Predictive Coding of Dynamical Variables in Balanced Spiking Networks

Two observations about the cortex have puzzled neuroscientists for a long time. First, neural responses are highly variable. Second, the level of excitation and inhibition received by each neuron is tightly balanced at all times. Here, we demonstrate that both properties are necessary consequences of neural networks that represent information efficiently in their spikes. We illustrate this insight with spiking networks that represent dynamical variables. Our approach is based on two assumptions: We assume that information about dynamical variables can be read out linearly from neural spike trains, and we assume that neurons only fire a spike if that improves the representation of the dynamical variables. Based on these assumptions, we derive a network of leaky integrate-and-fire neurons that is able to implement arbitrary linear dynamical systems. We show that the membrane voltage of the neurons is equivalent to a prediction error about a common population-level signal. Among other things, our approach allows us to construct an integrator network of spiking neurons that is robust against many perturbations. Most importantly, neural variability in our networks cannot be equated to noise. Despite exhibiting the same single unit properties as widely used population code models (e.g. tuning curves, Poisson distributed spike trains), balanced networks are orders of magnitudes more reliable. Our approach suggests that spikes do matter when considering how the brain computes, and that the reliability of cortical representations could have been strongly underestimated.     

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.     

Multi-scale detection of rate changes in spike trains with weak dependencies

The statistical analysis of neuronal spike trains by models of point processes often relies on the assumption of constant process parameters. However, it is a well-known problem that the parameters of empirical spike trains can be highly variable, such as for example the firing rate. In order to test the null hypothesis of a constant rate and to estimate the change points, a Multiple Filter Test (MFT) and a corresponding algorithm (MFA) have been proposed that can be applied under the assumption of independent inter spike intervals (ISIs). As empirical spike trains often show weak dependencies in the correlation structure of ISIs, we extend the MFT here to point processes associated with short range dependencies. By specifically estimating serial dependencies in the test statistic, we show that the new MFT can be applied to a variety of empirical firing patterns, including positive and negative serial correlations as well as tonic and bursty firing. The new MFT is applied to a data set of empirical spike trains with serial correlations, and simulations show improved performance against methods that assume independence. In case of positive correlations, our new MFT is necessary to reduce the number of false positives, which can be highly enhanced when falsely assuming independence. For the frequent case of negative correlations, the new MFT shows an improved detection probability of change points and thus, also a higher potential of signal extraction from noisy spike trains.     

Spike train timing-dependent associative modification of hippocampal CA3 recurrent synapses by mossy fibers

In the CA3 region of the hippocampus, extensive recurrent associational/commissural (A/C) connections made by pyramidal cells may function as a network for associative memory storage and recall. We here report that long-term potentiation (LTP) at the A/C synapses can be induced by association of brief spike trains in mossy fibers (MFs) from the dentate gyrus and A/C fibers. This LTP not only required substantial overlap between spike trains in MFs and A/C fibers, but also depended on the temporal order of these spike trains in a manner not predicted by the well-known rule of spike timing-dependent plasticity and requiring activation of type 1 metabotropic glutamate receptors. Importantly, spike trains in a putative single MF input provided effective postsynaptic activity for the induction of LTP at A/C synapses. Thus, the timing of spike trains in individual MFs may code information that is crucial for the associative modification of CA3 recurrent synapses.     

Analysis of point process signals applied to motor unit firing patterns: I. Superposition of independent spike trains

The aim of the present study was to examine whether statistical methods common for the analysis of point process signals could be applied to the electromyogram, in order to extract information concerning the physiological mechanisms involved. This was carried out on the assumption that the electromyogram can be treated as the superposition result of a number of point process signals, each representing the firing pattern of one motor unit. No correlated activity between the different spike trains was assumed at this stage. A digital model for the superposition of event sequences was constructed, assigning to the individual sequences a Gaussian interval distribution. The effects of varying the number of spike trains participating in the superposition process, and changing the mean rates of firing were explored. The statistical methods used in the analysis were serial correlation, event autocorrelation, and power spectrum studies. It has been found that serial correlograms of the superimposed processes may be helpful in detecting the number of spike trains involved in the superposition, whereas power spectrum studies are useful in determining the mean rates of firing of the individual sequences.     

