Protein Dynamics and Enzymatic Catalysis

Abstract

This Perspective presents a review of our work and that of others in the highly controversial topic of the coupling of protein dynamics to reaction in enzymes. We have been involved in studying this topic for many years. Thus, this perspective will nàturally present our own views, but it also is designed to present an overview of the variety of viewpoints of this topic, both experimental and theoretical. This is obviously a large and contentious topic.

Graphical Abstract

1. INTRODUCTION

This Perspective presents our views of the status of the current understanding of how protein dynamics is or is not coupled to chemical reaction and catalysis in enzymatic reactions. As any who have followed this field know, this is a highly contentious question. Views range from those who strongly feel there is no need to invoke any protein dynamics^1–3 in order to understand enzyme function to those who feel that dynamics on some level is central to the catalytic process.^4–37 There are important intermediary views that recognize the dynamic nature of proteins and focus instead on other properties than catalysis, for example, capacity for evolutionary change.^38,39 From the outset, we state that the views presented in this Perspective are, as expected, our own and this could not possibly be a definitive review of all work on the topic. A search of the past 10 years with the keywords “protein dynamics” and “enzymes” yields over 51,000 results, and application of a filter for reviews still yields over 4500 results. That this is a contentious subject is apparent to anyone who has attended a conference over the past 10–15 years which included this topic. It has been stated that much of this disagreement is definitional, i.e., what is dynamics and what is catalysis.⁴⁰ While there is some truth to this view, in fact, it can obscure real scientific discourse which focuses on mechanism.⁴¹ The arrangement of this Perspective will be designed to show our views of how dynamics on time scales from enzyme turnover to chemistry itself can be central to the function of an enzyme. We feel it would be disingenuous at best to argue that such motions are not “part” of catalysis, because the enzyme simply would not function, or would function in a highly weakened fashion without them. In this Perspective, we will present our views of the import of different types of protein motions and how one may rigorously define if they are part of catalysis, with at least one or two references to the central experimental results that support the point of view. Most of our work in this field has focused on rapid protein dynamics coupled to reaction in the temporal vicinity of the transition state, but we have also been involved in the issues of conformation fluctuation, and we begin with this time scale, later in the article focusing on protein dynamics directly coupled to passage over the transition state barrier, i.e., multidimensional reaction coordinates. We do acknowledge that there has been a significantly greater acceptance of all aspects of protein dynamics as central to enzyme function in the past few years, but there is still some controversy, and thus we are especially glad to present this review.

2. CONFORMATIONAL REARRANGEMENT

Prior to entering a discussion of the topic at hand, it is critical to state what the disagreement is NOT about. No one contends that proteins do not move, and no one on any side of this question contends that motion is not necessary for enzymatic activity (we think). For example, many enzymes include catalytic loops or flaps that are needed to open for substrate binding and close for chemistry. Closure of loops is often cited as a necessary step in water exclusion from the active site^42–44 which almost always is carefully arranged by nature to place charges in exactly the location that would be close to optimal if solvent were able to rearrange in the appropriate fashion. This arrangement of charges, referred to in one school of thought as electrostatic preorganization,^1,42–48 is certainly central to enzyme activity, and the concept is coupled to the Pauling conception of enzymatic catalysis, that is, that the enzyme binds most strongly to the transition state. Therefore, enzymes need to move at least in this fashion, but a simple solvent such as water needs to do the same thing in the case of successful barrier passage in solution, so, though the motion is required, one school of thought holds that it is inherently not catalytic. As will be described below, we personally find this argument to be unpersuasive, especially because of the vast biochemical literature showing that enzymatic reactions can be significantly slowed through remote mutations that effect dynamics alone. Simply acknowledging that “conformational rearrangements” exist in solution neither abrogates the importance of these motions in enzymes nor does it question that enzymes are arranged to create the needed motions with far greater regularity than simple solutions. The importance of such protein dynamics was forcefully made years ago in studies of the hydride transfer reaction catalyzed by dihydrofolate reductase.^49–59 In fact, the architecture of the protein is such that all the needed motions are “controlled” in some sense, and this motion is essential to bring the protein to the transition state and reaction. Often these motions are in fact the rate-determining step of enzyme turnover. Another example is presented by protein tyrosine phosphatases: these enzymes have common conserved cores, and identical chemical mechanisms with very similar transition states, yet the turnover numbers vary by orders of magnitude.⁶⁰

