As discussed above, the idea that enzymes act by compressing their reacting fragments (thus increasing tunneling) appears to persist in the literature, despite the arguments that it is a self-contradictory idea. An example of this is a recent work, which presents a novel take on the barrier compression issue [22
]. That is, this work has attempted to model the effect of barrier compression on both the shape of the potential energy surfaces and the reaction barriers for an enzymatic proton transfer (in aromatic amine dehydrogenase), as well as in the model malonaldehyde and methane/methyl radical anion systems. Here, the authors argue that they find that the barrier compression is associated with an approximately linear decrease in the activation energy, and, particularly, for partially non-adiabatic proton transfer, that barrier compression in fact enhances the rates of both classical and proton tunneling reactions to a similar extent, from which they conclude that barrier compression (whether occurring through fast promoting vibrations or otherwise) can provide a general mechanism for the enhancement of both the classical and tunneling rates in enzyme catalyzed proton transfer.
However, while clearly an extensive effort, this work [22
] involves several misunderstandings, starting with the assertion that Ref. [21
] proves the barrier compression idea. Unfortunately, Ref. [21
] derives a problematic relationship between the KIE and barrier compression, where the KIE increases upon compression (note that this relationship has now been corrected in of the authors’ most recent paper [22
], which shows the opposite trend to that presented in Fig. 4 of Ref. [21
]). For the benefit of the reader, we have presented an example of the correct behavior, as was deduced by the careful adiabatic studies of e.g. Ref. [23
] in , and point out that the same trend has been obtained by the most recent work of the authors [22
] as well as by other diabatic studies [24
], and that this trend is the opposite of the one reproduced in Ref. [21
]. It appears that the treatment of Ref. [21
] assumed that the observation of a small pressure effect on the change in
tells us that this trend would also hold true with regard to the dependence of the barrier on the tunneling distance. Thus, the authors changed the vibronic equation in order to reproduce this assumption, by the introduction of a non-physical change in the OH force constant (the problem with which will be clarified below). In other words, the authors forced
their theoretical treatment to reproduce their assumption that the observed increase in the KIE means that the barrier is being compressed with pressure. It should by now be obvious to all readers that the fact that the KIE is really inversely proportional to compression leads to the conclusion that the barrier is not
being compressed by pressure. Therefore, the conclusion of Ref. [21
] with regard to promoting modes and pressure is unfortunately based on an incorrect formulation. This problem is further compounded by the fact that in another recent work [28
], we see the opposite pressure dependence of the KIE (i.e., now the KIE decreases
with pressure). Thus, the argument that the pressure effect proves that the barrier is compressed is fundamentally incorrect.
Figure 3 The calculated kinetic isotope effect (triangles) as a function of the donor-acceptor distance, R(CO), in (a) the reference reaction in solution, and (b) lipoxygenase. As can be seen from this figure, the KIE increases dramatically from a comparatively (more ...)
Next, let us consider the argument that the pressure increases the rate, but reduces the isotope effect (which is what probably let to the unjustified idea [22
] that the tunneling increases when the KIE decreases). We have already established above that barrier decompression results in an increase in the KIE. Hence, the only remaining question is why the compression is an inverse of the absolute rate. The answer, of course, is that this issue should not be analyzed without the support of appropriate molecular simulations. Even more importantly, constructing an incorrect argument about an inverted relationship between tunneling and the KIE is not helpful. In contrast, it is reasonable to assume that the effect of pressure on the rate is due to a change in the reorganization energy and to the change in the activation entropy as a result of the reduction in the effective volume of the ground state.
At this point, it should be very useful to consider the arbitrary change in the OH force constant. That is, the application of external pressure to hydrogen bonded systems typically results in a shrinkage of the donor-acceptor distance, giving rise to an elongated proton-donor distance, which is in turn reflected in a red-shifted OH stretching band. In bulk water, the OH stretching is red-shifted by 20cm−1
, when applying a pressure of 10 kbar [29
]. In more strongly hydrogen-bonded systems, which have potentially mobile protons, more complex behavior can be observed. For example, in the formic acid crystal, the application of 120 kbar of pressure blue shifts the OH stretch by about 100cm−1
, followed by a red shift when applying additional pressure [30
]. Thus, the message from the spectroscopic studies is that huge pressure needs to be applied in order to change the force constant for the proton stretching motion. This finding illustrates that the changes assumed by Ref. [21
] (discussed above) are unrealistic and unjustified.
