Partner: Anna Marciniak-Czochra

University of Heidelberg (DE)

Recent publications
1.Lipniacki T., Paszek P., Marciniak-Czochra A., Brasier A.R., Kimmel M., Transcriptional stochasticity in gene expression, JOURNAL OF THEORETICAL BIOLOGY, ISSN: 0022-5193, DOI: 10.1016/j.jtbi.2005.05.032, Vol.238, pp.348-367, 2006

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.


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

Lipniacki T.-IPPT PAN
Paszek P.-Rice University (US)
Marciniak-Czochra A.-University of Heidelberg (DE)
Brasier A.R.-University of Texas Medical Branch (US)
Kimmel M.-Rice University (US)