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

Abstract

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.

Revisited Japanese research literature on the stalk contraction and relaxation of stalked ciliates

“…Thus, it appears that U r increased with respect to T with a rate of 9 μm/s/°C. We also noted that the relaxation speed of C. polypinum is one order of magnitude greater than that of V. convallaria (Ryu and Matsudaira 2020). Ueda (1952) applied repeated stimulations to C. polypinum with various time intervals (1, 5, 15 and 60 s) for 30 minutes and then observed the contraction-relaxation of fatigued C. polypinum at 19°C.…”

“…The fast stalk contraction of Vorticellidae is followed by the slow relaxation of the retracted stalk. In contrast to the contraction phase, the relaxation phase has been less studied (Sugi 1959;Ryu & Matsudaira 2020). In this section, we review Ueda's work on the stalk relaxation of C. polypinum (Ueda 1952) in which C. polypinum was stimulated by an electric current applied along the axial direction of the stalk.…”