Linear Free Energy Relationships in Enzymes. Theoretical Analysis of the Reaction of Tyrosyl-tRNA Synthetase

Abstract

Recent studies of genetically modified enzymes have indicated that changes in activation free energies, AAg*, and changes in reaction free energies, AAGq, are correlated by the relationship AAg* = ß • The present work explores the basis for such linear free energy relationships (LFERs) in enzymatic reactions, focusing on the effects of mutations in tyrosyl-tRNA-synthetase (TTS). It is demonstrated that the optimal way to analyze LFERs is by describing the reaction in terms of pure valence bond (VB) resonance structures rather than in terms of partially formed bonds. The use of the pure VB representation allows one to evaluate the relevant LFER using Marcus-type concepts and to compare the predicted ß to the observed one. Using a two-resonance-structure VB model for TTS produces ß 0.5, which disagrees with the observed values of ß ^0.83 and ß » 1 for two classes of mutations. Noting, however, that the phosphoryl transfer process in TTS has been described before as going through a high-energy intermediate, we describe this reaction in terms of three VB resonance structures. This accounts for the observed values of ß and supports the validity of LFER in TTS. It is pointed out that LFERs are valid in proteins even when the changes in Ag* involve very anharmonic interactions like hydrogen bonds, since such relationships reflect the correlation between AAg* and AAGq rather than the correlation between AAg* and the effect of specific residues. However, obtaining LFER in proteins requires that the active site environment responds linearly to the change of charges during the reaction, and such a linear response is far from obvious. Fortunately, the simulation study presented in this work as well as previous simulations has demonstrated that active sites of proteins obey the linear response approximation. Such a behavior of highly anharmonic systems is due to the availability of many compensating polar interactions. This finding provides a theoretical basis for the experimental observation of LFER in TTS.

Theory for rates, equilibrium constants, and Brønsted slopes in F 1 -ATPase single molecule imaging experiments

“…An α of 0.83 for ATP hydrolysis in tyrosyl-tRNA synthase was inferred by use of mutants, and an explanation of this high α for this reaction, where overall ΔG 0 is small, was given by Warshel, who postulated two transition states of about equal energy with a shallow minimum in between (28). Thereby the first step had a barrier almost equal to the energy to reach the shallow well, and so α was close to unity.…”

“…As noted earlier, the present formulation of the model is not intended to apply to the ATP hydrolysis step, which is believed to involve two or more substeps, rather than just one (28,30,50). An α of 0.83 for ATP hydrolysis in tyrosyl-tRNA synthase was inferred by use of mutants, and an explanation of this high α for this reaction, where overall ΔG 0 is small, was given by Warshel, who postulated two transition states of about equal energy with a shallow minimum in between (28).…”

“…Nevertheless, the general features of the model are intended to apply also to other rotation-coupled steps involving the reversible binding and release of a ligand molecule, such as ADP and P i , and to other ring-shaped NTPases, and can be tested once sufficient kinetic data become available. The model, as presently formulated, does not apply to the ATP hydrolysis (cleavage) step, because it may be a multistep process (28)(29)(30), as discussed in more detail in a later section.…”

Why nature really chose phosphate

“…From the discussion in this Sections 3.1-3.3, it was seen that phosphoryl transfer reactions can proceed through multiple distinct TSs, which is contrary to the classical interpretation of LFER, where it is assumed that each of the potential mechanisms (whether associative or dissociative) will proceed through merely a single TS. Thus, in order to accurately examine the LFER, it is important to consider the effect of the free-energy differences along each step of the pathway on the corresponding activation barriers (Å qvist & Warshel, 1993 ;Warshel et al 1992aWarshel et al , 1994. Changing the pK a of either the nucleophile or leaving group not only affects the energetics of any steps involving PT with that particular group, but also affects the pK a of the attached phosphate group and thus the overall free energy.…”

“…17e and f). These have all been drawn as the intersection of relevant parabola (including parabola representing PTs), in order to clarify the relationship between this and Marcus-type LFER treatments (Å qvist & Warshel, 1993 ;Warshel et al 1992aWarshel et al , 1994 (in which TS energies are correlated with the crossing of the relevant parabola). In all cases, PTs have been depicted as stepwise processes with distinct resonance structures in order to more clearly illustrate the effects of pK a shifts on the energy of each state.…”