Variability Of Spike Trains Research Articles

Differences in spike train variability in rat vasopressin and oxytocin neurons and their relationship to synaptic activity

The firing pattern of magnocellular neurosecretory neurons is intimately related to hormone release, but the relative contribution of synaptic versus intrinsic factors to the temporal dispersion of spikes is unknown. In the present study, we examined the firing patterns of vasopressin (VP) and oxytocin (OT) supraoptic neurons in coronal slices from virgin female rats, with and without blockade of inhibitory and excitatory synaptic currents. Inhibitory postsynaptic currents (IPSCs) were twice as prevalent as their excitatory counterparts (EPSCs), and both were more prevalent in OT compared with VP neurons. Oxytocin neurons fired more slowly and irregularly than VP neurons near threshold. Blockade of Cl- currents (including tonic and synaptic currents) with picrotoxin reduced interspike interval (ISI) variability of continuously firing OT and VP neurons without altering input resistance or firing rate. Blockade of EPSCs did not affect firing pattern. Phasic bursting neurons (putative VP neurons) were inconsistently affected by broad synaptic blockade, suggesting that intrinsic factors may dominate the ISI distribution during this mode in the slice. Specific blockade of synaptic IPSCs with gabazine also reduced ISI variability, but only in OT neurons. In all cases, the effect of inhibitory blockade on firing pattern was independent of any consistent change in input resistance or firing rate. Since the great majority of IPSCs are randomly distributed, miniature events (mIPSCs) in the coronal slice, these findings imply that even mIPSCs can impart irregularity to the firing pattern of OT neurons in particular, and could be important in regulating spike patterning in vivo. For example, the increased firing variability that precedes bursting in OT neurons during lactation could be related to significant changes in synaptic activity.

Linking non-binned spike train kernels to several existing spike train metrics

This work presents three kernel functions that can be used as inner product operators on non-binned spike trains, allowing the use of state-of-the-art classification techniques. One of the main advantages is that this approach does not require the spike trains to be binned. Thus a high temporal resolution is preserved which is needed when temporal coding is used. The kernels are closely related to several recent and often-used spike train metrics which take into account the biological variability of spike trains. It follows that the different existing metrics are unified by the spike train kernels presented. As a test of the classification potential of the new kernel functions, a jittered spike train template classification problem is solved.

Network Variability Limits Stimulus-Evoked Spike Timing Precision in Retinal Ganglion Cells

Visual, auditory, somatosensory, and olfactory stimuli generate temporally precise patterns of action potentials (spikes). It is unclear, however, how the precision of spike generation relates to the pattern and variability of synaptic input elicited by physiological stimuli. We determined how synaptic conductances evoked by light stimuli that activate the rod bipolar pathway control spike generation in three identified types of mouse retinal ganglion cells (RGCs). The relative amplitude, timing, and impact of excitatory and inhibitory input differed dramatically between On and Off RGCs. Spikes evoked by repeated somatic injection of identical light-evoked synaptic conductances were more temporally precise than those evoked by light. However, the precision of spikes evoked by conductances that varied from trial to trial was similar to that of light-evoked spikes. Thus, the rod bipolar pathway modulates different RGCs via unique combinations of synaptic input, and RGC temporal variability reflects variability in the input this circuit provides.

Trial-by-trial estimation of amplitude and latency variability in neuronal spike trains

The rate function underlying single-trial spike trains can vary from trial to trial. We propose to estimate the amplitude and latency variability in single-trial neuronal spike trains on a trial-by-trial basis. The firing rate over a trial is modeled by a family of rate profiles with trial-invariant waveform and trial-dependent amplitude scaling factors and latency shifts. Using a Bayesian inference framework we derive an iterative fixed-point algorithm from which the single-trial amplitude scaling factors and latency shifts are estimated. We test the performance of the algorithm on simulated data and then apply it to actual neuronal recordings from the sensorimotor cortex of the monkey.

