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A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics

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  • Yoram Zarai
  • Michael Margaliot
  • Tamir Tuller

Abstract

In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological “particles” move along some kind of “tracks”. The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites. The biological particles (e.g., ribosomes or RNAPs) have volume and cannot surpass one another. In some cases, there is a preferred direction of movement along the track, but in general the movement may be bidirectional, and furthermore the particles may attach or detach from various regions along the tracks. We derive a new deterministic mathematical model for such transport phenomena that may be interpreted as a dynamic mean-field approximation of an important model from mechanical statistics called the asymmetric simple exclusion process (ASEP) with Langmuir kinetics. Using tools from the theory of monotone dynamical systems and contraction theory we show that the model admits a unique steady-state, and that every solution converges to this steady-state. Furthermore, we show that the model entrains (or phase locks) to periodic excitations in any of its forward, backward, attachment, or detachment rates. We demonstrate an application of this phenomenological transport model for analyzing ribosome drop off in mRNA translation.

Suggested Citation

  • Yoram Zarai & Michael Margaliot & Tamir Tuller, 2017. "A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-25, August.
  • Handle: RePEc:plo:pone00:0182178
    DOI: 10.1371/journal.pone.0182178
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    References listed on IDEAS

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    1. Joshua W. Shaevitz & Elio A. Abbondanzieri & Robert Landick & Steven M. Block, 2003. "Backtracking by single RNA polymerase molecules observed at near-base-pair resolution," Nature, Nature, vol. 426(6967), pages 684-687, December.
    2. L. Stirling Churchman & Jonathan S. Weissman, 2011. "Nascent transcript sequencing visualizes transcription at nucleotide resolution," Nature, Nature, vol. 469(7330), pages 368-373, January.
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