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At least 775 records · Page 43Linked to original sources
PubMed1990

Chaotic dynamics in an ionic model of the propagated cardiac action potential.

We simulate the effect of periodic stimulation on a strand of ventricular muscle by numerically integrating the one-dimensional cable equation using the Beeler-Reuter model to represent the transmembrane currents. As stimulation frequency is increased, the rhythms of synchronization [1:1----2:2----2:1----4:2---- irregular----3:1----6:2----irregular----4:1----8:2----...----1:0] are successively encountered. We show that this sequence of rhythms can be accounted for by considering the response of the strand to premature stimulation. This involves deriving a one-dimensional finite-difference equation or "map" from the response to premature stimulation, and then iterating this map to predict the response to periodic stimulation. There is good quantitative agreement between the results of iteration of the map and the results of the numerical integration of the cable equation. Calculation of the Lyapunov exponent of the map yields a positive value, indicating sensitive dependence on initial conditions ("chaos"), at stimulation frequencies where irregular rhythms are seen in the corresponding numerical cable simulations. The chaotic dynamics occurs via a previously undescribed route, following two period-doubling bifurcations. Bistability (the presence of two different synchronization rhythms at a fixed stimulation frequency) is present both in the simulations and the map. Thus, we have been able to directly reduce consideration of the dynamics of a partial differential equation (which is of infinite dimension) to that of a one-dimensional map, incidentally demonstrating that concepts from the field of non-linear dynamics--such as period-doubling bifurcations, bistability, and chaotic dynamics--can account for the phenomena seen in numerical simulations of the cable equation. Finally, we sketch out how the one-dimensional description can be extended, and point out some implications of our work for the generation of malignant ventricular arrhythmias.

Action Potentials↗
PubMed1998

Nonstationarity in epileptic EEG and implications for neural dynamics.

In this paper, we use a recently developed method to analyze the nonstationarity in time series from intracranial depth and subdural recordings of patients with temporal lobe epilepsy. We show that the nonstationarity in the signal can be accounted for by the variation of a single parameter. We then show that the various dominant nonlinear waveforms observed in different electrodes can be explained by a simple stochastic model in which the mesoscopic collection of neurons, whose potential the electrodes measure, can be on one of two states. The nonstationarity observed in our analysis is a consequence of a time-dependent transition probability between these two states. In general, this transition probability increases as a seizure is approached. The model that we propose incorporates this bistability. We find good agreement between real data and simulated data generated by our model. We understand that this mesoscopic bistability may be associated with the existence of excitation waves traversing the brain in these patients.

Electroencephalography↗
PubMed1996

Architecture of a gain controller in the pursuit system.

A monkey can pursue faster target oscillations if they appear during ongoing smooth pursuit than if they appear while the monkey is fixating a stationary target. Others have proposed a switch in the pursuit circuit to account for this bistable sensitivity to high frequency targets. It is hypothesized that the switch is closed only during pursuit, permitting the retinal motion signal to pass through the circuit at full gain. Losses in pursuit gain caused by certain cortical lesions do mimic the effect of a switch jammed open. To explore this gain adjustment mechanism further, we measured in monkeys the smooth eye movements in response to a high frequency sinusoidal target (called 'humm') presented under a variety of testing conditions. Pursuit gain measured in response to this humm was not merely bistable. Rather, a graded gain modulation of the pursuit system was possible. Furthermore, the gain adjustment had some directional sensitivity to it, enhancing the response to humm along one axis more than the other. In exploring the factors which gated the gain adjustment, it appeared that the movement of the eyes and not the image motion that occurs during pursuit was paramount for enhancing pursuit gain. Gain was not enhanced by saccadic but only by smooth pursuit tracking movements. Finally, gain could be modulated somewhat by covert signals such as the expectation of future smooth pursuit movements.

Animals↗
PubMed1999

Mathematical analysis of binary activation of a cell cycle kinase which down-regulates its own inhibitor.

