Total Wiring Length Minimization of C. elegans Neural Network: A Constrained Optimization Approach

Using the most recent data on the connectivity of the C. elegans neural network, we find optimal two-dimensional positions of interneurons that minimize the total wiring length provided that the positions of motor and sensory neurons are fixed. The rationale behind fixing motor and sensory neurons is the following: while positions of motor and sensory neurons can be influenced by the locations of muscles and sensory organs they are attached to, the main function of interneurons is to connect other neurons, and their placement could try to minimize the wiring length. Solutions for l 1, l 2 and squared l 2–norm were obtained. For the Euclidean norm l 2, the relative and absolute difference between the real and optimal total wiring lengths is minimal among these functions of distance. Additional network constraints were discussed such as assignment of different weights to electrical or chemical connections, fixation of “tail” interneurons, minimal interneural distance limitation, and others. These constraints were compared by their influence on the optimal positions of interneurons.