The role of individual spikes and spike patterns in population coding of stimulus location in rat somatosensory cortex

This report addresses the nature of population coding in sensory cortex by applying information theoretic analysis to data recorded simultaneously from neuron pairs located in primary somatosensory cortex of anaesthetised rats. We studied how cortical spike trains code for the location of a whisker stimulus on the rat's snout. We found that substantially more information was conveyed by 10 ms precision spike timing compared with that conveyed by the number of spikes counted over a 40 ms response interval. Most of this information was accounted for by the timing of individual spikes. In particular, it was the first post-stimulus spikes that were crucial. Spike patterns within individual cells played a smaller role; spike patterns across cells were negligible. This pattern of results was robust both to the exact nature of the stimulus set and to the precision at which spikes were binned.     

Population coding of stimulus location in rat somatosensory cortex.

This study explores the nature of population coding in sensory cortex by applying information theoretic analyses to neuron pairs recorded simultaneously from rat barrel cortex. We quantified the roles of individual spikes and spike patterns in encoding whisker stimulus location. 82%-85% of the total information was contained in the timing of individual spikes: first spike time was particularly crucial. Spike patterns within neurons accounted for the remaining 15%-18%. Neuron pairs located in the same barrel column coded redundantly, whereas pairs in neighboring barrel columns coded independently. The barrel cortical population code for stimulus location appears to be the time of single neurons' first poststimulus spikes-a fast, robust coding mechanism that does not rely on "synergy" in crossneuronal spike patterns.     

Population coding in somatosensory cortex

Computational analyses have begun to elucidate which components of somatosensory cortical population activity may encode basic stimulus features. Recent results from rat barrel cortex suggest that the essence of this code is not synergistic spike patterns, but rather the precise timing of single neuron's first post-stimulus spikes. This may form the basis for a fast, robust population code.     

Membrane Potential Fluctuations Determine the Precision of Spike Timing and Synchronous Activity: A Model Study

It is much debated on what time scale information is encoded by neuronal spike activity. With a phenomenological model that transforms time-dependent membrane potential fluctuations into spike trains, we investigate constraints for the timing of spikes and for synchronous activity of neurons with common input. The model of spike generation has a variable threshold that depends on the time elapsed since the previous action potential and on the preceding membrane potential changes. To ensure that the model operates in a biologically meaningful range, the model was adjusted to fit the responses of a fly visual interneuron to motion stimuli. The dependence of spike timing on the membrane potential dynamics was analyzed. Fast membrane potential fluctuations are needed to trigger spikes with a high temporal precision. Slow fluctuations lead to spike activity with a rate about proportional to the membrane potential. Thus, for a given level of stochastic input, the frequency range of membrane potential fluctuations induced by a stimulus determines whether a neuron can use a rate code or a temporal code. The relationship between the steepness of membrane potential fluctuations and the timing of spikes has also implications for synchronous activity in neurons with common input. Fast membrane potential changes must be shared by the neurons to produce synchronous activity.     

Neural coding of natural stimuli: information at sub-millisecond resolution

Sensory information about the outside world is encoded by neurons in sequences of discrete, identical pulses termed action potentials or spikes. There is persistent controversy about the extent to which the precise timing of these spikes is relevant to the function of the brain. We revisit this issue, using the motion-sensitive neurons of the fly visual system as a test case. Our experimental methods allow us to deliver more nearly natural visual stimuli, comparable to those which flies encounter in free, acrobatic flight. New mathematical methods allow us to draw more reliable conclusions about the information content of neural responses even when the set of possible responses is very large. We find that significant amounts of visual information are represented by details of the spike train at millisecond and sub-millisecond precision, even though the sensory input has a correlation time of ~55 ms; different patterns of spike timing represent distinct motion trajectories, and the absolute timing of spikes points to particular features of these trajectories with high precision. Finally, the efficiency of our entropy estimator makes it possible to uncover features of neural coding relevant for natural visual stimuli: first, the system's information transmission rate varies with natural fluctuations in light intensity, resulting from varying cloud cover, such that marginal increases in information rate thus occur even when the individual photoreceptors are counting on the order of one million photons per second. Secondly, we see that the system exploits the relatively slow dynamics of the stimulus to remove coding redundancy and so generate a more efficient neural code.     

