Quantitative Analysis of Axonal Branch Dynamics in the Developing Nervous System

Branching is an important mechanism by which axons navigate to their targets during neural development. For instance, in the developing zebrafish retinotectal system, selective branching plays a critical role during both initial pathfinding and subsequent arborisation once the target zone has been reached. Here we show how quantitative methods can help extract new information from time-lapse imaging about the nature of the underlying branch dynamics. First, we introduce Dynamic Time Warping to this domain as a method for automatically matching branches between frames, replacing the effort required for manual matching. Second, we model branch dynamics as a birth-death process, i.e. a special case of a continuous-time Markov process. This reveals that the birth rate for branches from zebrafish retinotectal axons, as they navigate across the tectum, increased over time. We observed no significant change in the death rate for branches over this time period. However, blocking neuronal activity with TTX slightly increased the death rate, without a detectable change in the birth rate. Third, we show how the extraction of these rates allows computational simulations of branch dynamics whose statistics closely match the data. Together these results reveal new aspects of the biology of retinotectal pathfinding, and introduce computational techniques which are applicable to the study of axon branching more generally.Author Summary: The complex morphologies of neurons present challenges for analysis. Large data sets can be gathered, but extracting meaningful data from the hundreds of branches from one axon over a few hundred time points can be difficult. One problem in particular is matching a single unique branch through several images, when the branches can extend, retract, or be removed entirely. In addition, if the imaging is done in vivo, the environment itself can grow and shift. Here we introduce Dynamic Time Warping (DTW) analysis to follow the complex structures of neurons through time. DTW identifies individual branches and therefore allows the determination of branch lifetimes. Using this approach we find that for retinal ganglion cell axons, the branch birth rate increases over time as axons navigate to their targets, and that blocking neural activity slightly increases the branch death rate without impacting the birth rate. From the estimated birth and death rate parameters we create simulations based on a continuous-time Markov chain process. These tools expand the techniques available to study the development of neuronal structures and provide more information from large time-lapse imaging datasets.