1. A. v. Leeuwenhoek Philos. Trans. R. Soc. London Ser. B. 12 133 (1676).
2. An engine is a device that converts one form of energy to another. A muscle is a mechanochemical engine; rhodopsin is a photochemical engine.
3. Because springs convert some form of energy to mechanical motion a natural basis for their understanding arises from the thermodynamics of these systems. By combining the first and second laws of thermodynamics we can relate the internal energy dU of a system to the work dW done by it and to the change in entropy dS by dU = TdS − dW. The work done dW can arise from many causes; if a system expands by a volume dV against a pressure p it does mechanical work equal to pdV. If a contractile fiber shortens by an amount − dl under a force f it performs mechanical work equal to − fdl. If the system transports − dn i moles of the i th component from itself to its surroundings at a chemical potential μ i it performs chemical work equal to − μ i dn i etc. so that
dU=TdS−pdV+fdl+∑i μidni+ψde+….To determine the force generated by mechanochemical springs such as the spasmoneme and the Limulus acrosome one would need to consider only the subset of relevant terms that contribute to that particular system. For example energetic and entropic effects associated with contracting filaments lead to
f=∂U∂l e T ni−T ∂S∂l e T niwhere e T and n are constant. In principle we can calculate U μ and S from a microscopic description or write a phenomenological form based on the symmetries of the system. Using this force in the equation of motion for the contraction of the fiber complemented by structural information leads to a physicochemical description of the dynamics.
4. Amos W. B., Nature 229, 127 (1971).
5. Moriyama Y., Hiyama S., Asai H., Biophys. J. 75, 487 (1998).