Neural Spike Train Synchronization Indices: Definitions, Interpretations, and Applications

A comparison of previously defined spike train syncrhonization indices is undertaken within a stochastic point process framework. The second-order cumulant density (covariance density) is shown to be common to all the indices. Simulation studies were used to investigate the sampling variability of a single index based on the second-order cumulant. The simulations used a paired motoneurone model and a paired regular spiking cortical neurone model. The sampling variability of spike trains generated under identical conditions from the paired motoneurone model varied from 50% to 160% of the estimated value. On theoretical grounds, and on the basis of simulated data a rate dependence is present in all synchronization indices. The application of coherence and pooled coherence estimates to the issue of synchronization indices is considered. This alternative frequency domain approach allows an arbitrary number of spike train pairs to be evaluated for statistically significant differences, and combined into a single population measure. The pooled coherence framework allows pooled time domain measures to be derived, application of this to the simulated data is illustrated. Data from the cortical neurone model is generated over a wide range of firing rates (1-250 spikes/s). The pooled coherence framework correctly characterizes the sampling variability as not significant over this wide operating range. The broader applicability of this approach to multielectrode array data is briefly discussed.

Trial-to-Trial Variability and Its Effect on Time-Varying Dependency Between Two Neurons

The joint peristimulus time histogram (JPSTH) and cross-correlogram provide a visual representation of correlated activity for a pair of neurons, and the way this activity may increase or decrease over time. In a companion paper we showed how a Bootstrap evaluation of the peaks in the smoothed diagonals of the JPSTH may be used to establish the likely validity of apparent time-varying correlation. As noted in earlier studies by Brody and Ben-Shaul et al., trial-to-trial variation can confound correlation and synchrony effects. In this paper we elaborate on that observation, and present a method of estimating the time-dependent trial-to-trial variation in spike trains that may exceed the natural variation displayed by Poisson and non-Poisson point processes. The statistical problem is somewhat subtle because relatively few spikes per trial are available for estimating a firing-rate function that fluctuates over time. The method developed here decomposes the spike-train variability into a stimulus-related component and a trial-specific component, allowing many degrees of freedom to characterize the former while assuming a small number suffices to characterize the latter. The Bootstrap significance test of the companion paper is then modified to accommodate these general excitability effects. This methodology allows an investigator to assess whether excitability effects are constant or time-varying, and whether they are shared by two neurons. In data from two V1 neurons we find that highly statistically significant evidence of dependency disappears after adjustment for time-varying trial-to-trial variation.

The Possible Role of Spike Patterns in Cortical Information Processing

When the same visual stimulus is presented across many trials, neurons in the visual cortex receive stimulus-related synaptic inputs that are reproducible across trials (S) and inputs that are not (N). The variability of spike trains recorded in the visual cortex and their apparent lack of spike-to-spike correlations beyond that implied by firing rate fluctuations, has been taken as evidence for a low S/N ratio. A recent re-analysis of in vivo cortical data revealed evidence for spike-to-spike correlations in the form of spike patterns. We examine neural dynamics at a higher S/N in order to determine what possible role spike patterns could play in cortical information processing. In vivo-like spike patterns were obtained in model simulations. Superpositions of multiple sinusoidal driving currents were especially effective in producing stable long-lasting patterns. By applying current pulses that were either short and strong or long and weak, neurons could be made to switch from one pattern to another. Cortical neurons with similar stimulus preferences are located near each other, have similar biophysical properties and receive a large number of common synaptic inputs. Hence, recordings of a single neuron across multiple trials are usually interpreted as the response of an ensemble of these neurons during one trial. In the presence of distinct spike patterns across trials there is ambiguity in what would be the corresponding ensemble, it could consist of the same spike pattern for each neuron or a set of patterns across neurons. We found that the spiking response of a neuron receiving these ensemble inputs was determined by the spike-pattern composition, which, in turn, could be modulated dynamically as a means for cortical information processing.

