How the brain uses time to represent and process visual information

Information theory provides a theoretical framework for addressing fundamental questions concerning the nature of neural codes. Harnessing its power is not straightforward, because of the differences between mathematical abstractions and laboratory reality. We describe an approach to the analysis of neural codes that seeks to identify the informative features of neural responses, rather than to estimate the information content of neural responses per se. Our analysis, applied to neurons in primary visual cortex (V1), demonstrates that the informative precision of spike times varies with the stimulus modality being represented. Contrast is represented by spike times on the shortest time scale, and different kinds of pattern information are represented on longer time scales. The interspike interval distribution has a structure that is unanticipated from the firing rate. The significance of this structure is not that it contains additional information, but rather, that it may provide a means for simple synaptic mechanisms to decode the information that is multiplexed within a spike train. Extensions of this analysis to the simultaneous responses of pairs of neurons indicate that neighboring neurons convey largely independent information, if the decoding process is sensitive to the neuron of origin and not just the average firing rate. In summary, stimulus-related information is encoded into the precise times of spikes fired by V1 neurons. Much of this information would be obscured if individual spikes were merely taken to be estimators of the firing rate. Additional information would be lost by averaging across the responses of neurons in a local population. We propose that synaptic mechanisms sensitive to interspike intervals and dendritic processing beyond simple summation exist at least in part to enable the brain to take advantage of this extra information.     

Neural networks a century after Cajal

At the time of Golgi and Cajal's reception of the Nobel Prize in 1906 most scientists had accepted the notion that neurons are independent units. Although neuroscientists today still believe that neurons are independent anatomical units, functionally, it is thought that some sort of population coding occurs. Throughout this essay, we provide evidence that suggests that populations of neurons can code information through the synchronization of their responses. This synchronization occurs at several levels in the brain. Whereas spike synchrony refers to the correlation between spikes of different neurons' spike trains, oscillatory synchrony refers to the synchronization of oscillatory responses, generally among large groups of neurons. In the first section of this essay we describe the dependence of the brain's developmental processes on synchronous firing and how these processes form a brain that supports and is sensitive to synchronous spikes. Data are then presented that suggest that spike and oscillatory synchrony may serve as useful neural codes. Examples from sensory (auditory, olfactory and somatosensory), motor and higher cognitive (attention, memory) systems are then presented to illustrate potential roles for these synchronous codes in normal brain function. Results from these studies collectively suggest that spike synchrony in sensory and motor systems may provide detail information not available from changes in firing rate. Oscillatory synchrony, on the other hand, may be globally involved in the coordination of long-distance neuronal communication during higher cognitive processes. These concepts represent a dramatic shift in direction since the times of Golgi and Cajal.     

A comparative analysis of integrating visual information in local neuronal ensembles

Spike directivity, a new measure that quantifies the transient charge density dynamics within action potentials provides better results in discriminating different categories of visual object recognition. Specifically, intracranial recordings from medial temporal lobe (MTL) of epileptic patients have been analyzed using firing rate, interspike intervals and spike directivity. A comparative statistical analysis of the same spikes from a local ensemble of four selected neurons shows that electrical patterns in these neurons display higher separability to input images compared to spike timing features. If the observation vector includes data from all four neurons then the comparative analysis shows a highly significant separation between categories for spike directivity (p=0.0023) and does not display separability for interspike interval (p=0.3768) and firing rate (p=0.5492). Since electrical patterns in neuronal spikes provide information regarding different presented objects this result shows that related information is intracellularly processed in neurons and carried out within a millisecond-level time domain of action potential occurrence. This significant statistical outcome obtained from a local ensemble of four neurons suggests that meaningful information can be electrically inferred at the network level to generate a better discrimination of presented images.     

