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
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
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.