Modelling the impact of structural directionality on connectome-based models of neural activity

Understanding structure-function relationships in the brain remains an important challenge in neuroscience. However, whilst structural brain networks are intrinsically directed, due to the prevalence of chemical synapses in the cortex, most studies in network neuroscience represent the brain as an undirected network. Here, we explore the role that directionality plays in shaping transition dynamics of functional brain states. Using a system of Hopfield neural elements with heterogeneous structural connectivity given by different species and parcellations (cat, Caenorhabditis elegans and two macaque networks), we investigate the effect of removing directionality of connections on brain capacity, which we quantify via its ability to store attractor states. In addition to determining large numbers of fixed-point attractor sets, we deploy the recently developed basin stability technique in order to assess the global stability of such brain states, which can be considered a proxy for network state robustness. Our study indicates that not only can directed network topology have a significant effect on the information capacity of connectome-based networks, but it can also impact significantly the domains of attraction of the aforementioned brain states. In particular, we find network modularity to be a key mechanism underlying the formation of neural activity patterns, and moreover, our results suggest that neglecting network directionality has the scope to eliminate states that correlate highly with the directed modular structure of the brain. A numerical analysis of the distribution of attractor states identified a small set of prototypical direction-dependent activity patterns that potentially constitute a `skeleton' of the non-stationary dynamics typically observed in the brain. This study thereby emphasizes the substantial role network directionality can have in shaping the brain's ability to both store and process information.