We have also been involved in the investigation of conformational dynamics in enzymes. We studied collective motions in PNP using simple principle component analysis.⁶¹ Another enzyme we have studied in which conformational motions are needed to establish the approach to the transition state is lactate dehydrogenase.^62–65 Using Markovian networks, we identified the network of interconverting conformational states in the Michaelis complex of lactate dehydrogenase and how these conformations relate to each other and collectively result in an observed rate. In addition, we were able to relate the dominant network members to specific identifiable spectroscopically unique states. These different states have identifiably different rates of chemistry, so there is a direct connection here between the conformational rearrangement and function of the enzyme.

2.1. Relation to Transition State Theory.

Given the widely accepted importance of conformational dynamics in the function of the enzyme, we now need to understand and relate two very different pictures of these conformational dynamics and enzymatic catalysis. One school of thought is that, because using static or rather equilibrium pictures such as the many flavors of transition state theory^66–75 yields good comparison to experimental rates, one must conclude that dynamics is unimportant. In fact, in our view, one of the great misuses of Transition State Theory is the assertion that, if TST is employed, if there is little to no recrossing of the transition state barrier, then there is no “dynamics” contribution to the reaction. To understand the false equivalency here, we must remember what transition state theory posits, that is, that one may in many cases approximate exact dynamic rates calculated with full classical mechanics with a statistical theory dependent only on the density of states at the top of the free energy barrier to reaction. Even in the extensions that allow for an ensemble of barriers⁶⁹ there is a tacit assumption that all rates are determined by the top of the free energy barrier. In truly complex systems such as enzymes, there are many required “prerequisites” before chemistry approaches the free energy maximum, and in fact, we have always found that the enzyme is arranged so that there is no recrossing. Thus, a value of κ close to 1 when calculated assuming a simple free energy landscape dominated by a single extremal point is of limited utility. In addition, as Hammes-Schiffer and co-workers have argued, dynamics following chemistry⁷⁶ is also critical to enzyme turnover. There was some insight into enzyme function in Bruice’s “near attack conformation” concept, but unfortunately, though this was a highly useful thought construct, it did not allow for unbiased rigor.^77–80 It is also worth pointing out that biochemical measurements of the rate of chemistry are technically challenging (and, for some especially challenging ones, seemingly time dependent). The only measurement that comes close to isolating chemistry from the other steps is a single turnover measurement, and depending on the specific system, this will require a highly sensitive probe of product production.^34,81,82 Clearly a computed transition state theory rate would be meaninglessly compared to a steady state rate experiment which would confound the predicted rate of chemistry with any other conformational rates before and after reaction, even if as we stated they are in fact central to the overall function. Models that can predict rates in complex systems can suffer from a lack of uniqueness. It is predictive mechanistic questions, later probed by experiment, that present the greatest tests, which we will describe below.

Therefore, in fact, in the realm of conformational dynamics and catalysis, in our view, everyone is both partially right and partially wrong. Enzymes have been arranged by evolution to deliver reacting atoms and molecules to a chemical barrier in a highly optimal fashion. Once there, chemistry tends to proceed directly with no recrossing. What the enzyme does superbly well is get the substrates to this point. Likely it is strongly supported by electric fields that the enzyme arranges with no reorganization energy cost as has been stated forcefully by Warshel and coworkers¹ and also supported by Boxer and co-workers through experiments of vibrational Stark effects in approximate transition states.^48,83–87 Once at that point, chemistry happens, but the protein is still involved as we will discuss below. In addition, a one-dimensional transition state picture at this point is also problematic because the reaction coordinate in a great many cases is not one-dimensional. As a final point, we note such concepts of conformational rearrangement are now becoming more and more important even in heterogeneous catalysis where simple one-dimensional static pictures are being found to be as incorrect as the static picture of a protein.^88,89

