Weak pairwise correlations imply strongly correlated network states in a neural population

Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher order interactions among large groups of elements play an important role. In the vertebrate retina, we show that weak correlations between pairs of neurons coexist with strongly collective behavior in the responses of ten or more neurons. Surprisingly, we find that this collective behavior is described quantitatively by models that capture the observed pairwise correlations but assume no higher order interactions. These maximum entropy models are equivalent to Ising models, and predict that larger networks are completely dominated by correlation effects. This suggests that the neural code has associative or error-correcting properties, and we provide preliminary evidence for such behavior. As a first test for the generality of these ideas, we show that similar results are obtained from networks of cultured cortical neurons.Comment: Full account of work presented at the conference on Computational and Systems Neuroscience (COSYNE), 17-20 March 2005, in Salt Lake City, Utah (http://cosyne.org

Incremental Mutual Information: A New Method for Characterizing the Strength and Dynamics of Connections in Neuronal Circuits

Understanding the computations performed by neuronal circuits requires characterizing the strength and dynamics of the connections between individual neurons. This characterization is typically achieved by measuring the correlation in the activity of two neurons. We have developed a new measure for studying connectivity in neuronal circuits based on information theory, the incremental mutual information (IMI). By conditioning out the temporal dependencies in the responses of individual neurons before measuring the dependency between them, IMI improves on standard correlation-based measures in several important ways: 1) it has the potential to disambiguate statistical dependencies that reflect the connection between neurons from those caused by other sources (e. g. shared inputs or intrinsic cellular or network mechanisms) provided that the dependencies have appropriate timescales, 2) for the study of early sensory systems, it does not require responses to repeated trials of identical stimulation, and 3) it does not assume that the connection between neurons is linear. We describe the theory and implementation of IMI in detail and demonstrate its utility on experimental recordings from the primate visual system

Information transmission in oscillatory neural activity

Periodic neural activity not locked to the stimulus or to motor responses is usually ignored. Here, we present new tools for modeling and quantifying the information transmission based on periodic neural activity that occurs with quasi-random phase relative to the stimulus. We propose a model to reproduce characteristic features of oscillatory spike trains, such as histograms of inter-spike intervals and phase locking of spikes to an oscillatory influence. The proposed model is based on an inhomogeneous Gamma process governed by a density function that is a product of the usual stimulus-dependent rate and a quasi-periodic function. Further, we present an analysis method generalizing the direct method (Rieke et al, 1999; Brenner et al, 2000) to assess the information content in such data. We demonstrate these tools on recordings from relay cells in the lateral geniculate nucleus of the cat.Comment: 18 pages, 8 figures, to appear in Biological Cybernetic

Variability Measures of Positive Random Variables

During the stationary part of neuronal spiking response, the stimulus can be encoded in the firing rate, but also in the statistical structure of the interspike intervals. We propose and discuss two information-based measures of statistical dispersion of the interspike interval distribution, the entropy-based dispersion and Fisher information-based dispersion. The measures are compared with the frequently used concept of standard deviation. It is shown, that standard deviation is not well suited to quantify some aspects of dispersion that are often expected intuitively, such as the degree of randomness. The proposed dispersion measures are not entirely independent, although each describes the interspike intervals from a different point of view. The new methods are applied to common models of neuronal firing and to both simulated and experimental data

Effects of Active Conductance Distribution over Dendrites on the Synaptic Integration in an Identified Nonspiking Interneuron

The synaptic integration in individual central neuron is critically affected by how active conductances are distributed over dendrites. It has been well known that the dendrites of central neurons are richly endowed with voltage- and ligand-regulated ion conductances. Nonspiking interneurons (NSIs), almost exclusively characteristic to arthropod central nervous systems, do not generate action potentials and hence lack voltage-regulated sodium channels, yet having a variety of voltage-regulated potassium conductances on their dendritic membrane including the one similar to the delayed-rectifier type potassium conductance. It remains unknown, however, how the active conductances are distributed over dendrites and how the synaptic integration is affected by those conductances in NSIs and other invertebrate neurons where the cell body is not included in the signal pathway from input synapses to output sites. In the present study, we quantitatively investigated the functional significance of active conductance distribution pattern in the spatio-temporal spread of synaptic potentials over dendrites of an identified NSI in the crayfish central nervous system by computer simulation. We systematically changed the distribution pattern of active conductances in the neuron's multicompartment model and examined how the synaptic potential waveform was affected by each distribution pattern. It was revealed that specific patterns of nonuniform distribution of potassium conductances were consistent, while other patterns were not, with the waveform of compound synaptic potentials recorded physiologically in the major input-output pathway of the cell, suggesting that the possibility of nonuniform distribution of potassium conductances over the dendrite cannot be excluded as well as the possibility of uniform distribution. Local synaptic circuits involving input and output synapses on the same branch or on the same side were found to be potentially affected under the condition of nonuniform distribution while operation of the major input-output pathway from the soma side to the one on the opposite side remained the same under both conditions of uniform and nonuniform distribution of potassium conductances over the NSI dendrite

