Slow Resting State Fluctuations Enhance Neuronal and Behavioral Responses to Looming Sounds.

We investigate both experimentally and using a computational model how the power of the electroencephalogram (EEG) recorded in human subjects tracks the presentation of sounds with acoustic intensities that increase exponentially (looming) or remain constant (flat). We focus on the link between this EEG tracking response, behavioral reaction times and the time scale of fluctuations in the resting state, which show considerable inter-subject variability. Looming sounds are shown to generally elicit a sustained power increase in the alpha and beta frequency bands. In contrast, flat sounds only elicit a transient upsurge at frequencies ranging from 7 to 45 Hz. Likewise, reaction times (RTs) in an audio-tactile task at different latencies from sound onset also present significant differences between sound types. RTs decrease with increasing looming intensities, i.e. as the sense of urgency increases, but remain constant with stationary flat intensities. We define the reaction time variation or "gain" during looming sound presentation, and show that higher RT gains are associated with stronger correlations between EEG power responses and sound intensity. Higher RT gain further entails higher relative power differences between loom and flat in the alpha and beta bands. The full-width-at-half-maximum of the autocorrelation function of the eyes-closed resting state EEG also increases with RT gain. The effects are topographically located over the central and frontal electrodes. A computational model reveals that the increase in stimulus-response correlation in subjects with slower resting state fluctuations is expected when EEG power fluctuations at each electrode and in a given band are viewed as simple coupled low-pass filtered noise processes jointly driven by the sound intensity. The model assumes that the strength of stimulus-power coupling is proportional to RT gain in different coupling scenarios, suggesting a mechanism by which slower resting state fluctuations enhance EEG response and shorten reaction times.

Cooling reverses pathological bifurcations to spontaneous firing caused by mild traumatic injury.

Mild traumatic injury can modify the key sodium (Na+) current underlying the excitability of neurons. It causes the activation and inactivation properties of this current to become shifted to more negative trans-membrane voltages. This so-called coupled left shift (CLS) leads to a chronic influx of Na+ into the cell that eventually causes spontaneous or "ectopic" firing along the axon, even in the absence of stimuli. The bifurcations underlying this enhanced excitability have been worked out in full ionic models of this effect. Here, we present computational evidence that increased temperature T can exacerbate this pathological state. Conversely, and perhaps of clinical relevance, mild cooling is shown to move the naturally quiescent cell further away from the threshold of ectopic behavior. The origin of this stabilization-by-cooling effect is analyzed by knocking in and knocking out, one at a time, various processes thought to be T-dependent. The T-dependence of the Na+ current, quantified by its Q 10-Na factor, has the biggest impact on the threshold, followed by Q 10-pump of the sodium-potassium exchanger. Below the ectopic boundary, the steady state for the gating variables and the resting potential are not modified by temperature, since our model separately tallies the Na+ and K+ ions including their separate leaks through the pump. When only the gating kinetics are considered, cooling is detrimental, but in the full T-dependent model, it is beneficial because the other processes dominate. Cooling decreases the pump's activity, and since the pump hyperpolarizes, less hyperpolarization should lead to more excitability and ectopic behavior. But actually the opposite happens in the full model because decreased pump activity leads to smaller gradients of Na+ and K+, which in turn decreases the driving force of the Na+ current.

Optimal heterogeneity for coding in spiking neural networks.

The effect of cellular heterogeneity on the coding properties of neural populations is studied analytically and numerically. We find that heterogeneity decreases the threshold for synchronization, and its strength is nonlinearly related to the network mean firing rate. In addition, conditions are shown under which heterogeneity optimizes network information transmission for either temporal or rate coding, with high input frequencies leading to different effects for each coding strategy. The results are shown to be robust for more realistic conditions.

Envelope gating and noise shaping in populations of noisy neurons.

Narrowband signals have fast and slow time scales. The transmission of narrowband signal features on both times cales, by spiking neurons, is demonstrated experimentally and theoretically. The interaction of the narrowband input and the threshold nonlinearity may create out-of-band interference, hindering the transmission of signals in a low-frequency range. The resultant out-of-band signal is the "envelope," or time-varying modulation of the narrowband signal. The levels of noise and nonlinearity intrinsic to the neuron gate transmission on the slow "envelope" time scale. When a narrowband and a distinct slow signal drive the neuron, the slow signal may be poorly transmitted. Increasing intrinsic noise in an averaging network removes the envelope in favor of the slow signal, paradoxically increasing the signal-to-noise ratio. These gating effects are generic for threshold and excitable systems.

