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Bistable systems

Andy Jenkins, Matthew Macauley
The lactose operon in Escherichia coli was the first known gene regulatory network, and it is frequently used as a prototype for new modeling paradigms. Historically, many of these modeling frameworks use differential equations. More recently, Stigler and Veliz-Cuba proposed a Boolean model that captures the bistability of the system and all of the biological steady states. In this paper, we model the well-known arabinose operon in E. coli with a Boolean network. This has several complex features not found in the lac operon, such as a protein that is both an activator and repressor, a DNA looping mechanism for gene repression, and the lack of inducer exclusion by glucose...
June 21, 2017: Bulletin of Mathematical Biology
Erik Bernitt, Hans-Günther Döbereiner, Nir S Gov, Arik Yochelis
During macropinocytosis, cells remodel their morphologies for the uptake of extracellular matter. This endocytotic mechanism relies on the collapse and closure of precursory structures, which are propagating actin-based, ring-shaped vertical undulations at the dorsal (top) cell membrane, a.k.a. circular dorsal ruffles (CDRs). As such, CDRs are essential to a range of vital and pathogenic processes alike. Here we show, based on both experimental data and theoretical analysis, that CDRs are propagating fronts of actin polymerization in a bistable system...
June 19, 2017: Nature Communications
Francesco Marino, Giovanni Giacomelli, Stephane Barland
We investigate the formation of localized domains through front pinning in a periodically forced, bistable semiconductor laser with long-delayed optoelectronic feedback. At difference with 1D spatially extended systems, the transition from the pinning to the propagation regime occurs via two separated bifurcations, each corresponding to the unpinning of one of the fronts surrounding the localized domain. The bifurcation splitting is systematically explored, unveiling the crucial role played by the forcing frequency...
May 2017: Physical Review. E
Gabriel A Zarza, Sergio E Mangioni, Javier Fernandez Acevedo, Roberto R Deza
We have devised an experiment whereby a bistable system is confined away from its deterministic attractors by means of multiplicative noise. Together with previous numerical results, our experimental results validate the hypothesis that the higher the slope of the noise's multiplicative factor, the more it shifts the stationary states.
May 2017: Physical Review. E
Yun Kang, Sourav Kumar Sasmal, Komi Messan
Foraging movements of predator play an important role in population dynamics of prey-predator systems, which have been considered as mechanisms that contribute to spatial self-organization of prey and predator. In nature, there are many examples of prey-predator interactions where prey is immobile while predator disperses between patches non-randomly through different factors such as stimuli following the encounter of a prey. In this work, we formulate a Rosenzweig-MacArthur prey-predator two patch model with mobility only in predator and the assumption that predators move towards patches with more concentrated prey-predator interactions...
August 1, 2017: Mathematical Biosciences and Engineering: MBE
Joung-Hun Lee, Marko Jusup, Yoh Iwasa
Maintaining human cooperation in the context of common-pool resource management is extremely important because otherwise we risk overuse and corruption. To analyse the interplay between economic and ecological factors leading to corruption, we couple the resource dynamics and the evolutionary dynamics of strategic decision making into a powerful analytical framework. The traits of this framework are: (i) an arbitrary number of harvesters share the responsibility to sustainably exploit a specific part of an ecosystem, (ii) harvesters face three strategic choices for exploiting the resource, (iii) a delegated enforcement system is available if called upon, (iv) enforcers are either honest or corrupt, and (v) the resource abundance reflects the choice of harvesting strategies...
June 7, 2017: Journal of Theoretical Biology
Mitchell Eithun, Anne Shiu
Phosphorylation, the enzyme-mediated addition of a phosphate group to a molecule, is a ubiquitous chemical mechanism in biology. Multisite phosphorylation, the addition of phosphate groups to multiple sites of a single molecule, may be distributive or processive. Distributive systems, which require an enzyme and substrate to bind several times in order to add multiple phosphate groups, can be bistable. Processive systems, in contrast, require only one binding to add all phosphate groups, and were recently shown to be globally stable...
June 6, 2017: Mathematical Biosciences
Alexander T Topham, Rachel E Taylor, Dawei Yan, Eiji Nambara, Iain G Johnston, George W Bassel
Plants perceive and integrate information from the environment to time critical transitions in their life cycle. Some mechanisms underlying this quantitative signal processing have been described, whereas others await discovery. Seeds have evolved a mechanism to integrate environmental information by regulating the abundance of the antagonistically acting hormones abscisic acid (ABA) and gibberellin (GA). Here, we show that hormone metabolic interactions and their feedbacks are sufficient to create a bistable developmental fate switch in Arabidopsis seeds...
June 20, 2017: Proceedings of the National Academy of Sciences of the United States of America
Albert S Y Wong, Aleksandr A Pogodaev, Ilia N Vialshin, Britta Helwig, Wilhelm T S Huck
Living systems rely on complex networks of chemical reactions to control the concentrations of molecules in space and time. Despite the enormous complexity in biological networks, it is possible to identify network motifs that lead to functional outputs such as bistability or oscillations. One of the greatest challenges in chemistry is the creation of such functionality from chemical reactions. A key limitation is our lack of understanding of how molecular structure impacts on the dynamics of chemical reaction networks, preventing the design of networks that are robust (i...
June 21, 2017: Journal of the American Chemical Society
Bo Zheng, Moxun Tang, Jianshe Yu, Junxiong Qiu
Mosquitoes are primary vectors of life-threatening diseases such as dengue, malaria, and Zika. A new control method involves releasing mosquitoes carrying bacterium Wolbachia into the natural areas to infect wild mosquitoes and block disease transmission. In this work, we use differential equations to describe Wolbachia spreading dynamics, focusing on the poorly understood effect of imperfect maternal transmission. We establish two useful identities and employ them to prove that the system exhibits monomorphic, bistable, and polymorphic dynamics, and give sufficient and necessary conditions for each case...
