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PubMed1987

Bistability and irreversible transitions in a simple substrate cycle.

The dynamic properties of a simple substrate cycle involving two antagonist enzymes are investigated. One of these enzymes exhibits a non-linearity through inhibition by excess substrate. Depending either on the interconverted substrate pool concentration or the maximal activity of the non-inhibited enzyme, monostability, bistability and irreversible transitions may occur. A reversible bistable cycle is shown to present interesting features for regulatory purposes as it can respond to external (and/or internal) modulations in two different ways: A buffering effect by efficient stabilization of the steady-states, or, an increase in sensitivity by switching the system from one regime to the opposite one. The plausible biochemical and biological implications of irreversible transitions are discussed and emphasized in terms of "metabolic transitions".

Enzymes↗
PubMed2003

Bistability in a size-structured population model of cannibalistic fish--a continuation study.

By numerical continuation of equilibria, we study a size-structured model for the dynamics of a cannibalistic fish population and its alternative resource. Because we model the cannibalistic interaction as dependent on the ratio of cannibal length and victim length, a cannibal experiences a size distribution of potential victims which depends on its own body size. We show how equilibria of the resulting infinite-dimensional dynamical system can be traced with an existing method for numerical continuation for physiologically structured population models. With this approach we found that cannibalism can induce bistability associated with a fold (or, saddle-node) bifurcation. The two stable states can be qualified as 'stunted' and 'piscivorous', respectively. We identify a new ecological mechanism for bistability, in which the energy gain from cannibalism plays a crucial role: Whereas in the stunted population state cannibals consume their victims, on average, while they are very small and yield little energy, in the piscivorous state cannibals consume their victims not before they have become much bigger, which results in a much higher mean yield of cannibalism. We refer to this mechanism as the 'Hansel and Gretel' effect. It is not related to any individual 'choice' or 'strategy', but depends purely on a difference in population size distribution. We argue that studying dynamics of size-structured population models with this new approach of equilibrium continuation extends the insight that can be gleaned from numerical simulations of the model dynamics.

Animals↗
PubMed2003

Hysteresis in response of nonlinear bistable interface to continuously varying acoustic loading.

In many experimental situations it is an equation of the forced relaxator and not of the forced oscillator that describes a variation in the acoustic field of the interface width (i.e. of a characteristic distance between the surfaces composing the interface). The developed theory predicts that some types of the nonlinear relaxators (depending on the structure of the nonlinear interaction force between the surfaces) exhibit hysteresis in their response to continuous acoustic loading of first increasing and then decreasing amplitude. Nonlinear (unharmonic) variation of the interface width starts at threshold amplitude of the incident sinusoidal acoustic wave, which is higher than threshold amplitude for returning to sinusoidal motion. This dynamic hysteresis (and accompanying it bistability) are possible, in particular, if the dependence of the effective interaction force on the interface width admits two quasi-equilibrium positions of the interface (bistable interface) or if the force itself is hysteretic (hysteretic interface). These theoretical predictions are relevant to some recent experimental observations on the interaction of powerful ultrasonic fields with cracks.

Acoustics↗
PubMed2000

Oscillations and bistability predicted by a model for a cyclical bienzymatic system involving the regulated isocitrate dehydrogenase reaction.

We analyze the dynamics of a bienzymatic system consisting of isocitrate dehydrogenase (IDH, EC. 1.1.1.42), which transforms NADP+ into NADPH, and of diaphorase (DIA, EC 1.8.1.4), which catalyzes the reverse reaction. Experimental evidence as well as a theoretical model showed the possibility of a coexistence between two stable steady states in this reaction system G.M. Guidi et al. Biophys. J. 74 (1998) 1229-1240[, owing to the regulatory properties of IDH. Here we extend this analysis by considering the behavior of the model proposed for the IDH-DIA bienzymatic system in conditions where the system is open to an influx of its substrates isocitrate and NADP+ and to an efflux of all metabolic species. The analysis indicates that in addition to different modes of bistability (including mushrooms and isolas), sustained oscillations can be observed in such conditions. These results point to the isocitrate dehydrogenase reaction coupled to diaphorase as a suitable candidate for further experimental and theoretical studies of bistability and oscillations in biochemical systems. The results obtained in this particular bienzymatic system bear on other enzymatic systems possessing a cyclical nature, which are known to play significant roles in a variety of metabolic and cellular regulatory processes.

Dihydrolipoamide Dehydrogenase↗
PubMed1998

Analysis and biophysical interpretation of bistable behaviour in thalamocortical neurons.

