Implications of variable synaptic weights for rate and temporal coding of cerebellar outputs.

Purkinje cell (PC) synapses onto cerebellar nuclei (CbN) neurons allow signals from the cerebellar cortex to influence the rest of the brain. PCs are inhibitory neurons that spontaneously fire at high rates, and many PC inputs are thought to converge onto each CbN neuron to suppress its firing. It has been proposed that PCs convey information using a rate code, a synchrony and timing code, or both. The influence of PCs on CbN neuron firing was primarily examined for the combined effects of many PC inputs with comparable strengths, and the influence of individual PC inputs has not been extensively studied. Here, we find that single PC to CbN synapses are highly variable in size, and using dynamic clamp and modeling we reveal that this has important implications for PC-CbN transmission. Individual PC inputs regulate both the rate and timing of CbN firing. Large PC inputs strongly influence CbN firing rates and transiently eliminate CbN firing for several milliseconds. Remarkably, the refractory period of PCs leads to a brief elevation of CbN firing prior to suppression. Thus, individual PC-CbN synapses are suited to concurrently convey rate codes and generate precisely timed responses in CbN neurons. Either synchronous firing or synchronous pauses of PCs promote CbN neuron firing on rapid time scales for nonuniform inputs, but less effectively than for uniform inputs. This is a secondary consequence of variable input sizes elevating the baseline firing rates of CbN neurons by increasing the variability of the inhibitory conductance. These findings may generalize to other brain regions with highly variable inhibitory synapse sizes.

Rate versus synchrony codes for cerebellar control of motor behavior.

Information transmission between neural populations could occur through either coordinated changes in firing rates or the precise transmission of spike timing. We investigate the code for information transmission from a part of the cerebellar cortex that is crucial for the accurate execution of a quantifiable motor behavior. Simultaneous recordings from Purkinje cell pairs in the cerebellum of rhesus macaques reveal how these cells coordinate their activity to drive smooth pursuit eye movements. Purkinje cells show millisecond-scale coordination of spikes (synchrony), but the level of synchrony is small and insufficient to impact the firing of downstream vestibular nucleus neurons. Analysis of previous metrics that purported to reveal Purkinje cell synchrony demonstrates that these metrics conflate changes in firing rate and neuron-neuron covariance. We conclude that the output of the cerebellar cortex uses primarily a rate rather than a synchrony code to drive the activity of downstream neurons and thus control motor behavior.

Sparse spike trains and the limitation of rate codes underlying rapid behaviours.

Animals live in dynamic worlds where they use sensorimotor circuits to rapidly process information and drive behaviours. For example, dragonflies are aerial predators that react to movements of prey within tens of milliseconds. These pursuits are likely controlled by identified neurons in the dragonfly, which have well-characterized physiological responses to moving targets. Predominantly, neural activity in these circuits is interpreted in context of a rate code, where information is conveyed by changes in the number of spikes over a time period. However, such a description of neuronal activity is difficult to achieve in real-world, real-time scenarios. Here, we contrast a neuroscientists' post-hoc view of spiking activity with the information available to the animal in real-time. We describe how performance of a rate code is readily overestimated and outline a rate code's significant limitations in driving rapid behaviours.

Differences in auditory temporal processing in the left and right auditory cortices of the rat.

In the present study, we examined hemispheric differences in the representation and processing of temporally structured auditory stimuli. Neuronal responses evoked by sinusoidally frequency modulated (FM) tones, frequency sweeps, amplitude modulated (AM) tones and noise, click trains with constant inter-click intervals and natural vocalizations were recorded from the left (LAC) and right (RAC) auditory cortices in adult (4-6 months old) anaesthetized F344 rats. Using vector strength, modulation-transfer functions, van Rossum distances, or direction-selectivity index, representation and processing of structured auditory stimuli were compared in the LAC and the RAC. The RAC generally tended to exhibit a higher ability to synchronize with the stimulus, a higher reproducibility of responses, and a higher proportion of direction-selective units. The LAC, on the other hand, mostly had higher relative response magnitudes in the modulation transfer functions. Importantly, the hemispheric differences were dependent on the type of the stimulus and there was also a significant inter-individual variability. Our findings indicate that neural coding in the RAC is based more on timing of action potentials (temporal code), while the LAC uses more the response magnitudes (rate code). It is thus necessary to distinguish between the type of the neural code and the stimulus feature it encodes and reconsider the simple opinion about dominance of the LAC for temporal processing, as it may not hold in general for all types of temporally structured stimuli.

