A unified approach to the study of temporal, correlational, and rate coding

Towards in vivo neural decoding

Conventional spike sorting and motor intention decoding algorithms are mostly implemented on an external computing device, such as a personal computer. The innovation of high-resolution and high-density electrodes to record the brain's activity at the single neuron level may eliminate the need for spike sorting altogether while potentially enabling in vivo neural decoding. This article explores the feasibility and efficient realization of in vivo decoding, with and without spike sorting. The efficiency of neural network-based models for reliable motor decoding is presented and the performance of candidate neural decoding schemes on sorted single-unit activity and unsorted multi-unit activity are evaluated. A programmable processor with a custom instruction set architecture, for the first time to the best of our knowledge, is designed and implemented for executing neural network operations in a standard 180-nm CMOS process. The processor's layout is estimated to occupy 49 mm 2 of silicon area and to dissipate 12 mW of power from a 1.8 V supply, which is within the tissue-safe operation of the brain.

Modulation of dynamics in a pre-existing hippocampal network by neural stem cells on a microelectrode array

Objective.Neural stem cells (NSCs) are continuously produced throughout life in the hippocampus, which is a vital structure for learning and memory. NSCs in the brain incorporate into the functional hippocampal circuits and contribute to processing information. However, little is known about the mechanisms of NSCs' activity in a pre-existing neuronal network. Here, we investigate the role of NSCs in the neuronal activity of a pre-existing hippocampalin vitronetwork grown on microelectrode arrays.Approach.We assessed the change in internal dynamics of the network by additional NSCs based on spontaneous activity. We also evaluated the networks' ability to discriminate between different input patterns by measuring evoked activity in response to external inputs.Main results.Analysis of spontaneous activity revealed that additional NSCs prolonged network bursts with longer intervals, generated a lower number of initiating patterns, and decreased synchronization among neurons. Moreover, the network with NSCs showed higher synchronicity in close connections among neurons responding to external inputs and a larger difference in spike counts and cross-correlations during evoked response between two different inputs. Taken together, our results suggested that NSCs alter the internal dynamics of the pre-existing hippocampal network and produce more specific responses to external inputs, thus enhancing the ability of the network to differentiate two different inputs.Significance.We demonstrated that NSCs improve the ability to distinguish external inputs by modulating the internal dynamics of a pre-existing network in a hippocampal culture. Our results provide novel insights into the relationship between NSCs and learning and memory.

Embedding optimization reveals long-lasting history dependence in neural spiking activity

Information processing can leave distinct footprints on the statistics of neural spiking. For example, efficient coding minimizes the statistical dependencies on the spiking history, while temporal integration of information may require the maintenance of information over different timescales. To investigate these footprints, we developed a novel approach to quantify history dependence within the spiking of a single neuron, using the mutual information between the entire past and current spiking. This measure captures how much past information is necessary to predict current spiking. In contrast, classical time-lagged measures of temporal dependence like the autocorrelation capture how long-potentially redundant-past information can still be read out. Strikingly, we find for model neurons that our method disentangles the strength and timescale of history dependence, whereas the two are mixed in classical approaches. When applying the method to experimental data, which are necessarily of limited size, a reliable estimation of mutual information is only possible for a coarse temporal binning of past spiking, a so-called past embedding. To still account for the vastly different spiking statistics and potentially long history dependence of living neurons, we developed an embedding-optimization approach that does not only vary the number and size, but also an exponential stretching of past bins. For extra-cellular spike recordings, we found that the strength and timescale of history dependence indeed can vary independently across experimental preparations. While hippocampus indicated strong and long history dependence, in visual cortex it was weak and short, while in vitro the history dependence was strong but short. This work enables an information-theoretic characterization of history dependence in recorded spike trains, which captures a footprint of information processing that is beyond time-lagged measures of temporal dependence. To facilitate the application of the method, we provide practical guidelines and a toolbox.

Bladder pressure encoding by sacral dorsal root ganglion fibres: implications for decoding

OBJECTIVE

We aim at characterising the encoding of bladder pressure (intravesical pressure) by a population of sensory fibres. This research is motivated by the possibility to restore bladder function in elderly patients or after spinal cord injury using implanted devices, so called bioelectronic medicines. For these devices, nerve-based estimation of intravesical pressure can enable a personalized and on-demand stimulation paradigm, which has promise of being more effective and efficient. In this context, a better understanding of the encoding strategies employed by the body might in the future be exploited by informed decoding algorithms that enable a precise and robust bladder-pressure estimation.

APPROACH

To this end, we apply information theory to microelectrode-array recordings from the cat sacral dorsal root ganglion while filling the bladder, conduct surrogate data studies to augment the data we have, and finally decode pressure in a simple informed approach.

MAIN RESULTS

We find an encoding scheme by different main bladder neuron types that we divide into three response types (slow tonic, phasic, and derivative fibres). We show that an encoding by different bladder neuron types, each represented by multiple cells, offers reliability through within-type redundancy and high information rates through semi-independence of different types. Our subsequent decoding study shows a more robust decoding from mean responses of homogeneous cell pools.

SIGNIFICANCE

We have here, for the first time, established a link between an information theoretic analysis of the encoding of intravesical pressure by a population of sensory neurons to an informed decoding paradigm. We show that even a simple adapted decoder can exploit the redundancy in the population to be more robust against cell loss. This work thus paves the way towards principled encoding studies in the periphery and towards a new generation of informed peripheral nerve decoders for bioelectronic medicines.

Variety Is the Spice of Life: Positive and Negative Effects of Noise in Electrical Stimulation of the Nervous System

Noisy stimuli may hold the key for optimal electrical stimulation of the nervous system. Possible mechanisms of noise’s impact upon neuronal function are discussed, including intracellular, extracellular, and systems-level mechanisms. Specifically, channel resonance, stochastic resonance, high conductance states, and network binding are investigated. These mechanisms are examined and possible directions of growth for the field are discussed, with examples of applications provided from the fields of deep brain stimulation or spinal cord injury. Together, this review highlights the theoretical basis and evidence base for the use of noise to enhance current stimulation paradigms of the nervous system.

Neuronal Correlates of Tactile Working Memory in Prefrontal and Vibrissal Somatosensory Cortex

Tactile working memory engages a broad network of cortical regions in primates. To assess whether the conclusions drawn from primates apply to rodents, we examined the vibrissal primary somatosensory cortex (vS1) and the prelimbic cortex (PL) in a delayed comparison task. Rats compared the speeds of two vibrissal vibrations, stimulus1 and stimulus2, separated by a delay of 2 s. Neuronal firing rates in vS1 and PL encode both stimuli in real time. Across the delay, the stimulus1 representation declines more precipitously in vS1 than in PL. Theta-band local field potential (LFP) coherence between vS1 and PL peaks at trial onset and remains elevated during the interstimulus interval; simultaneously, vS1 spikes become phase locked to PL LFP. Phase locking is stronger on correct (versus error) trials. Tactile working memory in rats appears to be mediated by a posterior (vS1) to anterior (PL) flow of information, with performance facilitated through coherent LFP oscillation.

