The science of complexity has moved to center stage within the past few decades. Complex systems range from glasses to the immune system and the brain. Glasses are too simple to possess all aspects of complexity; brains are too complex to expose common concepts and laws of complexity. Proteins, however, are systems where many concepts and laws of complexity can be explored experimentally, theoretically, and computationally. Such studies have elucidated crucial aspects. The energy landscape has emerged as one central concept; it describes the free energy of a system as a function of temperature and the coordinates of all relevant atoms. A second concept is that of fluctuations. Without fluctuations, proteins would be dead and life impossible. A third concept is slaving. Proteins are not isolated systems; they are embedded in cells and membranes. Slaving arises when the fluctuations in the surroundings of a protein dominate many of the motions of the protein proper.

Diagrams of cellular processes present a clean, deterministic view of how biomolecules regulate the processes of life. Attempts to construct reaction networks which are true to the microscopic complexity of the system are intractable when only a few proteins are included. We argue here that several layers of microscopic modeling are needed to characterize the fluctuations, or noise, of biochemical systems and that this is necessary to develop predictive models of cellular processes. Our arguments are illustrated with the specific examples of myoglobin and protein kinases.

We present Unzipping Force Analysis of Protein Association (UFAPA) as a novel and versatile method for detection of the position and dynamic nature of protein-DNA interactions. A single DNA double helix was unzipped in the presence of DNA-binding proteins using a feedback-enhanced optical trap. When the unzipping fork in a DNA reached a bound protein molecule, we observed a dramatic increase in the tension in the DNA, followed by a sudden tension reduction. Analysis of the unzipping force throughout an unbinding "event" revealed information about the spatial location and dynamic nature of the protein-DNA complex.

The problems studied here are relevant for an understanding of the functioning of hydrolytic enzyme molecules. These enzymes work like molecular machines breaking off the valence peptid bonds of substrates. In particular the role of Fermi resonance which is evident from a spectral lines of valence oscillations is studied. The influence of this resonance on valence splitting is discussed. It is shown that the breaking of these bonds has a higher probability, if the stochastic oscillations of atoms in catalytic groups at the active site have a large quality coefficient. We show that the corresponding low damping is essential for the Fermi resonance modes of these oscillations.

We consider an exactly tractable model of the Kramers type for the voltage-dependent gating dynamics of single ion channels. It is assumed that the gating dynamics is caused by the thermally activated transitions in a bistable potential. Moreover, the closed state of the channel is highly degenerate and embraces the whole manifold of closed substrates. Opening of the ion channel is energetically prohibited from most of the closed substates and requires a special conformation where the voltage sensor can move along an activation pathway and trigger the transition into the open conformation. When the corresponding activation barrier towards the channel's opening is removed by the applied voltage, the statistics of non-conducting time intervals become strongly influenced by the conformational diffusion. For the corresponding supra-threshold voltages, our model explains the origin of the power law distribution of the closed time intervals. The exponential-linear dependence of the opening rate on voltage, often used as an experimental fit, is also reproduced by our model.

The reversible binding of sugar to a single maltoporin channel allows us to study time and ensemble variations in the channel functional properties and interpret them using the language of static and dynamic disorder in protein folding. The channel is a trimer that is characterized by two primary parameters: the rate of sugar binding and the ion conductance. Time-resolved binding of maltohexasose molecules shows that whereas dynamic disorder -- the fluctuations in binding rate or in ionic conductance of a single trimer channel with time -- is relatively small, static disorder -- the heterogeneity of reaction rates or conductances among different trimers -- is highly pronounced. This heterogeneity suggests variations in maltoporin folding. The disorder in conductance shows no measurable correlation with the disorder in binding strength; variations in protein folding that are responsible for variations in protein folding that are responsible for variations in ionic conductance do not seem to affect sugar binding. We find 'cooperativity' in static disroder: conductances of monomers in the same trimer are closely similar compared to the range of possible conductances seen over an ensemble of trimers.

