Adaptive Spike Threshold Enables Robust and Temporally Precise Neuronal Encoding

Neural processing rests on the intracellular transformation of information as synaptic inputs are translated into action potentials. This transformation is governed by the spike threshold, which depends on the history of the membrane potential on many temporal scales. While the adaptation of the threshold after spiking activity has been addressed before both theoretically and experimentally, it has only recently been demonstrated that the subthreshold membrane state also influences the effective spike threshold. The consequences for neural computation are not well understood yet. We address this question here using neural simulations and whole cell intracellular recordings in combination with information theoretic analysis. We show that an adaptive spike threshold leads to better stimulus discrimination for tight input correlations than would be achieved otherwise, independent from whether the stimulus is encoded in the rate or pattern of action potentials. The time scales of input selectivity are jointly governed by membrane and threshold dynamics. Encoding information using adaptive thresholds further ensures robust information transmission across cortical states i.e. decoding from different states is less state dependent in the adaptive threshold case, if the decoding is performed in reference to the timing of the population response. Results from in vitro neural recordings were consistent with simulations from adaptive threshold neurons. In summary, the adaptive spike threshold reduces information loss during intracellular information transfer, improves stimulus discriminability and ensures robust decoding across membrane states in a regime of highly correlated inputs, similar to those seen in sensory nuclei during the encoding of sensory information.     

Spike correlation measures that eliminate stimulus effects in response to white noise

When measured in response to non-repeating white noise, standard covariance measures of two neuronal spike trains contain components due simply to a shared stimulus. We argue that, without stimulus repeats, model-free measures cannot in general remove these stimulus-induced components. We present spike correlation measures that eliminate them when the neural response can be approximated by a linear-nonlinear system. One of these measures fully characterizes the correlations in the special case that all remaining correlations are due to small reciprocal connections between the neurons. In addition, we demonstrate that the proposed measures can give accurate results with a more realistic, integrate-and-fire model of neural response, provided that it is driven like a linear-nonlinear system.     

Neural coding properties based on spike timing and pattern correlation of retinal ganglion cells

Correlation between spike trains or neurons sometimes indicates certain neural coding rules in the visual system. In this paper, the relationship between spike timing correlation and pattern correlation is discussed, and their ability to represent stimulus features is compared to examine their coding strategies not only in individual neurons but also in population. Two kinds of stimuli, natural movies and checkerboard, are used to arouse firing activities in chicken retinal ganglion cells. The spike timing correlation and pattern correlation are calculated by cross-correlation function and Lempel–Ziv distance respectively. According to the correlation values, it is demonstrated that spike trains with similar spike patterns are not necessarily concerted in firing time. Moreover, spike pattern correlation values between individual neurons’ responses reflect the difference of natural movies and checkerboard; neurons cooperate with each other with higher pattern correlation values which represent spatiotemporal correlations during response to natural movies. Spike timing does not reflect stimulus features as obvious as spike patterns, caused by their particular coding properties or physiological foundation. As a result, separating the pattern correlation out of traditional timing correlation concept uncover additional insight in neural coding.     

Decorrelation of Neural-Network Activity by Inhibitory Feedback

Correlations in spike-train ensembles can seriously impair the encoding of information by their spatio-temporal structure. An inevitable source of correlation in finite neural networks is common presynaptic input to pairs of neurons. Recent studies demonstrate that spike correlations in recurrent neural networks are considerably smaller than expected based on the amount of shared presynaptic input. Here, we explain this observation by means of a linear network model and simulations of networks of leaky integrate-and-fire neurons. We show that inhibitory feedback efficiently suppresses pairwise correlations and, hence, population-rate fluctuations, thereby assigning inhibitory neurons the new role of active decorrelation. We quantify this decorrelation by comparing the responses of the intact recurrent network (feedback system) and systems where the statistics of the feedback channel is perturbed (feedforward system). Manipulations of the feedback statistics can lead to a significant increase in the power and coherence of the population response. In particular, neglecting correlations within the ensemble of feedback channels or between the external stimulus and the feedback amplifies population-rate fluctuations by orders of magnitude. The fluctuation suppression in homogeneous inhibitory networks is explained by a negative feedback loop in the one-dimensional dynamics of the compound activity. Similarly, a change of coordinates exposes an effective negative feedback loop in the compound dynamics of stable excitatory-inhibitory networks. The suppression of input correlations in finite networks is explained by the population averaged correlations in the linear network model: In purely inhibitory networks, shared-input correlations are canceled by negative spike-train correlations. In excitatory-inhibitory networks, spike-train correlations are typically positive. Here, the suppression of input correlations is not a result of the mere existence of correlations between excitatory (E) and inhibitory (I) neurons, but a consequence of a particular structure of correlations among the three possible pairings (EE, EI, II).     

