Mean field theory for larval Drosophila peristalsis

With the rise and proliferation of low-cost imaging and automated tracking solutions, we can now measure the posture dynamics of individual animals at unprecedented resolution. However, theoretical approaches that would allow us to predict and explain our observations at this scale and resolution are relatively underdeveloped, and are often frustrated by the complexity and diversity of microscopic interactions that underlie animal behaviour. We describe a first-principles theoretical understanding of animal posture, using the Drosophila melanogaster larva (fruitfly maggot) as a model system. The larva locomotes via peristalsis: it propagates localised, longitudinal compression waves along its rod-like body. Larval posture during peristalsis can be represented via a scalar strain field, allowing us to probe the locomotor dynamics via non-equilibrium classical field theory. We construct a mean field theory (MFT) for the larva’s strain field via gradient expansion of the field’s equation of motion, and an assessment of symmetry, stability, and scaling properties of terms in this expansion. Our MFT admits soliton solutions in which damping and driving effects balance to produce a localised compression wave, similar to peristaltic waves observed in the real larva. Renormalisation group calculations suggests that this MFT is self-consistent in the presence of weak fluctuations.