Thalamocortical neurons display a wide spectrum of activity patterns that are the expressions of the non-linear interactions between the various voltage-gated ion channels. Here, we show how bistable behaviour can emerge in these neurons, and how it is brought about by the steady-state residual ("window") component of IT, the low-threshold Ca2+ current. In particular, we present results that describe the dependence of bistability on two system parameters: the injected current and the leakage conductance. In addition, we provide a biophysical interpretation of these results by means of the properties of the electrical circuit representing the neuron membrane.

Algorithms↗
PubMed2002

Bistable ferroelectric liquid crystal photoswitch triggered by a dithienylethene dopant.

The spontaneous polarization (PS) of a ferroelectric liquid crystal is modulated reversibly by photocyclization of the dopant 1,2-bis[5'-(4' '-heptyloxyphenyl)-2'-methylthien-3'-yl]perfluorocyclopentene. The magnitude of PS photomodulation increases with dopant concentration up to 3 mol %, and the resulting photoswitch is fatigue resistant and bistable. To the best of our knowledge, this is the first example of a bistable ferroelectric liquid crystal photoswitch to be reported in the literature.

Journal Article↗
PubMed2005

Structures and properties of self-assembled monolayers of bistable [2]rotaxanes on Au (111) surfaces from molecular dynamics simulations validated with experiment.

Bistable [2]rotaxanes display controllable switching properties in solution, on surfaces, and in devices. These phenomena are based on the electrochemically and electrically driven mechanical shuttling motion of the ring-shaped component, cyclobis(paraquat-p-phenylene) (CBPQT(4+)) (denoted as the ring), between a tetrathiafulvalene (TTF) unit and a 1,5-dioxynaphthalene (DNP) ring system located along a dumbbell component. When the ring is encircling the TTF unit, this co-conformation of the rotaxane is the most stable and thus designated the ground-state co-conformer (GSCC), whereas the other co-conformation with the ring surrounding the DNP ring system is less favored and so designated the metastable-state co-conformer (MSCC). We report here the structure and properties of self-assembled monolayers (SAMs) of a bistable [2]rotaxane on Au (111) surfaces as a function of surface coverage based on atomistic molecular dynamics (MD) studies with a force field optimized from DFT calculations and we report several experiments that validate the predictions. On the basis of both the total energy per rotaxane and the calculated stress that is parallel to the surface, we find that the optimal packing density of the SAM corresponds to a surface coverage of 115 A(2)/molecule (one molecule per 4 x 4 grid of surface Au atoms) for both the GSCC and MSCC, and that the former is more stable than the latter by 14 kcal/mol at the optimum packing density. We find that the SAM retains hexagonal packing, except for the case at twice the optimum packing density (65 A(2)/molecule, the 3 x 3 grid). For the GSCC and MSCC, investigated at the optimum coverage, the tilt of the ring with respect to the normal is theta = 39 degrees and 61 degrees, respectively, while the tilt angle of the entire rotaxane is psi = 41 degrees and 46 degrees , respectively. Although the tilt angle of the ring decreases with decreasing surface coverage, the tilt angle of the rotaxane has a maximum at 144 A(2)/molecule (the 4 x 5 grid/molecule) of 50 degrees and 51 degrees for the GSCC and MSCC, respectively. The hexafluorophosphate counterions (PF(6)(-)) stay localized around the ring during the 2 ns MD simulation. On the basis of the calculated density profile, we find that the thickness of the SAM is 40.5 A at the optimum coverage for the GSCC and 40.0 A for MSCC, and that the thicknesses become less with decreasing surface coverage. The calculated surface tension at the optimal packing density is 45 and 65 dyn/cm for the GSCC and MSCC, respectively. This difference suggests that the water contact angle for the GSCC is larger than for the MSCC, a prediction that is verified by experiments on Langmuir-Blodgett monolayers of amphiphilic [2]rotaxanes.

Journal Article↗
PubMed2005

Molecular dynamics simulation of amphiphilic bistable [2]rotaxane langmuir monolayers at the air/water interface.

