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The idea that tunneling is enhanced by the compression of the donor acceptor distance has attracted significant interest. In particular, recent studies argued that this proposal is consistent with pressure effects on enzymatic reactions, and that the observed pressure effects support the idea of vibrationally enhanced catalysis. However, a careful analysis of the current works reveals serious inconsistencies in the evidence presented to support these hypotheses. Apparently, tunneling decreases upon compression, and external pressure does not lead to the applicable compression of the free energy surface. Additionally, pressure experiments do not provide actual evidence for vibrationally enhanced catalysis. Finally, the temperature dependence of the entropy change in hydride transfer reactions is shown to reflect simple electrostatic effects.
It has long been proposed that steric strain and compression can help catalysis. An early example of this is the long-popular idea that strain makes a significant contribution to catalysis [1–6]. A recent version of this proposal involved the “near attack conformation” (NAC) of Bruice and coworkers (e.g. Refs. [7,8]), where it was proposed that enzymes help catalyze reactions by bringing the reacting atoms of the substrate to a typical NAC distance, which was assumed to be rarely attained in the reference reaction in water. This issue has been analyzed and discussed in detail in Ref. , where it was shown that the NAC proposal does not account for enzyme catalysis. Arguably the last bastion of this proposal was the catalytic power of enzymes that contain the coenzyme B12 cofactor, a careful EVB study of which demonstrated that the major part of the catalytic effect is not actually due to strain, but rather, it is due to the electrostatic interaction between the ribose moiety and the protein, and the strain contribution is in fact very small. It should be noted that this issue has also been examined in elegant independent computational studies by other workers [11,12], and these studies have provided strong support for the conclusions of Ref. , thus independently validating our findings.
Now, a relatively similar incarnation of this idea has emerged when discussing tunneling and promoting modes, where several proponents of the importance of tunneling in enzyme catalysis have put forth the idea that enzymes catalyze their reactions by compressing the distance between the donor and the acceptor, thus leading to a narrower potential and to tunneling (e.g. Refs. [13–20] amongst others, see Fig. 1A). However, this appealing idea has since been found to be inconsistent with the gradual realization that in proton and hydrogen transfer reactions, compression in fact reduces the KIE, and thus the tunneling contribution (see the discussion in Section II, and Fig. 1B for the current view). More recently, the compression idea has been promoted in the context of pressure experiments, where it has again been argued that this produces a compressed system with large tunneling and corresponding rate enhancement (e.g. Refs. [21,22]). Herein, we provide a detailed analysis of the current arguments in favor of the importance of barrier compression and vibrationally enhanced tunneling (amongst other factors), and demonstrate that, in fact, the analyses of the compression effect and related theoretical studies that have been presented in the literature are very problematic, and do not actually disprove the current view, which was presented in Ref.  and is illustrated in Fig. 1B.
As mentioned in the introduction, one of the central arguments with regard to the role of tunneling in enzyme catalysis starts with the assumption that enzymes compress the distance between the donor and the acceptor, thus leading to a narrower potential, which in turn leads to tunneling [13–20]. This view, which is illustrated in Fig. 1A, would mean that the enzyme leads to a change in the shape of the barrier, and, presumably, in the process, enhances the tunneling contribution to the overall catalysis [13–20]. Additionally, this idea has also been used in order to rationalize the temperature dependence of observed KIEs, as will be discussed in Section III.
The traditional view of NQM contributions to catalysis implies that the protein compresses the reacting fragments, leading to a narrower potential and greater tunneling. This concept assumes a relationship of the form :
where V0 and L designate the width and height of the barrier respectively and K is a constant. However, this relationship does not apply in the relevant cases. That is, both others and we have observed [23–25] that, even in the vibronic formulation, the isotope effect in fact increases due to the sharp distance dependence of the zero-zero vibrational overlap. This is illustrated in Fig. 1B, and in this situation, the tunneling contribution follows the relationship :
and, in fact, upon compression, the NQM effects decrease rather than increase. This effect arises from the fact that tunneling in proton and hydride transfer reactions is strongly dependent on the overlap between the vibrational wavefunctions of the reactant and product states, which in turn is dependent on the distance between the corresponding minima (as discussed in Ref. ). Thus, the ratio between the NQM contributions of H and D changes according to the relationship of Eq. 2, and, when the donor and acceptor are pushed to a short enough distance, the mixing between the two states makes the adiabatic surface very flat, which in turn results in the tunneling effect disappearing. In other words, for very short donor-acceptor distances the barrier disappears, and, per definition, proton transfer take place over the barrier.
