Julia implementation of Path Weight Sampling (PWS) to compute information transmission rates
Author manuel-rhdt
1 Star
Updated Last
1 Year Ago
Started In
May 2020


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PathWeightSampling.jl is a Julia package to compute information transmission rates using the novel Path Weight Sampling (PWS) method.


The documentation for PathWeightSampling.jl is hosted on github.


For instructions for how to install Julia itself, see the official website.

To install this package, type from the Julia REPL

julia> import Pkg; Pkg.add("PathWeightSampling")

Alternatively, you can install this package by starting Julia, typing ] and then

pkg> add PathWeightSampling

Quick Start

After installation, the package can be loaded from directly from julia.

julia> using PathWeightSampling

We then need a system of reactions for which we want to compute the mutual information. We can use one of the included example systems, such as a simple model for gene expression.

julia> system = PathWeightSampling.gene_expression_system()
SimpleSystem with 4 reactions
Input variables: S(t)
Output variables: X(t)
Initial condition:
    S(t) = 50
    X(t) = 50
    κ = 50.0
    λ = 1.0
    ρ = 10.0
    μ = 10.0

This specific model is very simple, consisting of only 4 reactions:

  • ∅ → S with rate κ
  • S → ∅ with rate λ
  • S → S + X with rate ρ
  • X → ∅ with rate μ

S represents the input and X represents the output. The values of the parameters can be inspected from the output above. For this system, we can perform a PWS simulation to compute the mutual information between its input and output trajectories:

julia> result = mutual_information(system, DirectMCEstimate(256), num_samples=1000)

Here we just made a default choice for which marginalization algorithm to use (see documentation for more details). This computation takes approximately a minute on a typical laptop. The result is a DataFrame with three columns and 1000 rows:

1000×3 DataFrame
  Row │ TimeConditional  TimeMarginal  MutualInformation                 
      │ Float64          Float64       Vector{Float64}                   
    10.000180898     0.0508378  [0.0, -0.67167, 0.388398, -0.343…
  ⋮   │        ⋮              ⋮                        ⋮
 10000.00020897      0.0694072  [0.0, 0.254173, 0.362607, 0.2584998 rows omitted

Each row represents one Monte Carlo sample.

  • TimeConditional is the CPU time in seconds for the computation of the conditional probability P(x|s)
  • TimeMarginal is the CPU time in seconds for the computation of the marginal probability P(x|s)
  • MutualInformation is the resulting mutual information estimate. This is a vector for each sample giving the mutual information for trajectories of different durations. The durations to which these individual values correspond is given by
julia> system.dtimes

So we computed the mutual information for trajectories of duration 0.0, 0.1, 0.2, ..., 2.0.

We can plot the results (assuming the package Plots.jl is installed):

julia> using Plots, Statistics
julia> plot(
           xlabel="trajectory duration",
           ylabel="mutual information (nats)"

Plot of the mutual information as a function of trajectory duration for the simple gene expression system.

Here we plot mean(result.MutualInformation), i.e. we compute the average of our Monte Carlo samples, which is the PWS estimate for the mutual information.

More examples and a guide can be found in the documentation


This work was performed at the research institute AMOLF. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 885065) and was financially supported by the Dutch Research Council (NWO) through the “Building a Synthetic Cell (BaSyC)” Gravitation grant (024.003.019).

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