Why Proteins are Big: Length Scale Effects on Equilibria and Kinetics

Proteins are polymers, and yet the language used in describing their thermodynamics and kinetics is most often that of small molecules. Using the terminology and mathematical descriptions of small molecules impedes understanding why proteins have evolved to be big in comparison. Many properties of the proteins should be interpreted as polymer behavior, and these arise because of the longer length scale of polymer dimensions. For example, entropic rubber elasticity arises only because of polymer properties, and understanding the separation of entropic and enthalpic contributions shows that the entropic contributions mostly reside within the polymer and enthalpy originates mostly at the site of small-molecule binding. Recognizing the physical chemistry of polymers in descriptions of proteins' structure and function can add clarity to what might otherwise appear to be confusing or even paradoxical behavior. Two of these paradoxes include, first, highly selective binding that is, nevertheless, weak, and, second, small perturbations of an enzyme that cause large changes in reaction rates. Further, for larger structures such as proteins every thermodynamic measurement depends on the length scale of the structure. One reason is that the larger molecule can control up to thousands of waters resulting in collective movements with kcal sums of single-calorie-per-molecule solvent energy changes. In addition, the nature of covalent polypeptides commonly leads to multiple binding-i.e., multivalency-and the benefits of multivalent binding can be assessed semiquantitatively drawing from understanding the chelate effect in coordination chemistry. Such approaches clarify the origins, inter alia, of many low energies of protein denaturation, which lie in the range of only a few kcal mol^-1, and the difficulties in finding the structures of proteins in the multiple substates postulated within complex kinetic schemes. These models involving longer length scales can be used to elucidate why such observed behavior occurs, and can provide insight and clarity where the phenomena modeled employing experimentally inseparable translational, vibrational, and rotational entropy along with charge, dipole moment, hydration, hydrogen bonding, and van der Waals energies together obscure such origins. The short-distance, long distance separation does not include explaining any enzymatic lowering of activation energies due to stabilization of the intermediate(s) along the reaction path. However, well known small-molecule methods that treat electrostatics and bonding can be used to explain the local chemistry that contributes most of the changes in enthalpy and activation enthalpy for the process.