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Related Concept Videos

Mutation, Gene Flow, and Genetic Drift01:09

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Measuring Microbial Mutation Rates with the Fluctuation Assay
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Fluctuating-rate model with multiple gene states.

Jingwei Li1, Hao Ge2, Yunxin Zhang3

  • 1Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai, 200240, China.

Journal of Mathematical Biology
|October 1, 2020
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Summary
This summary is machine-generated.

This study extends the fluctuating-rate (FR) model to multiple gene states, offering a simplified approach to understanding single-cell dynamics. The new model accurately characterizes fluctuations and transitions between phenotypic states, crucial for complex biological systems.

Keywords:
Dominant generalised eigenvalueFluctuating-rate modelNonequilibrium landscape functionTransition rates

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Area of Science:

  • Systems Biology
  • Computational Biology
  • Biophysics

Background:

  • Single cells can exhibit multiple phenotypic states due to positive feedback loops.
  • Stochastic gene expression and low protein counts lead to significant cellular fluctuations.
  • The Chemical Master Equation (CME) models these dynamics but can be computationally intensive.

Purpose of the Study:

  • To generalize the fluctuating-rate (FR) model for systems with multiple gene states.
  • To analyze the dynamics of phenotypic transitions and fluctuations in single cells.
  • To develop a novel numerical algorithm for large deviation principle (LDP) rate functions.

Main Methods:

  • Generalization of the FR model to multi-state gene switching.
  • Application of Freidlin-Wentzell-type large deviation theory.
  • Derivation of the LDP rate function via a generalized eigenvalue problem.
  • Proof of the Lyapunov property for mean-field dynamics.

Main Results:

  • The derivative of the LDP rate function is linked to a generalized eigenvalue problem.
  • A new numerical algorithm is presented for calculating LDP rate functions.
  • The Lyapunov property of the rate function is established for mean-field dynamics.
  • Local fluctuations differ between intermediate and rapid gene-switching regimes.

Conclusions:

  • The generalized FR model provides a tractable framework for multi-state cellular dynamics.
  • The developed numerical method efficiently computes LDP rate functions.
  • Understanding fluctuations is key to characterizing phenotypic plasticity in biological systems.