Computational modeling of dendritic tiling by diffusible extracellular suppressor.

The development of neuronal class-specific dendrites is a basis for the correct functioning of the nervous system. For instance, tiling of dendritic arbors (complete, but minimum-overlapping innervation of a field) supports uniform reception of input stimuli. Previous studies have attempted to show the molecular and cellular basis of tiling, and it has been argued that the underlying inhibitory interaction between dendrites is realized by contact-dependent retraction and/or by repulsion of dendrites via extracellular branch suppressors. In this study, we showed that the development and regeneration of the tiling pattern could be reproduced by two different mathematical models (the cell compartment model and the end capped-segment model), in both of which dendrite growth is coupled with the dynamics of an extracellular suppressor that is secreted from dendrites. The analysis of the end capped-segment model in three-dimensional space showed that it generated both non-overlapping arbors as well as overlapping dendritic arbors, which patterns are reminiscent of phenotypes of previously reported tiling mutants in vivo. Moreover, the results of our numerical analysis of the 2 models suggest that tiling patterns could be achieved either by a local increase in the concentration of an intracellular branching activator or by a local decrease in the production of a suppressor at branch ends.