Spatiotemporal burst coding for extracting features of spatiotemporally varying stimuli

Encoding features of spatiotemporally varying stimuli is quite important for understanding the neural mechanisms of various sensory coding. Temporal coding can encode features of time-varying stimulus, and population coding with temporal coding is adequate for encoding spatiotemporal correlation of stimulus features into spatiotemporal activity of neurons. However, little is known about how spatiotemporal features of stimulus are encoded by spatiotemporal property of neural activity. To address this issue, we propose here a population coding with burst spikes, called here spatiotemporal burst (STB) coding. In STB coding, the temporal variation of stimuli is encoded by the precise onset timing of burst spike, and the spatiotemporal correlation of stimuli is emphasized by one specific aspect of burst firing, or spike packet followed by silent interval. To show concretely the role of STB coding, we study the electrosensory system of a weakly electric fish. Weakly electric fish must perceive the information about an object nearby by analyzing spatiotemporal modulations of electric field around it. On the basis of well-characterized circuitry, we constructed a neural network model of the electrosensory system. Here we show that STB coding encodes well the information of object distance and size by extracting the spatiotemporal correlation of the distorted electric field. The burst activity of electrosensory neurons is also affected by feedback signals through synaptic plasticity. We show that the control of burst activity caused by the synaptic plasticity leads to extracting the stimulus features depending on the stimulus context. Our results suggest that sensory systems use burst spikes as a unit of sensory coding in order to extract spatiotemporal features of stimuli from spatially distributed stimuli.     

The postnatal development of intrinsic properties and spike encoding at cortical GABAergic neurons

GABAergic neurons play a critical role in maintaining the homeostasis of brain functions for well-organized behaviors. It is not known about the dynamical change in signal encoding at these neurons during postnatal development. We investigated this issue at GFP-labeled GABAergic neurons by whole-cell recording in cortical slices of mice. Our results show that the ability of spike encoding at GABAergic neurons is improved during postnatal development. This change is associated with the reduction of refractory periods and threshold potentials of sequential spikes, as well as the improvement of linear correlations between intrinsic properties and spike capacity. Therefore, the postnatal maturation of the spike encoding capacity at GABAergic neurons will stabilize the excitatory state of cerebral cortex.     

Modeling the impact of common noise inputs on the network activity of retinal ganglion cells

Synchronized spontaneous firing among retinal ganglion cells (RGCs), on timescales faster than visual responses, has been reported in many studies. Two candidate mechanisms of synchronized firing include direct coupling and shared noisy inputs. In neighboring parasol cells of primate retina, which exhibit rapid synchronized firing that has been studied extensively, recent experimental work indicates that direct electrical or synaptic coupling is weak, but shared synaptic input in the absence of modulated stimuli is strong. However, previous modeling efforts have not accounted for this aspect of firing in the parasol cell population. Here we develop a new model that incorporates the effects of common noise, and apply it to analyze the light responses and synchronized firing of a large, densely-sampled network of over 250 simultaneously recorded parasol cells. We use a generalized linear model in which the spike rate in each cell is determined by the linear combination of the spatio-temporally filtered visual input, the temporally filtered prior spikes of that cell, and unobserved sources representing common noise. The model accurately captures the statistical structure of the spike trains and the encoding of the visual stimulus, without the direct coupling assumption present in previous modeling work. Finally, we examined the problem of decoding the visual stimulus from the spike train given the estimated parameters. The common-noise model produces Bayesian decoding performance as accurate as that of a model with direct coupling, but with significantly more robustness to spike timing perturbations.     

