Noise-assisted spike propagation in myelinated neurons

We consider noise-assisted spike propagation in myelinated axons within a multi-compartment stochastic Hodgkin-Huxley model. The noise originates from a finite number of ion channels in each node of Ranvier. For the subthreshold internodal electric coupling, we show that (i) intrinsic noise removes the sharply defined threshold for spike propagation from node to node, and (ii) there exists an optimum number of ion channels which allows for the most efficient signal propagation and it corresponds to the actual physiological values.Comment: 8 pages, 12 figures, accepted for publication in Phys. Rev.

Noise analysis of ion channels in non-space-clamped cables: estimates of channel parameters in olfactory cilia

Ion channels in the cilia of olfactory neurons are part of the transduction machinery of olfaction. Odorant stimuli have been shown to induce a biphasic current response, consisting of a cAMP-activated current and a Ca(2+)-activated Cl- current. We have developed a noise analysis method to study ion channels in leaky cables, such as the olfactory cilium, under non-space-clamp conditions. We performed steady-state noise analysis on ligand-induced currents in excised cilia, voltage-clamped at input and internally perfused with cAMP or Ca2+. The cAMP-activated channels analyzed by this method gave results similar to those of single-channel recordings (gamma = 8.3 pS). Single-channel currents have not yet been recorded for the Ca(2+)-activated Cl- channels. Using our noise analysis method, we estimate a unit conductance, gamma = 0.8 pS, for these channels. The density of channels was found to be approximately 70 channels/micron2 for both channel species

Instability of the Gravitational N-Body Problem in the Large-N Limit

We use a systolic N-body algorithm to evaluate the linear stability of the gravitational N-body problem for N up to 1.3 x 10^5, two orders of magnitude greater than in previous experiments. For the first time, a clear ~ln N-dependence of the perturbation growth rate is seen. The e-folding time for N = 10^5 is roughly 1/20 of a crossing time.Comment: Accepted for publication in The Astrophysical Journa

Stochastic resonance as a collective property of ion channel assemblies

By use of a stochastic generalization of the Hodgkin-Huxley model we investigate both the phenomena of stochastic resonance (SR) and coherence resonance (CR) in variable size patches of an excitable cell membrane. Our focus is on the challenge how internal noise stemming from individual ion channels does affect collective properties of the whole ensemble. We investigate both an unperturbed situation with no applied stimuli and one in which the membrane is stimulated externally by a periodic signal and additional external noise. For the nondriven case, we demonstrate the existence of an optimal size of the membrane patch for which the internal noise causes a most regular spike activity. This phenomenon shall be termed intrinsic CR. In presence of an applied periodic stimulus we demonstrate that the signal-to-noise ratio (SNR) exhibits SR vs. decreasing patch size, or vs. increasing internal noise strength, respectively. Moreover, we demonstrate that conventional SR vs. the external noise intensity occurs only for sufficiently large membrane patches, when the intensity of internal noise is below its optimal level. Thus, biological SR seemingly is rooted in the collective properties of large ion channel ensembles rather than in the individual stochastic dynamics of single ion channels.Comment: 9 pages, 2 figure

A numerical comparison of theories of violent relaxation

Using N-body simulations with a large set of massless test particles we compare the predictions of two theories of violent relaxation, the well known Lynden-Bell theory and the more recent theory by Nakamura. We derive ``weaken'' versions of both theories in which we use the whole equilibrium coarse-grained distribution function as a constraint instead of the total energy constraint. We use these weaken theories to construct expressions for the conditional probability $K_i(\tau)$ that a test particle initially at the phase-space coordinate $\tau$ would end-up in the $i$'th macro-cell at equilibrium. We show that the logarithm of the ratio $R_{ij}(\tau) \equiv K_i(\tau)/K_j(\tau)$ is directly proportional to the initial phase-space density $f_0(\tau)$ for the Lynden-Bell theory and inversely proportional to $f_0(\tau)$ for the Nakamura theory. We then measure $R_{ij}(\tau)$ using a set of N-body simulations of a system undergoing a gravitational collapse to check the validity of the two theories of violent relaxation. We find that both theories are at odds with the numerical results, qualitatively and quantitatively.Comment: Replaced with a revised version, which is now accepted to MNRAS. LaTeX, 12 pages, 6 figure

Effect of channel block on the spiking activity of excitable membranes in a stochastic Hodgkin-Huxley model

