The mechanics of correlated variability in segregated cortical excitatory subnetworks.

Understanding the genesis of shared trial-to-trial variability in neuronal population activity within the sensory cortex is critical to uncovering the biological basis of information processing in the brain. Shared variability is often a reflection of the structure of cortical connectivity since it likely arises, in part, from local circuit inputs. A series of experiments from segregated networks of (excitatory) pyramidal neurons in the mouse primary visual cortex challenge this view. Specifically, the across-network correlations were found to be larger than predicted given the known weak cross-network connectivity. We aim to uncover the circuit mechanisms responsible for these enhanced correlations through biologically motivated cortical circuit models. Our central finding is that coupling each excitatory subpopulation with a specific inhibitory subpopulation provides the most robust network-intrinsic solution in shaping these enhanced correlations. This result argues for the existence of excitatory-inhibitory functional assemblies in early sensory areas which mirror not just response properties but also connectivity between pyramidal cells. Furthermore, our findings provide theoretical support for recent experimental observations showing that cortical inhibition forms structural and functional subnetworks with excitatory cells, in contrast to the classical view that inhibition is a nonspecific blanket suppression of local excitation.

Correlation Transfer by Layer 5 Cortical Neurons Under Recreated Synaptic Inputs In Vitro.

Correlated electrical activity in neurons is a prominent characteristic of cortical microcircuits. Despite a growing amount of evidence concerning both spike-count and subthreshold membrane potential pairwise correlations, little is known about how different types of cortical neurons convert correlated inputs into correlated outputs. We studied pyramidal neurons and two classes of GABAergic interneurons of layer 5 in neocortical brain slices obtained from rats of both sexes, and we stimulated them with biophysically realistic correlated inputs, generated using dynamic clamp. We found that the physiological differences between cell types manifested unique features in their capacity to transfer correlated inputs. We used linear response theory and computational modeling to gain clear insights into how cellular properties determine both the gain and timescale of correlation transfer, thus tying single-cell features with network interactions. Our results provide further ground for the functionally distinct roles played by various types of neuronal cells in the cortical microcircuit.SIGNIFICANCE STATEMENT No matter how we probe the brain, we find correlated neuronal activity over a variety of spatial and temporal scales. For the cerebral cortex, significant evidence has accumulated on trial-to-trial covariability in synaptic inputs activation, subthreshold membrane potential fluctuations, and output spike trains. Although we do not yet fully understand their origin and whether they are detrimental or beneficial for information processing, we believe that clarifying how correlations emerge is pivotal for understanding large-scale neuronal network dynamics and computation. Here, we report quantitative differences between excitatory and inhibitory cells, as they relay input correlations into output correlations. We explain this heterogeneity by simple biophysical models and provide the most experimentally validated test of a theory for the emergence of correlations.

Training and Spontaneous Reinforcement of Neuronal Assemblies by Spike Timing Plasticity.

The synaptic connectivity of cortex is plastic, with experience shaping the ongoing interactions between neurons. Theoretical studies of spike timing-dependent plasticity (STDP) have focused on either just pairs of neurons or large-scale simulations. A simple analytic account for how fast spike time correlations affect both microscopic and macroscopic network structure is lacking. We develop a low-dimensional mean field theory for STDP in recurrent networks and show the emergence of assemblies of strongly coupled neurons with shared stimulus preferences. After training, this connectivity is actively reinforced by spike train correlations during the spontaneous dynamics. Furthermore, the stimulus coding by cell assemblies is actively maintained by these internally generated spiking correlations, suggesting a new role for noise correlations in neural coding. Assembly formation has often been associated with firing rate-based plasticity schemes; our theory provides an alternative and complementary framework, where fine temporal correlations and STDP form and actively maintain learned structure in cortical networks.

Scaling Properties of Dimensionality Reduction for Neural Populations and Network Models.

Recent studies have applied dimensionality reduction methods to understand how the multi-dimensional structure of neural population activity gives rise to brain function. It is unclear, however, how the results obtained from dimensionality reduction generalize to recordings with larger numbers of neurons and trials or how these results relate to the underlying network structure. We address these questions by applying factor analysis to recordings in the visual cortex of non-human primates and to spiking network models that self-generate irregular activity through a balance of excitation and inhibition. We compared the scaling trends of two key outputs of dimensionality reduction-shared dimensionality and percent shared variance-with neuron and trial count. We found that the scaling properties of networks with non-clustered and clustered connectivity differed, and that the in vivo recordings were more consistent with the clustered network. Furthermore, recordings from tens of neurons were sufficient to identify the dominant modes of shared variability that generalize to larger portions of the network. These findings can help guide the interpretation of dimensionality reduction outputs in regimes of limited neuron and trial sampling and help relate these outputs to the underlying network structure.