Statistical analysis of high-resolution current recordings from a single ion channel reconstituted into a planar lipid membrane allows us to study transport of antibiotics at the molecular detail. Working with the general bacterial porin, OmpF, we demonstrate that addition of zwitterionic β-lactam antibiotics to the membrane-bathing solution introduces transient interruptions in the small-ion current through the channel. Time-resolved measurements reveal that one antibiotic molecule blocks one of the monomers in the OmpF trimer for characteristic times from microseconds to hundreds of microseconds. Spectral noise analysis enables us to perform measurements over a wide range of changing parameters. In all cases studied, the residence time of an antibiotic molecule in the channel exceeds the estimated time for free diffusion by orders of magnitude. This demonstrates that, in analogy to substrate-specific channels that evolved to bind specific metabolite molecules, antibiotics have 'evolved' to be channel-specific. The charge distribution of an efficient antibiotic complements the charge distribution at the narrowest part of the bacterial porin. Interaction of these charges creates a zone of attraction inside the channel and compensates the penetrating molecule's entropy loss and desolvation energy. This facilitates antibiotic translocation through the narrowest part of the channel and accounts for higher antibiotic permeability rates.

The advent of techniques to detect and manipulate individual molecules has revealed that mechanical tension on a DNA polymer can control both the speed and direction of the DNA polymerase (DNAp) motor. Reconciling the interpretation of these single molecule experiments with crystal structural data has been the focus of our previous work. In more recent work, we are developing a more broadly applicable conceptual framework to describe how tension on a DNA polymer can produce both the "tuning" and "switching" phenomena observed in DNA polymerase motors. The chief aims are to elucidate the mechanism by which DNA replication is controlled in cells and to seek novel strategies for controlling molecular scale processes and the function of nanodevices.

We hypothesized that 1/f noise is more beneficial than the conventional white noise in optimizing the brain's response to a weak input signal, and showed that externally added 1/f noise outperforms white noise in sensitizing human baroreflex centers in the brain. We examined the compensatory heart rate response to weak periodic signal introduced at the venous blood pressure receptor, while adding either 1/f or white noise with the same variance to the brain stem by electrically stimulating the bilateral vestibular afferents cutaneously. This stochastic galvanic vestibular stimulation, activating the vestibulo-sympathetic pathway in the brain stem, optimized covariance between weak input signals and the heart rate responses both with 1/f and white noise. Further, the optimal noise level with 1/f noise was significantly lower than that with white noise, suggesting the functional benefit of 1/f noise for the neuronal information transfer in the brain.

The incorporation of low levels of noise into an electrical stimulus has been shown to improve auditory thresholds in human subjects. In this paper, thresholds for noise-modulated pulse-train stimuli are predicted by utilizing a stochastic neural-behavioral model of ensemble fiber responses to bi-phasic stimuli. A neural spike count comparison rule has been presented for both threshold and intensity discrimination under the assumption that loudness is a monotonic function of the number of neuron spikes. An alternative approach which we have pursued involves analyzing the neural response to each individual pulse within a pulse train to investigate the threshold behavior. The refractory effect is described using a Markov model for a noise-free pulse-train stimulus. A recursive method using the conditional probability is utilized to track the neural responses to each successive pulse for a noise-modulated pulse-train stimulus. After determining the stochastic properties of the auditory nerve response to each pulse within the pulse train, a logarithmic rule is hypothesized for pulse-train threshold and the predictions are shown to match psychophysical data not only for noise-free stimuli but also for noise-modulated stimuli. Results indicate that threshold decreases as noise variance increases.

In this article we discuss the possible use of a novel form of stochastic resonance, termed suprathreshold stochastic resonance (SSR), to improve signal encoding/transmission in cochlear implants. A model, based on the leaky-integrate-and-fire (LIF) neuron, has been developed from physiological data and use to model information flow in a population of cochlear nerve fibers. It is demonstrated that information flow can, in principle, be enhanced by the SSR effect. Furthermore, SSR was found to enhance information transmission for signal parameters that are commonly encountered in cochlear implants. This, therefore, gives hope that SSR may be implemented in cochlear implants to improve speech comprehension.