Physiological noise facilitates multiplexed coding of vibrotactile-like signals in somatosensory cortex.

Neurons can use different aspects of their spiking to simultaneously represent (multiplex) different features of a stimulus. For example, some pyramidal neurons in primary somatosensory cortex (S1) use the rate and timing of their spikes to, respectively, encode the intensity and frequency of vibrotactile stimuli. Doing so has several requirements. Because they fire at low rates, pyramidal neurons cannot entrain 1:1 with high-frequency (100 to 600 Hz) inputs and, instead, must skip (i.e., not respond to) some stimulus cycles. The proportion of skipped cycles must vary inversely with stimulus intensity for firing rate to encode stimulus intensity. Spikes must phase-lock to the stimulus for spike times (intervals) to encode stimulus frequency, but, in addition, skipping must occur irregularly to avoid aliasing. Using simulations and in vitro experiments in which mouse S1 pyramidal neurons were stimulated with inputs emulating those induced by vibrotactile stimuli, we show that fewer cycles are skipped as stimulus intensity increases, as required for rate coding, and that intrinsic or synaptic noise can induce irregular skipping without disrupting phase locking, as required for temporal coding. This occurs because noise can modulate the reliability without disrupting the precision of spikes evoked by small-amplitude, fast-onset signals. Specifically, in the fluctuation-driven regime associated with sparse spiking, rate and temporal coding are both paradoxically improved by the strong synaptic noise characteristic of the intact cortex. Our results demonstrate that multiplexed coding by S1 pyramidal neurons is not only feasible under in vivo conditions, but that background synaptic noise is actually beneficial.

Temporal Encoding is Required for Categorization, But Not Discrimination.

Core auditory cortex (AC) neurons encode slow fluctuations of acoustic stimuli with temporally patterned activity. However, whether temporal encoding is necessary to explain auditory perceptual skills remains uncertain. Here, we recorded from gerbil AC neurons while they discriminated between a 4-Hz amplitude modulation (AM) broadband noise and AM rates >4 Hz. We found a proportion of neurons possessed neural thresholds based on spike pattern or spike count that were better than the recorded session's behavioral threshold, suggesting that spike count could provide sufficient information for this perceptual task. A population decoder that relied on temporal information outperformed a decoder that relied on spike count alone, but the spike count decoder still remained sufficient to explain average behavioral performance. This leaves open the possibility that more demanding perceptual judgments require temporal information. Thus, we asked whether accurate classification of different AM rates between 4 and 12 Hz required the information contained in AC temporal discharge patterns. Indeed, accurate classification of these AM stimuli depended on the inclusion of temporal information rather than spike count alone. Overall, our results compare two different representations of time-varying acoustic features that can be accessed by downstream circuits required for perceptual judgments.

Age-related changes in the temporal processing of acoustical signals in the auditory cortex of rats.

Age-related hearing loss is manifested primarily by a decreased sensitivity to faint sounds, that is, by elevation of the hearing thresholds. Nevertheless, aging also affects the ability of the auditory system to process temporal parameters of the sound stimulus. To explore the precision and reliability of auditory temporal processing during aging, responses to several types of sound stimuli were recorded from neurons of the auditory cortex (AC) of young and aged anaesthetized Fischer 344 rats. In response to broad-band noise bursts, the aged rats exhibited larger response magnitudes, a higher proportion of monotonic units, and also a larger variability of response magnitudes, suggesting a lower stability of the rate code. Of primary interest were the responses to temporally structured stimuli (amplitude-modulated (AM) noise, frequency-modulated (FM) tones, and click trains) recorded separately in the right and left AC. Significant differences of temporal processing were already found between the neuronal responses in the left and right AC in the young animals: for the click trains, the left hemisphere exhibited a greater responsiveness to higher repetition rates, lower vector strength values, and a lower similarity of responses. The two hemispheres were also affected differently by aging. In the right hemisphere, neurons in the aged animals displayed worse synchronization with the AM noise and clicks, but better synchronization with the FM tone. In the left hemisphere, neuronal synchronization with the stimulus modulation improved at a higher age for all three stimuli. The results show that the ability of the aging auditory system to process temporal parameters of the stimulus strongly depends on the stimulus type and on laterality. Furthermore, the commonly reported age-related decline in the temporal processing ability cannot be regarded as general as, at least at the neuronal level in the AC, objective measures of the temporal representation often exhibit age-related improvement instead of deterioration.

