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Exact solving and sensitivity analysis of stochastic continuous time Boolean models.

Mihály Koltai1,2,3, Vincent Noel4,5,6, Andrei Zinovyev4,5,6

  • 1Institut Curie, PSL Research University, Paris, F-75005, France. mihaly.koltai@curie.fr.

BMC Bioinformatics
|June 13, 2020
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Summary
This summary is machine-generated.

An exact matrix method precisely calculates stationary solutions for stochastic Boolean models, avoiding Monte Carlo simulations. This approach reveals how transition rates influence model behavior, identifying sensitive parameters for biological insights.

Keywords:
Asynchronous updatingBoolean modelingContinuous time Markov chainExact methodSteady state solutionStochastic model

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Area of Science:

  • Computational Biology
  • Systems Biology
  • Mathematical Modeling

Background:

  • Stochastic Boolean models are crucial for systems biology but often rely on Monte Carlo simulations for solutions.
  • Monte Carlo methods introduce uncertainty in accuracy and attractor coverage due to large state spaces.
  • Timescale parameters (transition rates) complicate stationary solutions, necessitating sensitivity analysis.

Purpose of the Study:

  • To develop an exact calculation method for stochastic Boolean models.
  • To address limitations of Monte Carlo simulations regarding accuracy and parameter sensitivity.
  • To provide a computational framework for analyzing the impact of transition rates on model dynamics.

Main Methods:

  • Utilizes graph theoretical and matrix calculation methods, adapted from chemical kinetics.
  • Defines model states as a continuous time Markov chain.
  • Employs topological sorting and nullspace analysis of the master equation's kinetic matrix for exact stationary solution calculation.

Main Results:

  • Demonstrates exact calculation of stationary probability values for attractors in asynchronous continuous time Boolean models.
  • Shows that transition rates can significantly impact stationary solutions, identifying sensitive parameters.
  • Successfully applies the method to published Boolean models, offering methodological and biological insights.

Conclusions:

  • An exact matrix method efficiently solves stochastic Boolean models up to intermediate sizes (e.g., 23 nodes) without simulations.
  • Sensitivity analysis highlights a small subset of parameters critically influencing attractor state probabilities.
  • The method offers a robust alternative for analyzing Boolean model dynamics and parameter dependencies.