The aim of this study was to demonstrate the occurrence of stochastic resonance (SR) in spinal and cortical potentials elicited by periodic tactile stimuli in the anaesthetised cat. The periodic tactile stimuli were applied on the central pad of the hindpaw and the noisy tactile stimuli on the glabrous skin of the third hindpaw digit. This protocol allowed that the signal and noise were mixed not in the skin but in the somatosensory regions of the central nervous system. The results show that a particular level of tactile noise can increase the amplitude of the spinal and cortical potentials elicited by periodic tactile stimuli. The topographical distribution of evoked potentials indicates that the effects of noise were spatially restricted. All cats showed distinct SR behavior at the spinal and cortical stages of the sensory encoding. Such SR was abolished in the cortical but not in the spinal recording after the sectioning of the ascending pathways. This suggests that the spinal neurones may also contribute to the SR observed at the cortical level. The present study documents the first evidence that the SR phenomenon occurs in the spinal and cortical somatosensory system itself and not only in the peripheral sensory receptors.

Mesoscopic modeling of intracellular kinetics is usually performed on the premise that diffusion is so fast that all concentrations are homogenous in space. However, this supposition is not necessarily valid even for small prokaryotic cells, as indicated by recent experimental data on intracellular diffusion constants. When diffusion and spatial heterogeneity are taken into account, stochastic simulation of chemical reactions in single cells is computationally demanding. We present an efficient Monte Carlo algorithm for simulation of mesoscopic reaction-diffusion kinetics in single cells. The total system (e.g. a single prokaryotic cell) is divided into N subvolumes (SVs), chosen so small that the concentrations of reactants in a SV are near-homogeneous in space. The molecules in a SV can either undergo chemical reactions or diffuse to a neighboring SV. The expected time for the next chemical reaction or diffusion event is only recalculated for those SVs that were involved in the previous event. The time for the next event in each SV is ordered in an event queue, which makes the computation time linear in log N, rather than in N.

Plasmids are self-replicating gene clusters present in on average 2-100 copies per bacterial cell. To reduce random fluctuations and thereby avoid extinction, they ubiquitously autoregulate their own synthesis using negative feedback loops. Here I use van Kampen's Ω-expansion for a two-dimensional model of negative feedback including plasmids and ther replication inhibitors. This analytically summarizes the standard perspective on replication control -- including the effects of sensitivity amplification, exponential time-delays and noisy signaling. I further review the two most common molecular sensitivity mechanisms: multistep control and cooperativity. Finally, I discuss more controversial sensitivity schemes, such as noise-enhanced sensitivity, the exploitation of small-number combinatorics and double-layered feedback loops to suppress noise in disordered environments.

We demonstrate the existence of two types of oscillators embedded in the electroreceptor system of paddlefish. The first type of oscillator is represented by the collective activity of hundreds of epithelial cells. It produces stochastic oscillations with a well-expressed peak in the power spectrum at approx. 25 Hz. The second oscillator resides in the afferent terminals and is driven by the first, epithelial oscillations. We show that the existence of the epithelial oscillation leads to two main effects. On the one hand, it busts variability of afferent firing, expressed as an increase of the coefficient of variation of interspike intervals. On the other hand, however, the epithelial oscillations involve additional degree of ordering expressed in the extended negative correlations between sequential interspike intervals. We discuss implications of extended negative correlations on the performance of electroreceptors.

We examine the roll of an extracellular gel in the functioning of the electrosensors of elasmobranchs (sharks, skates, and rays). Here we focus on physical characteristics of the gel and their mechanistic relevance to the observed functioning of the electrosensors. The electrosensitive organs show sharp transient responses to both tiny electrical fluctuations and temperature fluctuations. We present a thermoelectric characterization of the gel. The data suggest a gel-mediated mechanism of transducing thermal fluctuations to electrical fluctuations in the electrosensor, independent of the sensing cells. We also present frequency-dependent electrical properties of the gel collected using electrical impedance spectroscopy. From these measurements we try to extract characteristic relaxation times. We analyze these results within the context of the electrosensors’ bandwidth, as demonstrated in previous behavioral experiments.

