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Bistable reaction-diffusion systems can have robust zero-velocity fronts.

We show that for a class of bistable reaction-diffusion systems, zero-velocity fronts can be robust in the singular limit where one of the diffusion coefficients vanishes. In this case, stationary fronts can persist along variations of the system parameters. This property contrasts with the standard result that the front velocity v(&mgr;), expressed as a function of a control parameter &mgr;, is zero only at some isolated values &mgr;(0), and thus not giving robustness to zero-velocity fronts when &mgr; is varied. (c) 2000 American Institute of Physics.

Journal Article↗

Dynamics of one- and two-dimensional kinks in bistable reaction-diffusion equations with quasidiscrete sources of reaction.

We study the evolution of fronts in a bistable reaction-diffusion system when the nonlinear reaction term is spatially inhomogeneous. This equation has been used to model wave propagation in various biological systems. Extending previous works on homogeneous reaction terms, we derive asymptotically an equation governing the front motion, which is strongly nonlinear and, for the two-dimensional case, generalizes the classical mean curvature flow equation. We study the motion of one- and two-dimensional fronts, finding that the inhomogeneity acts as a "potential function" for the motion of the front; i.e., there is wave propagation failure and the steady state solution depends on the structure of the function describing the inhomogeneity. (c) 2001 American Institute of Physics.

Journal Article↗

Traveling fronts in an array of coupled symmetric bistable units.

Traveling fronts are shown to occur in an array of nearest-neighbor coupled symmetric bistable units. When the local dynamics is given by the Lorenz equations we observe the route: standing-->oscillating-->traveling front, as the coupling is increased. A key step in this route is a gluing bifurcation of two cycles in cylindrical coordinates. When this is mediated by a saddle with real leading eigenvalues, the asymptotic behavior of the front velocity is found straightforwardly. If the saddle is focus-type instead, the front's dynamics may become quite complex, displaying several oscillating and propagating regimes and including (Shil'nikov-type) chaotic front propagation. These results stand as well for other nearest-neighbor coupling schemes and local dynamics.

Journal Article↗

On the global orbits in a bistable CML.

In an infinite one-dimensional coupled map lattice (CML) for which the local map is piecewise affine and bistable, we study the global orbits using a spatiotemporal coding introduced in a previous work. The set of all the fixed points is first considered. It is shown that, under some restrictions on the parameters, the latter is a Cantor set, and we introduce an order to study the fixed points' existence. This also involves the proof of the coexistence of propagating fronts and stationary structures. In the second part, we analyze the global orbits which occur for strong coupling using the splitting of the dynamics into two independent (sub-)lattices, and emphasize the description of various traveling structures. (c) 1997 American Institute of Physics.

Journal Article↗

Bistability in a complementary metal oxide semiconductor inverter circuit.

Radiofrequency signals can disrupt the operation of low frequency circuits. A digital inverter circuit would seem to be immune to such disruption, because its output state usually jumps abruptly between 0 and 5 V. Nevertheless, when driven with a high frequency signal, the inverter can have two coexisting stable states (which are not at 0 and 5 V). Slow switching between these states (by changing the rf signal) will produce a low frequency signal. I demonstrate the bistability in a circuit experiment and in a simple model of the circuit.

Artifacts↗

Chaos control and synchronization in Bragg acousto-optic bistable systems driven by a separate chaotic system.

In this paper we propose a new scheme to achieve chaos control and synchronization in Bragg acousto-optic bistable systems. In the scheme, we use the output of one system to drive two identical chaotic systems. Using the maximal conditional Lyapunov exponent (MCLE) as the criterion, we analyze the conditions for realizing chaos synchronization. Numerical calculation shows that the two identical systems in chaos with negative MCLEs and driven by a chaotic system can go into chaotic synchronization whether or not they were in chaos initially. The two systems can go into different periodic states from chaos following an inverse period-doubling bifurcation route as well when driven by a periodic system.

Acoustics↗

Theoretical analysis of internal fluctuations and bistability in CO oxidation on nanoscale surfaces.

The bistable CO oxidation on a nanoscale surface is characterized by a limited number of reacting molecules on the catalytic area. Internal fluctuations due to finite-size effects are studied by the master equation with a Langmuir-Hinshelwood mechanism for CO oxidation. Analytical solutions can be found in a reduced one-component model after the adiabatic elimination of one variable which in our case is the oxygen coverage. It is shown that near the critical point, with decreasing surface area, one cannot distinguish between two macroscopically stable stationary states. This is a consequence of the large fluctuations in the coverage which occur on a fast time scale. Under these conditions, the transition times between the macroscopic states also are no longer separated from the short-time scale of the coverage fluctuations as is the case for large surface areas and far away from the critical point. The corresponding stationary solutions of the probability distribution and the mean first passage times calculated in the reduced model are supported by numerics of the full two-component model.

