Five key factors determining pairwise correlations in visual cortex

The recovery of parabolic avalanches in spatially subsampled neuronal networks at criticality

Scaling relationships are key in characterizing complex systems at criticality. In the brain, they are evident in neuronal avalanches-scale-invariant cascades of neuronal activity quantified by power laws. Avalanches manifest at the cellular level as cascades of neuronal groups that fire action potentials simultaneously. Such spatiotemporal synchronization is vital to theories on brain function yet avalanche synchronization is often underestimated when only a fraction of neurons is observed. Here, we investigate biases from fractional sampling within a balanced network of excitatory and inhibitory neurons with all-to-all connectivity and critical branching process dynamics. We focus on how mean avalanche size scales with avalanche duration. For parabolic avalanches, this scaling is quadratic, quantified by the scaling exponent, χ = 2 , reflecting rapid spatial expansion of simultaneous neuronal firing over short durations. However, in networks sampled fractionally, χ is significantly lower. We demonstrate that applying temporal coarse-graining and increasing a minimum threshold for coincident firing restores χ = 2 , even when as few as 0.1% of neurons are sampled. This correction crucially depends on the network being critical and fails for near sub- and supercritical branching dynamics. Using cellular 2-photon imaging, our approach robustly identifies χ = 2 over a wide parameter regime in ongoing neuronal activity from frontal cortex of awake mice. In contrast, the common 'crackling noise' approach fails to determine χ under similar sampling conditions at criticality. Our findings overcome scaling bias from fractional sampling and demonstrate rapid, spatiotemporal synchronization of neuronal assemblies consistent with scale-invariant, parabolic avalanches at criticality.

Preconfigured architecture of the developing mouse brain

In the adult brain, structural and functional parameters, such as synaptic sizes and neuronal firing rates, follow right-skewed and heavy-tailed distributions. While this organization is thought to have significant implications, its development is still largely unknown. Here, we address this knowledge gap by investigating a large-scale dataset recorded from the prefrontal cortex and the olfactory bulb of mice aged 4-60 postnatal days. We show that firing rates and spike train interactions have a largely stable distribution shape throughout the first 60 postnatal days and that the prefrontal cortex displays a functional small-world architecture. Moreover, early brain activity exhibits an oligarchical organization, where high-firing neurons have hub-like properties. In a neural network model, we show that analogously right-skewed and heavy-tailed synaptic parameters are instrumental to consistently recapitulate the experimental data. Thus, functional and structural parameters in the developing brain are already extremely distributed, suggesting that this organization is preconfigured and not experience dependent.

Learning what matters: Synaptic plasticity with invariance to second-order input correlations

Cortical populations of neurons develop sparse representations adapted to the statistics of the environment. To learn efficient population codes, synaptic plasticity mechanisms must differentiate relevant latent features from spurious input correlations, which are omnipresent in cortical networks. Here, we develop a theory for sparse coding and synaptic plasticity that is invariant to second-order correlations in the input. Going beyond classical Hebbian learning, our learning objective explains the functional form of observed excitatory plasticity mechanisms, showing how Hebbian long-term depression (LTD) cancels the sensitivity to second-order correlations so that receptive fields become aligned with features hidden in higher-order statistics. Invariance to second-order correlations enhances the versatility of biologically realistic learning models, supporting optimal decoding from noisy inputs and sparse population coding from spatially correlated stimuli. In a spiking model with triplet spike-timing-dependent plasticity (STDP), we show that individual neurons can learn localized oriented receptive fields, circumventing the need for input preprocessing, such as whitening, or population-level lateral inhibition. The theory advances our understanding of local unsupervised learning in cortical circuits, offers new interpretations of the Bienenstock-Cooper-Munro and triplet STDP models, and assigns a specific functional role to synaptic LTD mechanisms in pyramidal neurons.

Chaotic dynamics in spatially distributed neuronal networks generate population-wide shared variability

Neural activity in the cortex is highly variable in response to repeated stimuli. Population recordings across the cortex demonstrate that the variability of neuronal responses is shared among large groups of neurons and concentrates in a low dimensional space. However, the source of the population-wide shared variability is unknown. In this work, we analyzed the dynamical regimes of spatially distributed networks of excitatory and inhibitory neurons. We found chaotic spatiotemporal dynamics in networks with similar excitatory and inhibitory projection widths, an anatomical feature of the cortex. The chaotic solutions contain broadband frequency power in rate variability and have distance-dependent and low-dimensional correlations, in agreement with experimental findings. In addition, rate chaos can be induced by globally correlated noisy inputs. These results suggest that spatiotemporal chaos in cortical networks can explain the shared variability observed in neuronal population responses.