Outer hair cells in the mammalian ear has a membrane based motor which directly converts electrical energy into mechanical energy. Such a motor is associated with the function of these cells in providing feedback to vibration in the inner ear. To obtain insights into the motor mechanism, we examined kinetics of charge transfer across the membrane in two different modes. One is to monitor charge transfer induced by changes in the membrane potential as an excess membrane capacitance. The other is to measure spontaneous flip-flops of charges across the membrane under voltage clamp condition as current noise. The noise spectrum of current was inverse Lorentzian and the capacitance was Lorentzian as theoretically expected. The characteristic frequency of the capacitance was about 10 kHz and that for current noise was about 30 kHz. This result is inconsistent with the prediction. The difference can be explained by a reciprocal effect of being a piezoelectric motor in that mechanical motion which is subjected to friction affects the frequency response.

We use the model of interacting self-propelled particles as a rough model for the collective motions of cells and organisms. First we study self-propelled motion with linear attracting interactions. This way we develop the dynamics of swarms with self-confinement by global coupling in coordinate- and velocity-space. Further we study the model of Morse-type attracting forces and global velocity-coupling. We begin with pairs N=2; the attractors and distribution functions are discussed, then the case N>2 is discussed. Simulations for several dynamical modes of swarms of active Brownian particles are presented. In particular we study rotations, drift, fluctuations of shape and cluster formation. Finally we study the symmetry-breaking effects of hydrodynamic interactions of Oseen-type.

Swarm theories have become fashionable in theoretical physics over the last decade. They span the range of interactions from individual agents moving in a mean field to coherent collective motions of large agent populations, such as vortex-swarming. But controlled laboratory tests of these theories using real biological agents have been problematic due primarily to poorly known agent-agent interactions (in the case of e.g. bacteria and slime molds) or the large swarm size (e.g. for flocks of birds and schools of fish). Moreover, the entire range of behaviors from single agent interactions to collective vortex motions of the swarm have here-to-fore not been observed with a single animal. We present the results of well defined experiments with the zooplankton Daphnia in light fields showing this range of behaviors. We interpret our results with a theory of the motions of self-propelled agents in a field.

Specification of the anteroposterior (head-to-tail) axis in the fruit fly Drosophila melanogaster is one of the best understood examples of embryonic pattern formation, at the genetic level. A network of some 14 segmentation genes controls protein expression in narrow domains which are the first manifestation of the segments of the insect body. Work in the New York lab has led to a databank of more than 3300 confocal microscope images, quantifying protein expression for the segmentation genes, over a series of times during which protein pattern is developing (http://flyex.ams.sunysb.edu/FlyEx/). Quantification of the variability in expression evident in this data (both between embryos and within single embryos) allows us to determine error propagation in segmentation signalling. The maternal signal to the egg is highly variable, with noise levels more than several times those seen for expression of downstream genes. This implies that error suppression is active in the embryonic patterning mechanism. Error suppression is not possible with the favored mechanism of local concentration gradient reading for positional specification. We discuss possible patterning mechanisms which do reliably filter input noise.

We introduce a model for simulating mutation of prokaryote DNA sequences. Using that model we can then evaluated traditional techniques like parsimony and maximum likelihood methods for computing phylogenetic relationships. We also use the model to mimic large scale genomic changes, and use this to evaluate multifractal and related information theory techniques which take into account these large changes in determining phylogenetic relationships.

The pyramidal cells of weakly electric fish respond to environmental broadband electrical stimuli. They have recently been shown to exhibit oscillations in mean firing rate in response to global stimuli that affect the whole body simultaneously similar to communication stimuli for these animals. In contrast, for spatially localized stimuli such as those produced by prey, the firing rate simply fluctuates around a constant mean. This switch in coding strategy relies on delayed negative (inhibitory) feedback connections in the neural network. We first summarize these experimental findings, as well as our mathematical modeling of this effect using a globally-coupled delayed inhibitory network of leaky integrate-and-fire neurons (LIF's). Here we study the mechanism of the transition from oscillatory to non-oscillatory firing states in such networks. This is done using simulations of a simpler network of LIF's with current based Gaussian white noise stimuli, rather than conductance based bandlimited Gaussian stimuli. We focus on the effect of feedback gain, current bias, and stimulus intensity on the oscillation under global conditions, and see how the decrease of these parameters brings on a response characteristic of the local case. These simulations are performed for a fixed amount of individual synaptic noise to each cell. We also show how insights into these results can be obtained from the analysis of stimulus-induced oscillations in a simpler rate model description of this spatially-extended excitable system.

