Fluctuation and Noise Letters

Hair cells are the mechanoelectrical transducers in the auditory system of many species, including humans. Experiments show that transduction in individual hair cells displays stochastic resonance, with optimum response at the natural noise level of living cells. We find that many of the observed features are captured by a simple version of a physiologically faithful model of the transduction mechanism. These findings may resolve a longstanding puzzle in evolutionary biology concerning the structure of the cochlea.

Although stochastic resonance has been demonstrated for many physical and biological systems, in both dynamic and threshold forms, its study in whole human beings presents special problems. Psychophysics provides theoretical and methodological tools for measuring information processing by humans, but modern psychophysics seems to be incompatible with some of the concepts of current theories of stochastic resonance. In this paper I review some of these problems, providing suggestions for solutions where none have as yet appeared. In particular, I discuss incompatibilities between signal detection theory and threshold stochastic resonance, and the problem of the effect of noise on information transfer across a "soft" threshold.

Understanding the role of noise at cellular and higher hierarchical levels depends on our knowledge of the physical mechanisms of its generation. Conversely, noise is a rich source of information about these mechanisms. Using channel-forming protein molecules reconstituted into artificial 5-nm-thick insulating lipid films, it is possible to investigate noise in single-molecule experiments and to relate its origins to protein function. Recent progress in this field is reviewed with an emphasis on how this experimental technique can be used to study low-frequency protein dynamics, including not only reversible ionization of sites on the channel-forming protein molecule, but also molecular mechanisms of 1/f-noise generation. Several new applications of the single-molecule noise analysis to membrane transport problem are also addressed. Among those is a study on antibiotic translocation across bacterial walls. High-resolution recording of ionic current through the single channel, formed by the general bacterial porin, OmpF, enables us to resolve single-molecule events of antibiotic translocation.

We consider the statistical properties of action potentials generated by clusters of sodium and potassium channels due to channel noise and/or external stimulation. Since the fluctuations are related to the cluster size, a size-resonance effect — analog to stochastic resonance — is observed that facilitates optimal decoding of small external stimuli at optimal cluster sizes. Furthermore, in analogy to the coherence resonance effect, the channel-noise induced firing patterns exhibit a resonant-like temporal coherence as a function of the cluster size even in the absence of a periodic stimulus. In the presence of additional synaptic noise, SR occurs only for large cluster sizes which possess suboptimal internal noise levels.

We formulate and argue in favor of the following conjecture: There exists an intimate connection between Wigner's quantum mechanical phase space distribution function and classical Fresnel optics.

In this article we review the application of the synchronization theory to the analysis of multivariate biological signals. We address the problem of phase estimation from data and detection and quantification of weak interaction, as well as quantification of the direction of coupling. We discuss the potentials as well as limitations and misinterpretations of the approach.

We study the problem of detecting a small dc signal by quantifying its effect on the mean difference ΔT in residence times in the stable steady states of a bistable dynamical measurement device, in the presence of a noise-floor and a known time-sinusoidal bias signal. Errors in the measurement process occur due to a finite observation time that is present in most practical scenarios; in turn, noise degrades the measurement. Adjusting the bias signal amplitude to a slightly subthreshold operating regime, leads to a non-monotonic dependence of the (suitably defined) error on the noise intensity; at a critical noise intensity, the error is minimized. This phenomenon, reminiscent of the well-known Stochastic Resonance effect [1–4], appears to be most pronounced for subthreshold bias signals in the strongly nonlinear response regime. The results can be applied to a variety of nonlinear systems, including neurons, that operate in the time-domain.

Recently a new technique for generating linear surrogates of multichannel data was introduced. This technique, referred to as the coherent digitally filtered surrogate method, preserves both the individual power spectra, and the coherence function, of the original data. This method is somewhat limited in that it can only be applied to multichannel data in which the cross-spectrum is real. We present here an alteration to this algorithm that can be used to test any linear-correlation model, with arbitrary complex cross-spectra. This is of particular interest for experiments in which two channels are coupled with some time lag, and it is necessary to determine if the coupling is linear. We also demonstrate that this algorithm can be used along with the synchronization to provide a much better estimate for the degree of phase-locking between two signals than the coherence analysis techniques traditionally used in neuroscience.

The error rate in a current-controlled logic microprocessor dominated by shot noise has been investigated. It is shown that the error rate increases very rapidly with increasing cutoff frequency. The maximum clock frequency of the processor, which works without errors, is obtained as a function of the operational current. The information channel capacity of the system is also studied.

