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Bistability analyses of a caspase activation model for receptor-induced apoptosis.

Apoptosis is an important physiological process crucially involved in development and homeostasis of multicellular organisms. Although the major signaling pathways have been unraveled, a detailed mechanistic understanding of the complex underlying network remains elusive. We have translated here the current knowledge of the molecular mechanisms of the death-receptor-activated caspase cascade into a mathematical model. A reduction down to the apoptotic core machinery enables the application of analytical mathematical methods to evaluate the system behavior within a wide range of parameters. Using parameter values from the literature, the model reveals an unstable status of survival indicating the need for further control. Based on recent publications we tested one additional regulatory mechanism at the level of initiator caspase activation and demonstrated that the resulting system displays desired characteristics such as bistability. In addition, the results from our model studies allowed us to reconcile the fast kinetics of caspase 3 activation observed at the single cell level with the much slower kinetics found at the level of a cell population.

Apoptosis↗

Epitope-specific regulation. II. A bistable, Igh-restricted regulatory mechanism central to immunologic memory.

Antibody responses to commonly used antigens are regulated by an epitope- specific system composed of Igh-restricted elements responsible for controlling the isotype and allotype responses mounted to each of the epitopes on the antigen. Because these elements can be independently induced to either suppress or support antibody production, this system as a whole provides an effector mechanism capable of selectively controlling the amount, affinity, isotype representation, and epitope-specificity of an antibody response. Sequential immunizations with a carrier molecule and a hapten conjugated to that carrier (carrier/hapten-carrier immunization) induce suppression for IgG responses to the hapten. IgG(2a), IgG(2b), and IgG(3) responses are easily suppressed, whereas IgG(1) responses tend to be more resistant. Once induced, suppression tends to be maintained; however, repeated stimulation with the hapten (on any carrier) eventually induces antibody production, first for IgG(1) and later for the more suppressible isotypes (IgG(2a), IgG(2b), IgG(3)). Antibody production, once initiated, also tends to be maintained. Ongoing IgG antihapten responses in animals primed with a hapten-carrier conjugate can be suppressed by subsequent carrier/hapten-carrier immunization (using a different carrier molecule); however, the suppression induced under these circumstances is substantially weaker, i.e., it mainly affects the more suppressible isotypes and is only strong enough to detect clearly in about one-half the immunized animals. Thus, the initiation of antibody production impairs the subsequent induction of suppression, and the initial induction of suppression tends to prevent subsequent initiation of antibody production. This reciprocal relationship defines a bistable regulatory mechanism, i.e., one that tends to maintain its initially induced state but is capable of shifting to the alternate state when stimulatory conditions so dictate. The operation of such a mechanism permits conditions surrounding the first immunization with an epitope (hapten) to strongly influence but not absolutely determine which and how many of the anti-epitope memory B cells generated by that immunization will subsequently be expressed. Thus, epitope- specific regulation, although subordinate to mechanisms that control memory B cell development (as opposed to expression), plays a key role in determining the magnitude, affinity, and isotype representation of anamnestic (memory) responses produced in response to previously encountered epitopes.

Animals↗

Motor neuron 'bistability'. A pathogenetic mechanism for cramps and myokymia.

In three patients suffering from chronic muscle cramps, spasms and myokymia, these involuntary contractions were triggered in the triceps surae, quadriceps, flexor carpi radialis or flexor digitorum by means of single or short-train stimulation of homonymous Ia afferents, elicited by electrical means or tendon taps. In some cases cramp was induced by the first afferent volleys; more often, however, continued stimulation produced stepwise recruitment of motor units (whose rhythmic firing was visible as myokymia in the muscle) until cramp developed. Cramps and myokymic discharges could usually be terminated by a single maximal stimulus to the motor axons (producing antidromic invasion and Renshaw inhibition of the motor neurons), or by short trains of volleys in inhibitory pathways from the skin. The fact that it was possible to induce myokymia and cramps by brief synaptic excitation and terminate them by antidromic invasion or synaptic inhibition, suggests that the mechanism generating these disturbances is intrinsic to alpha-motor neuron somata. Similar on-off switching of self-sustained motor discharges has been observed in the decerebrate cat and is known to depend on 'bistability' of the motor neuron membrane. We propose that a similar mechanism is responsible for discharges that produce cramp.

