NSci 8217 Fall 2007 - Neuronal Precision and Reliability

Membrane potential fluctuations determine the precision of spike timing and synchronous activity: a model study.
J. Kretzberg and M. Egelhaaf and A. K. Warzecha
J Comput Neurosci  10  79--97  (2001)
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.
Temporal precision of the encoding of motion information by visual interneurons.
A. K. Warzecha and J. Kretzberg and M. Egelhaaf
Curr Biol  8  359--368  (1998)
BACKGROUND: There is much controversy about the timescale on which neurons process and transmit information. On the one hand, a vast amount of information can be processed by the nervous system if the precise timing of individual spikes on a millisecond timescale is important. On the other hand, neuronal responses to identical stimuli often vary considerably and stochastic response fluctuations can exceed the mean response amplitude. Here, we examined the timescale on which neural responses could be locked to visual motion stimuli. RESULTS: Spikes of motion-sensitive neurons in the visual system of the blowfly are time-locked to visual motion with a precision in the range of several tens of milliseconds. Nevertheless, different motion-sensitive neurons with largely overlapping receptive fields generate a large proportion of spikes almost synchronously. This precision is brought about by stochastic rather than by motion-induced membrane-potential fluctuations elicited by the common peripheral input. The stochastic membrane-potential fluctuations contain more power at frequencies above 30-40 Hz than the motion-induced potential changes. A model of spike generation indicates that such fast membrane-potential changes are a major determinant of the precise timing of spikes. CONCLUSIONS: The timing of spikes in neurons of the motion pathway of the blowfly is controlled on a millisecond timescale by fast membrane-potential fluctuations. Despite this precision, spikes do not lock to motion stimuli on this timescale because visual motion does not induce sufficiently rapid changes in the membrane potential.
Information theoretic analysis of pulmonary stretch receptor spike trains.
R. F. Rogers and J. D. Runyan and A. G. Vaidyanathan and J. S. Schwaber
J Neurophysiol  85  448--461  (2001)
Primary afferent neurons transduce physical, continuous stimuli into discrete spike trains. Investigators have long been interested in interpreting the meaning of the number or pattern of action potentials in attempts to decode the spike train back into stimulus parameters. Pulmonary stretch receptors (PSRs) are visceral mechanoreceptors that respond to deformation of the lungs and pulmonary tree. They provide the brain stem with feedback that is used by cardiorespiratory control circuits. In anesthetized, paralyzed, artificially ventilated rabbits, we recorded the action potential trains of individual PSRs while continuously manipulating ventilator rate and volume. We describe an information theoretic-based analytical method for evaluating continuous stimulus and spike train data that is of general applicability to any continuous, dynamic system. After adjusting spike times for conduction velocity, we used a sliding window to discretize the stimulus (average tracheal pressure) and response (number of spikes), and constructed co-occurrence matrices. We systematically varied the number of categories into which the stimulus and response were evenly divided at 26 different sliding window widths (5, 10, 20, 30,..., 230, 240, 250 ms). Using the probability distributions defined by the co-occurrence matrices, we estimated associated stimulus, response, joint, and conditional entropies, from which we calculated information transmitted as a fraction of the maximum possible, as well as encoding and decoding efficiencies. We found that, in general, information increases rapidly as the sliding window width increases from 5 to approximately 50 ms and then saturates as observation time increases. In addition, the information measures suggest that individual PSRs transmit more "when" than "what" type of information about the stimulus, based on the finding that the maximum information at a given window width was obtained when the stimulus was divided into just a few (usually <6) categories. Our results indicate that PSRs provide quite reliable information about tracheal pressure, with each PSR conveying about 31% of the maximum possible information about the dynamic stimulus, given our analytical parameters. When the stimulus and response are divided into more categories, slightly less information is transmitted, and this quantity also saturates as a function of observation time. We consider and discuss the importance of information contained in window widths on the time scales of an excitatory postsynaptic potential and Hering-Breuer reflex central delay.
Metabolically efficient information processing.
V. Balasubramanian and D. Kimber and M. J. n. Berry
Neural Comput  13  799--815  (2001)
Energy-efficient information transmission may be relevant to biological sensory signal processing as well as to low-power electronic devices. We explore its consequences in two different regimes. In an "immediate" regime, we argue that the information rate should be maximized subject to a power constraint, and in an "exploratory" regime, the transmission rate per power cost should be maximized. In the absence of noise, discrete inputs are optimally encoded into Boltzmann distributed output symbols. In the exploratory regime, the partition function of this distribution is numerically equal to 1. The structure of the optimal code is strongly affected by noise in the transmission channel. The Arimoto-Blahut algorithm, generalized for cost constraints, can be used to derive and interpret the distribution of symbols for optimal energy-efficient coding in the presence of noise. We outline the possibilities and problems in extending our results to information coding and transmission in neurobiological systems.
Firing rate distributions and efficiency of information transmission of inferior temporal cortex neurons to natural visual stimuli.
A. Treves and S. Panzeri and E. Rolls and M. Booth and E. Wakeman
Neural Comput  11  601-32  (1999)
The distribution of responses of sensory neurons to ecological stimulation has been proposed to be designed to maximize information transmission, which according to a simple model would imply an exponential distribution of spike counts in a given time window. We have used recordings from inferior temporal cortex neurons responding to quasi-natural visual stimulation (presented using a video of everyday lab scenes and a large number of static images of faces and natural scenes) to assess the validity of this exponential model and to develop an alternative simple model of spike count distributions. We find that the exponential model has to be rejected in 84\% of cases (at the p < 0.01 level). A new model, which accounts for the firing rate distribution found in terms of slow and fast variability in the inputs that produce neuronal activation, is rejected statistically in only 16\% of cases. Finally, we show that the neurons are moderately efficient at transmitting information but not optimally efficient.
Reliability of spike timing is a general property of spiking model neurons.
R. Brette and E. Guigon
Neural Comput  15  279--308  (2003)
The responses of neurons to time-varying injected currents are reproducible on a trial-by-trial basis in vitro, but when a constant current is injected, small variances in interspike intervals across trials add up, eventually leading to a high variance in spike timing. It is unclear whether this difference is due to the nature of the input currents or the intrinsic properties of the neurons. Neuron responses can fail to be reproducible in two ways: dynamical noise can accumulate over time and lead to a desynchronization over trials, or several stable responses can exist, depending on the initial condition. Here we show, through simulations and theoretical considerations, that for a general class of spiking neuron models, which includes, in particular, the leaky integrate-and-fire model as well as nonlinear spiking models, aperiodic currents, contrary to periodic currents, induce reproducible responses, which are stable under noise, change in initial conditions and deterministic perturbations of the input. We provide a theoretical explanation for aperiodic currents that cross the threshold.
Variability in spike trains during constant and dynamic stimulation.
A. K. Warzecha and M. Egelhaaf
Science  283  1927--1930  (1999)
In a recent study, it was concluded that natural time-varying stimuli are represented more reliably in the brain than constant stimuli are. The results presented here disagree with this conclusion, although they were obtained from the same identified neuron (H1) in the fly's visual system. For large parts of the neuron's activity range, the variability of the responses was very similar for constant and time-varying stimuli and was considerably smaller than that in many visual interneurons of vertebrates.
Reliability of a fly motion-sensitive neuron depends on stimulus parameters.
A. K. Warzecha and J. Kretzberg and M. Egelhaaf
J Neurosci  20  8886--8896  (2000)
The variability of responses of sensory neurons constrains how reliably animals can respond to stimuli in the outside world. We show for a motion-sensitive visual interneuron of the fly that the variability of spike trains depends on the properties of the motion stimulus, although differently for different stimulus parameters. (1) The spike count variances of responses to constant and to dynamic stimuli lie in the same range. (2) With increasing stimulus size, the variance may slightly decrease. (3) Increasing pattern contrast reduces the variance considerably. For all stimulus conditions, the spike count variance is much smaller than the mean spike count and does not depend much on the mean activity apart from very low activities. Using a model of spike generation, we analyzed how the spike count variance depends on the membrane potential noise and the deterministic membrane potential fluctuations at the spike initiation zone of the neuron. In a physiologically plausible range, the variance is affected only weakly by changes in the dynamics or the amplitude of the deterministic membrane potential fluctuations. In contrast, the amplitude and dynamics of the membrane potential noise strongly influence the spike count variance. The membrane potential noise underlying the variability of the spike responses in the motion-sensitive neuron is concluded to be affected considerably by the contrast of the stimulus but by neither its dynamics nor its size.
Impact of photon noise on the reliability of a motion-sensitive neuron in the fly's visual system.
