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Published in final edited form as: Biochemistry. 2021 May 20;60(46):3529–3538. doi: 10.1021/acs.biochem.1c00211

Evolution of Enzyme Function and the Development of Catalytic Efficiency: Triosephosphate Isomerase, Jeremy R. Knowles, and W. John Albery

John A Gerlt 1
PMCID: PMC9437947  NIHMSID: NIHMS1831898  PMID: 34015914

Abstract

Every reader knows that an enzyme accelerates the rate of a reaction by reducing the activation-energy barrier. However, understanding how this is achieved by the structure of the enzyme and its interactions with stable complexes and transition states and, then, using this to (re)design enzymes to catalyze novel reactions remains the “holy grail” of mechanistic enzymology. The necessary foundation is the free-energy profile that specifies the energies of the bound substate, product and intervening intermediates as well as the transition states by which they are interconverted. When this free-energy profile is compared to that for the uncatalyzed reaction, strategies for establishing and enhancing catalysis can be identified. This Perspective reminds readers that the first free-energy profile determined for an enzyme-catalyzed reaction, that for triosephosphate isomerase, was published in Biochemistry in 1976 by Jeremy R. Knowles, W. John Albery, and coworkers. They used the profile to propose three steps of increasing “subtlety” that can be influenced by evolutionary pressure to increase the flux through the reaction coordinate: 1) “uniform binding” of substrate, product, and intermediates; 2) “differential binding” of complexes so that these are isoenergetic (to minimize the energy of the intervening transition states); and 3) “catalysis of an elementary step” in which the transition state for the kinetically significant chemical step is stabilized so that flux can be determined by the rate of substrate binding or product dissociation. These papers continue to guide mechanistic studies of enzyme-catalyzed reactions as well as provide principles for the (re)design of novel enzymes.

Graphical Abstract

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Introduction

On the occasion of Biochemistry’s 60th anniversary, this Perspective highlights the journal’s continued prominence in publishing important mechanistic enzymology. The Perspective focuses on a series of articles that remain “classics” in enzymology, reminding the readership of the continuing impact of these articles.

In 1976, Jeremy R. Knowles, W. John Albery, and their coworkers published a series of eight articles describing 1) experiments measuring the isotopic composition (deuterium and tritium) of substrates and products in the triosephosphate isomerase-catalyzed reaction with the goal of measuring the rate constants for all of the steps on the reaction coordinate1–6, 2) the integration of the rate constants to construct the free enzyme profile for the reaction, the first for an enzyme-catalyzed reaction7, and 3) an analysis of the free-energy profile to discover general evolutionary strategies used by Nature to maximize the catalytic efficiencies of enzymes8. Both the experimental approaches that were used and the basic principles of enzymatic catalysis that emerged continue to provide an essential foundation for mechanistic enzymology. Despite their “vintage” character, the author has continued to teach about these articles in his course on Enzymatic Reaction Mechanisms.

Now, the majority of enzymology articles are published on more “contemporary” topics, e.g., the discovery of enzymes in biosynthetic pathways for structurally complex natural products, the assignment of function to uncharacterized enzymes discovered in genome projects, and the (re)design of enzymes to catalyze novel reactions. However, the fundamental concepts of catalytic efficiency recognized by Knowles and his coworkers using triosephosphate isomerase (TIM) continue to guide our critical thinking about what we understand about enzymatic catalysis and reaction mechanisms and, therefore, what we still need to learn. This Perspective will summarize these articles to provide contemporary readers with easy access to their content and then provide comments about their continuing impact on enzymology.

Triosephosphate isomerase

These articles, and many others published by Knowles and coworkers in Biochemistry9–16, focused on discovering structure-function relationships in triosephosphate isomerase, the paradigm for understanding enzyme-catalyzed proton-transfer reactions at carbon17. Triosephosphate isomerase catalyzes the equilibration of the dihydroxyacetone phosphate (DHAP) and D-glyceraldehyde 3-phosphate (G3P) products of the fructose 1,6-biphosphate aldolase-catalyzed reaction in glycolysis (Figure 1A). G3P is converted to pyruvate with the formation of two molecules of ATP and one of NADH, providing energy for biosynthesis. Efficient production of ATP and NADH from glucose requires the facile conversion of DHAP to G3P; hence, TIM is subject to considerable evolutionary pressure for maximizing its catalytic efficiency.

