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Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro

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Sensitivity Analysis for Multiscale Stochastic Reaction Networks Using Hybrid Approximations.

Ankit Gupta¹, Mustafa Khammash²

¹Department of Biosystems Science and Engineering, ETH Zurich, Mattenstrasse 26, 4058, Basel, Switzerland.

Bulletin of Mathematical Biology

|October 11, 2018

Summary

Estimating parameter sensitivities for multiscale reaction networks is challenging. This study shows that Piecewise Deterministic Markov Process (PDMP) approximations enable accurate and efficient sensitivity estimation for these complex models.

Keywords:

Coupling Multiscale networks Parameter sensitivity Piecewise deterministic Markov processes Random time change representation Reduced models Stochastic reaction networks

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Area of Science:

Computational Biology
Chemical Kinetics
Stochastic Processes

Background:

Estimating parameter sensitivities is crucial for analyzing multiscale reaction networks.
Current simulation-based methods are computationally infeasible for multiscale systems due to disparate timescales.

Purpose of the Study:

To demonstrate the accuracy and efficiency of Piecewise Deterministic Markov Process (PDMP) approximations for parameter sensitivity estimation in multiscale stochastic models.
To establish theoretical convergence of sensitivities from stochastic models to PDMP approximations.

Main Methods:

Developing and analyzing Piecewise Deterministic Markov Process (PDMP) approximations for multiscale reaction networks.
Proving the convergence of parameter sensitivities in the limit of exact PDMP approximation.
Deriving a representation for PDMP sensitivity separating discrete and continuous contributions.

Main Results:

PDMP approximations provide an accurate and efficient method for estimating parameter sensitivities.
Theoretical convergence of sensitivities is proven as the PDMP approximation becomes exact.
A novel representation of PDMP sensitivity effectively separates contributions from discrete and continuous dynamics.

Conclusions:

PDMP approximations offer a computationally tractable approach to sensitivity analysis for multiscale stochastic models.
The proposed method significantly enhances the efficiency of parameter sensitivity estimation.
The separated sensitivity representation aids in understanding the influence of different dynamic components.