Power-limited contraction dynamics of Vorticella convallaria: an ultrafast biological spring

Abstract

Vorticella convallaria is one of the fastest and most powerful cellular machines. The cell body is attached to a substrate by a slender stalk containing a polymeric structure-the spasmoneme. Helical coiling of the stalk results from rapid contraction of the spasmoneme, an event mediated by calcium binding to a negatively charged polymeric backbone. We use high speed imaging to measure the contraction velocity as a function of the viscosity of the external environment and find that the maximum velocity scales inversely with the square root of the viscosity. This can be explained if the rate of contraction is ultimately limited by the power delivered by the actively contracting spasmoneme. Microscopically, this scenario would arise if the mechanochemical wave that propagates along the spasmoneme is faster than the rate at which the cell body can respond due to its large hydrodynamic resistance. We corroborate this by using beads as markers on the stalk and find that the contraction starts at the cell body and proceeds down the stalk at a speed that exceeds the velocity of the cell body.

FIGURE 1

Internal structure of the Vorticella spasmoneme. (a) A phase contrast image of a portion of the Vorticella stalk. A helically coiled spasmoneme can be seen inside an external elastic sheath. The length shown corresponds to 80 μm. (b) A schematic diagram of the internal structure of the spasmoneme showing roughly aligned bundles of spasmin filaments. (c) A schematic cross section of the spasmoneme showing the presence of putative membrane bound calcium stores.

FIGURE 2

Dynamics of Vorticella contraction. (a) Time series of contraction (time shown in ms). The scale bar is 35 μm. (b) Vorticella stalk length as a function of time during a contraction. The solid curve is an exponential fit. (c) Instantaneous velocity of the cell body as a function of time. The solid curve is an exponential fit to the decaying part of the velocity.

FIGURE 3

Viscosity dependence of Vorticella contraction velocity. (a) Plot of the instantaneous cell velocity as a function of time for different viscosities for a single cell. (b) Double logarithmic plot of the maximum contraction velocity as a function of the viscosity for several cells. The solid line has a slope of −0.5.

FIGURE 4

Instantaneous power dissipated during a contraction as a function of time. (a) The hydrodynamic dissipation rate as a function of time shows that the data for different viscosities collapses onto a single master curve. Symbols correspond to the legend for Fig. 3. (b) The maximum power as a function of the viscosity is constant as expected based on theoretical arguments.

FIGURE 5

Spatially resolved stalk dynamics. (a) Time series of a contraction with two beads along the Vorticella stalk (time is in ms). The arrow indicates the frame when the second bead starts moving. The scale bar is 30 μm. (b) Time course of the instantaneous velocity of the cell body (solid circles), first bead (open circles), and second bead (triangles). (c) Effect of viscosity on the velocities plotted on a log-log scale: wave speed (squares), maximum velocity of cell body (diamonds), maximum velocity of bead (stars).

FIGURE 6

Effect of external viscosity on contraction force. (a) Double logarithmic plot of the maximum total force as a function of the viscosity for five cells, calculated from Eq. 1. The solid line has a slope of 0.5. (b) Time series of forces (inertia, history, drag, and total force) for a representative cell at 1 cP. These forces were calculated from Eq. 1. The total force is f, inertia is the term on the left, drag is the second term on the right, and history is the third term on the right. (c) Time series of forces for a representative cell at 11.5 cp. The forces are calculated as in b.