3. RAPID PROTEIN DYNAMICS

Just as conformational transitions help bring substrates to the transition state for chemistry, over the past 15 years, we and others have shown that much lower amplitude, shorter time scale motions are also central to reaction in an enzyme. In this section, we will review some of these ideas and give both theoretical and experimental justifications for these conclusions. It is important at the outset to distinguish such motions from conformational transitions, not simply because of the absolute time scale but rather because of their time scale as compared to the time scale of barrier passage. When there is a time scale separation between conformational transition and barrier passage, the appropriate modeling approach would be to average a chemical rate over a static distribution of free energy barriers. This is exactly the approach taken by a number of groups using Marcus Theory appropriate for heavy particle transfer^90–92 also developed by Dogonadze and Levich.⁹³ Here the 1D picture of transition state theory is augmented with a distribution of barriers. Such an approach was used successfully to fit kinetic data by Klinman and co-workers.^5,35,94–98 While of value because it pointed directly to the modulation of barriers by motions orthogonal to the particle transfer coordinate, the ability to successfully fit kinetic data is not always equivalent to proving a specific model. In fact, our work and that of others have shown that the proper picture is not of a static distribution of barriers created only by conformational distributions but rather of protein motion coupled to barrier passage in which the protein motion is on a similar time scale as barrier passage. The inherent difference is in the static picture; barrier passage is largely one-dimensional, with the protein creating a milieu that provides a variety of barriers in different proteins in the ensemble. In our picture, which we term a promoting vibration picture, because the time scales of barrier passage and the degrees of freedom that modulate the barrier are similar, the overall picture is inherently multidimensional. Put another way appropriate to physical chemistry, the reaction coordinate is not simply comprised of the bonds that are made and broken in the enzymatic reaction but rather involves the protein dynamics in a way that cannot be separated. Such a picture is essentially different, and a variety of groups are now finding both theoretical and experimental support of the promoting vibration concept. As we study the coupling of motions in the protein on the same time scale of barrier passage, we require a method that allows the interrogation of individual trajectories that pass from reactants to products. Because the system is comprised of soft matter, we must generate an ensemble of such trajectories. Finally, because we hope to perform unbiased mechanistic analysis, we require a trajectory generation method that is itself as unbiased as possible. We have long used Transition Path Sampling, developed by Chandler and co-workers.^99–103 In the years since the initial development of TPS, there have been multiple flavors of the concept^104–108 and multiple methods of trajectory generation.^109–118 This Perspective is not a methods review, so we leave TPS and its variants to be reviewed by others. I begin with a review of the systems we have studied followed by both computations and experiments of others.

3.1. Lactate Dehydrogenase.

The first enzyme we studied with TPS was lactate dehydrogenase (LDH). LDH catalyzes the interconversion of lactate and pyruvate with NAD as a cofactor (Figure 1). LDH is a tetramer, with isoforms that consist of different combinations of two subunits, called heart and muscle. The properties of the heart and muscle isoforms are different: heart LDH favors production of pyruvate and muscle LDH of lactate. However, the structure and amino acid content of the active sites of the two isoforms are almost identical, raising the question of what causes their difference in activity. Our TPS analysis^119–122 found that the average donor–acceptor distance is shorter for the heart isoform than for the muscle isoform with lactate bound, and vice versa. The difference in activity between isoforms mentioned above is thus likely due to the reduced donor–acceptor distance when lactate is bound to the heart isoform compared to when pyruvate is bound to the muscle isoform. (Note: the chemical milieu in which the enzyme operates is also potentially important with such factors such as substrate concentration and pH important modulators.)

Figure 1.

Chemical reaction catalyzed by lactate dehydrogenase. The reaction involves the hydride transfer of the NC4 hydrogen of NADH from the pro-R side of the reduced nicotinamide ring to the C2 carbon of pyruvate and protein transfer from the imidozole group of His-193 to pyruvate’s keto oxygen.

