Nonlinear modeling of neural population dynamics for hippocampal prostheses

Developing a neural prosthesis for the damaged hippocampus requires restoring the transformation of population neural activities performed by the hippocampal circuitry. To bypass a damaged region, output spike trains need to be predicted from the input spike trains and then reinstated through stimulation. We formulate a multiple-input, multiple-output (MIMO) nonlinear dynamic model for the input–output transformation of spike trains. In this approach, a MIMO model comprises a series of physiologically-plausible multiple-input, single-output (MISO) neuron models that consist of five components each: (1) feedforward Volterra kernels transforming the input spike trains into the synaptic potential, (2) a feedback kernel transforming the output spikes into the spike-triggered after-potential, (3) a noise term capturing the system uncertainty, (4) an adder generating the pre-threshold potential, and (5) a threshold function generating output spikes. It is shown that this model is equivalent to a generalized linear model with a probit link function. To reduce model complexity and avoid overfitting, statistical model selection and cross-validation methods are employed to choose the significant inputs and interactions between inputs. The model is applied successfully to the hippocampal CA3–CA1 population dynamics. Such a model can serve as a computational basis for the development of hippocampal prostheses.     

Spike timing in auditory‐nerve fibers during spontaneous activity and phase locking

In vertebrates, all acoustic information transmitted from the inner ear to the central auditory system is relayed by primary auditory afferents (auditory‐nerve fibers; ANFs). These neurons are also the most peripheral elements to use action potentials (spikes) to encode the acoustic information. Here, we review what is known about the spiking of ANFs during spontaneous activity, when spike timing might be regarded as largely random, and during stimulation by low‐frequency sounds, when spikes are phase locked to the stimulus waveform, a phenomenon generally considered a hallmark of temporal precision and speed in the auditory system. We focus on mammals, in which each ANF is driven by a single ribbon synapse in a single receptor cell, but also cover relevant research on ANFs of vertebrates from other classes. For spontaneous activity, we highlight several spike‐history effects in interspike interval distributions, hazard‐rate functions, serial interval correlations, and spike‐count statistics. We also review models that have attempted to account for these properties. For phase locking, we focus on the responses to low‐frequency tones, rather than to low‐frequency components of broadband signals such as noise or clicks. We critically review the measures commonly used to quantify phase locking and urge caution when interpreting such measures with respect to spike‐timing precision. We also review the dependence of phase locking on stimulus amplitude and frequency. Finally, we identify some open questions.     

Short-term plasticity optimizes synaptic information transmission

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

Rate maintenance and resonance in the entorhinal cortex

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

A synfire chain in layered coincidence detectors with random synaptic delays.

In this paper we analyze a synfire chain in a spiking neuron network. We also employ a coincidence-detector model showing the characteristics of temporal information processing more directly than the integrate-and-fire (I&F) model often discussed in the literature. There are two sources of randomness in a feed-forward network, however, only randomness in input spikes has attracted the attention of researchers and the randomness in synaptic delays has largely been ignored. Theoretical analyses of the synfire chain in I&F neurons without randomness in synaptic delays have shown that the dynamics of pulse packets can be viewed as a shift of the membrane potential distribution made by random noise input spikes. We introduce jittered synaptic delays instead of random noise inputs in a network of coincidence detectors and show that the network has almost the same dynamics as that of the I&F neurons. The distribution of the output spikes can be approximately described by an ordinary differential equation useful in understanding the dynamics of the pulse packets.     

How the brain uses time to represent and process visual information(1)

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

Dynamics of information and emergent computation in generic neural microcircuit models

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

The effect of noise correlations in populations of diversely tuned neurons

The amount of information encoded by networks of neurons critically depends on the correlation structure of their activity. Neurons with similar stimulus preferences tend to have higher noise correlations than others. In homogeneous populations of neurons, this limited range correlation structure is highly detrimental to the accuracy of a population code. Therefore, reduced spike count correlations under attention, after adaptation, or after learning have been interpreted as evidence for a more efficient population code. Here, we analyze the role of limited range correlations in more realistic, heterogeneous population models. We use Fisher information and maximum-likelihood decoding to show that reduced correlations do not necessarily improve encoding accuracy. In fact, in populations with more than a few hundred neurons, increasing the level of limited range correlations can substantially improve encoding accuracy. We found that this improvement results from a decrease in noise entropy that is associated with increasing correlations if the marginal distributions are unchanged. Surprisingly, for constant noise entropy and in the limit of large populations, the encoding accuracy is independent of both structure and magnitude of noise correlations.     