J. Grewe and J. Kretzberg and A. Warzecha and M. Egelhaaf
J Neurosci  23  10776--10783  (2003)
Variable behavioral responses to identical visual stimuli can, in part, be traced back to variable neuronal signals that provide unreliable information about the outside world. This unreliability in encoding of visual information is caused by several noise sources such as photon noise, synaptic noise, or the stochastic nature of ion channels. Neurons of the fly's visual motion pathway have been claimed to represent perfect encoders, with photon noise as the main noise source limiting their performance. Other studies on the fly's visual system suggest, however, that internal noise emerging within the nervous system also affects the reliability of motion vision. To resolve these contradictory interpretations, we performed an electrophysiological investigation, inspired by the "equivalent noise" paradigm applied in psychophysics, on the fly's motion-sensitive H1 neuron. Noise-like brightness fluctuations of different strength were superimposed on the motion stimuli. Because the noise level found to affect the temporal properties of the spike responses is much larger than the estimate of photon noise under the experimental conditions, our results indicate that motion vision is more likely to be limited by internal sources of variability than by photon noise.
Motion adaptation leads to parsimonious encoding of natural optic flow by blowfly motion vision system.
J. Heitwerth and R. Kern and J. H. van Hateren and M. Egelhaaf
J Neurophysiol  94  1761--1769  (2005)
Neurons sensitive to visual motion change their response properties during prolonged motion stimulation. These changes have been interpreted as adaptive and were concluded, for instance, to adjust the sensitivity of the visual motion pathway to velocity changes or to increase the reliability of encoding of motion information. These conclusions are based on experiments with experimenter-designed motion stimuli that differ substantially with respect to their dynamical properties from the optic flow an animal experiences during normal behavior. We analyze for the first time motion adaptation under natural stimulus conditions. The experiments are done on the H1-cell, an identified neuron in the blowfly visual motion pathway that has served in many previous studies as a model system for visual motion computation. We reconstructed optic flow perceived by a blowfly in free flight and used this behaviorally generated optic flow to study motion adaptation. A variety of measures (variability in spike count, response latency, jitter of spike timing) suggests that the coding quality does not improve with prolonged stimulation. However, although the number of spikes decreases considerably during stimulation with natural optic flow, the amount of information that is conveyed stays nearly constant. Thus the information per spike increases, and motion adaptation leads to parsimonious coding without sacrificing the reliability with which behaviorally relevant information is encoded.
Spike generator limits efficiency of information transfer in a retinal ganglion cell.
N. K. Dhingra and R. G. Smith
J Neurosci  24  2914--2922  (2004)
The quality of the signal a retinal ganglion cell transmits to the brain is important for preception because it sets the minimum detectable stimulus. The ganglion cell converts graded potentials into a spike train with a selective filter but in the process adds noise. To explore how efficiently information is transferred to spikes, we measured contrast detection threshold and increment threshold from graded potential and spike responses of brisk-transient ganglion cells. Intracellular responses to a spot flashed over the receptive field center of the cell were recorded in an intact mammalian retina maintained in vitro at 37 degrees C. Thresholds were measured in a single-interval forced-choice procedure with an ideal observer. The graded potential gave a detection threshold of 1.5% contrast, whereas spikes gave 3.8%. The graded potential also gave increment thresholds approximately twofold lower and carried approximately 60% more gray levels. Increment threshold "dipped" below the detection threshold at a low contrast (<5%) but increased rapidly at higher contrasts. The magnitude of the "dipper" for both graded potential and spikes could be predicted from a threshold nonlinearity in the responses. Depolarization of the cell by current injection reduced the detection threshold for spikes but also reduced the range of contrasts they can transmit. This suggests that contrast sensitivity and dynamic range are related in an essential trade-off.
Information transmission rates of cat retinal ganglion cells.
C. L. Passaglia and J. B. Troy
J Neurophysiol  91  1217--1229  (2004)
To assess the information encoded in retinal spike trains and how it might be decoded by recipient neurons in the brain, we recorded from individual cat X and Y ganglion cells and visually stimulated them with randomly modulated patterns of various contrast and spatial configuration. For each pattern, we estimated the information rate of the cells using linear or nonlinear algorithms and for some patterns by directly measuring response probability distributions. We show that ganglion cell spike trains contain information from the receptive field center and surround, that the center and surround have similar signaling capacity, that antagonism between the mechanisms reduces information transmission, and that the total information rate is limited. We also show that a linear decoding algorithm can capture all of the information available in retinal spike trains about weak inputs, but it misses a substantial amount about strong inputs. For the strongest stimulus we used, the information rate of the best linear decoder averaged 40-70 bits/s across ganglion cell types, while the directly measured rate was around 20-40 bits/s greater. This implies that under certain stimulus conditions, visual information is encoded in the temporal structure of retinal spike trains and that a nonlinear decoding algorithm is needed to extract the temporally coded information. Using simulated spike trains, we demonstrate that much of the temporal structure may be explained by the threshold for spike generation and is not necessarily indicative of a complex coding scheme.
Precision of spike trains in primate retinal ganglion cells.
V. J. Uzzell and E. J. Chichilnisky
J Neurophysiol  92  780--789  (2004)
Recent studies have revealed striking precision in the spike trains of retinal ganglion cells in several species and suggested that this precision could be an important aspect of visual signaling. However, the precision of spike trains has not yet been described in primate retina. The spike time and count variability of parasol (magnocellular-projecting) retinal ganglion cells was examined in isolated macaque monkey retinas stimulated with repeated presentations of high contrast, spatially uniform intensity modulation. At the onset of clearly delineated periods of firing, retinal ganglion cells fired spikes time-locked to the stimulus with a variability across trials as low as 1 ms. Spike count variance across trials was much lower than the mean and sometimes approached the minimum variance possible with discrete counts, inconsistent with Poisson statistics expected from independently generated spikes. Spike time and count variability decreased systematically with stimulus strength. These findings were consistent with a model in which firing probability was determined by a stimulus-driven free firing rate modulated by a recovery function representing the action potential absolute and relative refractory period.
Quantal encoding of information in a retinal ganglion cell.
M. A. Freed
J Neurophysiol  94  1048--1056  (2005)
A retinal ganglion cell receives information about a white-noise stimulus as a flickering pattern of glutamate quanta. The ganglion cell reencodes this information as brief bursts of one to six spikes separated by quiescent periods. When the stimulus is repeated, the number of spikes in a burst is highly reproducible (variance < mean) and spike timing is precise to within 10 ms, leading to an estimate that each spike encodes about 2 bits. To understand how the ganglion cell reencodes information, we studied the quantal patterns by repeating a white-noise stimulus and recording excitatory currents from a voltage-clamped, brisk-sustained ganglion cell. Quanta occurred in synchronous bursts of 3 to 65; the resulting postsynaptic currents summed to form excitatory postsynaptic currents (EPSCs). The number of quanta in an EPSC was only moderately reproducible (variance = mean), quantal timing was precise to within 14 ms, and each quantum encoded 0.1-0.4 bit. In conclusion, compared to a spike, a quantum has similar temporal precision, but is less reproducible and encodes less information. Summing multiple quanta into discrete EPSCs improves the reproducibility of the overall quantal pattern and contributes to the reproducibility of the spike train.
Efficiency of information transmission by retinal ganglion cells.
K. Koch and J. McLean and M. Berry and P. Sterling and V. Balasubramanian and M. A. Freed
Curr Biol  14  1523--1530  (2004)
BACKGROUND: Different types of retinal ganglion cells convey different messages to the brain. Messages are in the form of spike patterns, and the number of possible patterns per second sets the coding capacity. We asked if different ganglion cell types make equally efficient use of their coding capacity or whether efficiency depends on the message conveyed. RESULTS: We recorded spike trains from retinal ganglion cells in an in vitro preparation of the guinea pig retina. By calculating, for the observed spike rate, the number of possible spike patterns per second, we calculated coding capacity, and by counting the actual number of patterns, we estimated information rate. Cells with "brisk" responses, i.e., high firing rates, and a general message transmitted information at high rates (21 +/- 9 bits s(-1)). Cells with "sluggish" responses, i.e., lower firing rates, and specific messages (direction of motion, local-edge) transmitted information at lower rates (13 +/- 7 bits s(-1)). Yet, for every type of ganglion cell examined, the information rate was about one-third of coding capacity. For every ganglion cell, information rate was very close (within 4%) to that predicted from Poisson noise and the cell's actual time-modulated rate. CONCLUSIONS: Different messages are transmitted with similar efficiency. Efficiency is limited by temporal correlations, but correlations may be essential to improve decoding in the presence of irreducible noise.
Spike count reliability and the Poisson hypothesis.