The mechanisms involved in respiratory rhythm and in its persistence along lifetime have not been completely elucidated yet. The debate if they rely on pacemaker units or on the emerging properties of neural networks is still on. We propose a simple model taking advantage of the synaptic noise and allowing to bridge network and pacemaker theories. The pBC (reticular preBotzinger Complex) and PC (pneumotaxic center) are two randomly and sparsely connected excitatory networks. pBC excites PC that in turn, strongly inhibits pBC. As a part of the reticular formation, the pBC, receives many uncorrelated inputs (noise). The model reproduces most of the experimental observations. Once started, the pBC, whose activity is started by synaptic noise, increase of activity is an emerging property of the excitatory network. This activates the PC that in turn inhibits the pBC and starts the expiration. If, for any reason, noise becomes too low, the network becomes silent, and pacemakers become the only active units able to restart a new inspiration. Safety measures of this kind are very much expected in the operation of a system as vital as respiration. Simulations using an enhanced biologically plausible model of neurons fully support the proposed model.

Brains consist of complex networks of neurons possessing highly non-linear interactions, suggesting that neural systems will show cooperative dynamics. Previous studies of the non-Gaussian statistics of 1/f noise in spin glasses and amorphous semiconductors have revealed important information concerning interaction kinetics not available through other techniques. Five male Brown-Norway-Cross rats were chronically implanted with arrays of microwire electrodes from which local field potentials (LFPs) were recorded from the dorsocentral striatum as the animals performed complex navigational tasks. The power spectra displayed a frequency dependence significantly different from 1/f. The correlation coefficients of the Fourier transform of the LFPs from striatum showed significant non-zero correlations between frequencies separated by less than three octaves. This novel technique may be useful in measuring functional interactions in neural systems.

Human motor activity is influenced by many factors both extrinsic (work, recreation, reactions to unforeseen random events) and intrinsic (circadian and ultradian rhythms). We investigate if these factors fully account for the complex features observed in recordings of human activity. First, we measure activity over two weeks from forearm motion in subjects undergoing their regular daily routine. We show that no systematic ultradian rhythms exist in human activity during wakefulness. Furthermore, we demonstrate that during wakefulness human activity possesses previously unrecognized dynamic patterns characterized by long-range fractal correlations and nonlinear Fourier phase interactions. These patterns are unaffected by changes in the average activity level occuring within individual subjects throughout the day, on different days, and between subjects. Second, we find that these patterns persist when the same subjects undergo time-isolation laboratory experiments designed to account for the phase of the circadian pacemaker, and to control the known extrinsic factors. We attribute these newly discovered patterns to an intrinsic multi-scale dynamic regulation of human activity that is independent of known extrinsic factors, as well as known intrinsic factors (the circadian and ultradian rhythms).

Shannon's information rate formula does not work for wideband (aperiodic) signals with nonlinear transfer. The classical signal and noise measures used to characterize stochastic resonance do not work either because their way of distinguishing signal from noise fails. In a study published earlier, a new way of measuring and identifying noise and aperiodic (wideband) signals during strongly nonlinear transfer was introduced. The method was based on using cross-spectra between the input and the output. According to the study, in the case of linear transfer and sinusoidal signals, the method gives the same results as the classical method and in the case of aperiodic signals it gives a sensible measure. In this paper we refine the theory and present detailed simulations which validate and refine the conclusions reached in that study. The simulation results clearly confirm that the cross-spctral identifications of output signal and noise are sensible measures and we put the theory on a firm footing. As neural and ion channel signal transfer is nolinear and aperiodic, the new method has direct applicability in biophysics and neural science.