Negative interspike interval correlations increase the neuronal capacity for encoding time-dependent stimuli.

Accurate detection of sensory input is essential for the survival of a species. Weakly electric fish use amplitude modulations of their self-generated electric field to probe their environment. P-type electroreceptors convert these modulations into trains of action potentials. Cumulative relative refractoriness in these afferents leads to negatively correlated successive interspike intervals (ISIs). We use simple and accurate models of P-unit firing to show that these refractory effects lead to a substantial increase in the animal's ability to detect sensory stimuli. This assessment is based on two approaches, signal detection theory and information theory. The former is appropriate for low-frequency stimuli, and the latter for high-frequency stimuli. For low frequencies, we find that signal detection is dependent on differences in mean firing rate and is optimal for a counting time at which spike train variability is minimal. Furthermore, we demonstrate that this minimum arises from the presence of negative ISI correlations at short lags and of positive ISI correlations that extend out to long lags. Although ISI correlations might be expected to reduce information transfer, in fact we find that they improve information transmission about time-varying stimuli. This is attributable to the differential effect that these correlations have on the noise and baseline entropies. Furthermore, the gain in information transmission rate attributable to correlations exhibits a resonance as a function of stimulus bandwidth; the maximum occurs when the inverse of the cutoff frequency of the stimulus is of the order of the decay time constant of refractory effects. Finally, we show that the loss of potential information caused by a decrease in spike-timing resolution is smaller for low stimulus cutoff frequencies than for high ones. This suggests that a rate code is used for the encoding of low-frequency stimuli, whereas spike timing is important for the encoding of high-frequency stimuli.

Irregular pupil cycling as a characteristic abnormality in patients with demyelinative optic neuropathy.

We used an infrared videopupillometer combined with an electronic circuit that regulated the retinal light level as a function of pupil area to assess the regularity of pupil cycling in normal subjects and in patients with known abnormalities in the pupil light reflex pathways. The light stimulus was turned on whenever pupil area exceeded a preset value. Two types of abnormalities were observed for patients with demyelinative optic neuropathy: a failure of the pupil to cycle despite a preserved pupillary response to a single light pulse; and, for those patients in whom cycling was possible, a characteristic intermittent irregularity in the amplitude of pupil cycling. These abnormalities were not seen in normal subjects or in patients with ischemic optic neuropathy, surgical lesions involving the optic chiasm, Adie's syndrome, or Horner's syndrome.

Evaluation of pupil constriction and dilation from cycling measurements.

Pupil cycling was produced using an electronic circuit so that the retina was illuminated in Maxwellian view only when pupil area exceeded an adjustable area threshold, Aref. The maximum (Amax) and minimum (Amin) amplitude of the oscillations varied linearly with Aref. These observations are described by a delay-differential equation. The Aref-dependent changes in Amax, Amin were used, respectively, to quantitate dilation and constriction. A comparison of the predicted and observed period of pupil cycling suggests that the latency times for light onset and offset are the same. Measurements of Amax, Amin provide a method for determining the average pupil light response.

Firing statistics of a neuron model driven by long-range correlated noise.

We study the statistics of the firing patterns of a perfect integrate and fire neuron model driven by additive long-range correlated Ornstein-Uhlenbeck noise. Using a quasistatic weak noise approximation we obtain expressions for the interspike interval (ISI) probability density, the power spectral density, and the spike count Fano factor. We find unimodal, long-tailed ISI densities, Lorenzian power spectra at low frequencies, and a minimum in the Fano factor as a function of counting time. The implications of these results for signal detection are discussed.

Spike train patterning and forecastability.

Theories of neural coding rely on a knowledge of correlations between firing events. These correlations are also useful to validate biophysical models for the neural activity. We present a methodology for validating models based on the assessment of linear and non-linear correlations between variables derived from the spike train. The firing pattern of an electroreceptor is analyzed in this framework. We show that a purely stochastic model fails to capture the essential correlations between interspike intervals, even though it reproduces the interval histogram and certain spike train spectral features. However, a biophysical model, based on the Fitzhugh-Nagumo equations with noise, does exhibit many of the correlations seen in the data, including those between successive firing phases.

