Theory of arachnid prey localization

Sand scorpions and many other arachnids locate their prey through highly sensitive slit sensilla at the tips (tarsi) of their eight legs. This sensor array responds to vibrations with stimulus-locked action potentials encoding the target direction. We present a neuronal model to account for stimulus angle determination using a population of second-order neurons, each receiving excitatory input from one tarsus and inhibition from a triad opposite to it. The input opens a time window whose width determines a neuron's firing probability. Stochastic optimization is realized through tuning the balance between excitation and inhibition. The agreement with experiments on the sand scorpion is excellent.     

Linear Response of General Observables in Spiking Neuronal Network Models

We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allow us to predict the influence of a weak amplitude time dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how the linear response is explicitly related to the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike train statistics. We illustrate our results with numerical simulations performed over a discrete time integrate and fire model.     

Optimal Population Coding for Dynamic Input by Nonequilibrium Networks

The efficient coding hypothesis states that neural response should maximize its information about the external input. Theoretical studies focus on optimal response in single neuron and population code in networks with weak pairwise interactions. However, more biological settings with asymmetric connectivity and the encoding for dynamical stimuli have not been well-characterized. Here, we study the collective response in a kinetic Ising model that encodes the dynamic input. We apply gradient-based method and mean-field approximation to reconstruct networks given the neural code that encodes dynamic input patterns. We measure network asymmetry, decoding performance, and entropy production from networks that generate optimal population code. We analyze how stimulus correlation, time scale, and reliability of the network affect optimal encoding networks. Specifically, we find network dynamics altered by statistics of the dynamic input, identify stimulus encoding strategies, and show optimal effective temperature in the asymmetric networks. We further discuss how this approach connects to the Bayesian framework and continuous recurrent neural networks. Together, these results bridge concepts of nonequilibrium physics with the analyses of dynamics and coding in networks.     

Models for the generation of the binaural difference response.

Two simple models are examined in order to explain the observation that a portion of the binaural-evoked response is less than the sum of monaural-evoked responses in human and animal subjects. The sum of monaural responses minus the binaural response is called the binaural difference (BD). Each model acts on binaural input signals and applies a single memoryless nonlinearity. One model (IE) applies a rectifying nonlinearity to the difference of input signals, while the other (EE) applies a compressive nonlinearity to the sum of input signals. These models are suggested by properties of inhibitory-excitatory (IE) and excitatory-excitatory (EE) neurons of the auditory brainstem. Parameters can be found that enable each model to produce a ratio of BD to summed monaural response which is invariant with input stimulus level. The IE model, but not the EE model, has a BD whose level is linearly related to input stimulus level.     

Stochastic phase resetting of stimulus-locked responses of two coupled oscillators: transient response clustering,synchronization, and desynchronization

Transient phase dynamics, synchronization, and desynchronization which are stimulus-locked (i.e., tightly time-locked to a repetitively administered stimulus) are studied in two coupled phase oscillators in the presence of noise. The presented method makes it possible to detect such processes in numerical and experimental signals. The time resolution is enormous, since it is only restricted by the sampling rate. Stochastic stimulus locking of the phases or the n:m phase difference at a particular time t relative to stimulus onset is defined by the presence of one or more prominent peaks in the cross-trial distribution of the phases or the n:m phase difference at time t relative to stimulus onset in an ensemble of poststimulus responses. The oscillators' coupling may cause a transient cross-trial response clustering of the poststimulus responses. In particular, the mechanism by which intrinsic noise induces symmetric antiphase cross-trial response clustering in coupled detuned oscillators is a stochastic resonance. Unlike the presented approach, both cross-trial averaging (where an ensemble of poststimulus responses is simply averaged) and cross-trial cross correlation (CTCC) lead to severe misinterpretations: Triggered averaging cannot distinguish a cross-trial response clustering or decorrelation from a mean amplitude decrease of the single responses. CTCC not only depends on the oscillators' phase difference but also on their phases and, thus, inevitably displays "artificial" oscillations that are not related to synchronization or desynchronization.     

Coherence depression in stochastic excitable systems with two-frequency forcing

We study the response of two generic neuron models, the leaky integrate-and-fire (LIF) model and the leaky integrate-and-fire model with dynamic threshold (LIFDT) (i.e., with memory) to a stimulus consisting of two sinusoidal drives with incommensurate frequency, an amplitude modulation ("envelope") noise and a relatively weak additive noise. Spectral and coherence analysis of responses to such naturalistic stimuli reveals how the LIFDT model exhibits better correlation between modulation and spike train even in the presence of both noises. However, a resonance-induced synchrony, occurring when the beat frequency between the sinusoids is close to the intrinsic neuronal firing rate, decreases the coherence in the dynamic threshold case. Under suprathreshold conditions, the modulation noise simultaneously decreases the linear spectral coherence between the spikes and the whole stimulus, as well as between spikes and the stimulus envelope. Our study shows that the coefficient of variation of the envelope fluctuations is positively correlated with the degree of coherence depression. As the coherence function quantifies the linear information transmission, our findings indicate that under certain conditions, a transmission loss results when an excitable system with adaptive properties encodes a beat with frequency in the vicinity of its mean firing rate.     

