A max-plus model of ribosome dynamics during mRNA translation

Christopher A. Brackley, David S. Broomhead, M Carmen Romano, Marco Thiel

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


We examine the dynamics of the translation stage of cellular protein production, in which ribosomes move uni-directionally along an mRNA strand, building amino acid chains as they go. We describe the system using a timed event graph—a class of Petri net useful for studying discrete events, which have to satisfy constraints. We use max-plus algebra to describe a deterministic version of the model, where the constraints represent steric effects which prevent more than one ribosome reading a given codon at a given time and delays associated with the availability of the different tRNAs. We calculate the protein production rate and density of ribosomes on the mRNA and find exact agreement between these analytical results and numerical simulations of the deterministic model, even in the case of heterogeneous mRNAs.
Original languageEnglish
Pages (from-to)128-140
Number of pages13
JournalJournal of Theoretical Biology
Issue number-
Early online date16 Mar 2012
Publication statusPublished - 21 Jun 2012

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  • protein biosynthesis
  • elongation
  • Petri net
  • tropical algebra


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