The spatial scale of somatostatin subnetworks increases from sensory to association cortex

Incoming signals interact with rich, ongoing population activity dynamics in cortical circuits. These intrinsic dynamics are the consequence of interactions among local excitatory and inhibitory neurons and affect inter-region communication and information coding. It is unclear whether specializations in the patterns of interactions among excitatory and inhibitory neurons underlie systematic differences in activity dynamics across the cortex. Here, in mice, we compare the functional interactions among somatostatin (SOM)-expressing inhibitory interneurons and the rest of the neural population in auditory cortex (AC), a sensory region of the cortex, and posterior parietal cortex (PPC), an association region. The spatial structure of shared variability among SOM and non-SOM neurons differs across regions: correlations decay rapidly with distance in AC but not in PPC. However, in both regions, activity of SOM neurons is more highly correlated than non-SOM neurons' activity. Our results imply both generalization and specialization in the functional structure of inhibitory subnetworks across the cortex.

Perceptual enhancement and suppression correlate with V1 neural activity during active sensing

Perception in multiple sensory modalities is an active process that involves exploratory behaviors. In humans and other primates, vision results from sensory sampling guided by saccadic eye movements. Saccades are known to modulate visual perception, and a corollary discharge signal associated with saccades appears to establish a sense of visual stability. Neural recordings have shown that saccades also modulate activity widely across the brain. To investigate the neural basis of saccadic effects on perception, simultaneous recordings from multiple neurons in area V1 were made as animals performed a contrast detection task. Perceptual and neural measures were compared when the animal made real saccades that brought a stimulus into V1 receptive fields and when simulated saccades were made (identical retinal stimulation but no eye movement). When real saccades were made and low spatial frequency stimuli were presented, we observed a reduction in both perceptual sensitivity and neural activity compared with simulated saccades; conversely, with higher spatial frequency stimuli, saccades increased visual sensitivity and neural activity. The performance of neural decoders, which used the activity of the population of simultaneously recorded neurons, showed saccade effects on sensitivity that mirrored the frequency-dependent perceptual changes, suggesting that the V1 population activity could support the perceptual effects. A minority of V1 neurons had significant choice probabilities, and the saccades decreased both average choice probability and pairwise noise correlations. Taken together, the findings suggest that a signal related to saccadic eye movements alters V1 spiking to increase the independence of spiking neurons and bias the system toward processing higher spatial frequencies, presumably to enhance object recognition. The effects of saccades on visual perception and noise correlations appear to parallel effects observed in other sensory modalities, suggesting a general principle of active sensory processing.

Local dendritic balance enables learning of efficient representations in networks of spiking neurons

How can neural networks learn to efficiently represent complex and high-dimensional inputs via local plasticity mechanisms? Classical models of representation learning assume that feedforward weights are learned via pairwise Hebbian-like plasticity. Here, we show that pairwise Hebbian-like plasticity works only under unrealistic requirements on neural dynamics and input statistics. To overcome these limitations, we derive from first principles a learning scheme based on voltage-dependent synaptic plasticity rules. Here, recurrent connections learn to locally balance feedforward input in individual dendritic compartments and thereby can modulate synaptic plasticity to learn efficient representations. We demonstrate in simulations that this learning scheme works robustly even for complex high-dimensional inputs and with inhibitory transmission delays, where Hebbian-like plasticity fails. Our results draw a direct connection between dendritic excitatory-inhibitory balance and voltage-dependent synaptic plasticity as observed in vivo and suggest that both are crucial for representation learning.

