Information Theory in Molecular Recognition: Efficiency of Molecular Machines

Frederick Cancer Research and Development Center, P. O. Box B, Frederick, MD 21702-1201. toms@alum.mit.edu, https://alum.mit.edu)

Abstract for 1998 American Association for the Advancement of Science (AAAS) Annual Meeting and Science Innovation Exposition Philadelphia, Pennsylvania Monday, February 16, 1998, 3:00pm-6:00pm Track: Emerging Science: Transforming the Next Generation Session number: 101.0

In contrast to the two-temperature thermodynamic efficiency defined by Carnot for heat engines, a thermodynamic efficiency can be defined for machines that are so small that they must operate at essentially one temperature. This ``isothermal efficiency'' was determined for several molecular-sized machines found in living organisms. DNA recognition proteins, the light sensitive pigment rhodopsin and muscle all have isothermal efficiencies approaching 70% even though efficiencies closer to 100% would confer greater evolutionary advantages to the organism that synthesizes and uses the machine. By comparison, many devices used by people have isothermal efficiencies around to .

A high dimensional coding space can be used to understand why 70% is the upper bound on efficiency. Spheres in this space define the possible states of the machine. Before a machine operates (performs its task) it is in the before state, which is represented by a large sphere. After a machine has operated it is in an after state, which is represented by a smaller sphere somewhere inside and usually near the surface of the before sphere. (It appears as a straight line in a diagram.) It can be shown that another after sphere exists that sits exactly in the center of the before sphere. Entering this degenerate sphere represents wasteful loss of the machine's energy. If the degenerate state is avoided by a molecular machine, then any molecular machine that makes choices between two or more states must have an efficiency less than the natural logarithm of 2, which is approximately 70%. Thus the observed efficiences of molecular machines can be explained by thermodynamics, information theory and geometry. For DNA binding proteins this implies that one can often predict the specific binding energy from the nucleotide sequence conservation.