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Sensitivity Analysis

The Sensitivity module provides functionality for performing sensitivity analysis on the ODE-based phosphorylation models in the PhosKinTime package. Using the Morris method from SALib, this module evaluates the influence of each model parameter on the output of the system, thereby helping to identify the most critical parameters and potential nonlinear interactions.

Two Sensitivity Analysis Implementations

PhosKinTime includes two separate sensitivity analysis implementations for the two modeling stacks:

sensitivity/analysis.py networkmodel/sensitivity.py
Scope Local per-protein ODE models Global coupled network ODE model
Method Morris elementary effects (via SALib) Morris elementary effects (trajectory-based perturbation)
Workflow Local pipeline (kinopt → model → sensitivity) Global pipeline (networkmodel → post-analysis)
Input Per-protein fitted parameters, ODE definitions Global model parameters, full network state vector
Output Per-protein sensitivity indices (μ*, σ), diagnostic plots Global sensitivity indices over full trajectory, perturbation cloud plots
When to use Identifying critical parameters for individual protein/site ODE fits Identifying critical global parameters driving network-scale dynamics

Do not confuse the two. They analyze different models and answer different questions.

sensitivity/analysis.py — Local Sensitivity

Overview

This module (primarily implemented in analysis.py) defines functions that:

  • Define the Sensitivity Problem:
    Two functions (define_sensitivity_problem_rand and define_sensitivity_problem_ds) generate the problem definition (number of variables, parameter names, and bounds) required for the Morris sensitivity analysis. The choice depends on whether the model is a random model (randmod) or a distributive/successive model.

  • Run Sensitivity Analysis:
    The sensitivity_analysis function:

    • Generates parameter samples using the Morris method.
    • Simulates the ODE system (via the package's solve_ode function) for each parameter set.
    • Computes a response metric (e.g., the sum of the phosphorylated states at the final time point).
    • Analyzes the sensitivity indices using SALib's analyze function.
    • Generates a suite of plots (bar plots, scatter, radial, CDF, and pie charts) to visually summarize the sensitivity of each parameter.

Invocation

Run as part of the local pipeline via the model CLI stage or directly:

phoskintime model

networkmodel/sensitivity.py — Global Sensitivity

Overview

This module performs trajectory-based perturbation sensitivity analysis for the global coupled ODE model.

  • Elementary Effects (Morris method): Perturbs each parameter independently across a grid of levels.
  • Parallel simulation: Each perturbed trajectory is simulated using the full coupled ODE system.
  • Output:
  • CSV file with per-parameter sensitivity indices (μ* and σ)
  • Perturbation cloud visualizations showing parameter influence on the full trajectory

The sensitivity metric (how the trajectory is collapsed to a scalar) is controlled by sensitivity_metric in config.toml (total_signal, mean, variance, l2_norm).

Configuration (in config.toml)

[networkmodel]
sensitivity_analysis      = true
sensitivity_perturbation  = 0.05
sensitivity_trajectories  = 100
sensitivity_levels        = 40
sensitivity_top_curves    = 20
sensitivity_metric        = "total_signal"

Invocation

Runs automatically after optimization if sensitivity_analysis = true in config.toml:

phoskintime-global

Or triggered from networkmodel/runner.py directly.