scholarly journals Self-regulating genes. Exact steady state solution by using Poisson representation

Open Physics ◽  
2014 ◽  
Vol 12 (9) ◽  
Author(s):  
István Sugár ◽  
István Simon
Keyword(s):  
Steady State ◽  
Cell Biology ◽  
Regulatory Networks ◽  
Steady State Solution ◽  
E Coli ◽  
Feedback Model ◽  
Quantitative Understanding ◽  
Poisson Representation ◽  
And Behavior ◽  
Steady State Solutions

AbstractSystems biology studies the structure and behavior of complex gene regulatory networks. One of its aims is to develop a quantitative understanding of the modular components that constitute such networks. The self-regulating gene is a type of auto regulatory genetic modules which appears in over 40% of known transcription factors in E. coli. In this work, using the technique of Poisson Representation, we are able to provide exact steady state solutions for this feedback model. By using the methods of synthetic biology (P.E.M. Purnick and Weiss, R., Nature Reviews, Molecular Cell Biology, 2009, 10: 410–422) one can build the system itself from modules like this.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

scholarly journals Stability of the positive steady-state solutions of systems of nonlinear Volterra difference equations of population models with diffusion and infinite delay

2000 ◽  
Vol 23 (4) ◽  
pp. 261-270 ◽  
Author(s):  
B. Shi
Keyword(s):  
Steady State ◽  
Difference Equations ◽  
Infinite Delay ◽  
Steady State Solution ◽  
Population Models ◽  
Monotone Iterative ◽  
Positive Steady State ◽  
Infinite Delays ◽  
Steady State Solutions ◽  
Volterra Difference Equations

An open problem given by Kocic and Ladas in 1993 is generalized and considered. A sufficient condition is obtained for each solution to tend to the positive steady-state solution of the systems of nonlinear Volterra difference equations of population models with diffusion and infinite delays by using the method of lower and upper solutions and monotone iterative techniques.

Nonlinear Stability Considerations in Thermoelastic Contact

1999 ◽  
Vol 66 (1) ◽  
pp. 109-116 ◽  
Author(s):  
J. A. Pelesko
Keyword(s):  
Steady State ◽  
Perturbation Technique ◽  
Multiple Scale ◽  
Steady State Solution ◽  
Rigid Wall ◽  
Stable Steady State ◽  
Dynamic Information ◽  
Multiple Steady State ◽  
Singular Perturbation Technique ◽  
Steady State Solutions

The behavior of a one-dimensional thermoelastic rod is modeled and analyzed. The rod is held fixed and at constant temperature at one end, while at the other end it is free to separate from or make contact with a rigid wall. At this free end a pressure and gap-dependent thermal boundary condition is imposed which couples the thermal and elastic problems. Such systems have previously been shown to undergo a bifurcation from a unique linearly stable steady-state solution to multiple steady-state solutions with alternating stability. Here, the system is studied using a two-timing or multiple-scale singular perturbation technique. In this manner, the analysis is extended into the nonlinear regime and dynamic information about the history dependence and temporal evolution of the solution is obtained.

scholarly journals Kinetic models of metabolism that consider alternative steady-state solutions of intracellular fluxes and concentrations

2018 ◽  
Author(s):  
Tuure Hameri ◽  
Georgios Fengos ◽  
Meric Ataman ◽  
Ljubisa Miskovic ◽  
Vassily Hatzimanikatis
Keyword(s):  
Steady State ◽  
Metabolic Engineering ◽  
Kinetic Models ◽  
Large Scale ◽  
Cellular Growth ◽  
Reverse Direction ◽  
Control Analysis ◽  
Omics Data ◽  
E Coli ◽  
Steady State Solutions

AbstractLarge-scale kinetic models are used for designing, predicting, and understanding the metabolic responses of living cells. Kinetic models are particularly attractive for the biosynthesis of target molecules in cells as they are typically better than other types of models at capturing the complex cellular biochemistry. Using simpler stoichiometric models as scaffolds, kinetic models are built around a steady-state flux profile and a metabolite concentration vector that are typically determined via optimization. However, as the underlying optimization problem is underdetermined, even after incorporating available experimental omics data, one cannot uniquely determine the operational configuration in terms of metabolic fluxes and metabolite concentrations. As a result, some reactions can operate in either the forward or reverse direction while still agreeing with the observed physiology. Here, we analyze how the underlying uncertainty in intracellular fluxes and concentrations affects predictions of constructed kinetic models and their design in metabolic engineering and systems biology studies. To this end, we integrated the omics data of optimally grownEscherichia coliinto a stoichiometric model and constructed populations of non-linear large-scale kinetic models of alternative steady-state solutions consistent with the physiology of theE. coliaerobic metabolism. We performed metabolic control analysis (MCA) on these models, highlighting that MCA-based metabolic engineering decisions are strongly affected by the selected steady state and appear to be more sensitive to concentration values rather than flux values. To incorporate this into future studies, we propose a workflow for moving towards more reliable and robust predictions that are consistent with all alternative steady-state solutions. This workflow can be applied to all kinetic models to improve the consistency and accuracy of their predictions. Additionally, we show that, irrespective of the alternative steady-state solution, increased activity of phosphofructokinase and decreased ATP maintenance requirements would improve cellular growth of optimally grownE. coli.

