Stability and structural constraints of random brain networks with excitatory and inhibitory neural populations

Abstract

The stability of brain networks with randomly connected excitatory and inhibitory neural populations is investigated using a simplified physiological model of brain electrical activity. Neural populations are randomly assigned to be excitatory or inhibitory and the stability of a brain network is determined by the spectrum of the network's matrix of connection strengths. The probability that a network is stable is determined from its spectral density which is numerically determined and is approximated by a spectral distribution recently derived by Rajan and Abbott. The probability that a brain network is stable is maximum when the total connection strength into a population is approximately zero and is shown to depend on the arrangement of the excitatory and inhibitory connections and the parameters of the network. The maximum excitatory and inhibitory input into a structure allowed by stability occurs when the net input equals zero and, in contrast to networks with randomly distributed excitatory and inhibitory connections, substantially increases as the number of connections increases. Networks with the largest excitatory and inhibitory input allowed by stability have multiple marginally stable modes, are highly responsive and adaptable to external stimuli, have the same total input into each structure with minimal variance in the excitatory and inhibitory connection strengths, and have a wide range of flexible, adaptable, and complex behavior.

Efficient Physical Embedding of Topologically Complex Information Processing Networks in Brains and Computer Circuits

“…Functional patterns on hierarchically modular architectures have specifically been shown to display computationally advantageous dynamics characterized by stability and diversity [33], unlike simulated dynamics on either random or non-hierarchically small-world architectures [34]. Sporns provides a simple generative model for fractal hierarchical networks and shows further relationships between their structural and functional properties, suggesting that connectivity may strongly constrain dynamics [32], [35]. Computational models of hierarchical modularity have shown that networks configured in this way have the distinctive advantage of being robustly stable under large scale reconnection of substructure [36].…”

Stability constraints on large-scale structural brain networks

“…To apply this continuum model to brain networks we previously used a number of simplifying assumptions. In particular, we assumed that all neural populations have instantaneous dendritic response times and there is no time delay for a signal to be sent from one population to the other (Gray and Robinson, 2006, 2008, 2009b,a; Robinson et al, 2009). For this study we relax some of these assumptions.…”

“…The specific random networks we investigate are the same random networks we have previously investigated (Gray and Robinson, 2006, 2008, 2009a,b). These networks consist of excitatory and inhibitory connections.…”

“…Based on the hypothesis that stability is a dynamical constraint on the structure and physiology of structural brain networks we have investigated the effect of stability of large-scale structural brain networks (Gray and Robinson, 2006, 2008, 2009b,a; Robinson et al, 2009). …”

Determination of effective brain connectivity from functional connectivity using propagator-based interferometry and neural field theory with application to the corticothalamic system

“…In (14) the quantity N a from (1) is only nonzero in the case of N s and has been written as an integral over an input from the n population activity Q n , which is included in the sum over b. If the sum over b were restricted to exclude the n population, an equivalent additional term N s would appear instead on the right of (14) for a = s, with [26,56] N s (r,t) = G sn L(ω)φ sn (r,t),…”