Figure 1.

Figure 1.

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The triosephosphate isomerase reaction. Panel A. Glycolysis. Panel B. The triosephosphate isomerase reaction, with the reactions that enforce irreversibility. Both panels are reprinted from Knowles, J. R., and Albery, W. J. (1977) Perfection in enzyme catalysis: the energetics of triosephosphate isomerase, Accounts of chemical research 10, 105–111. Copyright 1977, American Chemical Society.

TIM is a dimer of two identical (β/α)8-barrels, with the active sites located at the C-terminal ends of the β-strands (protomer in Figure 2A). The “TIM barrel” fold is one of the most abundant, presumably because of the adaptability of the scaffold for the evolution of diverse reactions. A flexible loop located at the end of the 6th β-strand (orange) closes over the active site to sequester the substrate from solvent; the closing of the loop is triggered by interactions of the substrate’s “remote” phosphate group with this loop as well as two others at the ends of the 7th and 8th β-strands (olive), providing the structural mechanism by which the “intrinsic binding energy” of the phosphate group is used to enhance catalysis. High-resolution structures, e.g., 1TPH, chicken muscle TIM determined in the presence of phosphoglycolohydroxamate (PGH)18, a mimic of the cis-enediolate intermediate, reveal the organization of the active site residues (Figure 2B) as well as importance of secondary structural elements in promoting catalysis, e.g., an active site α-helix (green) that lowers the pKa of the functional group of His 95 (imidazolium to imidazole; >2.5 pKa units), an electrophilic catalyst, via proximity to its N-terminus19.

Figure 2.

Figure 2.

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Triosephosphate isomerase. Panel A. Polypeptide 1 of chicken breast triosephosphate isomerase (PDB code 1TPH) showing the location of the active site in (β/α)8-barrel fold. Panel B. The active site with phosphoglycolohydroxamate (PGH) mimicking the enediolate intermediate. Panel C. Mechanism of the triosephosphate isomerase-catalyzed reaction.

The TIM-catalyzed reaction is a 1,2-proton-transfer reaction (Figure 2C), with a single acid/base catalyst (Glu 165 located at the base of the loop at the end of the 6th β-strand) mediating the syn-transfer of the 1-proR proton of DHAP to carbon-2 of the cis-enediolate intermediate to generate D-glyceraldehyde 3-phosphate in competition with its exchange with solvent-derived protons via the protonated Glu (vide infra). The enediolate intermediate is stabilized and, therefore, rendered kinetically competent as the result of its hydrogen-bonding to the neutral imidazole group His 95 and proximity to the ε-ammonium group of Lys 1320. Elimination of inorganic phosphate is prevented by its enforced coplanarity with the enediolate21, 22.

The reaction is reversible, with the equilibrium constant close to unity (22 in the direction of DHAP for the total concentrations of DHAP and G3P; 340 for the concentrations of DHAP and G3P with the unhydrated carbonyl groups); as a result, the reaction coordinate can be studied easily in either direction. In either direction, the reaction can be enforced to be “irreversible” with a second enzyme that “removes” the product (Figure 1): glyceraldehyde 3-phosphate dehydrogenase, NAD+, and arsenate when G3P is product; α-glycerophosphate dehydrogenase and NADH when DHAP is product. In both coupling reactions, the G3P and DHAP derived protons transferred in the isomerase reaction are retained and rendered “inert” to exchange with solvent hydrons (increased pKas as the result of oxidation and reduction, respectively, of the product carbonyl group; vide infra). Irreversibility is required to determine the fate of substrate- and solvent-derived protons as the reaction coordinate is traversed from substrate to product. Because the hydron of the conjugate acid of Glu 165 can exchange with solvent hydrons, reversibility, i.e., the return of dissociated product to the substrate pool, would prevent quantitative analyses of the relative energies of the transition states that reflect the isotopic content of the substrate and product.

