Wiring optimization can relate neuronal structure and function

Abstract

We pursue the hypothesis that neuronal placement in animals minimizes wiring costs for given functional constraints, as specified by synaptic connectivity. Using a newly compiled version of the Caenorhabditis elegans wiring diagram, we solve for the optimal layout of 279 nonpharyngeal neurons. In the optimal layout, most neurons are located close to their actual positions, suggesting that wiring minimization is an important factor. Yet some neurons exhibit strong deviations from ''optimal'' position. We propose that biological factors relating to axonal guidance and command neuron functions contribute to these deviations. We capture these factors by proposing a modified wiring cost function.Caenorhabditis elegans ͉ optimal placement B ecause brain structure is intimately related to its function, understanding structure should provide important clues to brain function. Traditionally, structural features of the brain are explained from the perspective of development, a complex process including such events as cell migration (1, 2), axonal guidance (3-5), cellular signaling (6), and synaptogenesis (7-10). Although much progress has been made in understanding the mechanisms of neural development, many unanswered questions remain. In particular, it is not known what determines the placement of neurons and synapses in the body, a question to be addressed in this paper.Our approach for understanding neuronal structures complements neural development and relies on the existence of general principles governing the architecture of a mature brain. Specifically, we exploit the wiring economy principle proposed by Ramón y Cajal more than 100 years ago (11). This principle postulates that, for a given wiring diagram, neurons are arranged in an animal to minimize the wiring cost. The evolutionary ''cost'' can be attributed to factors such as wire volume (12-14) and signal delay and attenuation (15-17), as well as metabolic expenditures associated with signal propagation and maintenance (18,19). Although the exact origin of the wiring cost is not known, the farther apart two neurons are, the more costly is the connection between them. The wiring cost can therefore be expressed as a function of distance between neurons and consequently minimized (12,(20)(21)(22)(23)(24)(25).Despite many successful applications of the wiring minimization principle (refs. 12-14 and 20-27, but see ref. 28), it has never been tested on the level of individual neurons for an entire nervous system. Such testing was precluded by the lack of wiring diagrams and by the computational complexity of the optimization problem. Previous works have shown that wire length minimization can explain the layout of small systems by tabulating the amount of wire required for every possible permutation of components in the network. The actual ordering of ganglia in Caenorhabditis elegans (20) and the arrangement of areas in the prefrontal cortex in the macaque (27) were found in this manner to have the shortest total wiring. Unfortunately, this brute force method is im...

Structure of deviations from optimality in biological systems

“…18-21; Materials and Methods). Previous theoretical analysis obtained the positions of cell bodies (somas) corresponding to minimum wiring cost, given the observed connectivity (18,21). The result of this calculation is reproduced in Fig.…”

High-accuracy neurite reconstruction for high-throughput neuroanatomy

“…For the C. elegans connectome a number of corrections were published recently 21 , using the original image series. Some form of proof-reading clearly is necessary during the connectomic reconstruction of neuronal networks [22][23] .…”

Disorder induces explosive synchronization

“…The construction of this data set started with the work by Albertson et al, and White et al [46,47], and has been contributed by many authors since then, in the multimedia project Wormatlas [45]. The particular wiring diagram we use was revised and completed by Chen et al [33] using other valuable sources [48,49]. The wiring information we have used is structured in four parts: connectivity data between neurons, neuron description, neuron connections to sensory organs and body muscles, and neuronal lineage.…”

“…(1) on the C. elegans neural network. The C. elegans neural network is a real network composed of 302 nodes (neurons) with a mildly heterogeneous degree distribution that undergoes synchronization dynamics [33]. For the details of the dataset, see Appendix A.…”