Concurrence of form and function in developing networks and its role in synaptic pruning

Abstract

A fundamental question in neuroscience is how structure and function of neural systems are related. We study this interplay by combining a familiar auto-associative neural network with an evolving mechanism for the birth and death of synapses. A feedback loop then arises leading to two qualitatively different types of behaviour. In one, the network structure becomes heterogeneous and dissasortative, and the system displays good memory performance; furthermore, the structure is optimised for the particular memory patterns stored during the process. In the other, the structure remains homogeneous and incapable of pattern retrieval. These findings provide an inspiring picture of brain structure and dynamics that is compatible with experimental results on early brain development, and may help to explain synaptic pruning. Other evolving networks—such as those of protein interactions—might share the basic ingredients for this feedback loop and other questions, and indeed many of their structural features are as predicted by our model.

How Memory Conforms to Brain Development

“…Taking the local probabilities to be normalized over the network, the number of edges that are added and removed at each time t depends only on the global probabilities u (κ( t )) and d (κ( t )). In this way, they determine the temporal evolution of the mean connectivity κ( t ), whereas the local probabilities π( I i ) and η( I i ) characterize the second order statistics of the network structure, such as the variance of the degree distribution or the degree-degree correlations, as we show below (see also Millán et al, 2018a). These definitions allow us to simulate the dynamics of the system via a Monte Carlo method (in particular, we make use here of the BKL algorithm Bortz et al, 1975) as follows.…”

“…The idea has been efficiently developed in the field of adaptive networks , in which a sort of coupling feedback loop sets in between the network dynamic activity and its topological structure. Outstanding phenomena then emerge, including self-organization into complex topologies that exhibit robust dynamics, spontaneous differentiation of the nodes, or complex mutual dynamics in both activity and topology, in any case mimicking many different conditions in nature (Bullmore and Sporns, 2009; Sayama et al, 2013; Millán et al, 2018a). This framework has revealed quite useful to understand fundamental questions concerning mammal brains, e.g., how structural and functional properties relate to each other both at the level of models involving sets of neurons and synapses and at the coarse-grained scale of connectomes and functional nets which is captured by imaging techniques (Bullmore and Sporns, 2009).…”

“…In any case, it now seems clear that such synaptic pruning involves in some way an optimization process, probably aimed at minimizing both energy consumption and the genetic information that otherwise would be needed to build an efficient and robust network (Chechik et al, 1999; Chklovskii et al, 2004; Johnson et al, 2010; Knoblauch et al, 2010; Navlakha et al, 2015). In particular, recent studies on associative memory have shown that this process could greatly improve memory retrieval under a noisy environment, such as it is the case in biological systems (Millán et al, 2018a). Moreover, ongoing structural plasticity in the adult brain has also been suggested to improve substantially the storage capacity (Chklovskii et al, 2004; Knoblauch et al, 2010), and has been related to graded amnesia, catastrophic forgetting, and the spacing effect (Knoblauch et al, 2014; Knoblauch and Sommer, 2016).…”

“…Here, we use an adaptive —sometimes also called co-evolving —brain network model, which has already been used by us to describe synaptic pruning in humans (Millán et al, 2018a,b), to analyze how the dynamical processes of adding and removing synapses during brain development can affect the ability of the network to store and optimally retrieve a given set of memories. Our system combines the auto-associative Amari-Hopfield neural network (Amari, 1972; Hopfield, 1982) with a preferential-attachment dynamics for the network evolution in a way that has been shown to accurately reproduce the observed variation of neuron connectivity data on human brains during infancy (Johnson et al, 2010; Millán et al, 2018b).…”

“…As empirically observed—see (Holtmaat and Svoboda, 2009) and references therein—this model assumes that the probabilities of growth and death of synapses depend on both the mean connectivity in the system and the neural activity. Previous studies have analyzed the effect of thermal noise in the system and its emergent behavior, and they have shown that the coupling between neuronal activity and connectivity creates a feedback loop between form and function since the system activity influences its topology and, in turn, it is affected by the network structure through the synaptic currents the neurons receive (Millán et al, 2018a). As a matter of fact, depending on parameters, this system is then able to produce heterogeneous networks with the presence of hubs, similar to the ones observed in actual neural systems (Van Den Heuvel and Sporns, 2011; Crossley et al, 2014; Oh et al, 2014; Stafford et al, 2014), with high memory retrieval and noise tolerance.…”