Strategy for determining relative rate constants

The experimental design and interpretation of their results are most easily described in the context of the free-energy profile that was determined7 (Figure 3). The energy profile is drawn for proton transfer with DHAP as substrate (S) and G3P as product (P; left to right), with the intervening cis-enediol(ate) intermediate (Z). Transition states 1 and 4 represent “physical” or “external” steps in which substrate/product bind/dissociate; their energies are not influenced by isotopic substitution of the substrate/product. Transition states 2 and 3 represent “chemical” or “internal” steps in which bound substrate/product are interconverted via the intermediate; their energies are influenced by isotopic substitution of the substrate/product (vide infra). Transition state “e” represents the exchange of the proton of Glu 165 with solvent protons. The relative energy of the transition state for DHAP binding/dissociation (transition state 1) could not be determined because it is not rate-determining in any of the reactions that were studied. Note that the remaining transition states are similar in energy, with the result that isotopic substitutions (deuterium and tritium) that alter the energies of transition states 2 and 3 can change the rate-determining step.

Figure 3.

Figure 3.

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The free-energy profile for the TIM-catalyzed reaction. Panel A. S is DHAP, Z is the enediolate intermediate, and P is G3P. Reprinted from Albery, W. J., and Knowles, J. R. (1976) Free-energy profile of the reaction catalyzed by triosephosphate isomerase, Biochemistry 15, 5627–5631. Copyright 1976, American Chemical Society. Panel B. Values of the rate constants that were determined (GAP is G3P). Reprinted from Knowles, J. R., and Albery, W. J. (1977) Perfection in enzyme catalysis: the energetics of triosephosphate isomerase, Accounts of chemical research 10, 105–111. Copyright 1977, American Chemical Society.

DHAP and G3P can be prepared isotopically labeled so the effect of substitution on rate (kcat; deuterium) or on isotopic discrimination (specific radioactivity of the remaining substrate pool; tritium) can be measured. Importantly, protiated DHAP or G3P can be used as substrate in tritiated solvent, allowing the introduction of a solvent-derived triton into the reaction coordinate at the intermediate via its exchange with the conjugate acid of Glu 165; the relative rates of the processing of the intermediate, forward into product and back in the remaining substrate pool, then can be determined, thereby providing information about the relative energies of the transition states in the forward and reverse directions. Note that isotopic substitutions increase the activation-energy barriers for the chemical steps (transition states 2 and 3) but not the binding/dissociation steps (transition states 1 and 4), so the free-energy profiles for transfer of protons and tritons are not the same; indeed, the rate-determining steps need not be, and are not, isotope-independent.

As summarized in the following sections, these experiments allow the relative energies of the rate-limiting transition states for processing of the intermediate to be determined in two separate free-energy profiles, one for transfer of protons that is responsible for the bulk conversion of substrate to product and the second for competing transfer of tritons.

1(R)-[3H]-DHAP as substrate: isotopic discrimination and exchange with solvent

When 1(R)-[3H]-DHAP is substrate, the specific radioactivity of the remaining DHAP increases as the reaction proceeds (Figure 4A; protiated substrate proceeds to product)2. This requires that transition state 2 is higher in energy than transition state 1 (Figure 3A), i.e., binding/dissociation of DHAP is faster than abstraction of the triton by Glu 165, allowing discrimination against/an accumulation of tritium in the remaining DHAP in competition with forward partitioning the enediolate intermediate by proton transfer.

Figure 4.

Figure 4.

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The discrimination against tritium using 1(R)-[3H]-DHAP as substrate. Panel A. The specific radioactivity of the DHAP substrate as a function of the extent of reaction. Panel B. The specific radioactivity of the G3P product as a function of the extent of reaction. Both panels are reprinted from Herlihy, J. M., Maister, S. G., Albery, W. J., and Knowles, J. R. (1976) Energetics of triosephosphate isomerase: the fate of the 1(R)-3H label of tritiated dihydroxyacetone phsophate in the isomerase reaction, Biochemistry 15, 5601–5607. Copyright 1976, American Chemical Society.

At a small extent of reaction, the specific radioactivity of the G3P product is ~2% that of the DHAP substrate, establishing that the exchange of the tritiated conjugate acid of Glu 165 with protiated solvent is faster than the forward flux of the intermediate to dissociated G3P (Figure 4B); it increases as the reaction proceeds because the specific radioactivity of the remaining substrate increases. The rate-determining transition state 4 allows the bound G3P to “equilibrate” with the intermediate (EZ), so the observed extent of exchange cannot be used to provide a quantitative comparison of the relative energies of transition state 3 and that for exchange of conjugate acid of Glu 165 with solvent (multiple crossings of transition state 3 and a single irreversible crossing of the transition state for the exchange reaction).