Inhibitory stabilization and visual coding in cortical circuits with multiple interneuron subtypes.

Recent anatomical and functional characterization of cortical inhibitory interneurons has highlighted the diverse computations supported by different subtypes of interneurons. However, most theoretical models of cortex do not feature multiple classes of interneurons and rather assume a single homogeneous population. We study the dynamics of recurrent excitatory-inhibitory model cortical networks with parvalbumin (PV)-, somatostatin (SOM)-, and vasointestinal peptide-expressing (VIP) interneurons, with connectivity properties motivated by experimental recordings from mouse primary visual cortex. Our theory describes conditions under which the activity of such networks is stable and how perturbations of distinct neuronal subtypes recruit changes in activity through recurrent synaptic projections. We apply these conclusions to study the roles of each interneuron subtype in disinhibition, surround suppression, and subtractive or divisive modulation of orientation tuning curves. Our calculations and simulations determine the architectural and stimulus tuning conditions under which cortical activity consistent with experiment is possible. They also lead to novel predictions concerning connectivity and network dynamics that can be tested via optogenetic manipulations. Our work demonstrates that recurrent inhibitory dynamics must be taken into account to fully understand many properties of cortical dynamics observed in experiments.

Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses.

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.

Correlated neural variability in persistent state networks.

Neural activity that persists long after stimulus presentation is a biological correlate of short-term memory. Variability in spiking activity causes persistent states to drift over time, ultimately degrading memory. Models of short-term memory often assume that the input fluctuations to neural populations are independent across cells, a feature that attenuates population-level variability and stabilizes persistent activity. However, this assumption is at odds with experimental recordings from pairs of cortical neurons showing that both the input currents and output spike trains are correlated. It remains unclear how correlated variability affects the stability of persistent activity and the performance of cognitive tasks that it supports. We consider the stochastic long-timescale attractor dynamics of pairs of mutually inhibitory populations of spiking neurons. In these networks, persistent activity was less variable when correlated variability was globally distributed across both populations compared with the case when correlations were locally distributed only within each population. Using a reduced firing rate model with a continuum of persistent states, we show that, when input fluctuations are correlated across both populations, they drive firing rate fluctuations orthogonal to the persistent state attractor, thereby causing minimal stochastic drift. Using these insights, we establish that distributing correlated fluctuations globally as opposed to locally improves network's performance on a two-interval, delayed response discrimination task. Our work shows that the correlation structure of input fluctuations to a network is an important factor when determining long-timescale, persistent population spiking activity.

Optimizing working memory with heterogeneity of recurrent cortical excitation.

A neural correlate of parametric working memory is a stimulus-specific rise in neuron firing rate that persists long after the stimulus is removed. Network models with local excitation and broad inhibition support persistent neural activity, linking network architecture and parametric working memory. Cortical neurons receive noisy input fluctuations that cause persistent activity to diffusively wander about the network, degrading memory over time. We explore how cortical architecture that supports parametric working memory affects the diffusion of persistent neural activity. Studying both a spiking network and a simplified potential well model, we show that spatially heterogeneous excitatory coupling stabilizes a discrete number of persistent states, reducing the diffusion of persistent activity over the network. However, heterogeneous coupling also coarse-grains the stimulus representation space, limiting the storage capacity of parametric working memory. The storage errors due to coarse-graining and diffusion trade off so that information transfer between the initial and recalled stimulus is optimized at a fixed network heterogeneity. For sufficiently long delay times, the optimal number of attractors is less than the number of possible stimuli, suggesting that memory networks can under-represent stimulus space to optimize performance. Our results clearly demonstrate the combined effects of network architecture and stochastic fluctuations on parametric memory storage.

Kv7 channels regulate pairwise spiking covariability in health and disease.

