Some Models of Neuronal Variability

The pattern of nerve action potentials produced by unit permeability changes (quantal inputs) occurring at random is considered analytically and by computer simulation methods. The important parameters of a quantal input are size and duration. Varying both the mean and the probability density function of these parameters has calculable effects on the distribution of interspike intervals. Particular attention is paid to the relation between the mean rate of excitatory inputs and the mean frequency of nerve action potentials (input-output curve) and the relation between the coefficient of variation for the interval distribution and the mean interval (variability curve). In the absence of action potentials one can determine the parameters of the voltage distribution including the autocorrelation function and the power spectrum. These parameters can sometimes be used to approximate the variability of interspike intervals as a function of the threshold voltage. Different neuronal models are considered including one containing the Hodgkin-Huxley membrane equations. The negative feedback inherent in the Hodgkin-Huxley equations tends to produce a small negative serial correlation between successive intervals. The results are discussed in relation to the interpretation of experimental results.     

Response dynamics of bullfrog ON-OFF RGCs to different stimulus durations

Stimulus duration is an important feature of visual stimulation. In the present study, response properties of bullfrog ON-OFF retinal ganglion cells (RGCs) in exposure to different visual stimulus durations were studied. By using a multi-electrode recording system, spike discharges from ON-OFF RGCs were simultaneously recorded, and the cells’ ON and OFF responses were analyzed. It was found that the ON response characteristics, including response latency, spike count, as well as correlated activity and relative latency between pair-wise cells, were modulated by different light OFF intervals, while the OFF response characteristics were modulated by different light ON durations. Stimulus information carried by the ON and OFF responses was then analyzed, and it was found that information about different light ON durations was more carried by transient OFF response, whereas information about different light OFF intervals were more carried by transient ON response. Meanwhile, more than 80 % information about stimulus durations was carried by firing rate. These results suggest that ON-OFF RGCs are sensitive to different stimulus durations, and they can efficiently encode the information about visual stimulus duration by firing rate.     

The entrainment of rhythmically discharging reticulospinal neurons of the eel by sensory nerve stimulation

Recordings made from decerebrated, paralyzed eels (Anguilla anguilla) producing rhythmical spinal motoneuronal activity showed that around 65% of identified reticulospinal units, belonging to the inferior reticular division, discharged rhythmically. The reticulospinal bursts, lasting from 300 up to 3000 ms, were in time with spinal motoneuronal bursting activity. In different fish the modal cycle period varied between 2 to 4 s and burst duration and firing frequency of each neuron showed large changes from cycle to cycle. Burst responses similar in form to those occurring spontaneously were evoked from reticular neurons when the ophthalmic nerve was stimulated regularly (intervals of 1 to 10 s) but the cycle period, firing frequency and burst duration were now more predictable. For stimulation intervals between 2 and 5 s, each ophthalmic nerve stimulus was normally followed by a burst from the reticulospinal neuron. The cycle period of the reticular rhythm then became equal to the interstimulus interval and the reticulospinal unit was entrained by the stimulus. Beyond this range of interstimulus intervals, complete entrainment was lost. We suggest that regular sensory input provides a powerful stabilising influence to rhythmically active motor systems in the brainstem and spinal cord.     

Interval timing in rats: tracking unsignaled changes in the fixed interval schedule requirement

The present experiment examined interval timing in rats under dynamic conditions. A session began with FI60 s intervals, changed to a FI20 s, FI30 s, or FI40 s schedule at an unpredictable point, and then returned to a FI60 s schedule after the rats received 1, 8, or 24 successive short FI intervals. Variations in the duration and number of shorter intervals occurred across sessions and conditions. We observed rapid control of wait time duration by the FI duration of the preceding interval (one-back tracking), and changes in wait time depended on the number and duration of the shorter intervals. Furthermore, we observed proportional and scalar timing effects in overall wait time duration. The results provide information about the relation between interval timing under dynamic and steady state conditions.     

Optimal stimulation settings for CMAP scan registrations

Background

The CMAP (Compound Muscle Action Potential) scan is a non-invasive electrodiagnostic tool, which provides a quick and visual assessment of motor unit potentials as electrophysiological components that together constitute the CMAP. The CMAP scan records the electrical activity of the muscle (CMAP) in response to transcutaneous stimulation of the motor nerve with gradual changes in stimulus intensity. Large MUs, including those that result from collateral reinnervation, appear in the CMAP scan as so-called steps, i.e., clearly visible jumps in CMAP amplitude. The CMAP scan also provides information on nerve excitability. This study aims to evaluate the influence of the stimulation protocol used on the CMAP scan and its quantification.