Testing resonating vector strength: auditory system, electric fish, and noise

Quite often a response to some input with a specific frequency ν(○) can be described through a sequence of discrete events. Here, we study the synchrony vector, whose length stands for the vector strength, and in doing so focus on neuronal response in terms of spike times. The latter are supposed to be given by experiment. Instead of singling out the stimulus frequency ν(○) we study the synchrony vector as a function of the real frequency variable ν. Its length turns out to be a resonating vector strength in that it shows clear maxima in the neighborhood of ν(○) and multiples thereof, hence, allowing an easy way of determining response frequencies. We study this "resonating" vector strength for two concrete but rather different cases, viz., a specific midbrain neuron in the auditory system of cat and a primary detector neuron belonging to the electric sense of the wave-type electric fish Apteronotus leptorhynchus. We show that the resonating vector strength always performs a clear resonance correlated with the phase locking that it quantifies. We analyze the influence of noise and demonstrate how well the resonance associated with maximal vector strength indicates the dominant stimulus frequency. Furthermore, we exhibit how one can obtain a specific phase associated with, for instance, a delay in auditory analysis.     

Using electrical noise to enhance the ability of humans to detect subthreshold mechanical cutaneous stimuli

Stochastic resonance (SR) is a phenomenon wherein the response of a nonlinear system to a weak input signal is optimized by the presence of a particular, nonzero level of noise. Our objective was to demonstrate cross-modality SR in human sensory perception. Specifically, we were interested in testing the hypothesis that the ability of an individual to detect a subthreshold mechanical cutaneous stimulus can be significantly enhanced by introducing a particular level of electrical noise. Psychophysical experiments were performed on 11 healthy subjects. The protocol consisted of the presentation of: (a) a subthreshold mechanical stimulus plus electrical noise, or (b) no mechanical stimulus plus electrical noise. The intensity of the electrical noise was varied between trials. Each subject's ability to identify correctly the presence of the mechanical stimulus was determined as a function of the noise intensity. In 9 of the 11 subjects, the introduction of a particular level of electrical noise significantly enhanced the subject's ability to detect the subthreshold mechanical cutaneous stimulus. In 2 of the 11 subjects, the introduction of electrical noise did not significantly change the subject's ability to detect the mechanical stimulus. These findings indicate that input electrical noise can serve as a negative masker for subthreshold mechanical tactile stimuli, i.e., electrical noise can increase the detectability of weak mechanical signals. Thus, for SR-type effects to be observed in human sensory perception, the noise and stimulus need not be of the same modality. From a bioengineering and clinical standpoint, this work suggests that an electrical noise-based technique could be used to improve tactile sensation in humans when the mechanical stimulus is around or below threshold. (c) 1998 American Institute of Physics.     

Conservation of adapting components in auditory-nerve responses

The responses of single auditory-nerve fibers of Mongolian gerbil were studied using tonal stimuli. The peristimulatory adaptation of firing rate in response to tone bursts presented in quiet and during a background stimulus is described quantitatively. The total transient response which can be produced to the onset of a tone burst, whether presented in quiet or as an intensity increment, is limited and appears to demonstrate a form of conservation. Specifically, the total numbers of spikes produced by the rapidly adapting component, and the slower short-term adaptation component, are proportional at all intensities, and are limited for each fiber. Furthermore, when an incremental stimulus is presented on a background, the total transient response to the background and to the increment is limited and depends upon the final intensity, not the background intensity. When the presumed underlying synaptic drive is derived by removing the effects of refractoriness from the spike train, the same conservation of the transient response components, and proportionality between rapid and short-term components, are observed.     

Simulation of auditory-neural transduction: further studies

A computational model of mechanical to neural transduction at the hair cell-auditory-nerve synapse is presented. It produces a stream of events (spikes) that are precisely located in time in response to an arbitrary stimulus and is intended for use as an input to automatic speech recognition systems as well as a contribution to the theory of the origin of auditory-nerve spike activity. The behavior of the model is compared to data from animal studies in the following tests: (a) rate-intensity functions for adapted and unadapted responding; (b) two-component short-term adaptation; (c) frequency-limited phase locking of events; (d) additivity of responding following stimulus-intensity increases and decreases; (e) recovery of spontaneous activity following stimulus offset; and (f) recovery of ability to respond to a second stimulus following offset of a first stimulus. The behavior of the model compares well with empirical data but discrepancies in tests (d) and (f) point to the need for further development. Additional functions that have been successfully simulated in previous tests include realistic interspike-interval histograms for silence and intense sinusoidal stimuli, realistic poststimulus period histograms at various intensities and nonmonotonic functions relating incremental and decremental responses to background stimulus intensity. The model is computationally convenient and well suited to use in automatic recognition devices that use models of the peripheral auditory system as input devices. It is particularly well suited to devices that require stimulus phase information to be preserved at low frequencies.     

