452 research outputs found
Modeling rhythmic patterns in the hippocampus
We investigate different dynamical regimes of neuronal network in the CA3
area of the hippocampus. The proposed neuronal circuit includes two fast- and
two slowly-spiking cells which are interconnected by means of dynamical
synapses. On the individual level, each neuron is modeled by FitzHugh-Nagumo
equations. Three basic rhythmic patterns are observed: gamma-rhythm in which
the fast neurons are uniformly spiking, theta-rhythm in which the individual
spikes are separated by quiet epochs, and theta/gamma rhythm with repeated
patches of spikes. We analyze the influence of asymmetry of synaptic strengths
on the synchronization in the network and demonstrate that strong asymmetry
reduces the variety of available dynamical states. The model network exhibits
multistability; this results in occurrence of hysteresis in dependence on the
conductances of individual connections. We show that switching between
different rhythmic patterns in the network depends on the degree of
synchronization between the slow cells.Comment: 10 pages, 9 figure
Fixed Point and Aperiodic Tilings
An aperiodic tile set was first constructed by R.Berger while proving the
undecidability of the domino problem. It turned out that aperiodic tile sets
appear in many topics ranging from logic (the Entscheidungsproblem) to physics
(quasicrystals) We present a new construction of an aperiodic tile set that is
based on Kleene's fixed-point construction instead of geometric arguments. This
construction is similar to J. von Neumann self-reproducing automata; similar
ideas were also used by P. Gacs in the context of error-correcting
computations. The flexibility of this construction allows us to construct a
"robust" aperiodic tile set that does not have periodic (or close to periodic)
tilings even if we allow some (sparse enough) tiling errors. This property was
not known for any of the existing aperiodic tile sets.Comment: v5: technical revision (positions of figures are shifted
Noise Induced Complexity: From Subthreshold Oscillations to Spiking in Coupled Excitable Systems
We study stochastic dynamics of an ensemble of N globally coupled excitable
elements. Each element is modeled by a FitzHugh-Nagumo oscillator and is
disturbed by independent Gaussian noise. In simulations of the Langevin
dynamics we characterize the collective behavior of the ensemble in terms of
its mean field and show that with the increase of noise the mean field displays
a transition from a steady equilibrium to global oscillations and then, for
sufficiently large noise, back to another equilibrium. Diverse regimes of
collective dynamics ranging from periodic subthreshold oscillations to
large-amplitude oscillations and chaos are observed in the course of this
transition. In order to understand details and mechanisms of noise-induced
dynamics we consider a thermodynamic limit of the ensemble, and
derive the cumulant expansion describing temporal evolution of the mean field
fluctuations. In the Gaussian approximation this allows us to perform the
bifurcation analysis; its results are in good agreement with dynamical
scenarios observed in the stochastic simulations of large ensembles
Waiting time distributions for clusters of complex molecules
Waiting time distributions are in the core of theories for a large variety of subjects ranging from the analysis of patch clamp records to stochastic excitable systems. Here, we present a novel exact method for the calculation of waiting time distributions for state transitions of complex molecules with independent subunit dynamics. The absorbing state is a specific set of subunit states, i.e. is defined on the molecule level. Consequently, we formulate the problem as a random walk in the molecule state space. The subunits can possess an arbitrary number of states and any topology of transitions between them. The method circumvents problems arising from combinatorial explosion due to subunit coupling and requires solutions of the subunit master equation only
Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map
We rationalize the somewhat surprising efficacy of the Hadamard transform in
simplifying the eigenstates of the quantum baker's map, a paradigmatic model of
quantum chaos. This allows us to construct closely related, but new, transforms
that do significantly better, thus nearly solving for many states of the
quantum baker's map. These new transforms, which combine the standard Fourier
and Hadamard transforms in an interesting manner, are constructed from
eigenvectors of the shift permutation operator that are also simultaneous
eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal)
symmetry.Comment: Version to appear in J. Phys. A. Added discussions; modified title;
corrected minor error
Noise Can Reduce Disorder in Chaotic Dynamics
We evoke the idea of representation of the chaotic attractor by the set of
unstable periodic orbits and disclose a novel noise-induced ordering
phenomenon. For long unstable periodic orbits forming the strange attractor the
weights (or natural measure) is generally highly inhomogeneous over the set,
either diminishing or enhancing the contribution of these orbits into system
dynamics. We show analytically and numerically a weak noise to reduce this
inhomogeneity and, additionally to obvious perturbing impact, make a
regularizing influence on the chaotic dynamics. This universal effect is rooted
into the nature of deterministic chaos.Comment: 11 pages, 5 figure
Selection of Inhibitor-Resistant Viral Potassium Channels Identifies a Selectivity Filter Site that Affects Barium and Amantadine Block
BACKGROUND:Understanding the interactions between ion channels and blockers remains an important goal that has implications for delineating the basic mechanisms of ion channel function and for the discovery and development of ion channel directed drugs. METHODOLOGY/PRINCIPAL FINDINGS:We used genetic selection methods to probe the interaction of two ion channel blockers, barium and amantadine, with the miniature viral potassium channel Kcv. Selection for Kcv mutants that were resistant to either blocker identified a mutant bearing multiple changes that was resistant to both. Implementation of a PCR shuffling and backcrossing procedure uncovered that the blocker resistance could be attributed to a single change, T63S, at a position that is likely to form the binding site for the inner ion in the selectivity filter (site 4). A combination of electrophysiological and biochemical assays revealed a distinct difference in the ability of the mutant channel to interact with the blockers. Studies of the analogous mutation in the mammalian inward rectifier Kir2.1 show that the T-->S mutation affects barium block as well as the stability of the conductive state. Comparison of the effects of similar barium resistant mutations in Kcv and Kir2.1 shows that neighboring amino acids in the Kcv selectivity filter affect blocker binding. CONCLUSIONS/SIGNIFICANCE:The data support the idea that permeant ions have an integral role in stabilizing potassium channel structure, suggest that both barium and amantadine act at a similar site, and demonstrate how genetic selections can be used to map blocker binding sites and reveal mechanistic features
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