A max-plus model of ribosome dynamics during mRNA translation

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

    Research output: Contribution to journalArticlepeer-review


    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. © 2012 Elsevier Ltd.
    Original languageEnglish
    Pages (from-to)128-140
    Number of pages12
    JournalJournal of Theoretical Biology
    Publication statusPublished - 21 Jun 2012


    • Elongation
    • Petri net
    • Protein biosynthesis
    • Tropical algebra


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