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Binary and graded evolution in time in a simple model of gene induction

Marcin Tabaka1 and Robert Hołyst1,2,*

  • 1Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
  • 2Department of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszyński University, Dewajtis 5, 01-815 Warsaw, Poland

  • *Corresponding author; holyst@ichf.edu.pl
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Phys. Rev. E 82, 052902 – Published 8 November, 2010

DOI: https://doi.org/10.1103/PhysRevE.82.052902

Abstract

We solve analytically the model of gene expression induction which consists of three steps: gene activation, gene products synthesis, and product degradation. The solution is given as a time-dependent probability distribution for gene products. Following the distribution in time from the inactive state of the gene to the stationary state we observe binary or graded response depending solely on the ratio r of the gene activation rate to the rate of the gene product degradation. If r⪡1 the response is binary and the continuous transition from binary to graded response occurs between r=0.1 and r=1. Therefore, if binary response is observed during relaxation to steady state, then the activation rate constant must be smaller than the degradation rate constant.

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Phys. Rev. E 82, 052902– Published 8 November, 2010
  • Received 19 February 2010

© 2010 American Physical Society

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