A. Amarasingham and T. Chen and S. Geman and M. T. Harrison and D. L. Sheinberg
J Neurosci  26  801--809  (2006)
The variability of cortical activity in response to repeated presentations of a stimulus has been an area of controversy in the ongoing debate regarding the evidence for fine temporal structure in nervous system activity. We present a new statistical technique for assessing the significance of observed variability in the neural spike counts with respect to a minimal Poisson hypothesis, which avoids the conventional but troubling assumption that the spiking process is identically distributed across trials. We apply the method to recordings of inferotemporal cortical neurons of primates presented with complex visual stimuli. On this data, the minimal Poisson hypothesis is rejected: the neuronal responses are too reliable to be fit by a typical firing-rate model, even allowing for sudden, time-varying, and trial-dependent rate changes after stimulus onset. The statistical evidence favors a tightly regulated stimulus response in these neurons, close to stimulus onset, although not further away.
Information content of auditory cortical responses to time-varying acoustic stimuli.
T. Lu and X. Wang
J Neurophysiol  91  301--313  (2004)
The present study explores the issue of cortical coding by spike count and timing using statistical and information theoretic methods. We have shown in previous studies that neurons in the auditory cortex of awake primates have an abundance of sustained discharges that could represent time-varying signals by temporal discharge patterns or mean firing rates. In particular, we found that a subpopulation of neurons can encode rapidly occurring sounds, such as a click train, with discharges that are not synchronized to individual stimulus events, suggesting a temporal-to-rate transformation. We investigated whether there were stimulus-specific temporal patterns embedded in these seemingly random spike times. Furthermore, we quantitatively analyzed the precision of spike timing at stimulus onset and during ongoing acoustic stimulation. The main findings are the following. 1) Temporal and rate codes may operate at separate stimulus domains or encode the same stimulus domain in parallel via different neuronal populations. 2) Spike timing was crucial to encode stimulus periodicity in "synchronized" neurons. 3) "Nonsynchronized" neurons showed little stimulus-specific spike timing information in their responses to time-varying signals. Such responses therefore represent processed (instead of preserved) information in the auditory cortex. And 4) spike timing on the occurrence of acoustic events was more precise at the first event than at successive ones and more precise with sparsely distributed events (longer time intervals between events) than with densely packed events. These results indicate that auditory cortical neurons mark sparse acoustic events (or onsets) with precise spike timing and transform rapidly occurring acoustic events into firing rate-based representations.
Spike-timing precision underlies the coding efficiency of auditory receptor neurons.
A. Rokem and S. Watzl and T. Gollisch and M. Stemmler and A. V. M. Herz and I. Samengo
J Neurophysiol  95  2541--2552  (2006)
Sensory systems must translate incoming signals quickly and reliably so that an animal can act successfully in its environment. Even at the level of receptor neurons, however, functional aspects of the sensory encoding process are not yet fully understood. Specifically, this concerns the question how stimulus features and neural response characteristics lead to an efficient transmission of sensory information. To address this issue, we have recorded and analyzed spike trains from grasshopper auditory receptors, while systematically varying the stimulus statistics. The stimulus variations profoundly influenced the efficiency of neural encoding. This influence was largely attributable to the presence of specific stimulus features that triggered remarkably precise spikes whose trial-to-trial timing variability was as low as 0.15 ms--one order of magnitude shorter than typical stimulus time scales. Precise spikes decreased the noise entropy of the spike trains, thereby increasing the rate of information transmission. In contrast, the total spike train entropy, which quantifies the variety of different spike train patterns, hardly changed when stimulus conditions were altered, as long as the neural firing rate remained the same. This finding shows that stimulus distributions that were transmitted with high information rates did not invoke additional response patterns, but instead displayed exceptional temporal precision in their neural representation. The acoustic stimuli that led to the highest information rates and smallest spike-time jitter feature pronounced sound-pressure deflections lasting for 2-3 ms. These upstrokes are reminiscent of salient structures found in natural grasshopper communication signals, suggesting that precise spikes selectively encode particularly important aspects of the natural stimulus environment.
Adaptive rescaling maximizes information transmission.
N. Brenner and W. Bialek and R. de Ruyter van Steveninck
Neuron  26  695-702  (2000)
Adaptation is a widespread phenomenon in nervous systems, providing flexibility to function under varying external conditions. Here, we relate an adaptive property of a sensory system directly to its function as a carrier of information about input signals. We show that the input/output relation of a sensory system in a dynamic environment changes with the statistical properties of the environment. Specifically, when the dynamic range of inputs changes, the input/output relation rescales so as to match the dynamic range of responses to that of the inputs. We give direct evidence that the scaling of the input/output relation is set to maximize information transmission for each distribution of signals. This adaptive behavior should be particularly useful in dealing with the intermittent statistics of natural signals.
Dynamics of population rate codes in ensembles of neocortical neurons.
G. Silberberg and M. Bethge and H. Markram and K. Pawelzik and M. Tsodyks
J Neurophysiol  91  704-9  (2004)
Information processing in neocortex can be very fast, indicating that neuronal ensembles faithfully transmit rapidly changing signals to each other. Apart from signal-to-noise issues, population codes are fundamentally constrained by the neuronal dynamics. In particular, the biophysical properties of individual neurons and collective phenomena may substantially limit the speed at which a graded signal can be represented by the activity of an ensemble. These implications of the neuronal dynamics are rarely studied experimentally. Here, we combine theoretical analysis and whole cell recordings to show that encoding signals in the variance of uncorrelated synaptic inputs to a neocortical ensemble enables faithful transmission of graded signals with high temporal resolution. In contrast, the encoding of signals in the mean current is subject to low-pass filtering.
Information tuning of populations of neurons in primary visual cortex.
K. Kang and R. M. Shapley and H. Sompolinsky
J Neurosci  24  3726-35  (2004)
Neurons in macaque primary visual cortex (V1) show a diversity of orientation tuning properties, exhibiting a broad distribution of tuning width, baseline activity, peak response, and circular variance (CV). Here, we studied how the different tuning features affect the performance of these cells in discriminating between stimuli with different orientations. Previous studies of the orientation discrimination power of neurons in V1 focused on resolving two nearby orientations close to the psychophysical threshold of orientation discrimination. Here, we developed a theoretical framework, the information tuning curve, that measures the discrimination power of cells as a function of the orientation difference, deltatheta, of the two stimuli. This tuning curve also represents the mutual information between the neuronal responses and the stimulus orientation. We studied theoretically the dependence of the information tuning curve on the orientation tuning width, baseline, and peak responses. Of main interest is the finding that narrow orientation tuning is not necessarily optimal for all angular discrimination tasks. Instead, the optimal tuning width depends linearly on deltatheta. We applied our theory to study the discrimination performance of a population of 490 neurons in macaque V1. We found that a significant fraction of the neuronal population exhibits favorable tuning properties for large deltatheta. We also studied how the discrimination capability of neurons is distributed and compared several other measures of the orientation tuning such as CV with Chernoff distances for normalized tuning curves.
Adaptation reduces spike-count reliability, but not spike-timing precision, of auditory nerve responses.
M. Avissar and A. C. Furman and J. C. Saunders and T. D. Parsons
J Neurosci  27  6461--6472  (2007)
Sensory systems use adaptive coding mechanisms to filter redundant information from the environment to efficiently represent the external world. One such mechanism found in most sensory neurons is rate adaptation, defined as a reduction in firing rate in response to a constant stimulus. In auditory nerve, this form of adaptation is likely mediated by exhaustion of release-ready synaptic vesicles in the cochlear hair cell. To better understand how specific synaptic mechanisms limit neural coding strategies, we examined the trial-to-trial variability of auditory nerve responses during short-term rate-adaptation by measuring spike-timing precision and spike-count reliability. After adaptation, precision remained unchanged, whereas for all but the lowest-frequency fibers, reliability decreased. Modeling statistical properties of the hair cell-afferent fiber synapse suggested that the ability of one or a few vesicles to elicit an action potential reduces the inherent response variability expected from quantal neurotransmitter release, and thereby confers the observed count reliability at sound onset. However, with adaptation, depletion of the readily releasable pool of vesicles diminishes quantal content and antagonizes the postsynaptic enhancement of reliability. These findings imply that during the course of short-term adaptation, coding strategies that employ a rate code are constrained by increased neural noise because of vesicle depletion, whereas those that employ a temporal code are not.
Time course of precision in smooth-pursuit eye movements of monkeys.
L. C. Osborne and S. S. Hohl and W. Bialek and S. G. Lisberger
J Neurosci  27  2987--2998  (2007)
To evaluate the nature and possible sources of variation in sensory-motor behavior, we measured the signal-to-noise ratio for the initiation of smooth-pursuit eye movements as a function of time and computed thresholds that indicate how well the pursuit system discriminates small differences in the direction, speed, or time of onset of target motion. Thresholds improved rapidly as a function of time and came close to their minima during the interval when smooth eye movement is driven only by visual motion inputs. Many features of the data argued that motor output and sensory discrimination are limited by the same noise source. Pursuit thresholds reached magnitudes similar to those for perception: <2-3 degrees of direction, approximately 11-15% of target speed, and 8 ms of change in the time of onset of target motion. Pursuit and perceptual thresholds had similar dependencies on the duration of the motion stimulus and showed similar effects of target speed. The evolution of information about direction of target motion followed the same time course in pursuit behavior and in a previously reported sample of neuronal responses from extrastriate area MT. Changing the form of the sensory input while keeping the motor response fixed had significant effects on the signal-to-noise ratio in pursuit for direction discrimination, whereas holding the sensory input constant while changing the combination of muscles used for the motor output did not. We conclude that noise in sensory processing of visual motion provides the major source of variation in the initiation of pursuit.
