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PubMed2005

Variability in noise-driven integrator neurons.

Neural variability in the presence of noise has been studied mainly in resonator neurons, such as Hodgkin-Huxley or FitzHugh-Nagumo models. Here we investigate this variability for integrator neurons, whose excitability is due to a saddle-node bifurcation of the rest state instead of a Hopf bifurcation. Using simple theoretical expressions for the interspike times distributions, we obtain coefficients of variation in good agreement with numerical calculations in realistic neuron models. The main features of this coefficient as a function of noise depend on the refractory period and on the presence of bistability. The bistability is responsible for the existence of two different time scales in the spiking behavior giving an antiresonance effect.

Action Potentials↗
PubMed2005

Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity.

We present a model combining a periodic array of rectangular potential wells [the Kronig-Penney (KP) potential] and the cubic-quintic (CQ) nonlinearity. A plethora of soliton states is found in the system: fundamental single-humped solitons, symmetric and antisymmetric double-humped ones, three-peak solitons with and without the phase shift pi between the peaks, etc. If the potential profile is shallow, the solitons belong to the semi-infinite gap beneath the band structure of the linear KP model, while finite gaps between the Bloch bands remain empty. However, in contrast with the situation known in the model combining a periodic potential and the self-focusing Kerr nonlinearity, the solitons fill only a finite zone near the top of the semi-infinite gap, which is a consequence of the saturable character of the CQ nonlinearity. If the potential structure is much deeper, then fundamental and double (both symmetric and antisymmetric) solitons with a flat-top shape are found in the finite gaps. Computation of stability eigenvalues for small perturbations and direct simulations show that all the solitons are stable. In the shallow KP potential, the soliton characteristics, in the form of the integral power Q (or width w) versus the propagation constant k, reveal strong bistability, with two and, sometimes, four different solutions found for a given k (the bistability disappears with the increase of the depth of the potential). Disobeying the Vakhitov-Kolokolov criterion, the solution branches with both dQ/dk > 0 and dQ/dk < 0 are stable. The curve Q(k) corresponding to each particular type of the solution (with a given number of local peaks and definite symmetry) ends at a finite maximum value of Q (breathers are found past the end points). The increase of the integral power gives rise to additional peaks in the soliton's shape, each corresponding to a subpulse trapped in a local channel of the KP structure (a beam-splitting property). It is plausible that these features are shared by other models combining saturable nonlinearity and a periodic substrate.

Journal Article↗
PubMed2006

Improving the speed of the genetic toggle switch without sacrificing its dynamic stability.

Determinants of the switching speed of the genetic toggle switch remain unknown. Analysis shows that the decay rate of proteins predominantly sets the speed limit, but its modification introduces a trade-off between increased speed and decreased bistability. Incorporating protein-modifying enzymes into the switch gives extra degrees of freedom to address this trade-off. The condition for bistability when such enzymes are incorporated is derived. Under this condition, speed increases with the maximal rate of gene expression.

Animals↗
PubMed2006

Dynamical response of the Hodgkin-Huxley model in the high-input regime.

The response of the Hodgkin-Huxley neuronal model subjected to stochastic uncorrelated spike trains originating from a large number of inhibitory and excitatory post-synaptic potentials is analyzed in detail. The model is examined in its three fundamental dynamical regimes: silence, bistability, and repetitive firing. Its response is characterized in terms of statistical indicators (interspike-interval distributions and their first moments) as well as of dynamical indicators (autocorrelation functions and conditional entropies). In the silent regime, the coexistence of two different coherence resonances is revealed: one occurs at quite low noise and is related to the stimulation of subthreshold oscillations around the rest state; the second one (at intermediate noise variance) is associated with the regularization of the sequence of spikes emitted by the neuron. Bistability in the low noise limit can be interpreted in terms of jumping processes across barriers activated by stochastic fluctuations. In the repetitive firing regime a maximization of incoherence is observed at finite noise variance. Finally, the mechanisms responsible for the different features appearing in the interspike-interval distributions (like multimodality and exponential tails) are clearly identified in the various regimes.

Action Potentials↗
PubMed2006

Regular patterns in dichotomically driven activator-inhibitor dynamics.

