Abstract

Understanding the principles governing axonal and dendritic branching is essential for unravelling the functionality of single neurons and the way in which they connect. Nevertheless, no formalism has yet been described which can capture the general features of neuronal branching. Here we propose such a formalism, which is derived from the expression of dendritic arborizations as locally optimized graphs. Inspired by Ramón y Cajal’s laws of conservation of cytoplasm and conduction time in neural circuitry, we show that this graphical representation can be used to optimize these variables. This approach allows us to generate synthetic branching geometries which replicate morphological features of any tested neuron. We demonstrate that the structure of a neuronal tree is captured by its spatial extent and by a single parameter, a balancing factor weighing the costs of conservation of cytoplasm and conduction time. This balancing factor allows a neuron to adjust its preferred electrotonic compartmentalization. A general set of tools can be derived from these simulations for analyzing, manipulating and generating dendritic structure, including a tool to generate artificial members of any particular cell group and an approach for model-based supervised automatic morphological reconstruction from fluorescent image stacks. These approaches provide new insights into the constraints governing dendritic architectures. They also provide a novel framework for modelling and analyzing neuronal branching structures and for constructing realistic artificial neural networks.