Detection sensitivity and temporal resolution of visual signals near absolute threshold in the salamander retina.
E. J. Chichilnisky and F. Rieke
J Neurosci  25  318--330  (2005)
Several studies have suggested that the visual system can detect dim lights with a fidelity limited only by Poisson fluctuations in photon absorption and spontaneous activation of rhodopsin. If correct, this implies that neural processing of responses produced by rod photoreceptors is efficient and effectively noiseless. However, experimental uncertainty makes this conclusion tenuous. Furthermore, previous work provided no information about how accurately stimulus timing is represented. Here, the detection sensitivity and temporal resolution of salamander rods and retinal ganglion cells (RGCs) are compared in nearly matched experimental conditions by using recorded responses to identify the time of a flash. At detection threshold, RGCs could reliably signal the absorption of 20-50 photons, but the rods within the RGC receptive field could signal stimuli 3-10 times weaker. For flash strengths 10 times higher than detection threshold, some RGCs could distinguish stimulus timing with a resolution finer than 100 msec, within a factor of 2 of the rod limit. The relationship between RGC and rod sensitivity could not be explained by added noise in the retinal circuitry but could be explained by a threshold acting after pooling of rod signals. Simulations of rod signals indicated that continuous noise, rather than spontaneous activation of rhodopsin or fluctuations in the single-photon response, limited temporal resolution. Thus, detection of dim lights was limited by retinal processing, but, at higher light levels, synaptic transmission, cellular integration of synaptic inputs, and spike generation in RGCs faithfully conveyed information about the time of photon absorption.
Fidelity of the ensemble code for visual motion in primate retina.
E. S. Frechette and A. Sher and M. I. Grivich and D. Petrusca and A. M. Litke and E. J. Chichilnisky
J Neurophysiol  94  119--135  (2005)
Sensory experience typically depends on the ensemble activity of hundreds or thousands of neurons, but little is known about how populations of neurons faithfully encode behaviorally important sensory information. We examined how precisely speed of movement is encoded in the population activity of magnocellular-projecting parasol retinal ganglion cells (RGCs) in macaque monkey retina. Multi-electrode recordings were used to measure the activity of approximately 100 parasol RGCs simultaneously in isolated retinas stimulated with moving bars. To examine how faithfully the retina signals motion, stimulus speed was estimated directly from recorded RGC responses using an optimized algorithm that resembles models of motion sensing in the brain. RGC population activity encoded speed with a precision of approximately 1%. The elementary motion signal was conveyed in approximately 10 ms, comparable to the interspike interval. Temporal structure in spike trains provided more precise speed estimates than time-varying firing rates. Correlated activity between RGCs had little effect on speed estimates. The spatial dispersion of RGC receptive fields along the axis of motion influenced speed estimates more strongly than along the orthogonal direction, as predicted by a simple model based on RGC response time variability and optimal pooling. on and off cells encoded speed with similar and statistically independent variability. Simulation of downstream speed estimation using populations of speed-tuned units showed that peak (winner take all) readout provided more precise speed estimates than centroid (vector average) readout. These findings reveal how faithfully the retinal population code conveys information about stimulus speed and the consequences for motion sensing in the brain.
Temporal resolution of ensemble visual motion signals in primate retina.
E. J. Chichilnisky and R. S. Kalmar
J Neurosci  23  6681--6689  (2003)
Recent studies have examined the temporal precision of spiking in visual system neurons, but less is known about the time scale that is relevant for behaviorally important visual computations. We examined how spatiotemporal patterns of spikes in ensembles of primate retinal ganglion cells convey information about visual motion to the brain. The direction of motion of a bar was estimated by comparing the timing of responses in ensembles of parasol (magnocellular-projecting) retinal ganglion cells recorded simultaneously, using a cross-correlation approach similar to standard models of motion sensing. To identify the temporal resolution of motion signals, spike trains were low-pass filtered before estimating the direction of motion. The filter time constant that resulted in most accurate motion sensing was in the range of 10-50 msec for a range of stimulus speeds and contrasts and approached a lower limit of approximately 10 msec at high speeds and contrasts. This time constant was, on average, comparable to the length of interspike intervals. These findings suggest that cortical neurons could filter their inputs on a time scale of tens of milliseconds, rather than relying on the precise times of individual input spikes, to sense motion most reliably.
Limits to the temporal fidelity of cortical spike rate signals.
M. E. Mazurek and M. N. Shadlen
Nat Neurosci  5  463-71  (2002)
The cerebral cortex processes information primarily through changes in the spike rates of neurons within local ensembles. To evaluate how reliably the average spike rate of a group of cortical neurons can represent a time-varying signal, we simulated an ensemble with realistic spike discharge behavior. We found that weak interneuronal correlation, or synchrony, allows the variability in spike rates of individual neurons to compromise the ensemble representation of time-varying signals. Brief cycles of sinusoidal modulation at frequencies above 115 Hz could not be represented by an ensemble of hundreds of neurons whose interneuronal correlation mimics that of the visual cortex. The spike variability and correlation assumed in our simulations are likely to apply to many areas of cortex and therefore may constrain the fidelity of neural computations underlying higher brain function.
Information conveyed by onset transients in responses of striate cortical neurons.
J. R. Muller and A. B. Metha and J. Krauskopf and P. Lennie
J Neurosci  21  6978--6990  (2001)
Normal eye movements ensure that the visual world is seen episodically, as a series of often stationary images. In this paper we characterize the responses of neurons in striate cortex to stationary grating patterns presented with abrupt onset. These responses are distinctive. In most neurons the onset of a grating gives rise to a transient discharge that decays with a time constant of 100 msec or less. The early stages of response have higher contrast gain and higher response gain than later stages. Moreover, the variability of discharge during the onset transient is disproportionately low. These factors together make the onset transient an information-rich component of response, such that the detectability and discriminability of stationary gratings grows rapidly to an early peak, within 150 msec of the onset of the response in most neurons. The orientation selectivity of neurons estimated from the first 150 msec of discharge to a stationary grating is indistinguishable from the orientation selectivity estimated from longer segments of discharge to moving gratings. Moving gratings are ultimately more detectable than stationary ones, because responses to the former are continuously renewed. The principal characteristics of the response of a neuron to a stationary grating-the initial high discharge rate, which decays rapidly, and the change of contrast gain with time-are well captured by a model in which each excitatory synaptic event leads to an immediate reduction in synaptic gain, from which recovery is slow.
Interspike intervals, receptive fields, and information encoding in primary visual cortex.
D. Reich and F. Mechler and K. Purpura and J. Victor
J Neurosci  20  1964-74  (2000)
In the primate primary visual cortex (V1), the significance of individual action potentials has been difficult to determine, particularly in light of the considerable trial-to-trial variability of responses to visual stimuli. We show here that the information conveyed by an action potential depends on the duration of the immediately preceding interspike interval (ISI). The interspike intervals can be grouped into several different classes on the basis of reproducible features in the interspike interval histograms. Spikes in different classes bear different relationships to the visual stimulus, both qualitatively (in terms of the average stimulus preceding each spike) and quantitatively (in terms of the amount of information encoded per spike and per second). Spikes preceded by very short intervals (3 msec or less) convey information most efficiently and contribute disproportionately to the overall receptive-field properties of the neuron. Overall, V1 neurons can transmit between 5 and 30 bits of information per second in response to rapidly varying, pseudorandom stimuli, with an efficiency of approximately 25\%. Although some (but not all) of our results would be expected from neurons that use a firing-rate code to transmit information, the evidence suggests that visual neurons are well equipped to decode stimulus-related information on the basis of relative spike timing and ISI duration.
The precision of single neuron responses in cortical area {V}1 during stereoscopic depth judgments.