Methods

The stimulus frequency (1, 2 and 3 Hz), duration (0.05, 0.1 and 0.3 ms), or number (300, 500 and 1000 stimuli) in CMAP scans of 23 subjects was systematically varied while the other two parameters were kept constant. Pain was measured by means of a visual analogue scale (VAS). Non-parametric paired tests were used to assess significant differences in excitability and step variables and VAS scores between the different stimulus parameter settings.

Results

We found no effect of stimulus frequency on CMAP scan variables or VAS scores. Stimulus duration affected excitability variables significantly, with higher stimulus intensity values for shorter stimulus durations. Step variables showed a clear trend towards increasing values with decreasing stimulus number.

Conclusions

A protocol delivering 500 stimuli at a frequency of 2 Hz with a 0.1 ms pulse duration optimized CMAP scan quantification with a minimum of subject discomfort, artefact and duration of the recording. CMAP scan variables were influenced by stimulus duration and number; hence, these need to be standardized in future studies.     

Firing rate of a retinal neuron are not predictable from interspike interval statistics.

The intervals between successive action potentials (impulses, or "spikes") produced the maintained firing of a neuron (ISIs) are often treated as if they were independent on each other; that is, an impulse train is considered as a stationary renewal process. If this is so, the variability of the mean rate of firing impulses in a sequence of temporal windows should be predictable from the distribution of ISIs. This was found not to be the case for the maintained firing of retinal ganglion cells in goldfish. Although some evident nonstationarity sometimes resulted in greater variability of the observed rate distributions than those predicted (for relatively long temporal windows), as a general rule the observed rate distributions were considerable less dispersed than would be predicted by sampling of the ISI distributions. This was taken as evidence of long-term serial dependency between successive ISIs; however, two standard test for dependency (autocorrelations and serial correlograms failed to to reveal structure of sufficiently long duration to account for the effect noted.     

Interaction between the Frontal and Left Parietotemporal Areas in Verbal Thinking

The synchronization of the rhythmical components of evoked potentials (EP) was studied during verbal-task solving. A novel method of the calculation of Wavelet curve correlation was used to reveal synchronization between the evoked rhythmical components in short time intervals. This method was applied to earlier EP records, which were conducted during the search for verbal associations and revealed the successive activation of the frontal and left parietal cortical areas. Two stages of task solving were identified. Independently of the task type, the first stage was characterized by a diffuse synchronization in a broad frequency band below 22 Hz immediately after the stimulus presentation. This stage results in a realization of the verbal stimulus. The second stage was manifested in a localized synchronization between the frontal and left temporal (Wernicke's) areas in the narrow frequency band about 17 Hz only during search for associations. This specific and local synchronization took place earlier than the diffuse activation of the left temporal cortex. This stage appears to reflect the information transmission from the frontal cortex to the left parietotemporal area.     

Visuomotor synchronization: Analysis of the initiation and stable synchronization phases

The initiation phase of visuomotor synchronization and the phase of stable synchronization were studied in an experiment where eight adult subjects synchronized their motor responses with an isochronous sequence of visual stimuli. The period of the sequence varied in a wide range (from 500 to 2200 ms). Analysis of the statistical characteristics of synchronization errors (asynchronies) showed that the phase of stable visuomotor synchronization fit the model of current phase correction of a central timer; as in the case of audiomotor synchronization, the variability of the intervals of the central timer and the phase correction coefficient increased with increasing period of the stimulus sequence. The initiation phase of visuomotor synchronization was characterized by a considerable inter-and intraindividual variability of the form (exponential, linear, or step) and duration (from one to ten responses) of the transition from reacting to a sensory signal to synchronization. The shape and duration of the transitional region depend on the phase correction coefficient and the possibility of using an estimate of the sequence period stored in memory. The obtained data indicate that the initiation stage is not automatic throughout the studied range of periods of the visual stimulus sequence; in particular, working memory plays a substantial role in its organization.     

