On the Periodic Gain of the Ribosome Flow Model

We consider a compartmental model for ribosome flow during RNA translation called the Ribosome Flow Model (RFM). This model includes a set of positive transition rates that control the flow from every site to the consecutive site. It has been shown that when these rates are time-varying and jointly T-periodic every solution of the RFM converges to a unique periodic solution with period T. In other words, the RFM entrains to the periodic excitation. In particular, the protein production rate converges to a unique T-periodic pattern. From a biological point of view, one may argue that the average of the periodic production rate, and not the instantaneous rate, is the relevant quantity. Here, we study a problem that can be roughly stated as: can periodic rates yield a higher average production rate than constant rates? We rigorously formulate this question and show via simulations, and rigorous analysis in one simple case, that the answer is no.

[1]  Tim A. Hoek,et al.  Imaging Translation Dynamics of Single mRNA Molecules in Live Cells. , 2018, Methods in molecular biology.

[2]  Nancy R. Zhang,et al.  SAVER: Gene expression recovery for single-cell RNA sequencing , 2018, Nature Methods.

[3]  Michael Margaliot,et al.  Controllability Analysis and Control Synthesis for the Ribosome Flow Model , 2016, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[4]  Mario Andrea Marchisio.  Computational Gene Circuit Design , 2018 .

[5]  R. A. Blythe,et al.  Nonequilibrium steady states of matrix-product form: a solver's guide , 2007, 0706.1678.

[6]  Isaac Meilijson,et al.  Genome-Scale Analysis of Translation Elongation with a Ribosome Flow Model , 2011, PLoS Comput. Biol..

[7]  F. Spitzer.  Interaction of Markov processes , 1970 .

[8]  G. Petsko,et al.  Endosomal Traffic Jams Represent a Pathogenic Hub and Therapeutic Target in Alzheimer’s Disease , 2017, Trends in Neurosciences.

[9]  A. Pipkin,et al.  Kinetics of biopolymerization on nucleic acid templates , 1968, Biopolymers.

[10]  Daniel Liberzon,et al.  Calculus of Variations and Optimal Control Theory: A Concise Introduction , 2012 .

[11]  Anna Feldman,et al.  The extent of ribosome queuing in budding yeast , 2018, PLoS Comput. Biol..

[12]  Jianyang Zeng,et al.  Modeling Translation Elongation Dynamics by Deep Learning Reveals New Insights into the Landscape of Ribosome Stalling , 2022 .

[13]  Rickard Sandberg,et al.  Identification of spatial expression trends in single-cell gene expression data , 2018, Nature Methods.

[14]  M. Margaliot,et al.  Maximizing protein translation rate in the non-homogeneous ribosome flow model: a convex optimization approach , 2014, Journal of The Royal Society Interface.

[15]  T. von der Haar,et al.  Mathematical and Computational Modelling of Ribosomal Movement and Protein Synthesis: an overview , 2012, Computational and structural biotechnology journal.

[16]  Nimrod D. Rubinstein,et al.  Molecular, spatial, and functional single-cell profiling of the hypothalamic preoptic region , 2018, Science.

[17]  Yun-Bo Zhao,et al.  mRNA translation and protein synthesis: an analysis of different modelling methodologies and a new PBN based approach , 2014, BMC Systems Biology.

[18]  David R. Liu,et al.  Evolution of Sequence-Defined Highly Functionalized Nucleic Acid Polymers , 2017, Nature Chemistry.

[19]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[20]  E. O’Shea,et al.  Global analysis of protein expression in yeast , 2003, Nature.

[21]  E B Lee,et al.  Foundations of optimal control theory , 1967 .

[22]  Lothar Reichel,et al.  Tridiagonal Toeplitz matrices: properties and novel applications , 2013, Numer. Linear Algebra Appl..

[23]  Michael Margaliot,et al.  Stability Analysis of the Ribosome Flow Model , 2012, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[24]  Michael Margaliot,et al.  Entrainment to Periodic Initiation and Transition Rates in a Computational Model for Gene Translation , 2014, PloS one.

[25]  B. Schmittmann,et al.  Modeling Translation in Protein Synthesis with TASEP: A Tutorial and Recent Developments , 2011, 1108.3312.

[26]  R. A. Silverman,et al.  Introductory Real Analysis , 1972 .

[27]  Allon M. Klein,et al.  The dynamics of gene expression in vertebrate embryogenesis at single-cell resolution , 2018, Science.

[28]  Yijie Wang,et al.  Ultra-Accurate Complex Disorder Prediction: Case Study of Neurodevelopmental Disorders , 2017, RECOMB.

[29]  Nicholas T. Ingolia,et al.  Genome-Wide Analysis in Vivo of Translation with Nucleotide Resolution Using Ribosome Profiling , 2009, Science.

[30]  Anna Niarakis,et al.  Computational Systems Biology Approach for the Study of Rheumatoid Arthritis: From a Molecular Map to a Dynamical Model , 2017, Genomics and computational biology.

[31]  Michael Margaliot,et al.  Contraction after small transients , 2015, Autom..

[32]  M. L. Chambers.  The Mathematical Theory of Optimal Processes , 1965 .

[33]  J. Hale,et al.  Ordinary Differential Equations , 2019, Fundamentals of Numerical Mathematics for Physicists and Engineers.