scholarly journals Ribosome flow model with positive feedback

2013 ◽  
Vol 10 (85) ◽  
pp. 20130267 ◽  
Author(s):  
Michael Margaliot ◽  
Tamir Tuller
Keyword(s):  
Steady State ◽  
Equilibrium Point ◽  
Positive Feedback ◽  
Flow Model ◽  
Linear Feedback ◽  
Model Parameters ◽  
Stable Equilibrium Point ◽  
Initiation Rate ◽  
Translation Rate ◽  
Unique Steady State

Eukaryotic mRNAs usually form a circular structure; thus, ribosomes that terminatae translation at the 3′ end can diffuse with increased probability to the 5′ 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.

scholarly journals Maximizing protein translation rate in the non-homogeneous ribosome flow model: a convex optimization approach

2014 ◽  
Vol 11 (100) ◽  
pp. 20140713 ◽  
Author(s):  
Gilad Poker ◽  
Yoram Zarai ◽  
Michael Margaliot ◽  
Tamir Tuller
Keyword(s):  
Synthetic Biology ◽  
Convex Optimization ◽  
Production Rate ◽  
Protein Production ◽  
Flow Model ◽  
Protein Translation ◽  
Optimization Approach ◽  
Initiation Rate ◽  
Translation Rate ◽  
Protein Production Rate

Translation is an important stage in gene expression. During this stage, macro-molecules called ribosomes travel along the mRNA strand linking amino acids together in a specific order to create a functioning protein. An important question, related to many biomedical disciplines, is how to maximize protein production. Indeed, translation is known to be one of the most energy-consuming processes in the cell, and it is natural to assume that evolution shaped this process so that it maximizes the protein production rate. If this is indeed so then one can estimate various parameters of the translation machinery by solving an appropriate mathematical optimization problem. The same problem also arises in the context of synthetic biology, namely, re-engineer heterologous genes in order to maximize their translation rate in a host organism. We consider the problem of maximizing the protein production rate using a computational model for translation–elongation called the ribosome flow model (RFM). This model describes the flow of the ribosomes along an mRNA chain of length n using a set of n first-order nonlinear ordinary differential equations. It also includes n + 1 positive parameters: the ribosomal initiation rate into the mRNA chain, and n elongation rates along the chain sites. We show that the steady-state translation rate in the RFM is a strictly concave function of its parameters. This means that the problem of maximizing the translation rate under a suitable constraint always admits a unique solution, and that this solution can be determined using highly efficient algorithms for solving convex optimization problems even for large values of n . Furthermore, our analysis shows that the optimal translation rate can be computed based only on the optimal initiation rate and the elongation rate of the codons near the beginning of the ORF. We discuss some applications of the theoretical results to synthetic biology, molecular evolution, and functional genomics.

scholarly journals Ribosome flow model with extended objects

2017 ◽  
Vol 14 (135) ◽  
pp. 20170128 ◽  
Author(s):  
Yoram Zarai ◽  
Michael Margaliot ◽  
Tamir Tuller
Keyword(s):  
Steady State ◽  
Production Rate ◽  
Protein Production ◽  
Flow Model ◽  
Mean Field ◽  
State Density ◽  
Transition Rates ◽  
Ribosome Density ◽  
Protein Production Rate ◽  
Unique Steady State

We study a deterministic mechanistic model for the flow of ribosomes along the mRNA molecule, called the ribosome flow model with extended objects  (RFMEO). This model encapsulates many realistic features of translation including non-homogeneous transition rates along mRNA, the fact that every ribosome covers several codons, and the fact that ribosomes cannot overtake one another. The RFMEO is a mean-field approximation of an important model from statistical mechanics called the totally asymmetric simple exclusion process with extended objects (TASEPEO). We demonstrate that the RFMEO describes biophysical aspects of translation better than previous mean-field approximations, and that its predictions correlate well with those of TASEPEO. However, unlike TASEPEO, the RFMEO is amenable to rigorous analysis using tools from systems and control theory. We show that the ribosome density profile along the mRNA in the RFMEO converges to a unique steady-state density that depends on the length of the mRNA, the transition rates along it, and the number of codons covered by every ribosome, but not on the initial density of ribosomes along the mRNA. In particular, the protein production rate also converges to a unique steady state. Furthermore, if the transition rates along the mRNA are periodic with a common period  T then the ribosome density along the mRNA and the protein production rate converge to a unique periodic pattern with period  T , that is, the model entrains to periodic excitations in the transition rates. Analysis and simulations of the RFMEO demonstrate several counterintuitive results. For example, increasing the ribosome footprint may sometimes lead to an increase in the production rate. Also, for large values of the footprint the steady-state density along the mRNA may be quite complex (e.g. with quasi-periodic patterns) even for relatively simple (and non-periodic) transition rates along the mRNA. This implies that inferring the transition rates from the ribosome density may be non-trivial. We believe that the RFMEO could be useful for modelling, understanding and re-engineering translation as well as other important biological processes.

