A mechanical model for the half-of-the-sites reactivity of oligomeric enzymes

Viscoelastic models for enzymes with multiple conformational states

In this article we represent an enzyme capable of exhibiting more than one conformational state as a viscoelastic unit embedded in a fluid medium. We show how this viscoelastic unit is thermally activated to make transitions between equilibrium states, and propose this model as a mesoscopic representation for transitions between conformational states of an enzyme. In this representation, kinetic constants for transitions between conformations are given explicitly in terms of interactions between the enzyme and the medium. Two applications of this model are discussed: mnemonic enzymes, and co-operative enzymes exhibiting half-of-the-sites reactivity.

The biological functions of low-frequency vibrations (phonons) 5. A phenomenological theory

Low-frequency internal motions of a biomacromolecule are thought to possess significant biological function from the dynamic point of view. In this paper, a general phenomenological theory is established by which it is clearly verified that low-frequency resonance plays a central role in the energy transmission required during the cooperative interaction between subunits in a protein oligomer. According to the present theory, it is found that the energy transmission between a pair of diagonal subunits in a protein oligomer with a polygon arrangement is the most efficient, so as to in a sense further predict that after a ligand is bound to a subunit by random collision, its diagonal subunit in the same protein oligomer will possess the greatest probability of binding with the next ligand. Furthermore, based on the concept of the 'resonance-controlled trigger' derived from the phenomenological theory, it is feasible to estimate the lower time limit of allosteric transition from one subunit to the other. Such a time limit depends on the dominant low-frequency mode of each subunit, the ratio of the coupling force constant to the corresponding inherent force constant, as well as the geometrical arrangement of subunits in a protein oligomer. So far none of the allosteric transitions observed in proteins has exceeded the time limit as defined here, indicating a logical consistency between our theory and the experiments.

Why are enzymes macromolecules?

The possible reasons for the macromolecular nature of enzymes are discussed. They are recognized in the necessity of creating a highly specific stereochemistry and microenvironment in the active site, in the necessity of maintaining the protein conformational rigidity, its fit with the physiological environment and overall stability, in allostery, and in the possible existence of fossil sequences, molecular tinkering, and specific hydrodynamic properties.