Reactions with DHAP and G3P in tritiated solvent

The facile exchange of the conjugate acid of Glu 165 with solvent provides the ability to quantitate the partitioning of the intermediate between the formation of product (e.g., G3P when DHAP is substrate) and return to the substrate pool (e.g., DHAP when DHAP is substrate). For example, with DHAP as substrate incorporation of solvent tritium into the substrate pool that is competitive with product formation requires that the energies of transition states 1 and 2 are less than the energies of transition states 3 and 4 (Figure 5A, Case 1). In contrast, incorporation of solvent tritium into the product pool without incorporation into the substrate pool would require that the energies of both transition states 3 are 4 be lower than the energies of transition states both 1 and 2 (Figure 5A, Case 2). Because tritium incorporation into either the substrate pool or product occurs in competition with the conversion of substrate to product (the reaction is irreversible because the product is “removed”), the extents of tritium incorporation provide the relative rates of the competing conversion of the intermediate to protiated and tritiated substrate or product.

Figure 5.

Figure 5.

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The incorporation of solvent-derived tritium as a function of extent of reaction. Panel A. Case 1, the incorporation on tritium in the substrate is much faster than the flux of substrate to protiated product; case 2, the incorporation on tritium in the substrate is much slower than the flux of substrate to protiated product. Reprinted from Maister, S. G., Pett, C. P., Albery, W. J., and Knowles, J. R. (1976) Energetics of triosephosphate isomerase: the appearance of solvent tritium in substrate dihydroxyacetone phosphate and in product, Biochemistry 15, 5607–5612. Copyright 1976, American Chemical Society. Panel B. The incorporation of tritium into the remaining DHAP substrate as a function of extent of reaction. Reprinted from Maister, S. G., Pett, C. P., Albery, W. J., and Knowles, J. R. (1976) Energetics of triosephosphate isomerase: the appearance of solvent tritium in substrate dihydroxyacetone phosphate and in product, Biochemistry 15, 5607–5612. Copyright 1976, American Chemical Society. Panel C. The incorporation of tritium into the remaining G3P substrate as a function of extent of reaction. Reprinted from Fletcher, S. J., Herlihy, J. M., Albery, W. J., and Knowles, J. R. (1976) Energetics of triosephosphate isomerase: the appearance of solvent tritium in substrate glyceraldehyde 3-phosphate and in product, Biochemistry 15, 5612–5617. Copyright 1976, American Chemical Society.

Using either DHAP (Figure 5B) or G3P (Figure 5C) as substrate in tritiated solvent3, 4, product formation (the result of proton transfer to the intermediate) proceeds ~3-fold faster than the incorporation of tritium into the unreacted substrate pool. These results are summarized in Figure 6 (DHAP substrate, Figure 6A; G3P substrate, Figure 6B).

Figure 6.

Figure 6.

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The relative rates of processing the enediolate intermediate. Panel A, incorporation of solvent tritium into DHAP substrate. Panel B, incorporation of solvent tritium into G3P substrate. Panel C, isotopic discrimination of solvent tritium in the formation of G3P product from DHAP substrate. Panel D, isotopic discrimination of solvent tritium in the formation of DHAP product from G3P substrate. Panel E, composite relative rates. The unprimed species represent protiated species; the primed species represent tritiated species. Reprinted from Fletcher, S. J., Herlihy, J. M., Albery, W. J., and Knowles, J. R. (1976) Energetics of triosephosphate isomerase: the appearance of solvent tritium in substrate glyceraldehyde 3-phosphate and in product, Biochemistry 15, 5612–5617. Copyright 1976, American Chemical Society.

Referring to the free-energy profile, this can be “easily” rationalized when G3P is substrate: transition states 1 and 2 for conversion of the protiated intermediate to DHAP are both lower in energy than transition states 3 and 4 for return of the intermediate to G3P with incorporation of tritium (the energy of transition state 4 is independent of isotope substitution; the energy of transition state 3 is necessarily increased by tritium substitution). However, when DHAP is substrate, the energy of transition state 2 for the return of the intermediate to DHAP with incorporation of tritium must be increased so that it exceeds the energy of transition state 4 for G3P dissociation that is independent of isotope.