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Rats compared the speeds of two sequential vibrissal vibrations, separated by 2 s

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Neurons in the primary somatosensory (vS1) and prelimbic (PL) cortex coded the stimuli

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Theta local field potential coherence between vS1 and PL peaked at trial onset

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Intracortical coherent oscillations may play a role in rat tactile working memory

Neural codes – Necessary but not sufficient for understanding brain function

Brains are information processing systems whose operational principles ultimately cannot be understood without resource to information theory. We suggest that understanding how external signals are represented in the brain is a necessary step towards employing further engineering tools (such as control theory) to understand the information processing performed by brain circuits during behaviour.

Estimating the Mutual Information between Two Discrete, Asymmetric Variables with Limited Samples

Determining the strength of nonlinear, statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual information from limited samples is a challenging task. Since the mutual information is the difference of two entropies, the existing Bayesian estimators of entropy may be used to estimate information. This procedure, however, is still biased in the severely under-sampled regime. Here, we propose an alternative estimator that is applicable to those cases in which the marginal distribution of one of the two variables—the one with minimal entropy—is well sampled. The other variable, as well as the joint and conditional distributions, can be severely undersampled. We obtain a consistent estimator that presents very low bias, outperforming previous methods even when the sampled data contain few coincidences. As with other Bayesian estimators, our proposal focuses on the strength of the interaction between the two variables, without seeking to model the specific way in which they are related. A distinctive property of our method is that the main data statistics determining the amount of mutual information is the inhomogeneity of the conditional distribution of the low-entropy variable in those states in which the large-entropy variable registers coincidences.

Quantifying encoding redundancy induced by rate correlations in Poisson neurons

Temporal correlations in neuronal spike trains are known to introduce redundancy to stimulus encoding. However, exact methods to describe how these correlations impact neural information transmission quantitatively are lacking. Here, we provide a general measure for the information carried by correlated rate modulations only, neglecting other spike correlations, and use it to investigate the effect of rate correlations on encoding redundancy. We derive it analytically by calculating the mutual information between a time-correlated, rate modulating signal and the resulting spikes of Poisson neurons. Whereas this information is determined by spike autocorrelations only, the redundancy in information encoding due to rate correlations depends on both the distribution and the autocorrelation of the rate histogram. We further demonstrate that at very small signal strengths the information carried by rate correlated spikes becomes identical to that of independent spikes, in effect measuring the signal modulation depth. In contrast, a vanishing signal correlation time maximizes information but does not generally yield the information of independent spikes. Overall, our study sheds light on the role of signal-induced temporal correlations for neural coding, by providing insight into how signal features shape redundancy and by establishing mathematical links between existing methods.

Improved lower bound for the mutual information between signal and neural spike count

The mutual information between a stimulus signal and the spike count of a stochastic neuron is in many cases difficult to determine. Therefore, it is often approximated by a lower bound formula that involves linear correlations between input and output only. Here, we improve the linear lower bound for the mutual information by incorporating nonlinear correlations. For the special case of a Gaussian output variable with nonlinear signal dependencies of mean and variance we also derive an exact integral formula for the full mutual information. In our numerical analysis, we first compare the linear and nonlinear lower bounds and the exact integral formula for two different Gaussian models and show under which conditions the nonlinear lower bound provides a significant improvement to the linear approximation. We then inspect two neuron models, the leaky integrate-and-fire model with white Gaussian noise and the Na-K model with channel noise. We show that for certain firing regimes and for intermediate signal strengths the nonlinear lower bound can provide a substantial improvement compared to the linear lower bound. Our results demonstrate the importance of nonlinear input-output correlations for neural information transmission and provide a simple nonlinear approximation for the mutual information that can be applied to more complicated neuron models as well as to experimental data.

Assessing the Relevance of Specific Response Features in the Neural Code

The study of the neural code aims at deciphering how the nervous system maps external stimuli into neural activity—the encoding phase—and subsequently transforms such activity into adequate responses to the original stimuli—the decoding phase. Several information-theoretical methods have been proposed to assess the relevance of individual response features, as for example, the spike count of a given neuron, or the amount of correlation in the activity of two cells. These methods work under the premise that the relevance of a feature is reflected in the information loss that is induced by eliminating the feature from the response. The alternative methods differ in the procedure by which the tested feature is removed, and the algorithm with which the lost information is calculated. Here we compare these methods, and show that more often than not, each method assigns a different relevance to the tested feature. We demonstrate that the differences are both quantitative and qualitative, and connect them with the method employed to remove the tested feature, as well as the procedure to calculate the lost information. By studying a collection of carefully designed examples, and working on analytic derivations, we identify the conditions under which the relevance of features diagnosed by different methods can be ranked, or sometimes even equated. The condition for equality involves both the amount and the type of information contributed by the tested feature. We conclude that the quest for relevant response features is more delicate than previously thought, and may yield to multiple answers depending on methodological subtleties.

Quantifying Neuronal Information Flow in Response to Frequency and Intensity Changes in the Auditory Cortex

Studies increasingly show that behavioral relevance alters the population representation of sensory stimuli in the sensory cortices. However, the mechanisms underlying this behavior are incompletely understood. Here, we record neuronal responses in the auditory cortex while a highly trained, awake, normal-hearing gerbil listens passively to target tones of high versus low behavioral relevance. Using an information theoretic framework, we model the overall transmission chain from acoustic input stimulus to recorded cortical response as a communication channel. To quantify how much information core auditory cortex carries about high versus low relevance sound, we then compute the mutual information of the multi-unit neuronal responses. Results show that the output over the stimulus-to-response channel can be modeled as a Poisson mixture. We derive a closed-form fast approximation for the entropy of a mixture of univariate Poisson random variables. A purely rate-code based model reveals reduced information transfer for high relevance compared to low relevance tones, hinting that changes in temporal discharge pattern may encode behavioral relevance.