Studying spike trains using a van Rossum metric with a synapse-like filter

Spike trains are unreliable. For example, in the primary sensory areas, spike patterns and precise spike times will vary between responses to the same stimulus. Nonetheless, information about sensory inputs is communicated in the form of spike trains. A challenge in understanding spike trains is to assess the significance of individual spikes in encoding information. One approach is to define a spike train metric, allowing a distance to be calculated between pairs of spike trains. In a good metric, this distance will depend on the information the spike trains encode. This method has been used previously to calculate the timescale over which the precision of spike times is significant. Here, a new metric is constructed based on a simple model of synaptic conductances which includes binding site depletion. Including binding site depletion in the metric means that a given individual spike has a smaller effect on the distance if it occurs soon after other spikes. The metric proves effective at classifying neuronal responses by stimuli in the sample data set of electro-physiological recordings from the primary auditory area of the zebra finch fore-brain. This shows that this is an effective metric for these spike trains suggesting that in these spike trains the significance of a spike is modulated by its proximity to previous spikes. This modulation is a putative information-coding property of spike trains.     

Unitary IPSPs drive precise thalamic spiking in a circuit required for learning

Song learning in birds requires a basal ganglia-thalamo-pallial loop that contains a calyceal GABAergic synapse in the thalamus. Information processing within this circuit is critical for proper song development; however, it is unclear whether activation of the inhibitory output of the basal ganglia structure Area X can drive sustained activity in its thalamic target, the medial portion of the dorsolateral thalamic nucleus (DLM). We show that high-frequency, random activation of this GABAergic synapse can drive precisely timed firing in DLM neurons in brain slices in the absence of excitatory input. Complex IPSP trains, including spike trains recorded in vivo, drive spiking in slices with high reproducibility, even between animals. Using a simple model, we can predict much of DLM's response to natural stimulus trains. These data elucidate basic rules by which thalamic relay neurons translate IPSPs into suprathreshold output and demonstrate extrathalamic GABAergic activation of thalamus.     

Linear-nonlinear-time-warp-poisson models of neural activity

Prominent models of spike trains assume only one source of variability – stochastic (Poisson) spiking – when stimuli and behavior are fixed. However, spike trains may also reflect variability due to internal processes such as planning. For example, we can plan a movement at one point in time and execute it at some arbitrary later time. Neurons involved in planning may thus share an underlying time course that is not precisely locked to the actual movement. Here we combine the standard Linear-Nonlinear-Poisson (LNP) model with Dynamic Time Warping (DTW) to account for shared temporal variability. When applied to recordings from macaque premotor cortex, we find that time warping considerably improves predictions of neural activity. We suggest that such temporal variability is a widespread phenomenon in the brain which should be modeled.     

Proposed mechanisms for coincidence detection in the auditory brainstem

Sound localization in mammals uses two distinct neural circuits, one for low- and one for high-frequency bands. Recent experiments call for revision of the theory explaining how the direction of incoming sound is calculated. We propose such a revised theory. Our theory is based on probabilistic spiking and probabilistic delay of spikes from both sides. We have applied the mechanism originally proposed as an operation on spike trains resulting in multiplication of firing rates. We have adapted this mechanism for the case of synchronous spike trains. The mechanism has to detect spikes from both sides within a short time window. Therefore, in both circuits neurons act as coincidence detectors. In the excitatory low-frequency circuit we call the mechanism the excitatory coincidence detection, to distinguish it from the mechanism of the inhibitory coincidence detection in the high-frequency circuit. The times to first spike and gains of the two mechanisms are calculated. We show how the output gains of the mechanisms predict the dip within the human frequency sensitivity range. This dip has been described in human psychophysical experiments.     

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.     