For both experiments, the tritium isotope effects (kH/kT) for product formation provide comparisons of the energies of the transition states for forward processing of the intermediate in the proton and triton energy profiles. With DHAP as substrate, the tritium isotope effect for formation of G3P is 1.33 (Figure 6C); therefore, dissociation of the G3P is rate-determining (transition state 4; transition state 3 for proton/triton transfer to the intermediate is kinetically insignificant). With G3P as substrate, the isotope effect for formation of DHAP is 94 (Figure 6D) therefore, proton/triton transfer to the enediolate intermediate to form DHAP is rate-determining (transition state 2; transition state 1 for DHAP dissociation is kinetically insignificant).

The relative rates for partitioning of the enediolate intermediate derived from these experiments are summarized in Figure 6E. Note that the partitioning is different for protiated and tritiated substrate, enediolate intermediate, and product, i.e., the free-energy profiles are not the same. The differential effects caused by isotopic substitution are possible because of the near equivalence of the transition state energies that results from the evolution of catalytic efficiency (vide infra).

Reactions with deuteriated DHAP and G3P

Substrate deuterium isotope effects (kH/kD) were measured (deuterium isotope effects influence the flux of bulk substrate to product in contrast to tritium isotope effects that measure isotopic discrimination). For DHAP, the deuterium isotope effect on kcat for formation of G3P was 2.9; for G3P, the deuterium isotope effect on kcat for formation of DHAP was 1.06.

Referring to the energy profile (Figure 3), when deuteriated G3P is the substrate, the binding of G3P is rate-determining for formation of the enediolate intermediate (transition state 4) so no isotope effect will occur in forming the enediolate intermediate. Then, the deuteriated conjugate acid of Glu 165 rapidly exchanges with the protiated solvent, so formation of DHAP from the intermediate (fully protiated) occurs at the same rate as when protiated G3P is used as substrate.

When deuteriated DHAP is the substrate, at first glance, it might appear that no isotope effect would be expected because transition state 4 is the highest energy point on the free-energy profile. However, the rate of formation of the intermediate is determined by the rate of abstraction of a deuteron from the bound DHAP by Glu 165 (DHAP binding is fast), so the rate of formation of the intermediate is decreased by deuterium substitution. Again, the deuteriated conjugate acid of Glu 165 rapidly exchanges with protiated solvent, so formation of G3P from the intermediate (fully protiated) occurs at the same rate as when protiated DHAP is used as substrate. Because the rate of formation of the intermediate is subject to an isotope effect, the rate of formation of G3P will be subject to an isotope effect.

The free-energy profile

When the experimental results were integrated and the rate constants for formation of the various intermediates were determined, the free-energy profile displayed in Figure 3 was obtained7. The energy profile was constructed using the in vivo concentrations of DHAP and G3P (40 μM total)—the relative energies of the bound species are concentration-independent (the “chemical” steps are unimolecular reactions) but the relative energies of the free enzyme and substrate/product and bound substrate/product are concentration-dependent (the “physical” steps are bimolecular reactions). The quantitative analyses to determine the rate constants involved considerable algebraic sophistication and manipulation, but the description of the experiments and results described in the previous sections provides the reader with a qualitative understanding of how the relative and absolute energies of the substrate and product (both free and bound) and of the transition states for the physical and chemical steps were determined.

Two features are noteworthy: 1) the energies of all of the transition states, i.e., for both the “physical” and “chemical” steps, are similar (transition state 4 for the binding/dissociation of G3P is marginally higher than transition states 1, 2 and 3); and 2) the energies of the bound species are similar (although the energies of the bound intermediate and G3P are not well-determined). These allow the generalizations that 1) the rate of the reaction is limited by G3P dissociation/binding, with the rate constant diffusion-controlled, and 2) the energies of the bound species are comparable to those of the free substrate, so the bound species do not accumulate and thereby impede the flux through the reaction coordinate. As described in following section, with the free-energy for the nonenzymatic (acetate anion-catalyzed) reaction23, these two observations were used by Knowles and Albery to identify strategies used by enzymes to optimize catalytic efficiency.

Evolution of catalytic efficiency: the “perfect” enzyme

Hall and Knowles previously had determined the free-energy profile for the acetate anion-catalyzed interconversion of DHAP and G3P23. That free-energy profile (profile “a”) and the TIM-catalyzed profile (profile “d”) are compared in Figure 7.

Figure 7.

Figure 7.

