Generative models of rich clubs in Hebbian neuronal networks and large-scale human brain networks

Abstract

Rich clubs arise when nodes that are 'rich' in connections also form an elite, densely connected 'club'. In brain networks, rich clubs incur high physical connection costs but also appear to be especially valuable to brain function. However, little is known about the selection pressures that drive their formation. Here, we take two complementary approaches to this question: firstly we show, using generative modelling, that the emergence of rich clubs in large-scale human brain networks can be driven by an economic trade-off between connection costs and a second, competing topological term. Secondly we show, using simulated neural networks, that Hebbian learning rules also drive the emergence of rich clubs at the microscopic level, and that the prominence of these features increases with learning time. These results suggest that Hebbian learning may provide a neuronal mechanism for the selection of complex features such as rich clubs. The neural networks that we investigate are explicitly Hebbian, and we argue that the topological term in our model of large-scale brain connectivity may represent an analogous connection rule. This putative link between learning and rich clubs is also consistent with predictions that integrative aspects of brain network organization are especially important for adaptive behaviour.

Nonlinear growth: an origin of hub organization in complex networks

“…Indeed, studies on brain evolution and development support an exponential increase in the number of brain regions [9] and neurons [29–32]. Interestingly, in contrast with the model in Vértes et al [33], nonlinear growth explains how rich-club organization arises without any access to non-local information. Moreover, our model is in agreement with observations of brain structure following neurodevelopmental disruption after very preterm birth; counterintuitively, rich-club organization is increased in such atypical scenarios [24].…”

A Network Neuroscience of Human Learning: Potential to Inform Quantitative Theories of Brain and Behavior

“…A generative model is one that posits a set of parameterized wiring rules that can produce network architectures consistent with the observed data [109,110]. In recent applications to brain networks, these models have been exercised in the context of static network representations in both health [111] and disease [112], and in both humans and non-human animals [113]. Extending these tools into the temporal domain is a particularly exciting prospect which could offer fundamental insights into the mechanisms of network reconfiguration, and alterations in those mechanisms that may accompany normative neurodevelopment [114], healthy aging [115], or aberrant dynamics in neurological disease [116-118] or psychiatric disorders [107,119,120] that impact on learning.…”

Complex network theory and the brain

“…Generative models are thus essentially explanations of the emergence of distributions, under constraints. Vertés et al [37] use this strategy to investigate the formation of the rich club of interconnected hubs in brain networks. Because rich club nodes are spatially distributed within the whole brain network their functioning is associated with relatively high wiring and metabolic costs, raising questions about the selection pressures favouring their formation.…”