Low-threshold M currents are mediated by the Kv7 family of potassium channels. Kv7 channels are important regulators of spiking activity, having a direct influence on the firing rate, spike time variability, and filter properties of neurons. How Kv7 channels affect the joint spiking activity of populations of neurons is an important and open area of study. Using a combination of computational simulations and analytic calculations, we show that the activation of Kv7 conductances reduces the covariability between spike trains of pairs of neurons driven by common inputs. This reduction is beyond that explained by the lowering of firing rates and involves an active cancellation of common fluctuations in the membrane potentials of the cell pair. Our theory shows that the excess covariance reduction is due to a Kv7-induced shift from low-pass to band-pass filtering of the single neuron spike train response. Dysfunction of Kv7 conductances is related to a number of neurological diseases characterized by both elevated firing rates and increased network-wide correlations. We show how changes in the activation or strength of Kv7 conductances give rise to excess correlations that cannot be compensated for by synaptic scaling or homeostatic modulation of passive membrane properties. In contrast, modulation of Kv7 activation parameters consistent with pharmacological treatments for certain hyperactivity disorders can restore normal firing rates and spiking correlations. Our results provide key insights into how regulation of a ubiquitous potassium channel class can control the coordination of population spiking activity.

Axonal and synaptic failure suppress the transfer of firing rate oscillations, synchrony and information during high frequency deep brain stimulation.

High frequency deep brain stimulation (DBS) of the subthalamic nucleus (STN) is a widely used treatment for Parkinson's disease, but its effects on neural activity in basal ganglia circuits are not fully understood. DBS increases the excitation of STN efferents yet decouples STN spiking patterns from the spiking patterns of STN synaptic targets. We propose that this apparent paradox is resolved by recent studies showing an increased rate of axonal and synaptic failures in STN projections during DBS. To investigate this hypothesis, we combine in vitro and in vivo recordings to derive a computational model of axonal and synaptic failure during DBS. Our model shows that these failures induce a short term depression that suppresses the synaptic transfer of firing rate oscillations, synchrony and rate-coded information from STN to its synaptic targets. In particular, our computational model reproduces the widely reported suppression of parkinsonian ß oscillations and synchrony during DBS. Our results support the idea that short term depression is a therapeutic mechanism of STN DBS that works as a functional lesion by decoupling the somatic spiking patterns of STN neurons from spiking activity in basal ganglia output nuclei.

Timescale-dependent shaping of correlation by olfactory bulb lateral inhibition.

Neurons respond to sensory stimuli by altering the rate and temporal pattern of action potentials. These spike trains both encode and propagate information that guides behavior. Local inhibitory networks can affect the information encoded and propagated by neurons by altering correlations between different spike trains. Correlations introduce redundancy that can reduce encoding but also facilitate propagation of activity to downstream targets. Given this trade-off, how can networks maximize both encoding and propagation efficacy? Here, we examine this problem by measuring the effects of olfactory bulb inhibition on the pairwise statistics of mitral cell spiking. We evoked spiking activity in the olfactory bulb in vitro and measured how lateral inhibition shapes correlations across timescales. We show that inhibitory circuits simultaneously increase fast correlation (i.e., synchrony increases) and decrease slow correlation (i.e., firing rates become less similar). Further, we use computational models to show the benefits of fast correlation/slow decorrelation in the context of odor coding. Olfactory bulb inhibition enhances population-level discrimination of similar inputs, while improving propagation of mitral cell activity to cortex. Our findings represent a targeted strategy by which a network can optimize the correlation structure of its output in a dynamic, activity-dependent manner. This trade-off is not specific to the olfactory system, but rather our work highlights mechanisms by which neurons can simultaneously accomplish multiple, and sometimes competing, aspects of sensory processing.

The logic of recurrent circuits in the primary visual cortex.

Recurrent cortical activity sculpts visual perception by refining, amplifying or suppressing visual input. However, the rules that govern the influence of recurrent activity remain enigmatic. We used ensemble-specific two-photon optogenetics in the mouse visual cortex to isolate the impact of recurrent activity from external visual input. We found that the spatial arrangement and the visual feature preference of the stimulated ensemble and the neighboring neurons jointly determine the net effect of recurrent activity. Photoactivation of these ensembles drives suppression in all cells beyond 30 µm but uniformly drives activation in closer similarly tuned cells. In nonsimilarly tuned cells, compact, cotuned ensembles drive net suppression, while diffuse, cotuned ensembles drive activation. Computational modeling suggests that highly local recurrent excitatory connectivity and selective convergence onto inhibitory neurons explain these effects. Our findings reveal a straightforward logic in which space and feature preference of cortical ensembles determine their impact on local recurrent activity.

Opposing Motor Memories in the Direct and Indirect Pathways of the Basal Ganglia.