An improved method for the estimation of firing rate dynamics using an optimal digital filter

In most neural systems, neurons communicate by means of sequences of action potentials or 'spikes'. Information encoded by spike trains is often quantified in terms of the firing rate which emphasizes the frequency of occurrence of action potentials rather than their exact timing. Common methods for estimating firing rates include the rate histogram, the reciprocal interspike interval, and the spike density function. In this study, we demonstrate the limitations of these aforementioned techniques and propose a simple yet more robust alternative. By convolving the spike train with an optimally designed Kaiser window, we show that more robust estimates of firing rate are obtained for both low and high-frequency inputs. We illustrate our approach by considering spike trains generated by simulated as well as experimental data obtained from single-unit recordings of first-order sensory neurons in the vestibular system. Improvements were seen in the prevention of aliasing, phase and amplitude distortion, as well as in the noise reduction for sinusoidal and more complex input profiles. We review the generality of the approach, and show that it can be adapted to describe neurons with sensory or motor responses that are characterized by marked nonlinearities. We conclude that our method permits more robust estimates of neural dynamics than conventional techniques across all stimulus conditions.     

Interactions between behaviorally relevant rhythms and synaptic plasticity alter coding in the piriform cortex

Understanding how neural and behavioral timescales interact to influence cortical activity and stimulus coding is an important issue in sensory neuroscience. In air-breathing animals, voluntary changes in respiratory frequency alter the temporal patterning olfactory input. In the olfactory bulb, these behavioral timescales are reflected in the temporal properties of mitral/tufted (M/T) cell spike trains. As the odor information contained in these spike trains is relayed from the bulb to the cortex, interactions between presynaptic spike timing and short-term synaptic plasticity dictate how stimulus features are represented in cortical spike trains. Here, we demonstrate how the timescales associated with respiratory frequency, spike timing, and short-term synaptic plasticity interact to shape cortical responses. Specifically, we quantified the timescales of short-term synaptic facilitation and depression at excitatory synapses between bulbar M/T cells and cortical neurons in slices of mouse olfactory cortex. We then used these results to generate simulated M/T population synaptic currents that were injected into real cortical neurons. M/T population inputs were modulated at frequencies consistent with passive respiration or active sniffing. We show how the differential recruitment of short-term plasticity at breathing versus sniffing frequencies alters cortical spike responses. For inputs at sniffing frequencies, cortical neurons linearly encoded increases in presynaptic firing rates with increased phase-locked, firing rates. In contrast, at passive breathing frequencies, cortical responses saturated with changes in presynaptic rate. Our results suggest that changes in respiratory behavior can gate the transfer of stimulus information between the olfactory bulb and cortex.     

Dynamics of information and emergent computation in generic neural microcircuit models

Numerous methods have already been developed to estimate the information contained in single spike trains. In this article we explore efficient methods for estimating the information contained in the simultaneous firing activity of hundreds of neurons. Obviously such methods are needed to analyze data from multi-unit recordings. We test these methods on generic neural microcircuit models consisting of 800 neurons, and analyze the temporal dynamics of information about preceding spike inputs in such circuits. It turns out that information spreads with high speed in such generic neural microcircuit models, thereby supporting—without the postulation of any additional neural or synaptic mechanisms—the possibility of ultra-rapid computations on the first input spikes.     

Testing a neural coding hypothesis using surrogate data

Determining how a particular neuron, or population of neurons, encodes information in their spike trains is not a trivial problem, because multiple coding schemes exist and are not necessarily mutually exclusive. Coding schemes generally fall into one of two broad categories, which we refer to as rate and temporal coding. In rate coding schemes, information is encoded in the variations of the average firing rate of the spike train. In contrast, in temporal coding schemes, information is encoded in the specific timing of the individual spikes that comprise the train. Here, we describe a method for testing the presence of temporal encoding of information. Suppose that a set of original spike trains is given. First, surrogate spike trains are generated by randomizing each of the original spike trains subject to the following constraints: the local average firing rate is approximately preserved, while the overall average firing rate and the distribution of primary interspike intervals are perfectly preserved. These constraints ensure that any rate coding of information present in the original spike trains is preserved in the members of the surrogate population. The null-hypothesis is rejected when additional information is found to be present in the original spike trains, implying that temporal coding is present. The method is validated using artificial data, and then demonstrated using real neuronal data.     

Frequency-dependent synaptic potentiation, depression and spike timing induced by Hebbian pairing in cortical pyramidal neurons.