Modeling cancelation of periodic inputs with burst-STDP and feedback.

Prediction and cancelation of redundant information is an important feature that many neural systems must display in order to efficiently code external signals. We develop an analytic framework for such cancelation in sensory neurons produced by a cerebellar-like structure in wave-type electric fish. Our biologically plausible mechanism is motivated by experimental evidence of cancelation of periodic input arising from the proximity of conspecifics as well as tail motion. This mechanism involves elements present in a wide range of systems: (1) stimulus-driven feedback to the neurons acting as detectors, (2) a large variety of temporal delays in the pathways transmitting such feedback, responsible for producing frequency channels, and (3) burst-induced long-term plasticity. The bursting arises from back-propagating action potentials. Bursting events drive the input frequency-dependent learning rule, which in turn affects the feedback input and thus the burst rate. We show how the mean firing rate and the rate of production of 2- and 4-spike bursts (the main learning events) can be estimated analytically for a leaky integrate-and-fire model driven by (slow) sinusoidal, back-propagating and feedback inputs as well as rectified filtered noise. The effect of bursts on the average synaptic strength is also derived. Our results shed light on why bursts rather than single spikes can drive learning in such networks "online", i.e. in the absence of a correlative discharge. Phase locked spiking in frequency specific channels together with a frequency-dependent STDP window size regulate burst probability and duration self-consistently to implement cancelation.

Oscillatory response in a sensory network of ON and OFF cells with instantaneous and delayed recurrent connections.

A neural field model with multiple cell-to-cell feedback connections is investigated. Our model incorporates populations of ON and OFF cells, receiving sensory inputs with direct and inverted polarity, respectively. Oscillatory responses to spatially localized stimuli are found to occur via Andronov-Hopf bifurcations of stationary activity. We explore the impact of multiple delayed feedback components as well as additional excitatory and/or inhibitory non-delayed recurrent signals on the instability threshold. Paradoxically, instantaneous excitatory recurrent terms are found to enhance network responsiveness by reducing the oscillatory response threshold, allowing smaller inputs to trigger oscillatory activity. Instantaneous inhibitory components do the opposite. The frequency of these response oscillations is further shaped by the polarity of the non-delayed terms.

Pulse-coupled neuron models as investigative tools for musical consonance.

We investigate the mode locking properties of simple dynamical models of pulse-coupled neurons to two tones, i.e., simple musical intervals. A recently proposed nonlinear synchronization theory of musical consonance links the subjective ranking from consonant to dissonant intervals to the universal ordering of robustness of mode locking ratios in forced nonlinear oscillators. The theory was illustrated using two leaky integrate-and-fire neuron models with mutual excitatory coupling, with each neuron firing at one of the two frequencies in the musical interval. We show that the ordering of mode locked states in such models is not universal, but depends on coupling strength. Further, unless the coupling is weak, the observed ratio of firing frequencies is higher than that of the input tones. We finally explore generic aspects of a possible synchronization theory by driving the model neurons with sinusoidal forcing, leading to down-converted, more realistic firing rates. This model exhibits one-to-one entrainment when the input frequencies are in simple ratios. We also consider the robustness to the presence of noise that is present in the neural firing activity. We briefly discuss agreements and discrepancies between predictions from this theory and physiological/psychophysical data, and suggest directions in which to develop this theory further.

Encoding with bursting, subthreshold oscillations, and noise in mammalian cold receptors.

Mammalian cold thermoreceptors encode steady-state temperatures into characteristic temporal patterns of action potentials. We propose a mechanism for the encoding process. It is based on Plant's ionic model of slow wave bursting, to which stochastic forcing is added. The model reproduces firing patterns from cat lingual cold receptors as the parameters most likely to underlie the thermosensitivity of these receptors varied over a 25 degrees C range. The sequence of firing patterns goes from regular bursting, to simple periodic, to stochastically phase-locked firing or "skipping." The skipping at higher temperatures is shown to necessitate an interaction between noise and a subthreshold endogenous oscillation in the receptor. The basic period of all patterns is robust to noise. Further, noise extends the range of encodable stimuli. An increase in firing irregularity with temperature also results from the loss of stability accompanying the approach by the slow dynamics of a reverse Hopf bifurcation. The results are not dependent on the precise details of the Plant model, but are generic features of models where an autonomous slow wave arises through a Hopf bifurcation. The model also addresses the variability of the firing patterns across fibers. An alternate model of slow-wave bursting (Chay and Fan 1993) in which skipping can occur without noise is also analyzed here in the context of cold thermoreception. Our study quantifies the possible origins and relative contribution of deterministic and stochastic dynamics to the coding scheme. Implications of our findings for sensory coding are discussed.

