Circuit models of low dimensional shared variability in cortical networks

Abstract

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...

The correlated state in balanced neuronal networks

“…Another alternative mechanism for achieving larger correlations in balanced networks is through instabilities of the balanced state. Such instabilities can create patternforming dynamics that produce intrinsically generated spike train correlations [42,43,[62][63][64][65][66][67][68]. Some recordings show that local circuit connectivity can increase correlations [69], which is consistent with internally generated correlations, but inconsistent with the mechanisms that we consider here.…”

“…The overall finding in this previous work is that spike train correlations in the recurrent network are O(1/N ). Some exceptions to this O(1/N ) scaling have been demonstrated in spatially extended networks with distance-dependent connection probabilities and in networks with singular mean-field connectivity matrices [39][40][41][42]46], a topic to which we return in Section VI.…”

“…This raises the question of how larger correlation magnitudes can arise in balanced cortical circuits. Later theoretical work showed that larger correlations can be obtained between some cell pairs in densely connected networks with specially constructed connectivity structure [38][39][40][41][42], offering a potential explanation of the larger correlations often observed in recordings.…”

Flexible and accurate decoding of neural populations through stochastic comodulation

“…On the one hand (Bondy et al, 2018) suggests that a top-down source of the modulation changes pairwise correlations in V1 in a task-dependent manner. On the other hand, (Huang et al, 2019) show that detailed noise correlation structure can be produced locally. Changes in these locally produced correlations could be triggered via recruitment of inhibitory neurons (Middleton et al, 2012).…”

Reinforcement regulates timing variability in thalamus

“…It is therefore possible that variability of firing rates in thalamus originates in cortex. However, to act as an effective mechanism in our motor timing task, correlated cortical variability must be additionally sensitive to reward-dependent neuromodulatory signals such as dopamine (Frank et al, 2009) possibly by acting on local inhibitory neurons (Huang et al, 2019) . The basal ganglia could also play a role in reward-dependent control of thalamic firing rates (Kunimatsu and Tanaka, 2016;Kunimatsu et al, 2018) .…”