Adult↗

Bistable behaviour in a neocortical neurone model.

Intracellular recordings have shown that neocortical pyramidal neurones have an intrinsic capacity for regenerative firing. The cellular mechanism of this firing was investigated by computer simulations of a model neurone endowed with standard action potential and persistent sodium (gNaP) conductances. The firing mode of the neurone was determined as a function of leakage and NaP maximal conductances (gl and gNaP). The neurone had two stable states of activity (bistable) over wide range of gl and gNaP, one at the resting potential and the other in a regenerative firing mode, that could be triggered by a transient input. This model points to a cellular mechanism that may contribute to the generation and maintenance of long-lasting sustained neuronal discharges in the cerebral cortex.

Action Potentials↗

Stochastic resonance in extended bistable systems: the role of potential symmetry.

We study the role of potential symmetry in a three-field reaction-diffusion system presenting bistability by means of a two-state theory for stochastic resonance in general asymmetric systems. By analyzing the influence of different parameters in the optimization of the signal-to-noise ratio, we observe that this magnitude always increases with the symmetry of the system's potential, indicating that it is this feature which governs the optimization of the system's response to periodic signals.

Journal Article↗

Metastable states of an Ising-like thermally bistable system.

The lifetimes of the metastable states are investigated in an Ising-like model associated with thermally bistable systems. A discrete mesoscopic Markovian dynamic is established using an optimized version of the previously presented Monte Carlo entropic sampling method. This is well suited to an extensive study of the role of the physical parameters: temperature, interaction parameter, electronic energy gap. By combining a discrete Markovian mesoscopic dynamic and the absorbing Markov chain technique, we obtain an analytical access to the average lifetime of the metastable state. One-variable and two-variable approximations for the original microscopic master equation are presented and discussed. A typical difference in the thermal dependence of the lifetime of the low- and the high-temperature metastable states is found, and explained as a consequence of the temperature-dependent field associated with the Ising-like model. The validity, the advantages, and the limits of the method are discussed, as well as the possible consequences on the behavior of spin transition systems. A prospective for a possible phenomenological finite-size scaling is presented.

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Analysis of the bifurcation diagram of a hybrid bistable system with feedback controls of chaos.

Based on the dynamic equation of a hybrid bistable system with a delayed feedback, we have studied changes of the bifurcation diagram of its output oscillation under chaos suppression and delayed feedback control of chaos, respectively, and the physical origin of these changes. The result clearly shows that, in this case, the input intensity of the system is replaced by a smaller effective input intensity. So the bifurcation diagram is shifted to its right side, and a certain part of the chaotic oscillation becomes periodic oscillation.

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Distribution of escape times for a deterministically driven bistable system

In this paper, we analyze the sequence of escape times for a particle in a symmetric double-well potential coupled to a chain of monodimensional oscillators and we find that, in some range of energies, the probability of escape exhibits the multimodal form that is characteristic of bistable systems driven by a periodic signal embedded in noise. We identify two different modes contributing to the overall hopping dynamics of the particle, each one having a definite dependence on the energy of the chain. Those findings suggest a model for internal fluctuations that could be useful in the study of some problems of interest in physics and biology.

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Competing spatial and temporal instabilities in a globally coupled bistable semiconductor system near a codimension-two bifurcation

We study complex spatiotemporal dynamics in a globally coupled bistable reaction-diffusion model on a two-dimensional spatial domain. It is demonstrated that complex behavior appears near a codimension-two bifurcation point due to the competition of spatial and temporal instabilities. We derive sufficient conditions for the appearance of mixed spatiotemporal modes, and clarify the origin of a menagery of complex dynamics, such as periodic and chaotic oscillations of current filaments, low-dimensional spatiotemporal chaos including a Shil'nikov attractor, and periodic back-and-forth motion of current density fronts. Such dynamics is found in a wide range of domain sizes for square and rectangular domains. The type of dynamics is sensitive to small variations in the domain shape. We discuss and explain the differences between spatiotemporal dynamics on one-dimensional and two-dimensional domains.

