Amino acid deprotonation rates from classical force fields

Acid ionization constants (pK_a's) of titratable amino acid side chains have received a large amount of experimental and theoretical attention. In many situations, however, the rates of protonation and deprotonation, k_on and k_off, may also be important, for example, in understanding the mechanism of action of proton channels or membrane proteins that couple proton transport to other processes. Protonation and deprotonation involve the making and breaking of covalent bonds, which cannot be studied by classical force fields. However, environment effects on the rates should be captured by such methods. Here, we present an approach for estimating deprotonation rates based on Warshel's extension of Marcus's theory of electron transfer, with input from molecular simulations. The missing bond dissociation energy is represented by a constant term determined by fitting the pK_a value in solution. The statistics of the energy gap between protonated and deprotonated states is used to compute free energy curves of the two states and, thus, free energy barriers, from which the rate can be deduced. The method is applied to Glu, Asp, and His in bulk solution and select membrane proteins: the M2 proton channel, bacteriorhodopsin, and cytochrome c oxidase.