At this point, it is worth clarifying that the prediction of the vibronic formula, which can be used to obtain an approximated analytical relationship between the KIE and the donor-acceptor distance, was discovered prior to our recent studies [24,25]. However, with the exception of Ref. , we are not aware of any early works other than our study  which realized that the change in distance of the KIE results in a scenario other than the traditional (and now shown to be incorrect) view illustrated in Fig. 1A. Furthermore, to the best of our knowledge, we are not aware of workers other than us  that have been able to establish the distance dependence of the KIE by proper microscopic simulations, without use of the problematic diabatic approximation and the vibronic formula, or understand that this finding makes it hard to rationalize enzyme catalysis by a perceived increase in tunneling. Nevertheless, there have been some preliminary steps in the right direction, in the form of a recent work  which does acknowledge that the KIE decreases upon barrier compression (even though this issue, which is only just starting to be fully realized and accepted by the wider community, is presented as a well-known fact). Finally, while this discussion may sound strange to some, as it is counter to the traditional view, it is important to emphasize that the key workers in the field (e.g. Refs. [24,25]) are now essentially obtaining the dependence of Eq. 2.
In fact, the correct picture of the effect of compression on the barrier has been obtained by any consistent study of hydrogen bonding systems, where it is demonstrated that compression simultaneously lowers both the barrier height and the barrier width. To the best of our knowledge, there exists no hydrogen-bonded system where, upon compression of the donor-acceptor distance, the barrier just becomes narrower and the height is preserved (see Fig. 2). This is particularly important, since this was also demonstrated for a series of proton potentials for malonaldehyde, corresponding to different O-O distances (see Fig. 2A of Ref. ). In fact, textbooks (e.g. Ref. ) usually state that tunneling is, per definition, quantum-mechanical transport through the barrier forbidden to classical mechanics. This can be either adiabatic (where the proton remains in the same vibrational state during the transfer) or diabatic (where transfer is associated with hopping between the vibrational states). If, for the extremely compressed donor-acceptor distances the barrier vanishes, then it is difficult to penetrate a nonexistent barrier, and thus, per definition, tunneling ceases to exist for such states. Finally, if is worth mentioning in passing that such simplified models as those presented in Ref.  are clearly inadequate to examine such problems, as can be seen by, for example, the unphysically short interatomic distances presented in Fig. 4a of this work. This once again emphasizes the need for detailed simulations with a firm physical basis when examining enzyme catalysis.
Now of course, the above analysis is crucial to the idea that NQM effects make a significant contribution to enzyme catalysis, as, by this argument, the effects that lead to an increase in the NQM contributions appear to actually be anticatalytic. That is, the rate constant is smaller for larger donor-acceptor distances. However, the observation that a large KIE reflects an increase and not a decrease in the donor-acceptor distance has not yet been fully realized by many workers in the field. That is, the “traditional” view with regard to barrier compression is still considered to be “general knowledge” by some, and, as such, continues to appear in the literature (see, for instance, Fig. 2 of Ref. ). Thus, we will expand on this issue at length in the subsequent sections.
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 . 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  involves several misunderstandings, starting with the assertion that Ref.  proves the barrier compression idea. Unfortunately, Ref.  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 Fig. 3 of the authors’ most recent paper , which shows the opposite trend to that presented in Fig. 4 of Ref. ). 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.  in Fig. 3, and point out that the same trend has been obtained by the most recent work of the authors  as well as by other diabatic studies [24,25], and that this trend is the opposite of the one reproduced in Ref. . It appears that the treatment of Ref.  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.  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 , 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.