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Stochastic resonance in a bistable system subject to multiplicative and additive noise

The stochastic resonance (SR) phenomenon in a bistable system under the simultaneous action of multiplicative and additive noise and periodic signal is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. Two cases have been considered: the case of no correlations between multiplicative and additive noise and the case of correlations between two noises. The expressions of the SNR for both cases are obtained. The effects of intensity of multiplicative and additive noise and the intensity of the correlations between noises on the SNR are discussed for both cases, respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomenon. In the case of no correlations between multiplicative and additive noise, the SNR is independent of the initial condition of the system. However, the SNR is not only dependent on the intensity of correlations between noises, but also on the initial condition of the system in the presence of correlations between two noises.

Journal Article↗

Intrawell stochastic resonance versus interwell stochastic resonance in underdamped bistable systems

We show that, for periodically driven noisy underdamped bistable systems, an intrawell stochastic resonance can exist, together with the conventional interwell stochastic resonance, resulting in a double maximum in the power spectral amplitude at the forcing frequency as a function of the noise intensity. The locations of the maxima correspond to matchings of deterministic and stochastic time scales in the system. In this paper we present experimental evidence of these phenomena and a phemonological nonadiabatic description in terms of a noise-controlled nonlinear dynamic resonance.

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Front propagation and pattern formation in anisotropic bistable media

The effects of diffusion anisotropy on pattern formation in bistable media are studied using a FitzHugh-Nagumo reaction-diffusion model. A relation between the normal velocity of a front and its curvature is derived and used to identify distinct spatiotemporal patterns induced by the diffusion anisotropy. In a wide parameter range anisotropy is found to have an ordering effect: initial patterns evolve into stationary or breathing periodic stripes parallel to one of the principal axes. In a different parameter range, anisotropy is found to induce spatiotemporal chaos confined to one space dimension, a state we term "stratified chaos."

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Self-organized localization of macrostates by additive noise in a fast-slow dynamical system: effect of the slow nonreactive mode on the barrier crossing rate of the fast, bistable mode

We have studied the stochastic dynamics of a two-dimensional gradient system composed of a fast, bistable mode and a slow, monotonically decaying mode. The coupling is bidirectional and cooperative. Additive white noise acts on the fast mode only. We find that the noise intensity controls the location of macrostates (shape of the probability density function), the appearance of bimodality in the slow-mode probability distribution and, together with the coupling strength, the rate of fast-mode barrier crossing. These features arise from the interplay of noise, widely separated time scales, and bidirectional, excitatory coupling. They are believed to be generic.

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Stochastic resonance enhanced by dichotomic noise in a bistable system

We study linear responses of a stochastic bistable system driven by dichotomic noise to a weak periodic signal. We show that the effect of stochastic resonance can be greatly enhanced in comparison with the conventional case when dichotomic forcing is absent, that is, both the signal-to-noise ratio and the spectral power amplification reach much greater values than in the standard stochastic resonance setup.

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Effects of colored noise on stochastic resonance in a bistable system subject to multiplicative and additive noise.

The effects of colored noise on stochastic resonance (SR) in a bistable system driven by multiplicative colored noise and additive white noise and a periodic signal are studied by using the unified colored noise approximation and the theory of signal-to-noise ratio (SNR) in the adiabatic limit. In the case of no correlations between noises, there is an optimal noise intensities ratio R at which SNR is a maximum that identifies the characteristics of the SR when the correlation time tau of the multiplicative colored noise is small. However, when tau is increased, a second optimal value of R appears, and two peaks appear in the SNR simultaneously. In the case of correlations between noises, the SNR is not only dependent on the correlation time tau, but also on the intensity of correlations between noises. Moreover, the double peak phenomenon can also appear as tau is increased in certain situations.

Journal Article↗

Propagation failure in discrete bistable reaction-diffusion systems: theory and experiments.

Wave front propagation failure is investigated in discrete bistable reaction-diffusion systems. We present a theoretical approach including dissipative effects and leading to an analytical expression of the critical coupling beyond which front propagation can occur as a function of the nonlinearity threshold parameter. Our theoretical predictions are confirmed by numerical simulations and experimental results on an equivalent electrical diffusive lattice.

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Onset of wave fronts in a discrete bistable medium.

The transition from a standing front to a traveling front is studied in an array of symmetric bistable coupled oscillators. The mechanism leading to propagation may be understood in the context of a gluing bifurcation involving a pair of homoclinic loops. The velocity of the front shows a logarithmic dependence with the coupling strength according to this mechanism.

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