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

Title data

Ofir, Ron ; Kriecherbauer, Thomas ; Grüne, Lars ; Margaliot, Michael:
On the gain of entrainment in the n-dimensional ribosome flow model.
Bayreuth ; Tel Aviv , 2022 . - 25 p.

Official URL: Volltext

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Project information

Project title:
Project's official titleProject's id
Analysis of Random Transport in Chains using Modern Tools from Systems and Control TheoryGR 1569/24-1, KR 1673/7-1

Project financing: Deutsche Forschungsgemeinschaft
Israel Science Foundation Grants

Abstract in another language

The ribosome flow model (RFM) is a phenomenological model for the flow of particles along a 1D chain of 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. Entrainment to periodic excitations like the 24h solar day or the 50Hz frequency of the electric grid is important in numerous natural and artificial systems. An interesting question, called the gain of entrainment (GOE), is whether proper coordination of the periodic translation rates along the mRNA can lead to a larger average protein production rate. Analyzing 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 along the chain.

Further data

Item Type: Preprint, postprint
Refereed: No
Keywords: Ribosome flow model; entrainment; periodic solution; production rate maximization
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics) > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics) - Univ.-Prof. Dr. Thomas Kriecherbauer
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Research Institutions
Research Institutions > Research Centres
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
500 Science > 570 Life sciences, biology
Date Deposited: 24 Oct 2022 11:47
Last Modified: 24 Oct 2022 11:47
URI: https://eref.uni-bayreuth.de/id/eprint/72495