Journal Article↗

Structural relaxation in complex liquids: non-Markovian dynamics in a bistable potential.

The time correlation function C(t) identical with of the distance fluctuations of a particle moving in a bistable potential under the action of fractional Gaussian noise (fGn) is calculated from a Smoluchowski-type equation derived from a generalized Langevin equation (GLE). The time derivative of this function, dC(t)dt, is compared with data from optical Kerr effect measurements of liquid crystal dynamics in the vicinity of the isotropic-to-nematic transition, which are related to the time derivative of an orientational correlation function. A number of characteristic features of the experimental decay curves, including short and intermediate time power law behavior and long time exponential relaxation, are qualitatively reproduced by the analytical calculations, even though the latter do not explicitly treat orientational degrees of freedom. The GLE formalism with fGn was, in fact, originally proposed as a model of protein conformational fluctuations, so the present results suggest that it may also serve more generally as a model of structural relaxation in complex condensed phase media.

Journal Article↗

Bistable phase control via rocking in a nonlinear electronic oscillator.

We experimentally demonstrate the effective rocking [de Valcarcel and Staliunas, Phys. Rev. E 67, 026604 (2003)] of a nonlinear electronic circuit operating in a periodic regime. Namely, we show that by driving a Chua circuit with a periodic signal, whose phase alternates (also periodically) in time, we lock the oscillation frequency of the circuit to that of the driving signal, and its phase to one of two possible values shifted by pi, and lying between the alternating phases of the input signal. In this way, we show that a rocked nonlinear oscillator displays phase bistability. We interpret the experimental results via a theoretical analysis of rocking on a simple oscillator model, based on a normal form description (complex Landau equation) of the rocked Hopf bifurcation.

Journal Article↗

The relationship between visual persistence and event perception in bistable motion display.

Observers viewed two alternating frames, each consisting of three rectangular bars displaced laterally by one cycle in one frame with respect to the other. At long interframe intervals (IFIs) observers perceived a group of three bars moving as a whole (group motion), and at short IFIs the overlapping elements in the two frames appeared stationary, while the third element appeared to move from one end of the display to the other (element motion). The upper temporal limit for perceiving element motion was reduced when bars with blurred edges were used and when either frame duration or bar size was increased. However, when inner and outer elements had different sizes, the element motion percept was dominant up to 230 ms IFI. These findings may be interpreted in terms of spatial tuning of motion mechanisms involved in the perception of bistable apparent motion.

Attention↗

Effect of depth information on a bistable spiral-motion aftereffect.

Two types of spiral-motion aftereffects were elicited by a single pattern: subjects reported seeing the pattern expand in the two-dimensional viewing plane or bulge toward them in three-dimensional space. Under binocular-viewing conditions reports of two-dimensional translations predominated. But when depth information was restricted under monocular-viewing conditions, reports of three-dimensional translations were more frequent. It appears that the bistability of these aftereffects can be influenced by the degree of depth information available about a stimulus pattern.

Attention↗

Bistability and biasing effects in the perception of ambiguous point-light walkers.

The perceptually bistable character of point-light walkers has been examined in three experiments. A point-light figure without explicit depth cues constitutes a perfectly ambiguous stimulus: from all viewpoints, multiple interpretations are possible concerning the depth orientation of the figure. In the first experiment, it is shown that non-lateral views of the walker are indeed interpreted in two orientations, either as facing towards the viewer or as facing away from the viewer, but that the interpretation in which the walker is oriented towards the viewer is reported more frequently. In the second experiment the point-light figure was walking backwards, making the global orientation of the point-light figure opposite to the direction of global motion. The interpretation in which the walker was facing the viewer was again reported more frequently. The robustness of these findings was examined in the final experiment, in which the effects of disambiguating the stimulus by introducing a local depth cue (occlusion) or a more global depth cue (applying perspective projection) were explored.

Adult↗

Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations.

Stochastic effects in biomolecular systems have now been recognized as a major physiologically and evolutionarily important factor in the development and function of many living organisms. Nevertheless, they are often thought of as providing only moderate refinements to the behaviors otherwise predicted by the classical deterministic system description. In this work we show by using both analytical and numerical investigation that at least in one ubiquitous class of (bio)chemical-reaction mechanisms, enzymatic futile cycles, the external noise may induce a bistable oscillatory (dynamic switching) behavior that is both quantitatively and qualitatively different from what is predicted or possible deterministically. We further demonstrate that the noise required to produce these distinct properties can itself be caused by a set of auxiliary chemical reactions, making it feasible for biological systems of sufficient complexity to generate such behavior internally. This new stochastic dynamics then serves to confer additional functional modalities on the enzymatic futile cycle mechanism that include stochastic amplification and signaling, the characteristics of which could be controlled by both the type and parameters of the driving noise. Hence, such noise-induced phenomena may, among other roles, potentially offer a novel type of control mechanism in pathways that contain these cycles and the like units. In particular, observations of endogenous or externally driven noise-induced dynamics in regulatory networks may thus provide additional insight into their topology, structure, and kinetics.

