Linear Spring Motors

An example of a biological motor, the spasmoneme spring, is shown in Figure

This system, first observed by the famous microscopist Leeuwenhoek in 1676, has a large literature. When extended, the spring may be mm in length. When exposed to calcium, which neutralizes the net negative charge in the extended state, the stalk contracts in a few ms to 40% of its length, at velocities approaching 8 cm/s.

Figure 3.1 Spasmoneme spring. (A). The spasmoneme in Vorticella in its fully extended (left), fully contracted (middle), and partly extended (right) states [6]. (B). The extended spring state (left) consists of aligned filaments held apart by negative charges (dots). On the right, with plus and minus charges (dots) equally likely, the stalk collapses to a rubber-like state

In consideration of the viscous drag forces that are involved, as described in Chapter 2, noting that the diameter of the head is as much as 50 (im, the force of contraction is estimated to be on the order of lOnN, and the power is of order 100 pW.

As sketched in Figure 3.1 (B), the stalk is modeled [6] to consist of a bundle of filaments, each about 2 nm in diameter, which are roughly aligned but only weakly cross-linked. The extended structure is net negatively charged, forced into this extended state simply by Coulombic repulsion within the linear constraint of the filament bundle. Many further subtleties of this situation are known, including a helical aspect, so that the spasmoneme rotates as it contracts.

A somewhat similar spring motor is believed to operate in sperm cells exemplified by the horseshoe crab Limulus polyphemus in which a 60 [im finger, called the "acrosomal process", extends quickly across a jelly-like barrier to accomplish fertilization of egg plasma. Again, the extension motion seems clearly to be the result of Coulombic repulsion, as the ionic charge in the system is changed. There seems to be an opportunity to reanalyze some of this careful and extensive literature in more simple electrostatic terms.

The microbiological literature scarcely contains mention of electrostatic forces, yet these must be the essential origin of motions in bio-molecular motors, from a perhaps naive, but unavoidably basic point of view. (Magnetic forces are certainly to be excluded, in the context of motors, but not in the context of sensors, as we will see below.)

Interdisciplinary approaches involving applied physicists familiar with semiconductor charge layers, screened electrostatic forces, etc., working with biologists, are likely to be very productive.

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