Friedrich Förstner

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. The essential structure of a neuronal tree is thereby captured by the density profile of its spanning field and by a single parameter, a balancing factor weighing the costs for material and conduction time. This balancing factor determines a neuron's electrotonic compartmentalization. Additions to this rule, when required in the construction process, can be directly attributed to developmental processes or a neuron's computational role within its neural circuit. The simulations presented here are implemented in an open-source software package, the "TREES toolbox," which provides a general set of tools for analyzing, manipulating, and generating dendritic structure, including a tool to create synthetic members of any particular cell group and an approach for a 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 synthetic neural networks.

Motion vision is essential for navigating through the environment. Due to its genetic amenability, the fruit fly Drosophila has been serving for a lengthy period as a model organism for studying optomotor behavior as elicited by large-field horizontal motion. However, the neurons underlying the control of this behavior have not been studied in Drosophila so far. Here we report the first whole cell recordings from three cells of the horizontal system (HSN, HSE, and HSS) in the lobula plate of Drosophila. All three HS cells are tuned to large-field horizontal motion in a direction-selective way; they become excited by front-to-back motion and inhibited by back-to-front motion in the ipsilateral field of view. The response properties of HS cells such as contrast and velocity dependence are in accordance with the correlation-type model of motion detection. Neurobiotin injection suggests extensive coupling among ipsilateral HS cells and additional coupling to tangential cells that have their dendrites in the contralateral hemisphere of the brain. This connectivity scheme accounts for the complex layout of their receptive fields and explains their sensitivity both to ipsilateral and to contralateral motion. Thus the main response properties of Drosophila HS cells are strikingly similar to the responses of their counterparts in the blowfly Calliphora, although we found substantial differences with respect to their dendritic structure and connectivity. This long-awaited functional characterization of HS cells in Drosophila provides the basis for the future dissection of optomotor behavior and the underlying neural circuitry by combining genetics, physiology, and behavior.