Rhythmic activities of the brain: Quantifying the high complexity of beta and gamma oscillations during visuomotor tasks

Electroencephalography (EEG) signals depict the electrical activity that takes place at the surface of the brain and provide an important tool for understanding a variety of cognitive processes. The EEG is the product of synchronized activity of the brain, and variations in EEG oscillations patterns reflect the underlying changes in neuronal synchrony. Our aim is to characterize the complexity of the EEG rhythmic oscillations bands when the subjects perform a visuomotor or imagined cognitive tasks (imagined movement), providing a causal mapping of the dynamical rhythmic activities of the brain as a measure of attentional investment. We estimate the intrinsic correlational structure of the signals within the causality entropy-complexity plane H×C, where the enhanced complexity in the gamma 1, gamma 2, and beta 1 bands allows us to distinguish motor-visual memory tasks from control conditions. We identify the dynamics of the gamma 1, gamma 2, and beta 1 rhythmic oscillations within the zone of a chaotic dissipative behavior, whereas in contrast the beta 2 band shows a much higher level of entropy and a significant low level of complexity that correspond to a non-invertible cubic map. Our findings enhance the importance of the gamma band during attention in perceptual feature binding during the visuomotor/imagery tasks.

A Tutorial for Information Theory in Neuroscience

Understanding how neural systems integrate, encode, and compute information is central to understanding brain function. Frequently, data from neuroscience experiments are multivariate, the interactions between the variables are nonlinear, and the landscape of hypothesized or possible interactions between variables is extremely broad. Information theory is well suited to address these types of data, as it possesses multivariate analysis tools, it can be applied to many different types of data, it can capture nonlinear interactions, and it does not require assumptions about the structure of the underlying data (i.e., it is model independent). In this article, we walk through the mathematics of information theory along with common logistical problems associated with data type, data binning, data quantity requirements, bias, and significance testing. Next, we analyze models inspired by canonical neuroscience experiments to improve understanding and demonstrate the strengths of information theory analyses. To facilitate the use of information theory analyses, and an understanding of how these analyses are implemented, we also provide a free MATLAB software package that can be applied to a wide range of data from neuroscience experiments, as well as from other fields of study.

Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains

The spiking activity of neuronal networks follows laws that are not time-reversal symmetric; the notion of pre-synaptic and post-synaptic neurons, stimulus correlations and noise correlations have a clear time order. Therefore, a biologically realistic statistical model for the spiking activity should be able to capture some degree of time irreversibility. We use the thermodynamic formalism to build a framework in the context maximum entropy models to quantify the degree of time irreversibility, providing an explicit formula for the information entropy production of the inferred maximum entropy Markov chain. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics.

Advances in two photon scanning and scanless microscopy technologies for functional neural circuit imaging

Recent years have seen substantial developments in technology for imaging neural circuits, raising the prospect of large scale imaging studies of neural populations involved in information processing, with the potential to lead to step changes in our understanding of brain function and dysfunction. In this article we will review some key recent advances: improved fluorophores for single cell resolution functional neuroimaging using a two photon microscope; improved approaches to the problem of scanning active circuits; and the prospect of scanless microscopes which overcome some of the bandwidth limitations of current imaging techniques. These advances in technology for experimental neuroscience have in themselves led to technical challenges, such as the need for the development of novel signal processing and data analysis tools in order to make the most of the new experimental tools. We review recent work in some active topics, such as region of interest segmentation algorithms capable of demixing overlapping signals, and new highly accurate algorithms for calcium transient detection. These advances motivate the development of new data analysis tools capable of dealing with spatial or spatiotemporal patterns of neural activity, that scale well with pattern size.

Effect of interacting second- and third-order stimulus-dependent correlations on population-coding asymmetries

Spike correlations among neurons are widely encountered in the brain. Although models accounting for pairwise interactions have proved able to capture some of the most important features of population activity at the level of the retina, the evidence shows that pairwise neuronal correlation analysis does not resolve cooperative population dynamics by itself. By means of a series expansion for short time scales of the mutual information conveyed by a population of neurons, the information transmission can be broken down into firing rate and correlational components. In a proposed extension of this framework, we investigate the information components considering both second- and higher-order correlations. We show that the existence of a mixed stimulus-dependent correlation term defines a new scenario for the interplay between pairwise and higher-than-pairwise interactions in noise and signal correlations that would lead either to redundancy or synergy in the information-theoretic sense.

Coding of Sensory Signals by Neuronal Populations: The Role of Correlated Activity

How is sensory information encoded by the patterns of action potentials emitted by ensembles of neurons? Computational methods have recently been applied to this fundamental question and have found, both in the somatosensory and visual system, that the basic unit of information transmission is the timing of individual spikes. In systems studied to date, the neuronal population codes appear to be simple ones that do not rely on complex patterns of correlated spikes.

A minimum-error, energy-constrained neural code is an instantaneous-rate code

Sensory neurons code information about stimuli in their sequence of action potentials (spikes). Intuitively, the spikes should represent stimuli with high fidelity. However, generating and propagating spikes is a metabolically expensive process. It is therefore likely that neural codes have been selected to balance energy expenditure against encoding error. Our recently proposed optimal, energy-constrained neural coder (Jones et al. Frontiers in Computational Neuroscience, 9, 61 2015) postulates that neurons time spikes to minimize the trade-off between stimulus reconstruction error and expended energy by adjusting the spike threshold using a simple dynamic threshold. Here, we show that this proposed coding scheme is related to existing coding schemes, such as rate and temporal codes. We derive an instantaneous rate coder and show that the spike-rate depends on the signal and its derivative. In the limit of high spike rates the spike train maximizes fidelity given an energy constraint (average spike-rate), and the predicted interspike intervals are identical to those generated by our existing optimal coding neuron. The instantaneous rate coder is shown to closely match the spike-rates recorded from P-type primary afferents in weakly electric fish. In particular, the coder is a predictor of the peristimulus time histogram (PSTH). When tested against in vitro cortical pyramidal neuron recordings, the instantaneous spike-rate approximates DC step inputs, matching both the average spike-rate and the time-to-first-spike (a simple temporal code). Overall, the instantaneous rate coder relates optimal, energy-constrained encoding to the concepts of rate-coding and temporal-coding, suggesting a possible unifying principle of neural encoding of sensory signals.

Superlinear Summation of Information in Premotor Neuron Pairs

Whether premotor/motor neurons encode information in terms of spiking frequency or by their relative time of firing, which may display synchronization, is still undetermined. To address this issue, we used an information theory approach to analyze neuronal responses recorded in the premotor (area F5) and primary motor (area F1) cortices of macaque monkeys under four different conditions of visual feedback during hand grasping. To evaluate the sensitivity of spike timing correlation between single neurons, we investigated the stimulus dependent synchronization in our population of pairs. We first investigated the degree of correlation of trial-to-trial fluctuations in response strength between neighboring neurons for each condition, and second estimated the stimulus dependent synchronization by means of an information theoretical approach. We compared the information conveyed by pairs of simultaneously recorded neurons with the sum of information provided by the respective individual cells. The information transmission across pairs of cells in the primary motor cortex seems largely independent, whereas information transmission across pairs of premotor neurons is summed superlinearly. The brain could take advantage of both the accuracy provided by the independency of F1 and the synergy allowed by the superlinear information population coding in F5, distinguishing thus the generalizing role of F5.