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  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 . 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 . 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.  (discussed above) are unrealistic and unjustified.
Interestingly (and instructively), the authors of Ref.  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. , 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 . 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  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  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 Fig. 4). 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.  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  are incorrect (as is indeed suggested in Ref. ). 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 , or the continued propagation of “the deep tunneling” argument (i.e. that the enzymatic reaction occurs predominantly by tunneling) of Ref.  (an issue which was dissected at length in Ref. ). 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. , 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.  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. ). Figure 8 in Ref.  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.  argue that barrier compression is enhancing kTST and ktun at a similar rate. However, if one were to carefully examine Fig. 7D of the authors’ article (presented here in an adapted version in Fig. 5), 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.
More serious is the assertion (mentioned above) that, in Figs. 3 and 7 of Ref. , 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 ), 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. , 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.
The authors of Ref.  conclude their article on high pressure effects on tunneling in morphinone reductase by emphasizing the necessity of considering promoting modes and full tunneling models to explain the experimental data. They then  extend their argument to encompass the idea that promoting vibrations also cause barrier compression, which would, in principle, lead to a similar increase in the catalysis rate as is the case with pressure. This idea is similar to other (related) proposals that promoting modes lead to catalysis (such as those of Ref. [37–40], to name a few examples), which have been shown to be problematic (see e.g. Refs. [41,42]). At any rate, as far as the pressure argument is concerned, firstly, all the promoting modes idea does is address the (obvious) fact that under Boltzmann conditions, there will exist populations at r<r0, which are generated by atomic fluctuations of the entire system. Only fluctuations that do not satisfy the Boltzmann distribution can be considered as being genuine vibrational effects that represent specific modes. Secondly, and more importantly, the entire rate enhancement the authors observe with pressure can be explained by the fact that the pressure reduces the RS partition function (by reducing VRS), making this a moot argument.
In any case, the fact that the promoting vibration idea is problematic can also easily be realized by, for instance, examining Ref. . This study argues that the importance of promoting modes is established by the fact that the two different substrates have a difference in rate of about a factor of 10, and that the reactive structures are probably similar. However, there are in fact countless reasons for a small difference in the rate enhancement (most of which are due to small changes in the local electrostatic reorganization), and, one should not state that since we do not know the origin of the difference this proves that promoting modes are important, without a physically based analysis.
At this point it is crucial to re-clarify the most serious issue with the promoting mode idea, namely the fact that a properly defined reference state has not been considered. That is, the only way that a promoting mode will have any catalytic effect is when there is no similar promoting mode contribution in the reference reaction in solution (note that the water modes have a very wide and interesting spectrum, see for example Ref. ). Now none of the calculations that purport to show the effect of promoting modes have ever demonstrated or quantified any effect that is different from the corresponding effect in the reference reaction in solution, and, in fact, almost all promoting mode studies never consider any reference reaction. On the other hand, studies that consistently considered the reactive modes in proteins and solution found very similar behavior in the two cases [41,44,45].
Since the discussion above is related to entropic effects (i.e. the change in the ground state volume), we use this in order to analyze and discuss a major issue, namely the temperature dependence of the enthalpy and entropy of the catalytic reaction of some enzymes [20,24]. Whilst this issue was originally proposed as proof of dynamical effects [20,46,47], we pointed out that it must be a change in entropy, and provided a qualitative model for this [41,44,48] (a more quantitative analysis will be provided below). Subsequently, Klinman and coworkers modified their point of view, but moved towards a new proposal of an entropy funnel [19,49] (see specifically Fig. 9 of Ref. ). This (poorly-defined) model takes the frame of reference as being at the top of a funnel, which is defined as a 100% probability for any protein conformer to achieve one of many catalytically relevant interactions, which can be either formed between difference substrates with each other, or with the protein. It was then suggested that moving down the funnel progressively decreases the probability of finding conformers with an increasing number of substrate/protein interactions, until the family of conformers with sufficient numbers of interactions for catalysis to proceed is reached. Thus, progression from top to bottom along the funnel is supposed to represent an overall decrease in entropy.
