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.
Graphical Abstract
Similar content being viewed by others
References
S. Ryu, R.E. Pepper, M. Nagai, D.C. France, Vorticella: a protozoan for bio-inspired engineering. Micromachines 8, 4 (2017)
S. Ryu, P. Matsudaira, Unsteady motion, finite Reynolds numbers, and wall effect on Vorticella convallaria contribute contraction force greater than the Stokes drag. Biophys. J. 98, 2574–2581 (2010)
S. Ryu, M.J. Lang, P. Matsudaira, Maximal force characteristics of the Ca2+-powered actuator of Vorticella convallaria. Biophys. J. 103, 860–867 (2012)
E.G. Chung, S. Ryu, Stalk-length-dependence of the contractility of Vorticella convallaria. Phys. Biol. 14, 066002 (2017)
Y. Moriyama, S. Hiyama, H. Asai, High-speed video cinematographic demonstration of stalk and zooid contraction of Vorticella convallaria. Biophys. J. 74, 487–491 (1998)
A. Upadhyaya, M. Baraban, J. Wong, P. Matsudaira, A. van Oudenaarden, L. Mahadevan, Power-limited contraction dynamics of Vorticella convallaria: an ultrafast biological spring. Biophys. J. 94, 265–272 (2008)
K. Ueda, Studies on the stalk muscle of Carchesium (I). Zool. Mag. 61, 367–371 (1952)
H. Sugi, Contraction and relaxation in the stalk muscle of Carchesium. Annot. Zool. Jpn. 32, 163–169 (1959)
E.J. Vacchiano, J.L. Kut, M.L. Wyatt, H.E. Buhse Jr., A novel method for mass-culturing Vorticella. J. Protozool. 38, 608–613 (1991)
G.D.M. MacKay, S.G. Mason, Approach of a solid sphere to a rigid plane interface. J. Colloid Sci. 16, 632–635 (1961)
G.D.M. MacKay, M. Suzuki, S.G. Mason, Approach of a solid sphere to a rigid plane interface, part 2. J. Colloid Sci. 18, 103–104 (1963)
Y. Moriyama, H. Okamoto, H. Asai, Rubber-like elasticity and volume changes in the isolated spasmoneme of giant Zoothamnium sp. under Ca2+-induced contraction. Biophys. J. 76, 993–1000 (1999)
M. Rahat, Y. Pri-Paz, I. Parnas, Properties of stalk-‘muscle’ contractions of Carchesium sp. J. Exp. Biol. 58, 463–471 (1973)
D. C. France, Structure and mechanics of the spasmoneme, a biological spring within the protozoan Vorticella convallaria, Doctoral dissertation, Massachusetts Institute of Technology (2007)
M. Nagai, S. Ryu, T. Thorsen, P. Matsudaira, H. Fujita, Chemical control of Vorticella bioactuator using microfluidics. Lab. Chip 10, 1574–1578 (2010)
M. Nagai, N. Matsumoto, T. Kawashima, T. Shibata, Reversible motion control of Vorticella stalk in microchannel. Microelectr. Eng. 108, 28–32 (2013)
M. Nagai, H. Asai, H. Fujita, Reciprocation of micro-objects by contraction and extension of Vorticella convallaria using polylysine as adhesive material. Mech. Eng. J. 1, 1–8 (2014)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Rights and permissions
About this article
Cite this article
Ryu, S., Matsudaira, P. Fluid dynamic estimation of the effective spring constant of the relaxing stalk of Vorticella convallaria. JMST Adv. 2, 9–14 (2020). https://doi.org/10.1007/s42791-019-00028-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42791-019-00028-x