Neural population codes

In many regions of the brain, information is represented by patterns of activity occurring over populations of neurons. Understanding the encoding of information in neural population activity is important both for grasping the fundamental computations underlying brain function, and for interpreting signals that may be useful for the control of prosthetic devices. We concentrate on the representation of information in neurons with Poisson spike statistics, in which information is contained in the average spike firing rate. We analyze the properties of population codes in terms of the tuning functions that describe individual neuron behavior. The discussion centers on three computational questions: first, what information is encoded in a population; second, how does the brain compute using populations; and third, when is a population optimal? To answer these questions, we discuss several methods for decoding population activity in an experimental setting. We also discuss how computation can be performed within the brain in networks of interconnected populations. Finally, we examine questions of optimal design of population codes that may help to explain their particular form and the set of variables that are best represented. We show that for population codes based on neurons that have a Poisson distribution of spike probabilities, the behavior and computational properties of the code can be understood in terms of the tuning properties of individual cells.     

Information processing with population codes

Information is encoded in the brain by populations or clusters of cells, rather than by single cells. This encoding strategy is known as population coding. Here we review the standard use of population codes for encoding and decoding information, and consider how population codes can be used to support neural computations such as noise removal and nonlinear mapping. More radical ideas about how population codes may directly represent information about stimulus uncertainty are also discussed.     

Encoding time in neural dynamic regimes with distinct computational tradeoffs

Converging evidence suggests the brain encodes time in dynamic patterns of neural activity, including neural sequences, ramping activity, and complex dynamics. Most temporal tasks, however, require more than just encoding time, and can have distinct computational requirements including the need to exhibit temporal scaling, generalize to novel contexts, or robustness to noise. It is not known how neural circuits can encode time and satisfy distinct computational requirements, nor is it known whether similar patterns of neural activity at the population level can exhibit dramatically different computational or generalization properties. To begin to answer these questions, we trained RNNs on two timing tasks based on behavioral studies. The tasks had different input structures but required producing identically timed output patterns. Using a novel framework we quantified whether RNNs encoded two intervals using either of three different timing strategies: scaling, absolute, or stimulus-specific dynamics. We found that similar neural dynamic patterns at the level of single intervals, could exhibit fundamentally different properties, including, generalization, the connectivity structure of the trained networks, and the contribution of excitatory and inhibitory neurons. Critically, depending on the task structure RNNs were better suited for generalization or robustness to noise. Further analysis revealed different connection patterns underlying the different regimes. Our results predict that apparently similar neural dynamic patterns at the population level (e.g., neural sequences) can exhibit fundamentally different computational properties in regards to their ability to generalize to novel stimuli and their robustness to noise—and that these differences are associated with differences in network connectivity and distinct contributions of excitatory and inhibitory neurons. We also predict that the task structure used in different experimental studies accounts for some of the experimentally observed variability in how networks encode time.     

What we see is how we are: new paradigms in visual research

As most sensory modalities, the visual system needs to deal with very fast changes in the environment. Instead of processing all sensory stimuli, the brain is able to construct a perceptual experience by combining selected sensory input with an ongoing internal activity. Thus, the study of visual perception needs to be approached by examining not only the physical properties of stimuli, but also the brain's ongoing dynamical states onto which these perturbations are imposed. At least three different models account for this internal dynamics. One model is based on cardinal cells where the activity of few cells by itself constitutes the neuronal correlate of perception, while a second model is based on a population coding that states that the neuronal correlate of perception requires distributed activity throughout many areas of the brain. A third proposition, known as the temporal correlation hypothesis states that the distributed neuronal populations that correlate with perception, are also defined by synchronization of the activity on a millisecond time scale. This would serve to encode contextual information by defining relations between the features of visual objects. If temporal properties of neural activity are important to establish the neural mechanisms of perception, then the study of appropriate dynamical stimuli should be instrumental to determine how these systems operate. The use of natural stimuli and natural behaviors such as free viewing, which features fast changes of internal brain states as seen by motor markers, is proposed as a new experimental paradigm to study visual perception.     

