Emergence Of Bistability Research Articles

Mathematical modelling of SigE regulatory network reveals new insights into bistability of mycobacterial stress response

BackgroundThe ability to rapidly adapt to adverse environmental conditions represents the key of success of many pathogens and, in particular, of Mycobacterium tuberculosis. Upon exposition to heat shock, antibiotics or other sources of stress, appropriate responses in terms of genes transcription and proteins activity are activated leading part of a genetically identical bacterial population to express a different phenotype, namely to develop persistence. When the stress response network is mathematically described by an ordinary differential equations model, development of persistence in the bacterial population is associated with bistability of the model, since different emerging phenotypes are represented by different stable steady states.ResultsIn this work, we develop a mathematical model of SigE stress response network that incorporates interactions not considered in mathematical models currently available in the literature. We provide, through involved analytical computations, accurate approximations of the system’s nullclines, and exploit the obtained expressions to determine, in a reliable though computationally efficient way, the number of equilibrium points of the system.ConclusionsTheoretical analysis and perturbation experiments point out the crucial role played by the degradation pathway involving RseA, the anti-sigma factor of SigE, for coexistence of two stable equilibria and the emergence of bistability. Our results also indicate that a fine control on RseA concentration is a necessary requirement in order for the system to exhibit bistability.

Modelling co-translational dimerization for programmable nonlinearity in synthetic biology.

Nonlinearity plays a fundamental role in the performance of both natural and synthetic biological networks. Key functional motifs in living microbial systems, such as the emergence of bistability or oscillations, rely on nonlinear molecular dynamics. Despite its core importance, the rational design of nonlinearity remains an unmet challenge. This is largely due to a lack of mathematical modelling that accounts for the mechanistic basis of nonlinearity. We introduce a model for gene regulatory circuits that explicitly simulates protein dimerization-a well-known source of nonlinear dynamics. Specifically, our approach focuses on modelling co-translational dimerization: the formation of protein dimers during-and not after-translation. This is in contrast to the prevailing assumption that dimer generation is only viable between freely diffusing monomers (i.e. post-translational dimerization). We provide a method for fine-tuning nonlinearity on demand by balancing the impact of co- versus post-translational dimerization. Furthermore, we suggest design rules, such as protein length or physical separation between genes, that may be used to adjust dimerization dynamics in vivo. The design, build and test of genetic circuits with on-demand nonlinear dynamics will greatly improve the programmability of synthetic biological systems.

Bifurcation Analysis for a Food Chain Model with Nonmonotonic Nutrition Conversion Rate of Predator to Top Predator

In this paper, a prey–predator-top predator food chain model with nonmonotonic functional response in the predators is studied. With an emphasis on the nutrition conversion rate of predator to top predator, one can get two important thresholds: the top predator extinction threshold and the coexistence threshold. The top predator will die out if the nutrition conversion rate of predator to top predator is less than the top predator extinction threshold; the prey, predator and top predator will coexist if the rate is larger than the coexistence threshold. While between the two thresholds is a bistable interval. When the nutrition conversion rate of predator to top predator is in the bistable interval, the system will see the emergence of bistability. The bifurcation analysis of the system depending on parameters indicates that it exhibits saddle-node bifurcation and Hopf bifurcation phenomena.

Correction to "Local Concentration Deviations in a Glycolytic Model of Nonequilibrium Thermodynamics: Emergence of Bistability from Thermodynamic Theories due to Violation of Lyapunov Stability Theory".

