Deterministic and Stochastic Rules of Branching Govern Dendrite Morphogenesis of Sensory Neurons

Abstract

Highlights d Core vpda neuron morphology is established during embryogenesis d The primary branch grows deterministically but secondary branches are stochastic d Tree architecture can increase or decrease the local probability of branch survival d Contact-induced retraction selects secondary branches perpendicular to the primary

Theory of branching morphogenesis by local interactions and global guidance

“…A strength of our “mesoscopic” approach is that it extracts a small number of such coarsegrained parameters, to identify which ones are key at the scale of the overall branching pattern, and thus guiding subsequent, more detailed modelling. Our proposed framework builds upon previous simulations of stochastic branching morphogenesis, which had considered local cues such as branching and repulsion [20, 22, 33, 35]. We find that adding global extrinsic guidance-a key element in different contexts to break the isotropy in tissue growth-in the model gives rise to significantly different dynamics, enriching the phase diagram of possible branching patterns.…”

“…To analyze the influence of both the local selforganizing (intrinsic) cues and the global (extrinsic) guidance on the formation of branched structures, we first turned to a modelling approach inspired by the physics of branching random walks, which represents tips as particles undergoing both stochastic and deterministic elongation movements (which generates branches at speed υ ), as well as stochastic branching events into two tips with probability p b . This type of model [20, 22, 33–35] has the advantage of coarsening many microscopic features of branching regulation (for instance that have been addressed via reaction-diffusion models [36, 37]) into simple sets of rules. In this work, we include both the possibility for global guidance via gradients quantified by a guidance strength f c (which acts as a deterministic force on tip motion) as well as local self-avoidance of neighbouring branch segments.…”

“…In this work, we include both the possibility for global guidance via gradients quantified by a guidance strength f c (which acts as a deterministic force on tip motion) as well as local self-avoidance of neighbouring branch segments. Such self-avoidance can typically occur in neurons by cycles of contact-retraction when a tip touches a neighbouring branch of the same cell [20, 38], or in branched multicellular organs via diffusible molecules [39]. Here we concentrate on the morphogenesis of single neurons, and therefore model self-avoidance effectively by tips moving deterministically away from neighbouring branches of the same tree at strength f s .…”

“…in Ref. [12]. In contrast with the latter study, here we do not focus on the statistics of the retraction events and could therefore describe the self-recognition via a more simplified effective modelling.…”

“…A complementary question has been to understand the dynamical mechanisms through which branching complexity can arise during development. It has been shown in particular that branching morphogenesis proceeds via tip-driven growth and/or side branching events, which are shaped by combinations of deterministic and stochastic rules [4, 18–20]. Indeed, different cellular strategies have been demonstrated to regulate the final branching pattern, from stereotypic transcription factor expression [21], stochastic local rules [22, 23], mechanical forces and local reaction-diffusion mechanisms [2, 3, 24] to epigenetic mechanisms [25] and codes of cell adhesion molecules [19, 26].…”