Thalamic neuron models encode stimulus information by burst-size modulation

Thalamic neurons have been long assumed to fire in tonic mode during perceptive states, and in burst mode during sleep and unconsciousness. However, recent evidence suggests that bursts may also be relevant in the encoding of sensory information. Here, we explore the neural code of such thalamic bursts. In order to assess whether the burst code is generic or whether it depends on the detailed properties of each bursting neuron, we analyzed two neuron models incorporating different levels of biological detail. One of the models contained no information of the biophysical processes entailed in spike generation, and described neuron activity at a phenomenological level. The second model represented the evolution of the individual ionic conductances involved in spiking and bursting, and required a large number of parameters. We analyzed the models' input selectivity using reverse correlation methods and information theory. We found that n-spike bursts from both models transmit information by modulating their spike count in response to changes to instantaneous input features, such as slope, phase, amplitude, etc. The stimulus feature that is most efficiently encoded by bursts, however, need not coincide with one of such classical features. We therefore searched for the optimal feature among all those that could be expressed as a linear transformation of the time-dependent input current. We found that bursting neurons transmitted 6 times more information about such more general features. The relevant events in the stimulus were located in a time window spanning ~100 ms before and ~20 ms after burst onset. Most importantly, the neural code employed by the simple and the biologically realistic models was largely the same, implying that the simple thalamic neuron model contains the essential ingredients that account for the computational properties of the thalamic burst code. Thus, our results suggest the n-spike burst code is a general property of thalamic neurons.

Extracting information in spike time patterns with wavelets and information theory

We present a new method to assess the information carried by temporal patterns in spike trains. The method first performs a wavelet decomposition of the spike trains, then uses Shannon information to select a subset of coefficients carrying information, and finally assesses timing information in terms of decoding performance: the ability to identify the presented stimuli from spike train patterns. We show that the method allows: 1) a robust assessment of the information carried by spike time patterns even when this is distributed across multiple time scales and time points; 2) an effective denoising of the raster plots that improves the estimate of stimulus tuning of spike trains; and 3) an assessment of the information carried by temporally coordinated spikes across neurons. Using simulated data, we demonstrate that the Wavelet-Information (WI) method performs better and is more robust to spike time-jitter, background noise, and sample size than well-established approaches, such as principal component analysis, direct estimates of information from digitized spike trains, or a metric-based method. Furthermore, when applied to real spike trains from monkey auditory cortex and from rat barrel cortex, the WI method allows extracting larger amounts of spike timing information. Importantly, the fact that the WI method incorporates multiple time scales makes it robust to the choice of partly arbitrary parameters such as temporal resolution, response window length, number of response features considered, and the number of available trials. These results highlight the potential of the proposed method for accurate and objective assessments of how spike timing encodes information.

Spike count, spike timing and temporal information in the cortex of awake, freely moving rats

OBJECTIVE

Sensory processing of peripheral information is not stationary but is, in general, a dynamic process related to the behavioral state of the animal. Yet the link between the state of the behavior and the encoding properties of neurons is unclear. This report investigates the impact of the behavioral state on the encoding mechanisms used by cortical neurons for both detection and discrimination of somatosensory stimuli in awake, freely moving, rats.

APPROACH

Neuronal activity was recorded from the primary somatosensory cortex of five rats under two different behavioral states (quiet versus whisking) while electrical stimulation of increasing stimulus strength was delivered to the mystacial pad. Information theoretical measures were then used to measure the contribution of different encoding mechanisms to the information carried by neurons in response to the whisker stimulation.

MAIN RESULTS

We found that the behavioral state of the animal modulated the total amount of information conveyed by neurons and that the timing of individual spikes increased the information compared to the total count of spikes alone. However, the temporal information, i.e. information exclusively related to when the spikes occur, was not modulated by behavioral state.

SIGNIFICANCE

We conclude that information about somatosensory stimuli is modulated by the behavior of the animal and this modulation is mainly expressed in the spike count while the temporal information is more robust to changes in behavioral state.

Influence of external inputs and asymmetry of connections on information-geometric measures involving up to ten neuronal interactions

The investigation of neural interactions is crucial for understanding information processing in the brain. Recently an analysis method based on information geometry (IG) has gained increased attention, and the property of the pairwise IG measure has been studied extensively in relation to the two-neuron interaction. However, little is known about the property of IG measures involving more neuronal interactions. In this study, we systematically investigated the influence of external inputs and the asymmetry of connections on the IG measures in cases ranging from 1-neuron to 10-neuron interactions. First, the analytical relationship between the IG measures and external inputs was derived for a network of 10 neurons with uniform connections. Our results confirmed that the single and pairwise IG measures were good estimators of the mean background input and of the sum of the connection weights, respectively. For the IG measures involving 3 to 10 neuronal interactions, we found that the influence of external inputs was highly nonlinear. Second, by computer simulation, we extended our analytical results to asymmetric connections. For a network of 10 neurons, the simulation showed that the behavior of the IG measures in relation to external inputs was similar to the analytical solution obtained for a uniformly connected network. When the network size was increased to 1000 neurons, the influence of external inputs almost disappeared. This result suggests that all IG measures from 1-neuron to 10-neuron interactions are robust against the influence of external inputs. In addition, we investigated how the strength of asymmetry influenced the IG measures. Computer simulation of a 1000-neuron network showed that all the IG measures were robust against the modulation of the asymmetry of connections. Our results provide further support for an information-geometric approach and will provide useful insights when these IG measures are applied to real experimental spike data.