Experiments by Markram and Tsodyks (Nature, 382 (1996) 807-810) have suggested that Hebbian pairing in cortical pyramidal neurons potentiates or depresses the transmission of a subsequent pre-synaptic spike train at steady-state depending on whether the spike train is of low frequency or high frequency, respectively. The frequency above which pairing induced a significant decrease in steady-state synaptic efficacy was as low as about 20 Hz and this value depends on such synaptic properties as probability of release and time constant of recovery from short-term synaptic depression. These characteristics of cortical synapses have not yet been fully explained by neural models, notably the decreased steady-state synaptic efficacy at high pre-synaptic firing rates. This article suggests that this decrease in synaptic efficacy in cortical synapses was not observed at steady-state, but rather during a transition period preceding it whose duration is frequency-dependent. It is shown that the time taken to reach steady-state may be frequency-dependent, and may take considerably longer to occur at high than low frequencies. As a result, the pairing-induced decrease in synaptic efficacy at high pre-synaptic firing rates helps to localize the firing of the post-synaptic neuron to a short time interval following the onset of high-frequency pre-synaptic spike trains. This effect may "speed up the time scale" in response to high-frequency bursts of spikes, and may contribute to rapid synchronization of spike firing across cortical cells that are bound together by associatively learned connections.     

Frequency-Dependent Reliability of Spike Propagation Is Function of Axonal Voltage-Gated Sodium Channels in Cerebellar Purkinje Cells

The spike propagation on nerve axons, like synaptic transmission, is essential to ensure neuronal communication. The secure propagation of sequential spikes toward axonal terminals has been challenged in the neurons with a high firing rate, such as cerebellar Purkinje cells. The shortfall of spike propagation makes some digital spikes disappearing at axonal terminals, such that the elucidation of the mechanisms underlying spike propagation reliability is crucial to find the strategy of preventing loss of neuronal codes. As the spike propagation failure is influenced by the membrane potentials, this process is likely caused by altering the functional status of voltage-gated sodium channels (VGSC). We examined this hypothesis in Purkinje cells by using pair-recordings at their somata and axonal blebs in cerebellar slices. The reliability of spike propagation was deteriorated by elevating spike frequency. The frequency-dependent reliability of spike propagation was attenuated by inactivating VGSCs and improved by removing their inactivation. Thus, the functional status of axonal VGSCs influences the reliability of spike propagation.     

Short-term plasticity optimizes synaptic information transmission

Short-term synaptic plasticity (STP) is widely thought to play an important role in information processing. This major function of STP has recently been challenged, however, by several computational studies indicating that transmission of information by dynamic synapses is broadband, i.e., frequency independent. Here we developed an analytical approach to quantify time- and rate-dependent synaptic information transfer during arbitrary spike trains using a realistic model of synaptic dynamics in excitatory hippocampal synapses. We found that STP indeed increases information transfer in a wide range of input rates, which corresponds well to the naturally occurring spike frequencies at these synapses. This increased information transfer is observed both during Poisson-distributed spike trains with a constant rate and during naturalistic spike trains recorded in hippocampal place cells in exploring rodents. Interestingly, we found that the presence of STP in low release probability excitatory synapses leads to optimization of information transfer specifically for short high-frequency bursts, which are indeed commonly observed in many excitatory hippocampal neurons. In contrast, more reliable high release probability synapses that express dominant short-term depression are predicted to have optimal information transmission for single spikes rather than bursts. This prediction is verified in analyses of experimental recordings from high release probability inhibitory synapses in mouse hippocampal slices and fits well with the observation that inhibitory hippocampal interneurons do not commonly fire spike bursts. We conclude that STP indeed contributes significantly to synaptic information transfer and may serve to maximize information transfer for specific firing patterns of the corresponding neurons.     