大鼠初级传入纤维与脊髓背角神经元间的动作电序列的突触传递

外周感觉神经元通过动作电位序列对信号进行编码,这些动作电位序列经过突触传递最终到达脑部。但是各种脉冲序列如何通过神经元之间的化学突触进行传递依然是一个悬而未决的问题。研究了初级传入A6纤维与背角神经元之间各种动作电位序列的突触传递过程。用于刺激的规则,周期、随机脉冲序列由短簇脉冲或单个脉冲构成。定义“事件”(event)为峰峰问期(intefspike interval)小于或等于规定阈值的最长动作电位串,然后从脉冲序列中提取事件间间期(interevent interval,IEI)。用时间,IEI图与回归映射的方法分析IEI序列,结果表明在突触后输出脉冲序列中可以检测到突触前脉冲序列的主要时间结构特征,特别是在短簇脉冲作为刺激单位时。通过计算输入与输出脉冲序列的互信息,发现短簇脉冲可以更可靠地跨突触传递由输入序列携带的神经信息。这些结果表明外周输入脉冲序列的主要时间结构特征可以跨突触传递,在突触传递神经信息的过程中短簇脉冲更为有效。这一研究在从突触传递角度探索神经信息编码方面迈出了一步。     

The temporal structure of transient ON/OFF ganglion cell responses and its relation to intra-retinal processing

A subpopulation of transient ON/OFF ganglion cells in the turtle retina transmits changes in stimulus intensity as series of distinct spike events. The temporal structure of these event sequences depends systematically on the stimulus and thus carries information about the preceding intensity change. To study the spike events' intra-retinal origins, we performed extracellular ganglion cell recordings and simultaneous intracellular recordings from horizontal and amacrine cells. Based on these data, we developed a computational retina model, reproducing spike event patterns with realistic intensity dependence under various experimental conditions. The model's main features are negative feedback from sustained amacrine onto bipolar cells, and a two-step cascade of ganglion cell suppression via a slow and a fast transient amacrine cell. Pharmacologically blocking glycinergic transmission results in disappearance of the spike event sequence, an effect predicted by the model if a single connection, namely suppression of the fast by the slow transient amacrine cell, is weakened. We suggest that the slow transient amacrine cell is glycinergic, whereas the other types release GABA. Thus, the interplay of amacrine cell mediated inhibition is likely to induce distinct temporal structure in ganglion cell responses, forming the basis for a temporal code. Action Editor: Jonathan D. Victor     

Stochasticity,spikes and decoding: sufficiency and utility of order statistics

For over 75 years it has been clear that the number of spikes in a neural response is an important part of the neuronal code. Starting as early as the 1950’s with MacKay and McCullough, there has been speculation over whether each spike and its exact time of occurrence carry information. Although it is obvious that the firing rate carries information it has been less clear as to whether there is information in exactly timed patterns, when they arise from the dynamics of the neurons and networks, as opposed to when they represent some strong external drive that entrains them. One strong null hypothesis that can be applied is that spike trains arise from stochastic sampling of an underlying deterministic temporally modulated rate function, that is, there is a time-varying rate function. In this view, order statistics seem to provide a sufficient theoretical construct to both generate simulated spike trains that are indistinguishable from those observed experimentally, and to evaluate (decode) the data recovered from experiments. It remains to learn whether there are physiologically important signals that are not described by such a null hypothesis. This article is part of a special issue on Neuronal Dynamics of Sensory Coding.     

Neural coding in antennal olfactory cells of tsetse flies (Glossina spp.)

Spike trains from individual antennal olfactory cells of tsetse flies (Glossina spp.) obtained during steady-state conditions (spontaneous as well as during stimulation with 1-octen-3-ol) and dynamic stimulation with repetitive pulses of 1-octen-3-ol were investigated by studying the spike frequency and the temporal structure of the trains. In general, stimulation changes the intensity of the spike activity but leaves the underlying stochastic structure unaffected. This structure turns out to be a renewal process. The only independently varying parameter in this process is the mean interspike interval length, suggesting that olfactory cells of tsetse flies may transmit information via a frequency coding. In spike records with high firing rates, however, the stationary records had significant negative first- order serial correlation coefficients and were non-renewal. Some cells in this study were capable of precisely encoding the onset of the odour pulses at frequencies up to at least 3 Hz. Cells with a rapid return to pre-stimulus activity at the end of stimulation responded more adequately to pulsed stimuli than cells with a long increased spike frequency. While short-firing cells process information via a frequency code, long-firing cells responded with two distinctive phases: a phasic, non-renewal response and a tonic, renewal response which may function as a memory of previous stimulations.      