The Spatial Structure of Stimuli Shapes the Timescale of Correlations in Population Spiking Activity

Throughout the central nervous system, the timescale over which pairs of neural spike trains are correlated is shaped by stimulus structure and behavioral context. Such shaping is thought to underlie important changes in the neural code, but the neural circuitry responsible is largely unknown. In this study, we investigate a stimulus-induced shaping of pairwise spike train correlations in the electrosensory system of weakly electric fish. Simultaneous single unit recordings of principal electrosensory cells show that an increase in the spatial extent of stimuli increases correlations at short () timescales while simultaneously reducing correlations at long () timescales. A spiking network model of the first two stages of electrosensory processing replicates this correlation shaping, under the assumptions that spatially broad stimuli both saturate feedforward afferent input and recruit an open-loop inhibitory feedback pathway. Our model predictions are experimentally verified using both the natural heterogeneity of the electrosensory system and pharmacological blockade of descending feedback projections. For weak stimuli, linear response analysis of the spiking network shows that the reduction of long timescale correlation for spatially broad stimuli is similar to correlation cancellation mechanisms previously suggested to be operative in mammalian cortex. The mechanism for correlation shaping supports population-level filtering of irrelevant distractor stimuli, thereby enhancing the population response to relevant prey and conspecific communication inputs.     

The effect of neural adaptation on population coding accuracy

Most neurons in the primary visual cortex initially respond vigorously when a preferred stimulus is presented, but adapt as stimulation continues. The functional consequences of adaptation are unclear. Typically a reduction of firing rate would reduce single neuron accuracy as less spikes are available for decoding, but it has been suggested that on the population level, adaptation increases coding accuracy. This question requires careful analysis as adaptation not only changes the firing rates of neurons, but also the neural variability and correlations between neurons, which affect coding accuracy as well. We calculate the coding accuracy using a computational model that implements two forms of adaptation: spike frequency adaptation and synaptic adaptation in the form of short-term synaptic plasticity. We find that the net effect of adaptation is subtle and heterogeneous. Depending on adaptation mechanism and test stimulus, adaptation can either increase or decrease coding accuracy. We discuss the neurophysiological and psychophysical implications of the findings and relate it to published experimental data.     

Decoding spike timing: the differential reverse-correlation method

It is widely acknowledged that detailed timing of action potentials is used to encode information, for example, in auditory pathways; however, the computational tools required to analyze encoding through timing are still in their infancy. We present a simple example of encoding, based on a recent model of time-frequency analysis, in which units fire action potentials when a certain condition is met, but the timing of the action potential depends also on other features of the stimulus. We show that, as a result, spike-triggered averages are smoothed so much that they do not represent the true features of the encoding. Inspired by this example, we present a simple method, differential reverse correlations, that can separate an analysis of what causes a neuron to spike, and what controls its timing. We analyze with this method the leaky integrate-and-fire neuron and show the method accurately reconstructs the model's kernel.     

Measuring Fisher Information Accurately in Correlated Neural Populations

Neural responses are known to be variable. In order to understand how this neural variability constrains behavioral performance, we need to be able to measure the reliability with which a sensory stimulus is encoded in a given population. However, such measures are challenging for two reasons: First, they must take into account noise correlations which can have a large influence on reliability. Second, they need to be as efficient as possible, since the number of trials available in a set of neural recording is usually limited by experimental constraints. Traditionally, cross-validated decoding has been used as a reliability measure, but it only provides a lower bound on reliability and underestimates reliability substantially in small datasets. We show that, if the number of trials per condition is larger than the number of neurons, there is an alternative, direct estimate of reliability which consistently leads to smaller errors and is much faster to compute. The superior performance of the direct estimator is evident both for simulated data and for neuronal population recordings from macaque primary visual cortex. Furthermore we propose generalizations of the direct estimator which measure changes in stimulus encoding across conditions and the impact of correlations on encoding and decoding, typically denoted by I_shuffle and I_diag respectively.     

Stimulus dependent neural correlations in the auditory midbrain of the grassfrog (Rana temporaria L.)