ADVERTISEMENT RETURN TO ISSUEPREVAddition/CorrectionNEXTORIGINAL ARTICLEThis notice is a correctionCorrection to “Local Concentration Deviations in a Glycolytic Model of Nonequilibrium Thermodynamics: Emergence of Bistability from Thermodynamic Theories due to Violation of Lyapunov Stability Theory”Arun K. Dutt*Arun K. DuttMore by Arun K. Dutthttp://orcid.org/0000-0001-7557-2351Cite this: J. Phys. Chem. B 2019, 123, 4, 954Publication Date (Web):January 17, 2019Publication History Published online17 January 2019Published inissue 31 January 2019https://doi.org/10.1021/acs.jpcb.8b12497Copyright © 2019 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views421Altmetric-Citations-LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (207 KB) Get e-Alerts Get e-Alerts

Local Concentration Deviations in a Glycolytic Model of Nonequilibrium Thermodynamics: Emergence of Bistability from Thermodynamic Theories due to Violation of the Lyapunov Stability Theory.

The thermodynamics of nonequilibrium states in the reversible Sel'kov model, a mathematical model of glycolytic oscillations, is reported in terms of the Lyapunov properties of the second differential of its local equilibrium entropy ( S) and that of its entropy production (e.p.) function (σ) per unit volume. This theory interprets the appropriate limit of validity of the generalized Le Chatelier-Braun (LCB) principle for stable nonequilibrium and equilibrium steady states obeying the Lyapunov stability postulate and its implications in terms of the local concentration deviations of the reacting intermediate species S(ATP) and P(ADP) in response to external excitations. The local concentration deviations of the reacting intermediates are reported to be asymmetric for stable steady states in this model system obeying the Lyapunov stability postulate out of equilibrium (both linear and nonlinear domains), whereas symmetrical local concentration deviations prevail at the state of thermodynamic equilibrium, which however never exists in a living cell. In the unstable steady states in this model reaction, as for example, along a limit cycle trajectory not obeying any Lyapunov stability postulate, the two bistable e.p. branches characterized by two forms of deviation product function δ sδ p may be identified separated by a large δ p > 0 value ( p being scaled concentration of the species P) for dσ > 0 and dσ < 0, respectively, which may be generalized as LCB principle for bistability/hysteresis in this model reaction. The method outlined here may be applied safely to other well-known two-variable models of chemistry/biology. For an appropriate three-variable model with one variable in a pseudo-steady-state approximation, this method may be applicable, albeit with some constraints.

Bistability in a nonequilibrium quantum system with electron-phonon interactions

The existence of more than one steady state in a many-body quantum system driven out of equilibrium has been a matter of debate, both in the context of simple impurity models and in the case of inelastic tunneling channels. In this paper, we combine a reduced density matrix formalism with the multilayer multiconfiguration time-dependent Hartree method to address this problem. This allows us to obtain a converged numerical solution of the nonequilibrium dynamics. Considering a generic model for quantum transport through a quantum dot with electron-phonon interaction, we prove that a unique steady state exists regardless of the initial electronic preparation of the quantum dot, consistent with the converged numerical results. However, a bistability can be observed for different initial phonon preparations. The effects of the phonon frequency and strength of the electron-phonon couplings on the nonequilibrium dynamics and on the emergence of bistability is discussed.

Transient dynamics of a molecular quantum dot with a vibrational degree of freedom

We investigate the transient effects occurring in a molecular quantum dot described by an Anderson-Holstein Hamiltonian which is instantly coupled to two fermionic leads biased by a finite voltage. In the limit of weak electron-phonon interaction, we use perturbation theory to determine the time-dependence of the dot population and the average current. The limit of strong coupling is accessed by means of a self-consistent time-dependent mean-field approximation. These comple- mentary approaches allow us to investigate the dynamics of the inelastic effects occurring when the applied bias voltage exceeds the phonon frequency and the emergence of bistability.

Bistability in self-mode-locked lasers with radially varying gain

Theoretically discussed is the emergence of bistability in self-mode-locking without apertures by using a Gaussian beam approximation in which both spatial and temporal effects are simultaneously taken into account. It is shown that cavity configuration where mode-locking operation is favoured lead to a bistable behavior in the pulse characteristics and the transition from the lower-to the upper-branch favours the suppression of cw oscillations.