Bistable [2]rotaxanes display controllable switching properties in solution, on surfaces, and in devices. These phenomena are based on the electrochemically and electrically driven mechanical shuttling motion of the ring-shaped component, cyclobis(paraquat-p-phenylene) (CBPQT(4+)), between a monopyrrolotetrathiafulvalene (mpTTF) unit and a 1,5-dioxynaphthalene (DNP) unit located along a dumbbell component. The most stable state of the rotaxane (CBPQT(4+)@mpTTF) is that in which the CBPQT(4+) ring encircles the mpTTF unit, but a second less favored metastable co-conformation with the CBPQT(4+) ring surrounding the DNP (CBPQT(4+)@DNP) can be formed experimentally. For both co-conformations of an amphiphilic bistable [2]rotaxane, we report here the structure and surface pressure-area isotherm of a Langmuir monolayer (LM) on a water subphase as a function of the area per molecule. These results from atomistic molecular dynamics (MD) studies are validated by comparing with experiments based on similar amphiphilic rotaxanes. For both co-conformations, we found that as the area per molecule increases the thickness of the LM decreases while the molecular tilt increases. Both co-conformations led to similar LM thicknesses at the same packing area. From the simulated LM systems, we calculated the electron density profiles of the monolayer as a function of area per molecule, which show good agreement with experimental analyses from synchrotron X-ray reflectivity measurements of related systems. Decomposing the overall electron density profiles into component contributions, we found distinct differences in molecular packing in the film depending upon the co-conformation. Thus we find that the necessity of allowing the tetracationic ring to become solvated by water leads to differences in the structures for the two co-conformations in the LM. At the same packing area, the value of the overall tilt angle does not seem to be sensitive to whether the CBPQT(4+) ring is encircling the mpTTF or the DNP unit. However, the conformation of the dumbbell does depend on the location of the CBPQT(4+) ring, which is reflected in the segmental tilt angles of the mpTTF and DNP units. Using the Kirkwood-Buff formula in conjunction with MD calculations, we find the surface pressure-area isotherms for each co-conformation in which the CBPQT(4+)@mpTTF form has smaller surface tension and therefore larger surface pressure than the CBPQT(4+)@DNP at the same packing area, differences that decreases with increasing area per molecule, which is verified experimentally.

Air↗
PubMed2006

Order-disorder transition coupled with magnetic bistability in the ferricinium salt of a radical nickel dithiolene complex.

The ferricinium salt of the anionic, S = (1)/(2), dithiolene complex [Ni(tfadt)(2)](-) (where tfadt is the asymmetrically substituted 2-(trifluoromethyl)acrylonitrile-1,2-dithiolate) crystallizes at room temperature (rt) into uniform chains of dithiolene complexes, separated by ferricinium cations. Both ionic entities are characterized by disorder affecting one CF(3) and one Cp moiety. Above 250 K, this compound displays a Curie-type behavior. At lower temperatures, two first-order transitions around 249 and 137 K are revealed by susceptibility measurements and the observation of hysteresis effects. Crystal structure determinations performed at 230 and 120 K show that the high-temperature transition is associated with an ordering of the CF(3) and Cp groups together with a dimerization of the anionic stacks that thus induces a drop of the susceptibility. The second, low-temperature transition leads to a tetramerization of these nickel dithiolene stacks now in a complete diamagnetic state while the remaining susceptibility originates from the sole ferricinium contribution. The first order character of the 249 K transition with its associated bistable behavior is likely correlated with the structural order-disorder transition, an original behavior in this class of materials where bistability is most often associated with a strengthening of interstack intermolecular interactions (hydrogen bonding, pi-pi interactions ...).

Journal Article↗
PubMed2005

Master equation simulations of bistable and excitable dynamics in a model of a thermochemical system.

The effect of fluctuations on the dynamics of a model of a bistable thermochemical system is studied by means of the master equation. The system has three stationary states and exhibits two types of bistability: the coexistence of two stable focuses and the coexistence of a stable focus with a stable limit cycle separated by a saddle point. Stochastic effects are important when the system is close to the bifurcation, in which the stable limit cycle disappears through a homoclinic orbit. In this case the distribution of the first passage time from the stable limit cycle to the stable focus has a multipeak form. The dependence of this distribution on the number of particles is presented. Near the homoclinic orbit bifurcation, the system also exhibits excitability due to a particular shape of the basin of attraction of the stable focus.

Journal Article↗
PubMed2005

Spatial bistability in a pH autocatalytic system: from long to short range activation.

The acid-auto-activated chlorite-tetrathionate reaction is studied in a one-side-fed spatial reactor. It was previously shown that in these conditions the unstirred reaction-diffusion system can generate oscillatory and excitable states even though under well-stirred nonequilibrium conditions only steady-state bistability is observed. Numerical simulations suggest that these temporal reaction-diffusion instabilities result from long-range activation by rapidly diffusing protons. We study here experimentally and numerically the effect of introducing into this reaction-diffusion system macromolecular carboxylate species that reduce the effective diffusivity of protons. Consistent with the original assumption, the introduction of such slow mobility proton-binding species quenches both oscillatory and excitability dynamics. Within the bistability domain the direction of the propagation of an interface between the two steady states depends on control parameter value. We elaborate on the fact that beyond a low critical concentration of macromolecular carboxylate species, the stability limit of the "thermodynamic" branch of spatial steady state does not depend on this concentration. Despite the relative simplicity of the kinetic model used in the numerical simulations, the results are in quasi-quantitative agreement with the experimental observations.

