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Data Acquisition Protocol for Determining Embedded Sensitivity Functions
07:46

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Published on: April 20, 2016

Spectral methods for parametric sensitivity in stochastic dynamical systems.

D Kim1, B J Debusschere, H N Najm

  • 1Sandia National Laboratories, Livermore, California, USA.

Biophysical Journal
|November 7, 2006
PubMed
Summary
This summary is machine-generated.

We present a new method using spectral polynomial chaos expansions to analyze parametric sensitivity in stochastic biological systems. This approach accurately captures system dynamics and noise effects, even in small molecular populations.

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Area of Science:

  • Computational Biology
  • Systems Biology
  • Biophysics

Background:

  • Stochastic dynamical systems modeled by the chemical master equation are crucial for biological phenomena, especially with small molecular populations.
  • Deterministic models fall short in capturing inherent noise and stochastic effects in these systems.
  • Analyzing parametric sensitivity requires methods that account for both parameter variations and internal stochasticity.

Purpose of the Study:

  • To develop and apply a novel method for assessing parametric sensitivity in stochastic dynamical systems.
  • To accurately represent the nonlinear behavior of system statistics in response to parameter perturbations.
  • To provide a robust framework for analyzing sensitivity in biologically relevant models.

Main Methods:

  • Utilizing spectral polynomial chaos expansions to represent system dynamics statistics as polynomial functions of model parameters.
  • Capturing nonlinear system behaviors arising from finite-sized parameter changes.
  • Deriving normalized sensitivity coefficients by differentiating the functional representation with respect to parameters.

Main Results:

  • The spectral polynomial chaos expansion method effectively represents system statistics and their nonlinear responses.
  • Normalized sensitivity coefficients were successfully obtained for the analyzed systems.
  • The method was validated on two stochastic dynamical systems exhibiting bimodal behavior, including a viral infection model.

Conclusions:

  • Spectral polynomial chaos expansions offer a powerful tool for parametric sensitivity analysis in stochastic biological systems.
  • This method accurately captures the influence of parameter variations amidst inherent noise.
  • The approach is applicable to complex biological models, enhancing our understanding of system dynamics.