Interestingly (and instructively), the authors of Ref. [22
] have changed their model from one where the compression is increasing the KIE to one where the compression is decreasing the KIE, without emphasizing this change for the readers, and while still maintaining the same argument that the compression increases tunneling. Of course, any researcher can (and has) the full right to change their opinion, however, this should be done in a way which clarifies to the readers that the previous conclusions are based on an incorrect model, rather than maintaining that the previous works prove the author’s current completely different assertion, as was done here. Additionally, we note in passing that the observed inverse KIE is quite small (from 4 to 5.2), and can arise simply from changes in the donor-acceptor orientation, or other factors, but this obviously cannot be analyzed by unjustified approaches such as that of e.g. Ref. [21
], and then used to confirm a model where barrier compression enhances tunneling.
Another issue is the assertion that pressure results in a reduction of the barrier [31
]. That is, the simulations of this work have not evaluated any barrier (i.e. no model of any reaction or potential surface). Rather, the simulations have simply tried to assess the average reactant state (RS) population, and the authors have demonstrated [31
] that the average donor-acceptor distance shrinks from 3.93A to 3.76Å and becomes narrower when the pressure is increased from 1 bar to 2 kbar. So, firstly, the simulation does not provide information about the barrier shape
, and, secondly, in order to be physically meaningful, the probability calculations should have been evaluated by a reliable potential of mean force treatment (which allows one to obtain decent sampling), and never by direct simulations. On the other hand, careful simulation studies [32
] that do
examine the effect of pressure on the barrier for an enzyme catalyzed proton transfer as well as the corresponding reaction in solution have demonstrated that the effect of increasing pressure from 1 bar to 5000 bars on both the shape and height of the activation barrier for the enzymatic reaction are negligible (see ). In any case, the KIE is by far the best way to assess the donor-acceptor distance, and, the observed KIE is inconsistent with the compression idea.
Obviously, if the conclusions of Ref. [22
] were supported by the authors’ experimental and theoretical data, this work would be truly groundbreaking and would provide experimental proof that the conclusions of the work of Liu and Warshel [23
] are incorrect (as is indeed suggested in Ref. [22
]). However, unfortunately, as mentioned above, this work is problematic on several counts, and the data being presented seems in fact to contradict the conclusions the authors are drawing. Below, we will continue to discuss a few of the more concerning problems with the work, aside from minor problems such as the authors’ statement that “there has been no systematic computational study of the effects of barrier compression on the shape of enzymatic reaction barriers”, despite the fact that studies of this precise issue date back as early as 1976 [33
], or the continued propagation of “the deep tunneling” argument (i.e. that the enzymatic reaction occurs predominantly by tunneling) of Ref. [34
] (an issue which was dissected at length in Ref. [35
]). At any rate, to clarify this issue, we point out that a change in rate from e.g. 0.005 s−1
to 16.7 s−1
, as was observed in Ref. [34
], does not
correspond to a reaction that is progressing 99% by tunneling if one takes into account the tremendous effect of the classical barrier compared to the base rate with no barrier (see Ref. [35
] for discussion of this issue), and the authors would realize the problems with this statement, if for instance they tried to reproduce the reaction rate using only the tunneling correction, which should be feasible if the reaction were really proceeding 99% by tunneling. This point should be even more clear now that the authors have finally calculated the tunneling correction (κ), which is the quantum correction, and have also reported the ratio between the classical and QM rate constants (see Figs. 3 and 7 of Ref. [22
]). Figure 8 in Ref. [22
] clearly shows that the applied vibronic formula predicts an increase in the H/D KIE with an increase in the donor-acceptor distance.