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Evolution of catalytic efficiency. Profile “a”, the acetate anion-catalyzed reaction. Profile “b”, uniform binding of the bound substrate, enediolate intermediate, and product. Profile “c”, differential binding of the bound substrate, enediolate intermediate, and product. Profile “d”, the optimized TIM-catalyzed reaction. Reprinted from Albery, W. J., and Knowles, J. R. (1976) Evolution of enzyme function and the development of catalytic efficiency, Biochemistry 15, 5631–5640. Copyright 1976, American Chemical Society.

A comparison of those profiles allows several important observations:

  1. The transition states for the “chemical” steps (2 and 3) and for all of the bound species (substrate, product, and enediolate intermediate) are higher in energy for the acetate-anion-catalyzed reaction (otherwise there would be no rate enhancement).

  2. The relative energies of the substrate, product, and enediolate intermediate for the acetate anion-catalyzed reaction differ significantly in energy while they are similar for the TIM-catalyzed reaction (but the energy of the bound enediolate intermediate was not well-determined).

  3. The transition states for the “chemical” steps in the TIM-catalyzed reaction are stabilized relative to the substrate/product more than for the acetate-anion catalyzed reaction.

These observations provided the bases for the proposal that optimization of catalytic efficiency by TIM occurs in three steps of increasing “complexity” (structural “difficulty”) by evolving/modulating the nature of the interactions between the enzyme active site and substrate, product, and intermediate8:

  1. “Uniform binding” in which the stabilities of bound substrate, product, and enediolate intermediate and, therefore, the energies of the transition states by which they are interconverted are decreased relative to the energies of the unbound substrate, product and enolate intermediate (profile “b” in Figure 7). The energies of the complexes are decreased but not so much that the rate of product dissociation dominates the flux of substrate to product (the complexes are lower in energy than the free substrate and product). Uniform binding may be accomplished by favorable interactions with the shared phosphate group within the active site (“intrinsic binding energy”; vide infra).

  2. “Differential binding” of the bound substrate, product, and/or intermediate so that they are isoenergetic (equilibrium constants for the bound species are unity (profile “c” in Figure 7). By making these species isoenergetic, the transition states by which they are interconverted are decreased in energy (Hammond postulate). Differential binding may be accomplished by changes in hydrogen-bond strengths as the reaction coordinate is traversed and the locations and proton affinities of the oxygens are changed (hydroxyl group of a sp3-hybridized carbon vs. a carbonyl group of a sp2-hybridized carbon).

  3. “Catalysis of elementary steps” to differentially stabilize the transition states for the chemical steps so that these are isoenergetic relative to their isoenergetic substrates and products (profile “d” in Figure 7; the TIM-catalyzed reaction). Using the terminology of Marcus theory, the reduction in the energy of a transition state can be accomplished by a reduction in the intrinsic energy of activation (rate constant when the substrate and product are isoenergetic). The interactions with the active site may occur via highly specific hydrogen-bonding, electrostatic, polarity, or steric effects.

Knowles and Albery defined an “efficiency function” that provides a quantitative measure of the flux through the reaction coordinate, with the maximum value determined by the rate of diffusional encounter of enzyme with substrate/product (value of the efficiency function is 1.0) and the minimum value the rate of the uncatalyzed reaction (value of the efficiency function is 2.5 × 10−11). They also developed equations to quantitate the contributions of each of the strategies for optimizing catalysis to the “efficiency function”. Uniform binding of the substrate, product, and intermediate provided the greatest improvement in catalytic efficiency (approximately one-half of the reduction in the activation-energy barrier; a factor of 105 of the 1011 rate enhancement). Differential binding of the bound species to produce isoenergetic complexes provided a more modest factor of 50 improvement in the efficiency function. And, catalysis of elementary steps (isoenergetic transition states) provided a final improvement of a factor of 400. The efficiency (almost) reached perfection (the value of the efficiency function is 0.6; controlled by G3P binding/dissociation); that the transition states for the chemical steps are only slightly lower in energy than the transition state for G3P binding/dissociation has the consequence that these contribute, albeit modestly, to the determining the flux through the reaction coordinate and reduce the value of the efficiency function from 1.0, its upper limit.

Energy of the enediolate intermediate

The experiments were unable to determine the energy of the bound enediolate intermediate (EZ in the free-energy profile). Without this energy, the importance of isoenergetic bound species in reducing the activation-energy barriers cannot be evaluated for the TIM-catalyzed reaction.

