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.

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 A model for competition for ribosomes in the cell

2016 ◽  
Vol 13 (116) ◽  
pp. 20151062 ◽  
Author(s):  
Alon Raveh ◽  
Michael Margaliot ◽  
Eduardo D. Sontag ◽  
Tamir Tuller
Keyword(s):  
Steady State ◽  
Large Scale ◽  
Mrna Translation ◽  
Local Effect ◽  
The Other ◽  
Translation Regulation ◽  
Compound System ◽  
Transition Rates ◽  
Translation Rate ◽  
Mrna Molecule

A single mammalian cell includes an order of 10 4 –10 5 mRNA molecules and as many as 10 5 –10 6 ribosomes. Large-scale simultaneous mRNA translation induces correlations between the mRNA molecules, as they all compete for the finite pool of available ribosomes. This has important implications for the cell's functioning and evolution. Developing a better understanding of the intricate correlations between these simultaneous processes, rather than focusing on the translation of a single isolated transcript, should help in gaining a better understanding of mRNA translation regulation and the way elongation rates affect organismal fitness. A model of simultaneous translation is specifically important when dealing with highly expressed genes, as these consume more resources. In addition, such a model can lead to more accurate predictions that are needed in the interconnection of translational modules in synthetic biology. We develop and analyse a general dynamical model for large-scale simultaneous mRNA translation and competition for ribosomes. This is based on combining several ribosome flow models (RFMs) interconnected via a pool of free ribosomes. We use this model to explore the interactions between the various mRNA molecules and ribosomes at steady state. We show that the compound system always converges to a steady state and that it always entrains or phase locks to periodically time-varying transition rates in any of the mRNA molecules. We then study the effect of changing the transition rates in one mRNA molecule on the steady-state translation rates of the other mRNAs that results from the competition for ribosomes. We show that increasing any of the codon translation rates in a specific mRNA molecule yields a local effect, an increase in the translation rate of this mRNA, and also a global effect, the translation rates in the other mRNA molecules all increase or all decrease. These results suggest that the effect of codon decoding rates of endogenous and heterologous mRNAs on protein production is more complicated than previously thought. In addition, we show that increasing the length of an mRNA molecule decreases the production rate of all the mRNAs.

Cyclic Breathing Simulations in Large Scale Models of the Lung Airway From the Oronasal Opening to the Terminal Bronchioles

2012 ◽  
Author(s):  
D. Keith Walters ◽  
Greg W. Burgreen ◽  
Robert L. Hester ◽  
David S. Thompson ◽  
David M. Lavallee ◽  
...  
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Large Scale ◽  
Whole Body ◽  
Patient Specific ◽  
Cfd Simulations ◽  
Reduced Order ◽  
Scale Models ◽  
Steady State Simulation ◽  
Conducting Zone

Computational fluid dynamics (CFD) simulations were performed for unsteady periodic breathing conditions, using large-scale models of the human lung airway. The computational domain included fully coupled representations of the orotracheal region and large conducting zone up to generation four (G4) obtained from patient-specific CT data, and the small conducting zone (to G16) obtained from a stochastically generated airway tree with statistically realistic geometrical characteristics. A reduced-order geometry was used, in which several airway branches in each generation were truncated, and only select flow paths were retained to G16. The inlet and outlet flow boundaries corresponded to the oronasal opening (superior), the inlet/outlet planes in terminal bronchioles (distal), and the unresolved airway boundaries arising from the truncation procedure (intermediate). The cyclic flow was specified according to the predicted ventilation patterns for a healthy adult male at three different activity levels, supplied by the whole-body modeling software HumMod. The CFD simulations were performed using Ansys FLUENT. The mass flow distribution at the distal boundaries was prescribed using a previously documented methodology, in which the percentage of the total flow for each boundary was first determined from a steady-state simulation with an applied flow rate equal to the average during the inhalation phase of the breathing cycle. The distal pressure boundary conditions for the steady-state simulation were set using a stochastic coupling procedure to ensure physiologically realistic flow conditions. The results show that: 1) physiologically realistic flow is obtained in the model, in terms of cyclic mass conservation and approximately uniform pressure distribution in the distal airways; 2) the predicted alveolar pressure is in good agreement with previously documented values; and 3) the use of reduced-order geometry modeling allows accurate and efficient simulation of large-scale breathing lung flow, provided care is taken to use a physiologically realistic geometry and to properly address the unsteady boundary conditions.

