Single-Cell Membrane Potential Fluctuations Evince Network Scale-Freeness and Quasicriticality

Abstract

What information single neurons receive about general neural circuit activity is a fundamental question for neuroscience. Somatic membrane potential (V m ) fluctuations are driven by the convergence of synaptic inputs from a diverse cross-section of upstream neurons. Furthermore, neural activity is often scale-free, implying that some measurements should be the same, whether taken at large or small scales. Together, convergence and scale-freeness support the hypothesis that single V m recordings carry useful information about high-dimensional cortical activity. Conveniently, the theory of "critical branching networks" (one purported explanation for scale-freeness) provides testable predictions about scale-free measurements that are readily applied to V m fluctuations. To investigate, we obtained whole-cell current-clamp recordings of pyramidal neurons in visual cortex of turtles with unknown genders. We isolated fluctuations in V m below the firing threshold and analyzed them by adapting the definition of "neuronal avalanches" (i.e., spurts of population spiking). The V m fluctuations which we analyzed were scale-free and consistent with critical branching. These findings recapitulated results from large-scale cortical population data obtained separately in complementary experiments using microelectrode arrays described previously (Shew et al., 2015). Simultaneously recorded single-unit local field potential did not provide a good match, demonstrating the specific utility of V m . Modeling shows that estimation of dynamical network properties from neuronal inputs is most accurate when networks are structured as critical branching networks. In conclusion, these findings extend evidence of critical phenomena while also establishing subthreshold pyramidal neuron V m fluctuations as an informative gauge of high-dimensional cortical population activity. The relationship between membrane potential (V m ) dynamics of single neurons and population dynamics is indispensable tounderstanding cortical circuits. Just as important to the biophysics of computation are emergent properties such as scale-freeness, where critical branching networks offer insight. This report makes progress on both fronts by comparing statistics from singleneuron whole-cell recordings with population statistics obtained with microelectrode arrays. Not only are fluctuations of somatic V m scale-free, they match fluctuations of population activity. Thus, our results demonstrate appropriation of the brain's own subsampling method (convergence of synaptic inputs) while extending the range of fundamental evidence for critical phenomena in neural systems from the previously observed mesoscale (fMRI, LFP, population spiking) to the microscale, namely, V m fluctuations.

Temporal signatures of criticality in human cortical excitability as probed by early somatosensory responses

“…In addition, assuming that fluctuations of the early SEP reflect changes in EPSCs which in turn depend on pre-stimulus membrane potentials, it follows that these dynamics may be manifested in ongoing modulations of membrane potentials. Intriguingly, dynamics close to criticality have been demonstrated for membrane potential fluctuations in pyramidal neurons of the visual cortices in turtles (Johnson et al, 2019), consistent with our idea of the origin of power-law dynamics in early human SEPs.…”

“…Furthermore, when focusing on the temporal domain, power-law dynamics can be found in human resting-state fMRI networks (Tagliazucchi et al, 2013), as well as in amplitude fluctuations of alpha band activity in the MEG (Linkenkaer-Hansen, Nikouline, Palva, & Ilmoniemi, 2001;Palva et al, 2013). In addition, a recent study observed that even single-cell membrane potentials in the turtle visual cortex show critical dynamics (Johnson, Wright, Xia, & Wessel, 2019). These findings suggest that fluctuations of the instantaneous brain state are characterized by a complex spatio-temporal structure, leading to endogenous dynamics in cortical excitability which, in turn, should affect the commonly observed variability in brain responses, such as ERPs.…”

Multi-structure Cortical States Deduced From Intracellular Representations of Fixed Tactile Input Patterns

“…Moreover, it was observed that stimuli during a Downstate could often evoke disproportionately large responses, by inducing transitions to an Upstate. More recent studies suggest such effects to be inducible because the neocortex is a system with criticality phenomena, where small changes at critical states can cause avalanche effects of increased excitability that spread widely through the cortical network (Wright and Wessel, 2017 ; Johnson et al, 2019 ). Although our data indicate a much more fine-grained subdivision of cortical states than the binary dichotomy between Up and Down states, such avalanche effects could be the underlying reason for the response types we observed here.…”

Impact of Physical Obstacles on the Structural and Effective Connectivity of in silico Neuronal Circuits

“…The latter can be employed to capture the non-Euclidean geometry of the human brain and its relation with developmental traits and multi-scale dynamics (Werner, 2010 ; Hofman, 2014 ). Fractality and multi-scale organization are indeed inherent properties of cortical circuits and are closely related to the concept of criticality (Poil et al, 2008 ; Friedman et al, 2012 ; Haimovici et al, 2013 ; Massobrio et al, 2015 ; Marshall et al, 2016 ; Johnson et al, 2019 ), in which a neuronal circuit operates at the boundary between an ordered, strongly coupled state and a disordered, weakly coupled one. Neuronal systems at criticality exhibit long-range spatial and temporal correlations with power-law distributed statistics, facilitating a broad dynamic repertoire and swift communication among distant areas.…”