In order to further clarify the issues with the above assertions, we will start by pointing out that the authors of Ref. [22
] argue that barrier compression is enhancing kTST
at a similar rate. However, if one were to carefully examine of the authors’ article (presented here in an adapted version in ), one would see that, in fact, the increase in kTST
is much faster than the corresponding change in ktun
. In other words, of course ktun
is larger than kTST
(as this is the tunneling correction), but ktun
also increases more slowly than kTST
, which is in direct contradiction to the authors’ interpretation of their data.
Figure 7 A schematic of the reaction catalyzed by alcohol dehydrogenase (ADH), which illustrates the fact that in this reaction (left to right), entropy changes could reflect restrictions on the fluctuations of the protein dipoles in the highly polar reactant (more ...)
Figure 5 The dependence of proton transfer in aromatic amine dehydrogenase (AADH) on V0. The two lines were obtained by extremely carefully tracing best fit curves through the data presented in Fig. 7D of Ref. , in order to highlight the difference between (more ...)
More serious is the assertion (mentioned above) that, in Figs. 3 and 7 of Ref. [22
], upon barrier compression, the authors observe a decrease in KIE, which is accompanied by a corresponding increase in ktun
. Unfortunately, while the finding that barrier compression results in a decrease in KIE is correct, reproducible by the EVB and any other physical model, and is in line with the current view on the effect of barrier compression (which was presented by Liu and Warshel [23
]), to then state that this results in an increase in ktun
is to effectively state that ktun
is inversely proportional to the KIE. Unfortunately, such an idea leads to an unrealistic scenario in which the increase in tunneling is inversely proportional to the isotope effect. Of course, this idea also (incorrectly) implies that when the tunneling correction (κ) decreases, the tunneling effect inverts. Finally, on a minor note, the argument that the diabatic approach is the only method that can account for the strong temperature dependence of the KIE is factually incorrect, and overlooks for instance the work of Liu and Warshel, who did this successfully with the QCP. The latter method is unifying, and takes into account adiabatic and all diabatic channels.
In summary, while Hay and coworkers provided instructive observations with regard to the effect of pressure on the rates of enzyme catalyzed proton transfer reactions, we unfortunately do not find any evidence in their work that supports their analysis of the assumed tunneling effects, and emphasize that currently, the most likely scenario is the “current” view presented in the figure above, which was introduced by Liu and Warshel. In conclusion, based on this, the argument of Hay and coworkers that their pressure experiments provide experimental proof that the work of Liu and Warshel is incorrect is unjustified. That is, even though the actual effect of pressure on the donor-acceptor distance is unknown, since barrier compression results in a decrease in the KIE (a point which the authors agree with in their paper), the fact that pressure results in an increase in the tunneling rate and the KIE means that even by the authors’ own (indirect) admission, it cannot be leading to barrier compression, and thus, the authors are inadvertently proving Liu and Warshel’s point.
The risk of superficial interpretations of pressure effects and the effect of promoting modes is also apparent from an examination of Ref. [36
], in which the authors argue that their study of alcohol dehydrogenase (ADH) contradicts the electrostatic and preorganization proposals. The problems start with unfamiliarity with the meaning of the reorganization energy, and the idea that the solvent reorganization should be expressed in the binding step rather than in the chemical step, not realizing that the issue is the Marcus reorganization energy of the chemical step in water (which is never considered by the authors) relative to the same reorganization in the enzyme. It was also argued that the activation volume changes upon pressure, since pressure presumably drives charges apart as the electrostriction increases with charge separation. Unfortunately, several key points were missed, ranging from (a) the fact that the formation of an ion pair and the energy of this ion pair has little to do with the increase in solvation upon charge separation (the issue is the difference in solvation in the enzyme and in water for the same distance), (b) the point that in ADH, the reaction involves a ground state ion pair (rather than a TS ion pair), and (c) the fact that the volume during the reaction must be compared to the corresponding process in water. Of course, the nature of the generalized solvation in the preorganized enzyme active site, and its distance dependence has nothing to do with conventional ideas about electrostriction in solution. At any rate, the main problem is that only examining a given experimental observation without a clear physical model that relates it to the change in the activation barriers in water and in the protein cannot tell us about the validity of different ideas about enzyme catalysis.