In mammalian cells, the heterodimeric kinase cyclin E/CDK2 (EK2) mediates cell cycle progress from G1 phase into S phase. The protein p27Kip1 (p27) binds to and inhibits EK2; but EK2 can phosphorylate p27, and that leads to the deactivation of p27, presumably liberating more EK2 and forming a positive-feedback loop. It has been proposed that this positive-feedback loop gives rise to binary (all-or-none) release of EK2 from its inactive complex with p27. Binary release suggests a bistable biochemical system in which a stable steady state with low EK2 activity is extinguished in a saddle-node bifurcation, causing the system to shift abruptly to a stable steady state with high EK2 activity. Two mathematical models are discussed, one in which free EK2 deactivates p27 in the EK2-p27 inhibitory complex as well as free p27, and one in which the rate of EK2-catalyzed deactivation of free p27 has saturable kinetics with respect to free p27. In general, if inhibitory binding is approximately in equilibrium, bistability requires that there be a potential unstable steady state where the reaction order of p27 deactivation is greater with respect to EK2 than with respect to p27.

Animals↗
PubMedDate not supplied

Physiologically realistic modelling of a mechanism for neural representation of intervals of time.

A model for a recurrent network of bistable spiking neurons is examined. Each neuron is described by a leaky-integrate-and-fire formulation with biophysically realistic currents and noise. Specially, neuronal bistability is equipped by after-depolarisation current. Results obtained by computer simulation show that spiking of each neuron starting at an initial time continues for an extended period and then suddenly ceases at around a certain time. We hypothesise that activation of neurons that starts at t = 0 and voluntarily ceases at t = T is a neural underpinning of internal representation of an interval of time T. The above results theoretically support this hypothesis by demonstrating one possible mechanism to generate such time course of neuronal activation.

Action Potentials↗
PubMed2001

Stimulation of D1-type dopamine receptors enhances excitability in prefrontal cortical pyramidal neurons in a state-dependent manner.

Prefrontal cortex neurons recorded in vivo exhibit bistable activity states, consisting of a depolarized phase (-55mV) and a hyperpolarized phase (-85mV). These "up" and "down" states have durations ranging from 800ms to 1s and a periodicity of approximately 1Hz. This study examines the state-dependency of prefrontal cortical neuron responses to dopamine, in which the bistable-state was approximated in vitro by intracellular current injection. At resting membrane potential (n=10), dopamine caused a significant depolarization of the membrane potential without altering any of the other electrophysiological characteristics tested. In contrast, both dopamine (30 microM, 5min) and the D1 receptor agonist SKF 38393 (5 and 10 microM) increased cell excitability when the cell was in the depolarized state (i.e., -55mV) but not the hyperpolarized state (i.e., -85 mV; n=10). This increase in excitability was accompanied by a decrease in the rheobase current. The SKF 38393-enhanced excitability was dose-dependent and could be blocked by bath administration of the D1 receptor antagonist SCH 23390 (5 and 10 microM). Administration of the GABA antagonist bicuculline (7 microM) plus the N-methyl-D-aspartate channel blocker CPP (10 microM) produced an additional increase in the excitability of prefrontal cortex neurons that was not dependent on the membrane potential. From these data we suggest that dopamine exerts state-dependent modulatory effects on the excitability of neurons in deep layers of the prefrontal cortex.

2,3,4,5-Tetrahydro-7,8-dihydroxy-1-phenyl-1H-3-ben↗
PubMed1998

Effects of tapering geometry and inhomogeneous ion channel distribution in a neuron model.

Recent experiments have produced direct evidence on the existence of various dendritic voltage-gated ion channels, indicating that these neuronal components are not just a passive medium for the propagation of synaptic excitation but a putative source of neuronal excitability that is reflected in the activity patterns occurring on the soma. In order to study possible changes in neuronal excitability when the distribution of dendritic voltage-activated channels is non-uniform, and the dendritic geometry is not necessarily cylindric, we have developed a neuron model that incorporates two voltage-activated currents [I(Na) and I(K)], and in which space-dependent distributions of the system parameters can be treated in a mathematically simple and efficient way. Simulation results with the model showed that both linearly and exponentially tapering geometries led to marked anisotropy of the propagation of excitation, favouring the soma-to-dendrite direction. Exponentially decaying densities of dendritic voltage-activated channels, with appropriate choice of the parameters, induced bistable behaviour between the normal resting state and an intrinsic, sustained oscillation with cylindric as well as linear and exponential tapering dendritic geometry. Bistability could not be evoked when the model was reduced to a space-independent one (point-like soma). These results suggest that both tapering dendritic geometry and inhomogeneous distribution of ion channels may crucially affect the propagation and integration of synaptic potentials, and that changes in dendritic channel densities might underlie pathological electrophysiological activities.

