Development of nerve connections under the control of neurotrophic factors: parallels with consumer-resource systems in population biology

From Caenorhabditis elegans to the human connectome: a specific modular organization increases metabolic, functional and developmental efficiency

The connectome, or the entire connectivity of a neural system represented by a network, ranges across various scales from synaptic connections between individual neurons to fibre tract connections between brain regions. Although the modularity they commonly show has been extensively studied, it is unclear whether the connection specificity of such networks can already be fully explained by the modularity alone. To answer this question, we study two networks, the neuronal network of Caenorhabditis elegans and the fibre tract network of human brains obtained through diffusion spectrum imaging. We compare them to their respective benchmark networks with varying modularities, which are generated by link swapping to have desired modularity values. We find several network properties that are specific to the neural networks and cannot be fully explained by the modularity alone. First, the clustering coefficient and the characteristic path length of both C. elegans and human connectomes are higher than those of the benchmark networks with similar modularity. High clustering coefficient indicates efficient local information distribution, and high characteristic path length suggests reduced global integration. Second, the total wiring length is smaller than for the alternative configurations with similar modularity. This is due to lower dispersion of connections, which means each neuron in the C. elegans connectome or each region of interest in the human connectome reaches fewer ganglia or cortical areas, respectively. Third, both neural networks show lower algorithmic entropy compared with the alternative arrangements. This implies that fewer genes are needed to encode for the organization of neural systems. While the first two findings show that the neural topologies are efficient in information processing, this suggests that they are also efficient from a developmental point of view. Together, these results show that neural systems are organized in such a way as to yield efficient features beyond those given by their modularity alone.

A cost-benefit analysis of neuronal morphology

Over hundreds of millions of years, evolution has optimized brain design to maximize its functionality while minimizing costs associated with building and maintenance. This observation suggests that one can use optimization theory to rationalize various features of brain design. Here, we attempt to explain the dimensions and branching structure of dendritic arbors by minimizing dendritic cost for given potential synaptic connectivity. Assuming only that dendritic cost increases with total dendritic length and path length from synapses to soma, we find that branching, planar, and compact dendritic arbors, such as those belonging to Purkinje cells in the cerebellum, are optimal. The theory predicts that adjacent Purkinje dendritic arbors should spatially segregate. In addition, we propose two explicit cost function expressions, falsifiable by measuring dendritic caliber near bifurcations.

Competition in neurite outgrowth and the development of nerve connections

During the development of the nervous system, neurons form their characteristic morphologies and become assembled into synaptically connected networks. In both neuronal morphogenesis and the development of nerve connections, competition plays an important role. Although the notion of competition is commonly used in neurobiology, there is little understanding of the nature of the competitive process and the underlying molecular and cellular mechanisms. In this chapter, we review a model of competition between outgrowing neurites, as well as various models of competition that have been proposed for the refinement of connections that takes place in the development of the neuromuscular and visual systems. We describe in detail a model that links competition in the development of nerve connections with the underlying actions and biochemistry of neurotrophic factors.

Mathematical analysis of competition between sensory ganglion cells for neurotrophic factor in the skin

A model is presented of competition between sensory axons for trophic molecules (e.g. a neurotrophin such as NGF), produced in a region of skin small enough to permit their free diffusion throughout it; e.g., a touch dome, or a vibrissal follicle hair sinus. The variables specified are the number of high affinity trophic factor receptors per axon terminal and the concentration of trophic factor in the extracellular space. Previous models of this class predicted the loss of all the axons innervating the region except the one requiring least trophic factor for its maintenance, even with high rates of trophic factor production. In the present model, we have imposed upper limits to axonal growth, thereby introducing new equilibria, and we show by a global analysis using LaSalle's theorem, and also by local analysis, that several axons can then coexist if the rate of production of trophic molecules is sufficiently high.