From convergence of operator semigroups to gene expression, and back again

Volume 80 / 2008

Adam Bobrowski Banach Center Publications 80 (2008), 83-99 MSC: 47D07, 60J25, 60J35, 60J55. DOI: 10.4064/bc80-0-5


The subject of the paper is reciprocal influence of pure mathematics and applied sciences. We illustrate the idea by giving a review of mathematical results obtained recently, related to the model of stochastic gene expression due to Lipniacki et al. \cite{lipniacki}. In this model, featuring mRNA and protein levels, and gene activity, the stochastic part of processes involved in gene expression is distinguished from the part that seems to be mostly deterministic, and the dynamics is expressed by means of a piece-wise deterministic Markov process. Mathematical results pertain to asymptotic behavior of the process in time as well as limit behavior when certain parameters may be assumed to be large. These results are but an inspiration to considering the ways applied sciences influence pure mathematics by supplying fresh ideas and providing new challenges. On the other hand, they may also be seen as an exemplification of the fact that statements that seem to be almost obvious and are often taken for granted in applied sciences may require mathematical scrutiny and non-standard proofs.


  • Adam BobrowskiInstitute of Mathematics
    Polish Academy of Sciences
    Katowice branch
    Bankowa 14
    40-007 Katowice, Poland
    Department of Mathematics
    Faculty of Electrical Engineering and Computer Science
    Lublin University of Technology
    Nadbystrzycka 38A
    20-618 Lublin, Poland

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