Action Potentials↗
PubMed2001

The Bifurcating Neuron network 1.

The Bifurcating Neuron (BN), a chaotic integrate-and-fire neuron, is a model of a neuron augmented by coherent modulation from its environment. The BN is mathematically equivalent to the sine-circle map, and this equivalence relationship allowed us to apply the mathematics of one-dimensional maps to the design of BN networks. The study of symmetry in the BN revealed that the BN can be configured to exhibit bistability that is controlled by attractor-merging crisis. Also, the symmetry of the bistability can be controlled by the introduction of a sinusoidal fluctuation to the threshold level of the BN. These two observations led us to the design of the BN Network 1 (BNN-1), a chaotic pulse-coupled neural network exhibiting associative memory. In numerical simulations, the BNN-1 showed a better performance than the continuous-time Hopfield network, as far as the spurious-minima problem is concerned and exhibited many biologically plausible characteristics.

Action Potentials↗
PubMed1991

A conformational switch is associated with receptor affinity in peptides derived from the CD4-binding domain of gp120 from HIV I.

A 15-residue region within the CD4-binding domain of gp120 from HIV I was identified with use of folding algorithms as conserving the potential for forming a particular secondary structure throughout 11 sequenced HIV strains. The region chosen has a potential for forming both beta-sheet and alpha-helix; the helical form would be amphipathic with the five hydrophobic residues all totally or functionally conserved. Five peptides were synthesized corresponding to this region in strain LAV and the strain most highly divergent from it in primary structure (Z3) plus three additional peptides with critical substitutions in the LAV sequence. The conformation of these five peptides was examined under various conditions with circular dichroism, and the results were compared with the ability of each peptide to bind to a CD4-expressing strain of HeLa cells (HeLa T4). In solution, the unmodified peptides exhibit a bistable structure, existing as beta-sheet in dilute buffer and converting to alpha-helix under more apolar conditions. The transition is reversible and sharp, occurring at a particular point in the polar/apolar gradient with virtually no intermediate state. The ability to undergo this bistable flip is closely associated with binding ability, amino acid substitutions that eliminate binding ability also eliminating the switch, and vice versa. The transition thus may reflect conformational changes occurring in this region of gp120 as it binds to the CD4 receptor.

Algorithms↗
PubMed2001

Molecular-based electronically switchable tunnel junction devices.

Solid-state tunnel junction devices were fabricated from Langmuir Blodgett molecular monolayers of a bistable [2]catenane, a bistable [2]pseudorotaxane, and a single-station [2]rotaxane. All devices exhibited a (noncapacitive) hysteretic current-voltage response that switched the device between high- and low-conductivity states, although control devices exhibited no such response. Correlations between the structure and solution-phase dynamics of the molecular and supramolecular systems, the crystallographic domain structure of the monolayer film, and the room-temperature device performance characteristics are reported.

Journal Article↗
PubMed2004

Two-state folding observed in individual protein molecules.

The folding dynamics of small proteins are often described in terms of a simple two-state kinetic model. Within this notion, the behavior of individual molecules is expected to be stochastic, with a protein molecule residing in either the unfolded or the folded state for extended periods of time, with intermittent rapid jumps across the free energy barrier. However, a direct observation of this bistable behavior has not been made to date. Rather, previous reports of folding trajectories of individual proteins have shown an unexpected degree of complexity. This raises the question whether the simple kinetic properties derived from classical experiments on large ensembles of molecules are reflected in the folding paths taken by individual proteins. Here we report single-molecule folding/unfolding trajectories observed by fluorescence resonance energy transfer for a protein that meets all criteria of a two state-system. The trajectories, measured on molecules immobilized in lipid vesicles, demonstrate the anticipated bistable behavior, with steplike transitions between folded and unfolded conformations. They further allow us to put an upper bound on the barrier crossing time.

Bacterial Proteins↗
PubMed2005

Ribose 2'-F labeling: a simple tool for the characterization of RNA secondary structure equilibria by 19F NMR spectroscopy.

We present a facile 19F NMR spectroscopic approach for the characterization of bistable RNA. The concept is based on the site-specific labeling of RNA with single 2'-deoxy-2'-fluoro (2'-F) nucleosides. Depending on the position of the 2'-F label (either within a double helix or a single-stranded region), significantly different 19F chemical shifts were observed and assigned to the particular alternative folds. This has been exemplified for a series of bistable RNAs. The approach is promising for the detailed investigation of complex RNA folding pathways.