How the brain uses time to represent and process visual information

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

Editing trains of action potentials from multi-electrode arrays

When recording from multi-electrode arrays, only a short period around the time of a threshold crossing is generally saved for later analysis. Then, waveforms are often sorted automatically to identify templates of spikes from individual neurons near an electrode. As spikes sum from different neurons and noise is present, some spikes may be missed and others erroneously accepted. This paper describes methods for identifying and correcting errors in recorded spike trains to recover the pattern of spikes from each neuron as faithfully as possible. These methods are complementary to, but distinct from methods to reconstruct waveforms that arise from summation of individual templates that overlap one another. Our methods are based on the local statistics of the firing rates or inter-spike intervals and the methods work best for neurons that fire regularly (small standard deviation relative to the mean interval). First, we test whether accepting more spikes, whose waveforms are close to the templates that have been identified, will increase the regularity or smoothness of the firing rates. Then, after accepting spikes that increase regularity, we test whether individual intervals are sufficiently longer (or shorter) than their neighbors to identify spikes that have been omitted (or accepted) erroneously. The methods are tested on simulated spike trains, where spikes have been inserted or deleted at random, and on spike trains recorded from multi-electrode arrays in dorsal root ganglia of cats walking on a treadmill.     

Face identification using one spike per neuron: resistance to image degradations.

The short response latencies of face selective neurons in the inferotemporal cortex impose major constraints on models of visual processing. It appears that visual information must essentially propagate in a feed-forward fashion with most neurons only having time to fire one spike. We hypothesize that flashed stimuli can be encoded by the order of firing of ganglion cells in the retina and propose a neuronal mechanism, that could be related to fast shunting inhibition, to decode such information. Based on these assumptions, we built a three-layered neural network of retino-topically organized neuronal maps. We showed, by using a learning rule involving spike timing dependant plasticity, that neuronal maps in the output layer can be trained to recognize natural photographs of faces. Not only was the model able to generalize to novel views of the same faces, it was also remarkably resistant to image noise and reductions in contrast.     

Energy‐efficient encoding by shifting spikes in neocortical neurons

The speed of computations in neocortical networks critically depends on the ability of populations of spiking neurons to rapidly detect subtle changes in the input and translate them into firing rate changes. However, high sensitivity to perturbations may lead to explosion of noise and increased energy consumption. Can neuronal networks reconcile the requirements for high sensitivity, operation in a low‐noise regime, and constrained energy consumption? Using intracellular recordings in slices from the rat visual cortex, we show that layer 2/3 pyramidal neurons are highly sensitive to minor input perturbations. They can change their population firing rate in response to small artificial excitatory postsynaptic currents (aEPSCs) immersed in fluctuating noise very quickly, within 2–2.5 ms. These quick responses were mediated by the generation of new, additional action potentials (APs), but also by shifting spikes into the response peak. In that latter case, the spike count increase during the peak and the decrease after the peak cancelled each other, thus producing quick responses without increases in total spike count and associated energy costs. The contribution of spikes from one or the other source depended on the aEPSCs timing relative to the waves of depolarization produced by ongoing activity. Neurons responded by shifting spikes to aEPSCs arriving at the beginning of a depolarization wave, but generated additional spikes in response to aEPSCs arriving towards the end of a wave. We conclude that neuronal networks can combine high sensitivity to perturbations and operation in a low‐noise regime. Moreover, certain patterns of ongoing activity favor this combination and energy‐efficient computations.     

Classification of neuronal spikes over the reconstructed phase space

Spike information is beneficial to correlate neuronal activity to various stimuli or determine target neural area for deep brain stimulation. Data clustering based on neuronal spike features provides a way to separate spikes generated from different neurons. Nevertheless, some spikes are aligned incorrectly due to spike deformation or noise interference, thereby reducing the accuracy of spike classification. In the present study, we proposed unsupervised spike classification over the reconstructed phase spaces of neuronal spikes in which the derived phase space portraits are less affected by alignment deviations. Principal component analysis was used to extract major principal components of the portrait features and k-means clustering was used to distribute neuronal spikes into various clusters. Finally, similar clusters were iteratively merged based upon inter-cluster portrait differences.     

