout of which is defined in lib/animate.jl

Fluorescence Microscopy Data Processing

All microscopy data processing as described in the supplementary was done using get_boundary.py and the bulk-processing.ipynb notebook. The input data are large TIFF hyperstacks and are not uploaded here; but can be provided upon request

Modifying the Model and Parameters

If you would like to change the model you can modify models/protected-degradation.jl. Two methods need to be modified: the rate function rates( states::Dict, parameters::Dict, t::Float64 ) and jacobian in logspace jacobian( u::Array, c₆::Float64, c₁₂::Float64 ; parameters::Dict=θ). You are advised to use the testing utility test/jacobian.jl to ensure that the symbolic jacobian matches the finite difference approximation of the rates.

The inferred parameters are also contained in models/protected-degradation.jl. Simply change or import new sets of parameters to global variable θ and re-run the simulation to see the effects

θ = Dict(

	# growth
	"ρ" => 0.002,
	"K" => 2.7,
	"r" => 1.0,
  
  ...
)

Installation and Dependencies

Download and install Julia 1.3.1 then run a julia session by typing julia in the terminal or command prompt. Install the dependencies - including the library PseudoArcLengthContinuation.jl written by R.Veltz - with the following commands

using Pkg
Pkg.add(["DifferentialEquations","Plots","PyPlot","LaTeXStrings","StatsBase","LinearAlgebra","Parameters"])
Pkg.add(PackageSpec(path="https://github.com/rveltz/PseudoArcLengthContinuation.jl"))

then clone this repo and run the main script

git clone https://github.com/gszep/double-exclusive-reporter.git
cd double-exclusive-reporter
julia main.jl