On the Interpretation of the Observed Linear Free Energy Relationship in Phosphate Hydrolysis: A Thorough Computational Study of Phosphate Diester Hydrolysis in Solution

Abstract

The hydrolysis of phosphate esters is crucially important to biological systems, being involved in, among other things, signaling, energy transduction, biosynthesis, and the regulation of protein function. Despite this, there are many questions that remain unanswered in this important field, particularly with regard to the preferred mechanism of hydrolysis of phosphate esters, which can proceed through any of multiple pathways that are either associative or dissociative in nature. Previous comparisons of calculated and observed linear free energy relationships (LFERs) for phosphate monoester dianions with different leaving groups showed that the TS character gradually changes from associative to dissociative with the increasing acidity of the leaving group, while reproducing the experimental LFER. Here, we have generated ab initio potential energy surfaces for the hydrolysis of phosphate diesters in solution, with a variety of leaving groups. Once again, the reaction changes from a compact concerted pathway to one that is more expansive in character when the acidity of the leaving group increases. When such systems are examined in solution, it is essential to take into consideration the contribution of solute to the overall activation entropy, which remains a major computational challenge. The popular method of calculating the entropy using a quasi-harmonic approximation appears to markedly overestimate the configurational entropy for systems with multiple occupied energy wells. We introduce an improved restraint release approach for evaluating configurational entropies and apply this approach to our systems. We demonstrate that when this factor is taken into account, it is possible to reproduce the experimental LFER for this system with reasonable accuracy.

Why nature really chose phosphate

“…However, these works employed quite a low level of theory, and, as was also highlighted by (Hou & Cui, 2012), the Zn 2+ -Zn 2+ distance in these simulations increased to an unphysical value of as high as 7Á0 Å (Lopéz-Canut et al 2011), in sharp contrast to the crystal structure and also to data from Extended X-ray Absorption Fine Structure (EXAFS) and X-ray crystallography, which suggests little change in the binuclear Zn 2+ catalytic site during the course of the reactions catalyzed by AP and NPP (Bobyr et al 2012). In contrast to this, a more careful (but, as argued below, not yet fully reliable) study by (Hou & Cui, 2012) obtains a qualitatively similar phosphodiester TS in aqueous solution to that obtained by our earlier study (Rosta et al 2008), coupled with the more reasonable observation of a significant tightening of the TS in the enzyme active site (see also Luo et al 2012b).…”

“…18 (and Fig. 11 of Rosta et al 2008), we were able to computationally reproduce the observed trend over a very wide range of rate constants. Our point is that the rate determining TS are very different for the different compounds considered in our LFER studies.…”

“…This is best illustrated in recent computational studies of both phosphate monoester (Fig. 18) ; and diester (Rosta et al 2008) hydrolysis, mentioned in Section 3.2, which demonstrated that the mechanism is highly dependent on the pK a of the leaving group: that is, in both cases, leaving groups with a high pK a tend to prefer a more associative mechanism, which becomes progressively more dissociative as the leaving group becomes more acidic. Overall, as shown in Fig.…”

“…The first of these is that, as highlighted in Section 3, and illustrated by e.g. Kamerlin et al 2008aKamerlin et al , 2009cKlähn et al 2006 ;Rosta et al 2008), traditional mechanistic markers such as LFER, activation entropies and KIEs do not have unique mechanistic interpretations, with both different mechanisms giving rise to similar experimental observables, and also gradual changes in mechanism being masked by LFER. Therefore, in and of itself, none of the experimental evidence presented for the idea that the TS does not change upon moving from solution to the enzyme active site is conclusive without further support from careful computational studies that can reproduce all relevant available experimental observables.…”

“…3 and Table 4 of Hou & Cui, 2012) demonstrate a significant shift toward a more associative TS (as was also observed in the related case of PAS, Luo et al 2012a ;Luo et al 2012b). This could partially be due to the fact that the authors appear to overlook the fact that concerted TSs for phosphoryl transfer reactions lie on a spectrum from more expansive/dissociative to more compact/associative TSs (Kamerlin & Wilkie, 2007 ;Kamerlin et al 2008a ;Rosta et al 2008), and the discussion in (Hou & Cui, 2012) focuses on the idea that a change in mechanism necessarily would constitute a shift toward a more dissociative TS, whereas the authors are clearly presenting a shift toward a more associative TS, which is still a shift in mechanism compared with aqueous solution.…”