Non-Linear Population Firing Rates and Voltage Sensitive Dye Signals in Visual Areas 17 and 18 to Short Duration Stimuli

Visual stimuli of short duration seem to persist longer after the stimulus offset than stimuli of longer duration. This visual persistence must have a physiological explanation. In ferrets exposed to stimuli of different durations we measured the relative changes in the membrane potentials with a voltage sensitive dye and the action potentials of populations of neurons in the upper layers of areas 17 and 18. For durations less than 100 ms, the timing and amplitude of the firing and membrane potentials showed several non-linear effects. The ON response became truncated, the OFF response progressively reduced, and the timing of the OFF responses progressively delayed the shorter the stimulus duration. The offset of the stimulus elicited a sudden and strong negativity in the time derivative of the dye signal. All these non-linearities could be explained by the stimulus offset inducing a sudden inhibition in layers II–III as indicated by the strongly negative time derivative of the dye signal. Despite the non-linear behavior of the layer II–III neurons the sum of the action potentials, integrated from the peak of the ON response to the peak of the OFF response, was almost linearly related to the stimulus duration

Variance and Autocorrelation of the Spontaneous Slow Brain Activity

Slow (<0.1 Hz) oscillatory activity in the human brain, as measured by functional magnetic imaging, has been used to identify neural networks and their dysfunction in specific brain diseases. Its intrinsic properties may also be useful to investigate brain functions. We investigated the two functional maps: variance and first order autocorrelation coefficient (r1). These two maps had distinct spatial distributions and the values were significantly different among the subdivisions of the precuneus and posterior cingulate cortex that were identified in functional connectivity (FC) studies. The results reinforce the functional segregation of these subdivisions and indicate that the intrinsic properties of the slow brain activity have physiological relevance. Further, we propose a sample size (degree of freedom) correction when assessing the statistical significance of FC strength with r1 values, which enables a better understanding of the network changes related to various brain diseases

Summation of connectivity strengths in the visual cortex reveals stability of neuronal microcircuits after plasticity

Abstract : Background: Within sensory systems, neurons are continuously affected by environmental stimulation. Recently, we showed that, on cell-pair basis, visual adaptation modulates the connectivity strength between similarly tuned neurons to orientation and we suggested that, on a larger scale, the connectivity strength between neurons forming sub-networks could be maintained after adaptation-induced-plasticity. In the present paper, based on the summation of the connectivity strengths, we sought to examine how, within cell-assemblies, functional connectivity is regulated during an exposure-based adaptation. Results: Using intrinsic optical imaging combined with electrophysiological recordings following the reconfiguration of the maps of the primary visual cortex by long stimulus exposure, we found that within functionally connected cells, the summed connectivity strengths remain almost equal although connections among individual pairs are modified. Neuronal selectivity appears to be strongly associated with neuronal connectivity in a “homeodynamic” manner which maintains the stability of cortical functional relationships after experience-dependent plasticity. Conclusions: Our results support the “homeostatic plasticity concept” giving new perspectives on how the summation in visual cortex leads to the stability within labile neuronal ensembles, depending on the newly acquired properties by neurons

Timescales of Multineuronal Activity Patterns Reflect Temporal Structure of Visual Stimuli

The investigation of distributed coding across multiple neurons in the cortex remains to this date a challenge. Our current understanding of collective encoding of information and the relevant timescales is still limited. Most results are restricted to disparate timescales, focused on either very fast, e.g., spike-synchrony, or slow timescales, e.g., firing rate. Here, we investigated systematically multineuronal activity patterns evolving on different timescales, spanning the whole range from spike-synchrony to mean firing rate. Using multi-electrode recordings from cat visual cortex, we show that cortical responses can be described as trajectories in a high-dimensional pattern space. Patterns evolve on a continuum of coexisting timescales that strongly relate to the temporal properties of stimuli. Timescales consistent with the time constants of neuronal membranes and fast synaptic transmission (5–20 ms) play a particularly salient role in encoding a large amount of stimulus-related information. Thus, to faithfully encode the properties of visual stimuli the brain engages multiple neurons into activity patterns evolving on multiple timescales

Biphasic Synaptic Ca Influx Arising from Compartmentalized Electrical Signals in Dendritic Spines

Dendritic spines compartmentalize synaptically-evoked biochemical signals. The authors show that electrical compartmentalization provided by a spine endows the associated synapse with additional modes of calcium signaling by shaping the kinetics of synaptic calcium currents