scholarly journals Large-scale mRNA translation and the intricate effects of competition for the finite pool of ribosomes

2021 ◽  
Author(s):  
Aditi Jain ◽  
Michael Margaliot ◽  
Arvind Kumar Gupta
Keyword(s):  
Steady State ◽  
Large Scale ◽  
Flow Model ◽  
Mrna Translation ◽  
Shared Resources ◽  
Initiation Rate ◽  
Internal Ribosome Entry ◽  
Langmuir Kinetics ◽  
State Production ◽  
Entire Network

We present a new theoretical framework for large-scale mRNA translation using a network of models called the ribosome flow model with Langmuir kinetics (RFMLK), interconnected via a pool of free ribosomes. The input to each RFMLK depends on the pool density, and it affects the initiation rate and the internal ribosome entry rates at each site along each RFMLK. Ribosomes that detach from an RFMLK due to termination or premature drop-off are fed back into the pool. We prove that the network always converges to a steady-state, and study its sensitivity to variations in the parameters. For example, we show that if the drop-off rate at some site in some RFMLK is increased then the pool density increases and consequently the steady-state production rate in all the other RFMLKs increases. Surprisingly, we also show that modifying a parameter of a certain RFMLK can lead to arbitrary effects on the densities along the modified RFMLK, depending on the parameters in the entire network. We conclude that the competition for shared resources generates an indirect and intricate web of mutual effects between the mRNA molecules, that must be accounted for in any analysis of translation.

Holdup and holdup profiles in the reciprocating plate extractor VPE

1990 ◽  
Vol 55 (11) ◽  
pp. 2648-2661 ◽  
Author(s):  
Helena Sovová ◽  
Vladislav Bízek ◽  
Jaroslav Procházka
Keyword(s):  
Steady State ◽  
Experimental Results ◽  
Model Parameters ◽  
Dispersed Phase ◽  
Pulse Form ◽  
Sieve Plates

In this work measurements of mean holdup of dispersed phase, of axial holdup profiles and of flooding points in a reciprocating plate contactor with both the VPE-type plates and the sieve plates were carried out. The experimental results were compared with a monodisperse model of steady-state column hydrodynamics and the model parameters were evaluated. Important differences in the behaviour of the two plate types could be identified. Comparison was also made between two reciprocating drives of different pulse form.

scholarly journals Research of Trajectory Optimization Approaches in Synthesized Optimal Control

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 336
Author(s):  
Askhat Diveev ◽  
Elizaveta Shmalko
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Trajectory Optimization ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Control Object ◽  
Symbolic Regression ◽  
Optimal Location ◽  
Stable Equilibrium Point ◽  
Stabilization System

This article presents a study devoted to the emerging method of synthesized optimal control. This is a new type of control based on changing the position of a stable equilibrium point. The object stabilization system forces the object to move towards the equilibrium point, and by changing its position over time, it is possible to bring the object to the desired terminal state with the optimal value of the quality criterion. The implementation of such control requires the construction of two control contours. The first contour ensures the stability of the control object relative to some point in the state space. Methods of symbolic regression are applied for numerical synthesis of a stabilization system. The second contour provides optimal control of the stable equilibrium point position. The present paper provides a study of various approaches to find the optimal location of equilibrium points. A new problem statement with the search of function for optimal location of the equilibrium points in the second stage of the synthesized optimal control approach is formulated. Symbolic regression methods of solving the stated problem are discussed. In the presented numerical example, a piece-wise linear function is applied to approximate the location of equilibrium points.