The TPS analysis revealed the microscopic mechanism of the hydride transfer chemical step. We found that hydride transfer was accompanied in all reactive trajectories by a compressive motion of residues that facilitate catalysis by bringing the donor and acceptor atoms closer, thus lowering the adiabatic barrier to reaction. The residues that participate in this motion are Leu65 and Val31 (located behind the NAD cofactor and transferring hydride) and Arg106 and Asp195 (located on the acceptor side behind the substrate), as shown in Figure 2. We note that each trajectory presents a distribution of barriers, rather than a static conformational distribution. Chemistry invariably happens when the donor–acceptor distance is minimized in a single trajectory. The overall motion needed to create this barrier compression is small compared to conformational fluctuations, but chemical barriers are highly sensitive to distance and a variation of an Angstrom can cause the complete abrogation of the barrier.^123,124

Figure 2.

Promoting vibration in human heart LDH. This protein motion is along the donor–acceptor axis for hydride transfer, and compression always proceeds reaction.

An important question is if the compressive motion is a random fluctuation in the protein (as for example compression in a liquid cage for a solution phase reaction) or if in fact the architecture of the protein creates a non-stochastic channel for this energy transmission. In a simulation, we coupled the NAD ring of one component of the substrates to a Nosé–Hoover thermostat, thus allowing continuous injection of thermal energy to the active site, and monitored the temperatures of several residues selected along concentric shells around the active site and we monitored if the energy dissipated isotropically.¹²⁵ We found that the residues that are part of the promoting vibration had higher temperature than other residues equidistant from the thermal excitation site. Because nature must be reversible, this implies that this channel of residues forms a thermal transmission path from the outside to the active site. Calculation of the dynamical structure factor S(k, ω)

$$S(\text{k},\omega )=\int \text{d}t{\text{e}}^{-i\omega t}\sum _{i,j}\langle {\text{e}}^{-ik{r}_i(t)}{\text{e}}^{+ik{r}_j(t)}\rangle$$ (1)

confirmed this result.

Peaks in this function signify density fluctuations with frequency ω at wavevector k and half-life inversely proportional to the width of the peak. We found that the direction along the promoting motion supports a density fluctuation absent from perpendicular directions (Figure 3), indicating that density fluctuations exhibit an anisotropy. Figure 4 shows the path through the protein—it lies directly on the promoting vibration.

Figure 3.

Structure factor S(k, ω) for k = 0.2 Å⁻¹ along the PV axis (black line) and along an axis perpendicular to the promoting vibration. There is strong anisotropy. The sharpness of the peak at 125 cm⁻¹ means that there are stable fluctuations along the PV axis for that frequency.

Figure 4.

Different spherical shells containing members of the promoting vibration. The highlighted residues represent the different members of the promoting vibration.

These results suggest that the rate promoting motion in LDH lies on an axis that is favorable for thermal energy transfer, raising the possibility that the protein may have evolved in a way that allows transfer of thermal energy to a motion that is coupled to the chemical step. There will be further discussion of this issue later in this Perspective when we discuss laboratory evolved artificial enzymes. While predicted over 11 years ago, this kind of energy transfer from the surface of the protein to the active site has now been observed experimentally in soybean lipoxygenase¹²⁶ and also bacterial DHFR for slower motions.¹²⁷

3.2. Alcohol Dehydrogenase.

This enzyme catalyzes essentially the same reaction as lactate dehydrogenase and is part of the same enzyme family, so it is not surprising that we found a very similar promoting vibration in this case. I include the work for two technical reasons. First, in any hydrogen transfer enzyme, the argument can be made that tunneling may well play a large role in reaction. Since TPS is inherently a classical trajectory method, we included quantum effects at least approximately through path integral methods.¹²³ The other question that we asked in this work, is what is the free energy barrier encountered in only the reactive trajectories. From the force on the transferring particle, we can calculate the work

$$W=-{\int }_{\text{RC}}f\text{\hspace{0.17em}d}r$$ (2)

and from the work calculate a free energy of particle transfer as the ensemble average of the reversible work:

$$\Delta G={\langle W\rangle }_{\text{TPE}}$$ (3)