Subcircuits of Deep and Superficial CA1 Place Cells Support Efficient Spatial Coding across Heterogeneous Environments.

The hippocampus is thought to guide navigation by forming a cognitive map of space. Different environments differ in geometry and the availability of cues that can be used for navigation. Although several spatial coding mechanisms are known to coexist in the hippocampus, how they are influenced by various environmental features is not well understood. To address this issue, we examined the spatial coding characteristics of hippocampal neurons in mice and rats navigating in different environments. We found that CA1 place cells located in the superficial sublayer were more active in cue-poor environments and preferentially used a firing rate code driven by intra-hippocampal inputs. In contrast, place cells located in the deep sublayer were more active in cue-rich environments and used a phase code driven by entorhinal inputs. Switching between these two spatial coding modes was supported by the interaction between excitatory gamma inputs and local inhibition.

A Time-Varying Information Measure for Tracking Dynamics of Neural Codes in a Neural Ensemble.

The amount of information that differentially correlated spikes in a neural ensemble carry is not the same; the information of different types of spikes is associated with different features of the stimulus. By calculating a neural ensemble's information in response to a mixed stimulus comprising slow and fast signals, we show that the entropy of synchronous and asynchronous spikes are different, and their probability distributions are distinctively separable. We further show that these spikes carry a different amount of information. We propose a time-varying entropy (TVE) measure to track the dynamics of a neural code in an ensemble of neurons at each time bin. By applying the TVE to a multiplexed code, we show that synchronous and asynchronous spikes carry information in different time scales. Finally, a decoder based on the Kalman filtering approach is developed to reconstruct the stimulus from the spikes. We demonstrate that slow and fast features of the stimulus can be entirely reconstructed when this decoder is applied to asynchronous and synchronous spikes, respectively. The significance of this work is that the TVE can identify different types of information (for example, corresponding to synchronous and asynchronous spikes) that might simultaneously exist in a neural code.

Tapping Into the Language of Touch: Using Non-invasive Stimulation to Specify Tactile Afferent Firing Patterns.

The temporal pattern of action potentials can convey rich information in a variety of sensory systems. We describe a new non-invasive technique that enables precise, reliable generation of action potential patterns in tactile peripheral afferent neurons by brief taps on the skin. Using this technique, we demonstrate sophisticated coding of temporal information in the somatosensory system, that shows that perceived vibration frequency is not encoded in peripheral afferents as was expected by either their firing rate or the underlying periodicity of the stimulus. Instead, a burst gap or silent gap between trains of action potentials conveys frequency information. This opens the possibility of new encoding strategies that could be deployed to convey sensory information using mechanical or electrical stimulation in neural prostheses and brain-machine interfaces, and may extend to senses beyond artificial encoding of aspects of touch. We argue that a focus on appropriate use of effective temporal coding offers more prospects for rapid improvement in the function of these interfaces than attempts to scale-up existing devices.

Simultaneous spike-time locking to multiple frequencies.