Differential coding of humoral stimuli by timing and amplitude of intracellular calcium spike trains

The ubiquitous Ca2(+)-phosphoinositide pathway transduces extracellular signals to cellular effectors. Using a mathematical model, we simulated intracellular Ca2+ fluctuations in hepatocytes upon humoral stimulation. We estimated the information encoded about random humoral stimuli in these Ca2+ spike trains using an information-theoretic approach based on stimulus estimation methods. We demonstrate accurate transfer of information about random humoral signals with low temporal cutoff frequencies. In contrast, our results suggest that high-frequency stimuli are poorly transduced by the transmembrane machinery. We found that humoral signals are encoded in both the timing and amplitude of intracellular Ca2+ spikes. The information transmitted per spike is similar to that of sensory neuronal systems, in spite of several orders of magnitude difference in firing rate.     

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.     

Object localization with whiskers

Rats use their large facial hairs (whiskers) to detect, localize and identify objects in their proximal three-dimensional (3D) space. Here, we focus on recent evidence of how object location is encoded in the neural sensory pathways of the rat whisker system. Behavioral and neuronal observations have recently converged to the point where object location in 3D appears to be encoded by an efficient orthogonal scheme supported by primary sensory-afferents: each primary-afferent can signal object location by a spatial (labeled-line) code for the vertical axis (along whisker arcs), a temporal code for the horizontal axis (along whisker rows), and an intensity code for the radial axis (from the face out). Neuronal evidence shows that (i) the identities of activated sensory neurons convey information about the vertical coordinate of an object, (ii) the timing of their firing, in relation to other reference signals, conveys information about the horizontal object coordinate, and (iii) the intensity of firing conveys information about the radial object coordinate. Such a triple-coding scheme allows for efficient multiplexing of 3D object location information in the activity of single neurons. Also, this scheme provides redundancy since the same information may be represented in the activity of many neurons. These features of orthogonal coding increase accuracy and reliability. We propose that the multiplexed information is conveyed in parallel to different readout circuits, each decoding a specific spatial variable. Such decoding reduces ambiguity, and simplifies the required decoding algorithms, since different readout circuits can be optimized for a particular variable.     

Computing Complex Visual Features with Retinal Spike Times

Neurons in sensory systems can represent information not only by their firing rate, but also by the precise timing of individual spikes. For example, certain retinal ganglion cells, first identified in the salamander, encode the spatial structure of a new image by their first-spike latencies. Here we explore how this temporal code can be used by downstream neural circuits for computing complex features of the image that are not available from the signals of individual ganglion cells. To this end, we feed the experimentally observed spike trains from a population of retinal ganglion cells to an integrate-and-fire model of post-synaptic integration. The synaptic weights of this integration are tuned according to the recently introduced tempotron learning rule. We find that this model neuron can perform complex visual detection tasks in a single synaptic stage that would require multiple stages for neurons operating instead on neural spike counts. Furthermore, the model computes rapidly, using only a single spike per afferent, and can signal its decision in turn by just a single spike. Extending these analyses to large ensembles of simulated retinal signals, we show that the model can detect the orientation of a visual pattern independent of its phase, an operation thought to be one of the primitives in early visual processing. We analyze how these computations work and compare the performance of this model to other schemes for reading out spike-timing information. These results demonstrate that the retina formats spatial information into temporal spike sequences in a way that favors computation in the time domain. Moreover, complex image analysis can be achieved already by a simple integrate-and-fire model neuron, emphasizing the power and plausibility of rapid neural computing with spike times.     

First-spike latency of auditory neurons revisited

The timing of the first, and sometimes only, spike of auditory neurons evoked by an acoustic stimulus depends on a variety of parameters. Recent studies have suggested that several of these dependencies originate from processes in the first synapse of the auditory system and that first-spike timing is further modified by central processing. The variation of first-spike latency with stimulus parameters contains considerable information about those parameters, as recently explored in several sensory systems. Codes based on the relative timing of first spikes in ensembles of neurons appear to be easily decodable, energetically efficient, reliable, and fast.     

