Simple spontaneously active Hebbian learning model: Homeostasis of activity and connectivity, and consequences for learning and epileptogenesis

Abstract

As suggested by recent experimental evidence, a spontaneously active neural system that is capable of continual learning should also be capable of homeostasis of both activity and connectivity. The connectivity appears to be maintained at a level that is optimal for information transmission and storage. We present a simple stochastic computational Hebbian learning model that incorporates homeostasis of both activity and connectivity, and we explore its stability and connectivity properties. We find that homeostasis of activity and connectivity imposes structural and dynamic constraints on the behavior of the system. For instance, the connectivity pattern is sparse and activation patterns are scale-free. Additionally, homeostasis of connectivity must occur on a timescale faster than homeostasis of activity. We demonstrate the clinical relevance of these constraints by simulating a prolonged seizure and acute deafferentation. Based on our simulations, we predict that in both the post-seizure and post-deafferentation states, the system is over-connected and, hence, epileptogenic. We further predict that interventions that boost spontaneous activity should be protective against epileptogenesis, while interventions that boost stimulated or connectivity-related activity are pro-epileptogenic.

An open hypothesis: Is epilepsy learned, and can it be unlearned?

“…This finding has also attracted increasing theoretical and computational interest. Simple computational models have demonstrated that a branching ratio of σ = 1 indeed gives a power law size distribution, and it has the correct power of −1.5 [21,30,31]. Thus we refer to systems with σ = 1 as being at the critical point, while systems with σ < 1 are subcritical and systems with σ > 1are supercritical.…”

“…Each population spike represents the near simultaneous discharge of a group of local principal neurons. The exact number of neurons contributing to a given population spike is not known and is not essential to our discussion, but based on lengthscale and neuronal density estimates, this may be as high as 1000 [21]. In practice, population spikes are identified as excursions of electrode potentials that are more than 3 standard deviations above or below the mean.…”

“…The power law distribution of avalanche sizes suggests that these networks are operating near a "critical point," so named because the power laws are reminiscent of the critical point of phase transitions of matter [21,[27][28][29]. Although not identical to the critical point of phase transitions, because it lacks the property of universality, the critical point of neural systems has attracted increasing theoretical and computational interest because of its importance to neural systems function [21,[30][31][32][33][34][35][36][37][38][39][40].…”

“…Although not identical to the critical point of phase transitions, because it lacks the property of universality, the critical point of neural systems has attracted increasing theoretical and computational interest because of its importance to neural systems function [21,[30][31][32][33][34][35][36][37][38][39][40]. A critical neural system is balanced between a phase where activity is damped and a phase where activity is expanding.…”

“…When the network deviates from the critical point, information processing and stability will be compromised [21,27]. A neural network whose job it is to process information, to learn and to adapt, must therefore maintain itself near the critical point, even when synaptic weights change strengths during the process of learning.…”