Long bone articular and diaphyseal structure in Old World monkeys and apes. II: Estimation of body mass

Body mass estimation equations are generated from long bone cross-sectional diaphyseal and articular surface dimensions in 176 individuals and 12 species of hominoids and cercopithecoids. A series of comparisons is carried out to determine the best body mass predictors for each of several taxonomic/locomotor groupings. Articular breadths are better predictors than articular surface areas, while cross-sectional shaft strengths are better predictors than shaft external breadths. Percent standard errors of estimate (%SEEs) and percent prediction errors for most of the better predictors range between 10-20%. Confidence intervals of equations using sex/species means are fairly representative of those calculated using individual data, except for sex/species means equations with very low %SEEs (under about 10%), where confidence intervals (CIs) based on individuals are likely to be larger. Given individual variability, or biological "error," this may represent a lower limit of precision in estimating individual body masses. In general, it is much more preferable to determine at least broad locomotor affinities, and thus appropriate modern reference groups, before applying body mass estimation equations. However, some structural dimensions are less sensitive to locomotor distinctions than others; for example, proximal tibial articular M-L breadth is apparently "locomotor blind" regarding body mass estimation within the present study sample. In other cases where locomotor affiliation is uncertain, mean estimates from different reference groups can be used, while for some dimensions no estimation should be attempted. The techniques are illustrated by estimating the body masses of four fossil anthropoid specimens of Proconsul nyanzae, Proconsul heseloni, Morotopithecus bishopi, and Theropithecus oswaldi.     

Effects on discrimination performance of selective attention to tactile features

This study examined selective attention to tactile dimensions by combining a selective cueing paradigm with a test of integrality. In Experiment 1, subjects selectively attended to changes in the frequency or duration of pairs of vibrotactile stimuli and identified the higher frequency or longer duration stimulus. In Experiment 2, using surface gratings in an identical experimental procedure, subjects identified the rougher or longer duration stimulus. In both experiments, greater performance accuracy was found on trials where the cue correctly (valid) predicted the changing dimension, vs incorrectly (invalid) cued or no-cue (neutral) trials. More errors on the invalidly vs neutrally cued trials show the cost of focal attention. Increases in performance on validly vs neutrally cued trials show a benefit of filtering irrelevant stimuli in the cued conditions. Results effectively demonstrate focal attention to tactile features. Tests of integrality, in terms of the effects of correlated change in both dimensions, showed no redundancy gain for either vibrotactile or grating tasks, suggesting that frequency and roughness are separable from stimulus duration. Interference of negative correlated change for frequency but not roughness discriminations may be explained by differences in task difficulty.     

Effects on discrimination performance of selective attention to tactile features

This study examined selective attention to tactile dimensions by combining a selective cueing paradigm with a test of integrality. In Experiment 1, subjects selectively attended to changes in the frequency or duration of pairs of vibrotactile stimuli and identified the higher frequency or longer duration stimulus. In Experiment 2, using surface gratings in an identical experimental procedure, subjects identified the rougher or longer duration stimulus. In both experiments, greater performance accuracy was found on trials where the cue correctly (valid) predicted the changing dimension, vs incorrectly (invalid) cued or no-cue (neutral) trials. More errors on the invalidly vs neutrally cued trials show the cost of focal attention. Increases in performance on validly vs neutrally cued trials show a benefit of filtering irrelevant stimuli in the cued conditions. Results effectively demonstrate focal attention to tactile features. Tests of integrality, in terms of the effects of correlated change in both dimensions, showed no redundancy gain for either vibrotactile or grating tasks, suggesting that frequency and roughness are separable from stimulus duration. Interference of negative correlated change for frequency but not roughness discriminations may be explained by differences in task difficulty.     

Resolution of pheromone pulses in receptor cells of Antheraea polyphemus at different temperatures

The ability of pheromone receptor cells of male Antheraea polyphemus (Saturniidae) to resolve stimulus pulses was determined at different temperatures (8°, 18°, 28°C). The cells were stimulated by repeated 20-ms puffs of the pheromone components (E, Z)-6, 11-hexadecadienyl acetate and (E, Z)-6,11-hexadecadienal. At higher temperatures, higher frequencies of stimulus pulses were resolved by the nerve-impulse response: about 1.25 pulses per second at 8°C, 2.5 pulses/s at 18°C and 5 pulses/s at 28°C. The decreased ability of receptor cells to resolve stimulus pulses at low temperatures may reduce the male moth's chance of reaching the pheromone source. The peak nerve-impulse frequency increased whereas the duration of nerve-impulse responses to single stimulus pulses decreased at higher temperatures. At a given temperature and stimulus intensity the peak nerveimpulse frequency decreased with shorter intervals between the stimulus pulses, but the duration of the responses remained almost constant. The time needed for recovery from adaptation caused by a single stimulus pulse was longer at lower temperatures. The aldehyde receptor cell recovered more quickly than the acetate cell. At low stimulus concentration, the resolution ability of the acetate cell was strongly decreased, whereas in the aldehyde cell it was only slightly impaired.     

