Models of branching morphogenesis of dendrites in fly sensory neurons

Over approximately one week of larval development in the fruit fly, class IV sensory neurons form an approximately planar and highly branched meshwork of dendrites just under the cuticle. The mesh serves to detect localized noxious stimuli such as penetration by the barbs of parasitic wasps. The tips of the dendrites are highly dynamic: they undergo transitions between growing, shrinking and paused states on the minute timescale (much faster than development), they form lateral branches, and they retract upon contact with other dendrites. To test models of morphogenesis, we have developed a mean-field, continuum model of dendrite growth in which polar branch segments grow at one end (the tip), stochastically nucleate new segments, and disappear randomly at a rate proportional to branch density (to simulate contact-triggered retraction). The model generalizes the Dogterom-Leibler model of microtubule dynamic instability. We solved the model analytically in the central region of the dendrite where the density is spatially uniform and unchanging in time. The analytic results were verified by numerical simulations. The model predictions, when using experimentally measured microscopic parameters, predicted many of the observed mean-field properties of the dendrites including: the mean and exponential distribution of the branch lengths, the mean tip density, and the surprising parabolic relationship between branch and tip densities. The agreement between models and experiment demonstrates that a slow, large-scale and complex morphogenetic process can be understood in terms of the rapid, microscopic properties of the constituent elements, the dendrite tips.