Applying this to Yeast alcohol dehydrogenase we found the results shown below:

1. Crystal structure donor–acceptor distance = 3.8 Å

2. DA distances explored over 500 fs trajectory = 2.8–4.5 Å

3. Average DA distance for classical transfer = 2.8 Å

4. Average free energy barrier = 1 kcal/mol

5. Barrier when the distance is restrained to 3.44 Å = 29 kcal/mol

In other words, the donor–acceptor distance is modulated by almost 2 Å over the course of an average reactive trajectory, the reaction happens when it is minimized and the minimization of this distance essentially abrogates the barrier to chemistry (note restraining the distance to a distance that is still less than the crystal structure distance results in a barrier of over 30 kcal/mol). One might at this point ask what happened to the measurable barrier found by experimentalists—it is clear that is essentially an entropic barrier which allows the protein to find the right set of conformations that allow the promoting vibration to become effective. More on this later.

3.3. Purine Nucleoside Phosphorylase.

The promoting vibration concept seems most likely to be important in a hydrogen transfer reaction such as LDH. As a next step in studying this coupling of rapid protein motions to enzymatic catalysis, we focused on purine nucleoside phosphorylase. The reaction catalyzed is shown in Figure 5. Clearly, a bond scission reaction presents a very different challenge to an enzyme than a hydrogen transfer reaction, and in fact, an organic chemist studying the reaction in solution would likely describe this as an S_N2 reaction with phosphate as the attacking nucleophile. In fact, experimental evidence showed that the phosphate does not approach to bonding distance until well after the glycosidic bond is fully broken, so the weakening of this bond must come from a different physical effect than the approach of the phosphate.¹²⁸ The advantage to the TPS and reaction coordinate identification methods we have used is they are unbiased. We might guess the existence of a promoting vibration that modulates donor–acceptor distance, but it is not easy to guess the source of polarization and thus weakening of the glycosidic bond in this case. The mechanism turned out to be at least partially provided by compression of a stack of highly electronegative oxygen atoms most proximally by a histidine (HIS257) in the active site.^11,61,122

Figure 5.

Chemical reaction catalyzed by human purine nucleoside phosphorylase. The promoting vibration compresses O₄′ and O₅′.

In this relatively early stage of our investigations into the coupling of rapid protein dynamics to reaction, while we felt we had significant computational support for the assertion that such an effect is important, we lacked experimental support. This changed when our colleague Vern Schramm developed his so-called Born–Oppenheimer enzyme. He replaced carbon, nitrogen, and hydrogen with heavy isotopic analogues.³⁴ When this was done for PNP, no changes in kinetic signatures of slow conformational motion were detected, but on-enzyme chemistry was slowed by 30%. Using TPS we were able to show that this effect was caused by a mistiming of the oxygen compression described above, further validating the concept of the protein promoting vibration. We next examined a heavy enzyme effect in lactate dehydrogenase,¹⁰ and these results also argue strongly for the presence of a promoting vibration coupled to reaction, and this result was also subsequently validated by heavy enzyme kinetic experiments.⁸²

3.4. Evolution’s Effect on Protein Dynamics—DHFR.

A case in which evolution has seemingly altered the function of a protein vis a vis protein dynamics is presented by DHFR. As we discussed above, it has long been the “H atom” for conformational motion and protein function, but little was known about rapid protein dynamics; in fact, the E. coli enzyme, the one most studied, was given as a counter example to the importance of rapid protein dynamics. We studied both the E. coli enzyme and the human variant and found another example of “everyone being right”. By this we mean that the bacterial enzyme showed no coupling of rapid dynamics to barrier passage, but the slightly less well studied human protein did.¹²⁹ This result was supported by later heavy enzyme studies,¹³⁰ and just recently, these predictions received experimental support from other rate measurements reported in this journal.¹³¹ We will return to the subject of evolution and the coupling of protein dynamics to enzymatic catalysis presently.