Evidence for a persistent sodium conductance in neurons from the nucleus prepositus hypoglossi

Intracellular recordings were made from 39 neurons in a slice preparation of the prepositus hypoglossi nucleus from guinea pigs. Morphological characteristics were confirmed by dying neurons with Lucifer yellow. The neurons were spontaneously active, firing in the range of 8–50 spikes/s. Spike duration was short (0.32 ms) and the spikes were followed by fast and slow afterhyperpolarizations. The current vs frequency relationship was linear during steady state firing, but showed dual firing ranges corresponding to the first, third and fifth interspike interval. The instantaneous frequency of the first few interspike intervals could reach 500 spikes/s. Depolarizing and hyperpolarizing responses to square pulses displayed initial sag and rebound responses sensitive to extracellular Cs⁺, pharmacologically classifying the responses as a result of a Q-like current. Substitution of Ca²⁺ in the medium with the inorganic calcium blockers Mn²⁺ or Co²⁺ resulted in oscillatory firing, depolarizing excursions being sensitive to tetrodotoxin (TTX). Mn²⁺ or Co²⁺ in combination with extracellular Cs⁺ elicited TTX-sensitive plateau potentials, blocked in Na⁺-free solution. In conclusion, the prepositus neurons displayed spontaneous activity in the slice preparation and active membrane properties above as well as below the threshold of the action potential. In addition, the prepositus neurons possess a persistent sodium conductance that can be uncovered by inorganic calcium blockers. It may be involved in sustaining the spontaneous discharge.     

Ionic currents underlying spontaneous action potentials in isolated cerebellar Purkinje neurons.

Acutely dissociated cell bodies of mouse Purkinje neurons spontaneously fired action potentials at approximately 50 Hz (25 degrees C). To directly measure the ionic currents underlying spontaneous activity, we voltage-clamped the cells using prerecorded spontaneous action potentials (spike trains) as voltage commands and used ionic substitution and selective blockers to isolate individual currents. The largest current flowing during the interspike interval was tetrodotoxin-sensitive sodium current (approximately -50 pA between -65 and -60 mV). Although the neurons had large voltage-dependent calcium currents, the net current blocked by cobalt substitution for calcium was outward at all times during spike trains. Thus, the electrical effect of calcium current is apparently dominated by rapidly activated calcium-dependent potassium currents. Under current clamp, all cells continued firing spontaneously (though approximately 30% more slowly) after block of T-type calcium current by mibefradil, and most cells continued to fire after block of all calcium current by cobalt substitution. Although the neurons possessed hyperpolarization-activated cation current (Ih), little current flowed during spike trains, and block by 1 mM cesium had no effect on firing frequency. The outward potassium currents underlying the repolarization of the spikes were completely blocked by 1 mM TEA. These currents deactivated quickly (<1 msec) after each spike. We conclude that the spontaneous firing of Purkinje neuron cell bodies depends mainly on tetrodotoxin-sensitive sodium current flowing between spikes. The high firing rate is promoted by large potassium currents that repolarize the cell rapidly and deactivate quickly, thus preventing strong hyperpolarization and restoring a high input resistance for subsequent depolarization.     

Single neuron firing properties impact correlation-based population coding

Correlated spiking has been widely observed, but its impact on neural coding remains controversial. Correlation arising from comodulation of rates across neurons has been shown to vary with the firing rates of individual neurons. This translates into rate and correlation being equivalently tuned to the stimulus; under those conditions, correlated spiking does not provide information beyond that already available from individual neuron firing rates. Such correlations are irrelevant and can reduce coding efficiency by introducing redundancy. Using simulations and experiments in rat hippocampal neurons, we show here that pairs of neurons receiving correlated input also exhibit correlations arising from precise spike-time synchronization. Contrary to rate comodulation, spike-time synchronization is unaffected by firing rate, thus enabling synchrony- and rate-based coding to operate independently. The type of output correlation depends on whether intrinsic neuron properties promote integration or coincidence detection: "ideal" integrators (with spike generation sensitive to stimulus mean) exhibit rate comodulation, whereas ideal coincidence detectors (with spike generation sensitive to stimulus variance) exhibit precise spike-time synchronization. Pyramidal neurons are sensitive to both stimulus mean and variance, and thus exhibit both types of output correlation proportioned according to which operating mode is dominant. Our results explain how different types of correlations arise based on how individual neurons generate spikes, and why spike-time synchronization and rate comodulation can encode different stimulus properties. Our results also highlight the importance of neuronal properties for population-level coding insofar as neural networks can employ different coding schemes depending on the dominant operating mode of their constituent neurons.     