S. Prince and A. Pointon and B. Cumming and A. Parker
J Neurosci  20  3387-400  (2000)
The performance of single neurons in cortical area V1 of alert macaque monkeys was compared against the animals' psychophysical performance during a binocular disparity discrimination task. Performance was assessed with stimuli that consisted of a patch of dynamic random dots, whose disparity varied from trial to trial, surrounded by an annulus of similar dots at a fixed disparity. On each trial, the animals indicated whether the depth of the central patch was in front of or behind the annulus. For each disparity of the center patch, neural performance was assessed by calculating the probability that the response of the neuron was greater or less than the response when the center disparity was the same as that of the annulus. Initially the animals performed the task simultaneously with the neural recording. However, the range of disparities used, which was appropriate for the neuronal recording, may have affected performance, because the thresholds were substantially lower (2.6x) when the psychophysical measurements were repeated later. Average neuronal thresholds were approximately 4x poorer than these behavioral thresholds, although the best neurons were marginally better than the animals' behavior. Thus, the well known precision of relative depth judgments can be supported with signals from a small number of V1 neurons. Interference with the relative depth information in the stimulus profoundly affected behavioral thresholds, which were approximately 10x poorer when the surround was absent or contained binocularly uncorrelated dots. In this case, single V1 neurons consistently outperform the observer: presumably here, psychophysical thresholds are limited by other factors (such as uncertainty about vergence eye position).
Stochastic nature of precisely timed spike patterns in visual system neuronal responses.
M. Oram and M. Wiener and R. Lestienne and B. Richmond
J Neurophysiol  81  3021-33  (1999)
It is not clear how information related to cognitive or psychological processes is carried by or represented in the responses of single neurons. One provocative proposal is that precisely timed spike patterns play a role in carrying such information. This would require that these spike patterns have the potential for carrying information that would not be available from other measures such as spike count or latency. We examined exactly timed (1-ms precision) triplets and quadruplets of spikes in the stimulus-elicited responses of lateral geniculate nucleus (LGN) and primary visual cortex (V1) neurons of the awake fixating rhesus monkey. Large numbers of these precisely timed spike patterns were found. Information theoretical analysis showed that the precisely timed spike patterns carried only information already available from spike count, suggesting that the number of precisely timed spike patterns was related to firing rate. We therefore examined statistical models relating precisely timed spike patterns to response strength. Previous statistical models use observed properties of neuronal responses such as the peristimulus time histogram, interspike interval, and/or spike count distributions to constrain the parameters of the model. We examined a new stochastic model, which unlike previous models included all three of these constraints and unlike previous models predicted the numbers and types of observed precisely timed spike patterns. This shows that the precise temporal structures of stimulus-elicited responses in LGN and V1 can occur by chance. We show that any deviation of the spike count distribution, no matter how small, from a Poisson distribution necessarily changes the number of precisely timed spike patterns expected in neural responses. Overall the results indicate that the fine temporal structure of responses can only be interpreted once all the coarse temporal statistics of neural responses have been taken into account.
Efficient discrimination of temporal patterns by motion-sensitive neurons in primate visual cortex.
G. Buracas and A. Zador and M. DeWeese and T. Albright
Neuron  20  959-69  (1998)
Although motion-sensitive neurons in macaque middle temporal (MT) area are conventionally characterized using stimuli whose velocity remains constant for 1-3 s, many ecologically relevant stimuli change on a shorter time scale (30-300 ms). We compared neuronal responses to conventional (constant-velocity) and time-varying stimuli in alert primates. The responses to both stimulus ensembles were well described as rate-modulated Poisson processes but with very high precision (approximately 3 ms) modulation functions underlying the time-varying responses. Information-theoretic analysis revealed that the responses encoded only approximately 1 bit/s about constant-velocity stimuli but up to 29 bits/s about the time-varying stimuli. Analysis of local field potentials revealed that part of the residual response variability arose from 'noise' sources extrinsic to the neuron. Our results demonstrate that extrastriate neurons in alert primates can encode the fine temporal structure of visual stimuli.
The variable discharge of cortical neurons: implications for connectivity, computation, and information coding.
M. Shadlen and W. Newsome
J Neurosci  18  3870-96  (1998)
Cortical neurons exhibit tremendous variability in the number and temporal distribution of spikes in their discharge patterns. Furthermore, this variability appears to be conserved over large regions of the cerebral cortex, suggesting that it is neither reduced nor expanded from stage to stage within a processing pathway. To investigate the principles underlying such statistical homogeneity, we have analyzed a model of synaptic integration incorporating a highly simplified integrate and fire mechanism with decay. We analyzed a 'high-input regime' in which neurons receive hundreds of excitatory synaptic inputs during each interspike interval. To produce a graded response in this regime, the neuron must balance excitation with inhibition. We find that a simple integrate and fire mechanism with balanced excitation and inhibition produces a highly variable interspike interval, consistent with experimental data. Detailed information about the temporal pattern of synaptic inputs cannot be recovered from the pattern of output spikes, and we infer that cortical neurons are unlikely to transmit information in the temporal pattern of spike discharge. Rather, we suggest that quantities are represented as rate codes in ensembles of 50-100 neurons. These column-like ensembles tolerate large fractions of common synaptic input and yet covary only weakly in their spike discharge. We find that an ensemble of 100 neurons provides a reliable estimate of rate in just one interspike interval (10-50 msec). Finally, we derived an expression for the variance of the neural spike count that leads to a stable propagation of signal and noise in networks of neurons-that is, conditions that do not impose an accumulation or diminution of noise. The solution implies that single neurons perform simple algebra resembling averaging, and that more sophisticated computations arise by virtue of the anatomical convergence of novel combinations of inputs to the cortical column from external sources.
Encoding of visual motion information and reliability in spiking and graded potential neurons.
J. Haag and A. Borst
J Neurosci  17  4809-19  (1997)
We investigated the information about stimulus velocity inherent in the membrane signals of two types of directionally selective, motion-sensitive interneurons in the fly visual system. One of the cells, the H1-cell, is a spiking neuron, whereas the other, the HS-cell, encodes sensory information mainly by a graded shift of its membrane potential. Using a pseudo-random velocity waveform by which a visual grating is moving along the horizontal axis of the eye, both cell types follow the stimulus velocity at higher precision than in response to a step-like velocity function. To measure how much information about the stimulus velocity is preserved in the cellular responses, we calculated the coherence between the stimulus and the neural signals as a function of stimulus frequency. At frequencies up to approximately 10 Hz motion information is well contained in the electrical signals of HS- and H1-cells: For HS-cells the coherence value amounts to approximately 70\%, and for H1-cells this value is approximately 60\%. Comparing these values with the coherence expected from a linear encoding reveals that the fidelity of the original stimulus is deteriorated in the neural signal partly by neural noise and partly by the nonlinearity inherent in the process of visual motion detection. The degree to which this nonlinearity contributes to the decrease in coherence depends on the maximum velocity used in the experiments; the smaller the stimulus amplitude, the higher the coherence and, thus, the smaller the nonlinearity in encoding of stimulus motion. All these results are in agreement with model simulations in which visual motion is processed by an array of local motion detectors, the spatially integrated output of which is considered the equivalent of the neural signals of HS- and H1-cells.
On the relationship between synaptic input and spike output jitter in individual neurons.
P. Marsalek and C. Koch and J. Maunsell
Proc Natl Acad Sci U S A  94  735-40  (1997)
What is the relationship between the temporal jitter in the arrival times of individual synaptic inputs to a neuron and the resultant jitter in its output spike? We report that the rise time of firing rates of cells in striate and extrastriate visual cortex in the macaque monkey remain equally sharp at different stages of processing. Furthermore, as observed by others, multiunit recordings from single units in the primate frontal lobe reveal a strong peak in their cross-correlation in the 10-150 msec range with very small temporal jitter (on the order of 1 msec). We explain these results using numerical models to study the relationship between the temporal jitter in excitatory and inhibitory synaptic input and the variability in the spike output timing in integrate-and-fire units and in a biophysically and anatomically detailed model of a cortical pyramidal cell. We conclude that under physiological circumstances, the standard deviation in the output jitter is linearly related to the standard deviation in the input jitter, with a constant of less than one. Thus, the timing jitter in successive layers of such neurons will converge to a small value dictated by the jitter in axonal propagation times.
High response reliability of neurons in primary visual cortex (V1) of alert, trained monkeys.
M. Gur and D. M. Snodderly
Cereb Cortex  16  888-95  (2006)
The reliability of neuronal responses determines the resources needed to represent the external world and constrains the nature of the neural code. Studies of anesthetized animals have indicated that neuronal responses become progressively more variable as information travels from the retina to the cortex. These results have been interpreted to indicate that perception must be based on pooling across relatively large numbers of cells. However, we find that in alert monkeys, responses in primary visual cortex (V1) are as reliable as the inputs from the retina and the thalamus. Moreover, when the effects of fixational eye movements were minimized, response variability (variance/mean - Fano factor, FF) in all V1 layers was low. When presenting optimal stimuli, the median FF was 0.3. High variability, FF approximately 1, was found only near threshold. Our results suggest that in natural vision, suprathreshold perception can be based on small numbers of optimally stimulated cells.
Precise spatiotemporal repeating patterns in monkey primary and supplementary motor areas occur at chance levels.
