Abstracts

Rationale: Real brains learn by associative (Hebbian) processes, such that neurons that fire in the right sequence have the connection between them strengthened. Computational models of such systems, however, are highly unstable – they tend to develop either into overconnected systems that fire tonically, or they freeze into global silence. Thus real brains must have mechanisms for maintaining homeostasis of activity and connectivity. In particular, a specific level of connectivity can be defined such that information transmission and storage capacity are optimal. This level of connectivity is referred to as being critical. We describe a simple computational model that incorporates homeostasis of both activity and critical connectivity, and we show how these constraints lead to a natural interplay between the ability to learn, and the ability to develop seizures. Methods: A stochastic neural system is defined with nodes that can either fire spontaneously or after receiving excitatory input from another node. A simple scaling mechanism scales the spontaneous firing probability S(i) for node i and the connection strengths P(i,j) linking node j to node i either up or down depending on the state of activity and the state of connectivity of each node. The conditions for stability are investigated both analytically and by exhaustive simulations using LTP, LTD and STDP rules of learning.Results: (1) The spontaneous firing probability S contributes only 2-12% to the total activity; nonetheless, S must be greater than zero or else the system is unstable. (2) For systems that learn, firing rate homeostasis cannot guarantee homeostasis of connectivity. Homeostasis of connectivity is a separate principle. (3) Firing rate homeostasis is controlled by scaling of S. (4) Homeostasis of connectivity is controlled by scaling of P. (5) Scaling of P must be faster than scaling of S. (6) If S is perturbed away from its steady state value, then P will attempt to compensate. For instance, driving S to low levels causes P to rise to supercritical levels, and vice versa. (7) The post-ictal and acute post-deafferentation states result in levels of S that are below steady state values, and hence connectivity rises to supercritical levels lasting for many hours at a time.Conclusions: Requiring a neural learning system to maintain stable levels of activity and connectivity introduces strong constraints on its dynamics. These constraints are of intrinsic interest. For instance, that real brains are spontaneously active derives from our first condition of stability. Secondly, we find that the post-ictal and acute post-deafferentation states should be supercritical. Since prolonged supercriticality helps burn into memory hypersynchronous states, such states are epileptogenic. This is an example of maladaptive learning. Thirdly, we predict that increasing the rate of spontaneous activity, for instance by deep brain stimulation, can decrease the time spent in the supercritical state and help prevent epileptogenesis.