Stability Analysis of the Ribosome Flow Model

IEEE/ACM Trans. Comput. Biol. and Bioinf.

Tuller

2012

Self Cite

We consider the steady-state distribution of the HRFM. We provide formulas that relate the different parameters of the model in steadystate. We prove the following properties: 1) the ribosomal density profile is monotonically decreasing along the coding sequence; 2) the ribosomal density at each codon monotonically increases with the initiation rate; and 3) for a constant initiation rate, the translation rate monotonically decreases with the length of the coding sequence. In addition, we analyze the translation rate of the HRFM at the limit of very high and very low initiation rate, and provide explicit formulas for the translation rate in these two cases. We discuss the relationship between these theoretical results and biological findings on the translation process.

“…It was already shown that this model admits a unique equilibrium point e ∈ Int(C), and that any trajectory emanating from a feasible initial condition converges to e [52].…”

Section: Discussionmentioning

confidence: 92%

“…It was shown in [52] that the dynamical behavior of the RFM is relatively simple. Let Int(C) denote the interior of C, i.e.…”

Section: Introductionmentioning

confidence: 99%

On the Steady-State Distribution in the Homogeneous Ribosome Flow Model

IEEE/ACM Trans. Comput. Biol. and Bioinf.

Tuller

2012

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“…As noted in Margaliot & Tuller [20], the RFM (1.1) is an SCTS on the open unit cube Int(C). For example, since _ x 2 ¼ f 2 ðxÞ, with f 2 (x) ¼ l 1 x 1 (1 2 x 2 ) 2 l 2 x 2 (1 2 x 3 ), we have @f 2 =@x i ðxÞ = 0 only for i ¼ 1,2,3.…”

Section: Monotone Dynamical Systemsmentioning

confidence: 83%

“…In the study of Margaliot & Tuller [20], we showed that there exists a unique equilibrium point e [ IntðCÞ, where…”

Section: > > > > > > > = > > > > > > > ; ð1:1þmentioning

confidence: 99%

Ribosome flow model with positive feedback

Tuller

2013

J. R. Soc. Interface.

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Eukaryotic mRNAs usually form a circular structure; thus, ribosomes that terminatae translation at the 3 0 end can diffuse with increased probability to the 5 0 end of the transcript, initiating another cycle of translation. This phenomenon describes ribosomal flow with positive feedback-an increase in the flow of ribosomes terminating translating the open reading frame increases the ribosomal initiation rate. The aim of this paper is to model and rigorously analyse translation with feedback. We suggest a modified version of the ribosome flow model, called the ribosome flow model with input and output.In this model, the input is the initiation rate and the output is the translation rate. We analyse this model after closing the loop with a positive linear feedback. We show that the closed-loop system admits a unique globally asymptotically stable equilibrium point. From a biophysical point of view, this means that there exists a unique steady state of ribosome distributions along the mRNA, and thus a unique steady-state translation rate. The solution from any initial distribution will converge to this steady state. The steady-state distribution demonstrates a decrease in ribosome density along the coding sequence. For the case of constant elongation rates, we obtain expressions relating the model parameters to the equilibrium point. These results may perhaps be used to re-engineer the biological system in order to obtain a desired translation rate.

“…[15], [16], [17], [18], [19], [20], [21]). In this case, every ribosome that leaves the chain releases the produced protein, so R(t) is the protein production rate at time t.…”

Section: Examplementioning

confidence: 99%

On Approximating Contractive Systems

Botner

Zarai

IEEE Trans. Automat. Contr.

et al. 2017

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We study the problem of approximating the trajectories of a contractive system using a simpler system (e.g. an LTI system). We derive bounds on the approximation error that depend on the trajectories of the simpler system. We describe several applications of our results to models from systems biology. Index TermsContractive systems, matrix measures, linearized model, input to state dynamical stability, systems biology.