Locking of neural firing is ubiquitously observed in the brain and occurs when neurons fire at a particular phase or in synchronization with an external signal. Here we study in detail the locking of single neurons to multiple distinct frequencies at the example of p-type electroreceptor afferents in the electrosensory system of the weakly electric fish Apteronotus leptorhynchus (brown ghost knifefish). We find that electrosensory afferents and pyramidal cells in the electrosensory lateral line lobe (ELL) lock to multiple frequencies, including the electric organ discharge (EOD) frequency, beat, and stimulus itself. We identify key elements necessary for locking to multiple frequencies, study its limits, and provide concise mathematical models reproducing our main findings. Our findings provide another example of how rate and temporal codes can coexist and complement each other in single neurons and demonstrate that sensory coding in p-type electroreceptor afferents provides a much richer representation of the sensory environment than commonly assumed. Since the underlying mechanisms are not specific to the electrosensory system, our results could provide the basis for studying multiple frequency locking in other systems.NEW & NOTEWORTHY Locking of neuronal spikes to external and internal signals is a ubiquitous neurophysiological mechanism that has been extensively studied in several brain areas and species. Using experimental data from the electrosensory system and concise mathematical models, we analyze how a single neuron can simultaneously lock to multiple frequencies. Our findings demonstrate how temporal and rate codes can complement each other and lead to rich neuronal representations of sensory signals.

The neural circuitry supporting successful spatial navigation despite variable movement speeds.

Ants who have successfully navigated the long distance between their foraging spot and their nest dozens of times will drastically overshoot their destination if the size of their legs is doubled by the addition of stilts. This observation reflects a navigational strategy called path integration, a strategy also utilized by mammals. Path integration necessitates that animals keep track of their movement speed and use it to precisely and instantly modify where they think they are and where they want to go. Here we review the neural circuitry that has evolved to integrate speed and space. We start with the rate and temporal codes for speed in the hippocampus and work backwards towards the motor and sensory systems. We highlight the need for experiments designed to differentiate the respective contributions of motor efference copy versus sensory inputs. In particular, we discuss the importance of high-resolution tracking of the latency of speed-encoding as a precise way to disentangle the sensory versus motor computations that enable successful spatial navigation at very different speeds.

Pitch of harmonic complex tones: rate and temporal coding of envelope repetition rate in inferior colliculus of unanesthetized rabbits.

Harmonic complex tones (HCTs) found in speech, music, and animal vocalizations evoke strong pitch percepts at their fundamental frequencies. The strongest pitches are produced by HCTs that contain harmonics resolved by cochlear frequency analysis, but HCTs containing solely unresolved harmonics also evoke a weaker pitch at their envelope repetition rate (ERR). In the auditory periphery, neurons phase lock to the stimulus envelope, but this temporal representation of ERR degrades and gives way to rate codes along the ascending auditory pathway. To assess the role of the inferior colliculus (IC) in such transformations, we recorded IC neuron responses to HCT and sinusoidally modulated broadband noise (SAMN) with varying ERR from unanesthetized rabbits. Different interharmonic phase relationships of HCT were used to manipulate the temporal envelope without changing the power spectrum. Many IC neurons demonstrated band-pass rate tuning to ERR between 60 and 1,600 Hz for HCT and between 40 and 500 Hz for SAMN. The tuning was not related to the pure-tone best frequency of neurons but was dependent on the shape of the stimulus envelope, indicating a temporal rather than spectral origin. A phenomenological model suggests that the tuning may arise from peripheral temporal response patterns via synaptic inhibition. We also characterized temporal coding to ERR. Some IC neurons could phase lock to the stimulus envelope up to 900 Hz for either HCT or SAMN, but phase locking was weaker with SAMN. Together, the rate code and the temporal code represent a wide range of ERR, providing strong cues for the pitch of unresolved harmonics.NEW & NOTEWORTHY Envelope repetition rate (ERR) provides crucial cues for pitch perception of frequency components that are not individually resolved by the cochlea, but the neural representation of ERR for stimuli containing many harmonics is poorly characterized. Here we show that the pitch of stimuli with unresolved harmonics is represented by both a rate code and a temporal code for ERR in auditory midbrain neurons and propose possible underlying neural mechanisms with a computational model.

Cerebellar Purkinje cells control eye movements with a rapid rate code that is invariant to spike irregularity.