The Research of Production Process Statistical Steady-State Based on the Hypothesis Test

2011 ◽  
Vol 314-316 ◽  
pp. 2433-2438
Author(s):  
Wei Zhi Wang
Keyword(s):  
Quality Control ◽  
Steady State ◽  
Production Process ◽  
Quantitative Method ◽  
Large Scale ◽  
Hypothesis Test ◽  
Influence Factors ◽  
Normal Operation ◽  
Scale Production ◽  
Large Scale Production

By only applying a after the event exam in the quality control of the batch production is not enough to meet the needs of modern large-scale production. To a certain extent, modern quality control is a dynamic process of the steady-state judge and adjustment. A simple and reliable steady-state judge rule and method is the premise to guarantee the normal operation. This paper provides a quantitative method to evaluate production process steady-state by analyzing influence factors based on mathematical statistics. The method is both suitable for simple production process and complex production process with sub-processes.

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 Nonlinear Steady-State Optimization of Large-Scale Gas Transmission Networks

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2832
Author(s):  
Andrzej J. Osiadacz ◽  
Małgorzata Kwestarz
Keyword(s):  
Steady State ◽  
Large Scale ◽  
Optimization Problem ◽  
Operating Cost ◽  
Network Efficiency ◽  
Major Objective ◽  
Transmission Networks ◽  
Sqp Method ◽  
Gas Network ◽  
Compressor Power

The major optimization problem of the gas transmission system is to determine how to operate the compressors in a network to deliver a given flow within the pressure bounds while using minimum compressor power (minimum fuel consumption or maximum network efficiency). Minimization of fuel usage is a major objective to control gas transmission costs. This is one of the problems that has received most of the attention from both practitioners and researchers because of its economic impact. The article describes the algorithm of steady-state optimization of a high-pressure gas network of any structure that minimizes the operating cost of compressors. The developed algorithm uses the “sequential quadratic programming (SQP)” method. The tests carried out on the real network segment confirmed the correctness of the developed algorithm and, at the same time, proved its computational efficiency. Computational results obtained with the SQP method demonstrate the viability of this approach.

Coriolis force influence on the AKA effect

2021 ◽  
Author(s):  
Peter Rutkevich ◽  
Georgy Golitsyn ◽  
Anatoly Tur
Keyword(s):  
Steady State ◽  
Stokes Equation ◽  
Nonlinear Equations ◽  
Coriolis Force ◽  
Large Scale ◽  
Fluid Velocity ◽  
Navier Stokes ◽  
Basic Solution ◽  
Navier Stokes Equation ◽  
Alpha Effect

<p>Large-scale instability in incompressible fluid driven by the so called Anisotropic Kinetic Alpha (AKA) effect satisfying the incompressible Navier-Stokes equation with Coriolis force is considered. The external force is periodic; this allows applying an unusual for turbulence calculations mathematical method developed by Frisch et al [1]. The method provides the orders for nonlinear equations and obtaining large scale equations from the corresponding secular relations that appear at different orders of expansions. This method allows obtaining not only corrections to the basic solutions of the linear problem but also provides the large-scale solution of the nonlinear equations with the amplitude exceeding that of the basic solution. The fluid velocity is obtained by numerical integration of the large-scale equations. The solution without the Coriolis force leads to constant velocities at the steady-state, which agrees with the full solution of the Navier-Stokes equation reported previously. The time-invariant solution contains three families of solutions, however, only one of these families contains stable solutions. The final values of the steady-state fluid velocity are determined by the initial conditions. After account of the Coriolis force the solutions become periodic in time and the family of solutions collapses to a unique solution. On the other hand, even with the Coriolis force the fluid motion remains two-dimensional in space and depends on a single spatial variable. The latter fact limits the scope of the AKA method to applications with pronounced 2D nature. In application to 3D models the method must be used with caution.</p><p>[1] U. Frisch, Z.S. She and P. L. Sulem, “Large-Scale Flow Driven by the Anisotropic Kinetic Alpha Effect,” Physica D, Vol. 28, No. 3, 1987, pp. 382-392.</p>