Fluorine↗
PubMed2006

Chiroptical and computational studies of a bridled chiroporphyrin and of its nickel(II), copper(II), and zinc(II) complexes.

Circular dichroism (CD) spectra and density functional theory (DFT) calculations are reported for a series of conformationally bistable chiroporphyrins with 8-methylene bridles MBCP-8, which can display either an alphaalphaalphaalpha or an alphabetaalphabeta orientation of their meso substituents. From DFT geometry optimizations, the most stable form of ZnBCP-8 is found to be the alphaalphaalphaalpha conformer. By passing to NiBCP-8, there is a strong stabilization of the alphabetaalphabeta conformation with respect to the alphaalphaalphaalpha conformation, consistent with the X-ray structures of alphaalphaalphaalpha-ZnBCP-8 and alphabetaalphabeta-NiBCP-8. A correlation between the sign of the CD signal in the Soret region and the conformation of the BCP-8 compounds is reported: the alphaalphaalphaalpha conformers H2BCP-8 and ZnBCP-8 show a positive CD signal, whereas the alphabetaalphabeta conformers NiBCP-8 and CuBCP-8 exhibit a negative signal. The possible contributions to the rotational strengths of alphabetaalphabeta-NiBCP-8 and alphaalphaalphaalpha-ZnBCP-8, calculated on the basis of their crystal structures, have been analyzed. The CD signals are found to result from a combination of both the inherent chirality of the porphyrin and of extrinsic contributions due to the chiral bridles. These results may have a broad significance for understanding the chiroptical properties of chiral porphyrins and hemoproteins and for monitoring stimuli-responsive, conformationally bistable chiroporphyrin compounds.

Journal Article↗
PubMed2005

Modeling chlorite-iodide reaction dynamics using a chlorine dioxide-iodide reaction mechanism.

The mechanism of Lengyel, Li, Kustin, and Epstein (J. Am. Chem. Soc. 1996, 118, 3708) for the oscillatory chlorine dioxide-iodide reaction accurately models the reaction in closed and open systems. We investigated whether this mechanism minus the single reaction involving chlorine dioxide models the chlorite-iodide reaction equally well. It agrees qualitatively with clock reaction results. As for open system dynamics, the mechanism predicts the existence of two steady states and bistability in very nearly the same regions where these features are found experimentally in the pH range 2-4. A discrepancy in the range of bistability emerges as pH decreases, and it cannot be remedied by taking into account chlorous acid decomposition. That we were unable to locate an oscillatory region is of greater significance. Because the chlorite-iodide reaction is sensitive to mixing effects, we incorporated a two-parameter model of imperfect mixing but still found no oscillations at physically reasonable parameter values. These discrepancies strongly suggest that to obtain predictive utility for the chlorite-iodide reaction, revision of the chlorine dioxide-iodide mechanism is required.

Journal Article↗
PubMed2005

Kinetic studies on the tensile state of water in trees.

The solar-powered generation and turnover of tensile, cohesive water in trees is described as a kinetic phenomenon of irreversible thermodynamics. A molecular kinetic model for tensile water formation and turnover is presented, which is found to be mathematically equivalent with an autocatalytic reaction (Brusselator). It is also shown to be consistent with the van der Waals equation for real liquid-gas systems, which empirically considers intermolecular forces. It can therefore be used to explain both the irreversible thermodynamics and the kinetics of the tensile liquid state of water. A nonlinear bistable evaporation behavior of tensile water is predicted, which has not yet been experimentally characterized in trees. Conventional sap flow techniques in combination with infrared imaging of heat flow around a local heat source were used to study the dynamics and energetics of water transport of trees during the eclipse of August 11, 1999. The evaporative "pulling force" in a tree was demonstrated with infrared techniques and shown to respond within seconds. While the ambient temperature during the eclipse did not drop by more than 2 degrees C, evaporative water transport was reduced by a factor of up to 2-3. The expected hysteresis (with an up to 50% decrease in energy-conversion-related entropy production) was measured, reflecting a bistable mode of conversion of solar energy into tensile water flow. This nonlinear (autocatalytic) phenomenon, together with tensile molecular order, damped the oscillating behavior of xylem tensile water, and its occasional all-or-none rupture (cavitation) can thus be explained by the nonlinear nature of intermolecular forces active in the water conduit/parenchyma environment. This characterizes the physical chemistry and energetics of tensile water in trees as an active-solar-energy-driven self-organizing process. Water is handled in the form of microcanonical ensembles and transformed into a stretched, metastable icelike state with stronger hydrogen bonding and increased heat of evaporation. The discussed model may open new opportunities for research and understanding toward innovative water technologies.