Loss of dopamine neurons causes motor deterioration in Parkinson's disease patients. We have previously reported that in addition to acute motor impairment, the impaired motor behavior is encoded into long-term memory in an experience-dependent and task-specific manner, a phenomenon we refer to as aberrant inhibitory motor learning. Although normal motor learning and aberrant inhibitory learning oppose each other and this is manifested in apparent motor performance, in the present study, we found that normal motor memory acquired prior to aberrant inhibitory learning remains preserved in the brain, suggesting the existence of independent storage. To investigate the neuronal circuits underlying these two opposing memories, we took advantage of the RNA-binding protein YTHDF1, an m 6 A RNA methylation reader involved in the regulation of protein synthesis and learning/memory. Conditional deletion of Ythdf1 in either D1 or D2 receptor-expressing neurons revealed that normal motor memory is stored in the D1 (direct) pathway of the basal ganglia, while inhibitory memory is stored in the D2 (indirect) pathway. Furthermore, fiber photometry recordings of GCaMP signals from striatal D1 (dSPN) and D2 (iSPN) receptor-expressing neurons support the preservation of normal memory in the direct pathway after aberrant inhibitory learning, with activities of dSPN predictive of motor performance. Finally, a computational model based on activities of motor cortical neurons, dSPN and iSPN neurons, and their interactions through the basal ganglia loops supports the above observations. These findings have important implications for novel approaches in treating Parkinson's disease by reactivating preserved normal memory, and in treating hyperkinetic movement disorders such as chorea or tics by erasing aberrant motor memories.

Neural correlation is stimulus modulated by feedforward inhibitory circuitry.

Correlated variability of neural spiking activity has important consequences for signal processing. How incoming sensory signals shape correlations of population responses remains unclear. Cross-correlations between spiking of different neurons may be particularly consequential in sparsely firing neural populations such as those found in layer 2/3 of sensory cortex. In rat whisker barrel cortex, we found that pairs of excitatory layer 2/3 neurons exhibit similarly low levels of spike count correlation during both spontaneous and sensory-evoked states. The spontaneous activity of excitatory-inhibitory neuron pairs is positively correlated, while sensory stimuli actively decorrelate joint responses. Computational modeling shows how threshold nonlinearities and local inhibition form the basis of a general decorrelating mechanism. We show that inhibitory population activity maintains low correlations in excitatory populations, especially during periods of sensory-evoked coactivation. The role of feedforward inhibition has been previously described in the context of trial-averaged phenomena. Our findings reveal a novel role for inhibition to shape correlations of neural variability and thereby prevent excessive correlations in the face of feedforward sensory-evoked activation.

Short-term synaptic depression and stochastic vesicle dynamics reduce and shape neuronal correlations.

Correlated neuronal activity is an important feature in many neural codes, a neural correlate of a variety of cognitive states, as well as a signature of several disease states in the nervous system. The cellular and circuit mechanics of neural correlations is a vibrant area of research. Synapses throughout the cortex exhibit a form of short-term depression where increased presynaptic firing rates deplete neurotransmitter vesicles, which transiently reduces synaptic efficacy. The release and recovery of these vesicles are inherently stochastic, and this stochasticity introduces variability into the conductance elicited by depressing synapses. The impact of spiking and subthreshold membrane dynamics on the transfer of neuronal correlations has been studied intensively, but an investigation of the impact of short-term synaptic depression and stochastic vesicle dynamics on correlation transfer is lacking. We find that short-term synaptic depression and stochastic vesicle dynamics can substantially reduce correlations, shape the timescale over which these correlations occur, and alter the dependence of spiking correlations on firing rate. Our results show that short-term depression and stochastic vesicle dynamics need to be taken into account when modeling correlations in neuronal populations.

Short term synaptic depression imposes a frequency dependent filter on synaptic information transfer.

Depletion of synaptic neurotransmitter vesicles induces a form of short term depression in synapses throughout the nervous system. This plasticity affects how synapses filter presynaptic spike trains. The filtering properties of short term depression are often studied using a deterministic synapse model that predicts the mean synaptic response to a presynaptic spike train, but ignores variability introduced by the probabilistic nature of vesicle release and stochasticity in synaptic recovery time. We show that this additional variability has important consequences for the synaptic filtering of presynaptic information. In particular, a synapse model with stochastic vesicle dynamics suppresses information encoded at lower frequencies more than information encoded at higher frequencies, while a model that ignores this stochasticity transfers information encoded at any frequency equally well. This distinction between the two models persists even when large numbers of synaptic contacts are considered. Our study provides strong evidence that the stochastic nature neurotransmitter vesicle dynamics must be considered when analyzing the information flow across a synapse.

