Documentation

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

Finds oscillatory parameter sets in a protein interaction network

Arguments (Required)

• connectivity::AbstractMatrix: Connectivity matrix of the protein interaction network
• samples::Int: Number of parameter sets to test

Arguments (Optional)

• initial_conditions::AbstractVector: Initial conditions for the ODEs provided as a vector of vectors. If not specified, the initial conditions are set to 0.5 for all variables.

Returns

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

pin_result = Dict("model" => "ReactionSystem of the protein interaction 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",)

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

Calculates the equilibration times for each dataset

Arguments (Required)

• model::ReactionSystem: Model generated with protein_interaction_network
• parameter_sets::AbstractArray: Parameter sets generated with pin_parameter_sets

Arguments (Optional)

• equilibration_time_multiplier::Real: Factor by which the slowest timescale in the parameter set is multiplied by in order to calculate the final equilibration time

Returns

• equilibration_times::Array{Float64}: Array of equilibration times

pin_hit_rate(connectivity::AbstractMatrix, initial_samples::Int; target_oscillations::Int=100, max_samples::Int=1000000, max_trials::Int=5)

Estimates the hit rate of the oscillatory parameter set search in a protein interaction network

Arguments (Required)

• connectivity::AbstractMatrix: Connectivity matrix of the protein interaction network
• initial_samples::Int: Number of parameter sets to sample in the first trial

Arguments (Optional)

• target_oscillations::Int: Target number of oscillatory parameter sets
• max_samples::Int: Maximum number of samples allowed
• max_trials::Int: Maximum number of trials allowed

Returns

• hit_rate::Real: Estimated hit rate

pin_nodes_edges(model::ReactionSystem)

Returns the node and edge count of a protein interaction network

Arguments

• model::ReactionSystem: Model generated with protein_interaction_network

Returns

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

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

Creates an array of parameter sets for a protein interaction network model.

Arguments (Required)

• model::ReactionSystem: Model generated with protein_interaction_network
• samples::Int: Number of parameter sets to be generated

Arguments (Optional)

• dimensionless_time::Bool: If true, α₁ is set to 1.0 for all parameter sets, making time dimensionless. Default value is true
• parameter_limits::Dict: Dictionary encoding the lower and upper limit of each parameter (in the form of a tuple). Default value is

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

• sampling_scales::Dict: Dictionary with strings encoding the sampling scale for each individual parameter in a model. Accepted strings are "linear" and "log". Default value is

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

• sampling_style::String: Sampling style of the algorithm. Accepted strings are "lhc" and "random". Default value is "lhc".

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

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

Arguments

• model::ReactionSystem: Model generated with protein_interaction_network
• α:AbstractVector: Vector of intrinsic protein activation rates for each node
• β:AbstractVector: Vector of intrinsic protein deactivation rates for each node
• 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.

pin_timescale(α::AbstractVector, β::AbstractVector, γ::AbstractVector)

Calculate the slowest timescale of the protein interaction network

Arguments

• α:AbstractVector: Vector of intrinsic protein activation rates for each node
• β:AbstractVector: Vector of intrinsic protein deactivation rates for each node
• γ:AbstractVector: Vector of strengths for each network interaction

Returns

• timescale::Real

protein_interaction_network(connectivity::AbstractMatrix)

Creates a ReactionSystem of interacting 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.