S. N. Baker and R. N. Lemon
J Neurophysiol  84  1770-80  (2000)
Precise spatiotemporal patterns in neural discharge are a possible mechanism for information encoding in the brain. Previous studies have found that such patterns repeat and appear to relate to key behavioral events. Whether these patterns occur above chance levels remains controversial. To address this question, we have made simultaneous recordings from between two and nine neurons in the primary motor cortex and supplementary motor area of three monkeys while they performed a precision grip task. Out of a total of 67 neurons, 46 were antidromically identified as pyramidal tract neurons. Sections of recordings 60 s long were searched for patterns involving three or more spikes that repeated at least twice. The allowed jitter for pattern repetition was 3 ms, and the pattern length was limited to 192 ms. In all 11 recordings analyzed, large numbers of repeating patterns were found. To assess the expected chance level of patterns, "surrogate" datasets were generated. These had the same moment-by-moment modulation in firing rate as the experimental spike trains, and matched their interspike interval distribution, but did not preserve the precise timing of individual spikes. The number of repeating patterns in 10 randomly generated surrogates was used to form 99% confidence limits on the repeating pattern count expected by chance. There was close agreement between these confidence limits and the number of patterns seen in the experimental data. Analysis of high complexity patterns was carried out in four long recordings (mean duration 23.2 min, mean number of neurons simultaneously recorded 7.5). This analysis logged only patterns composed of a larger number (7-11) of spikes. The number of patterns seen in the surrogate datasets showed a small but significant excess over those seen in the original experimental data; this is discussed in the context of surrogate generation. The occurrence of repeating patterns in the experimental data were strongly associated with particular phases of the precision grip task; however, a similar task dependence was seen for the surrogate data. When a repeating pattern was used as a template to find inexact matches, in which up to half of the component spikes could be missing, similar numbers of matches were found in experimental and surrogate data, and the time of occurrence of such matches showed the same task dependence. We conclude that the existence of precise repeating patterns in our data are not due to cortical mechanisms that favor this form of coding, since as many, if not more, patterns are produced by spike trains constructed only to modulate their firing rate in the same way as the experimental data, and to match the interspike interval histograms. The task dependence of pattern occurrence is explicable as an artifact of the modulation of neural firing rate. The consequences for theories of temporal coding in the cortex are discussed.
Precision of the pacemaker nucleus in a weakly electric fish: network versus cellular influences.
K. Moortgat and T. Bullock and T. Sejnowski
J Neurophysiol  83  971-83  (2000)
We investigated the relative influence of cellular and network properties on the extreme spike timing precision observed in the medullary pacemaker nucleus (Pn) of the weakly electric fish Apteronotus leptorhynchus. Of all known biological rhythms, the electric organ discharge of this and related species is the most temporally precise, with a coefficient of variation (CV = standard deviation/mean period) of 2 x 10(-4) and standard deviation (SD) of 0.12-1.0 micros. The timing of the electric organ discharge is commanded by neurons of the Pn, individual cells of which we show in an in vitro preparation to have only a slightly lesser degree of precision. Among the 100-150 Pn neurons, dye injection into a pacemaker cell resulted in dye coupling in one to five other pacemaker cells and one to three relay cells, consistent with previous results. Relay cell fills, however, showed profuse dendrites and contacts never seen before: relay cell dendrites dye-coupled to one to seven pacemaker and one to seven relay cells. Moderate (0.1-10 nA) intracellular current injection had no effect on a neuron's spiking period, and only slightly modulated its spike amplitude, but could reset the spike phase. In contrast, massive hyperpolarizing current injections (15-25 nA) could force the cell to skip spikes. The relative timing of subthreshold and full spikes suggested that at least some pacemaker cells are likely to be intrinsic oscillators. The relative amplitudes of the subthreshold and full spikes gave a lower bound to the gap junctional coupling coefficient of 0.01-0.08. Three drugs, called gap junction blockers for their mode of action in other preparations, caused immediate and substantial reduction in frequency, altered the phase lag between pairs of neurons, and later caused the spike amplitude to drop, without altering the spike timing precision. Thus we conclude that the high precision of the normal Pn rhythm does not require maximal gap junction conductances between neurons that have ordinary cellular precision. Rather, the spiking precision can be explained as an intrinsic cellular property while the gap junctions act to frequency- and phase-lock the network oscillations.
EPSP amplification and the precision of spike timing in hippocampal neurons
D. Fricker and R. Miles
Neuron  28  559-69  (2000)
The temporal precision with which EPSPs initiate action potentials in postsynaptic cells determines how activity spreads in neuronal networks. We found that small EPSPs evoked from just subthreshold potentials initiated firing with short latencies in most CA1 hippocampal inhibitory cells, while action potential timing in pyramidal cells was more variable due to plateau potentials that amplified and prolonged EPSPs. Action potential timing apparently depends on the balance of subthreshold intrinsic currents. In interneurons, outward currents dominate responses to somatically injected EPSP waveforms, while inward currents are larger than outward currents close to threshold in pyramidal cells. Suppressing outward potassium currents increases the variability in latency of synaptically induced firing in interneurons. These differences in precision of EPSP-spike coupling in inhibitory and pyramidal cells will enhance inhibitory control of the spread of excitation in the hippocampus.
Detecting and estimating signals over noisy and unreliable synapses: information-theoretic analysis.
A. Manwani and C. Koch
Neural Comput  13  1-33  (2001)
The temporal precision with which neurons respond to synaptic inputs has a direct bearing on the nature of the neural code. A characterization of the neuronal noise sources associated with different sub-cellular components (synapse, dendrite, soma, axon, and so on) is needed to understand the relationship between noise and information transfer. Here we study the effect of the unreliable, probabilistic nature of synaptic transmission on information transfer in the absence of interaction among presynaptic inputs. We derive theoretical lower bounds on the capacity of a simple model of a cortical synapse under two different paradigms. In signal estimation, the signal is assumed to be encoded in the mean firing rate of the presynaptic neuron, and the objective is to estimate the continuous input signal from the postsynaptic voltage. In signal detection, the input is binary, and the presence or absence of a presynaptic action potential is to be detected from the postsynaptic voltage. The efficacy of information transfer in synaptic transmission is characterized by deriving optimal strategies under these two paradigms. On the basis of parameter values derived from neocortex, we find that single cortical synapses cannot transmit information reliably, but redundancy obtained using a small number of multiple synapses leads to a significant improvement in the information capacity of synaptic transmission.
Predicting every spike: a model for the responses of visual neurons.
J. Keat and P. Reinagel and R. C. Reid and M. Meister
Neuron  30  803-17  (2001)
In the early visual system, neuronal responses can be extremely precise. Under a wide range of stimuli, cells in the retina and thalamus fire spikes very reproducibly, often with millisecond precision on subsequent stimulus repeats. Here we develop a mathematical description of the firing process that, given the recent visual input, accurately predicts the timing of individual spikes. The formalism is successful in matching the spike trains from retinal ganglion cells in salamander, rabbit, and cat, as well as from lateral geniculate nucleus neurons in cat. It adapts to many different response types, from very precise to highly variable. The accuracy of the model allows a compact description of how these neurons encode the visual stimulus.
Variability and information in a neural code of the cat lateral geniculate nucleus.
R. C. Liu and S. Tzonev and S. Rebrik and K. D. Miller
J Neurophysiol  86  2789-806  (2001)
A central theme in neural coding concerns the role of response variability and noise in determining the information transmission of neurons. This issue was investigated in single cells of the lateral geniculate nucleus of barbiturate-anesthetized cats by quantifying the degree of precision in and the information transmission properties of individual spike train responses to full field, binary (bright or dark), flashing stimuli. We found that neuronal responses could be highly reproducible in their spike timing (approximately 1-2 ms standard deviation) and spike count (approximately 0.3 ratio of variance/mean, compared with 1.0 expected for a Poisson process). This degree of precision only became apparent when an adequate length of the stimulus sequence was specified to determine the neural response, emphasizing that the variables relevant to a cell's response must be controlled to observe the cell's intrinsic response precision. Responses could carry as much as 3.5 bits/spike of information about the stimulus, a rate that was within a factor of two of the limit the spike train could transmit. Moreover, there appeared to be little sign of redundancy in coding: on average, longer response sequences carried at least as much information about the stimulus as would be obtained by adding together the information carried by shorter response sequences considered independently. There also was no direct evidence found for synergy between response sequences. These results could largely, but not entirely, be explained by a simple model of the response in which one filters the stimulus by the cell's impulse response kernel, thresholds the result at a fairly high level, and incorporates a postspike refractory period.
Excess synchrony in motor cortical neurons provides redundant direction information with that from coarse temporal measures.
