Fluid dynamic estimation of the effective spring constant of the relaxing stalk of Vorticella convallaria

The stalk of Vorticella convallaria, a sessile ciliated protozoan, contracts in a few milliseconds at a maximum speed of ~ 10 mm/s and generates a contractile force of ~ 10 nN. After powerful contraction, the stalk slowly returns to its extended state, and this relaxation process completes and resets the contraction cycle. The stalk relaxation needs to be better characterized because it is indispensable to the contraction-relaxation cycle of V. convallaria. In contrast to the spasmoneme-based contraction force, the driving force for the stalk relaxation is thought to be the elastic restoring force of the coiled stalk. In this study, relaxing V. convallaria was modeled as the damped spring system to estimate the effective spring constant of the relaxing stalk in different viscous media. In the order of 0.1 pN/μm, the effective spring constant was found to increase with the medium viscosity, which suggests that the stalk relaxation is affected by the final status of the contraction phase.