Multicompartment model of lung dynamics.

A mathematical model was developed to simulate the function of the lungs. The lungs are represented by 24 compartments each corresponding to a generation of the Weibel model A. In the model it is assumed that gases are transported in the lungs by convection and diffusion from one compartment to the other. Furthermore, the clearance of gases from the lungs by the blood perfusion is taken into account. The driving force of the inhalation and exhalation processes is the filling and emptying of the alveolar volume which follows a sinusoidal pattern. Mathematically the model is represented by two sets (one for inhalation, the other for exhalation) of 24 first-order coupled ordinary differential equations which were numerically integrated by means of a computer. The model predicts quite well the buildup of gases in the lungs and the washout of gases from the lungs.

A new model of the acoustic reflex.

A system-type model of the acoustic reflex in man is proposed with the intention of sheding light on certain of its nonlinear behaviors. This model is the first to incorporate into the multipath structure of the reflex arc the adaptation and recovery processes. Parameter distribution in the parallel pathways is based on the current knowledge on the stapedius muscle and on motoneuron pool organization. A piecewise linear system is used in modeling adaptation at onset and recovery at offset. The model is calibrated at 2000 Hz, a frequency for which all the important parameters are available. Two nonlinear behaviors of the adaptation rate are explained: the frequency and intensity dependence, related respectively to the frequency dependence of the feedback gain and to the sigmoidal shape of the closed-loop stimulus-response curve. Underlying physiological mechanisms are discussed, along with other plausible nonlinear models, and extensions of the model to other stimuli are suggested.

Insight into the transfer function, gain, and oscillation onset for the pupil light reflex using nonlinear delay-differential equations.

Analogies are drawn between a physiologically relevant nonlinear delay-differential equation (DDE) model for the pupil light reflex and servo control analytic approaches. This DDE is shown to be consistent with the measured open loop transfer function and hence physiological insight can be obtained into the gain of the reflex and its properties. A Hopf bifurcation analysis of the DDE shows that a limit cycle oscillation in pupil area occurs when the first mode of the characteristic equation becomes unstable. Its period agrees well with experimental measurements. Beyond the point of instability onset, more modes become unstable corresponding to multiple encirclings of (-1, 0) on the Nyquist plot. These modes primarily influence the shape of the oscillation. Techniques from dynamical systems theory, e.g. bifurcation analysis, can augment servo control analytic methods for the study of oscillations produced by nonlinear neural feedback mechanisms.

Modelling autonomous oscillations in the human pupil light reflex using non-linear delay-differential equations.

Neurophysiological and anatomical observations are used to derive a non-linear delay-differential equation for the pupil light reflex with negative feedback. As the gain or the time delay in the reflex is increased, a supercritical Hopf bifurcation occurs from a stable fixed point to a stable limit cycle oscillation in pupil area. A Hopf bifurcation analysis is used to determine the conditions for instability and the period and amplitude of these oscillations. The more complex waveforms typical of the occurrence of higher order bifurcations were not seen in numerical simulations of the model. This model provides a general framework to study the different types of dynamical behaviors which can be produced by the pupil light reflex, e.g. edge-light pupil cycling.

Bistability and the dynamics of periodically forced sensory neurons.

Many neurons at the sensory periphery receive periodic input, and their activity exhibits entrainment to this input in the form of a preferred phase for firing. This article describes a modeling study of neurons which skip a random number of cycles of the stimulus between firings over a large range of input intensities. This behavior was investigated using analog and digital simulations of the motion of a particle in a double-well with noise and sinusoidal forcing. Well residence-time distributions were found to exhibit the main features of the interspike interval histograms (ISIH) measured on real sensory neurons. The conditions under which it is useful to view neurons as simple bistable systems subject to noise are examined by identifying the features of the data which are expected to arise for such systems. This approach is complementary to previous studies of such data based, e.g., on non-homogeneous point processes. Apart from looking at models which form the backbone of excitable models, our work allows us to speculate on the role that stochastic resonance, which can arise in this context, may play in the transmission of sensory information.