The above model is then used to try to account for the TΔS≠ temperature dependence in thermophilic ADH . In other words, the “freezing out” of protein flexibility, which is supposed to accompany a reduction in temperature for the thermophilic proteins is argued as being representative of a more restrictive conformational space, which occurs further down the funnel (where it becomes necessary to increase protein disorder in such a way that the protein moves into the range required for optimal catalytic conditions). However, whilst elegant, this proposal mixes undefined “catalytic conditions” (and thus also presumably the catalytic coordinate) with some ad hoc protein coordinate. Now, firstly, a surface is not described by the formation of different interactions, but rather, by the effect of all the interactions on the potential surface along a given reaction coordinate, and, unless this proposal is formulated in clear physical terms which can be thoroughly explored, it cannot really be considered a proposal and, anyhow, the nature of the proposed funnel has no relationship to the clear landscape description, or to any conceivable description of physical landscapes.
In order to progress in a logical way, we must select one of the options presented in Fig. 6. The first of these is related to the entropic effect in the ES region (point A of Fig. 6). Here, the proposal implies that there is a large entropic contribution to kcat, even though, in most cases, this contribution is actually very small [44,50]. In any case, it is unimportant whether the entropic effect comes from the nearby protein groups [44,51], or from the relaxation of the whole protein (see the analysis of Ref.  for an example of this), as it anyhow occurs in the closed configuration, which has little to do with the implications of the funnel proposal. The second possibility is that the funnel proposal implies that the reactive trajectories are capable of passing through many points at the TS (i.e. moving from C to C′ of Fig. 6), having started from a restricted ground state region. This, however, would be inconsistent with any modeling study [53,54], as, while the landscape can of course be very complex, a complexity which can in principle include a scenario where the TS region has more configurations than the RS, however, real enzymatic reactions do not have large activation entropies [44,55], making it highly unlikely that such a scenario can occur. Transition states for an enzymatic reaction almost always involve the creation of stiffer bonds, giving rise to increased vibrational frequencies and the activation entropy is therefore difficult to increase. In fact, even in a situation with a heterogeneous set of barriers (as was observed in e.g. Ref. ), the average rate is still determined by the highest barriers for the chemical step, which is in turn determined by the corresponding reorganization energy, and, as long as the barriers between the different ground state conformations are lower than the chemical barrier, the solution of the multistate rate equation will simply follow the trend dictated by the highest activation barrier(s).
The final possibility illustrated in Fig. 6 is that somehow, at point B, the landscape is very narrow, leading to a large entropic effect upon moving to point A. This however is simply a case of a binding entropy effect, which is not observed experimentally, and, more importantly, has no effect on the chemical step (i.e. the binding free energy does not effect the chemical barrier, which reflects the differential binding of the TS). It would seem to us that this proposal implies a configurational search on the way to the TS, however, it does not define how this can actually be achieved. It should also be remembered that the activation entropy simply does not reflect any such search, but rather, is simply the difference between the entropies in the initial and final state (being a state function). Thus, without a proper landscape diagram, the entropic funnel proposal has no well defined meaning which can be explored or excluded in a scientific way, however, even with the most reasonable definitions (as highlighted by our hypothetical landscape), this proposal is unlikely to account for catalysis.