Increase of Neuronal Response Variability at Higher Processing Levels as Revealed by Simultaneous Recordings

A key problem for neuronal information processing is the variability of spike trains, something that is likely to constrain the encoding of sensory signals. We measured interspike-interval variability (coefficient of variation) as well as spike-count variability (Fano factor) in the metathoracic auditory system of locusts. We performed simultaneous intracellular recordings at the first three processing levels to establish identical physiological conditions. This allows us to assess whether variability is generated anew or is reduced during synaptic transmission and processing. Both the interspike-interval variability as well as the spike-count variability revealed similar trends and showed an increase from the periphery to higher processing levels. This result was confirmed by single-cell recordings. A comparison of ascending interneurons coding for sound direction and those encoding sound patterns showed that the latter respond more reliably to repeated stimulus presentations. In general, the variability of spiking responses was much lower than expected from a Poisson process. Furthermore, we observed a strong dependence of variability on the spike rate, which differed at the three levels investigated. The differences in spike rates account for most of the differences in variability observed between processing levels. For auditory receptors, we found a good agreement between the Fano factor and the squared coefficient of variation, suggesting similarities to a renewal process of spike generation at the periphery. At the level of interneurons, the Fano factor was lower than the squared coefficient of variation; this indicates a higher reliability than expected from the interspike-interval distribution.

Spike-Train Variability of Auditory Neurons In Vivo: Dynamic Responses Follow Predictions From Constant Stimuli

Reliable accounts of the variability observed in neural spike trains are a prerequisite for the proper interpretation of neural dynamics and coding principles. Models that accurately describe neural variability over a wide range of stimulation and response patterns are therefore highly desirable, especially if they can explain this variability in terms of basic neural observables and parameters such as firing rate and refractory period. In this work, we analyze the response variability recorded in vivo from locust auditory receptor neurons under acoustic stimulation. In agreement with results from other systems, our data suggest that neural refractoriness has a strong influence on spike-train variability. We therefore explore a stochastic model of spike generation that includes refractoriness through a recovery function. Because our experimental data are consistent with a renewal process, the recovery function can be derived from a single interspike-interval histogram obtained under constant stimulation. The resulting description yields quantitatively accurate predictions of the response variability over the whole range of firing rates for constant-intensity as well as amplitude-modulated sound stimuli. Model parameters obtained from constant stimulation can be used to predict the variability in response to dynamic stimuli. These results demonstrate that key ingredients of the stochastic response dynamics of a sensory neuron are faithfully captured by a simple stochastic model framework.

Activation of Metabotropic Glutamate 2/3 Receptors Reverses the Effects of NMDA Receptor Hypofunction on Prefrontal Cortex Unit Activity in Awake Rats

Systemic exposure to N-methyl-d-aspartate (NMDA) receptor antagonists can lead to psychosis and prefrontal cortex (PFC)-dependent behavioral impairments. Agonists of metabotropic glutamate 2/3 (mGlu2/3) receptors ameliorate the adverse behavioral effects of NMDA antagonists in humans and laboratory animals, and are being considered as a novel treatment for some symptoms of schizophrenia. Despite the compelling behavioral data, the cellular mechanisms by which potentiation of mGlu2/3 receptor function attenuates the effects of NMDA receptor hypofunction remain unclear. In freely moving rats, we recorded the response of medial PFC (prelimbic) single units to treatment with the NMDA antagonist MK801 and assessed the dose-dependent effects of pre- or posttreatment with the mGlu2/3 receptor agonist LY354740 on this response. NMDA receptor antagonist-induced behavioral stereotypy was measured during recording because it may relate to the psychotomimetic properties of this treatment and is dependent on the functional integrity of the PFC. In most PFC neurons, systemic administration of MK801 increased the spontaneous firing rate, decreased the variability of spike trains, and disrupted patterns of spontaneous bursts. Given alone, LY354740 (1, 3, and 10 mg/kg) decreased spontaneous activity of PFC neurons at the highest dose. Pre- or posttreatment with LY354740 blocked MK801-induced changes on firing rate, burst activity, and variability of spike activity. These physiological changes coincided with a reduction in MK801-induced behavioral stereotypy by LY354740. These data indicate that activation of mGlu2/3 receptors reduces the disruptive effects of NMDA receptor hypofunction on the spontaneous spike activity and bursting of PFC neurons. This mechanism may provide a physiological basis for reversal of NMDA antagonist-induced behaviors by mGlu2/3 agonists.

