Homeostatic structural plasticity increases the efficiency of small-world networks

Abstract

In networks with small-world topology, which are characterized by a high clustering coefficient and a short characteristic path length, information can be transmitted efficiently and at relatively low costs. The brain is composed of small-world networks, and evolution may have optimized brain connectivity for efficient information processing. Despite many studies on the impact of topology on information processing in neuronal networks, little is known about the development of network topology and the emergence of efficient small-world networks. We investigated how a simple growth process that favors short-range connections over long-range connections in combination with a synapse formation rule that generates homeostasis in post-synaptic firing rates shapes neuronal network topology. Interestingly, we found that small-world networks benefited from homeostasis by an increase in efficiency, defined as the averaged inverse of the shortest paths through the network. Efficiency particularly increased as small-world networks approached the desired level of electrical activity. Ultimately, homeostatic small-world networks became almost as efficient as random networks. The increase in efficiency was caused by the emergent property of the homeostatic growth process that neurons started forming more long-range connections, albeit at a low rate, when their electrical activity was close to the homeostatic set-point. Although global network topology continued to change when neuronal activities were around the homeostatic equilibrium, the small-world property of the network was maintained over the entire course of development. Our results may help understand how complex systems such as the brain could set up an efficient network topology in a self-organizing manner. Insights from our work may also lead to novel techniques for constructing large-scale neuronal networks by self-organization.

Associative properties of structural plasticity based on firing rate homeostasis in recurrent neuronal networks

“…We use a target rate ρ = 8 Hz and growth parameter β = 2 for both pre-and postsynaptic elements of all excitatory neurons, unless stated otherwise. Previous work on SP has used different functions to describe how these elements change with the neuron's activity, such as linear [6,7,8,53], gaussian [5,9,19], or logistic [10]. Since there is currently no direct experimental data showing how the number of these elements vary with firing rate, we chose a generic linear function to implement a simple phenomenological model of firing rate homeostasis.…”

Network remodeling induced by transcranial brain stimulation: A computational model of tDCS-triggered cell assembly formation

“…Butz et al (2014) first introduced the term homeostatic structural plasticity with reference to previously published versions of the theory (Butz et al, 2009;Butz and van Ooyen, 2013;Van Ooyen, 2011), which was based on ample experimental evidence that structural plasticity (Trachtenberg et al, 2002;Oray et al, 2004;Holtmaat and Svoboda, 2009;Pfeiffer et al, 2018) as well as homeostatic regulation of activity (Turrigiano and Nelson, 2004;Lee et al, 2013;Keck et al, 2013) are constantly taking place in many brain areas. This homeostatic structural plasticity model was able to provide explanations for cortical reorganization after stroke (Butz et al, 2009) and lesion (Butz-Ostendorf and van Ooyen, 2017), and for the formation of certain global network features during development (Butz et al, 2014;Gallinaro and Rotter, 2018). In this model, changing the number of synaptic contacts between two neurons leads to an apparent facilitation or depression of this specific connection, and the model may therefore also account for some cases of functional plasticity.…”

Combined Action Observation and Motor Imagery Neurofeedback for Modulation of Brain Activity

“…NFB learning has been shown to induce task-related changes in both white and gray matter volume, (Ghaziri et al, 2013; Butz et al, 2014) suggesting these transient changes can lead to lasting effects on the behavior of various functional neural networks. The presence of lasting changes in functional neural activity following training is referred to as NFB transfer, and it has been shown to last 6 months (Leins et al, 2007), 2 years (Gani, 2009), or even 9 years (Strehl, 2014) following NFB training.…”