We investigate Turing pattern formation in the presence of additive dichotomous fluctuations in the context of an extended system with diffusive coupling and FitzHugh-Nagumo kinetics. The fluctuations vary in space and/or time. Depending on the realization of the dichotomous switching the system is, at a given time (for spatial disorder at a given position) in one of two possible excitable dynamical regimes. Each of the two excitable dynamics for itself does not support pattern formation. With proper dichotomous fluctuations, however, the homogeneous steady state is destabilized via a Turing instability. We investigate the influence of different switching rates (different correlation length of the spatial disorder) on pattern formation. We find three distinct mechanisms: For slow switching existing boundaries become unstable, for high rates the system exhibits "effective bistability" which allows for a Turing instability. For medium rates the fluctuations create spatial structures via a new mechanism where the influence of the fluctuations is twofold. First they produce local inhomogeneities, which then grow (again caused by fluctuations) until the whole space is covered. Utilizing a nonlinear map approach we show bistability of a period-one and a period-two orbit being associated with the steady homogeneous and the Turing pattern state, respectively. Finally, for purely static dichotomous disorder we find destabilization of homogeneous steady states for finite nonzero correlation length of the disorder resulting again in Turing patterns.

Journal Article↗
PubMed2006

Pulsed addressing of a dual-frequency nematic liquid crystal.

A continuum theory of dielectric relaxation within liquid crystal materials is described and used to model the response of dual frequency materials to single pulse voltage waveforms. The equations governing the anisotropic axis (director) angle, electric field, and induced polarizations are solved numerically to investigate pulsed addressing of a model zenithally bistable liquid crystal device. By suitably tailoring the voltage pulse, it is found to be possible to switch between both bistable states. For short pulses the high frequency components of the leading edge of the voltage pulse excites the perpendicular polarization and forces the director to lie parallel to the cell substrates. For longer voltage pulses the constant dc component of the voltage pulse excites the parallel polarization causing the director to lie perpendicular to the substrates. It is also found that reducing rotational viscosity and increasing the achievable dielectric anisotropies (particularly the high frequency value) can significantly reduce the operating voltages of such a device.

Journal Article↗
PubMed2006

Optical bullets and double bullet complexes in dissipative systems.

We show that optical light bullets can coexist with double bullet complexes in nonlinear dissipative systems. Coexistence occurs for a relatively large range of the system parameters, and is associated with either marginal stability or bistable existence of the two dissipative soliton species. In the case of marginal stability, spontaneous transformations of single bullets into double bullet complexes are observed. Among the bistable cases, we show how both clockwise and anticlockwise rotating double bullet complexes can be formed out of the phase-controlled interaction of two single bullets. The internal dynamics of pulsating double bullet complexes, with oscillations in both the spatial separation between the two bullets and the bullet shape in time domain is also detailed.

Journal Article↗
PubMed2000

Reversible, nanometer-scale conductance transitions in an organic complex

Reversible conductance transitions are demonstrated on the molecular scale in a complex of 3-nitrobenzal malononitrile and 1, 4-phenylenediamine, by application of local electric field pulses. Both macroscopic and local current-voltage (I/V) measurements show similar electrical bistability behavior. The mechanism of the electrical bistability is discussed.

Journal Article↗
PubMed2003

Oscillatory dispersion and coexisting stable pulse trains in an excitable medium.

For planar wave trains in excitable media, we found a novel type of anomalous dispersion distinguished by bistable domains in the dependence of the propagation velocity on the wavelength. Within one medium alternative stable pulse trains can coexist having the same wavelength but different velocities. The phenomenon is related to oscillatory recovery of excitations, which causes small amplitude oscillations in the refractory tail of pulses. Crucial for the bistability is that the pulses in the trains are locked into one oscillation maximum in the tail of the preceding pulse in the train.

Journal Article↗
PubMed2005

Attractor selection in chaotic dynamics.

For different settings of a control parameter, a chaotic system can go from a region with two separate stable attractors (generalized bistability) to a crisis where a chaotic attractor expands, colliding with an unstable orbit. In the bistable regime jumps between independent attractors are mediated by external perturbations; above the crisis, the dynamics includes visits to regions formerly belonging to the unstable orbits and this appears as random bursts of amplitude jumps. We introduce a control method which suppresses the jumps in both cases by filtering the specific frequency content of one of the two dynamical objects. The method is tested both in a model and in a real experiment with a CO2 laser.