Journal Article↗
PubMed2006

Construction of an in vitro bistable circuit from synthetic transcriptional switches.

Information processing using biochemical circuits is essential for survival and reproduction of natural organisms. As stripped-down analogs of genetic regulatory networks in cells, we engineered artificial transcriptional networks consisting of synthetic DNA switches, regulated by RNA signals acting as transcription repressors, and two enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H. The synthetic switch design is modular with programmable connectivity and allows dynamic control of RNA signals through enzyme-mediated production and degradation. The switches support sharp and adjustable thresholds using a competitive hybridization mechanism, allowing arbitrary analog or digital circuits to be created in principle. As an example, we constructed an in vitro bistable memory by wiring together two synthetic switches and performed a systematic quantitative characterization. Good agreement between experimental data and a simple mathematical model was obtained for switch input/output functions, phase plane trajectories, and the bifurcation diagram for bistability. Construction of larger synthetic circuits provides a unique opportunity for evaluating model inference, prediction, and design of complex biochemical systems and could be used to control nanoscale devices and artificial cells.

Escherichia coli↗
PubMed2005

Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance.

Stochastic resonance is a counterintuitive concept: the addition of noise to a noisy system induces coherent amplification of its response. First suggested as a mechanism for the cyclic recurrence of ice ages, stochastic resonance has been seen in a wide variety of macroscopic physical systems: bistable ring lasers, superconducting quantum interference devices (SQUIDs), magnetoelastic ribbons and neurophysiological systems such as the receptors in crickets and crayfish. Although fundamentally important as a mechanism of coherent signal amplification, stochastic resonance has yet to be observed in nanoscale systems. Here we report the observation of stochastic resonance in bistable nanomechanical silicon oscillators. Our nanomechanical systems consist of beams that are clamped at each end and driven into transverse oscillation with the use of a radiofrequency source. Modulation of the source induces controllable switching of the beams between two stable, distinct states. We observe that the addition of white noise causes a marked amplification of the signal strength. Stochastic resonance in nanomechanical systems could have a function in the realization of controllable high-speed nanomechanical memory cells, and paves the way for exploring macroscopic quantum coherence and tunnelling.

Journal Article↗
PubMed2001

Spatial bistability and waves in a reaction with acid autocatalysis.

The phenomenon of spatial bistability has recently been proposed for a comprehensive understanding of a number of chemical patterns observed in open spatial reactors consisting of thin films of gel diffusively fed from one side. We study experimentally and numerically this phenomenon in the tetrathionate-chlorite reaction characterized by an acid superautocatalysis. We focus on the similarities and differences with previous studies on the chlorine dioxide-iodide reaction. In addition, we show that this reaction, which is only bistable in a continuous stirred tank reactor, can exhibit oscillatory and traveling waves when diffusion comes into play. Our computations suggest that the nonstationary behaviour originates from differential diffusive transport.

Journal Article↗
PubMed2000

Dendritic L-type calcium currents in mouse spinal motoneurons: implications for bistability.

The intrinsic properties of mammalian spinal motoneurons provide them with the capability to produce high rates of sustained firing in response to transient inputs (bistability). Even though it has been suggested that a persistent dendritic calcium current is responsible for the depolarizing drive underlying this firing property, such a current has not been demonstrated in these cells. In this study, calcium currents are recorded from functionally mature mouse spinal motoneurons using somatic whole-cell patch-clamp techniques. Under these conditions a component of the current demonstrated kinetics consistent with a current originating at a site spatially segregated from the soma. In response to step commands this component was seen as a late-onset, low amplitude persistent current whilst in response to depolarizing-repolarizing ramp commands a low voltage clockwise current hysteresis was recorded. Simulations using a neuromorphic motoneuron model could reproduce these currents only if a noninactivating calcium conductance was placed in the dendritic compartments. Pharmacological studies demonstrated that both the late-onset and hysteretic currents demonstrated sensitivity to both dihydropyridines and the L-channel activator FPL-64176. Furthermore, the alpha1D subunits of L-type calcium channels were immunohistochemically demonstrated on motoneuronal dendrites. It is concluded that there are dendritically located L-type channels in mammalian motoneurons capable of mediating a persistent depolarizing drive to the soma and which probably mediate the bistable behaviour of these cells.