Stochastic phase synchronization is studied in an array of coupled neurons that are capable of exhibiting diverse bursting behaviors as a system parameter is tuned. It is found that synchronization occurs for lower coupling constants when the neurons are initially in a bursting state. Neurons not initially in a bursting state begin to exhibit bursting behavior concurrently with the onset of synchronization. The system passes through various synchronization regimes as the coupling constant is increased, with the number of spikes per burst increasing in each window of synchronization. In addition, spatial organization, measured by the distribution of local phase differences, is observed during the synchronization windows.

The issue of noise in biological systems is primarily a question of relations: between order and disorder, between stability and flexibility, and between processes at different temporal and spatial scales. In this paper, we use computational models of cortical structures to investigate relations between structure, dynamics, and function of such systems. In particular, we investigate the nature and role of noise at different organizational levels of the nervous system, emphasizing the neural network level. We show that microscopic noise can induce global network oscillations and pseudo-chaos, which make neural information processing more efficient. We find optimal noise levels for which the convergence to stored memory attractor states reaches a maximum, akin to stochastic resonance. We finally discuss the relation between neural and mental processes, and how computational models may relate to real neural systems.

The fluctuations observed in the task of stick balancing at the fingertip exhibit many of the properties predicted to occur in parametric stochastic dynamical systems, namely intermittency, truncated Lévy flights and truncated Lévy distributions. The development of virtual balancing tasks that involve the interplay between a human and computer and that exhibit the same dynamical properties as seen for stick balancing opens the door for experimental investigations into the nature of the neural motor control mechanisms that underlie these phenomena.

Transmission of stimulus-locked responses is studied in a model that shares basic features with stimulated neuronal rhythms: In two phase oscillators with bistable coupling and noise one oscillator is stimulated. The model presents a mechanism which causes a response clustering, i.e. a switching between two different responses across trials, without extinction of the averaged response (calculated over all trials). Transmission times are determined for all trials as well as for the two clusters separately with standard averaged responses. Transmission times calculated in this standard way correspond to the phase difference in the different stable synchronized states (when calculated for the two clusters separately) or their weighted superposition (when calculated over all trials). The standard method does not detect the time elapsing during the transmission of the stimulus' action. The consequences for the analysis of evoked responses are severe.

For many aquatic animals, the electrosense is an important sensory system used to detect prey or conspecifics at short to medium range and for long-range orientation. Passive electroreceptive animals sense the minute electric fields of animate and inanimate sources and it has been thought that they are most sensitive to sources that modulate the field around a few Hertz. Our data on the properties of the electrosensory system in the paddlefish reveal that the firing rate of electrosensory brain stem neurons represents the first derivative of the stimulus, i.e. the rate of change in intensity of an electric field. Furthermore, the responses to several non-periodic stimuli suggest that the electrosensory system monitors changes in field intensity caused by the relative movement between source and receiver and converts spatial field structure into its time derivative form. This new interpretation solves a number of contradictions between behavioural observations and electrophysiological studies on the electrosensory system of vertebrates.

Electroreceptors in paddlefish serve as accessible and well-defined biological models for studying the functional roles in sensory nervous systems of noisy oscillations and the nonlinear phenomena associated with them, including synchronization, noise-induced transitions, and noise-induced bursting. The spontaneous dynamics of paddlefish electroreceptors show two oscillatory modes: one associated with 26 Hz oscillations in the sensory epithelia, and another with 30-65 Hz periodicities of afferent terminals. This novel type of organization of peripheral sensory receptors, with two distinct types of embedded oscillators, results in stochastic biperiodic firing patterns of primary afferents. The biperiodicity can be explained qualitatively in terms of a simple model based on a stochastic circle map. Stimulation with broadband Gaussian noise changes the tonic firing pattern of electroreceptors to a bursting mode, indicating a noise-induced transition. This qualitative change in dynamics leads to burst synchronization among different electroreceptors.

The zooplankton Daphnia or "water flea" — one of the most common crustacean to be found in freshwater — is subject to recent studies. It is known to perform vortex motions under certain light conditions as well as more complex navigational tasks. Experimental data show that Daphnia move with a preferred turning angle, what is of main interest in this paper. The above-mentioned experimental fact is taken in order to derive a diffusion law for these types of motion. Deviations from the free diffusive behavior are investigated, based on random walk theory.