How much luxury is there in 'luxury perfusion'? An analysis of the BOLD response in the visual areas V1 and V2

We re-analyzed the functional magnetic resonance imaging data from a study involving awake, adult, human volunteers in order to examine the influence of vascular density on the blood oxygenation level-dependent (BOLD) response. We employed a flashed and reversing stimulus paradigm where the latter stimulated twice the number of receptive fields and with it doubled the neuronal metabolic load (CMRO2) compared to the former stimulus. The blood flow increase to these stimuli was identical, so that differences in the BOLD response are due to differences in the oxygen extraction fraction. By comparing the BOLD response in human striate cortex (V1) and its neighbor, extra-striate area V2 to the two stimuli, we were able to determine the influence of the higher vascular density of striate cortex on the BOLD response. In striate cortex, the extent of activation, as measured by the number of activated voxels, was larger for the flashed than for the reversing stimulus. In extra-striate area V2, no such difference in the extent of activation was noted. Gauging the local concentration of HbR using deltaR2*, we found it to be significantly lower for the flashed than for the reversing checkerboard. We estimated the HbR concentration in extra-striate area V2 to be double that of striate cortex independent of the stimulus presented. A frequency distribution of the deltaR2* values for the flashed and reversing checkerboard revealed a shift consistent with an increase in the HbR concentration between areas V1 and V2. The metabolically most demanding stimulus, the reversing checkerboard was associated with the highest HbR concentration and with the largest number of voxels with a negative BOLD response.     

Spiking dynamics of interacting oscillatory neurons

Spiking sequences emerging from dynamical interaction in a pair of oscillatory neurons are investigated theoretically and experimentally. The model comprises two unidirectionally coupled FitzHugh-Nagumo units with modified excitability (MFHN). The first (master) unit exhibits a periodic spike sequence with a certain frequency. The second (slave) unit is in its excitable mode and responds on the input signal with a complex (chaotic) spike trains. We analyze the dynamic mechanisms underlying different response behavior depending on interaction strength. Spiking phase maps describing the response dynamics are obtained. Complex phase locking and chaotic sequences are investigated. We show how the response spike trains can be effectively controlled by the interaction parameter and discuss the problem of neuronal information encoding.     

Transient-evoked otoacoustic emission generators in a nonlinear cochlea

This study focuses on the theoretical prediction and experimental evaluation of the latency of transient-evoked otoacoustic emissions. Response components with different delay have been identified in several studies. The main generator of the transient response is assumed to be coherent reflection from cochlear roughness near the resonant place. Additional components of different latency can be generated by different mechanisms. Experimental data are re-analyzed in this study to evaluate the dependence of the latency on stimulus level, for each component of the response, showing that previous estimates of the otoacoustic emission latency were affected by systematic errors. The latency of the emission from each generator changes very little with stimulus level, whereas their different growth rate causes sharp changes of the single-valued latency, estimated as the time of the absolute maximum of the bandpass filtered response. Results of passive linear models, in which gain and bandwidth of the cochlear amplifier are strictly related, are incompatible with the observations. Although active linear models including delayed stiffness terms do predict much slower dependence of latency on the stimulus level, a suitable nonlinear model should be designed, capable of decoupling more effectively the dependence on stimulus level of amplitude and phase of the otoacoustic response.     

A low-dimensional model of binocular rivalry using winnerless competition

We discuss a novel minimal model for binocular rivalry (and more generally perceptual dominance) effects. The model has only three state variables, but nonetheless exhibits a wide range of input and noise-dependent switching. The model has two reciprocally inhibiting input variables that represent perceptual processes active during the recognition of one of the two possible states and a third variable that represents the perceived output. Sensory inputs only affect the input variables.We observe, for rivalry-inducing inputs, the appearance of winnerless competition in the perceptual system. This gives rise to a behaviour that conforms to well-known principles describing binocular rivalry (the Levelt propositions, in particular proposition IV: monotonic response of residence time as a function of image contrast) down to very low levels of stimulus intensity.     

