A bilayer model of the non-linear elastodynamics of <i>Hydra </i>mouth opening

Mouth opening in Hydra involves extreme deformations, with radial cell strains of up to 30%. Hydra consists of two neuronally excitable, mechanically coupled epithelia-muscular cell layers, an outer ectoderm and an inner endoderm. The layers are coupled basally by a viscoelastic extracellular matrix, into which the cells extend contractile fibers (myonemes). In the head, ectodermal myonemes are arranged radially and endodermal myonemes in concentric rings. Experiments show that mouth opening proceeds through a series of radial ‘tugs’ – local myoneme contractions that must synchronize to produce a symmetric opening. We investigate if a bilayer model of viscoelastic sheets containing networks of radial and circular non-linear springs with Poisson distributed compressive forcing can capture mouth opening. Constraining the model using in vivo data, we test its ability to reproduce the time history of the mouth area during opening. We compare the kinematics generated by radially travelling contraction pulses with that for simultaneous contractions at all radii. Further, we explore the conditions required for space-time synchronization of ‘tugs’ into a quasi-symmetric opening and the dependence on the ratio of firing rate and the relaxation timescale of the viscoelastic sheet.