Journal Article↗
PubMed2006

High-contrast dispersive readout of a superconducting flux qubit using a nonlinear resonator.

We demonstrate high-contrast state detection of a superconducting flux qubit. Detection is realized by probing the microwave transmission of a nonlinear resonator, based on a SQUID. Depending on the driving strength of the resonator, the detector can be operated in the monostable or the bistable mode. The bistable operation combines high-sensitivity with intrinsic latching. The measured contrast of Rabi oscillations is as high as 87%; of the missing 13%, only 3% of the loss of contrast is unaccounted for. Experiments involving two consecutive detection pulses are consistent with preparation of the qubit state by the first measurement.

Journal Article↗
PubMed2006

Genetic toggle switch without cooperative binding.

Genetic switch systems with mutual repression of two transcription factors are studied using deterministic and stochastic methods. Numerous studies have concluded that cooperative binding is a necessary condition for the emergence of bistability in these systems. Here we show that, for a range of biologically relevant conditions, a suitable combination of network structure and stochastic effects gives rise to bistability even without cooperative binding.

Animals↗
PubMed2006

Dynamics of epileptic phenomena determined from statistics of ictal transitions.

In this paper, we investigate the dynamical scenarios of transitions between normal and paroxysmal state in epilepsy. We assume that some epileptic neural network are bistable i.e., they feature two operational states, ictal and interictal that co-exist. The transitions between these two states may occur according to a Poisson process, a random walk process or as a result of deterministic time-dependent mechanisms. We analyze data from animal models of absence epilepsy, human epilepsies and in vitro models. The distributions of durations of ictal and interictal epochs are fitted with a gamma distribution. On the basis of qualitative features of the fits, we identify the dynamical processes that may have generated the underlying data. The analysis showed that the following hold. 1) The dynamics of ictal epochs differ from those of interictal states. 2) Seizure initiation can be accounted for by a random walk process while seizure termination is often mediated by deterministic mechanisms. 3) In certain cases, the transitions between ictal and interictal states can be modeled by a Poisson process operating in a bistable network. These results imply that exact prediction of seizure occurrence is not possible but termination of an ictal state by appropriate counter stimulation might be feasible.

Adolescent↗
PubMed1998

Encoding properties induced by a persistent voltage-gated muscarinic sodium current in rabbit sympathetic neurones.

1. A time- and voltage-dependent Na(+)-selective current termed INa,M is activated by muscarinic agonists or splanchnic nerve stimulation in sympathetic neurones of rabbit coeliac and superior mesenteric ganglia. The firing patterns induced by INa,M were investigated in patch-clamped neurones within intact ganglia, and compared with those generated by a neuronal model including INa,M. 2. INa,M was characterized by voltage-dependent low threshold activation and high-threshold inactivation functions. The overlapping functions produced a persistent U-shaped current between -100 and -20 mV, which peaked at the cell resting potential. The activation and inactivation kinetics were fitted to single exponentials with time constants of approximately 100 and 400 ms, respectively. 3. Activating INa,M with muscarinic agonists or nerve stimulation depolarized and fired the neurones. The depolarization was paralleled by an apparent increase in input membrane resistance. The model showed that this paradox resulted from the turning off of INa,M during resistance tests, which also accounted for the all-or-none slow hyperpolarizing responses to current pulses. 4. INa,M gave the neurones an N-shaped I-V relationship capable of producing complex firing patterns. Under given conditions, carbachol-treated neurones could either fire regularly or remain silent at approximately -80 mV, i.e. they displayed bistability. Transitions from one state to the other were triggered with short current pulses. The transitions resulted from the turning on and off of INa,M. 5. Firing reduced INa,M, an effect abolished by blocking Ca2+ channels or adding BAPTA (40 mM) to the pipette. The Ca(2+)-related negative regulation of INa,M may have mediated endogenous bursting activity. Burst firing was generated by the model upon introducing Ca2+ regulation of INa,M. 6. The results demonstrate that INa,M gives prevertebral sympathetic neurones a wide repertoire of firing patterns: pacemaker-like properties, bistability and burst firing capability. They suggest that the INa,M-related encoding properties may provide sympathetic neurotransmission with new potentialities.

