GOLDMAN, E.B.*; DANIEL, T. L.: Material properties shape dynamical responses of hydrozoan jellyfish

Radially symmetrical and composed of acellular mesoglea, two cell layers, and a primitive nervous system, jellyfish are an elegantly simple launching point to investigate how material properties of the musculoskeletal system shape the dynamics of locomotion. Mesoglea, composed of mucopolysaccharides, collagen, and water, has a characteristic nonlinear response to an applied strain. This study asks how such nonlinearities determine the dynamical response of a jellyfish’s simple geometry subject to periodic forcing. We compare the strain-dependent stiffness of mesoglea between three species of jellyfish, Mitrocoma cellularia, Polyorchis penicillatus, and Aequorea victoria, each with a distinctive overall shape. Because of the nonlinear and time-dependent behavior of mesoglea, we measure the complex modulus by recording its stress in response to sinusoidal strains at a variety of frequencies and mean lengths. Using a simple power law to fit the resultant relationships between complex modulus and mean length, we describe the strength of nonlinearity in mesoglea by the size of the exponent. Aequorea victoria, a jellyfish with unevenly distributed mesoglea and unusual swimming kinematics, has the highest mesoglea exponent, making it the most strongly nonlinear, while Mitrocoma cellularia, a jellyfish with a relatively simple geometry and typical swimming kinematics, has the lowest . The exponent describing the mesoglea of Polyorchis penicillatus falls in between, although it more closely resembles Aequorea. Armed with these estimates, we use a simple dynamical model to show that very subtle changes in the strength of the nonlinearity are manifest as significant changes in the spectral responses of the musculoskeletal system to periodic forcing.