How Axon and Dendrite Branching Are Governed by Time, Energy, and Spatial Constraints

Abstract

Neurons are connected by complex branching processes - axons and dendrites - that collectively process information for organisms to respond to their environment. Classifying neurons according to differences in structure or function is a fundamental part of neuroscience. Here, by constructing new biophysical theory and testing against our empirical measures of branching structure, we establish a correspondence between neuron structure and function as mediated by principles such as time or power minimization for information processing as well as spatial constraints for forming connections. Specifically, based on these principles, we use undetermined Lagrange multipliers to predict scaling ratios for axon and dendrite sizes across branching levels. We test our predictions for radius and length scale factors against those extracted from neuronal images, measured for cell types and species that range from insects to whales. Notably, our findings reveal that the branching of axons and peripheral nervous system neurons is mainly determined by time minimization, while dendritic branching is mainly determined by power minimization. Further comparison of different dendritic cell types reveals that Purkinje cell dendrite branching is constrained by material costs while motoneuron dendrite branching is constrained by conduction time delay over a range of species. Our model also predicts a quarter-power scaling relationship between conduction time delay and species body size, which is supported by experimental data and may help explain the emergence of hemispheric specialization in larger animals as a means to offset longer time delays. Author summary Neurons are the basic building blocks of the nervous system, responsible for information processing and communication in animals. They consist of a centralized cell body and two types of processes - axons and dendrites - that connect to one another. Previous studies of the differences among neuron cell types have focused on comparisons of either structure or function separately, without considering combined effects. Based on theory for structure of and flow through biological resource distribution networks, we develop a new model that relates neuron structure to function. We find that differences in structure between axons and dendrites as well as between dendrites of different cell types can be related to differences in function and associated evolutionary pressures. Moreover, using our mathematical model, we find that the conduction time delay of electrical signals systematically varies with species body size - neurons in larger species have longer delays - providing a possible explanation for hemispheric specialization in larger animals.