4. CONNECTING SLOW CONFORMATIONAL TRANSITION TO PROMOTING VIBRATIONS

If one accepts that both slow conformational motion and rapid promoting vibrations are important to enzyme function, it is natural to question whether they are somehow connected. In fact, just such an idea has been previously suggested.^29,30 While the approaches described in the cited articles provide strong “circumstantial” evidence, proof is much harder to come by. This is simply because there are neither experimental tools nor computational ones that fully span the orders of magnitude of time scales of the different motions, which can also interrogate them and their effect on chemical reaction. As an attempt to find such a connection, we again turned to PNP.¹³² Figure 6 shows the approach we took. Our studies of promoting vibrations in this system as described above showed the importance of HIS257. This residue lies at the hinge of a loop that is known to control enzyme turnover via closing on substrate. As we report in the reference above, the constraint used to hold the loop open a small amount has measurable effects on both the promoting vibration and the apparent free energy barrier of the chemical step (Figure 7). The small perturbation shown in Figure 6 removed HIS257 from the reaction coordinate, and this in turn results in a higher free energy barrier to reaction.

Figure 6.

Constrained PNP Chain A (red) and active site (green). The loop is held open by constraining the α carbon of Glu250 to the α carbon of Pro122. The unconstrained loop is shown in blue. The difference in loop positions is less than 2 Å.

Figure 7.

Free energy profile for the unconstrained (left) and constrained (right) PNP systems calculated using the TPS based method. Standard deviations are calculated using the bootstrapping method and denoted as blue error bars, while the continuous black curve represents the polynomial fitting function.

Not every enzyme has a promoting vibration, and not every promoting vibration will involve residues so obviously directly affected through alteration of a conformational motion, but this result is suggestive of the immense complexity surrounding the design of active “theozymes”. If one needs to not only design a specific rapid motion into the body of an enzyme but also design a coupled dynamics across a range of time scales from picoseconds to milliseconds, the task at hand is complex to say the least. More on this in our conclusions and future directions.

5. OTHER SYSTEMS AND SOME CONVERGENCE

The field of rapid protein dynamics coupled to catalysis has expanded significantly in the past few years. Significant work comes from the Scrutton and Hay groups in Manchester, many in PCET systems.^{15–19,21,22} Many of these results rely on KIE measurements, and thus are by nature indirect, but show evidence of vibrational coupling to reaction. Klinman and coworkers have long argued for the importance of distance sampling as a component of their Marcus model fitting and recently have described paths of energy transmission much like ours from lactate dehydrogenase. The methods used do not allow the isolation of time scales, but the centrality of relatively rapid motion has been identified.^{95,98,133,134} It should be pointed out that the slow convergence of theoretical and experimental conclusions in this field is not surprising. Enzymes are soft protein systems with highly dense spectral densities. If we, for example, identify a motion of average frequency 100 wave-numbers for a promoting vibration, this is a motion embedded in a continuum of frequencies around that value. Even if computations of coherent structure factors show sharp peaks that should have a long lifetime, the spectral density is dense at these frequencies; thus, there is a thermal sink of similar frequencies available to absorb energy. One cannot, for example, likely pump this single frequency and see the rate of chemistry increase.