Reduction of information redundancy in the ascending auditory pathway

Information processing by a sensory system is reflected in the changes in stimulus representation along its successive processing stages. We measured information content and stimulus-induced redundancy in the neural responses to a set of natural sounds in three successive stations of the auditory pathway-inferior colliculus (IC), auditory thalamus (MGB), and primary auditory cortex (A1). Information about stimulus identity was somewhat reduced in single A1 and MGB neurons relative to single IC neurons, when information is measured using spike counts, latency, or temporal spiking patterns. However, most of this difference was due to differences in firing rates. On the other hand, IC neurons were substantially more redundant than A1 and MGB neurons. IC redundancy was largely related to frequency selectivity. Redundancy reduction may be a generic organization principle of neural systems, allowing for easier readout of the identity of complex stimuli in A1 relative to IC.     

Stimulus representation in SOP: II. An application to inhibition of delay

The componential extension of SOP accounts for conditioned response (CR) timing in Pavlovian conditioning by assuming that learning accrues with relative independence to stimulus elements that are differentially occasioned during the duration of the conditioned stimulus (CS). SOP, using a competitive learning rule and the assumption that temporal learning emerges via resolution of what is equivalent to an "AX+BX-" discrimination, predicts a progressive increase in the latency of the CR over training, or what Pavlov refer to as "inhibition of delay." Other componential models, which use noncompetitive learning rules, do not predict inhibition of delay. Either type of model makes the prediction indicated, independently of the length of the CS-unconditioned stimulus (US) interval. We report two experiments that demonstrated inhibition of delay when rabbits were trained with relatively long, but not with short, CS-US intervals. To account for this divergence, we assumed that the SOP stimulus trace involves two kinds of elements, some with a temporally distributed pattern of activity over the duration of the CS duration, and some with a randomly distributed pattern. This stimulus representation, not only allows for inhibition of delay with long but not short CS-US intervals, but in combination with SOP's performance rule deduces CR's with "Weber variability."     

When perceptual time stands still: long percept-memory in binocular rivalry

We have carried out binocular rivalry experiments with a large number of subjects to obtain high quality statistics on probability distribution of dominance duration (PDDD) for two cases where (a) the rival stimulus is continuously presented and (b) the rival stimulus is periodically removed, with stimulus-on and stimulus-off intervals T(on) and T(off) respectively. In the present study we have chosen to study the regime of relatively long stimulus-on time, i.e., T(on)> 1s, where the stimulus presentation duration is significantly longer than the human reaction and recognition time. In the case of periodically removed stimulus, the total probability for percept reversal during each of the successive stimulus-on intervals T(on) can be predicted using the PDDD for continuous viewing. More importantly, this total probability for percept reversal during any stimulus-on interval is independent of the length T(off) of the preceding blank time, which can be quite long. We argue that this suggests that, in the regime of long T(on) and T(off) considered here, the variables representing the perceptual state do not change significantly during long blank intervals. We discuss that these findings impose challenges to theoretical models which aim at describing visual perception.     

Multiscale spike train variability in primary electrosensory afferents.

Spike train variability is of fundamental importance for understanding how information is encoded and processed in the nervous system. Most studies in this area have focused on short-term variability, as characterized by the coefficient of variation of the interspike interval distribution. Here we discuss the importance of extending the analysis of spike train variability to longer time scales that span multiple interspike intervals. Recent experimental and modeling studies of probability coding (P-type) electrosensory afferent nerve fibers in weakly electric fish have provided new insights into the functional importance of multiscale spike train variability. P-type afferent spike trains are moderately irregular on short time scales of a few milliseconds, but show significantly enhanced regularity on time scales of a few hundred milliseconds. This increased regularity is beyond what would be expected for a renewal process model in which successive intervals are uncorrelated. Modeling studies suggest that the correlation structure that underlies spike train regularization arises from relative refractory effects associated with a dynamic spike threshold. Spike train regularization in P-type afferents has been shown to significantly enhance signal detectability and information transmission on time scales that are functionally relevant for electrolocation behavior.     

