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Chapter 11
An Optimization Approach to the Structure of
the Neuronal Layout of C. elegans
Alex Arenas, Alberto Fernandez and Sergio Gomez
Departament d'Enginyeria Informatica i Matematiques,
Universitat Rovira i Virgili, E-43007 Tarragona, Spain
11.1. Introduction
Between 1899 and 1904, in the masterpiece Textura del sistema nervioso del hom-
bre y de los vertebrados (published in separated folded sheets during these years),
S. Ramon y Cajal established the linchpin of modern neuroscience [1]. Among its
capital contributions, he stated the law of maximum economy in space, time and
inter-connective matter, that explicitly hypothesizes about an optimization of the
structure and function of the nervous systems during evolution, reected in an eco-
nomical principle for informational driving processes in neuronal circuitries. This
fascinating elucidation of the complex structure of nervous systems, has been how-
ever very dicult to quantify with real data. The topological mapping of each one
of the neurons of a vertebrate's brain is still out of nowadays technical possibilities.
However, it exists an invertebrate organism for which the complete neuronal layout
is known, the nematode C. elegans, syee Fig. 11.1. The current computational ca-
pabilities and the disposal of such a connectivity data set allow us to explore the
conjecture of S. Ramon y Cajal about the \wiring economy principle".
In this chapter we will review a recent optimization approach to the wiring
connectivity in C. elegans, discussing the possible outcomes of the optimization
process, its dependence on the optimization parameters, and its validation with
the actual neuronal layout data. We will follow the main procedure described
in the work by Chen et al. [2{4]. The results show that the current approach
to optimization of neuronal layouts is still not conclusive, and then the \wiring
economy principle" remains unproved.
11.2. The Dataset
The nematode Caenorhabditis Elegans has become in biology the experimental or-
ganism par excellence to understand the mechanisms underlying a whole animal's
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