Animals↗
PubMed1999

Hysteresis and bistability in the direct transition from 1:1 to 2:1 rhythm in periodically driven single ventricular cells.

The transmembrane potential of a single quiescent cell isolated from rabbit ventricular muscle was recorded using a suction electrode in whole-cell recording mode. The cell was then driven with a periodic train of current pulses injected into the cell through the same recording electrode. When the interpulse interval or basic cycle length (BCL) was sufficiently long, 1:1 rhythm resulted, with each stimulus pulse producing an action potential. Gradual decrease in BCL invariably resulted in loss of 1:1 synchronization at some point. When the pulse amplitude was set to a fixed low level and BCL gradually decreased, N+1:N rhythms (N>/=2) reminiscent of clinically observed Wenckebach rhythms were seen. Further decrease in BCL then yielded a 2:1 rhythm. In contrast, when the pulse amplitude was set to a fixed high level, a period-doubled 2:2 rhythm resembling alternans rhythm was seen before a 2:1 rhythm occurred. With the pulse amplitude set to an intermediate level (i.e., to a level between those at which Wenckebach and alternans rhythms were seen), there was a direct transition from 1:1 to 2:1 rhythm as the BCL was decreased: Wenckebach and alternans rhythms were not seen. When at that point the BCL was increased, the transition back to 1:1 rhythm occurred at a longer BCL than that at which the {1:1-->2:1} transition had initially occurred, demonstrating hysteresis. With the BCL set to a value within the hysteresis range, injection of a single well-timed extrastimulus converted 1:1 rhythm into 2:1 rhythm or vice versa, providing incontrovertible evidence of bistability (the coexistence of two different periodic rhythms at a fixed set of stimulation parameters). Hysteresis between 1:1 and 2:1 rhythms was also seen when the stimulus amplitude, rather than the BCL, was changed. Simulations using numerical integration of an ionic model of a single ventricular cell formulated as a nonlinear system of differential equations provided results that were very similar to those found in the experiments. The steady-state action potential duration restitution curve, which is a plot of the duration of the action potential during 1:1 rhythm as a function of the recovery time or diastolic interval immediately preceding that action potential, was determined. Iteration of a finite-difference equation derived using the restitution curve predicted the direct {1:1<-->2:1} transition, as well as bistability, in both the experimental and modeling work. However, prediction of the action potential duration during 2:1 rhythm was not as accurate in the experiments as in the model. Finally, we point out a few implications of our findings for cardiac arrhythmias (e.g., Mobitz type II block, ischemic alternans). (c) 1999 American Institute of Physics.

Journal Article↗
PubMed2006

Spatial bistability: a source of complex dynamics. From spatiotemporal reaction-diffusion patterns to chemomechanical structures.

We show experimentally and theoretically that reaction systems characterized by a slow induction period followed by a fast evolution to equilibrium can readily generate "spatial bistability" when operated in thin gel reactors diffusively fed from one side. This phenomenon which corresponds to the coexistence of two different stable steady states, not breaking the symmetry of the boundary conditions, can be at the origin of diverse reaction-diffusion instabilities. Using different chemical reactions, we show how stationary pulses, labyrinthine patterns or spatiotemporal oscillations can be generated. Beyond simple reaction-diffusion instabilities, we also demonstrate that the cross coupling of spatial bistability with the size responsiveness of a chemosensitive gel can give rise to autonomous spatiotemporal shape patterns, referred to as chemomechanical structures.

Catalysis↗
PubMed2006

Designing an enzymatic oscillator: bistability and feedback controlled oscillations with glucose oxidase in a continuous flow stirred tank reactor.

The reaction of glucose with ferricyanide catalyzed by glucose oxidase from Aspergillus niger gives rise to a wide range of bistability as the flow rate is varied in a continuous flow stirred tank reactor. Oscillations in pH can be obtained by introducing a negative feedback on the autocatalytic production of H+ that drives the bistability. In our experiments, this feedback consists of an inflow of hydroxide ion at a rate that depends on [H+] in the reactor as k0[OH-]0[H+]/(K+[H+]). pH oscillations are found over a broad range of enzyme and ferricyanide concentrations, residence times (k0 (-1)), and feedback parameters. A simple mathematical model quantitatively accounts for the experimentally found oscillations.

Aspergillus niger↗