The influence of intrinsic channel noise on the spontaneous spiking activity of poisoned excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic dynamics of individual ion channels is known to affect the collective properties of the whole ion channel cluster. For example, there exists an optimal size of the membrane patch for which the internal noise alone causes a regular spontaneous generation of action potentials. In addition to varying the size of ion channel clusters, living organisms may adapt the densities of ion channels in order to optimally regulate the spontaneous spiking activity. The influence of channel block on the excitability of a membrane patch of certain size is twofold: First, a variation of ion channel densities primarily yields a change of the conductance level. Second, a down-regulation of working ion channels always increases the channel noise. While the former effect dominates in the case of sodium channel block resulting in a reduced spiking activity, the latter enhances the generation of spontaneous action potentials in the case of a tailored potassium channel blocking. Moreover, by blocking some portion of either potassium or sodium ion channels, it is possible to either increase or to decrease the regularity of the spike train.Comment: 10 pages, 3 figures, published 200

Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems

Voltage-dependent ion channels determine the electric properties of axonal cell membranes. They not only allow the passage of ions through the cell membrane but also contribute to an additional charging of the cell membrane resulting in the so-called capacitance loading. The switching of the channel gates between an open and a closed configuration is intrinsically related to the movement of gating charge within the cell membrane. At the beginning of an action potential the transient gating current is opposite to the direction of the current of sodium ions through the membrane. Therefore, the excitability is expected to become reduced due to the influence of a gating current. Our stochastic Hodgkin-Huxley like modeling takes into account both the channel noise -- i.e. the fluctuations of the number of open ion channels -- and the capacitance fluctuations that result from the dynamics of the gating charge. We investigate the spiking dynamics of membrane patches of variable size and analyze the statistics of the spontaneous spiking. As a main result, we find that the gating currents yield a drastic reduction of the spontaneous spiking rate for sufficiently large ion channel clusters. Consequently, this demonstrates a prominent mechanism for channel noise reduction.Comment: 18 page

The role of input noise in transcriptional regulation

Even under constant external conditions, the expression levels of genes fluctuate. Much emphasis has been placed on the components of this noise that are due to randomness in transcription and translation; here we analyze the role of noise associated with the inputs to transcriptional regulation, the random arrival and binding of transcription factors to their target sites along the genome. This noise sets a fundamental physical limit to the reliability of genetic control, and has clear signatures, but we show that these are easily obscured by experimental limitations and even by conventional methods for plotting the variance vs. mean expression level. We argue that simple, global models of noise dominated by transcription and translation are inconsistent with the embedding of gene expression in a network of regulatory interactions. Analysis of recent experiments on transcriptional control in the early Drosophila embryo shows that these results are quantitatively consistent with the predicted signatures of input noise, and we discuss the experiments needed to test the importance of input noise more generally.Comment: 11 pages, 5 figures minor correction

P/2010A2 LINEAR - I: An impact in the Asteroid Main Belt

Comet P/2010A2 LINEAR is a good candidate for membership with the Main Belt Comet family. It was observed with several telescopes (ESO NTT, La Silla; Gemini North, Mauna Kea; UH 2.2m, Mauna Kea) from 14 Jan. until 19 Feb. 2010 in order to characterize and monitor it and its very unusual dust tail, which appears almost fully detached from the nucleus; the head of the tail includes two narrow arcs forming a cross. The immediate surroundings of the nucleus were found dust-free, which allowed an estimate of the nucleus radius of 80-90m. A model of the thermal evolution indicates that such a small nucleus could not maintain any ice content for more than a few million years on its current orbit, ruling out ice sublimation dust ejection mechanism. Rotational spin-up and electrostatic dust levitations were also rejected, leaving an impact with a smaller body as the favoured hypothesis, and ruling out the cometary nature of the object. The impact is further supported by the analysis of the tail structure. Finston-Probstein dynamical dust modelling indicates the tail was produced by a single burst of dust emission. More advanced models, independently indicate that this burst populated a hollow cone with a half-opening angle alpha~40degr and with an ejection velocity v_max ~ 0.2m/s, where the small dust grains fill the observed tail, while the arcs are foreshortened sections of the burst cone. The dust grains in the tail are measured to have radii between a=1-20mm, with a differential size distribution proportional to a^(-3.44 +/- 0.08). The dust contained in the tail is estimated to at least 8x10^8kg, which would form a sphere of 40m radius. Analysing these results in the framework of crater physics, we conclude that a gravity-controlled crater would have grown up to ~100m radius, i.e. comparable to the size of the body. The non-disruption of the body suggest this was an oblique impact.Comment: 15 pages, 11 figures, in pres