Differences in olfactory bulb mitral cell spiking with ortho- and retronasal stimulation revealed by data-driven models

The majority of olfaction studies focus on orthonasal stimulation where odors enter via the front nasal cavity, while retronasal olfaction, where odors enter the rear of the nasal cavity during feeding, is understudied. The coding of retronasal odors via coordinated spiking of neurons in the olfactory bulb (OB) is largely unknown despite evidence that higher level processing is different than orthonasal. To this end, we use multi-electrode array in vivo recordings of rat OB mitral cells (MC) in response to a food odor with both modes of stimulation, and find significant differences in evoked firing rates and spike count covariances (i.e., noise correlations). Differences in spiking activity often have implications for sensory coding, thus we develop a single-compartment biophysical OB model that is able to reproduce key properties of important OB cell types. Prior experiments in olfactory receptor neurons (ORN) showed retro stimulation yields slower and spatially smaller ORN inputs than with ortho, yet whether this is consequential for OB activity remains unknown. Indeed with these specifications for ORN inputs, our OB model captures the salient trends in our OB data. We also analyze how first and second order ORN input statistics dynamically transfer to MC spiking statistics with a phenomenological linear-nonlinear filter model, and find that retro inputs result in larger linear filters than ortho inputs. Finally, our models show that the temporal profile of ORN is crucial for capturing our data and is thus a distinguishing feature between ortho and retro stimulation, even at the OB. Using data-driven modeling, we detail how ORN inputs result in differences in OB dynamics and MC spiking statistics. These differences may ultimately shape how ortho and retro odors are coded.

Olfaction is a key sense for many cognitive and behavioral tasks, and is particularly unique because odors can naturally enter the nasal cavity from the front or rear, i.e., ortho- and retro-nasal, respectively. Yet little is known about the differences in coordinated spiking in the olfactory bulb with ortho versus retro stimulation, let alone how these different modes of olfaction may alter coding of odors. We simultaneously record many cells in rat olfactory bulb to assess the differences in spiking statistics, and develop a biophysical olfactory bulb network model to study the reasons for these differences. Using theoretical and computational methods, we find that the olfactory bulb transfers input statistics differently for retro stimulation relative to ortho stimulation. Furthermore, our models show that the temporal profile of inputs is crucial for capturing our data and is thus a distinguishing feature between ortho and retro stimulation, even at the olfactory bulb. Understanding the spiking dynamics of the olfactory bulb with both ortho and retro stimulation is a key step for ultimately understanding how the brain codes odors with different modes of olfaction.

Probing the structure-function relationship with neural networks constructed by solving a system of linear equations

Neural network models are an invaluable tool to understand brain function since they allow us to connect the cellular and circuit levels with behaviour. Neural networks usually comprise a huge number of parameters, which must be chosen carefully such that networks reproduce anatomical, behavioural, and neurophysiological data. These parameters are usually fitted with off-the-shelf optimization algorithms that iteratively change network parameters and simulate the network to evaluate its performance and improve fitting. Here we propose to invert the fitting process by proceeding from the network dynamics towards network parameters. Firing state transitions are chosen according to the transition graph associated with the solution of a task. Then, a system of linear equations is constructed from the network firing states and membrane potentials, in a way that guarantees the consistency of the system. This allows us to uncouple the dynamical features of the model, like its neurons firing rate and correlation, from the structural features, and the task-solving algorithm implemented by the network. We employed our method to probe the structure–function relationship in a sequence memory task. The networks obtained showed connectivity and firing statistics that recapitulated experimental observations. We argue that the proposed method is a complementary and needed alternative to the way neural networks are constructed to model brain function.