The spatial structure of stimuli shapes the timescale of correlations in population spiking activity.

Throughout the central nervous system, the timescale over which pairs of neural spike trains are correlated is shaped by stimulus structure and behavioral context. Such shaping is thought to underlie important changes in the neural code, but the neural circuitry responsible is largely unknown. In this study, we investigate a stimulus-induced shaping of pairwise spike train correlations in the electrosensory system of weakly electric fish. Simultaneous single unit recordings of principal electrosensory cells show that an increase in the spatial extent of stimuli increases correlations at short (≈ 10 ms) timescales while simultaneously reducing correlations at long (≈ 100 ms) timescales. A spiking network model of the first two stages of electrosensory processing replicates this correlation shaping, under the assumptions that spatially broad stimuli both saturate feedforward afferent input and recruit an open-loop inhibitory feedback pathway. Our model predictions are experimentally verified using both the natural heterogeneity of the electrosensory system and pharmacological blockade of descending feedback projections. For weak stimuli, linear response analysis of the spiking network shows that the reduction of long timescale correlation for spatially broad stimuli is similar to correlation cancellation mechanisms previously suggested to be operative in mammalian cortex. The mechanism for correlation shaping supports population-level filtering of irrelevant distractor stimuli, thereby enhancing the population response to relevant prey and conspecific communication inputs.

Correlation between neural spike trains increases with firing rate.

Populations of neurons in the retina, olfactory system, visual and somatosensory thalamus, and several cortical regions show temporal correlation between the discharge times of their action potentials (spike trains). Correlated firing has been linked to stimulus encoding, attention, stimulus discrimination, and motor behaviour. Nevertheless, the mechanisms underlying correlated spiking are poorly understood, and its coding implications are still debated. It is not clear, for instance, whether correlations between the discharges of two neurons are determined solely by the correlation between their afferent currents, or whether they also depend on the mean and variance of the input. We addressed this question by computing the spike train correlation coefficient of unconnected pairs of in vitro cortical neurons receiving correlated inputs. Notably, even when the input correlation remained fixed, the spike train output correlation increased with the firing rate, but was largely independent of spike train variability. With a combination of analytical techniques and numerical simulations using 'integrate-and-fire' neuron models we show that this relationship between output correlation and firing rate is robust to input heterogeneities. Finally, this overlooked relationship is replicated by a standard threshold-linear model, demonstrating the universality of the result. This connection between the rate and correlation of spiking activity links two fundamental features of the neural code.

The mechanics of correlated variability in segregated cortical excitatory subnetworks.

Understanding the genesis of shared trial-to-trial variability in neural activity within sensory cortex is critical to uncovering the biological basis of information processing in the brain. Shared variability is often a reflection of the structure of cortical connectivity since this variability likely arises, in part, from local circuit inputs. A series of experiments from segregated networks of (excitatory) pyramidal neurons in mouse primary visual cortex challenge this view. Specifically, the across-network correlations were found to be larger than predicted given the known weak cross-network connectivity. We aim to uncover the circuit mechanisms responsible for these enhanced correlations through biologically motivated cortical circuit models. Our central finding is that coupling each excitatory subpopulation with a specific inhibitory subpopulation provides the most robust network-intrinsic solution in shaping these enhanced correlations. This result argues for the existence of excitatory-inhibitory functional assemblies in early sensory areas which mirror not just response properties but also connectivity between pyramidal cells.

Sampling-based Bayesian inference in recurrent circuits of stochastic spiking neurons.

Two facts about cortex are widely accepted: neuronal responses show large spiking variability with near Poisson statistics and cortical circuits feature abundant recurrent connections between neurons. How these spiking and circuit properties combine to support sensory representation and information processing is not well understood. We build a theoretical framework showing that these two ubiquitous features of cortex combine to produce optimal sampling-based Bayesian inference. Recurrent connections store an internal model of the external world, and Poissonian variability of spike responses drives flexible sampling from the posterior stimulus distributions obtained by combining feedforward and recurrent neuronal inputs. We illustrate how this framework for sampling-based inference can be used by cortex to represent latent multivariate stimuli organized either hierarchically or in parallel. A neural signature of such network sampling are internally generated differential correlations whose amplitude is determined by the prior stored in the circuit, which provides an experimentally testable prediction for our framework.