Summary Shared neural variability is ubiquitous in cortical populations. While this variability is presumed to arise from overlapping synaptic input, its precise relationship to local circuit architecture remains unclear. We combine computational models and in vivo recordings to study the relationship between the spatial structure of connectivity and correlated variability in neural circuits. Extending the theory of networks with balanced excitation and inhibition we find that spatially localized lateral projections promote weakly correlated spiking, but broader lateral projections produce a distinctive spatial correlation structure: Nearby neuron pairs are positively correlated, pairs at intermediate distances are negatively correlated and distant pairs are weakly correlated. This non-monotonic dependence of correlation on distance is revealed in a new analysis of recordings from superficial layers of macaque primary visual cortex. Our findings show that incorporating distance-dependent connectivity improves the extent to which balanced network theory can explain correlated neural variability.

Simultaneous recordings from large neural populations are becoming increasingly common. An important feature of the population activity are the trial-to-trial correlated fluctuations of the spike train outputs of recorded neuron pairs. Like 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 network mechanisms that underlie these changes are not fully understood. We review recent theoretical results that identify three separate biophysical 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.

Networks of model neurons with balanced recurrent excitation and inhibition capture the irregular and asynchronous spiking activity reported in cortex. While mean-field theories of spatially homogeneous balanced networks are well understood, a mean-field analysis of spatially heterogeneous balanced networks has not been fully developed. We extend the analysis of balanced networks to include a connection probability that depends on the spatial separation between neurons. In the continuum limit, we derive that stable, balanced firing rate solutions require that the spatial spread of external inputs be broader than that of recurrent excitation, which in turn must be broader than or equal to that of recurrent inhibition. Notably, this implies that network models with broad recurrent inhibition are inconsistent with the balanced state. For finite size networks, we investigate the pattern-forming dynamics arising when balanced conditions are not satisfied. Our study highlights the new challenges that balanced networks pose for the spatiotemporal dynamics of complex systems.

Highlights d Low-dimensional shared variability can be generated in spatial network models d Synaptic spatial and temporal scales determine the dimensions of shared variability d Depolarizing inhibitory neurons suppresses the populationwide fluctuations d Modeling the attentional modulation of variability within and between brain areas

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.

A pervasive yet puzzling feature of cortical circuits is that despite their complex wiring, population-wide shared spiking variability is low dimensional.Neuronal variability is often used as a probe to understand how recurrent circuitry supports network dynamics. However, current models cannot internally produce low dimensional shared variability, and rather assume that it is inherited from outside the circuit. We analyze population recordings from the visual pathway where directed attention differentially modulates shared variability within and between areas, which is difficult to explain with externally imposed variability. We show that if the spatial and temporal scales of inhibitory coupling match physiology, network models capture the low dimensional shared 1 . CC-BY-NC-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under aThe copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/217976 doi: bioRxiv preprint first posted online Nov. 11, 2017; variability of our population data. Our theory provides a critical link between measured cortical circuit structure and recorded population activity.One Sentence Summary: Circuit models with spatio-temporal excitatory and inhibitory interactions generate population variability that captures recorded neuronal activity across cognitive states. IntroductionThe trial-to-trial variability of neuronal responses gives a critical window into how the circuit structure connecting neurons drives brain activity. This idea combined with the widespread use of population recordings has prompted a deep interest in how variability is distributed over a population (1, 2). There has been a proliferation of data sets where the shared variability over a population is low dimensional (3-7), meaning that neuronal activity waxes and wanes as a group. How cortical networks generate low dimensional shared variability is currently unknown.Theories of cortical variability can be broadly separated into two categories: ones where variability is internally generated through recurrent network interactions ( Fig. 1Ai) and ones where variability originates external to the network (Fig. 1Aii). Networks of spiking neuron models where strong excitation is balanced by opposing recurrent inhibition produce high single neuron variability through internal mechanisms (8-10). However, these networks famously enforce an asynchronous solution, and as such fail to explain population-wide shared variability (11)(12)(13). This lack of success is contrasted with the ease of producing arbitrary correlation structure from external sources. Indeed, many past cortical models assume a global fluctuation from an external source (2,7,(14)(15)(16), and accurately capture the structure of population data.However, such phenomenological models are circular, with an assumption of variability from 2 . CC-BY-NC-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http...

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.

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 β 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.