Temperature dependence of reactions with multiple pathways

The rate coefficient k(T) of a barrier-limited, two-state reaction proceeding through multiple pathways is determined by using transition state theory. The entropic and enthalpic contributions to the overall rate are treated separately. The rate coefficient of reaction is determined as a function of the variance of the distribution of pathways and activation energies. The relative densities of state in the initial and transition state lead to curvature in the dependence of ln(k) on 1/T. The sign of the curvature depends on the relative increase in densities of state of the initial and the transition (saddle) state. The analysis has implications for the interpretation of macromolecular reactions, including the protein-folding process. The inclusion of the density of states in the initial and the saddle states yields rate coefficients whose temperature dependence reproduces the curvatures in experimental Arrhenius plots for protein-folding and unfolding processes