We analyze a model for a walker moving on an asymmetric periodic ratchet potential. This model is motivated by the properties of transport of the motor protein kinesin. The walker consists of two feet represented as two particles coupled nonlinearly through a double-well bistable potential. In contrast to linear coupling, the bistable potential admits a richer dynamics where the ordering of the particles can alternate during the walking. The transitions between the two stable points on the bistable potential, correspond to a walking with alternating particles. In our model, each particle is acted upon by independent white noises, modeling thermal noise, and additionally we have an external time-dependent force that drives the system out of equilibrium, allowing directed transport. In the equilibrium case, where only white noise is present, we perform a bifurcation analysis which reveals different walking patterns. In particular, we distinguish between two main walking styles: alternating and no alternating. These two ways of walking resemble the hand-over-hand and the inchworm walking in kinesin, respectively. Numerical simulations showed the existence of current reversals and significant changes in the effective diffusion constant. We obtained an optimal coherent transport, characterized by a maximum dimensionless ratio of the current and the effective diffusion (Péclet number), when the periodicity of the ratchet potential coincides with the equilibrium distance between the two particles.

The motion of an ion through a channel is described as a classical/quantum mechanical hopping process between the individual sites of a channel. The transition rates are due to the coupling of an ion to suitable reservoirs. If fluctuating forces are added to the rate equations for the occupation numbers, the equations become quantum mechanical operator equations. Using previous results, the fluctuating forces are uniquely determined by the requirement of quantum mechanical consistency. The resulting equations are solved for several cases and the occupation number fluctuations discussed. Particular emphasis is laid on a model of correlated transport.

Finite pulse width effects in level crossing detectors and similar systems, such as neurons, can yield an output noise that is, in the low frequency limit, a monotonically increasing function of the frequency. The phenomenon can well be observed at excitations with strong noise when the firing frequency is high. Blue noise effects have been observed in stochastically driven dynamical systems like harmonic oscillators. However it is surprising that it exists in a non-dynamical system like the level crossing detector.

We consider here the effect of Fermi resonance on the rate of stochastic transitions over potential barriers. As a typical phenomenon for Fermi resonance we investigate the fading of the energy between the oscillations in different degrees of freedom. Due to this fading phenomenon we see from time to time rather large amplitudes of oscillations along the reaction path which may support transitions over reaction barriers in the underdamped regime. As as an application we study the influence of Fermi resonance on enzyme reactions. In particular we investigate the possible effect of Fermi resonance on the breaking of peptide bonds.

Neurons produce action potentials or spikes in response to a wide variety of inputs. Correlations between interspike intervals are often seen in data from single neurons, and are due to a combination of intrinsic mechanisms and the temporal properties of the input stimulus. Here we review recent progress in our understanding of how intrinsic correlations arise in simple biophysically justified neuron models. We further describe the generic conditions under which these correlations enhance the rate of transfer of information about time-varying stimuli. This work points to the importance of studying non-renewal first passage time problems in nonlinear dynamical systems.

In recent years biophysical approaches have had particular impact on the progress in physiological and biological research. In systems biology such progress is often associated with the terms "noise" and "chaos". The introduction of these physically based concepts into life sciences has essentially been promoted by the work of Frank Moss and his group. This paper provides evidence of the physiological relevance of such biophysically based approaches with examples from quite different physiological and pathophysiological functions like temperature transduction in peripheral sensory receptors and the progression of mood disorders. We will use modelling studies, based on experimental and clinical data, to illustrate that both systems can attain specific dynamical states where chaos and/or noise plays an essential role and we will try to describe under which conditions functionally relevant noise effects or chaotic behaviour can be expected.

We study the behavior of an instantaneous phase and mean frequency of chaotic self-sustained oscillations and noise-induced stochastic oscillations. The results obtained by using various methods of the phase definition are compared to each other. We also compare two methods for describing synchronization of chaotic self-sustained oscillations, namely, instantaneous phase locking and locking of characteristic frequencies in power spectra. It is shown that the technique for diagnostics of the chaos synchronization based on the instantaneous phase locking is not universal.

We analyze the statistics of skipping events in a deterministic and a noisy thermoreceptor within the model developed by Braun et al (Int. J. Bif. Chaos 8 881 (1998)). The statistics of skips can be captured by an intermittent map, which, for sufficient noise, can be approximated by a one-step Markov process with transition amplitudes that depend on the noise intensity. The theoretical and model results are in reasonable agreement with experimental data on cat coldreceptors.