The convergence we mention is simply a statement of the fact that some of the so-called “competing” models of catalysis may not be competing at all. The concept of electrostatic preorganization in the most simplified form says that the enzyme works because it creates an optimal electrostatic environment. Forces in chemistry are of course created by electron densities. We showed a few years ago that we were able to reproduce the types of electric fields measured by Boxer and co-workers^48,83–87 from our TPS trajectories, and further that the fields are strongly shaped by the promoting vibration. The experimental measurements are of a single point—an assumed transition state analogue—but we can show the approach to that point in the immediate vicinity of the transition state is created by the promoting vibration.^132,135,136 An elegant formal synthesis of such concepts is presented in a recent paper by Alexandrova and colleagues.¹³⁷

6. ENZYME DESIGN, ARTIFICIAL ENZYMES, AND DIRECTED EVOLUTION

The concept of artificial enzyme design is straightforward, but the implementation has been truly virtuoso. If the simple picture of Pauling transition state binding holds, then if we can create an artificial protein that has a binding pocket complementary to an assumed transition state both in geometry and electrostatics, we would have a powerful artificial enzyme. This was the motivating concept behind the catalytic antibody work.¹³⁸ The moderate catalytic power of these protein catalysts has been at least partially ascribed to inefficient binding of substrates and similar inefficient release of products, and therefore, artificial enzymes based on protein scaffolds that are derived from existing enzymes seemed a rational next approach. The design of protein structure has seen quantum leaps in the past few decades.^139–142 We view the current state of “theozyme” design as strong evidence for the importance of protein dynamics in enzyme catalysis. While active proteins have been generated, the complexities of the challenge are manifest by the fact that the designers do not have a clear justification for why certain designs show activity and others do not.^143,144 Our interpretation of this fact is there seems to be a missing design principle, and we will describe here how we queried these systems to see if protein dynamics might at least be part of it.

As an initial attempt we returned to the study of the heavy isotopic substituted protein of PNP and attempted to correct the timing of the compression we noted as a cause of the loss of catalytic efficiency. In our first attempt, we were able to correct the timing¹⁴⁵ but the overall compression was not strong enough. In a second attempt at design, we were able to make a mutant heavy enzyme that was faster than the light enzyme (an inverse heavy enzyme isotope effect¹⁴⁶). We made a similar proposal for a mutant form or aromatic amine dehydrogenase, a more complex PCET chemical reaction.¹⁴

Attempting to address the design question from a different direction, we employed TPS studies of families of artificial catalytic proteins “designed” by directed evolution. The advantage to using this approach is the evolutionary process is completely agnostic to any specific mechanism of catalytic efficiency. Mutations are chosen purely because they (in these cases) speed turnover, and increased rates of chemistry may be accomplished by any of the effects mentioned: transition state stabilization, electrostatic preorganization, or any other method. In fact, for a variety of laboratory evolved species, we have found that initial designs are altered by the optimization of rate to introduce specific coupling of protein dynamics to chemistry. We began the studies on the completely abiologic Kemp eliminase reaction.¹⁴⁷ We did see evidence of the development of protein dynamics, but the starting structure is so rigid and the dynamics was quite modest. The next system we studied was the retro-aldolase reaction. In this case, optimization of chemistry results in much more significant inclusion of protein dynamics as a part of the reaction coordinate.¹⁴⁸ Knowing that protein dynamics is altered and in fact coupled to chemistry is only a first step, however. If one is to use this knowledge in an eventual design methodology, it is necessary to understand how the mutations that evolution employed caused this to happen. We were able to show it happens as regions of greater rigidity introduced by increased hydrogen bonding and greater flexibility created by reduced hydrogen bonding cause directed thermal energy transmission in the body of the protein.¹⁴⁹ This change in hydrogen bonding is graphically represented in Figure 8. We note similar effects have been posited to occur via hydrophobic packing.¹⁵⁰

Figure 8.

Region of the most evolved variant, that introduced protein dynamics shown in both panels (A) and (B) with key interactions highlighted. (A) has internal residues associated with decreased hydrogen bonding compared to variant IV highlighted in orange; the direction of the rate promoting vibration is out of the page. (B) has internal residues associated with increased hydrogen bonding compared to variant IV highlighted in purple and pink; the direction of the rate promoting vibration is going from right to left. The substrate and QM residues (the active site) are highlighted in red.