Disparity Sensitivity and Binocular Integration in Mouse Visual Cortex Areas

Binocular disparity, the difference between the two eyes' images, is a powerful cue to generate the 3D depth percept known as stereopsis. In primates, binocular disparity is processed in multiple areas of the visual cortex, with distinct contributions of higher areas to specific aspects of depth perception. Mice, too, can perceive stereoscopic depth, and neurons in primary visual cortex (V1) and higher-order, lateromedial (LM) and rostrolateral (RL) areas were found to be sensitive to binocular disparity. A detailed characterization of disparity tuning across mouse visual areas is lacking, however, and acquiring such data might help clarifying the role of higher areas for disparity processing and establishing putative functional correspondences to primate areas. We used two-photon calcium imaging in female mice to characterize the disparity tuning properties of neurons in visual areas V1, LM, and RL in response to dichoptically presented binocular gratings, as well as random dot correlograms (RDC). In all three areas, many neurons were tuned to disparity, showing strong response facilitation or suppression at optimal or null disparity, respectively, even in neurons classified as monocular by conventional ocular dominance (OD) measurements. Neurons in higher areas exhibited broader and more asymmetric disparity tuning curves compared with V1, as observed in primate visual cortex. Finally, we probed neurons' sensitivity to true stereo correspondence by comparing responses to correlated RDC (cRDC) and anticorrelated RDC (aRDC). Area LM, akin to primate ventral visual stream areas, showed higher selectivity for correlated stimuli and reduced anticorrelated responses, indicating higher-level disparity processing in LM compared with V1 and RL.SIGNIFICANCE STATEMENT A major cue for inferring 3D depth is disparity between the two eyes' images. Investigating how binocular disparity is processed in the mouse visual system will not only help delineating the role of mouse higher areas for visual processing, but also shed light on how the mammalian brain computes stereopsis. We found that binocular integration is a prominent feature of mouse visual cortex, as many neurons are selectively and strongly modulated by binocular disparity. Comparison of responses to correlated and anticorrelated random dot correlograms (RDC) revealed that lateromedial area (LM) is more selective to correlated stimuli, while less sensitive to anticorrelated stimuli compared with primary visual cortex (V1) and rostrolateral area (RL), suggesting higher-level disparity processing in LM, resembling primate ventral visual stream areas.

Cortical State Fluctuations across Layers of V1 during Visual Spatial Perception

Many factors modulate the state of cortical activity, but the importance of cortical state variability for sensory perception remains debated. We trained mice to detect spatially localized visual stimuli and simultaneously measured local field potentials and excitatory and inhibitory neuron populations across layers of primary visual cortex (V1). Cortical states with low spontaneous firing and correlations in excitatory neurons, and suppression of 3- to 7-Hz oscillations in layer 4, accurately predicted single-trial visual detection. Our results show that cortical states exert strong effects at the initial stage of cortical processing in V1 and can play a prominent role for visual spatial behavior in mice.

Stimulus-Tuned Structure of Correlated fMRI Activity in Human Visual Cortex

Processing units are interconnected in the visual system, where a sensory organ and downstream cortical regions communicate through hierarchical connections, and local sites within the regions communicate through horizontal connections. In such networks, neural activities at local sites are likely to influence one another in complex ways and thus are intricately correlated. Recognizing the functional importance of correlated activity in sensory representation, spontaneous activities have been studied via diverse local or global measures in various time scales. Here, measuring functional magnetic resonance imaging (fMRI) signals in human early visual cortex, we explored systematic patterns that govern the correlated activities arising spontaneously. Specifically, guided by previously identified biases in anatomical connection patterns, we characterized all possible pairs of gray matter sites in 3 relational factors: "retinotopic distance," "cortical distance," and "stimulus tuning similarity." By evaluating and comparing the unique contributions of these factors to the correlated activity, we found that tuning similarity factors overrode distance factors in accounting for the structure of correlated fMRI activity both within and between V1, V2, and V3, irrespective of the presence or degree of visual stimulation. Our findings indicate that the early human visual cortex is intrinsically organized as a network tuned to the stimulus features.

Stimulus complexity shapes response correlations in primary visual cortex

Spike count correlations (SCCs) are ubiquitous in sensory cortices, are characterized by rich structure, and arise from structured internal dynamics. However, most theories of visual perception treat contributions of neurons to the representation of stimuli independently and focus on mean responses. Here, we argue that, in a functional model of visual perception, featuring probabilistic inference over a hierarchy of features, inferences about high-level features modulate inferences about low-level features ultimately introducing structured internal dynamics and patterns in SCCs. Specifically, high-level inferences for complex stimuli establish the local context in which neurons in the primary visual cortex (V1) interpret stimuli. Since the local context differentially affects multiple neurons, this conjecture predicts specific modulations in the fine structure of SCCs as stimulus identity and, more importantly, stimulus complexity varies. We designed experiments with natural and synthetic stimuli to measure the fine structure of SCCs in V1 of awake behaving macaques and assessed their dependence on stimulus identity and stimulus statistics. We show that the fine structure of SCCs is specific to the identity of natural stimuli and changes in SCCs are independent of changes in response mean. Critically, we demonstrate that stimulus specificity of SCCs in V1 can be directly manipulated by altering the amount of high-order structure in synthetic stimuli. Finally, we show that simple phenomenological models of V1 activity cannot account for the observed SCC patterns and conclude that the stimulus dependence of SCCs is a natural consequence of structured internal dynamics in a hierarchical probabilistic model of natural images.