Animals↗
PubMed2006

Inheritance and state switching of genetic toggle switch in different culture growth phases.

Using the gene engineering methods, one can construct simple artificial gene networks with two stable functioning regimes (bistable genetic systems). Such genetic systems make it possible for cells with identical genotype to inherit two alternative phenotypes. The toggle switch is just one of the types of bistable genetic systems. In this work, we investigate the inheritance and switching of toggle switch functioning regimes in the cells at different culture growth phases. It is shown that during transition into the stationary growth phase the inheritance of stable states is disturbed and variations in the toggle-switching rate are more possible in different cells. Also, simultaneous expression of two genes of the system has been experimentally modelled. According to our results, the culture growth phase in this period determines later on the ratio between cell phenotypes in a population.

Escherichia coli↗
PubMed2004

Recruitment of motor neuronal persistent inward currents shapes withdrawal reflexes in the frog.

The details of behaviour are determined by the interplay of synaptic connectivity within neuronal circuitry and the intrinsic membrane properties of individual neurones. One particularly dramatic intrinsic property displayed by neurones in many regions of the nervous system is membrane potential bistability, in which transient excitation of a neurone results in a persistent depolarization outlasting the initial excitation. Here we characterize the contribution of such intrinsic bistability, also referred to as plateau properties and mediated by persistent inward currents (PICs), in spinal motor neurones to the production of withdrawal behaviours in the frog. We performed experiments on the isolated frog spinal cord with attached hindlimb. This preparation allowed the simultaneous monitoring of muscle activations during motor behaviour and intracellular neuronal recordings. We found that PICs, following their potentiation by serotonin (5-HT), are recruited and contribute to the production of withdrawal behaviours. These properties conferred a voltage-dependent prolongation to the duration of motor neuronal activity. Consistent with this potentiation of motor neuronal PICs, 5-HT also increased the duration of evoked muscle activations. This behavioural potentiation, as well as the expression of PICs in individual neurones, was reduced following antagonism of L-type Ca(2+) channels. These results demonstrate that PICs in motor neurones can be recruited during the production of behaviour and play a role in specifying the temporal details of motor output.

Animals↗
PubMed2004

The 'window' T-type calcium current in brain dynamics of different behavioural states.

All three forms of recombinant low voltage-activated T-type Ca(2)(+) channels (Ca(v)3.1, Ca(v)3.2 and Ca(v)3.3) exhibit a small, though clearly evident, window T-type Ca(2)(+) current (I(Twindow)) which is also present in native channels from different neuronal types. In thalamocortical (TC) and nucleus reticularis thalami (NRT) neurones, and possibly in neocortical cells, an I(Twindow)-mediated bistability is the key cellular mechanism underlying the expression of the slow (< 1 Hz) sleep oscillation, one of the fundamental EEG rhythms of non-REM sleep. As the I(Twindow)-mediated bistability may also represent one of the cellular mechanisms underlying the expression of high frequency burst firing in awake conditions, I(Twindow) is of critical importance in neuronal population dynamics associated with different behavioural states.

Animals↗
PubMed2002

MAP kinase phosphatase as a locus of flexibility in a mitogen-activated protein kinase signaling network.

Intracellular signaling networks receive and process information to control cellular machines. The mitogen-activated protein kinase (MAPK) 1,2/protein kinase C (PKC) system is one such network that regulates many cellular machines, including the cell cycle machinery and autocrine/paracrine factor synthesizing machinery. We used a combination of computational analysis and experiments in mouse NIH-3T3 fibroblasts to understand the design principles of this controller network. We find that the growth factor-stimulated signaling network containing MAPK 1, 2/PKC can operate with one (monostable) or two (bistable) stable states. At low concentrations of MAPK phosphatase, the system exhibits bistable behavior, such that brief stimulus results in sustained MAPK activation. The MAPK-induced increase in the amounts of MAPK phosphatase eliminates the prolonged response capability and moves the network to a monostable state, in which it behaves as a proportional response system responding acutely to stimulus. Thus, the MAPK 1, 2/PKC controller network is flexibly designed, and MAPK phosphatase may be critical for this flexible response.

3T3 Cells↗