A causal perspective on the analysis of signal and noise correlations and their role in population coding

The role of correlations between neuronal responses is crucial to understanding the neural code. A framework used to study this role comprises a breakdown of the mutual information between stimuli and responses into terms that aim to account for different coding modalities and the distinction between different notions of independence. Here we complete the list of types of independence and distinguish activity independence (related to total correlations), conditional independence (related to noise correlations), signal independence (related to signal correlations), coding independence (related to information transmission), and information independence (related to redundancy). For each type, we identify the probabilistic criterion that defines it, indicate the information-theoretic measure used as statistic to test for it, and provide a graphical criterion to recognize the causal configurations of stimuli and responses that lead to its existence. Using this causal analysis, we first provide sufficiency conditions relating these types. Second, we differentiate the use of the measures as statistics to test for the existence of independence from their use for quantification. We indicate that signal and noise correlation cannot be quantified separately. Third, we explicitly define alternative system configurations used to construct the measures, in which noise correlations or noise and signal correlations are eliminated. Accordingly, we examine which measures are meaningful only as a comparison across configurations and which ones provide a characterization of the actually observed responses without resorting to other configurations. Fourth, we compare the commonly used nonparametric approach to eliminate noise correlations with a functional (model-based) approach, showing that the former approach does not remove those effects of noise correlations captured by the tuning properties of the individual neurons, and implies nonlocal causal structure manipulations. These results improve the interpretation of the measures on the framework and help in understanding how to apply it to analyze the role of correlations.

Information-geometric measures estimate neural interactions during oscillatory brain states

The characterization of functional network structures among multiple neurons is essential to understanding neural information processing. Information geometry (IG), a theory developed for investigating a space of probability distributions has recently been applied to spike-train analysis and has provided robust estimations of neural interactions. Although neural firing in the equilibrium state is often assumed in these studies, in reality, neural activity is non-stationary. The brain exhibits various oscillations depending on cognitive demands or when an animal is asleep. Therefore, the investigation of the IG measures during oscillatory network states is important for testing how the IG method can be applied to real neural data. Using model networks of binary neurons or more realistic spiking neurons, we studied how the single- and pairwise-IG measures were influenced by oscillatory neural activity. Two general oscillatory mechanisms, externally driven oscillations and internally induced oscillations, were considered. In both mechanisms, we found that the single-IG measure was linearly related to the magnitude of the external input, and that the pairwise-IG measure was linearly related to the sum of connection strengths between two neurons. We also observed that the pairwise-IG measure was not dependent on the oscillation frequency. These results are consistent with the previous findings that were obtained under the equilibrium conditions. Therefore, we demonstrate that the IG method provides useful insights into neural interactions under the oscillatory condition that can often be observed in the real brain.

Information-geometric measures for estimation of connection weight under correlated inputs

The brain processes information in a highly parallel manner. Determination of the relationship between neural spikes and synaptic connections plays a key role in the analysis of electrophysiological data. Information geometry (IG) has been proposed as a powerful analysis tool for multiple spike data, providing useful insights into the statistical interactions within a population of neurons. Previous work has demonstrated that IG measures can be used to infer the connection weight between two neurons in a neural network. This property is useful in neuroscience because it provides a way to estimate learning-induced changes in synaptic strengths from extracellular neuronal recordings. A previous study has shown, however, that this property would hold only when inputs to neurons are not correlated. Since neurons in the brain often receive common inputs, this would hinder the application of the IG method to real data. We investigated the two-neuron-IG measures in higher-order log-linear models to overcome this limitation. First, we mathematically showed that the estimation of uniformly connected synaptic weight can be improved by taking into account higher-order log-linear models. Second, we numerically showed that the estimation can be improved for more general asymmetrically connected networks. Considering the estimated number of the synaptic connections in the brain, we showed that the two-neuron IG measure calculated by the fourth- or fifth-order log-linear model would provide an accurate estimation of connection strength within approximately a 10% error. These studies suggest that the two-neuron IG measure with higher-order log-linear expansion is a robust estimator of connection weight even under correlated inputs, providing a useful analytical tool for real multineuronal spike data.

Estimating the amount of information conveyed by a population of neurons

Recent technological advances have made the simultaneous recording of the activity of many neurons common. However, estimating the amount of information conveyed by the discharge of a neural population remains a significant challenge. Here we describe our recently published analysis method that assists in such estimates. We describe the key concepts and assumptions on which the method is based, illustrate its use with data from both simulated and real neurons recorded from the lateral geniculate nucleus of a monkey, and show how it can be used to calculate redundancy and synergy among neuronal groups.

The Ising decoder: reading out the activity of large neural ensembles

The Ising model has recently received much attention for the statistical description of neural spike train data. In this paper, we propose and demonstrate its use for building decoders capable of predicting, on a millisecond timescale, the stimulus represented by a pattern of neural activity. After fitting to a training dataset, the Ising decoder can be applied "online" for instantaneous decoding of test data. While such models can be fit exactly using Boltzmann learning, this approach rapidly becomes computationally intractable as neural ensemble size increases. We show that several approaches, including the Thouless-Anderson-Palmer (TAP) mean field approach from statistical physics, and the recently developed Minimum Probability Flow Learning (MPFL) algorithm, can be used for rapid inference of model parameters in large-scale neural ensembles. Use of the Ising model for decoding, unlike other problems such as functional connectivity estimation, requires estimation of the partition function. As this involves summation over all possible responses, this step can be limiting. Mean field approaches avoid this problem by providing an analytical expression for the partition function. We demonstrate these decoding techniques by applying them to simulated neural ensemble responses from a mouse visual cortex model, finding an improvement in decoder performance for a model with heterogeneous as opposed to homogeneous neural tuning and response properties. Our results demonstrate the practicality of using the Ising model to read out, or decode, spatial patterns of activity comprised of many hundreds of neurons.

Temporal encoding in a nervous system

We examined the extent to which temporal encoding may be implemented by single neurons in the cercal sensory system of the house cricket Acheta domesticus. We found that these neurons exhibit a greater-than-expected coding capacity, due in part to an increased precision in brief patterns of action potentials. We developed linear and non-linear models for decoding the activity of these neurons. We found that the stimuli associated with short-interval patterns of spikes (ISIs of 8 ms or less) could be predicted better by second-order models as compared to linear models. Finally, we characterized the difference between these linear and second-order models in a low-dimensional subspace, and showed that modification of the linear models along only a few dimensions improved their predictive power to parity with the second order models. Together these results show that single neurons are capable of using temporal patterns of spikes as fundamental symbols in their neural code, and that they communicate specific stimulus distributions to subsequent neural structures.

The information coding schemes used within nervous systems have been the focus of an entire field within neuroscience. An unresolved issue within the general coding problem is the determination of the neural “symbols” with which information is encoded in neural spike trains, analogous to the determination of the nucleotide sequences used to represent proteins in molecular biology. The goal of our study was to determine if pairs of consecutive action potentials contain more or different information about the stimuli that elicit them than would be predicted from an analysis of individual action potentials. We developed linear and non-linear coding models and used likelihood analysis to address this question for sensory interneurons in the cricket cercal sensory system. Our results show that these neurons' spike trains can be decomposed into sequences of two neural symbols: isolated single spikes and short-interval spike doublets. Given the ubiquitous nature of similar neural activity reported in other systems, we suspect that the implementation of such temporal encoding schemes may be widespread across animal phyla. Knowledge of the basic coding units used by single cells will help in building the large-scale neural network models necessary for understanding how nervous systems function.

