Documentation

find_grn_oscillations(connectivity::AbstractMatrix, samples::Int; initial_conditions::AbstractVector=NaN)

Find oscillatory parameter sets in a gene regulatory network.

Arguments (Required)

• connectivity::AbstractMatrix: Connectivity matrix for the gene regulatory network
• samples::Int: Number of parameter sets to test

Arguments (Optional)

• initial_conditions::AbstractVector=NaN: Initial conditions for the ODEs. If not provided, the initial conditions are set to 0.5 for all variables.

Returns

• pin_result::Dict: A ditionary containing the results of the oscillatory parameter set search. Output is encoded as:

pin_result = Dict("model" => "ReactionSystem of the gene regulatory network",
                  "parameter_sets" => "Dataframe of parameter sets",
                  "equilibration_result" => "Dataframe containing result metrics for the equilibration of parameter sets",
                  "simulation_result" => "Dataframe containing result metrics for the simulated parameter sets",)

gene_regulatory_network(connectivity::AbstractMatrix)

Creates a ReactionSystem of interacting mRNA and proteins based on the provided connectivity.

Arguments

• connectivity::AbstractMatrix: A 2 dimensional matrix filled with -1, 0, and 1 values indicating the edges of the network.

grn_equilibration_times(model::ReactionSystem, parameter_sets::AbstractArray; equilibration_time_multiplier=10)

Calculate the equilibration times for a group of parameter sets.

Arguments (Required)

• model::ReactionSystem: Model generated with gene_regulatory_network
• parameter_sets::AbstractArray: Parameter sets generated with grn_parameter_sets

Arguments (Optional)

• equilibration_time_multiplier::Real=10: Multiplier for the equilibration time. The equilibration time is calculated as the timescale of the system multiplied by this value.

Returns

• equilibration_times::AbstractVector: Equilibration times for each parameter set.

grn_nodes_edges(model::ReactionSystem)

Returns the number of nodes and edges of a model created with gene_regulatory_network.

Arguments

• model::ReactionSystem: Model generated with gene_regulatory_network

Returns

• AbstractVector: Array with 2 elements representing the number of nodes and edges

grn_parameter_sets(model::ReactionSystem, samples::Int; dimensionless_time=true, parameter_limits=Dict("α" => (1e-2, 1e2), "β" => (1e-2, 1e2), "δ" => (1e-2, 1e2), "γ" => (1e2, 1e4), "κ" => (0.2, 1.0), "η" => (1.0, 5.0)), sampling_scales=Dict("α" => "log", "β" => "log", "δ" => "log", "γ" => "log", "κ" => "linear", "η" => "linear"), sampling_style="lhc")

Generate a set of parameter values for a gene regulatory network model.

Arguments (Required)

• model::ReactionSystem: Model generated with gene_regulatory_network
• samples::Int: Number of parameter sets to generate

Arguments (Optional)

• dimensionless_time::Bool=true: If true, α₁ is set to 1.0 as well as the first N κ's with N=number of nodes. This is done to make the timescale of the system dimensionless.
• parameter_limits::Dict: Dict with keys "α", "β", "δ", "γ", "κ", "η" and values of tuples with lower and upper limits for each parameter. Default values are:

parameter_limits = Dict("α" => (1e-2, 1e2), "β" => (1e-2, 1e2), "δ" => (1e-2, 1e2),
                        "γ" => (1e2, 1e4), "κ" => (0.2, 1.0), "η" => (1.0, 5.0))

• sampling_scales::Dict: Dict with keys "α", "β", "δ", "γ", "κ", "η" and values of strings with the sampling scale for each parameter. Default values are:

sampling_scales = Dict("α" => "log", "β" => "log", "δ" => "log", "γ" => "log", "κ" => "linear", "η" => "linear")

• sampling_style::String="lhc": Sampling style. Options are "lhc" for latin hypercube sampling and "random" for random sampling.

grn_parameters(model:ReactionSystem, α::AbstractVector, β::AbstractVector, δ::AbstractVector, γ::AbstractVector, κ::AbstractVector, η::AbstractVector)

Creates an ordered parameter vector for a model created with the gene_regulatory_network function to use in ODEProblem.

Arguments

• model::ReactionSystem: Model generated with gene_regulatory_network
• α:AbstractVector: Vector of intrinsic mRNA degradation rates
• β:AbstractVector: Vector of intrinsic protein synthesis rates
• δ:AbstractVector: Vector of intrinsic protein degradation rates
• γ:AbstractVector: Vector of strengths for each network interaction
• κ:AbstractVector: Vector of midpoints for each network interaction
• η:AbstractVector: Vector of sensitivity values for each network interaction

Note

It is assumed that parameters follow the same order as the connectivity matrix. Namely, the first node is encoded on the first row of the connectivty matrix and the first edge comes from the first nonzero element of the connectivity.

grn_timescale(α::AbstractVector, δ::AbstractVector)

Calculate the slowest timescale of the gene regulatory network

Arguments

• α:AbstractVector: Vector of intrinsic mRNA degradation rates
• δ:AbstractVector: Vector of intrinsic protein degradation rates

Returns

• timescale::Real