Correlated states in balanced neuronal networks

Different Excitation-Inhibition Correlations Between Spontaneous and Tone-evoked Activity in Primary Auditory Cortex Neurons

Tone-evoked synaptic excitation and inhibition are highly correlated in many neurons with V-shaped tuning curves in the primary auditory cortex of pentobarbital-anesthetized rats. In contrast, there is less correlation between spontaneous excitation and inhibition in visual cortex neurons under the same anesthetic conditions. However, it was not known whether the primary auditory cortex resembles visual cortex in having spontaneous excitation and inhibition that is less correlated than tone-evoked excitation and inhibition. Here we report whole-cell voltage-clamp measurements of spontaneous excitation and inhibition in primary auditory cortex neurons of pentobarbital-anesthetized rats. Spontaneous excitatory and inhibitory currents appeared to mainly consist of distinct events, with the inhibitory event rate typically lower than the excitatory event rate. We use the ratio of the excitatory event rate to the inhibitory event rate, and the assumption that the excitatory and inhibitory synaptic currents can each be reasonably described as a filtered Poisson process, to estimate the maximum spontaneous excitatory-inhibitory correlation for each neuron. In a subset of neurons, we also measured tone-evoked excitation and inhibition. In neurons with V-shaped tuning curves, although tone-evoked excitation and inhibition were highly correlated, the spontaneous inhibitory event rate was typically sufficiently lower than the spontaneous excitatory event rate to indicate a lower excitatory-inhibitory correlation for spontaneous activity than for tone-evoked responses.

Evaluating the extent to which homeostatic plasticity learns to compute prediction errors in unstructured neuronal networks

The brain is believed to operate in part by making predictions about sensory stimuli and encoding deviations from these predictions in the activity of "prediction error neurons." This principle defines the widely influential theory of predictive coding. The precise circuitry and plasticity mechanisms through which animals learn to compute and update their predictions are unknown. Homeostatic inhibitory synaptic plasticity is a promising mechanism for training neuronal networks to perform predictive coding. Homeostatic plasticity causes neurons to maintain a steady, baseline firing rate in response to inputs that closely match the inputs on which a network was trained, but firing rates can deviate away from this baseline in response to stimuli that are mismatched from training. We combine computer simulations and mathematical analysis systematically to test the extent to which randomly connected, unstructured networks compute prediction errors after training with homeostatic inhibitory synaptic plasticity. We find that homeostatic plasticity alone is sufficient for computing prediction errors for trivial time-constant stimuli, but not for more realistic time-varying stimuli. We use a mean-field theory of plastic networks to explain our findings and characterize the assumptions under which they apply.

Global organization of neuronal activity only requires unstructured local connectivity

Modern electrophysiological recordings simultaneously capture single-unit spiking activities of hundreds of neurons spread across large cortical distances. Yet, this parallel activity is often confined to relatively low-dimensional manifolds. This implies strong coordination also among neurons that are most likely not even connected. Here, we combine in vivo recordings with network models and theory to characterize the nature of mesoscopic coordination patterns in macaque motor cortex and to expose their origin: We find that heterogeneity in local connectivity supports network states with complex long-range cooperation between neurons that arises from multi-synaptic, short-range connections. Our theory explains the experimentally observed spatial organization of covariances in resting state recordings as well as the behaviorally related modulation of covariance patterns during a reach-to-grasp task. The ubiquity of heterogeneity in local cortical circuits suggests that the brain uses the described mechanism to flexibly adapt neuronal coordination to momentary demands.

On the Complexity of Resting State Spiking Activity in Monkey Motor Cortex

Resting state has been established as a classical paradigm of brain activity studies, mostly based on large-scale measurements such as functional magnetic resonance imaging or magneto- and electroencephalography. This term typically refers to a behavioral state characterized by the absence of any task or stimuli. The corresponding neuronal activity is often called idle or ongoing. Numerous modeling studies on spiking neural networks claim to mimic such idle states, but compare their results with task- or stimulus-driven experiments, or to results from experiments with anesthetized subjects. Both approaches might lead to misleading conclusions. To provide a proper basis for comparing physiological and simulated network dynamics, we characterize simultaneously recorded single neurons' spiking activity in monkey motor cortex at rest and show the differences from spontaneous and task- or stimulus-induced movement conditions. We also distinguish between rest with open eyes and sleepy rest with eyes closed. The resting state with open eyes shows a significantly higher dimensionality, reduced firing rates, and less balance between population level excitation and inhibition than behavior-related states.

Balanced networks under spike-time dependent plasticity

The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory–inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in plastic neural networks. In particular, it is not fully understood how plasticity induced changes in the network affect balance, and in turn, how correlated, balanced activity impacts learning. How do the dynamics of balanced networks change under different plasticity rules? How does correlated spiking activity in recurrent networks change the evolution of weights, their eventual magnitude, and structure across the network? To address these questions, we develop a theory of spike–timing dependent plasticity in balanced networks. We show that balance can be attained and maintained under plasticity–induced weight changes. We find that correlations in the input mildly affect the evolution of synaptic weights. Under certain plasticity rules, we find an emergence of correlations between firing rates and synaptic weights. Under these rules, synaptic weights converge to a stable manifold in weight space with their final configuration dependent on the initial state of the network. Lastly, we show that our framework can also describe the dynamics of plastic balanced networks when subsets of neurons receive targeted optogenetic input.