June 1, 2017: Journal of Mathematical Biology
David Rudrauf, Daniel Bennequin, Isabela Granic, Gregory Landini, Karl Friston, Kenneth Williford
We introduce a mathematical model of embodied consciousness, the Projective Consciousness Model (PCM), which is based on the hypothesis that the spatial field of consciousness (FoC) is structured by a projective geometry and under the control of a process of active inference. The FoC in the PCM combines multisensory evidence with prior beliefs in memory, and frames them by selecting points of view and perspectives according to preferences. The choice of projective frames governs how expectations are transformed by consciousness...
May 26, 2017: Journal of Theoretical Biology
Kiran Yadav, Neeraj Kumar Kamal, Manish Dev Shrimali
We present a method for attractor selection in multistable dynamical systems. It involves a feedback term that is active only when the dynamics of the system is in a particular fraction of state space of the attractor. We implement this method first on a simplest symmetric chaotic flow and then on a bistable neuronal system. We find that adding this space-dependent feedback term to the dynamical equations of these systems will drive the dynamics to the desired attractor by annihilating the other. We further demonstrate that the attractor selection due to this feedback term can be used in construction of logic gates, which is one of the practical applications of the proposed method...
April 2017: Physical Review. E
R K Singh
The Kramers problem for a dimer in a bistable piecewise linear potential is studied in the presence of correlated noise processes. The effect of such a correlation is to redistribute the thermal power between the dynamical degrees of freedom, and this leads to significant deviations in the dynamics of the system from the case of independent noise processes. The distribution of first passage times from one minima to the basin of attraction of the other minima is found to have exponentially decaying tails with the parameter dependent on the amount of correlation and the coupling between the particles...
April 2017: Physical Review. E
Jan O Haerter, Albert Díaz-Guilera, M Ángeles Serrano
The combination of bistability and noise is ubiquitous in complex systems, from biology to social interactions, and has important implications for their functioning and resilience. Here we use a simple three-state dynamical process, in which nodes go from one pole to another through an intermediate state, to show that noise can induce polarization switching in bistable systems if dynamical correlations are significant. In large, fully connected networks, where dynamical correlations can be neglected, increasing noise yields a collapse of bistability to an unpolarized configuration where the three possible states of the nodes are equally likely...
April 2017: Physical Review. E
Dominique Zander, Daniel Samaga, Ronny Straube, Katja Bettenbrock
The Escherichia coli lac operon is regulated by a positive feedback loop whose potential to generate an all-or-none response in single cells has been a paradigm for bistable gene expression. However, so far bistable lac induction has only been observed using gratuitous inducers, raising the question about the biological relevance of bistable lac induction in the natural setting with lactose as the inducer. In fact, the existing experimental evidence points to a graded rather than an all-or-none response in the natural lactose uptake system...
May 9, 2017: Biophysical Journal
Maria D Manrique-Juarez, Fabrice Mathieu, Victoria Shalabaeva, Jean Cacheux, Sylvain Rat, Liviu Nicu, Thierry Leïchlé, Lionel Salmon, Gábor Molnár, Azzedine Bousseksou
We report on a bistable MEMS device actuated by spin-crossover molecules. The device consists of a freestanding silicon microcantilever with an integrated piezoresistive detection system, which was coated with a 140 nm thick film of the [Fe(HB(tz)3 )2 ] (tz=1,2,4-triazol-1-yl) molecular spin-crossover complex. Switching from the low-spin to the high-spin state of the ferrous ions at 338 K led to a reversible upward bending of the cantilever in agreement with the change in the lattice parameters of the complex...
May 10, 2017: Angewandte Chemie
F Ricci, R A Rica, M Spasenović, J Gieseler, L Rondin, L Novotny, R Quidant
Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance...
May 9, 2017: Nature Communications
Johannes Falk, Marc Mendler, Barbara Drossel
We investigate the influence of intrinsic noise on stable states of a one-dimensional dynamical system that shows in its deterministic version a saddle-node bifurcation between monostable and bistable behaviour. The system is a modified version of the Schlögl model, which is a chemical reaction system with only one type of molecule. The strength of the intrinsic noise is varied without changing the deterministic description by introducing bursts in the autocatalytic production step. We study the transitions between monostable and bistable behavior in this system by evaluating the number of maxima of the stationary probability distribution...
2017: PloS One
Zhaoyang Zhang, Danmeng Ma, Jun Liu, Yanyong Sun, Lin Cheng, Ghulam Abbas Khan, Yanpeng Zhang
By making use of the changes in optical properties such as absorption and dispersion around the resonance generated via electromagnetically induced transparency (EIT), we theoretically and experimentally investigate a "∞"-shape optical bistability (OB) versus frequency on the probe transmission with a Λ-shape EIT window in a rubidium atomic ensemble confined in a three-mirror optical ring cavity. Compared to the traditional OB reflected by a hysteresis loop versus power, such newly demonstrated optical bistable behavior (represented by a "∞"-shape non-overlapping region) by scanning probe and cavity detuning can experience dual bistabilities and be more sensitive to the change of experimental parameters...
April 17, 2017: Optics Express
Osama R Bilal, André Foehr, Chiara Daraio
The realization of acoustic devices analogous to electronic systems, like diodes, transistors, and logic elements, suggests the potential use of elastic vibrations (i.e., phonons) in information processing, for example, in advanced computational systems, smart actuators, and programmable materials. Previous experimental realizations of acoustic diodes and mechanical switches have used nonlinearities to break transmission symmetry. However, existing solutions require operation at different frequencies or involve signal conversion in the electronic or optical domains...
May 2, 2017: Proceedings of the National Academy of Sciences of the United States of America
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