Variability of spike trains and the processing of temporal patterns of acoustic signals-problems, constraints, and solutions.

Object recognition and classification by sensory pathways is rooted in spike trains provided by sensory neurons. Nervous systems had to evolve mechanisms to extract information about relevant object properties, and to separate these from spurious features. In this review, problems caused by spike train variability and counterstrategies are exemplified for the processing of acoustic signals in orthopteran insects. Due to size limitations of their nervous system we expect to find solutions that are stripped to the computational basics. A key feature of auditory systems is temporal resolution, which is likely limited by spike train variability. Basic strategies to reduce such variability are to integrate over time, or to average across several neurons. The first strategy is constrained by its possible interference with temporal resolution. Grasshoppers do not seem to explore temporal integration much, in spite of the repetitive structure of their songs, which invites for 'multiple looks' at the signal. The benefits of averaging across neurons depend on uncorrelated responses, a factor that may be crucial for the performance and evolution of small nervous systems. In spite of spike train variability the temporal information necessary for the recognition of conspecifics is preserved to a remarkable degree in the auditory pathway.

Neuronal discrimination capacity

We explore neuronal mechanisms of discriminating between masked signals. It is found that when the correlation between input signals is zero, the output signals are separable if and only if input signals are separable. With positively (negatively) correlated signals, the output signals are separable (mixed) even when input signals are mixed (separable). Exact values of discrimination capacity are obtained for two most interesting cases: the exactly balanced inhibitory and excitatory input case and the uncorrelated input case. Interestingly, the discrimination capacity obtained in these cases is independent of model parameters, input distribution and is universal. Our results also suggest a functional role of inhibitory inputs and correlated inputs or, more generally, the large variability of efferent spike trains observed in in vivo experiments: the larger the variability of efferent spike trains, the easier it is to discriminate between masked input signals.

Elimination of response latency variability in neuronal spike trains

Neuronal activity in the mammalian cortex exhibits a considerable amount of trial-by-trial variability. This may be reflected by the magnitude of the activity as well as by the response latency with respect to an external event, such as the onset of a sensory stimulus, or a behavioral event. Here we present a novel nonparametric method for estimating trial-by-trial differences in response latency from neuronal spike trains. The method makes use of the dynamic rate profile for each single trial and maximizes their total pairwise correlation by appropriately shifting all trials in time. The result is a new alignment of trials that largely eliminates the variability in response latency and provides a new internal trigger that is independent of experiment time. To calibrate the method, we simulated spike trains based on stochastic point processes using a parametric model for phasic response profiles. We illustrate the method by an application to simultaneous recordings from a pair of neurons in the motor cortex of a behaving monkey. It is demonstrated how the method can be used to study the temporal relation of the neuronal response to the experiment, to investigate whether neurons share the same dynamics, and to improve spike correlation analysis. Differences between this and other previously published methods are discussed.

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.

Integrate-and-fire neurons driven by correlated stochastic input.