Millisecond encoding precision of auditory cortex neurons

Neurons in auditory cortex are central to our perception of sounds. However, the underlying neural codes, and the relevance of millisecond-precise spike timing in particular, remain debated. Here, we addressed this issue in the auditory cortex of alert nonhuman primates by quantifying the amount of information carried by precise spike timing about complex sounds presented for extended periods of time (random tone sequences and natural sounds). We investigated the dependence of stimulus information on the temporal precision at which spike times were registered and found that registering spikes at a precision coarser than a few milliseconds significantly reduced the encoded information. This dependence demonstrates that auditory cortex neurons can carry stimulus information at high temporal precision. In addition, we found that the main determinant of finely timed information was rapid modulation of the firing rate, whereas higher-order correlations between spike times contributed negligibly. Although the neural coding precision was high for random tone sequences and natural sounds, the information lost at a precision coarser than a few milliseconds was higher for the stimulus sequence that varied on a faster time scale (random tones), suggesting that the precision of cortical firing depends on the stimulus dynamics. Together, these results provide a neural substrate for recently reported behavioral relevance of precisely timed activity patterns with auditory cortex. In addition, they highlight the importance of millisecond-precise neural coding as general functional principle of auditory processing--from the periphery to cortex.

General Poisson exact breakdown of the mutual information to study the role of correlations in populations of neurons

We present an integrative formalism of mutual information expansion, the general Poisson exact breakdown, which explicitly evaluates the informational contribution of correlations in the spike counts both between and within neurons. The formalism was validated on simulated data and applied to real neurons recorded from the rat somatosensory cortex. From the general Poisson exact breakdown, a considerable number of mutual information measures introduced in the neural computation literature can be directly derived, including the exact breakdown (Pola, Thiele, Hoffmann, & Panzeri, 2003), the Poisson exact breakdown (Scaglione, Foffani, Scannella, Cerutti, & Moxon, 2008) the synergy and redundancy between neurons (Schneidman, Bialek, & Berry, 2003), and the information lost by an optimal decoder that assumes the absence of correlations between neurons (Nirenberg & Latham, 2003; Pola et al., 2003). The general Poisson exact breakdown thus offers a convenient set of building blocks for studying the role of correlations in population codes.

Information Carried by Population Spike Times in the Whisker Sensory Cortex can be Decoded Without Knowledge of Stimulus Time

Computational analyses have revealed that precisely timed spikes emitted by somatosensory cortical neuronal populations encode basic stimulus features in the rat's whisker sensory system. Efficient spike time based decoding schemes both for the spatial location of a stimulus and for the kinetic features of complex whisker movements have been defined. To date, these decoding schemes have been based upon spike times referenced to an external temporal frame – the time of the stimulus itself. Such schemes are limited by the requirement of precise knowledge of the stimulus time signal, and it is not clear whether stimulus times are known to rats making sensory judgments. Here, we first review studies of the information obtained from spike timing referenced to the stimulus time. Then we explore new methods for extracting spike train information independently of any external temporal reference frame. These proposed methods are based on the detection of stimulus-dependent differences in the firing time within a neuronal population. We apply them to a data set using single-whisker stimulation in anesthetized rats and find that stimulus site can be decoded based on the millisecond-range relative differences in spike times even without knowledge of stimulus time. If spike counts alone are measured over tens or hundreds of milliseconds rather than milliseconds, such decoders are much less effective. These results suggest that decoding schemes based on millisecond-precise spike times are likely to subserve robust and information-rich transmission of information in the somatosensory system.

The impact of high-order interactions on the rate of synchronous discharge and information transmission in somatosensory cortex

Understanding the operations of neural networks in the brain requires an understanding of whether interactions among neurons can be described by a pairwise interaction model, or whether a higher order interaction model is needed. In this article we consider the rate of synchronous discharge of a local population of neurons, a macroscopic index of the activation of the neural network that can be measured experimentally. We analyse a model based on physics' maximum entropy principle that evaluates whether the probability of synchronous discharge can be described by interactions up to any given order. When compared with real neural population activity obtained from the rat somatosensory cortex, the model shows that interactions of at least order three or four are necessary to explain the data. We use Shannon information to compute the impact of high-order correlations on the amount of somatosensory information transmitted by the rate of synchronous discharge, and we find that correlations of higher order progressively decrease the information available through the neural population. These results are compatible with the hypothesis that high-order interactions play a role in shaping the dynamics of neural networks, and that they should be taken into account when computing the representational capacity of neural populations.

Spatial pattern coding of sensory information by climbing fiber-evoked calcium signals in networks of neighboring cerebellar Purkinje cells

Climbing fiber input produces complex spike synchrony across populations of cerebellar Purkinje cells oriented in the parasagittal axis. Elucidating the fine spatial structure of this synchrony is crucial for understanding its role in the encoding and processing of sensory information within the olivocerebellar cortical circuit. We investigated these issues using in vivo multineuron two-photon calcium imaging in combination with information theoretic analysis. Spontaneous dendritic calcium transients linked to climbing fiber input were observed in multiple neighboring Purkinje cells. Spontaneous synchrony of calcium transients between individual Purkinje cells falls off over approximately 200 microm mediolaterally, consistent with the presence of cerebellar microzones organized by climbing fiber input. Synchrony was increased after administration of harmaline, consistent with an olivary origin. Periodic sensory stimulation also resulted in a transient increase of synchrony after stimulus onset. To examine how synchrony affects the neural population code provided by the spatial pattern of complex spikes, we analyzed its information content. We found that spatial patterns of calcium events from small ensembles of cells provided substantially more stimulus information (59% more for seven-cell ensembles) than available by counting events across the pool without taking into account spatial origin. Information theoretic analysis indicated that, rather than contributing significantly to sensory coding via stimulus dependence, correlational effects on sensory coding are dominated by redundancy attributable to the prevalent spontaneous synchrony. The olivocerebellar circuit thus uses a labeled line code to report sensory signals, leaving open a role for synchrony in flexible selection of signals for output to deep cerebellar nuclei.

