Pairwise Ising Model Analysis of Human Cortical Neuron Recordings

Abstract

Abstract. During wakefulness and deep sleep brain states, cortical neural networks show a different behavior, with the second characterized by transients of high network activity. To investigate their impact on neuronal behavior, we apply a pairwise Ising model analysis by inferring the maximum entropy model that reproduces single and pairwise moments of the neuron's spiking activity. In this work we first review the inference algorithm introduced in Ferrari, Phys. Rev. E (2016) [1]. We then succeed in applying the algorithm to infer the model from a large ensemble of neurons recorded by multi-electrode array in human temporal cortex. We compare the Ising model performance in capturing the statistical properties of the network activity during wakefulness and deep sleep. For the latter, the pairwise model misses relevant transients of high network activity, suggesting that additional constraints are necessary to accurately model the data. Keywords: Ising model, maximum entropy principle, natural gradient, human temporal cortex, multielectrode array recording, brain states Advances in experimental techniques have recently enabled the recording of the activity of tens to hundreds of neurons simultaneously [2] and has spurred the interest in modeling their collective behavior [3,4,5,6,7,8,9]. To this purpose, the pairwise Ising model has been introduced as the maximum entropy (most generic [10]) model able to reproduce the first and second empirical moments of the recorded neurons. Moreover it has already been applied to different brain regions in different animals [3,5,6,9] and shown to work efficiently [11] .The inference problem for a pairwise Ising model is a computationally challenging task [12], that requires devoted algorithms [13,14,15]. Recently, we proposed a data-driven algorithm and applied it on rat retinal recordings [1]. In the present work we first review the algorithm structure and then describe our successful application to a recording in the human temporal cortex [4].We use the inferred Ising model to test if a model that reproduces empirical pairwise covariances without assuming any other additional information, also predicts empirical higher-order statistics. We apply this strategy separately to brain states of wakefulness (Awake) and Slow-Wave Sleep (SWS). In contrast to arXiv:1710.09929v1 [q-bio.NC]

Maximum entropy models reveal the correlation structure in cortical neural activity during wakefulness and sleep

“…The inference can thus be performed by an ascendant dynamics that requires to estimate model averages of observables. For the Ising model we applied the Markov-Chain Monte-Carlo method introduced in [3,10]. For the one population model, we applied the Newton dynamics proposed in [5] For the two-population model, we modify the algorithm of [5] to take into account two populations.…”

Disrupted excitation-inhibition balance in cognitively normal individuals at risk of Alzheimer’s disease

“…Note that although our framework for constructing the rs-SC does not explicitly model brain activity at a neuronal level, several seminal studies have used the Ising model to investigate neuronal firing patterns with success, showing that ensemble level activities can be well explained by pairwise Ising interactions [24,57]. To be clear, from a connectomics perspective, if several brain regions are identified to have an increase in positive edges in the rs-SC, collectively, that would suggest a wider-spread pattern of coupling (i.e., more likely to exhibit a pattern of global coupling) that may subserve hyperexcitation.…”

Bridging Single Neuron Dynamics to Global Brain States

“…The Ising model for spin glasses (Jaynes, 1982) fitted to neural data (Schneidman et al, 2006) has revealed divergent types of emergent neuronal dynamics in conscious and unconscious states. While neuronal interactions are pairwise in wakefulness (Nghiem et al, 2017), coupling becomes population-wide in deep sleep (Tavoni et al, 2017; Nghiem et al, 2018b). In particular, inhibitory neurons organize synchronous activity across populations (Nghiem et al, 2018b; Zanoci et al, 2019), especially during deep sleep (Peyrache et al, 2012; Le Van Quyen et al, 2016; Olcese et al, 2016) where inhibitory neurons regulate rhythms of slow wave dynamics (Compte et al, 2008; Funk et al, 2017; Zucca et al, 2017, 2019).…”