The inability to determine this energy also is “frustrating” for mechanistic enzymologists because the energy differences between the intermediate and the free and bound DHAP/G3P are determined, in part, by the pKas of the 1(R)-proton of DHAP and the 2-proton of G3P in solution and in the active site. DHAP and G3P are weakly acidic “carbon acids” (pKas in solution are ~18 for both)24; the kinetic competence of the enediolate intermediate is determined by ΔpKa between the conjugate acid of Glu 165 and the bound DHAP/G3P. The observed values of kcat (750 sec−1 for DHAP substrate and 8700 sec−1 for G3P substrate) “require” that the ΔpKa be no larger than ~ 9, assuming a negligible contribution from the “intrinsic” barrier for transfer of the proton from the substrate to Glu 165 (activation-energy barrier when the reaction is isoenergetic). Thus, the pKa of G3P/DHAP must be decreased and/or the pKa of Glu 165 must be increased (vide infra).

The pKas of carbon acid substrates and how enzymes reduce these to allow kinetic competence of intermediates has been a topic of interest to mechanistic enzymologists since Thibblin and Jencks proposed that enolate-anions are too unstable to be intermediates in enzyme active sites so the reactions must be concerted and proceed via an preassociation mechanism in which the general base, substrate carbon acid, and product-forming electrophile (e.g., general acid or carbonyl group in a carbon-carbon bond forming reaction) are positioned for product formation25. Although the protons adjacent to the carbonyl groups of DHAP and G3P are not very acidic (~ 18), they are considerably more acidic than the pKas of the proton adjacent to a carboxylate group, e.g., 29 for mandelate in the mandelate racemase-catalyzed reaction26, 27 and 34 for 2-phosphoglycerate in the enolase-catalyzed reaction28. Presumably, the reductions in pKas are accomplished primarily by differential stabilization of the conjugate base, i.e., the enolate-anion, by differential binding, e.g., hydrogen-bonding with an active site donor as the proton affinities of the enolate-anion and donor become similar (short-strong hydrogen-bonds) and/or increased electrostatic interactions with an active site metal ion.

To the best of the knowledge of the author, the pKas of DHAP and G3P bound in the active site of TIM have not been directly measured, i.e., the enediolate intermediate has not been spectroscopically observed nor have the rate constants for its formation/reprotonation to form bound DHAP and G3P been measured. However, upper limits on the pKas of bound DHAP and G3P have been estimated from the rate constants for reprotonation of the enolate-anion intermediate by the conjugate acid of the active site base that have been estimated by global fitting of the kinetic constants to the free-energy profile/reaction coordinate described by Knowles and coworkers29, 30. Toney estimated that the ΔpKa between DHAP and Glu 165 is 4.8 to 8.4; assuming the pKa of Glu 165 is 6, the pKa of DHAP is 10.4 to 14.4. Similarly, he estimated that the pKa of DHAP is 9.3 to 12.3. However, Richard and coworkers recently estimated that the pKa of Glu 165 is increased by > 6 units because of its location in a hydrophobic pocket (Ile 170 and Leu 230; Figure 2B) in the loop-closed, solvent-sequestered active site, which would increase the estimated pKas of bound DHAP and G3P31, 32.

Pollack and coworkers determined the free-energy profile for Δ5-3-oxo-ketosteroid isomerase that interconverts α,β- and β,γ-unsaturated 3-oxosteroids33, 34. The pKas of the carbon acid substrate and product are “low”, 16.1 and 12.7, respectively, so the intermediate enolate-anion can be generated chemically and used to measure the rates of its processing to substrate and product. The energies for the bound substrate, product, and enolate-anion intermediate were measured, with the β,γ-unsaturated substrate and enediolate intermediate being isoenergetic; however, the energy difference between bound substrate and product was similar to that measured in solution.

The author and his coworkers estimated the pKa for mandelate anion in the active site of mandelate racemase using the rate of exchange of the α-proton of S-mandelate with solvent deuterons catalyzed by the racemase-inactive H297N mutant (two-base mechanism; Lys 166 is the S-specific general basic catalyst and His 297 is the R-specific general basic catalyst)27. The pKa of Lys 166 (~ 6) was estimated from the observed dependence of the exchange reaction on pH; the pKa of the bound S-mandelate (≤ 15) was estimated from the rate of the exchange reaction, assuming the upper limit for the rate of protonation of the intermediate by the conjugate acid of Lys 166 is the bond vibrational frequency. The energy of the enediolate intermediate could not be determined.