The rate and temporal pattern of neural spiking each have the potential to influence computation. In the cerebellum, it has been hypothesized that the irregularity of interspike intervals in Purkinje cells affects their ability to transmit information to downstream neurons. Accordingly, during oculomotor behavior in mice and rhesus monkeys, mean irregularity of Purkinje cell spiking varied with mean eye velocity. However, moment-to-moment variations revealed a tight correlation between eye velocity and spike rate, with no additional information conveyed by spike irregularity. Moreover, when spike rate and irregularity were independently controlled using optogenetic stimulation, the eye movements elicited were well-described by a linear population rate code with 3-5 ms temporal precision. Biophysical and random-walk models identified biologically realistic parameter ranges that determine whether spike irregularity influences responses downstream. The results demonstrate cerebellar control of movements through a remarkably rapid rate code, with no evidence for an additional contribution of spike irregularity.

Differentially synchronized spiking enables multiplexed neural coding.

Multiplexing refers to the simultaneous encoding of two or more signals. Neurons have been shown to multiplex, but different stimuli require different multiplexing strategies. Whereas the frequency and amplitude of periodic stimuli can be encoded by the timing and rate of the same spikes, natural scenes, which comprise areas over which intensity varies gradually and sparse edges where intensity changes abruptly, require a different multiplexing strategy. Recording in vivo from neurons in primary somatosensory cortex during tactile stimulation, we found that stimulus onset and offset (edges) evoked highly synchronized spiking, whereas other spikes in the same neurons occurred asynchronously. Stimulus intensity modulated the rate of asynchronous spiking, but did not affect the timing of synchronous spikes. From this, we hypothesized that spikes driven by high- and low-contrast stimulus features can be distinguished on the basis of their synchronization, and that differentially synchronized spiking can thus be used to form multiplexed representations. Applying a Bayesian decoding method, we verified that information about high- and low-contrast features can be recovered from an ensemble of model neurons receiving common input. Equally good decoding was achieved by distinguishing synchronous from asynchronous spikes and applying reverse correlation methods separately to each spike type. This result, which we verified with patch clamp recordings in vitro, demonstrates that neurons receiving common input can use the rate of asynchronous spiking to encode the intensity of low-contrast features while using the timing of synchronous spikes to encode the occurrence of high-contrast features. We refer to this strategy as synchrony-division multiplexing.

Evaluating performance of neural codes in model neural communication networks.

Information needs to be appropriately encoded to be reliably transmitted over physical media. Similarly, neurons have their own codes to convey information in the brain. Even though it is well-known that neurons exchange information using a pool of several protocols of spatio-temporal encodings, the suitability of each code and their performance as a function of network parameters and external stimuli is still one of the great mysteries in neuroscience. This paper sheds light on this by modeling small-size networks of chemically and electrically coupled Hindmarsh-Rose spiking neurons. We focus on a class of temporal and firing-rate codes that result from neurons' membrane-potentials and phases, and quantify numerically their performance estimating the Mutual Information Rate, aka the rate of information exchange. Our results suggest that the firing-rate and interspike-intervals codes are more robust to additive Gaussian white noise. In a network of four interconnected neurons and in the absence of such noise, pairs of neurons that have the largest rate of information exchange using the interspike-intervals and firing-rate codes are not adjacent in the network, whereas spike-timings and phase codes (temporal) promote large rate of information exchange for adjacent neurons. If that result would have been possible to extend to larger neural networks, it would suggest that small microcircuits would preferably exchange information using temporal codes (spike-timings and phase codes), whereas on the macroscopic scale, where there would be typically pairs of neurons not directly connected due to the brain's sparsity, firing-rate and interspike-intervals codes would be the most efficient codes.

Embedded ensemble encoding hypothesis: The role of the "Prepared" cell.

We here reconsider current theories of neural ensembles in the context of recent discoveries about neuronal dendritic physiology. The key physiological observation is that the dendritic plateau potential produces sustained depolarization of the cell body (amplitude 10-20 mV, duration 200-500 ms). Our central hypothesis is that synaptically-evoked dendritic plateau potentials lead to a prepared state of a neuron that favors spike generation. The plateau both depolarizes the cell toward spike threshold, and provides faster response to inputs through a shortened membrane time constant. As a result, the speed of synaptic-to-action potential (AP) transfer is faster during the plateau phase. Our hypothesis relates the changes from "resting" to "depolarized" neuronal state to changes in ensemble dynamics and in network information flow. The plateau provides the Prepared state (sustained depolarization of the cell body) with a time window of 200-500 ms. During this time, a neuron can tune into ongoing network activity and synchronize spiking with other neurons to provide a coordinated Active state (robust firing of somatic APs), which would permit "binding" of signals through coordination of neural activity across a population. The transient Active ensemble of neurons is embedded in the longer-lasting Prepared ensemble of neurons. We hypothesize that "embedded ensemble encoding" may be an important organizing principle in networks of neurons.