Hi-Fi transmission of periodic signals amid cell-to-cell variability

Since information in intracellular calcium signaling is often frequency encoded, it is physiologically critical and experimentally useful to have reliable, convenient, and non-invasive methods to entrain it. Because of cell-to-cell variability, synchronization of intracellular signaling across a population of genetically identical cells can still be difficult to achieve. For intrinsically oscillatory signaling pathways, such as calcium, upon continuous stimulation, cell-to-cell variability is manifested as differences in intracellular response frequencies. Even with entrainment using periodic stimulation, cell-to-cell variability is manifested as differences in the fidelity with which extracellular inputs are converted into intracellular signals. Here we present a combined theoretical and experimental analysis that shows how to appropriately balance stimulation strength, duration, and rest intervals to achieve entrainment with high fidelity stimulation-to-response ratios for G-protein-coupled receptor-triggered intracellular calcium oscillations. We further demonstrate that stimulation parameters that give high fidelity entrainment are significantly altered upon changes in intracellular enzyme levels and cell surface receptor levels. Theoretical analysis suggests that, at key threshold values, even small changes in these protein concentrations or activities can result in precipitous changes in entrainment fidelity, with implications for pathophysiology.     

Effect of stimulus (postsynaptic current) shape on fibre excitation.

Effects of variation of the stimulus pulse shape on the excitation of a nonmyelinated nerve fibre were studied using a mathematical model based on the Hodgkin-Huxley equations. Efficiency of smoothly changing pulses was compared with that of rectangular pulses. For pulses shorter than the time to excitation, the rate of the stimulus rise did not determine the ability of a smoothly changing pulse to excite the fibre. For a given stimulus duration, the main factor was the pulse area or the charge delivered by the pulse. The strength-duration curve for smoothly changing pulses was a nonmonotonic function, in contrast to the curve for rectangular pulses. The dependence of latency on changes in the pulse area was non-linear. It would be nonmonotonic when the pulse area variation were due to the stimulus duration or the stimulus rise duration. More that one propagating intracellular action potential (IAP) could arise upon fibre activation by a long smoothly changing threshold stimulus. Upon activation of relatively short fibres the IAP could arise not at the site of the smoothly changing stimulus injection. The rectangular pulses of long duration were more efficient than the corresponding smoothly changing ones. Irrespective of the shape, the pulses whose duration at the foot is 1-2 ms, are more suitable for a prolonged threshold fibre activation.     

The frequency selectivity of information-processing channels in the tactile sensory system

The frequency selectivity of the P, NP I, and NP II channels of the four-channel model of mechanoreception for glabrous skin was measured psychophysically by an adaptation tuning curve procedure. The results substantially extend the frequency range over which the frequency selectivity of these channels is known and further confirm the hypothesis that the input stage of each of these channels consists of specific sensory nerve fibers and associated receptors. Specifically, the frequency characteristics of Pacinian nerve fibers, rapidly adapting (RA) nerve fibers, and slowly adapting Type II (SA II) nerve fibers were found to be the peripheral neurophysiological correlates of the P, NP I, and NP II channels, respectively. The finding that the tuning characteristic for a test stimulus of 250 Hz delivered through a small (0.008 cm2) contactor depended dramatically on the duration of the test stimulus whereas the detection threshold did not, provides new evidence in support of the hypothesis that separate NP II and P channels exist.     

Noise,not stimulus entropy,determines neural information rate

In the quest for deciphering the neural code, theoretical advances were made which allow for the determination of the information rate inherent in the spike trains of nerve cells. However, up to now, the dependence of the information rate on stimulus parameters has not been studied in any neuron in a systematic way. Here, I investigate the information carried by the spike trains of H1, a motion-sensitive visual interneuron of the blowfly (Calliphora vicina) using a moving grating as a stimulus. Stimulus parameters fall in two classes: those that have only a minor effect on the information rate like increasing the frequency bandwidth or the maximum amplitude of the stimulus velocity, and those which dramatically affect the neural information rate, like varying the spatial size or the contrast of the visual pattern being moved. It appears that, for a broad range of complex stimuli, the neuron covers the stimulus with its whole response repertoire regardless of the stimulus entropy, with the information rate being limited by the noise of the stimulus and the neural hardware.