Information about complex fingertip parameters in individual human tactile afferent neurons

Although information in tactile afferent neurons represented by firing rates has been studied extensively over nearly a century, recent studies suggest that precise spike timing might be more important than firing rates. Here, we used information theory to compare the information content in the discharges of 92 tactile afferents distributed over the entire terminal segment of the fingertip when it was contacted by surfaces with different curvatures and force directions representative of everyday manipulations. Estimates of the information content with regard to curvature and force direction based on the precise timing of spikes were at least 2.2 times and 1.6 times, respectively, larger than that of spike counts during a 125 ms period of force increase. Moreover, the information regarding force direction based on the timing of the very first elicited spike was comparable with that provided by spike counts and more than twice as large with respect to object shape. For all encoding schemes, afferents terminating close to the stimulation site tended to convey more information about surface curvature than more remote afferents that tended to convey more information about force direction. Finally, coding schemes based on spike timing and spike counts overall contributed mostly independent information. We conclude that information about tactile stimuli in timing of spikes in primary afferents, even if limited to the first spikes, surpasses that contained in firing rates and that these measures of afferents' responses might capture different aspects of the stimulus.

Neural coding and contextual influences in the whisker system

A fundamental problem in neuroscience, to which Prof. Segundo has made seminal contributions, is to understand how action potentials represent events in the external world. The aim of this paper is to review the issue of neural coding in the context of the rodent whiskers, an increasingly popular model system. Key issues we consider are: the role of spike timing; mechanisms of spike timing; decoding and context-dependence. Significant insight has come from the development of rigorous, information theoretic frameworks for tackling these questions, in conjunction with suitably designed experiments. We review both the theory and experimental studies. In contrast to the classical view that neurons are noisy and unreliable, it is becoming clear that many neurons in the subcortical whisker pathway are remarkably reliable and, by virtue of spike timing with millisecond-precision, have high bandwidth for conveying sensory information. In this way, even small (approximately 200 neuron) subcortical modules are able to support the sensory processing underlying sophisticated whisker-dependent behaviours. Future work on neural coding in cortex will need to consider new findings that responses are highly dependent on context, including behavioural and internal states.

Mutual information expansion for studying the role of correlations in population codes: how important are autocorrelations?

The role of correlations in the activity of neural populations responding to a set of stimuli can be studied within an information theory framework. Regardless of whether one approaches the problem from an encoding or decoding perspective, the main measures used to study the role of correlations can be derived from a common source: the expansion of the mutual information. Two main formalisms of mutual information expansion have been proposed: the series expansion and the exact breakdown. Here we clarify that these two formalisms have a different representation of autocorrelations, so that even when the total information estimated differs by less than 1%, individual terms can diverge. More precisely, the series expansion explicitly evaluates the informational contribution of autocorrelations in the count of spikes, that is, count autocorrelations, whereas the exact breakdown does not. We propose a new formalism of mutual information expansion, the Poisson exact breakdown, which introduces Poisson equivalents in order to explicitly evaluate the informational contribution of count autocorrelations with no approximation involved. Because several widely employed manipulations of spike trains, most notably binning and pooling, alter the structure of count autocorrelations, the new formalism can provide a useful general framework for studying the role of correlations in population codes.

Testing a neural coding hypothesis using surrogate data

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

Tight data-robust bounds to mutual information combining shuffling and model selection techniques

The estimation of the information carried by spike times is crucial for a quantitative understanding of brain function, but it is difficult because of an upward bias due to limited experimental sampling. We present new progress, based on two basic insights, on reducing the bias problem. First, we show that by means of a careful application of data-shuffling techniques, it is possible to cancel almost entirely the bias of the noise entropy, the most biased part of information. This procedure provides a new information estimator that is much less biased than the standard direct one and has similar variance. Second, we use a nonparametric test to determine whether all the information encoded by the spike train can be decoded assuming a low-dimensional response model. If this is the case, the complexity of response space can be fully captured by a small number of easily sampled parameters. Combining these two different procedures, we obtain a new class of precise estimators of information quantities, which can provide data-robust upper and lower bounds to the mutual information. These bounds are tight even when the number of trials per stimulus available is one order of magnitude smaller than the number of possible responses. The effectiveness and the usefulness of the methods are tested through applications to simulated data and recordings from somatosensory cortex. This application shows that even in the presence of strong correlations, our methods constrain precisely the amount of information encoded by real spike trains recorded in vivo.

Neuronal activity in rat barrel cortex underlying texture discrimination

Rats and mice palpate objects with their whiskers to generate tactile sensations. This form of active sensing endows the animals with the capacity for fast and accurate texture discrimination. The present work is aimed at understanding the nature of the underlying cortical signals. We recorded neuronal activity from barrel cortex while rats used their whiskers to discriminate between rough and smooth textures. On whisker contact with either texture, firing rate increased by a factor of two to ten. Average firing rate was significantly higher for rough than for smooth textures, and we therefore propose firing rate as the fundamental coding mechanism. The rat, however, cannot take an average across trials, but must make an immediate decision using the signals generated on each trial. To estimate single-trial signals, we calculated the mutual information between stimulus and firing rate in the time window leading to the rat's observed choice. Activity during the last 75 ms before choice transmitted the most informative signal; in this window, neuronal clusters carried, on average, 0.03 bits of information about the stimulus on trials in which the rat's behavioral response was correct. To understand how cortical activity guides behavior, we examined responses in incorrect trials and found that, in contrast to correct trials, neuronal firing rate was higher for smooth than for rough textures. Analysis of high-speed films suggested that the inappropriate signal on incorrect trials was due, at least in part, to nonoptimal whisker contact. In conclusion, these data suggest that barrel cortex firing rate on each trial leads directly to the animal's judgment of texture.

How cortical activity contributes to sensation is among biology's oldest problems. We studied the nature of the cortical representations underlying judgments of texture in rats. The rodent whisker sensory system is particularly intriguing because it is “active”: the animal generates sensory signals by palpating objects through self-controlled whisker motion (just as we move our fingertips along surfaces to measure their tactile features). Rats touched rough or smooth textures with their whiskers and turned left or right for a reward according to the texture identity. Monitoring behavior with high-speed videography, we have found that on trials when the rat correctly identified the stimulus, the firing rate of cortical neurons varies during a window of a few hundred milliseconds before making a decision according to the contacted texture: high for rough and lower for smooth. This firing-rate code is reversed on error trials (lower for rough than smooth). So when cortical neurons report the wrong stimulus, the rat, “feeling” the signals of its cortical neurons, fails to identify the stimulus. We conclude that barrel cortex firing rate on each trial predicts the animal's judgment of texture. This experiment begins to elucidate which features of cortical activity underlie the animal's capacity for tactile sensory discrimination.