Neuronal response impedance mechanism implementing cooperative networks with low firing rates and µs precision.

Realizations of low firing rates in neural networks usually require globally balanced distributions among excitatory and inhibitory links, while feasibility of temporal coding is limited by neuronal millisecond precision. We show that cooperation, governing global network features, emerges through nodal properties, as opposed to link distributions. Using in vitro and in vivo experiments we demonstrate microsecond precision of neuronal response timings under low stimulation frequencies, whereas moderate frequencies result in a chaotic neuronal phase characterized by degraded precision. Above a critical stimulation frequency, which varies among neurons, response failures were found to emerge stochastically such that the neuron functions as a low pass filter, saturating the average inter-spike-interval. This intrinsic neuronal response impedance mechanism leads to cooperation on a network level, such that firing rates are suppressed toward the lowest neuronal critical frequency simultaneously with neuronal microsecond precision. Our findings open up opportunities of controlling global features of network dynamics through few nodes with extreme properties.

Adaptation of short-term plasticity parameters via error-driven learning may explain the correlation between activity-dependent synaptic properties, connectivity motifs and target specificity.

The anatomical connectivity among neurons has been experimentally found to be largely non-random across brain areas. This means that certain connectivity motifs occur at a higher frequency than would be expected by chance. Of particular interest, short-term synaptic plasticity properties were found to colocalize with specific motifs: an over-expression of bidirectional motifs has been found in neuronal pairs where short-term facilitation dominates synaptic transmission among the neurons, whereas an over-expression of unidirectional motifs has been observed in neuronal pairs where short-term depression dominates. In previous work we found that, given a network with fixed short-term properties, the interaction between short- and long-term plasticity of synaptic transmission is sufficient for the emergence of specific motifs. Here, we introduce an error-driven learning mechanism for short-term plasticity that may explain how such observed correspondences develop from randomly initialized dynamic synapses. By allowing synapses to change their properties, neurons are able to adapt their own activity depending on an error signal. This results in more rich dynamics and also, provided that the learning mechanism is target-specific, leads to specialized groups of synapses projecting onto functionally different targets, qualitatively replicating the experimental results of Wang and collaborators.

The Neural Code for Motor Control in the Cerebellum and Oculomotor Brainstem.

A single extra spike makes a difference. Here, the size of the eye velocity in the initiation of smooth eye movements in the right panel depends on whether a cerebellar Purkinje cell discharges 3 (red), 4 (green), 5 (blue), or 6 (black) spikes in the 40-ms window indicated by the gray shading in the rasters on the left. Spike trains are rich in information that can be extracted to guide behaviors at millisecond time resolution or across longer time intervals. In sensory systems, the information usually is defined with respect to the stimulus. Especially in motor systems, however, it is equally critical to understand how spike trains predict behavior. Thus, our goal was to compare systematically spike trains in the oculomotor system with eye movement behavior on single movements. We analyzed the discharge of Purkinje cells in the floccular complex of the cerebellum, floccular target neurons in the brainstem, other vestibular neurons, and abducens neurons. We find that an extra spike in a brief analysis window predicts a substantial fraction of the trial-by-trial variation in the initiation of smooth pursuit eye movements. For Purkinje cells, a single extra spike in a 40 ms analysis window predicts, on average, 0.5 SDs of the variation in behavior. An optimal linear estimator predicts behavioral variation slightly better than do spike counts in brief windows. Simulations reveal that the ability of single spikes to predict a fraction of behavior also emerges from model spike trains that have the same statistics as the real spike trains, as long as they are driven by shared sensory inputs. We think that the shared sensory estimates in their inputs create correlations in neural spiking across time and across each population. As a result, one or a small number of spikes in a brief time interval can predict a substantial fraction of behavioral variation.