Dopamine modulation of spike dynamics in bursting neurons

The pyloric network of the lobster stomatogastric ganglion is a prime example of an oscillatory neural circuit. In our previous study on the firing patterns of pyloric neurons we observed characteristic temporal structures termed 'interspike interval (ISI) signatures' which were found to depend on the synaptic connectivity of the network. Dopamine, a well-known modulator of the pyloric network, is known to affect inhibitory synapses so it might also tune the fine temporal structure of intraburst spikes, a phenomenon not previously investigated. In the recent work we study the DA modulation of ISI patterns of two identified pyloric neurons in normal conditions and after blocking their glutamatergic synaptic connections. Dopamine (10-50 microM) strongly regularizes the firing of the lateral pyloric (LP) and pyloric dilator (PD) neurons by increasing the reliability of recurrent spike patterns. The most dramatic effect is observed in the LP, where precisely replicated spike multiplets appear in a normally 'noisy' neuron. The DA-induced regularization of intraburst spike patterns requires functional glutamatergic inputs to the LP neuron and this effect cannot be mimicked by simple intracellular depolarization. Inhibitory synaptic inputs arriving before the bursts are important factors in shaping the intraburst spike dynamics of both the PD and the LP neurons. Our data reveal a novel aspect of chemical neuromodulation in oscillatory neural networks. This effect sets in at concentrations lower than those affecting the overall burst pattern of the network. The sensitivity of intraburst spike dynamics to preceding synaptic inputs also suggests a novel method of temporal coding in neural bursters.     

Spatial information outflow from the hippocampal circuit: distributed spatial coding and phase precession in the subiculum

Hippocampal place cells convey spatial information through a combination of spatially selective firing and theta phase precession. The way in which this information influences regions like the subiculum that receive input from the hippocampus remains unclear. The subiculum receives direct inputs from area CA1 of the hippocampus and sends divergent output projections to many other parts of the brain, so we examined the firing patterns of rat subicular neurons. We found a substantial transformation in the subicular code for space from sparse to dense firing rate representations along a proximal-distal anatomical gradient: neurons in the proximal subiculum are more similar to canonical, sparsely firing hippocampal place cells, whereas neurons in the distal subiculum have higher firing rates and more distributed spatial firing patterns. Using information theory, we found that the more distributed spatial representation in the subiculum carries, on average, more information about spatial location and context than the sparse spatial representation in CA1. Remarkably, despite the disparate firing rate properties of subicular neurons, we found that neurons at all proximal-distal locations exhibit robust theta phase precession, with similar spiking oscillation frequencies as neurons in area CA1. Our findings suggest that the subiculum is specialized to compress sparse hippocampal spatial codes into highly informative distributed codes suitable for efficient communication to other brain regions. Moreover, despite this substantial compression, the subiculum maintains finer scale temporal properties that may allow it to participate in oscillatory phase coding and spike timing-dependent plasticity in coordination with other regions of the hippocampal circuit.     

Impact of correlated synaptic input on output firing rate and variability in simple neuronal models.

Cortical neurons are typically driven by thousands of synaptic inputs. The arrival of a spike from one input may or may not be correlated with the arrival of other spikes from different inputs. How does this interdependence alter the probability that the postsynaptic neuron will fire? We constructed a simple random walk model in which the membrane potential of a target neuron fluctuates stochastically, driven by excitatory and inhibitory spikes arriving at random times. An analytic expression was derived for the mean output firing rate as a function of the firing rates and pairwise correlations of the inputs. This stochastic model made three quantitative predictions. (1) Correlations between pairs of excitatory or inhibitory inputs increase the fluctuations in synaptic drive, whereas correlations between excitatory-inhibitory pairs decrease them. (2) When excitation and inhibition are fully balanced (the mean net synaptic drive is zero), firing is caused by the fluctuations only. (3) In the balanced case, firing is irregular. These theoretical predictions were in excellent agreement with simulations of an integrate-and-fire neuron that included multiple conductances and received hundreds of synaptic inputs. The results show that, in the balanced regime, weak correlations caused by signals shared among inputs may have a multiplicative effect on the input-output rate curve of a postsynaptic neuron, i.e. they may regulate its gain; in the unbalanced regime, correlations may increase firing probability mainly around threshold, when output rate is low; and in all cases correlations are expected to increase the variability of the output spike train.     