Few-unit recordings were obtained using metal microelectrodes. Separation into single-unit spike trains was based on differences in spike amplitude and spike waveform. For that purpose a hardware microprocessor based spike waveform analyser was designed and built. Spikes are filtered by four matched filters and filter outputs at the moments of spike occurrence are read by a computer and used for off-line separation and spike waveform reconstruction. Thirty-one double unit recordings were obtained and correlation between the separated spike trains was determined. After stimulus correction correlation remained in only 8 of the double unit records. It appeared that in most cases this neural correlation was stimulus dependent. Continuous noise stimulation resulted in the strongest neural correlation remaining after correction for stimulus coupling, stimulation with 48 ms duration tonepips presented once per second generally did not result in a significant neural correlation after the correction procedure for stimulus lock. The usefulness of the additive model for neural correlation and the correction procedure based thereupon is discussed.     

Spatial and temporal correlations of spike trains in frog retinal ganglion cells

For a neuron, firing activity can be in synchrony with that of others, which results in spatial correlation; on the other hand, spike events within each individual spike train may also correlate with each other, which results in temporal correlation. In order to investigate the relationship between these two phenomena, population neurons’ activities of frog retinal ganglion cells in response to binary pseudo-random checker-board flickering were recorded via a multi-electrode recording system. The spatial correlation index (SCI) and temporal correlation index (TCI) were calculated for the investigated neurons. Statistical results showed that, for a single neuron, the SCI and TCI values were highly related—a neuron with a high SCI value generally had a high TCI value, and these two indices were both associated with burst activities in spike train of the investigated neuron. These results may suggest that spatial and temporal correlations of single neuron’s spiking activities could be mutually modulated; and that burst activities could play a role in the modulation. We also applied models to test the contribution of spatial and temporal correlations for visual information processing. We show that a model considering spatial and temporal correlations could predict spikes more accurately than a model does not include any correlation.     

Relative spike timing in stochastic oscillator networks of the Hermissenda eye

The role of relative spike timing on sensory coding and stochastic dynamics of small pulse-coupled oscillator networks is investigated physiologically and mathematically, based on the small biological eye network of the marine invertebrate Hermissenda. Without network interactions, the five inhibitory photoreceptors of the eye network exhibit quasi-regular rhythmic spiking; in contrast, within the active network, they display more irregular spiking but collective network rhythmicity. We investigate the source of this emergent network behavior first analyzing the role of relative input to spike–timing relationships in individual cells. We use a stochastic phase oscillator equation to model photoreceptor spike sequences in response to sequences of inhibitory current pulses. Although spike sequences can be complex and irregular in response to inputs, we show that spike timing is better predicted if relative timing of spikes to inputs is accounted for in the model. Further, we establish that greater noise levels in the model serve to destroy network phase-locked states that induce non-monotonic stimulus rate-coding, as predicted in Butson and Clark (J Neurophysiol 99:146–154, 2008a; J Neurophysiol 99:155–165, 2008b). Hence, rate-coding can function better in noisy spiking cells relative to non-noisy cells. We then study how relative input to spike–timing dynamics of single oscillators contribute to network-level dynamics. Relative timing interactions in the network sharpen the stimulus window that can trigger a spike, affecting stimulus encoding. Also, we derive analytical inter-spike interval distributions of cells in the model network, revealing that irregular Poisson-like spike emission and collective network rhythmicity are emergent properties of network dynamics, consistent with experimental observations. Our theoretical results generate experimental predictions about the nature of spike patterns in the Hermissenda eye.     

The refractory periods and threshold potentials of sequential spikes measured by whole-cell recording

Neurons in the central nervous system are thought to program neural language via firing sequential spikes for guiding animal behaviors. The quantitative profiles of spike intrinsic properties are critically important to understand spike programming. We developed approaches with whole-cell recordings to measure the threshold potentials and refractory periods (RPs) of sequential spikes, and to analyze the relationships of these factors with spike timing precision and capacity at the regular-spiking and fast-spiking neurons in cortical slice. The RPs and threshold potentials of sequential spikes at these two groups of neurons are different and are linearly correlated with spike timing precision and capacity. These data suggest that RPs and threshold potentials essentially navigate the spike programming for the precise and loyal encoding of meaningful neural signals. Our study provides the avenues for decoding the spectrum of the neural signals quantitatively.     

