Transcriptional stochasticity in gene expression

Tomasz Lipniacki, Pawel Paszek, Anna Marciniak-Czochra, Allan R. Brasier, Marek Kimmel

Research output: Contribution to journalArticlepeer-review

88 Scopus citations


Due to the small number of copies of molecular species involved, such as DNA, mRNA and regulatory proteins, gene expression is a stochastic phenomenon. In eukaryotic cells, the stochastic effects primarily originate in regulation of gene activity. Transcription can be initiated by a single transcription factor binding to a specific regulatory site in the target gene. Stochasticity of transcription factor binding and dissociation is then amplified by transcription and translation, since target gene activation results in a burst of mRNA molecules, and each mRNA copy serves as a template for translating numerous protein molecules. In the present paper, we explore a mathematical approach to stochastic modeling. In this approach, the ordinary differential equations with a stochastic component for mRNA and protein levels in a single cells yield a system of first-order partial differential equations (PDEs) for two-dimensional probability density functions (pdf). We consider the following examples: Regulation of a single auto-repressing gene, and regulation of a system of two mutual repressors and of an activator-repressor system. The resulting PDEs are approximated by a system of many ordinary equations, which are then numerically solved.

Original languageEnglish (US)
Pages (from-to)348-367
Number of pages20
JournalJournal of Theoretical Biology
Issue number2
StatePublished - Jan 21 2006
Externally publishedYes


  • Gene regulation
  • Probability density function
  • Stochasticity
  • Transcription
  • Transport-type equations

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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