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Universality in stochastic exponential growth.

Srividya Iyer-Biswas1, Gavin E Crooks2, Norbert F Scherer1

  • 1James Franck Institute and Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois 60637, USA.

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|July 26, 2014
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Summary

A new model explains how bacterial cell size and division times scale exponentially. This stochastic Hinshelwood cycle (SHC) model reveals universal fluctuation signatures applicable to diverse growth processes.

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Area of Science:

  • Microbiology
  • Theoretical Biology
  • Biophysics

Background:

  • Bacterial cell size and division times exhibit exponential growth and size distribution scaling.
  • Existing models do not fully explain these observed scaling behaviors.

Purpose of the Study:

  • To develop a minimal microscopic theory for stochastic exponential growth.
  • To explain the observed scaling phenomena in bacterial cell size and division.

Main Methods:

  • Formulated a Master Equation model based on the stochastic Hinshelwood cycle (SHC).
  • Derived exact analytical solutions for the SHC and first passage time problems.
  • Investigated universal signatures of fluctuations in exponential growth.

Main Results:

  • The SHC model accurately reproduces the observed exponential scaling of bacterial cell size and division times.
  • Identified universal signatures of fluctuations inherent in stochastic exponential growth.
  • Demonstrated that complex reaction networks can simplify to the SHC model.

Conclusions:

  • The stochastic Hinshelwood cycle provides a minimal framework for understanding exponential growth dynamics.
  • The model's principles are expected to apply to diverse stochastic processes beyond bacterial growth.
  • This work offers insights into universal scaling behaviors in systems exhibiting exponential growth.