M. W. Oram and N. G. Hatsopoulos and B. J. Richmond and J. P. Donoghue
J Neurophysiol  86  1700-16  (2001)
Previous studies have shown that measures of fine temporal correlation, such as synchronous spikes, across responses of motor cortical neurons carries more directional information than that predicted from statistically independent neurons. It is also known, however, that the coarse temporal measures of responses, such as spike count, are not independent. We therefore examined whether the information carried by coincident firing was related to that of coarsely defined spike counts and their correlation. Synchronous spikes were counted in the responses from 94 pairs of simultaneously recorded neurons in primary motor cortex (MI) while monkeys performed arm movement tasks. Direct measurement of the movement-related information indicated that the coincident spikes (1- to 5-ms precision) carry approximately 10\% of the information carried by a code of the two spike counts. Inclusion of the numbers of synchronous spikes did not add information to that available from the spike counts and their coarse temporal correlation. To assess the significance of the numbers of coincident spikes, we extended the stochastic spike count matched (SCM) model to include correlations between spike counts of the individual neural responses and slow temporal dependencies within neural responses (approximately 30 Hz bandwidth). The extended SCM model underestimated the numbers of synchronous spikes. Therefore as with previous studies, we found that there were more synchronous spikes in the neural data than could be accounted for by this stochastic model. However, the SCM model accounts for most (R(2) = 0.93 +/- 0.05, mean +/- SE) of the differences in the observed number of synchronous spikes to different directions of arm movement, indicating that synchronous spiking is directly related to spike counts and their broad correlation. Further, this model supports the information theoretic analysis that the synchronous spikes do not provide directional information beyond that available from the firing rates of the same pool of directionally tuned MI neurons. These results show that detection of precisely timed spike patterns above chance levels does not imply that those spike patterns carry information unavailable from coarser population codes but leaves open the possibility that excess synchrony carries other forms of information or serves other roles in cortical information processing not studied here.
The statistical reliability of signals in single neurons in cat and monkey visual cortex.
D. Tolhurst and J. Movshon and A. Dean
Vision Res  23  775-85  (1983)
The variability of the discharge of visual cortical neurons in cats and macaque monkeys limits the reliability with which such neurons can relay signals about weak visual stimuli. In general, the variance of a neuron's firing rate is directly proportional to its mean firing rate. The probability that a neuron will fire a criterion number of impulses on a stimulus trial grows monotonically with the contrast of a sinusoidal grating stimulus. Neural probability functions prepared either by computing the probability of criterion response or by integrating receiver operating characteristics to yield the probability of correct choice in a two-alternative forced-choice situation resemble psychometric functions obtained in psychophysical and behavioral experiments on humans and animals, but are shallower in slope. The slopes of neuronal probability functions are slightly higher when they are estimated over short time periods, but even so do not equal the slopes measured psychophysically in human and monkey observers. This discrepancy in slope could be explained if the whole observer responded only when about four neurons were active together.
Reliability of spike timing in neocortical neurons.
Z. Mainen and T. Sejnowski
Science  268  1503-6  (1995)
It is not known whether the variability of neural activity in the cerebral cortex carries information or reflects noisy underlying mechanisms. In an examination of the reliability of spike generation using recordings from neurons in rat neocortical slices, the precision of spike timing was found to depend on stimulus transients. Constant stimuli led to imprecise spike trains, whereas stimuli with fluctuations resembling synaptic activity produced spike trains with timing reproducible to less than 1 millisecond. These data suggest a low intrinsic noise level in spike generation, which could allow cortical neurons to accurately transform synaptic input into spike sequences, supporting a possible role for spike timing in the processing of cortical information by the neocortex.
Response variability of neurons in primary visual cortex (V1) of alert monkeys.
M. Gur and A. Beylin and D. M. Snodderly
J Neurosci  17  2914-20  (1997)
Response variability of neurons limits the reliability and resolution of sensory systems. It is generally thought that response variability in the visual system increases at cortical levels, but the causes of the variability have not been identified. We have measured the response variability of neurons in primary visual cortex (V1) of alert monkeys. We recorded from 80 single cells distributed over all V1 layers and from 8 parvocellular cells of the lateral geniculate nucleus. All cells were stimulated with a bar of near-optimal orientation, color, and dimensions while continuously monitoring the eye movements of fixation. To minimize the effects of eye movements, responses that occurred while the eye was relatively steady were selected for analysis. The impulses elicited by each stimulus presentation were counted, and the variance and coefficient of variation were computed. Both measures of response variability were much lower than reported previously for V1 cells of both alert and anesthetized monkeys. Our data show that fixational eye movements cause a large component of response variance in alert monkeys. Moreover, the reliability of V1 neurons is not obviously degraded compared with lateral geniculate nucleus cells. The high reliability of neurons in alert monkeys is consistent with expectations from conventional biophysical models, and it suggests that activity in a modest number of neurons may suffice to form a perceptual decision.
The structure and precision of retinal spike trains.
M. Berry and D. Warland and M. Meister
Proc Natl Acad Sci U S A  94  5411-6  (1997)
Assessing the reliability of neuronal spike trains is fundamental to an understanding of the neural code. We measured the reproducibility of retinal responses to repeated visual stimuli. In both tiger salamander and rabbit, the retinal ganglion cells responded to random flicker with discrete, brief periods of firing. For any given cell, these firing events covered only a small fraction of the total stimulus time, often less than 5\%. Firing events were very reproducible from trial to trial: the timing jitter of individual spikes was as low as 1 msec, and the standard deviation in spike count was often less than 0.5 spikes. Comparing the precision of spike timing to that of the spike count showed that the timing of a firing event conveyed several times more visual information than its spike count. This sparseness and precision were general characteristics of ganglion cell responses, maintained over the broad ensemble of stimulus waveforms produced by random flicker, and over a range of contrasts. Thus, the responses of retinal ganglion cells are not properly described by a firing probability that varies continuously with the stimulus. Instead, these neurons elicit discrete firing events that may be the fundamental coding symbols in retinal spike trains.
Reproducibility and variability in neural spike trains.
R. de Ruyter van Steveninck and G. Lewen and S. Strong and R. Koberle and W. Bialek
Science  275  1805-8  (1997)
To provide information about dynamic sensory stimuli, the pattern of action potentials in spiking neurons must be variable. To ensure reliability these variations must be related, reproducibly, to the stimulus. For H1, a motion-sensitive neuron in the fly's visual system, constant-velocity motion produces irregular spike firing patterns, and spike counts typically have a variance comparable to the mean, for cells in the mammalian cortex. But more natural, time-dependent input signals yield patterns of spikes that are much more reproducible, both in terms of timing and of counting precision. Variability and reproducibility are quantified with ideas from information theory, and measured spike sequences in H1 carry more than twice the amount of information they would if they followed the variance-mean relation seen with constant inputs. Thus, models that may accurately account for the neural response to static stimuli can significantly underestimate the reliability of signal transfer under more natural conditions.
Impact of synaptic unreliability on the information transmitted by spiking neurons.
A. Zador
J Neurophysiol  79  1219-29  (1998)
The spike generating mechanism of cortical neurons is highly reliable, able to produce spikes with a precision of a few milliseconds or less. The excitatory synapses driving these neurons are by contrast much less reliable, subject both to release failures and quantal fluctuations. This suggests that synapses represent the primary bottleneck limiting the faithful transmission of information through cortical circuitry. How does the capacity of a neuron to convey information depend on the properties of its synaptic drive? We address this question rigorously in an information theoretic framework. We consider a model in which a population of independent unreliable synapses provides the drive to an integrate-and-fire neuron. Within this model, the mutual information between the synaptic drive and the resulting output spike train can be computed exactly from distributions that depend only on a single variable, the interspike interval. The reduction of the calculation to dependence on only a single variable greatly reduces the amount of data required to obtain reliable information estimates. We consider two factors that govern the rate of information transfer: the synaptic reliability and the number of synapses connecting each presynaptic axon to its postsynaptic target (i.e., the connection redundancy, which constitutes a special form of input synchrony). The information rate is a smooth function of both mechanisms; no sharp transition is observed from an 'unreliable' to a 'reliable' mode. Increased connection redundancy can compensate for synaptic unreliability, but only under the assumption that the fine temporal structure of individual spikes carries information. If only the number of spikes in some relatively long-time window carries information (a 'mean rate' code), an increase in the fidelity of synaptic transmission results in a seemingly paradoxical decrease in the information available in the spike train. This suggests that the fine temporal structure of spike trains can be used to maintain reliable transmission with unreliable synapses.
Refractoriness and neural precision.
