Protein Flexibility Partitions the Effects of Energy Landscape Roughness Between Activation Energy and Internal Friction

Abstract

The rate of protein conformational changes are usually not only limited by external but also internal friction, however, the origin and significance of this latter phenomenon is poorly understood. By investigating the internal friction during the activation of two trypsin mutants at various temperatures and external viscosities we have discovered that the temperature dependence of the internal friction shows an Arrhenius-like behavior. The characteristic energy of the Arrhenius formula, however, can change dramatically upon the replacement of a single amino acid at a hinge position (thereby affecting the flexibility of the protein), or by crossing a critical temperature. At the same time, the activation energy of the conformational transition also changes with a similar magnitude, but in the opposite direction. These observations shed light on the intricate interplay between the apparent internal friction and activation energy. Moreover, we have found that the more flexible a protein is the greater proportion of its activation energy is partitioned into internal friction. All these results have allowed us to come to the general conclusion that the different hierarchical levels of the roughness of the energy landscape along a conformational transition can be observed as either activation energy or internal friction depending on the degree of flexibility of the protein.