Acid/base
catalysis is an important catalytic strategy used by
ribonucleases and ribozymes; however, understanding the number and
identity of functional groups involved in proton transfer remains
challenging. The proton inventory (PI) technique analyzes the dependence
of the enzyme reaction rate on the ratio of D2O to H2O and can provide information about the number of exchangeable
sites that produce isotope effects and their magnitude. The Gross–Butler
(GB) equation is used to evaluate H/D fractionation factors from PI
data typically collected under conditions (i.e., a “plateau”
in the pH–rate profile) assuming minimal change in active site
residue ionization. However, restricting PI analysis to these conditions
is problematic for many ribonucleases, ribozymes, and their variants
due to ambiguity in the roles of active site residues, the lack of
a plateau within the accessible pL range, or cooperative interactions
between active site functional groups undergoing ionization. Here,
we extend the integration of species distributions for alternative
enzyme states in noncooperative models of acid/base catalysis into
the GB equation, first used by Bevilacqua and colleagues for the HDV
ribozyme, to develop a general population-weighted GB equation that
allows simulation and global fitting of the three-dimensional relationship
of the D2O ratio (n) versus pL versus kn
/k
0. Simulations
using the GPW-GB equation of PI results for RNase A, HDVrz, and VSrz
illustrate that data obtained at multiple selected pL values across
the pL–rate profile can assist in the planning and interpreting
of solvent isotope effect experiments to distinguish alternative mechanistic
models.