Investigating Fast- and Slow-settling Phosphorus Fractions in Lakes using Steady-state Modeling

2021 ◽  
Author(s):  
Hamed Khorasani ◽  
Zhenduo Zhu
Keyword(s):  
Steady State ◽  
Mass Balance ◽  
Large Scale ◽  
Hydraulic Residence Time ◽  
Simple Method ◽  
Retention Models ◽  
Mass Balance Models ◽  
Limiting Nutrient ◽  
Fast Settling ◽  
P Retention

<p>Phosphorus (P) is the key and limiting nutrient in the eutrophication of freshwater resources. Modeling P retention in lakes using steady-state mass balance models (i.e. Vollenweider-type models) provides insights into the lake P management and a simple method for large-scale assessments of P in lakes. One of the basic problems in the mass balance modeling of P in lakes is the removal of P from the lake water column by settling. A fraction of the incoming P into the lake from the watershed is associated with fast-settling particles (e.g. sediment particles) that result in the removal of that fraction of P quickly at the lake entrance. However, existing models considering a constant fraction of fast-settling TP for all lakes are shown to result in overestimation of the retention of P in lakes with short hydraulic residence time. In this study, we combine a hypothesis of the fast- and slow-settling P fractions into the steady-state mass balance models of P retention in lakes. We use a large database of lakes to calibrate the model and evaluate the hypothesis. The results of this work can be used for the improvement of the prediction power of P retention models in lakes and help to better understand the processes of P cycling in lakes.</p>

Codon replacement in the PGK1 gene of Saccharomyces cerevisiae: experimental approach to study the role of biased codon usage in gene expression

1987 ◽  
Vol 7 (8) ◽  
pp. 2914-2924
Author(s):  
A Hoekema ◽  
R A Kastelein ◽  
M Vasser ◽  
H A de Boer
Keyword(s):  
Gene Expression ◽  
Saccharomyces Cerevisiae ◽  
Steady State ◽  
Codon Usage ◽  
Experimental Approach ◽  
Mrna Translation ◽  
Yeast Cells ◽  
Expression Level ◽  
Start Codon ◽  
Mrna Levels

The coding sequences of genes in the yeast Saccharomyces cerevisiae show a preference for 25 of the 61 possible coding triplets. The degree of this biased codon usage in each gene is positively correlated to its expression level. Highly expressed genes use these 25 major codons almost exclusively. As an experimental approach to studying biased codon usage and its possible role in modulating gene expression, systematic codon replacements were carried out in the highly expressed PGK1 gene. The expression of phosphoglycerate kinase (PGK) was studied both on a high-copy-number plasmid and as a single copy gene integrated into the chromosome. Replacing an increasing number (up to 39% of all codons) of major codons with synonymous minor ones at the 5' end of the coding sequence caused a dramatic decline of the expression level. The PGK protein levels dropped 10-fold. The steady-state mRNA levels also declined, but to a lesser extent (threefold). Our data indicate that this reduction in mRNA levels was due to destabilization caused by impaired translation elongation at the minor codons. By preventing translation of the PGK mRNAs by the introduction of a stop codon 3' and adjacent to the start codon, the steady-state mRNA levels decreased dramatically. We conclude that efficient mRNA translation is required for maintaining mRNA stability in S. cerevisiae. These findings have important implications for the study of the expression of heterologous genes in yeast cells.

Sign in / Sign up

Export Citation Format

Share Document