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

Effective rate equations for the over-damped motion in fluctuating potentials

We discuss physical and mathematical aspects of the over-damped motion of a Brownian particle in fluctuating potentials. It is shown that such a system can be described quantitatively by fluctuating rates if the potential fluctuations are slow compared to relaxation within the minima of the potential, and if the position of the minima does not fluctuate. Effective rates can be calculated; they describe the long-time dynamics of the system. Furthermore, we show the existence of a stationary solution of the Fokker-Planck equation that describes the motion within the fluctuating potential under some general conditions. We also show that a stationary solution of the rate equations with fluctuating rates exists.Comment: 18 pages, 2 figures, standard LaTeX2

Correlation studies of open and closed states fluctuations in an ion channel: Analysis of ion current through a large conductance locust potassium channel

Ion current fluctuations occurring within open and closed states of large conductance locust potassium channel (BK channel) were investigated for the existence of correlation. Both time series, extracted from the ion current signal, were studied by the autocorrelation function (AFA) and the detrended fluctuation analysis (DFA) methods. The persistent character of the short- and middle-range correlations of time series is shown by the slow decay of the autocorrelation function. The DFA exponent $\alpha$ is significantly larger than 0.5. The existence of strongly-persistent long-range correlations was detected only for closed-states fluctuations, with $\alpha=0.98\pm0.02$. The long-range correlation of the BK channel action is therefore determined by the character of closed states. The main outcome of this study is that the memory effect is present not only between successive conducting states of the channel but also independently within the open and closed states themselves. As the ion current fluctuations give information about the dynamics of the channel protein, our results point to the correlated character of the protein movement regardless whether the channel is in its open or closed state.Comment: 12 pages, 5 figures; to be published in Phys. Rev.

Stochastic Resonance in Ion Channels Characterized by Information Theory

We identify a unifying measure for stochastic resonance (SR) in voltage dependent ion channels which comprises periodic (conventional), aperiodic and nonstationary SR. Within a simplest setting, the gating dynamics is governed by two-state conductance fluctuations, which switch at random time points between two values. The corresponding continuous time point process is analyzed by virtue of information theory. In pursuing this goal we evaluate for our dynamics the tau-information, the mutual information and the rate of information gain. As a main result we find an analytical formula for the rate of information gain that solely involves the probability of the two channel states and their noise averaged rates. For small voltage signals it simplifies to a handy expression. Our findings are applied to study SR in a potassium channel. We find that SR occurs only when the closed state is predominantly dwelled. Upon increasing the probability for the open channel state the application of an extra dose of noise monotonically deteriorates the rate of information gain, i.e., no SR behavior occurs.Comment: 10 pages, 2 figures, to appear in Phys. Rev.

Optically levitated nanoparticle as a model system for stochastic bistable dynamics

Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work contributes to showing the use of levitated nanoparticles as a model system for stochastic bistable dynamics, with applications to a wide variety of fields.inancial support from the ERC- QnanoMECA (Grant No. 64790), the Spanish Ministry of Economy and Competitiveness, under grant FIS2016-80293-R and through the ‘Severo Ochoa’ Programme for Centres of Excellence in R&D (SEV-2015-0522), Fundació Privada CELLEX and from the CERCA Programme/Generalitat de Catalunya. J.G. has been supported by H2020-MSCA-IF-2014 under REA grant Agreement No. 655369. L.R. acknowledges support from an ETH Marie Curie Cofund Fellowship

Photoreceptor sensitivity and the shot noise of chemical processes.

The general modeling of dose-response curves to very low stimuli in a photosensory-effector system is critically reshaped starting from basic assumptions on the fluctuations of chemical signals inside the receptor cell, which add to those of the stimulus itself, both arising from their granular (or quantal) structure. We have shown, both through the analytical treatment of a simple kinetic scheme and by means of Monte Carlo simulations of the same, that shot noise arising from chemical transduction ("chemical shot noise") contributes considerably to the output noise of the receptor-effector system, thus affecting both the shape and the abscissa shift of dose-response curves under these conditions; the latter phenomenon has indeed been reported in Halobacterium halobium. After evaluating the general properties of a single-step amplifying mechanism, the effects of introducing several low-amplifying steps in cascade were investigated briefly. The results obtained were qualitatively and quantitatively at variance from those of earlier models on the same phenomenon, and the discrepancies are discussed in order to highlight the fundamental contribution of chemical shot noise to the response of any kind of sensory system to very low stimuli