Of course, the origin of enzymatic activation entropies has to be computationally analyzed, and this can be done by our restraint release approach . In fact, we very recently performed restraint release studies of ADH, and found major support for our previous prediction, which is summarized in Fig. 7. That is, as was discussed in Ref. , we proposed that the experimentally observed decrease in ΔS≠ with temperature in ADH  can be rationalized by considering the expected interactions of the solute with its surroundings. Since the reaction in the direction considered by Kohen et al.  proceeds from a polar ion pair through a less polar TS to a nonpolar product (Fig. 7), the motions of the surroundings are expected to be less restricted in the TS than in the reactant state, which will contribute a positive term to ΔS≠. On the other hand, if the temperature is increased, the release of some of the motions that are frozen in the reactant state should make ΔS≠ less positive. Recently, we examined this issue by means of the restraint-release approach described in Ref. , which was used both for evaluating the contribution to the activation entropy from the reacting substrate (which gives the contribution from the configurational entropy), and, more importantly, for the evaluation of the entropy contribution due to the change in the configurational restriction of the active site (which is formally defined as the solvation entropy). The change in solvation entropy upon moving to the TS was determined by the same strategy recently used by us in determining solvation entropies in solution [58,59], and the preliminary analysis found  that upon changing the temperature from 270 to 300K, changes from 12.5 to 6.4 kcal/mol, whereas the corresponding changes in −TΔS≠ from the configurational entropy were only 4.6 and 6.8 kcal/mol respectively. Thus, the calculations reproduced the observed trend, further emphasizing our previous prediction and highlighting the fact that there is no need to invoke dynamical effects in order to explain the temperature dependence of ΔS≠ and ΔH≠ (ΔG≠ is temperature independent, so ΔH≠ is obtained from ΔS≠). Of course, the more recent entropy funnel idea [19,49] is not supported by our study.
The current work explores the interesting idea that the existing experimental findings support the proposal that enzymes compress the reacting system, and thus enhance reaction rates by increasing tunneling, which is in turn associated with promoting modes involving non-Boltzmann sampling and other dynamical effects. This work provides a careful and consistent analysis of the current studies, and points out the serious inconsistencies with the arguments in favor of the idea that enzymes apply compression when catalyzing reactions. The high pressure experiments show that compression of the donor-acceptor distance decreases the extent of tunneling, which is consistent with a reduction of the barrier height. That is, not only does tunneling decrease upon compression, but also, the idea that external pressure leads to the compression of the free energy surface is contradicted by direct simulations, and, similarly, the new idea that compression leads to a decrease in the KIE with a corresponding increase in tunneling is shown to be problematic. We also point out that the pressure experiments have not provided any support for the idea of vibrationally enhanced catalysis, and, in the process, provide the first physically based analysis of the temperature dependent entropy change in hydride transfer systems.
At this point it may be useful to conclude with a general clarification. That is, Ref.  argued that enzymes “only feel evolutionary pressure on the rate on the rate of the reaction and not the mechanism”, where the authors define “mechanism” as whether the reaction occurs classically (over the barrier), or by tunneling through the barrier. Whilst it is correct that enzymes evolve to optimize the reaction rate, the authors then proceed to imply that any factor that can lead to barrier compression (which, in their view may be achieved by promoting modes) will lead to an enhancement of the through-barrier reaction, and thus may be more important (presumably from an evolutionary perspective) than is generally acknowledged. However, as we explained above, compression does not enhance tunneling and promoting modes do not lead to compression (that is, they are just thermal motions along the reaction coordinate that occur both in the enzyme and in solution). The barrier is determined by the dependence of the potential energy (or more exactly the free energy) on the reaction coordinate, and not by the fluctuations of the reaction coordinate. For example, the reaction coordinate can even move up to the TS, but this will not change the height of the activation barrier (the chance of the coordinate reaching the TS will, of course, depend on the height of the barrier). Furthermore, enzymes demonstratably do not work by NAC type effects to compress the barrier, since this does not help catalysis (see Ref. ), and motions that reduce the donor-acceptor distance without significant energy cost would occur in solution. The real issue is the factors that are actually responsible for the enormous catalytic power of enzymes, and these factors (mainly the electrostatic preorganization) are those optimized by evolution.
This work was supported by Grant GM024492 from the National Institutes of Health (NIH). We also gratefully acknowledge the University of Southern California’s High Performance Computing and Communication Center (HPCC) for computer time.
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