Membrane Characteristics and Synaptic Responsiveness of Superficial Dorsal Horn Neurons in a Slice Preparation of Adult Rat Spinal Cord

Intracellular recordings have been made from neurons of the superficial dorsal horn in slices of the lumbar and thoracic spinal cord of young adult rats. Three broad categories of neurons could be distinguished on the basis of their firing patterns to intracellular current pulses and their afterhyperpolarizations (AHP); there was no detectable difference in the regional distribution of the three types. Category 1 cells were characterized by maintained firing to intracellular depolarizing current pulses, brief action potential durations and polyphasic AHPs. Category 2 cells showed spike adaptation, without spike attenuation, during intracellular current pulses, and had monophasic AHPs. Category 3 cells fired only 1 or 2 spikes to maintained depolarizing pulses and had smaller monophasic AHPs than category 2 neurons. Spontaneous excitatory and inhibitory postsynaptic potential (epsp and ipsp) activity was seen with psp durations varying widely. Low intensity electrical stimulation of afferent fibres, or of superficial white matter, resulted in polyphasic epsps and/or ipsps. The spike discharge in response to such afferent inputs correlated with the membrane properties of the cells, such that the synaptic responses of category 1 neurons were usually bursts of spikes, whereas category 2 and 3 neurons either failed to fire or fired only a single spike. These results in adult rat spinal cord suggest that the discharge pattern within synaptic sensory responses of superficial dorsal horn neurons is determined by postsynaptic membrane properties as well as by the pattern of the afferent input.     

Temporal coding of visual information in the thalamus.

The amount of information a sensory neuron carries about a stimulus is directly related to response reliability. We recorded from individual neurons in the cat lateral geniculate nucleus (LGN) while presenting randomly modulated visual stimuli. The responses to repeated stimuli were reproducible, whereas the responses evoked by nonrepeated stimuli drawn from the same ensemble were variable. Stimulus-dependent information was quantified directly from the difference in entropy of these neural responses. We show that a single LGN cell can encode much more visual information than had been demonstrated previously, ranging from 15 to 102 bits/sec across our sample of cells. Information rate was correlated with the firing rate of the cell, for a consistent rate of 3.6 +/- 0.6 bits/spike (mean +/- SD). This information can primarily be attributed to the high temporal precision with which firing probability is modulated; many individual spikes were timed with better than 1 msec precision. We introduce a way to estimate the amount of information encoded in temporal patterns of firing, as distinct from the information in the time varying firing rate at any temporal resolution. Using this method, we find that temporal patterns sometimes introduce redundancy but often encode visual information. The contribution of temporal patterns ranged from -3.4 to +25.5 bits/sec or from -9.4 to +24.9% of the total information content of the responses.     

Rate maintenance and resonance in the entorhinal cortex

Throughout the brain, neurons encode information in fundamental units of spikes. Each spike represents the combined thresholding of synaptic inputs and intrinsic neuronal dynamics. Here, we address a basic question of spike train formation: how do perithreshold synaptic inputs perturb the output of a spiking neuron? We recorded from single entorhinal principal cells in vitro and drove them to spike steadily at ～5 Hz (theta range) with direct current injection, then used a dynamic‐clamp to superimpose strong excitatory conductance inputs at varying rates. Neurons spiked most reliably when the input rate matched the intrinsic neuronal firing rate. We also found a striking tendency of neurons to preserve their rates and coefficients of variation, independently of input rates. As mechanisms for this rate maintenance, we show that the efficacy of the conductance inputs varied with the relationship of input rate to neuronal firing rate, and with the arrival time of the input within the natural period. Using a novel method of spike classification, we developed a minimal Markov model that reproduced the measured statistics of the output spike trains and thus allowed us to identify and compare contributions to the rate maintenance and resonance. We suggest that the strength of rate maintenance may be used as a new categorization scheme for neuronal response and note that individual intrinsic spiking mechanisms may play a significant role in forming the rhythmic spike trains of activated neurons; in the entorhinal cortex, individual pacemakers may dominate production of the regional theta rhythm.