Automated optimal detection and classification of neural action potentials in extra-cellular recordings

Determination of single unit spikes from multiunit spike trains plays a critical role in neurophysiological coding studies which require information about the precise timing of events underlying the neural codes that are the basis of behavior. Searching for optimal spike detection strategies has therefore been the focus of many studies over the past two decades. In this study we describe and implement an algorithm for the optimal real time detection and classification of neural spikes. The algorithm consists of three steps: noise analysis, template generation and real time detection and classification. The first step involves estimating the background noise statistics. In this step, a "cap-fitting" algorithm is used to automatically detect a spike free segment and then the mean, standard deviation and autocorrelation function of the noise are computed. The second step involves generating optimal templates of the spikes from a segment containing both noise and multiunit activity. In this step, a generalized matched filter is used to isolate a set of preliminary spikes from the noise. The first principal component of previously recorded templates is used as the deterministic signal. The preliminary spikes are then clustered in a sub-space spanned by the first three principal components to form new templates. The third step uses these templates for the real time spike detection and classification. In this step the incoming data are projected into a lower dimensional space that is designed to maximally separate the signal from the noise energy. This algorithm provides an accurate estimate of the signal to noise ratio and provides an accurate estimate of spike times and spike shapes.     

Neural networks a century after Cajal

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

Schaffer-specific local field potentials reflect discrete excitatory events at gamma frequency that may fire postsynaptic hippocampal CA1 units

Information processing and exchange between brain nuclei are made through spike series sent by individual neurons in highly irregular temporal patterns. Synchronization in cell assemblies, proposed as a network language for internal neural representations, still has little experimental support. We use a novel technique to extract pathway-specific local field potentials (LFPs) in the hippocampus to explore the ongoing temporal structure of a single presynaptic input, the CA3 Schaffer pathway, and its contribution to the spontaneous output of CA1 units in anesthetized rat. We found that Schaffer-specific LFPs are composed of a regular succession of pulse-like excitatory packages initiated by spontaneous clustered firing of CA3 pyramidal cells to which individual units contribute variably. A fraction of these packages readily induce firing of CA1 pyramidal cells and interneurons, the so-called Schaffer-driven spikes, revealing the presynaptic origin in the output code of single CA1 units. The output of 70% of CA1 pyramidal neurons contains up to 10% of such spikes. Our results suggest a hierarchical internal operation of the CA3 region based on sequential oscillatory activation of pyramidal cell assemblies whose activity partly gets in the output code at the next station. We conclude that CA1 output may directly reflect the activity of specific ensembles of CA3 neurons. Thus, the fine temporal structure of pathway-specific LFPs, as an accurate readout of the activity of a presynaptic population, is useful in searching for hidden presynaptic code in irregular spikes series of individual neurons and assemblies.     

Synapses as dynamic memory buffers

This article throws new light on the possible role of synapses in information transmission through theoretical analysis and computer simulations. We show that the internal dynamic state of a synapse may serve as a transient memory buffer that stores information about the most recent segment of the spike train that was previously sent to this synapse. This information is transmitted to the postsynaptic neuron through the amplitudes of the postsynaptic response for the next few spikes. In fact, we show that most of this information about the preceding spike train is already contained in the postsynaptic response for just two additional spikes. It is demonstrated that the postsynaptic neuron receives simultaneously information about the specific type of synapse which has transmitted these pulses. In view of recent findings by Gupta et al. [Science, 287 (2000) 273] that different types of synapses are characteristic for specific types of presynaptic neurons, the postsynaptic neuron receives in this way partial knowledge about the identity of the presynaptic neuron from which it has received information. Our simulations are based on recent data about the dynamics of GABAergic synapses. We show that the relatively large number of synaptic release sites that make up a GABAergic synaptic connection makes these connections suitable for such complex information transmission processes.     

Interictal spike EEG source analysis in hypothalamic hamartoma epilepsy.

OBJECTIVE: The epilepsy associated with the hypothalamic hamartomas constitutes a syndrome with peculiar seizures, usually refractory to medical therapy, mild cognitive delay, behavioural problems and multifocal spike activity in the scalp electroencephalogram (EEG). The cortical origin of spikes has been widely assumed but not specifically demonstrated. METHODS: We present results of a source analysis of interictal spikes from 4 patients (age 2-25 years) with epilepsy and hypothalamic hamartoma, using EEG scalp recordings (32 electrodes) and realistic boundary element models constructed from volumetric magnetic resonance imaging (MRIs). Multifocal spike activity was the most common finding, distributed mainly over the frontal and temporal lobes. A spike classification based on scalp topography was done and averaging within each class performed to improve the signal to noise ratio. Single moving dipole models were used, as well as the Rap-MUSIC algorithm. RESULTS: All spikes with good signal to noise ratio were best explained by initial deep sources in the neighbourhood of the hamartoma, with late sources located in the cortex. Not a single patient could have his spike activity explained by a combination of cortical sources. CONCLUSIONS: Overall, the results demonstrate a consistent origin of spike activity in the subcortical region in the neighbourhood of the hamartoma, with late spread to cortical areas.