Millisecond-timescale local network coding in the rat primary somatosensory cortex

Correlation among neocortical neurons is thought to play an indispensable role in mediating sensory processing of external stimuli. The role of temporal precision in this correlation has been hypothesized to enhance information flow along sensory pathways. Its role in mediating the integration of information at the output of these pathways, however, remains poorly understood. Here, we examined spike timing correlation between simultaneously recorded layer V neurons within and across columns of the primary somatosensory cortex of anesthetized rats during unilateral whisker stimulation. We used bayesian statistics and information theory to quantify the causal influence between the recorded cells with millisecond precision. For each stimulated whisker, we inferred stable, whisker-specific, dynamic bayesian networks over many repeated trials, with network similarity of 83.3±6% within whisker, compared to only 50.3±18% across whiskers. These networks further provided information about whisker identity that was approximately 6 times higher than what was provided by the latency to first spike and 13 times higher than what was provided by the spike count of individual neurons examined separately. Furthermore, prediction of individual neurons' precise firing conditioned on knowledge of putative pre-synaptic cell firing was 3 times higher than predictions conditioned on stimulus onset alone. Taken together, these results suggest the presence of a temporally precise network coding mechanism that integrates information across neighboring columns within layer V about vibrissa position and whisking kinetics to mediate whisker movement by motor areas innervated by layer V.     

Identifying temporal codes in spontaneously active sensory neurons

The manner in which information is encoded in neural signals is a major issue in Neuroscience. A common distinction is between rate codes, where information in neural responses is encoded as the number of spikes within a specified time frame (encoding window), and temporal codes, where the position of spikes within the encoding window carries some or all of the information about the stimulus. One test for the existence of a temporal code in neural responses is to add artificial time jitter to each spike in the response, and then assess whether or not information in the response has been degraded. If so, temporal encoding might be inferred, on the assumption that the jitter is small enough to alter the position, but not the number, of spikes within the encoding window. Here, the effects of artificial jitter on various spike train and information metrics were derived analytically, and this theory was validated using data from afferent neurons of the turtle vestibular and paddlefish electrosensory systems, and from model neurons. We demonstrate that the jitter procedure will degrade information content even when coding is known to be entirely by rate. For this and additional reasons, we conclude that the jitter procedure by itself is not sufficient to establish the presence of a temporal code.     

Coding of deflection velocity and amplitude by whisker primary afferent neurons: implications for higher level processing

Within the rat whisker-to-barrel pathway, local circuits in cortical layer IV are more sensitive to the initial timing of deflection-evoked thalamic responses than to the total number of spikes comprising them. Because thalamic response timing better reflects whisker deflection velocity than amplitude, cortical neurons are more responsive to the former than the latter. The aim of this study is to determine how deflection velocity and amplitude may be encoded by the primary afferent neurons innervating the vibrissae. Responses of 81 extracellularly recorded trigeminal ganglion neurons (60 slowly and 21 rapidly adapting) were studied using controlled whisker stimuli identical to those used previously to investigate the velocity and amplitude sensitivities of thalamic and cortical neurons. For either slowly (SA) or rapidly adapting (RA) neurons, velocity is reflected by both response magnitude, measured as the total number of evoked spikes/stimulus, and initial firing rate, measured as the number of spikes discharged during the first 2 ms of the response. Deflection amplitude, on the other hand, is represented only by the SA population in their response magnitudes. Thus, in both populations initial firing rates unambiguously reflect deflection velocity. Together with previous findings, results demonstrate that information about deflection velocity is preserved throughout the whisker-to-barrel pathway by central circuits sensitive to initial response timing.     

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.     