An information-geometric framework for statistical inferences in the neural spike train space

Statistical inferences are essentially important in analyzing neural spike trains in computational neuroscience. Current approaches have followed a general inference paradigm where a parametric probability model is often used to characterize the temporal evolution of the underlying stochastic processes. To directly capture the overall variability and distribution in the space of the spike trains, we focus on a data-driven approach where statistics are defined and computed in the function space in which spike trains are viewed as individual points. To this end, we at first develop a parametrized family of metrics that takes into account different warpings in the time domain and generalizes several currently used spike train distances. These new metrics are essentially penalized L ^p norms, involving appropriate functions of spike trains, with penalties associated with time-warping. The notions of means and variances of spike trains are then defined based on the new metrics when p = 2 (corresponding to the “Euclidean distance”). Using some restrictive conditions, we present an efficient recursive algorithm, termed Matching-Minimization algorithm, to compute the sample mean of a set of spike trains with arbitrary numbers of spikes. The proposed metrics as well as the mean spike trains are demonstrated using simulations as well as an experimental recording from the motor cortex. It is found that all these methods achieve desirable performance and the results support the success of this novel framework.     

Nonlinear principal components analysis of neuronal spike train data

Many recent approaches to decoding neural spike trains depend critically on the assumption that for low-pass filtered spike trains, the temporal structure is optimally represented by a small number of linear projections onto the data. We therefore tested this assumption of linearity by comparing a linear factor analysis technique (principal components analysis) with a nonlinear neural network based method. It is first shown that the nonlinear technique can reliably identify a neuronally plausible nonlinearity in synthetic spike trains. However, when applied to the outputs from primary visual cortical neurons, this method shows no evidence for significant temporal nonlinearities. The implications of this are discussed. Received: 29 November 1996 / Accepted in revised form: 1 July 1997     

Feature extraction from spike trains with Bayesian binning: ‘Latency is where the signal starts’

The peristimulus time histogram (PSTH) and its more continuous cousin, the spike density function (SDF) are staples in the analytic toolkit of neurophysiologists. The former is usually obtained by binning spike trains, whereas the standard method for the latter is smoothing with a Gaussian kernel. Selection of a bin width or a kernel size is often done in an relatively arbitrary fashion, even though there have been recent attempts to remedy this situation (DiMatteo et al., Biometrika 88(4):1055–1071, 2001; Shimazaki and Shinomoto 2007a, Neural Comput 19(6):1503–1527, 2007b, c; Cunningham et al. 2008). We develop an exact Bayesian, generative model approach to estimating PSTHs. Advantages of our scheme include automatic complexity control and error bars on its predictions. We show how to perform feature extraction on spike trains in a principled way, exemplified through latency and firing rate posterior distribution evaluations on repeated and single trial data. We also demonstrate using both simulated and real neuronal data that our approach provides a more accurate estimates of the PSTH and the latency than current competing methods. We employ the posterior distributions for an information theoretic analysis of the neural code comprised of latency and firing rate of neurons in high-level visual area STSa. A software implementation of our method is available at the machine learning open source software repository (www.mloss.org, project ‘binsdfc’).     

Millisecond-Scale Motor Encoding in a Cortical Vocal Area

Studies of motor control have almost universally examined firing rates to investigate how the brain shapes behavior. In principle, however, neurons could encode information through the precise temporal patterning of their spike trains as well as (or instead of) through their firing rates. Although the importance of spike timing has been demonstrated in sensory systems, it is largely unknown whether timing differences in motor areas could affect behavior. We tested the hypothesis that significant information about trial-by-trial variations in behavior is represented by spike timing in the songbird vocal motor system. We found that neurons in motor cortex convey information via spike timing far more often than via spike rate and that the amount of information conveyed at the millisecond timescale greatly exceeds the information available from spike counts. These results demonstrate that information can be represented by spike timing in motor circuits and suggest that timing variations evoke differences in behavior.