It is important to be clear here—we are in no way suggesting that the amino acid substitutions that directed evolution create results in active artificial enzymes purely because protein dynamics becomes coupled to chemical reaction. In fact, the entire range of catalytic effects are no doubt operative: electrostatic effects, substrate binding and product release, water exclusion, etc. In fact, to our knowledge, because directed evolution is an experimentally challenging task, the appearance of product (steady state) is often the reporter on clone selection. As such, it certainly cannot be claimed that the rate of chemistry is alone what drove the process. That having been said, unlike natural enzymes in which chemistry is almost never rate limiting, the starting point for directed evolution is a protein which is barely active, so it is likely that chemistry along with all other effects are optimized in the selection process.

7. CONCLUSIONS AND FUTURE DIRECTIONS

Our study and that of others of the coupling of protein dynamics to chemical reaction in enzymes had a genesis in simply wanting to know how catalytic proteins worked. There was little practical to be gained from the investigations. While the field of enzymology long accepted that conformational motions were important for enzyme function and in fact that different conformational substates could potentially have different chemical activities,¹⁵¹ the importance of picosecond time scale promoting vibrations was far more controversial. In fact, it was suggested that there could be no importance to such motions when they occurred so many orders of magnitude faster than the turnover of enzymes. This is of course a manifestly problematic complaint, electrons wave functions reconfigure on an atto-second time scale, but no one would suggest such electron dynamics is not necessary for chemical reactions that occur on time scales many orders of magnitude more slowly. The necessary breakthrough was found in the use of enhanced sampling methods that are unbiased and allow observation of individual reactive trajectories.

What is important now that the concept has been established is how one can use the knowledge. First, we can imagine such ideas informing artificial enzyme design. Enzymes present a great many advantages over nonprotein catalysts for certain chemistries, and it has been a long-held goal to design artificial ones. The inclusion of dynamics could possibly be one added component in the toolbox that will eventually make this program practical. The question is how to accomplish this goal. Analysis of the changes in laboratory evolved proteins points in one design direction, and other studies of energy transfer through the bodies of proteins via packing effects is another. Given the complexity we encountered when introducing a single change in timing in heavy PNP, it would clearly be highly challenging to imagine wholescale redesign of a protein matrix to provide the proper flexibility and stiffness we noted was created in the retroaldolases. One other approach that has recently been suggested is the use of machine learning to create the proper protein structure.¹⁴² When first-principles physics is simply too complex, such methods may provide a tool to employ our increased understanding of the goals with the appropriate promoting vibration of course dependent on the chemistry catalyzed. No matter the approach used to build a competent catalyst, increased knowledge of what creates such a protein is necessary as the enzyme design work has clearly illustrated.

Another area that is potentially available is in the realm of enzyme inhibition. Classical inhibitors have either been unreactive substrate mimics,¹⁵² mechanism-based chemistry inhibitors,¹⁵³ or transition state inhibitors.¹⁵⁴ There has been expanded interest in finding ways to inhibit enzymes remote from the active site (to avoid mutational escape from inhibition, for example). Allosteric sites present such a possibility. Initial studies, both computational and experimental, demonstrate that alteration of a promoting vibration via surface binding to the protein is at least feasible.^155,156 This would certainly fit in the general rubric of allosteric inhibition. One could imagine this would present an extremely complex a target for evolutionary escape.

This then is in our view one of the grand challenges of the next decade of molecular biophysical chemistry: using a deeper understanding of the details of enzymatic catalysis to allow both positive and negative manipulation of protein-based catalysts—either natural or created. While the challenges are great, they are insurmountable without a basic understanding of the physical principles by which the systems function.

Biography

Steven D. Schwartz is Regents Professor at the University of Arizona. He is appointed in the Department of Chemistry and Biochemistry. He received his Ph.D. degree from the University of California (Berkeley) studying with Bill Miller. Following a brief postdoctoral fellowship at Columbia University, he worked in Applied Mathematics at AT&T Bell Laboratories. Following this, he moved to the Albert Einstein College of Medicine in New York where he was a faculty member in Biochemistry and in Biophysics and Director of the Seaver Foundation Center for Computational Biology. He moved to the University of Arizona in 2012 and has been there since then.