Conversion of Phase Information into a Spike-Count Code by Bursting Neurons

Single neurons in the cerebral cortex are immersed in a fluctuating electric field, the local field potential (LFP), which mainly originates from synchronous synaptic input into the local neural neighborhood. As shown by recent studies in visual and auditory cortices, the angular phase of the LFP at the time of spike generation adds significant extra information about the external world, beyond the one contained in the firing rate alone. However, no biologically plausible mechanism has yet been suggested that allows downstream neurons to infer the phase of the LFP at the soma of their pre-synaptic afferents. Therefore, so far there is no evidence that the nervous system can process phase information. Here we study a model of a bursting pyramidal neuron, driven by a time-dependent stimulus. We show that the number of spikes per burst varies systematically with the phase of the fluctuating input at the time of burst onset. The mapping between input phase and number of spikes per burst is a robust response feature for a broad range of stimulus statistics. Our results suggest that cortical bursting neurons could play a crucial role in translating LFP phase information into an easily decodable spike count code.     

Predicting spike occurrence and neuronal responsiveness from LFPs in primary somatosensory cortex

Local Field Potentials (LFPs) integrate multiple neuronal events like synaptic inputs and intracellular potentials. LFP spatiotemporal features are particularly relevant in view of their applications both in research (e.g. for understanding brain rhythms, inter-areal neural communication and neuronal coding) and in the clinics (e.g. for improving invasive Brain-Machine Interface devices). However the relation between LFPs and spikes is complex and not fully understood. As spikes represent the fundamental currency of neuronal communication this gap in knowledge strongly limits our comprehension of neuronal phenomena underlying LFPs. We investigated the LFP-spike relation during tactile stimulation in primary somatosensory (S-I) cortex in the rat. First we quantified how reliably LFPs and spikes code for a stimulus occurrence. Then we used the information obtained from our analyses to design a predictive model for spike occurrence based on LFP inputs. The model was endowed with a flexible meta-structure whose exact form, both in parameters and structure, was estimated by using a multi-objective optimization strategy. Our method provided a set of nonlinear simple equations that maximized the match between models and true neurons in terms of spike timings and Peri Stimulus Time Histograms. We found that both LFPs and spikes can code for stimulus occurrence with millisecond precision, showing, however, high variability. Spike patterns were predicted significantly above chance for 75% of the neurons analysed. Crucially, the level of prediction accuracy depended on the reliability in coding for the stimulus occurrence. The best predictions were obtained when both spikes and LFPs were highly responsive to the stimuli. Spike reliability is known to depend on neuron intrinsic properties (i.e. on channel noise) and on spontaneous local network fluctuations. Our results suggest that the latter, measured through the LFP response variability, play a dominant role.     

Shifts in coding properties and maintenance of information transmission during adaptation in barrel cortex

Neuronal responses to ongoing stimulation in many systems change over time, or “adapt.” Despite the ubiquity of adaptation, its effects on the stimulus information carried by neurons are often unknown. Here we examine how adaptation affects sensory coding in barrel cortex. We used spike-triggered covariance analysis of single-neuron responses to continuous, rapidly varying vibrissa motion stimuli, recorded in anesthetized rats. Changes in stimulus statistics induced spike rate adaptation over hundreds of milliseconds. Vibrissa motion encoding changed with adaptation as follows. In every neuron that showed rate adaptation, the input–output tuning function scaled with the changes in stimulus distribution, allowing the neurons to maintain the quantity of information conveyed about stimulus features. A single neuron that did not show rate adaptation also lacked input–output rescaling and did not maintain information across changes in stimulus statistics. Therefore, in barrel cortex, rate adaptation occurs on a slow timescale relative to the features driving spikes and is associated with gain rescaling matched to the stimulus distribution. Our results suggest that adaptation enhances tactile representations in primary somatosensory cortex, where they could directly influence perceptual decisions.     

Regulation of spike timing in visual cortical circuits

A train of action potentials (a spike train) can carry information in both the average firing rate and the pattern of spikes in the train. But can such a spike-pattern code be supported by cortical circuits? Neurons in vitro produce a spike pattern in response to the injection of a fluctuating current. However, cortical neurons in vivo are modulated by local oscillatory neuronal activity and by top-down inputs. In a cortical circuit, precise spike patterns thus reflect the interaction between internally generated activity and sensory information encoded by input spike trains. We review the evidence for precise and reliable spike timing in the cortex and discuss its computational role.