Animals are able to learn complex tasks through changes in individual synapses between cells. Such changes lead to the coevolution of neural activity patterns and the structure of neural connectivity, but the consequences of these interactions are not fully understood. We consider plasticity in model neural networks which achieve an average balance between the excitatory and inhibitory synaptic inputs to different cells, and display cortical–like, irregular activity. We extend the theory of balanced networks to account for synaptic plasticity and show which rules can maintain balance, and which will drive the network into a different state. This theory of plasticity can provide insights into the relationship between stimuli, network dynamics, and synaptic circuitry.

Synaptic polarity and sign-balance prediction using gene expression data in the Caenorhabditis elegans chemical synapse neuronal connectome network

Graph theoretical analyses of nervous systems usually omit the aspect of connection polarity, due to data insufficiency. The chemical synapse network of Caenorhabditis elegans is a well-reconstructed directed network, but the signs of its connections are yet to be elucidated. Here, we present the gene expression-based sign prediction of the ionotropic chemical synapse connectome of C. elegans (3,638 connections and 20,589 synapses total), incorporating available presynaptic neurotransmitter and postsynaptic receptor gene expression data for three major neurotransmitter systems. We made predictions for more than two-thirds of these chemical synapses and observed an excitatory-inhibitory (E:I) ratio close to 4:1 which was found similar to that observed in many real-world networks. Our open source tool (http://EleganSign.linkgroup.hu) is simple but efficient in predicting polarities by integrating neuronal connectome and gene expression data.

Response nonlinearities in networks of spiking neurons

Combining information from multiple sources is a fundamental operation performed by networks of neurons in the brain, whose general principles are still largely unknown. Experimental evidence suggests that combination of inputs in cortex relies on nonlinear summation. Such nonlinearities are thought to be fundamental to perform complex computations. However, these non-linearities are inconsistent with the balanced-state model, one of the most popular models of cortical dynamics, which predicts networks have a linear response. This linearity is obtained in the limit of very large recurrent coupling strength. We investigate the stationary response of networks of spiking neurons as a function of coupling strength. We show that, while a linear transfer function emerges at strong coupling, nonlinearities are prominent at finite coupling, both at response onset and close to saturation. We derive a general framework to classify nonlinear responses in these networks and discuss which of them can be captured by rate models. This framework could help to understand the diversity of non-linearities observed in cortical networks.

Nonlinear stimulus representations in neural circuits with approximate excitatory-inhibitory balance

Balanced excitation and inhibition is widely observed in cortex. How does this balance shape neural computations and stimulus representations? This question is often studied using computational models of neuronal networks in a dynamically balanced state. But balanced network models predict a linear relationship between stimuli and population responses. So how do cortical circuits implement nonlinear representations and computations? We show that every balanced network architecture admits stimuli that break the balanced state and these breaks in balance push the network into a "semi-balanced state" characterized by excess inhibition to some neurons, but an absence of excess excitation. The semi-balanced state produces nonlinear stimulus representations and nonlinear computations, is unavoidable in networks driven by multiple stimuli, is consistent with cortical recordings, and has a direct mathematical relationship to artificial neural networks.

Inference of synaptic connectivity and external variability in neural microcircuits

A major goal in neuroscience is to estimate neural connectivity from large scale extracellular recordings of neural activity in vivo. This is challenging in part because any such activity is modulated by the unmeasured external synaptic input to the network, known as the common input problem. Many different measures of functional connectivity have been proposed in the literature, but their direct relationship to synaptic connectivity is often assumed or ignored. For in vivo data, measurements of this relationship would require a knowledge of ground truth connectivity, which is nearly always unavailable. Instead, many studies use in silico simulations as benchmarks for investigation, but such approaches necessarily rely upon a variety of simplifying assumptions about the simulated network and can depend on numerous simulation parameters. We combine neuronal network simulations, mathematical analysis, and calcium imaging data to address the question of when and how functional connectivity, synaptic connectivity, and latent external input variability can be untangled. We show numerically and analytically that, even though the precision matrix of recorded spiking activity does not uniquely determine synaptic connectivity, it is in practice often closely related to synaptic connectivity. This relation becomes more pronounced when the spatial structure of neuronal variability is jointly considered.

The asynchronous state's relation to large-scale potentials in cortex

Understanding the relation between large-scale potentials (M/EEG) and their underlying neural activity can improve the precision of research and clinical diagnosis. Recent insights into cortical dynamics highlighted a state of strongly reduced spike count correlations, termed the asynchronous state (AS). The AS has received considerable attention from experimenters and theorists alike, regarding its implications for cortical dynamics and coding of information. However, how reconcilable are these vanishing correlations in the AS with large-scale potentials such as M/EEG observed in most experiments? Typically the latter are assumed to be based on underlying correlations in activity, in particular between subthreshold potentials. We survey the occurrence of the AS across brain states, regions, and layers and argue for a reconciliation of this seeming disparity: large-scale potentials are either observed, first, at transitions between cortical activity states, which entail transient changes in population firing rate, as well as during the AS, and, second, on the basis of sufficiently large, asynchronous populations that only need to exhibit weak correlations in activity. Cells with no or little spiking activity can contribute to large-scale potentials via their subthreshold currents, while they do not contribute to the estimation of spiking correlations, defining the AS. Furthermore, third, the AS occurs only within particular cortical regions and layers associated with the currently selected modality, allowing for correlations at other times and between other areas and layers.