Metabolic energetics underlying attractors in neural models

Abstract

Neural population modeling, including the role of neural attractors, is a promising tool for understanding many aspects of brain function. We propose a modeling framework to connect the abstract variables used in modeling to recent cellular level estimates of the bioenergetic costs of different aspects of neural activity, measured in ATP consumed per second per neuron. Based on recent work, an empirical reference for brain ATP use for the awake resting brain was estimated as [~]2x109 ATP/s-neuron across several mammalian species. The energetics framework was applied to the Wilson-Cowan (WC) model of two interacting populations of neurons, one excitatory (E) and one inhibitory (I). Attractors were considered exhibiting steady-state behavior and limit cycle behavior, both of which end when the excitatory stimulus ends, and sustained activity that persists after the stimulus ends. The general finding was that the energy cost essentially follows the firing rate (average spikes/s) of the E-population, and firing rates of 8-10 spikes/s are in good agreement with the empirical reference value of ATP use. Self-sustained firing driven by recurrent excitation, though, involves higher firing rates and a higher energy cost. By considering a network in which each node is a WC model, we found that a combination of three nodes can serve as a circuit element that turns on when input passes a threshold and then persists after the input ends (an on-switch), with moderate overall ATP use. The proposed framework can serve as a guide for anchoring neural population models to plausible bioenergetics requirements.