Phase-Coherence Transitions and Communication in the Gamma Range between Delay-Coupled Neuronal Populations

Synchronization between neuronal populations plays an important role in information transmission between brain areas. In particular, collective oscillations emerging from the synchronized activity of thousands of neurons can increase the functional connectivity between neural assemblies by coherently coordinating their phases. This synchrony of neuronal activity can take place within a cortical patch or between different cortical regions. While short-range interactions between neurons involve just a few milliseconds, communication through long-range projections between different regions could take up to tens of milliseconds. How these heterogeneous transmission delays affect communication between neuronal populations is not well known. To address this question, we have studied the dynamics of two bidirectionally delayed-coupled neuronal populations using conductance-based spiking models, examining how different synaptic delays give rise to in-phase/anti-phase transitions at particular frequencies within the gamma range, and how this behavior is related to the phase coherence between the two populations at different frequencies. We have used spectral analysis and information theory to quantify the information exchanged between the two networks. For different transmission delays between the two coupled populations, we analyze how the local field potential and multi-unit activity calculated from one population convey information in response to a set of external inputs applied to the other population. The results confirm that zero-lag synchronization maximizes information transmission, although out-of-phase synchronization allows for efficient communication provided the coupling delay, the phase lag between the populations, and the frequency of the oscillations are properly matched.     

Comparing fluctuations of synaptic responses mediated via AMPA and NMDA receptor channels--implications for synaptic plasticity

Glutamate-releasing synapses are essential in fast neuronal signalling. Plasticity at these synapses is important for learning and memory as well as for the activity-dependent control of neuronal development. We have evaluated the trial-to-trial fluctuations of excitatory postsynaptic currents mediated by glutamate receptors of the AMPA and NMDA types in CA1 pyramidal cells. By using the whole cell patch clamp technique in brain slices from young rats, we have demonstrated that the relative variability of AMPA and NMDA receptor mediated responses, expressed as the coefficient of variation, is similar for these two types of responses [Brain Res. 800 (1998) 253-259]. The present paper summarizes and discusses these results in relation to current theories on hippocampal synaptic plasticity, especially with regard to the ideas of glutamate spillover and silent synapses. Our finding of a correspondence between AMPA and NMDA responses with respect to fluctuations is compatible with our previous finding of equal relative changes of the two during activity induced synaptic plasticity. However, the results argue against the glutamate spillover model according to which the effect of glutamate--and hence the induction of plasticity--may spread unspecifically between synapses. But how can silent synapses become functional if no spread of glutamate occurs and no initial signal is present to trigger the functionalization? Is it necessary that NMDA responses are present at these synapses, which are then silent merely with respect to AMPA receptors, or do other alternatives exist? Our discussion aims to elucidate these questions.     

High-Fidelity Coding with Correlated Neurons

Positive correlations in the activity of neurons are widely observed in the brain. Previous studies have shown these correlations to be detrimental to the fidelity of population codes, or at best marginally favorable compared to independent codes. Here, we show that positive correlations can enhance coding performance by astronomical factors. Specifically, the probability of discrimination error can be suppressed by many orders of magnitude. Likewise, the number of stimuli encoded—the capacity—can be enhanced more than tenfold. These effects do not necessitate unrealistic correlation values, and can occur for populations with a few tens of neurons. We further show that both effects benefit from heterogeneity commonly seen in population activity. Error suppression and capacity enhancement rest upon a pattern of correlation. Tuning of one or several effective parameters can yield a limit of perfect coding: the corresponding pattern of positive correlation leads to a ‘lock-in’ of response probabilities that eliminates variability in the subspace relevant for stimulus discrimination. We discuss the nature of this pattern and we suggest experimental tests to identify it.     

Intrinsic fluctuations within cortical systems account for intertrial variability in human behavior

The resting brain is not silent, but exhibits organized fluctuations in neuronal activity even in the absence of tasks or stimuli. This intrinsic brain activity persists during task performance and contributes to variability in evoked brain responses. What is unknown is if this intrinsic activity also contributes to variability in behavior. In the current fMRI study, we identify a relationship between human brain activity in the left somatomotor cortex and spontaneous trial-to-trial variability in button press force. We then demonstrate that 74% of this brain-behavior relationship is attributable to ongoing fluctuations in intrinsic activity similar to those observed during resting fixation. In addition to establishing a functional and behavioral significance of intrinsic brain activity, these results lend new insight into the origins of variability in human behavior.     

