Hamiltonian/thermalized dynamics of a driver and piston

Robert S. MacKay and David J.C. MacKay

Abstract by David MacKay

How do biological systems turn chemical energy into mechanical work? For many molecular systems, a sequence of structures is known, but what are the design principles that make these molecular engines so efficient?

We present a model in which mechanical work is done by an expanding `gas' such as a single phosphate ion liberated from an ATP molecule.

In order for such a system to function efficiently, the entropic potential energy of the gas must be matched against a mechanical potential energy. One model for this matching is as follows:

First, a binding event, involving say three hydrogen bonds being formed (15 kT or so of energy), takes place, and does work near-reversibly against the external load. At the same time, the ATP is placed in a pocket in which the conversion of ATP to ADP + P can take place with negligble enthalpy release. Now, the liberated P and ADP do work against the piston covering the pocket, which when it moves breaks the three hydrogen bonds. The expansion's entropic contribution pays back the debt that was created by the earlier binding event. [That binding energy could be associated with either the piston binding over the ATP, or the ATP binding to the pocket, or a bit of both.]

The key ideas are that a chemical change creating an increased number of molecules takes place with negligible enthalpy release, and that mechanical work is then done by these molecules expanding against a mechanical potential well-matched to the entropic free energy. The molecules suck thermal energy out of the surroundings during the expansion.