Energy coupling and Hill cycles in enzymatic processes.

We review how Hill's work on enzyme catalysis has nurtured our understanding of the mechanism by which enzymes can couple downhill processes to uphill processes. More specifically, we discuss the following questions: (i) Does it make sense to distinguish the chemical potential of the bound ligand from that of the binding enzyme? (ii) To what extent can free-energy transduction be localized at some crucial step in the catalytic cycle? (iii) Need enzymes be optimized so as to even out the profile of basic free energy along the catalytic cycle? (iv) How do continuous models of conformational transitions relate to discrete state diagrams and their kinetic elaborations? We conclude that (1) only in very special cases is it useful to designate a portion of the free energy of the enzyme-ligand complex as the free energy of the bound ligand; (2) only for some mechanisms can free-energy transduction be localized within a part of the catalytic cycle; (3) only in special cases should one expect enzymes to be "optimized" so as to have smooth basic free-energy profiles; and (4) transition rate constants can often be related to conformational diffusion constants, although in certain situations the kinetic description of an enzyme as if jumping between discrete states is impracticable; a diffusion-type description may then be preferable.