Reliable Neuronal Systems: The Importance of Heterogeneity

For every engineer it goes without saying: in order to build a reliable system we need components that consistently behave precisely as they should. It is also well known that neurons, the building blocks of brains, do not satisfy this constraint. Even neurons of the same type come with huge variances in their properties and these properties also vary over time. Synapses, the connections between neurons, are highly unreliable in forwarding signals. In this paper we argue that both these fact add variance to neuronal processes, and that this variance is not a handicap of neural systems, but that instead predictable and reliable functional behavior of neural systems depends crucially on this variability. In particular, we show that higher variance allows a recurrently connected neural population to react more sensitively to incoming signals, and processes them faster and more energy efficient. This, for example, challenges the general assumption that the intrinsic variability of neurons in the brain is a defect that has to be overcome by synaptic plasticity in the process of learning.     

Sensory processing and the network mechanisms for reading neuronal population codes

In many neuronal systems, information appears to be represented in the activity of populations of neurons. Such neuronal population codes must also be read out, or interpreted, by downstream networks. Recent studies in both vertebrate and invertebrate systems have begun to elucidate some of the general mechanisms underlying these processes. Directed behaviors, that involve a directional response to a directional sensory input, have been a particularly useful context for these studies because, among other things, their input-output relationship is easily defined and experimentally controlled. We have recently shown that the neuronal network underlying a directed behavior in the medicinal leech utilizes a specific population coding scheme based on a neuronal population vector. A population vector of mechanosensory neuron activity correlates well with behavioral output and the connectivity of the downstream network is well suited for accurately reading out this population code. Accepted: 17 April 1999     

Spreading depression sends microglia on Lévy flights

Spreading depression (SD) is thought to cause migraine aura, and perhaps migraine, and includes a transient loss of synaptic activity preceded and followed by increased neuronal excitability. Activated microglia influence neuronal activity and play an important role in homeostatic synaptic scaling via release of cytokines. Furthermore, enhanced neuronal function activates microglia to not only secrete cytokines but also to increase the motility of their branches, with somata remaining stationary. While SD also increases the release of cytokines from microglia, the effects on microglial movement from its synaptic activity fluctuations are unknown. Accordingly, we used time-lapse imaging of rat hippocampal slice cultures to probe for microglial movement associated with SD. We observed that in uninjured brain whole microglial cells moved. The movements were well described by the type of Lévy flight known to be associated with an optimal search pattern. Hours after SD, when synaptic activity rose, microglial cell movement was significantly increased. To test how synaptic activity influenced microglial movement, we enhanced neuronal activity with chemical long-term potentiation or LPS and abolished it with TTX. We found that microglial movement was significantly decreased by enhanced neuronal activity and significantly increased by activity blockade. Finally, application of glutamate and ATP to mimic restoration of synaptic activity in the presence of TTX stopped microglial movement that was otherwise seen with TTX. Thus, synaptic activity retains microglial cells in place and an absence of synaptic activity sends them off to influence wider expanses of brain. Perhaps increased microglial movements after SD are a long-lasting, and thus maladaptive, response in which these cells increase neuronal activity via contact or paracrine signaling, which results in increased susceptibility of larger brain areas to SD. If true, then targeting mechanisms that retard activity-dependent microglial Lévy flights may be a novel means to reduce susceptibility to migraine.     

Decoding defensive systems

Our understanding of the neuronal circuits and mechanisms of defensive systems has been primarily dominated by studies focusing on the contribution of individual cells in the processing of threat-predictive cues, defensive responses, the extinction of such responses and the contextual modulation of threat-related behavior. These studies have been key in establishing threat-related circuits and mechanisms. Yet, they fall short in answering long-standing questions related to the integrative processing of distinct threatening cues, behavioral states induced by threat-related events, or the bridging from sensory processing of threat-related cues to specific defensive responses. Recent conceptual and technical developments has allowed the monitoring of large populations of neurons, which in addition to advanced analytic tools, have improved our understanding of how collective neuronal activity supports threat-related behaviors. In this review, we discuss the current knowledge of neuronal population codes within threat-related networks, in the context of aversive motivated behavior and the study of defensive systems.     