scholarly journals The response to a hot spot in a combustion problem

1981 ◽  
Vol 23 (1) ◽  
pp. 95-102 ◽  
Author(s):  
K. K. Tam ◽  
M. T. Kiang
Keyword(s):  
Steady State ◽  
Simple Model ◽  
Initial Value Problem ◽  
Initial Temperature ◽  
Hot Spot ◽  
Steady State Solution ◽  
Initial Value ◽  
Multiple Steady State ◽  
Steady State Solutions ◽  
Combustion Problem

AbstractA simple model for a problem in combustion theory has multiple steady state solutions when a parameter is in a certain range. This note deals with the initial value problem when the initial temperature takes the form of a hot spot. Estimates on the extent and temperature of the spot for the steady state solution to be super-critical are obtained.

scholarly journals STABILITY ANALYSIS OF A LOTKA–VOLTERRA TYPE PREDATOR–PREY SYSTEM INVOLVING ALLEE EFFECTS

2010 ◽  
Vol 52 (2) ◽  
pp. 139-145 ◽  
Author(s):  
HÜSEYİN MERDAN
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Steady State Solution ◽  
Prey Population ◽  
Stable Steady State ◽  
Allee Effects ◽  
Predator Prey ◽  
Population Dynamics Model ◽  
Steady State Solutions ◽  
Model Subject

AbstractWe present a stability analysis of steady-state solutions of a continuous-time predator–prey population dynamics model subject to Allee effects on the prey population which occur at low population density. Numerical simulations show that the system subject to an Allee effect takes a much longer time to reach its stable steady-state solution. This result differs from that obtained for the discrete-time version of the same model.

Smoluchowski aggregation–fragmentation equations: Fast numerical method to find steady-state solutions

2015 ◽  
Vol 29 (29) ◽  
pp. 1550208 ◽  
Author(s):  
Vladimir Stadnichuk ◽  
Anna Bodrova ◽  
Nikolai Brilliantov
Keyword(s):  
Steady State ◽  
Numerical Method ◽  
Complete Solution ◽  
Numerical Procedure ◽  
Aggregate Size ◽  
Steady State Solution ◽  
New Approach ◽  
Seed System ◽  
Large Systems ◽  
Steady State Solutions

In this paper, we propose an efficient and fast numerical method of finding a stationary solution of large systems of aggregation–fragmentation equations of Smoluchowski type for concentrations of reacting particles. This method is applicable when the stationary concentrations steeply decrease with increasing aggregate size, which is fulfilled for the most important cases. We show that under rather mild restrictions, imposed on the kernel of the Smoluchowski equation, the following numerical procedure may be used: First, a complete solution for a relatively small number of equations (a “seed system”) is generated and then the result is exploited in a fast iterative scheme. In this way the new approach allows to obtain a steady-state solution for rather large systems of equations, by orders of magnitude faster than the standard schemes.

Convergence of a homotopy finite element method for computing steady states of Burgers’ equation

2019 ◽  
Vol 53 (5) ◽  
pp. 1629-1644 ◽  
Author(s):  
Wenrui Hao ◽  
Yong Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Steady State ◽  
Burgers Equation ◽  
Initial Conditions ◽  
Steady State Solution ◽  
State Problem ◽  
Steady State Problem ◽  
Steady State Solutions ◽  
Element Method

In this paper, the convergence of a homotopy method (1.1) for solving the steady state problem of Burgers’ equation is considered. When ν is fixed, we prove that the solution of (1.1) converges to the unique steady state solution as ε → 0, which is independent of the initial conditions. Numerical examples are presented to confirm this conclusion by using the continuous finite element method. In contrast, when ν = ε →, numerically we show that steady state solutions obtained by (1.1) indeed depend on initial conditions.

Nonlinear Peierls-Boltzmann Equation for Phonons: Structure and Stability of Solutions

1977 ◽  
Vol 32 (8) ◽  
pp. 805-812
Author(s):  
Fr. Kaiser
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
Phonon Transport ◽  
Model System ◽  
Steady States ◽  
Different Types ◽  
The Stability ◽  
Steady State Solutions ◽  
Different Order ◽  
Complicated Situation

Abstract Phonon transport in locally disturbed media is considered. The steady state solutions of the Peierls-Boltzmann type equations are studied. In particular, the flux-dependence of local excitations is investigated. It is proven that for a large class of scattering processes only two types of steady states are possible: a hysteresis type and a threshold one. 4 different types of factorization procedures are applied and it is shown that for these cases the steady states remain nearly unchanged. The stability conditions are reformulated in such a way that one can give a geometrical interpretation. The only stable solutions are nodes. The necessary modification of our model system to allow for limit cycles is indicated. Also, a more complicated situation, where the interaction Hamiltonian HI is a superposition of terms of different order, is investigated. The resulting steady state solution is again a hysteresis.

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