Spatiotemporal Spike Coding of Behavioral Adaptation in the Dorsal Anterior Cingulate Cortex

The frontal cortex controls behavioral adaptation in environments governed by complex rules. Many studies have established the relevance of firing rate modulation after informative events signaling whether and how to update the behavioral policy. However, whether the spatiotemporal features of these neuronal activities contribute to encoding imminent behavioral updates remains unclear. We investigated this issue in the dorsal anterior cingulate cortex (dACC) of monkeys while they adapted their behavior based on their memory of feedback from past choices. We analyzed spike trains of both single units and pairs of simultaneously recorded neurons using an algorithm that emulates different biologically plausible decoding circuits. This method permits the assessment of the performance of both spike-count and spike-timing sensitive decoders. In response to the feedback, single neurons emitted stereotypical spike trains whose temporal structure identified informative events with higher accuracy than mere spike count. The optimal decoding time scale was in the range of 70–200 ms, which is significantly shorter than the memory time scale required by the behavioral task. Importantly, the temporal spiking patterns of single units were predictive of the monkeys’ behavioral response time. Furthermore, some features of these spiking patterns often varied between jointly recorded neurons. All together, our results suggest that dACC drives behavioral adaptation through complex spatiotemporal spike coding. They also indicate that downstream networks, which decode dACC feedback signals, are unlikely to act as mere neural integrators.     

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.     

A glimpse of the brain transforming a sensory signal into a motor response

Averages were made of neuronal spike activity recorded successively from eight relay regions along the auditorimotor pathway of naive cats and cats conditioned to blink in response to a 70 dB click conditioned stimulus (CS). It was hypothesized that the patterns of activity could be distinguished as sensory or motor by differences in their relationship to the pattern of the acoustic CS vs that of the conditioned response (CR). If so, it was also hypothesized that the acoustic stimulus would be better expressed at early auditorimotor relays and the motor response at later relays along the pathway. To test these hypotheses, Pearson correlation coefficients were calculated between the mean patterns of unit activity at each of the auditorimotor relays and (1) the rectified sound pattern of the CS and (2) the averaged, rectified electromyographic (EMG) activity of the muscles (orbicularis oculis) that produced the CR. In both naive and conditioned cats, there were significant positive correlations between the patterns of spike activity and the sound at early relays along the auditorimotor pathway such as the cochlear nucleus and inferior colliculus. In the conditioned animals, the spike activity of later nuclei in the auditorimotor pathway, such as the rostral thalamus and the motor cortex, had the highest positive correlations with the motor response. These correlations were low in the naive animals. Thus, the mean patterns of spike activity along the auditorimotor pathway appeared to distinguish the sound from the motor response and provided a glimpse of the process supporting transformation of the CS into the incipient CR.     

A glimpse of the brain transforming a sensory signal into a motor response

Averages were made of neuronal spike activity recorded successively from eight relay regions along the auditorimotor pathway of naive cats and cats conditioned to blink in response to a 70 dB click conditioned stimulus (CS). It was hypothesized that the patterns of activity could be distinguished as sensory or motor by differences in their relationship to the pattern of the acoustic CS vs that of the conditioned response (CR). If so, it was also hypothesized that the acoustic stimulus would be better expressed at early auditorimotor relays and the motor response at later relays along the pathway. To test these hypotheses, Pearson correlation coefficients were calculated between the mean patterns of unit activity at each of the auditorimotor relays and (1) the rectified sound pattern of the CS and (2) the averaged, rectified electromyographic (EMG) activity of the muscles (orbicularis oculis) that produced the CR. In both naive and conditioned cats, there were significant positive correlations between the patterns of spike activity and the sound at early relays along the auditorimotor pathway such as the cochlear nucleus and inferior colliculus. In the conditioned animals, the spike activity of later nuclei in the auditorimotor pathway, such as the rostral thalamus and the motor cortex, had the highest positive correlations with the motor response. These correlations were low in the naive animals. Thus, the mean patterns of spike activity along the auditorimotor pathway appeared to distinguish the sound from the motor response and provided a glimpse of the process supporting transformation of the CS into the incipient CR.