M. Berry, 2nd and M. Meister
J Neurosci  18  2200-11  (1998)
The response of a spiking neuron to a stimulus is often characterized by its time-varying firing rate, estimated from a histogram of spike times. If the cell's firing probability in each small time interval depends only on this firing rate, one predicts a highly variable response to repeated trials, whereas many neurons show much greater fidelity. Furthermore, the neuronal membrane is refractory immediately after a spike, so that the firing probability depends not only on the stimulus but also on the preceding spike train. To connect these observations, we investigated the relationship between the refractory period of a neuron and its firing precision. The light response of retinal ganglion cells was modeled as probabilistic firing combined with a refractory period: the instantaneous firing rate is the product of a 'free firing rate, ' which depends only on the stimulus, and a 'recovery function,' which depends only on the time since the last spike. This recovery function vanishes for an absolute refractory period and then gradually increases to unity. In simulations, longer refractory periods were found to make the response more reproducible, eventually matching the precision of measured spike trains. Refractoriness, although often thought to limit the performance of neurons, may in fact benefit neuronal reliability. The underlying free firing rate derived by allowing for the refractory period often exceeded the observed firing rate by an order of magnitude and was found to convey information about the stimulus over a much wider dynamic range. Thus, the free firing rate may be the preferred variable for describing the response of a spiking neuron.
Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons
P. Kara and P. Reinagel and R. Reid
Neuron  27  635-46  (2000)
The response of a cortical cell to a repeated stimulus can be highly variable from one trial to the next. Much lower variability has been reported of retinal cells. We recorded visual responses simultaneously from three successive stages of the cat visual system: retinal ganglion cells (RGCs), thalamic (LGN) relay cells, and simple cells in layer 4 of primary visual cortex. Spike count variability was lower than that of a Poisson process at all three stages but increased at each stage. Absolute and relative refractory periods largely accounted for the reliability at all three stages. Our results show that cortical responses can be more reliable than previously thought. The differences in reliability in retina, LGN, and cortex can be explained by (1) decreasing firing rates and (2) decreasing absolute and relative refractory periods.
Postsynaptic variability of firing in rat cortical neurons: the roles of input synchronization and synaptic {NMDA} receptor conductance.
A. Harsch and H. Robinson
J Neurosci  20  6181-92  (2000)
Neurons in the functioning cortex fire erratically, with highly variable intervals between spikes. How much irregularity comes from the process of postsynaptic integration and how much from fluctuations in synaptic input? We have addressed these questions by recording the firing of neurons in slices of rat visual cortex in which synaptic receptors are blocked pharmacologically, while injecting controlled trains of unitary conductance transients, to electrically mimic natural synaptic input. Stimulation with a Poisson train of fast excitatory (AMPA-type) conductance transients, to simulate independent inputs, produced much less variability than encountered in vivo. Addition of NMDA-type conductance to each unitary event regularized the firing but lowered the precision and reliability of spikes in repeated responses. Independent Poisson trains of GABA-type conductance transients (reversing at the resting potential), which simulated independent activity in a population of presynaptic inhibitory neurons, failed to increase timing variability substantially but increased the precision of responses. However, introduction of synchrony, or correlations, in the excitatory input, according to a nonstationary Poisson model, dramatically raised timing variability to in vivo levels. The NMDA phase of compound AMPA-NMDA events conferred a time-dependent postsynaptic variability, whereby the reliability and precision of spikes degraded rapidly over the 100 msec after the start of a synchronous input burst. We conclude that postsynaptic mechanisms add significant variability to cortical responses but that substantial synchrony of inputs is necessary to explain in vivo variability. We suggest that NMDA receptors help to implement a switch from precise firing to random firing during responses to concerted inputs.
Frequency dependence of spike timing reliability in cortical pyramidal cells and interneurons.
J. Fellous and A. Houweling and R. Modi and R. Rao and P. Tiesinga and T. Sejnowski
J Neurophysiol  85  1782-7  (2001)
Pyramidal cells and interneurons in rat prefrontal cortical slices exhibit subthreshold oscillations when depolarized by constant current injection. For both types of neurons, the frequencies of these oscillations for current injection just below spike threshold were 2--10 Hz. Above spike threshold, however, the subthreshold oscillations in pyramidal cells remained low, but the frequency of oscillations in interneurons increased up to 50 Hz. To explore the interaction between these intrinsic oscillations and external inputs, the reliability of spiking in these cortical neurons was studied with sinusoidal current injection over a range of frequencies above and below the intrinsic frequency. Cortical neurons produced 1:1 phase locking for a limited range of driving frequencies for fixed amplitude. For low-input amplitude, 1:1 phase locking was obtained in the 5- to 10-Hz range. For higher-input amplitudes, pyramidal cells phase-locked in the 5- to 20-Hz range, whereas interneurons phase-locked in the 5- to 50-Hz range. For the amplitudes studied here, spike time reliability was always highest during 1:1 phase-locking, between 5 and 20 Hz for pyramidal cells and between 5 and 50 Hz for interneurons. The observed differences in the intrinsic frequency preference between pyramidal cells and interneurons have implications for rhythmogenesis and information transmission between populations of cortical neurons.
Temporal coding of visual information in the thalamus
P. Reinagel and R. Reid
J Neurosci  20  5392-400  (2000)
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.
Robustness and variability of neuronal coding by amplitude-sensitive afferents in the weakly electric fish eigenmannia.
G. Kreiman and R. Krahe and W. Metzner and C. Koch and F. Gabbiani
J Neurophysiol  84  189-204  (2000)
We investigated the variability of P-receptor afferent spike trains in the weakly electric fish, Eigenmannia, to repeated presentations of random electric field AMs (RAMs) and quantified its impact on the encoding of time-varying stimuli. A new measure of spike timing jitter was developed using the notion of spike train distances recently introduced by Victor and Purpura. This measure of variability is widely applicable to neuronal responses, irrespective of the type of stimuli used (deterministic vs. random) or the reliability of the recorded spike trains. In our data, the mean spike count and its variance measured in short time windows were poorly correlated with the reliability of P-receptor afferent spike trains, implying that such measures provide unreliable indices of trial-to-trial variability. P-receptor afferent spike trains were considerably less variable than those of Poisson model neurons. The average timing jitter of spikes lay within 1-2 cycles of the electric organ discharge (EOD). At low, but not at high firing rates, the timing jitter was dependent on the cutoff frequency of the stimulus and, to a lesser extent, on its contrast. When spikes were artificially manipulated to increase jitter, information conveyed by P-receptor afferents was degraded only for average jitters considerably larger than those observed experimentally. This suggests that the intrinsic variability of single spike trains lies outside of the range where it might degrade the information conveyed, yet still allows for improvement in coding by averaging across multiple afferent fibers. Our results were summarized in a phenomenological model of P-receptor afferents, incorporating both their linear transfer properties and the variability of their spike trains. This model complements an earlier one proposed by Nelson et al. for P-receptor afferents of Apteronotus. Because of their relatively high precision with respect to the EOD cycle frequency, P-receptor afferent spike trains possess the temporal resolution necessary to support coincidence detection operations at the next stage in the amplitude-coding pathway.
Information encoding and computation with spikes and bursts.
A. Kepecs and J. Lisman
Network  14  103-18  (2003)
Neurons compute and communicate by transforming synaptic input patterns into output spike trains. The nature of this transformation depends crucially on the properties of voltage-gated conductances in neuronal membranes. These intrinsic membrane conductances can enable neurons to generate different spike patterns including brief, high-frequency bursts that are commonly observed in a variety of brain regions. Here we examine how the membrane conductances that generate bursts affect neural computation and encoding. We simulated a bursting neuron model driven by random current input signal and superposed noise. We consider two issues: the timing reliability of different spike patterns and the computation performed by the neuron. Statistical analysis of the simulated spike trains shows that the timing of bursts is much more precise than the timing of single spikes. Furthermore, the number of spikes per burst is highly robust to noise. Next we considered the computation performed by the neuron: how different features of the input current are mapped into specific output spike patterns. Dimensional reduction and statistical classification techniques were used to determine the stimulus features triggering different firing patterns. Our main result is that spikes, and bursts of different durations, code for different stimulus features, which can be quantified without a priori assumptions about those features. These findings lead us to propose that the biophysical mechanisms of spike generation enables individual neurons to encode different stimulus features into distinct spike patterns.
A reciprocal relationship between reliability and responsiveness in developing visual cortical neurons.
N. C. Rust and S. R. Schultz and J. A. Movshon
J Neurosci  22  10519-23  (2002)
As the visual cortex matures, developmental modifications change the visually evoked firing patterns of single neurons. To explore the relationship between these developmental changes and the fidelity with which neurons transmit information, we measured the reliability of neuronal responses during postnatal development. Infant neurons have lower variability and higher dependence of transmitted information on firing rate than adult cells. Fewer spikes are needed by the infant cortex to convey the same amount of information. The increase in firing rates that occurs during development is largely offset, therefore, by a decrease in the reliability of responses. We propose that these changes are a consequence of the increasing ability of cortical cells to encode rapid changes in the visual environment.