Rats palpate objects with their whiskers to perceive texture. Their judgment of texture is predicted by the firing rate of neurons in the somatosensory cortex.

Coding processes involved in the cortical representation of complex tactile stimuli

To understand how information is coded in the primary somatosensory cortex (S1) we need to decipher the relationship between neural activity and tactile stimuli. Such a relationship can be formally measured by mutual information. The present study was designed to determine how S1 neuronal populations code for the multidimensional kinetic features (i.e. random, time-varying patterns of force) of complex tactile stimuli, applied at different locations of the rat forepaw. More precisely, the stimulus localization and feature extraction were analyzed as two independent processes, using both rate coding and temporal coding strategies. To model the process of stimulus kinetic feature extraction, multidimensional stimuli were projected onto lower dimensional subspace and then clustered according to their similarity. Different combinations of stimuli clustering were applied to differentiate each stimulus identification process. Information analyses show that both processes are synergistic, this synergy is enhanced within the temporal coding framework. The stimulus localization process is faster than the stimulus feature extraction process. The latter provides more information quantity with rate coding strategy, whereas the localization process maximizes the mutual information within the temporal coding framework. Therefore, combining mutual information analysis with robust clustering of complex stimuli provides a framework to study neural coding mechanisms related to complex stimuli discrimination.

Lack of Spike-Count and Spike-Time Correlations in the Substantia Nigra Reticulata Despite Overlap of Neural Responses

Previous studies of single neurons in the substantia nigra reticulata (SNr) have shown that many of them respond to similar events. These results, as well as anatomical studies, suggest that SNr neurons share inputs and thus may have correlated activity. Different types of correlation can exist between pairs of neurons. These are traditionally classified as either spike-count (“signal” and “noise”) or spike-timing (spike-to-spike and joint peristimulus time histograms) correlations. These measures of neuronal correlation are partially independent and have different implications. Our purpose was to probe the computational characteristics of the basal ganglia output nuclei through an analysis of these different types of correlation in the SNr. We carried out simultaneous multiple-electrode single-unit recordings in the SNr of two monkeys performing a probabilistic delayed visuomotor response task. A total of 113 neurons (yielding 355 simultaneously recorded pairs) were studied. Most SNr neurons responded to one or more task-related events, with instruction cue (69%) and reward (63%) predominating. Response-match analysis, comparing peristimulus time histograms, revealed a significant overlap between response vectors. However, no measure of average correlation differed significantly from zero. The lack of significant SNr spike-count population correlations appears to be an exceptional phenomenon in the brain, perhaps indicating unique event-related processing by basal ganglia output neurons to achieve better information transfer. The lack of spike-timing correlations suggests that the basal high-frequency discharge of SNr neurons is not driven by the common inputs and is probably intrinsic.

The role of correlations in direction and contrast coding in the primary visual cortex

The spiking activity of nearby cortical neurons is not independent. Numerous studies have explored the importance of this correlated responsivity for visual coding and perception, often by comparing the information conveyed by pairs of simultaneously recorded neurons with the sum of information provided by the respective individual cells. Pairwise responses typically provide slightly more information so that encoding is weakly synergistic. The simple comparison between pairwise and summed individual responses conflates several forms of correlation, however, making it impossible to judge the relative importance of synchronous spiking, basic tuning properties, and stimulus-independent and stimulus-dependent correlation. We have applied an information theoretic approach to this question, using the responses of pairs of neurons to drifting sinusoidal gratings of different directions and contrasts that have been recorded in the primary visual cortex of anesthetized macaque monkeys. Our approach allows us to break down the information provided by pairs of neurons into a number of components. This analysis reveals that, although synchrony is prevalent and informative, the additional information it provides frequently is offset by the redundancy arising from the similar tuning properties of the two cells. Thus coding is approximately independent with weak synergy or redundancy arising, depending on the similarity in tuning and the temporal precision of the analysis. We suggest that this would allow cortical circuits to enjoy the stability provided by having similarly tuned neurons without suffering the penalty of redundancy, because the associated information transmission deficit is compensated for by stimulus-dependent synchrony.

Dynamic switching of neural codes in networks with gap junctions

Population rate coding and temporal coding are common neural codes. Recent studies suggest that these two codes may be alternatively used in one neural system. Based on the fact that there are massive gap junctions in the brain, we explore how this switching behavior may be related to neural codes in networks of neurons connected by gap junctions. First, we show that under time-varying inputs, such neural networks show switching between synchronous and asynchronous states. Then, we quantify network dynamics by three mutual information measures to show that population rate coding carries more information in asynchronous states and temporal coding does so in synchronous states.

Selectivity for Multiple Stimulus Features in Retinal Ganglion Cells

Under normal viewing conditions, retinal ganglion cells transmit to the brain an encoded version of the visual world. The retina parcels the visual scene into an array of spatiotemporal features, and each ganglion cell conveys information about a small set of these features. We study the temporal features represented by salamander retinal ganglion cells by stimulating with dynamic spatially uniform flicker and recording responses using a multi-electrode array. While standard reverse correlation methods determine a single stimulus feature—the spike-triggered average—multiple features can be relevant to spike generation. We apply covariance analysis to determine the set of features to which each ganglion cell is sensitive. Using this approach, we found that salamander ganglion cells represent a rich vocabulary of different features of a temporally modulated visual stimulus. Individual ganglion cells were sensitive to at least two and sometimes as many as six features in the stimulus. While a fraction of the cells can be described by a filter-and-fire cascade model, many cells have feature selectivity that has not previously been reported. These reverse models were able to account for 80–100% of the information encoded by ganglion cells.

Effects of noise correlations on information encoding and decoding

Response variability is often correlated across populations of neurons, and these noise correlations may play a role in information coding. In previous studies, this possibility has been examined from the encoding and decoding perspectives. Here we used d prime and related information measures to examine how studies of noise correlations from these two perspectives are related. We found that for a pair of neurons, the effect of noise correlations on information decoding can be zero when the effect of noise correlations on the information encoded obtains its largest positive or negative values. Furthermore, there can be no effect of noise correlations on the information encoded when it has an effect on information decoding. We also measured the effect of noise correlations on information encoding and decoding in simultaneously recorded neurons in the supplementary motor area to see how well d prime accounted for the information actually present in the neural responses and to see how noise correlations affected encoding and decoding in real data. These analyses showed that d prime provides an accurate measure of information encoding and decoding in our population of neurons. We also found that the effect of noise correlations on information encoding was somewhat larger than the effect of noise correlations on information decoding, but both were relatively small. Finally, as predicted theoretically, the effects of correlations were slightly greater for larger ensembles (3-8 neurons) than for pairs of neurons.