Explosive synchronization enhances selectivity: Example of the cochlea

Acoustical signal transduction in the cochlea is an active process that involves nonlinear amplification and spontaneous otoacoustic emissions. Signal transduction involves individual subunits composed of globally coupled hair cells, which can be modeled as oscillators close to a Hopf bifurcation. The coupling may induce a transition toward synchronization, which in turn leads to a strong nonlinear response. In the model studied here, the synchronization transition of the subunit is discontinuous (explosive) in the absence of an external stimulus. We show that, in the presence of an external stimulus and for a coupling strength slightly lower than the critical value leading to explosive synchronization, the response of the subunit has better frequency selectivity and a larger signal-to-noise ratio. From physiological observations that subunits are themselves coupled together, we further propose a model of the complete cochlea, accounting for the ensemble of frequencies that the organ is able to detect.     

Effects of synaptic noise and filtering on the frequency response of spiking neurons

Noise can have a significant impact on the response dynamics of a nonlinear system. For neurons, the primary source of noise comes from background synaptic input activity. If this is approximated as white noise, the amplitude of the modulation of the firing rate in response to an input current oscillating at frequency omega decreases as 1/square root[omega] and lags the input by 45 degrees in phase. However, if filtering due to realistic synaptic dynamics is included, the firing rate is modulated by a finite amount even in the limit omega-->infinity and the phase lag is eliminated. Thus, through its effect on noise inputs, realistic synaptic dynamics can ensure unlagged neuronal responses to high-frequency inputs.     

Dynamics and nonlinearities of the BOLD response at very short stimulus durations

In designing a functional imaging experiment or analyzing data, it is typically assumed that task duration and hemodynamic response are linearly related to each other. However, numerous human and animal studies have previously reported a deviation from linearity for short stimulus durations (<4 s). Here, we investigated nonlinearities of blood-oxygenation-level-dependent (BOLD) signals following visual stimulation of 5 to 1000 ms duration at two different luminance levels in human subjects. It was found that (a) a BOLD response to stimulus durations as short as 5 ms can be reliably detected; this stimulus duration is shorter than employed in any previous study investigating BOLD signal time courses; (b) the responses are more nonlinear than in any other previous study: the BOLD response to 1000 ms stimulation is only twice as large as the BOLD response to 5 ms stimulation although 200 times more photons were projected onto the retina; (c) the degree of nonlinearity depends on stimulus intensity; that is, nonlinearities have to be characterized not only by stimulus duration but also by stimulus features like luminance. These findings are especially of most practical importance in rapid event-related functional magnetic resonance imaging (fMRI) experimental designs. In addition, an 'initial dip' response--thought to be generated by a rapid increase in cerebral metabolic rate of oxygen metabolism (CMRO2) relative to cerebral blood flow--was observed and shown to colocalize well with the positive BOLD response. Highly intense stimulation, better tolerated by human subjects for short stimulus durations, causes early CMRO2 increase, and thus, the experimental design utilized in this study is better for detecting the initial dip than standard fMRI designs. These results and those from other groups suggest that short stimulation combined with appropriate experimental designs allows neuronal events and interactions to be examined by BOLD signal analysis, despite its slow evolution.     

Optimal control of neuronal activity

We investigate the optimal control of neuronal spiking activity for neurons receiving a class of random synaptic inputs, characterized by a positive parameter alpha. Optimal control signals and optimal variances are found exactly for the diffusion process approximating an integrate and fire model. When synaptic inputs are "sub-Poisson" (alpha<0.5), we find that the optimal synaptic input is a delta function (corresponding to bang-bang control) and the optimal signal is not unique. Poisson synaptic input is the critical case: The control signal is unique, but the control signal is still a delta function. For "supra-Poisson" (alpha>0.5) inputs, the optimal control is smooth and unique. The optimal variance obtained in the current paper sets the lowest possible bound in controlling the stochasticity of neuronal activity. We also discuss how to implement the optimal control signal for certain model neurons.     

One-dimensional chain of quantum molecule motors as a mathematical physics model for muscle fibers

A quantum chain model of multiple molecule motors is proposed as a mathematical physics theory for the microscopic modeling of classical force-velocity relation and tension transients in muscle fibers. The proposed model was a quantum many-particle Hamiltonian to predict the force-velocity relation for the slow release of muscle fibers, which has not yet been empirically defined and was much more complicated than the hyperbolic relationships. Using the same Hamiltonian model, a mathematical force-velocity relationship was proposed to explain the tension observed when the muscle was stimulated with an alternative electric current. The discrepancy between input electric frequency and the muscle oscillation frequency could be explained physically by the Doppler effect in this quantum chain model. Further more, quantum physics phenomena were applied to explore the tension time course of cardiac muscle and insect flight muscle. Most of the experimental tension transient curves were found to correspond to the theoretical output of quantum two- and three-level models. Mathematical modeling electric stimulus as photons exciting a quantum three-level particle reproduced most of the tension transient curves of water bug Lethocerus maximus.