Oscillations of the membrane potential are a prominent feature of several neurons in the central and peripheral nervous system. Evidences exist that neurons combine intrinsic oscillations with stochastic influences to obtain sensitive encoding. Here we investigated the responses of oscillatory neurons with respect to different activity states and noise levels as well as different measures of the responses. For that we used a computational approach and studied systematically the responses of a physiologically motivated neuronal oscillator model. With subthreshold activation of the model, noise mediates oscillation-coupled spike generation. In this situation noise-tuning results in maximum curves for the coherence of oscillations and spikes (coherence resonance) whereas the mean spike frequencies increase monotonically. In contrast, with suprathreshold activation, noise suppresses oscillation-coupled spike generation. In this situation, noise tuning leads to a minimum curve for the mean spike frequency whereas the coherence measure decreases monotonically. In conclusion, our study shows interesting effects on neuronal responses depending on the level of stimulation and noise intensity. In addition, the study demonstrates how such dynamical behaviors might fulfill different purposes depending on the actual encoding strategy used.

The detection of external stimuli by peripheral sensory neurons and the downstream processing by cortical neurons quite often involves the operational mode of bursting activity, i.e., periods of rapid firing alternating with intervals of quiescence. In some systems, e.g. the electrosense of the paddlefish (Polyodon spathula), a transition from tonic firing to the bursting regime can be induced by external noise. Under the hypothesis that information about the external stimulus is encoded in the statistics of the interspike intervals (ISIs) we quantify the information content of these noisy bursters and the sensitivity to weak stimuli. Our analysis is based on analytic methods and numerical simulations of effective burster models.

We suggest a fresh approach to the modeling of the human cardiovascular system. Taking advantage of a new Bayesian inference technique, able to deal with stochastic nonlinear systems, we show that one can estimate parameters for models of the cardiovascular system directly from measured time series. We present preliminary results of inference of parameters of a model of coupled oscillators from measured cardiovascular data addressing cardiorespiratory interaction. We argue that the inference technique offers a very promising tool for the modeling, able to contribute significantly towards the solution of a long standing challenge -- development of new diagnostic techniques based on noninvasive measurements.

The modeling of the broad-band fluctuation of HRV is given using bounded cascade. The model characteristics are summarized and results from simulating multifractal HRV in health and in autonomic blockade are given. The cascade paradigm raises the question of the role of feedback which functions on the basis of additive law. A dynamic cascade model is given to show how the merge of additive law from feedback with cascade can be made based on a global-cascade-local-feedback framework. Finally, we show experimental evidence of discrete scale invariance in RRi data to support cascade HRV.

I will summarize results that describe the microsopic response of a system driven away from an initial state of thermal equilibrium. I will discuss the application of these results to the analysis of laser tweezer experiments, as well as to the numerical estimation of free energy differences in complex systems such as bio-molecules.

The rectification of thermal motion can give rise to a steady state flow of particles. This process is believed to occur in nature and to be of central importance for intra-cellular transport. Ajdari and Prost have proposed an "on-off" or "flashing" ratchet and Magnasco has proposed a similar "tilting" or "rocking" ratchet mechanism. These developments led to new and active fields of research in statistical physics and physical chemistry. Recent work by Gillespie and Eisenberg suggests that the effectiveness of the natural transport process, in biological ion channels, depends strongly on how we model the effect of ion to ion interactions. At high local ion concentrations the effect of the crowding of charge is significant. It is necessary to include this effect in the models. If we are interested in average ion currents then we can replace the complicated many-body problem with a time-average mean-field for the distribution of charge. To date, all analyses of artificial, human-made, ratchets require us to neglect the effect of distributed charge. This means that the analysis is only strictly valid for dilute solutions. The purpose of our present paper is to include the effect of distributed charge in the analysis of artificial Brownian ratchets. We formulate the Brownian ratchet problem for the case where distributed charge is significant. We investigate methods of solution and find that the finite difference approach is not adequate because the governing equations are very "stiff." We propose an alternative approach based on Fourier series.