Uncovering spatial topology represented by rat hippocampal population neuronal codes

Hippocampal population codes play an important role in representation of spatial environment and spatial navigation. Uncovering the internal representation of hippocampal population codes will help understand neural mechanisms of the hippocampus. For instance, uncovering the patterns represented by rat hippocampus (CA1) pyramidal cells during periods of either navigation or sleep has been an active research topic over the past decades. However, previous approaches to analyze or decode firing patterns of population neurons all assume the knowledge of the place fields, which are estimated from training data a priori. The question still remains unclear how can we extract information from population neuronal responses either without a priori knowledge or in the presence of finite sampling constraint. Finding the answer to this question would leverage our ability to examine the population neuronal codes under different experimental conditions. Using rat hippocampus as a model system, we attempt to uncover the hidden "spatial topology" represented by the hippocampal population codes. We develop a hidden Markov model (HMM) and a variational Bayesian (VB) inference algorithm to achieve this computational goal, and we apply the analysis to extensive simulation and experimental data. Our empirical results show promising direction for discovering structural patterns of ensemble spike activity during periods of active navigation. This study would also provide useful insights for future exploratory data analysis of population neuronal codes during periods of sleep.     

Under Construction: Building the Macromolecular Superstructure and Signaling Components of an Electrical Synapse

A great deal is now known about the protein components of tight junctions and adherens junctions, as well as how these are assembled. Less is known about the molecular framework of gap junctions, but these also have membrane specializations and are subject to regulation of their assembly and turnover. Thus, it is reasonable to consider that these three types of junctions may share macromolecular commonalities. Indeed, the tight junction scaffolding protein zonula occluden-1 (ZO-1) is also present at adherens and gap junctions, including neuronal gap junctions. On the basis of these earlier observations, we more recently found that two additional proteins, AF6 and MUPP1, known to be associated with ZO-1 at tight and adherens junctions, are also components of neuronal gap junctions in rodent brain and directly interact with connexin36 (Cx36) that forms these junctions. Here, we show by immunofluorescence labeling that the cytoskeletal-associated protein cingulin, commonly found at tight junctions, is also localized at neuronal gap junctions throughout the central nervous system. In consideration of known functions related to ZO-1, AF6, MUPP1, and cingulin, our results provide a context in which to examine functional relationships between these proteins at Cx36-containing electrical synapses in brain--specifically, how they may contribute to regulation of transmission at these synapses, and how they may govern gap junction channel assembly and/or disassembly.     

A shift in sensory processing that enables the developing human brain to discriminate touch from pain

When and how infants begin to discriminate noxious from innocuous stimuli is a fundamental question in neuroscience [1]. However, little is known about the development of the necessary cortical somatosensory functional prerequisites in the intact human brain. Recent studies of developing brain networks have emphasized the importance of transient spontaneous and evoked neuronal bursting activity in the formation of functional circuits [2, 3]. These neuronal bursts are present during development and precede the onset of sensory functions [4, 5]. Their disappearance and the emergence of more adult-like activity are therefore thought to signal the maturation of functional brain circuitry [2, 4]. Here we show the changing patterns of neuronal activity that underlie the onset of nociception and touch discrimination in the preterm infant. We have conducted noninvasive electroencephalogram (EEG) recording of the brain neuronal activity in response to time-locked touches and clinically essential noxious lances of the heel in infants aged 28-45?weeks gestation. We show a transition in brain response following tactile and noxious stimulation from nonspecific, evenly dispersed neuronal bursts to modality-specific, localized, evoked potentials. The results suggest that specific neural circuits necessary for discrimination between touch and nociception emerge from 35-37?weeks gestation in the human brain.     

Making scents of olfactory neurogenesis.

