Homeostatic structural plasticity increases the efficiency of small-world networks

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

A Model for Cortical Rewiring Following Deafferentation and Focal Stroke

It is still unclear to what extent structural plasticity in terms of synaptic rewiring is the cause for cortical remapping after a lesion. Recent two-photon laser imaging studies demonstrate that synaptic rewiring is persistent in the adult brain and is dramatically increased following brain lesions or after a loss of sensory input (cortical deafferentation). We use a recurrent neural network model to study the time course of synaptic rewiring following a peripheral lesion. For this, we represent axonal and dendritic elements of cortical neurons to model synapse formation, pruning and synaptic rewiring. Neurons increase and decrease the number of axonal and dendritic elements in an activity-dependent fashion in order to maintain their activity in a homeostatic equilibrium. In this study we demonstrate that synaptic rewiring contributes to neuronal homeostasis during normal development as well as following lesions. We show that networks in homeostasis, which can therefore be considered as adult networks, are much less able to compensate for a loss of input. Interestingly, we found that paused stimulation of the networks are much more effective promoting reorganization than continuous stimulation. This can be explained as neurons quickly adapt to this stimulation whereas pauses prevents a saturation of the positive stimulation effect. These findings may suggest strategies for improving therapies in neurologic rehabilitation

A simple rule for axon outgrowth and synaptic competition generates realistic connection lengths and filling fractions

Neural connectivity at the cellular and mesoscopic level appears very specific and is presumed to arise from highly specific developmental mechanisms. However, there are general shared features of connectivity in systems as different as the networks formed by individual neurons in Caenorhabditis elegans or in rat visual cortex and the mesoscopic circuitry of cortical areas in the mouse, macaque, and human brain. In all these systems, connection length distributions have very similar shapes, with an initial large peak and a long flat tail representing the admixture of long-distance connections to mostly short-distance connections. Furthermore, not all potentially possible synapses are formed, and only a fraction of axons (called filling fraction) establish synapses with spatially neighboring neurons. We explored what aspects of these connectivity patterns can be explained simply by random axonal outgrowth. We found that random axonal growth away from the soma can already reproduce the known distance distribution of connections. We also observed that experimentally observed filling fractions can be generated by competition for available space at the target neurons--a model markedly different from previous explanations. These findings may serve as a baseline model for the development of connectivity that can be further refined by more specific mechanisms.Comment: 31 pages (incl. supplementary information); Cerebral Cortex Advance Access published online on May 12, 200

An Algorithm for Finding Candidate Synaptic Sites in Computer Generated Networks of Neurons with Realistic Morphologies

Neurons make synaptic connections at locations where axons and dendrites are sufficiently close in space. Typically the required proximity is based on the dimensions of dendritic spines and axonal boutons. Based on this principle one can search those locations in networks formed by reconstructed neurons or computer generated neurons. Candidate synapses are then located where axons and dendrites are within a given criterion distance from each other. Both experimentally reconstructed and model generated neurons are usually represented morphologically by piecewise-linear structures (line pieces or cylinders). Proximity tests are then performed on all pairs of line pieces from both axonal and dendritic branches. Applying just a test on the distance between line pieces may result in local clusters of synaptic sites when more than one pair of nearby line pieces from axonal and dendritic branches is sufficient close, and may introduce a dependency on the length scale of the individual line pieces. The present paper describes a new algorithm for defining locations of candidate synapses which is based on the crossing requirement of a line piece pair, while the length of the orthogonal distance between the line pieces is subjected to the distance criterion for testing 3D proximity