Explicit Expression for the Steady-State Translation Rate in the Infinite-Dimensional Homogeneous Ribosome Flow Model

2013 ◽  
Vol 10 (5) ◽  
pp. 1322-1328 ◽  
Author(s):  
Yoram Zarai ◽  
Michael Margaliot ◽  
Tamir Tuller
Keyword(s):  
Steady State ◽  
Explicit Expression ◽  
Flow Model ◽  
Translation Rate ◽  
Infinite Dimensional

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 Observed Non–Steady State Cooling and the Moderate Cluster Cooling Flow Model

2003 ◽  
Vol 589 (2) ◽  
pp. 770-773 ◽  
Author(s):  
Noam Soker ◽  
Laurence P. David
Keyword(s):  
Steady State ◽  
Flow Model ◽  
Cooling Flow

scholarly journals Numerical modelling of the historic front variation and the future behaviour of the Pasterze glacier, Austria

1997 ◽  
Vol 24 ◽  
pp. 234-241 ◽  
Author(s):  
Z. Zuo ◽  
J. Oerlemans
Keyword(s):  
Steady State ◽  
Flow Model ◽  
Calibration Method ◽  
Climate Scenarios ◽  
Ice Dynamics ◽  
Ice Flow ◽  
Steady State Condition ◽  
Ice Volume ◽  
Future Warming ◽  
Dynamic Calibration Method

An ice-flow model is used to simulate the front variations of the Pasterze glacier, Austria. The model deals explicitly with the ice flux from sub-streams and tributaries to the main ice stream. The dynamic calibration method adopted successfully calibrates the ice-flow model under a non-steady-state condition. Despite the complexity of the glacier geometry, the ice dynamics of the Pasterze are adequately simulated.Results of the sensitivity experiments suggest that the Pasterze glacier has been in a non-steady state most of the time and has a response time of 34–50 years.Projections of the behaviour of the Pasterze in the next 100 years are made under various climate scenarios. Results suggest that the Pasterze will undergo a substantial retreat if there is future warming. The glacier is likely to retreat 2–5 km by the year 2100. The ice volume could be reduced by 24–63% by the end of the 21st century.

Prediction of mobile water in a tight gas sandstone reservoir using NMR and fractional flow model

2014 ◽  
Vol 54 (2) ◽  
pp. 1
Author(s):  
Maria Anantawati ◽  
Suryakant Bulgauda
Keyword(s):  
Steady State ◽  
Relative Permeability ◽  
Flow Model ◽  
Bound Water ◽  
Free Water ◽  
Development Project ◽  
Asia Pacific ◽  
Fractional Flow ◽  
Reservoir Properties ◽  
Mobile Water

One of the objectives of petrophysical interpretation is the estimation of the respective volumes of formation fluids. With traditional interpretation using conventional openhole logs it is only possible to determine the total amount of water. The challenge is to determine the volumes of bound water (clay-bound and capillary-bound) and free water. At the moment, NMR is the only measurement that can help distinguish the volumes of each water component (clay-bound, capillary-bound and mobile), using cut-offs on T2 (transverse relaxation time). However NMR interpretation also requires information on reservoir properties. Alternatively, steady-state relative permeability and fractional flow of water can be used to determine the potential of mobile water. The study area, located in the Cooper Basin, South Australia, is the target of a planned gas development project in the Patchawarra formation. It comprises multiple stacked fluvial sands which are heterogeneous, tight and of low deliverability. The sands are completed with multi-stage pin-point fracturing as a key enabling technology for the area. A comprehensive set of data, including conventional logs, cores and NMR logs, were acquired. Routine and special core analysis were performed, including NMR, electrical properties, centrifuge capillary pressure, high-pressure mercury injection, and full curve steady state relative permeability. A fractional flow model was built based on core and NMR data to determine potential mobile water and the results compared with production logs. This paper (SPE 165766) was prepared for presentation at the SPE Asia Pacific Oil & Gas Conference and Exhibition, held in Jakarta, Indonesia, from 22–24 October 2013.

Generalized Inverse of Upper Triangular Infinite Dimensional Hamiltonian Operators

2013 ◽  
Vol 20 (03) ◽  
pp. 395-402
Author(s):  
Junjie Huang ◽  
Xiang Guo ◽  
Yonggang Huang ◽  
Alatancang
Keyword(s):  
Explicit Expression ◽  
Generalized Inverse ◽  
Hamiltonian Operator ◽  
Operator Matrix ◽  
Infinite Dimensional ◽  
Symplectic Spaces ◽  
Hamiltonian Operators

In this paper, we deal with the generalized inverse of upper triangular infinite dimensional Hamiltonian operators. Based on the structure operator matrix J in infinite dimensional symplectic spaces, it is shown that the generalized inverse of an infinite dimensional Hamiltonian operator is also Hamiltonian. Further, using the decomposition of spaces, an upper triangular Hamiltonian operator can be written as a new operator matrix of order 3, and then an explicit expression of the generalized inverse is given.

Sign in / Sign up

Export Citation Format

Share Document