Investigating the Correlation-Firing Rate Relationship in Heterogeneous Recurrent Networks

The structure of spiking activity in cortical networks has important implications for how the brain ultimately codes sensory signals. However, our understanding of how network and intrinsic cellular mechanisms affect spiking is still incomplete. In particular, whether cell pairs in a neural network show a positive (or no) relationship between pairwise spike count correlation and average firing rate is generally unknown. This relationship is important because it has been observed experimentally in some sensory systems, and it can enhance information in a common population code. Here we extend our prior work in developing mathematical tools to succinctly characterize the correlation and firing rate relationship in heterogeneous coupled networks. We find that very modest changes in how heterogeneous networks occupy parameter space can dramatically alter the correlation-firing rate relationship.

Nonmonotonic spatial structure of interneuronal correlations in prefrontal microcircuits

Correlated fluctuations of single neuron discharges, on a mesoscopic scale, decrease as a function of lateral distance in early sensory cortices, reflecting a rapid spatial decay of lateral connection probability and excitation. However, spatial periodicities in horizontal connectivity and associational input as well as an enhanced probability of lateral excitatory connections in the association cortex could theoretically result in nonmonotonic correlation structures. Here, we show such a spatially nonmonotonic correlation structure, characterized by significantly positive long-range correlations, in the inferior convexity of the macaque prefrontal cortex. This functional connectivity kernel was more pronounced during wakefulness than anesthesia and could be largely attributed to the spatial pattern of correlated variability between functionally similar neurons during structured visual stimulation. These results suggest that the spatial decay of lateral functional connectivity is not a common organizational principle of neocortical microcircuits. A nonmonotonic correlation structure could reflect a critical topological feature of prefrontal microcircuits, facilitating their role in integrative processes.

Early steps toward understanding neuronal communication

PURPOSE OF REVIEW

The computational power of the brain arises from the complex interactions between neurons. One straightforward method to quantify the strength of neuronal interactions is by measuring correlation and coherence. Efforts to measure correlation have been advancing rapidly of late, spurred by the development of advanced recording technologies enabling recording from many neurons and brain areas simultaneously. This review highlights recent results that provide clues into the principles of neural coordination, connections to cognitive and neurological phenomena, and key directions for future research.

RECENT FINDINGS

The correlation structure of neural activity in the brain has important consequences for the encoding properties of neural populations. Recent studies have shown that this correlation structure is not fixed, but adapts in a variety of contexts in ways that appear beneficial to task performance. By studying these changes in biological neural networks and computational models, researchers have improved our understanding of the principles guiding neural communication.

SUMMARY

Correlation and coherence are highly informative metrics for studying coding and communication in the brain. Recent findings have emphasized how the brain modifies correlation structure dynamically in order to improve information-processing in a goal-directed fashion. One key direction for future research concerns how to leverage these dynamic changes for therapeutic purposes.

Adaptation modulates correlated subthreshold response variability in visual cortex

Cortical sensory responses are highly variable across stimulus presentations. This variability can be correlated across neurons (due to some combination of dense intracortical connectivity, cortical activity level, and cortical state), with fundamental implications for population coding. Yet the interpretation of correlated response variability (or "noise correlation") has remained fraught with difficulty, in part because of the restriction to extracellular neuronal spike recordings. Here, we measured response variability and its correlation at the most microscopic level of electrical neural activity, the membrane potential, by obtaining dual whole cell recordings from pairs of cortical pyramidal neurons during visual processing in the turtle whole brain ex vivo preparation. We found that during visual stimulation, correlated variability adapts toward an intermediate level and that this correlation dynamic is likely mediated by intracortical mechanisms. A model network with external inputs, synaptic depression, and structure reproduced the observed dynamics of correlated variability. These results suggest that intracortical adaptation self-organizes cortical circuits toward a balanced regime at which correlated variability is maintained at an intermediate level.NEW & NOTEWORTHY Correlated response variability has profound implications for stimulus encoding, yet our understanding of this phenomenon is based largely on spike data. Here, we investigate the dynamics and mechanisms of membrane potential-correlated variability (CC) in visual cortex with a combined experimental and computational approach. We observe a visually evoked increase in CC, followed by a fast return to baseline. Our results further suggest a link between this observation and the adaptation-mediated dynamics of emergent network phenomena.