Olfaction was long considered to belong more to the realm of art than to that of science. As a result, how the brain perceives, discriminates, and recognizes odorant molecules is still a mystery. Recent progress has nonetheless been made at early stages of the olfactory pathway when olfactory studies entered into the molecular era to elucidate the first contact of an odor molecule with a receptor. Our group focuses on the analysis of odor information in the olfactory bulb, the first processing relay in the mammalian brain. Using this model, we are attempting to decipher the code for odorant information. Furthermore, the olfactory bulb also provides an attractive model to investigate neuronal proliferation, differentiation, migration, and neuronal death, processes involving an interplay between genetic and epigenetic influences. Finally, our goal is to explore the possible consequences of the olfactory bulb plasticity, in olfactory performance. For these purposes, we aim to combine morphological, electrophysiological and behavioral approaches to investigate: (1) how the olfactory bulb processes odor molecule information, (2) how neural precursors differentiate into olfactory bulb interneurons, (3) how these newly-generated neurons integrate into an operational neural network, (4) what role they play in the adult olfactory bulb, and (5) how are basic olfactory functions maintained in such a sensory system subjected to continuous renewal of a large percentage of its neuronal population. These questions should provide new fuel for the molecular and cellular bases of sensory perception and shed light onto cellular bases of learning and memory.     

Real time computation: zooming in on population codes

Information processing in nervous systems intricately combines computation at the neuronal and network levels. Many computations may be envisioned as sequences of signal processing steps along some pathway. How can information encoded by single cells be mapped onto network population codes, and how do different modules or layers in the computation synchronize their communication and computation? These fundamental questions are particularly severe when dealing with real time streams of inputs. Here we study this problem within the context of a minimal signal perception task. In particular, we encode neuronal information by externally applying a space- and time-localized stimulus to individual neurons within a network. We show that a pulse-coupled recurrent neural network can successfully handle this task in real time, and obeys three key requirements: (i) stimulus dependence, (ii) initial-conditions independence, and (iii) accessibility by a readout mechanism. In particular, we suggest that the network's overall level of activity can be used as a temporal cue for a robust readout mechanism. Within this framework, the network can rapidly map a local stimulus onto a population code that can then be reliably read out during some narrow but well defined window of time.     

Neuronal Adaptation Translates Stimulus Gaps into a Population Code

Neurons in sensory pathways exhibit a vast multitude of adaptation behaviors, which are assumed to aid the encoding of temporal stimulus features and provide the basis for a population code in higher brain areas. Here we study the transition to a population code for auditory gap stimuli both in neurophysiological recordings and in a computational network model. Independent component analysis (ICA) of experimental data from the inferior colliculus of Mongolian gerbils reveals that the network encodes different gap sizes primarily with its population firing rate within 30 ms after the presentation of the gap, where longer gap size evokes higher network activity. We then developed a computational model to investigate possible mechanisms of how to generate the population code for gaps. Phenomenological (ICA) and functional (discrimination performance) analyses of our simulated networks show that the experimentally observed patterns may result from heterogeneous adaptation, where adaptation provides gap detection at the single neuron level and neuronal heterogeneity ensures discriminable population codes for the whole range of gap sizes in the input. Furthermore, our work suggests that network recurrence additionally enhances the network''s ability to provide discriminable population patterns.     

Failure of adaptive self-organized criticality during epileptic seizure attacks

Critical dynamics are assumed to be an attractive mode for normal brain functioning as information processing and computational capabilities are found to be optimal in the critical state. Recent experimental observations of neuronal activity patterns following power-law distributions, a hallmark of systems at a critical state, have led to the hypothesis that human brain dynamics could be poised at a phase transition between ordered and disordered activity. A so far unresolved question concerns the medical significance of critical brain activity and how it relates to pathological conditions. Using data from invasive electroencephalogram recordings from humans we show that during epileptic seizure attacks neuronal activity patterns deviate from the normally observed power-law distribution characterizing critical dynamics. The comparison of these observations to results from a computational model exhibiting self-organized criticality (SOC) based on adaptive networks allows further insights into the underlying dynamics. Together these results suggest that brain dynamics deviates from criticality during seizures caused by the failure of adaptive SOC.