Algorithms↗
PubMed1999

Attractors and pathological aspects in excitable cells.

In this article, physiological and pathological forms of excitability are studied in a two-dimensional electrical model of excitable cell endowed with a generic inward persistent conductance. Bifurcation analysis of the model is performed as a function of the maximal inward persistent conductance, the input current, or the voltage dependency of the activation function. Several discharge modes are exhibited, including: (1) a basic mode that corresponds to a resting potential and production of action potential; (2) bistability between resting potential and self-sustained spiking; (3) a pacemaker mode of discharge; and (4) bistability between resting potential and plateau potential. These behaviours can be compared to experimentally described physiological and pathological forms of excitability that depend upon inward persistent conductances. In the results obtained, attractors allow for a qualitative description of physiological and pathological states. However, it is not possible to obtain an unambiguous identification of particular 'physiological attractors' or 'pathological attractors'. In the perspective of the theory of dynamical systems, we suggest that pathological states can be modelled in two different ways, i.e. by bifurcation (as in the present model) or by perturbation. We also highlight some other theoretical concepts that may be relevant to a theoretical description of pathology.

Animals↗
PubMedDate not supplied

An analysis of the reliability phenomenon in the FitzHugh-Nagumo model.

The reliability of single neurons on realistic stimuli has been experimentally confirmed in a wide variety of animal preparations. We present a theoretical study of the reliability phenomenon in the FitzHugh-Nagumo model on white Gaussian stimulation. The analysis of the model's dynamics is performed in three regimes-the excitable, bistable, and oscillatory ones. We use tools from the random dynamical systems theory, such as the pullbacks and the estimation of the Lyapunov exponents and rotation number. The results show that for most stimulus intensities, trajectories converge to a single stochastic equilibrium point, and the leading Lyapunov exponent is negative. Consequently, in these regimes the discharge times are reliable in the sense that repeated presentation of the same aperiodic input segment evokes similar firing times after some transient time. Surprisingly, for a certain range of stimulus intensities, unreliable firing is observed due to the onset of stochastic chaos, as indicated by the estimated positive leading Lyapunov exponents. For this range of stimulus intensities, stochastic chaos occurs in the bistable regime and also expands in adjacent parts of the excitable and oscillating regimes. The obtained results are valuable in the explanation of experimental observations concerning the reliability of neurons stimulated with broad-band Gaussian inputs. They reveal two distinct neuronal response types. In the regime where the first Lyapunov has negative values, such inputs eventually lead neurons to reliable firing, and this suggests that any observed variance of firing times in reliability experiments is mainly due to internal noise. In the regime with positive Lyapunov exponents, the source of unreliable firing is stochastic chaos, a novel phenomenon in the reliability literature, whose origin and function need further investigation.

Computer Simulation↗
PubMedDate not supplied

Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics.

Behavior of a network of neurons is closely tied to the properties of the individual neurons. We study this relationship in models of layer II stellate cells (SCs) of the medial entorhinal cortex. SCs are thought to contribute to the mammalian theta rhythm (4-12 Hz), and are notable for the slow ionic conductances that constrain them to fire at rates within this frequency range. We apply "spike time response" (STR) methods, in which the effects of synaptic perturbations on the timing of subsequent spikes are used to predict how these neurons may synchronize at theta frequencies. Predictions from STR methods are verified using network simulations. Slow conductances often make small inputs "effectively large"; we suggest that this is due to reduced attractiveness or stability of the spiking limit cycle. When inputs are (effectively) large, changes in firing times depend nonlinearly on synaptic strength. One consequence of nonlinearity is to make a periodically firing model skip one or more beats, often leading to the elimination of the anti-synchronous state in bistable models. Biologically realistic membrane noise makes such "cycle skipping" more prevalent, and thus can eradicate bistability. Membrane noise also supports "sparse synchrony," a phenomenon in which subthreshold behavior is uncorrelated, but there are brief periods of synchronous spiking.

Animals↗