When do correlations increase with firing rates in recurrent networks?

A central question in neuroscience is to understand how noisy firing patterns are used to transmit information. Because neural spiking is noisy, spiking patterns are often quantified via pairwise correlations, or the probability that two cells will spike coincidentally, above and beyond their baseline firing rate. One observation frequently made in experiments, is that correlations can increase systematically with firing rate. Theoretical studies have determined that stimulus-dependent correlations that increase with firing rate can have beneficial effects on information coding; however, we still have an incomplete understanding of what circuit mechanisms do, or do not, produce this correlation-firing rate relationship. Here, we studied the relationship between pairwise correlations and firing rates in recurrently coupled excitatory-inhibitory spiking networks with conductance-based synapses. We found that with stronger excitatory coupling, a positive relationship emerged between pairwise correlations and firing rates. To explain these findings, we used linear response theory to predict the full correlation matrix and to decompose correlations in terms of graph motifs. We then used this decomposition to explain why covariation of correlations with firing rate—a relationship previously explained in feedforward networks driven by correlated input—emerges in some recurrent networks but not in others. Furthermore, when correlations covary with firing rate, this relationship is reflected in low-rank structure in the correlation matrix.

A central question in neuroscience is to understand how noisy firing patterns are used to transmit information. We quantify spiking patterns by using pairwise correlations, or the probability that two cells will spike coincidentally, above and beyond their baseline firing rate. One observation frequently made in experiments is that correlations can increase systematically with firing rate. Recent studies of a type of output cell in mouse retina found this relationship; furthermore, they determined that the increase of correlation with firing rate helped the cells encode information, provided the correlations were stimulus-dependent. Several theoretical studies have explored this basic structure, and found that it is generally beneficial to modulate correlations in this way. However—aside from mouse retinal cells referenced here—we do not yet have many examples of real neural circuits that show this correlation-firing rate pattern, so we do not know what common features (or mechanisms) might occur between them.

In this study, we address this question via a computational model. We set up a computational model with features representative of a generic cortical network, to see whether correlations would increase with firing rate. To produce different firing patterns, we varied excitatory coupling. We found that with stronger excitatory coupling, there was a positive relationship between pairwise correlations and firing rates. We used a network linear response theory to show why correlations could increase with firing rates in some networks, but not in others; this could be explained by how cells responded to fluctuations in inhibitory conductances.

The mechanics of state-dependent neural correlations

Simultaneous recordings from large neural populations are becoming increasingly common. An important feature of population activity is the trial-to-trial correlated fluctuation of spike train outputs from recorded neuron pairs. Similar to the firing rate of single neurons, correlated activity can be modulated by a number of factors, from changes in arousal and attentional state to learning and task engagement. However, the physiological mechanisms that underlie these changes are not fully understood. We review recent theoretical results that identify three separate mechanisms that modulate spike train correlations: changes in input correlations, internal fluctuations and the transfer function of single neurons. We first examine these mechanisms in feedforward pathways and then show how the same approach can explain the modulation of correlations in recurrent networks. Such mechanistic constraints on the modulation of population activity will be important in statistical analyses of high-dimensional neural data.

High noise correlation between the functionally connected neurons in emergent V1 microcircuits

Neural correlations (noise correlations and cross-correlograms) are widely studied to infer functional connectivity between neurons. High noise correlations between neurons have been reported to increase the encoding accuracy of a neuronal population; however, low noise correlations have also been documented to play a critical role in cortical microcircuits. Therefore, the role of noise correlations in neural encoding is highly debated. To this aim, through multi-electrodes, we recorded neuronal ensembles in the primary visual cortex of anaesthetized cats. By computing cross-correlograms, we divulged the functional network (microcircuit) between neurons within an ensemble in relation to a specific orientation. We show that functionally connected neurons systematically exhibit higher noise correlations than functionally unconnected neurons in a microcircuit that is activated in response to a particular orientation. Furthermore, the mean strength of noise correlations for the connected neurons increases steeply than the unconnected neurons as a function of the resolution window used to calculate noise correlations. We suggest that neurons that display high noise correlations in emergent microcircuits feature functional connections which are inevitable for information encoding in the primary visual cortex.