Enzyme Stability↗

Robust, bistable patterning of the dorsal surface of the Drosophila embryo.

In many developing systems, the fate of a cell is determined by its position in a time-independent spatial distribution of a morphogen. However, during dorsal-ventral patterning in the Drosophila embryo, an initial low-level signal refines to a narrow, high-intensity band. This refinement suggests that cells respond to the local transient morphogen distribution that results from interactions between bone morphogenetic proteins (BMPs), their receptors, the BMP-binding proteins Sog and Tsg, the metalloprotease Tld, and a putative, positively regulated component that locally enhances surface binding of BMPs within the region of high signaling. We develop a computational model for dorsal surface patterning and show that, when positive feedback of a cell surface BMP-binding protein is incorporated, bistability in the kinetic interactions transduces the transient BMP distribution into a switch-like spatial distribution of the BMP-bound receptor. We also show that the inclusion of positive feedback leads to the observed contraction of signaling, because cells near the dorsal midline outcompete adjacent lateral cells for limited amounts of BMP. In the model, cells interpret the morphogen distribution by differentiating according to the history of their exposure rather than to a threshold concentration in a static spatial gradient of the morphogen.

Animals↗

Bistable expression of WOR1, a master regulator of white-opaque switching in Candida albicans.

Candida albicans, a commensal organism and a pathogen of humans, can switch stochastically between a white phase and an opaque phase without an intermediate phase. The white and opaque phases have distinct cell shapes and gene expression programs. Once switched, each phase is stable for many cell divisions. White-opaque switching is under a1-alpha2 repression and therefore only happens in a or alpha cells. Mechanisms that control the switching are unknown. Here, we identify Wor1 (white-opaque regulator 1) as a master regulator of white-opaque switching. The deletion of WOR1 blocks opaque cell formation. The ectopic expression of WOR1 converts all cells to stable opaque cells in a or alpha cells. In addition, the ectopic expression of WOR1 in a/alpha cells is sufficient to induce opaque cell formation. Importantly, WOR1 expression displays an all-or-none pattern. It is undetectable in white cells, and it is highly expressed in opaque cells. The ectopic expression of Wor1 induces the transcription of WOR1 from the WOR1 locus, which correlates with the switch to opaque phase. We present genetic evidence for feedback regulation of WOR1 transcription. The feedback regulation explains the bistable and stochastic nature of white-opaque switching.

Amino Acid Sequence↗

Shape bistability of a membrane neck: a toggle switch to control vesicle content release.

Shape dynamics and permeability of a membrane neck connecting a vesicle and plasma membrane are considered. The neck is modeled by a lipid membrane tubule extended between two parallel axisymmetric rings. Within a range of lengths, defined by system geometry and mechanical properties of the membrane, the tubule has two stable shapes: catenoidal microtubule and cylindrical nanotubule. The permeabilities of these two shapes, measured as ionic conductivity of the tubule interior, differ by up to four orders of magnitude. Near the critical length the transitions between the shapes occur within less than a millisecond. Theoretical estimates show that the shape switching is controlled by a single parameter, the tubule length. Thus the tubule connection can operate as a conductivity microswitch, toggling the release of vesicle content in such cellular processes as "kiss-and-run" exocytosis. In support of this notion, bistable behavior of membrane connections between vesicles and the cell plasma membrane in macrophages is demonstrated.

Biophysical Phenomena↗

Optimal design of a bistable switch.

Determining optimally designed structures is important for diverse fields of science and engineering. Here we describe a procedure for calculating the optimal design of a switch and apply the method to a bistable microelectromechanical system relay switch. The approach focuses on characterizing the unstable transition state connecting the two stable equilibria to control the force displacements. Small modifications in component shape lead to a substantial improvement in device operation. Fabrication of the optimized devices confirms the predictions.

Journal Article↗

A mechanism for memory storage insensitive to molecular turnover: a bistable autophosphorylating kinase.

A mechanism is proposed for a molecular switch that can store information indefinitely, despite the complete turnover of the molecules that make up the switch. The design of the switch is based on known types of biochemical reactions. Central to the mechanism is a kinase that is activated by phosphorylation and capable of intermolecular autophosphorylation. It is shown that such a kinase and an associated phosphatase form a bistable chemical switch that can be turned on by an external stimulus and that is not reset by protein turnover.

Memory↗