Neurons are sensitive to correlations among synaptic inputs. However, analytical models that explicitly include correlations are hard to solve analytically, so their influence on a neuron's response has been difficult to ascertain. To gain some intuition on this problem, we studied the firing times of two simple integrate-and-fire model neurons driven by a correlated binary variable that represents the total input current. Analytic expressions were obtained for the average firing rate and coefficient of variation (a measure of spike-train variability) as functions of the mean, variance, and correlation time of the stochastic input. The results of computer simulations were in excellent agreement with these expressions. In these models, an increase in correlation time in general produces an increase in both the average firing rate and the variability of the output spike trains. However, the magnitude of the changes depends differentially on the relative values of the input mean and variance: the increase in firing rate is higher when the variance is large relative to the mean, whereas the increase in variability is higher when the variance is relatively small. In addition, the firing rate always tends to a finite limit value as the correlation time increases toward infinity, whereas the coefficient of variation typically diverges. These results suggest that temporal correlations may play a major role in determining the variability as well as the intensity of neuronal spike trains.

Gain Modulation from Background Synaptic Input

Gain modulation is a prominent feature of neuronal activity recorded in behaving animals, but the mechanism by which it occurs is unknown. By introducing a barrage of excitatory and inhibitory synaptic conductances that mimics conditions encountered in vivo into pyramidal neurons in slices of rat somatosensory cortex, we show that the gain of a neuronal response to excitatory drive can be modulated by varying the level of “background” synaptic input. Simultaneously increasing both excitatory and inhibitory background firing rates in a balanced manner results in a divisive gain modulation of the neuronal response without appreciable signal-independent increases in firing rate or spike-train variability. These results suggest that, within active cortical circuits, the overall level of synaptic input to a neuron acts as a gain control signal that modulates responsiveness to excitatory drive.

The impact of spike timing variability on the signal-encoding performance of neural spiking models.

It remains unclear whether the variability of neuronal spike trains in vivo arises due to biological noise sources or represents highly precise encoding of temporally varying synaptic input signals. Determining the variability of spike timing can provide fundamental insights into the nature of strategies used in the brain to represent and transmit information in the form of discrete spike trains. In this study, we employ a signal estimation paradigm to determine how variability in spike timing affects encoding of random time-varying signals. We assess this for two types of spiking models: an integrate-and-fire model with random threshold and a more biophysically realistic stochastic ion channel model. Using the coding fraction and mutual information as information-theoretic measures, we quantify the efficacy of optimal linear decoding of random inputs from the model outputs and study the relationship between efficacy and variability in the output spike train. Our findings suggest that variability does not necessarily hinder signal decoding for the biophysically plausible encoders examined and that the functional role of spiking variability depends intimately on the nature of the encoder and the signal processing task; variability can either enhance or impede decoding performance.

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.

Coefficient of variation vs. mean interspike interval curves: What do they tell us about the brain?

A number of models have been produced recently to explain the high variability of natural spike trains (Softky and Koch, J. Neurosci. 13 (1) (1993) 334). These models use a range of different biological mechanisms including partial somatic reset, concurrent inhibition and excitation, correlated inputs and network dynamics effects. In this paper we examine which model is more likely to reflect the mechanisms used in the brain and we evaluate the ability of each model to reproduce the experimental coefficient of variation (CV) vs. mean interspike interval (ISI) curves (CV=standard deviation/mean ISI). The results show that the partial somatic reset mechanism is the most likely candidate to reflect the mechanism used in the brain for reproducing irregular firing.

Behavior of integrate-and-fire and Hodgkin-Huxley models with correlated inputs

We assess, both numerically and theoretically, how positively correlated Poisson inputs affect the output of the integrate-and-fire and Hodgkin-Huxley models. For the integrate-and-fire model the variability of efferent spike trains is an increasing function of input correlation, and of the ratio between inhibitory and excitatory inputs. Interestingly for the Hodgkin-Huxley model the variability of efferent spike trains is a decreasing function of input correlation, and for fixed input correlation it is almost independent of the ratio between inhibitory and excitatory inputs. In terms of the signal to noise ratio of efferent spike trains the integrate-and-fire model works better in an environment of asynchronous inputs, but the Hodgkin-Huxley model has an advantage for more synchronous (correlated) inputs. In conclusion the integrate-and-fire and Hodgkin-Huxley models respond to correlated inputs in totally opposite ways.