It has been recently shown that the amplitude truncation of Gaussian 1/f noise does not change the shape of the power spectral density under rather general conditions, including the case when a Heaviside transformation results in a dichotomous noise. This invariance of 1/f noise seems to be an important addition to the knowledge about this kind of noise and may be promising in understanding dichotomous 1/f noise, noise-driven switching and stepping. Probably the most important application is the explanation of ion channel currents in biomembranes. In this work we have extended our investigations, especially concerning the level crossing properties of 1/f noises. We determined the level crossing time statistics for 1/f^α noises (0<α<2) and found an empirical formula for the level-crossing time distribution. The correlation properties of successive level crossing intervals are also explored by measurements and numerical simulations and it is shown that the case α=1 is unique in the range from 0 to 2. These time structure related additions to the knowledge about 1/f noise further emphasize the uniqueness of this kind of noise. These results may help to understand 1/f noises better and are strongly relevant to 1/f noise driven switching, dichotomous noises such as the case of ion channel current fluctuations.

The modeling of human motor behavior has followed the trend in other scientific disciplines. From purely biomechanical models to symbolic computer programs the recent development has incorporated novel insights from the study of self-organizing, complex dynamical systems. In creating non-linear models of motor behavior it is sometimes overlooked that human behavior is never completely deterministic. This is especially evident in spontaneous movement and decision making for instance in the timing of movement initiation. We present some recent simulations involving stochastic, discrete time, piecewise-linear models with multiple time-scales, describing simple movement tasks. We then give an outlook about the potential role of quantum entanglement in human movement coordination and timing.

Human cardiovascular and/or cardio-respiratory systems are shown to exhibit both multifractal and synchronous dynamics, and we recently developed a nonlinear, physiologically plausible model for the synchronization between heartbeat and respiration (Kotani, et al. Phys. Rev. E 65: 051923, 2002). By using the same model, we now show the multifractality in the heart rate dynamics. We find that beat-to-beat monofractal noise (fractional Brownian motion) added to the brain stem cardiovascular areas results in significantly broader singularity spectra for heart rate through interactions between sympathetic and parasympathetic nervous systems. We conclude that the model proposed here would be useful in studying the complex cardiovascular and/or cardio- respiratory dynamics in humans.

We report the results of two psychophysics experiments showing that the human brain can make use of externally added noise for behavioral responses. Subjects were instructed to respond to changing gray level signals presented to their right eye. The behavioral responses were optimized by presenting randomly changing gray level noise to their left eye. The results indicate that the behavioral stochastic resonance occurs at the cortical level where information from both eyes merges together.

Cochlear implants (CI) provide speech information to the hearing-impaired by transmitting temporal information from specific frequency bands to corresponding regions of the tonotopically organized auditory system via electrical stimulation. We are interested in the role of applied noise in temporal coding by CI listeners. We measured sensitivity to sinusoidal amplitude modulation in adult users of the Nucleus-22 cochlear implant. The carrier was a train of current pulses presented at various amplitudes within the subject's dynamic range, driving a single electrode pair in the middle of the implanted electrode array. Consistent with previous findings, modulation sensitivity in CI listeners was positively related to carrier level. Introducing uniformly distributed, pseudorandom noise into the carrier envelope produced level-dependent effects. At high levels, modulation sensitivity decreased with increasing noise. At less sensitive low carrier levels, modulation sensitivity showed a stochastic resonance (SR) signature with increasing noise, displaying maximum sensitivity at an optimal noise level. This finding was also consistent with previous work. In a new experiment, we tested two new ways of degrading modulation sensitivity without changing carrier level: (1) by increasing modulation frequency and (2) by introducing a concurrent, fluctuating masker on another channel. Under each of these two conditions, our results show that increasing noise in the signal carrier envelope improved sensitivity in a manner consistent with SR. These results suggest that conditions that weaken modulation sensitivity strengthen the potential for SR. We speculate that the effect arises at a relatively central stage of temporal processing in the auditory system.