Utilizing an Adaptive Controller (Azadi Controller) for Trajectory Planning of PUMA 560 Robot

2011 ◽  
Vol 403-408 ◽  
pp. 4880-4887
Author(s):  
Sassan Azadi
Keyword(s):  
Steady State ◽  
Trajectory Planning ◽  
Positive Feedback ◽  
Fuzzy Controller ◽  
Research Work ◽  
Adaptive Controller ◽  
The Novel ◽  
Transient Responses ◽  
Simulation Results ◽  
Good Substitute

This research work was devoted to present a novel adaptive controller which uses two negative stable feedbacks with a positive unstable positive feedback. The positive feedback causes the plant to do the break, therefore reaching the desired trajectory with tiny overshoots. However, the two other negative feedback gains controls the plant in two other sides of positive feedback, making the system to be stable, and controlling the steady-state, and transient responses. This controller was performed for PUMA-560 trajectory planning, and a comparison was made with a fuzzy controller. The fuzzy controller parameters were obtained according to the PSO technique. The simulation results shows that the novel adaptive controller, having just three parameters, can perform well, and can be a good substitute for many other controllers for complex systems such as robotic path planning.

scholarly journals Dynamics of transposable elements under the selection model

1999 ◽  
Vol 74 (2) ◽  
pp. 159-164 ◽  
Author(s):  
A. TSITRONE ◽  
S. CHARLES ◽  
C. BIÉMONT
Keyword(s):  
Equilibrium Point ◽  
Dynamic Characteristics ◽  
Time Scale ◽  
Copy Number ◽  
Stable Equilibrium ◽  
Stable Equilibrium Point ◽  
Asymptotically Stable ◽  
Weak Selection ◽  
Strong Selection ◽  
Long Time

We examine an analytical model of selection against the deleterious effects of transposable element (TE) insertions in Drosophila, focusing attention on the asymptotic and dynamic characteristics. With strong selection the only asymptotically stable equilibrium point corresponds to extinction of the TEs. With very weak selection a stable and realistic equilibrium point can be obtained. The dynamics of the system is fast for strong selection and slow, on the human time scale, for weak selection. Hence weak selection acts as a force that contributes to the stabilization of mean TE copy number. The consequence is that under weak selection, and ‘out-of-equilibrium’ situation can be maintained for a long time in populations, with mean TE copy number appearing stabilized.

scholarly journals THE RICH AND THE POOR IN A SIMPLE MODEL OF GROWTH AND DISTRIBUTION

2016 ◽  
Vol 20 (7) ◽  
pp. 1934-1952 ◽  
Author(s):  
Kirill Borissov
Keyword(s):  
Economic Growth ◽  
Steady State ◽  
Simple Model ◽  
Disposable Income ◽  
State Equilibrium ◽  
Positional Concerns ◽  
The Poor ◽  
The Rich ◽  
Intertemporal Equilibrium ◽  
Unique Steady State

We consider a model of economic growth with altruistic agents who care about their consumption and the disposable income of their offspring. The agents' consumption and the offspring's disposable income are subject to positional concerns. We show that, if the measure of consumption-related positional concerns is sufficiently low and/or the measure of offspring-related positional concerns is sufficiently high, then there is a unique steady-state equilibrium, which is characterized by perfect income and wealth equality, and all intertemporal equilibira converge to it. Otherwise, in steady-state equilibria, the population splits into two classes, the rich and the poor; under this scenario, in any intertemporal equilibrium, all capital is eventually owned by the households that were the wealthiest from the outset and all other households become poor.

SET STABILIZATION OF A MODIFIED CHUA'S CIRCUIT

2005 ◽  
Vol 15 (02) ◽  
pp. 567-604 ◽  
Author(s):  
SHIHUA LI ◽  
YU-PING TIAN
Keyword(s):  
Equilibrium Point ◽  
Lyapunov Stability ◽  
Closed Loop ◽  
Invariant Set ◽  
Linear Feedback ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Linear Feedback Controller ◽  
Simulation Results ◽  
First Time

In this paper, we develop a simple linear feedback controller, which employs only one of the states of the system, to stabilize the modified Chua's circuit to an invariant set which consists of its nontrivial equilibria. Moreover, we show for the first time that the closed loop modified Chua's circuit satisfies set stability which can be considered as a generalization of common Lyapunov stability of an equilibrium point. Simulation results are presented to verify our method.

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