In chaotic network models ( Sompolinsky et al., 1988), firing rates exhibit strong chaotic fluctuations, and certain types of stimuli can suppress chaos by forcing the dynamical state of the network to follow a specific trajectory, thus quenching across-trial variability ( Figure 1B Molgedey et al., 1992, Bertschinger and Natschläger, 2004, Sussillo and Abbott, 2009, Rajan et al., 2010). Stimuli then suppress this shared variability by pinning fluctuations to the vicinity of one particular attractor ( Figure 1A, bottom Blumenfeld et al., 2006, Litwin-Kumar and Doiron, 2012, Deco and Hugues, 2012, Burak and Fiete, 2012, Ponce-Alvarez et al., 2013, Doiron and Litwin-Kumar, 2014, Mochol et al., 2015). This wandering among attractors occurs in a concerted way across the population, resulting in substantial shared variability ( Figure 1A, top). In “multi-attractor” models, the network operates in a multi-stable regime in the absence of a stimulus, such that it noisily wanders among multiple possible stable states (“attractors”). There have been two dynamical mechanisms proposed to explain selected aspects of the modulation of cortical variability by stimuli. Although these patterned modulations of variability are increasingly included in quantitative analyses of neural recordings ( Renart and Machens, 2014, Orbán et al., 2016), it is still unclear what they imply about the dynamical regime in which the cortex operates. For example, in area MT, variability is quenched more strongly in cells that respond best to the stimulus, and correlations decrease more among neurons with similar stimulus preferences ( Ponce-Alvarez et al., 2013, Lombardo et al., 2015). Moreover, the degree of variability reduction can depend systematically on the tuning of individual cells. First, the onset of a stimulus quenches variability overall and, in particular, correlated variability in firing rates that is “shared” across many neurons ( Lin et al., 2015, Goris et al., 2014, Ecker et al., 2014, Ecker et al., 2016, Churchland et al., 2010).
Variability modulation shows stereotypical patterns. Modulation of variability occurs at the level of single-neuron activity, e.g., membrane potentials or spike counts ( Finn et al., 2007, Poulet and Petersen, 2008, Cardin et al., 2008, Gentet et al., 2010, Churchland et al., 2010, Tan et al., 2014), as well as in the patterns of joint activity across populations, as seen in multiunit activity or the local field potential (LFP) ( Tan et al., 2014, Chen et al., 2014, Lin et al., 2015). Moreover, variability is modulated by a variety of factors, most notably by external sensory stimuli ( Churchland et al., 2010, Kohn and Smith, 2005, Ponce-Alvarez et al., 2013), planning and execution of limb movements ( Churchland et al., 2006, Churchland et al., 2010), and attention ( Cohen and Maunsell, 2009, Mitchell et al., 2009). Neuronal activity throughout cerebral cortex is variable, both temporally during epochs of stationary dynamics and across repeated trials despite constant stimulus or task conditions ( Softky and Koch, 1993, Churchland et al., 2010). Specifying the cortical operating regime is key to understanding the computations underlying perception. Comparing to previously published and original data analyses, we show that this mechanism, unlike previous proposals, uniquely accounts for the spatial patterns and fast temporal dynamics of variability suppression. This shifts the balance from interactions that amplify variability to suppressive inhibitory feedback, quenching correlated variability around more strongly driven steady states. Given the supralinear input/output functions of cortical neurons, increased stimulus drive strengthens effective network connectivity. Here we show that a qualitatively different dynamical regime, involving fluctuations about a single, stimulus-driven attractor in a loosely balanced excitatory-inhibitory network (the stochastic “stabilized supralinear network”), best explains these modulations. These modulations have been attributed to circuit dynamics involving either multiple stable states (“attractors”) or chaotic activity. Correlated variability in cortical activity is ubiquitously quenched following stimulus onset, in a stimulus-dependent manner.
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