On the gain of entrainment in the n-dimensional ribosome flow model

Ron Ofir, Thomas Kriecherbauer, Lars Grüne, Michael Margaliot*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The ribosome flow model (RFM) is a phenomenological model for the flow of particles along a one-dimensional chain of n sites. It has been extensively used to study ribosome flow along the mRNA molecule during translation. When the transition rates along the chain are time-varying and jointly T-periodic the RFM entrains, i.e. every trajectory of the RFM converges to a unique T-periodic solution that depends on the transition rates, but not on the initial condition. In general, entrainment to periodic excitations like the 24 h solar day or the 50 Hz frequency of the electric grid is important in numerous natural and artificial systems. An interesting question, called the gain of entrainment (GOE) in the RFM, is whether proper coordination of the periodic translation rates along the mRNA can lead to a larger average protein production rate. Analysing the GOE in the RFM is non-Trivial and partial results exist only for the RFM with dimensions n = 1, 2. We use a new approach to derive several results on the GOE in the general n-dimensional RFM. Perhaps surprisingly, we rigorously characterize several cases where there is no GOE, so to maximize the average production rate in these cases, the best choice is to use constant transition rates all along the chain.

Original languageEnglish
Article number20220763
JournalJournal of the Royal Society Interface
Issue number199
StatePublished - 8 Feb 2023


  • contracting systems
  • entrainment
  • mRNA translation
  • periodic solutions
  • totally asymmetric simple exclusion process


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