Are all enzymes “perfect”?

Knowles selected TIM for his mechanistic studies for several reasons, including 1) TIM is a reaction familiar to all biochemists, 2) the reaction is reversible so it can be studied in either direction, 3) the reaction is unimolecular in both directions, 4) the substrate and product are readily available, 5) the DHAP/G3P functional groups promote binding (charge and hydrogen-bonding), and 6) the reaction is expected to be subject to evolutionary pressure for maximal flux and efficiency. Indeed, the successful determination of the free-energy profile establishes the focus on TIM and, importantly, reveals the strategies by which Nature optimizes catalytic efficiency.

However, not all enzymes have the potential to be metabolically “optimized” to provide fundamental principles of catalysis. Therefore, the question can be, and has been, asked whether the catalytic perfection exhibited by TIM is the rule? Or the exception?

Indeed, TIM is an exception, presumably the result of the extreme selective pressure it experiences to maximize flux for energy production (vide infra). A comprehensive analysis of the kinetic parameters for ~2500 enzymes35 revealed that the values of kcat/KM are largest for enzymes in primary metabolism involved in carbohydrate utilization and energy production followed by 1) enzymes in primary metabolism involved in metabolic pathways for amino acid, fatty acid, and nucleotide metabolism, 2) enzymes in intermediate metabolic pathways for vitamin and cofactor biosynthesis, and, finally, 3) enzymes in secondary metabolism, including natural products biosynthesis. Even within the enzymes in carbohydrate utilization and energy production, a broad range of values of kcat/KM was found; the average value of kcat/KM is 4.1 × 105 M−1 sec−1, ~3 orders of magnitude smaller than the value of kcat/KM for the binding of G3P to TIM, 3.7 × 108 M−1 sec−1.

Perspectives and Summary

As noted in the Introduction, enzymology articles that now are published in this journal, and elsewhere, including those from this author, usually do not include the mechanistic detail that characterized the studies published by Knowles and coworkers on TIM. That does not mean that we understand the relationships between enzyme structure and function that allow rate enhancements as large as 1017 to be explained36. Indeed, it reflects the greatly expanded scope and breadth of enzymology.

In the context of an ever-increasing number of protein sequences (214,971,037 in Release 2021_02 of the UniProt database; April 7, 2021), many enzymologists (including the author) are focused on discovering novel metabolic pathways, e.g., natural product biosynthesis, uncharacterized catabolic pathways for diverse carbohydrates, and assignments of function to the pathway enzymes37, 38. In these studies, the focus is the discovery of enzymes in the novel metabolic pathways in which they participate, with little regard to catalytic efficiency. As noted in the previous section, not all metabolic processes will be subject to the evolutionary pressure experienced by TIM. However, we now are in a better position to define the scope of natural enzymatic catalysis, including the evolutionary strategies used by Nature to generate functionally diverse enzyme superfamilies38–41.

Enzymology now also includes the (re)design of catalysts for novel reactions, using computational and directed evolution/library screening approaches. Baker, Mayo, Houk, Hilvert, Tawfik, and others have reported the initial computational design and subsequent directed evolution of enzymes to catalyze unnatural reactions42–44. The strategy starts with a scaffold (often based on a natural TIM barrel, but, also, de novo designed scaffolds) that is computationally engineered to create a binding pocket for the substrate in which functional groups are placed appropriately to catalyze the desired reaction. Rarely are these designed enzymes very efficient, illustrating that “first principles” are not (yet) sufficiently robust to design enzymes with high catalytic efficiency. Often the efficiencies can be improved by in vitro evolution, e.g., directed/random mutagenesis and high throughput screening, with the values of kcat/KM approaching the diffusion-controlled limit. In some cases, when structural information is available, the improvements in catalytic efficiency can be rationalized, e.g., the introduction of hydrogen-bonding networks in the active site that influence the reactivities of the functional groups, but not yet predicted45–47. This directed evolution strategy mimics the natural evolution of catalytic efficiency, e.g., pressure on a “primitive” progenitor to both enhance binding and also increase the rates of the chemical/internal steps (if in vitro evolution “obeys” the principles described by Albery and Knowles).

However, to the best of this author’s knowledge, free-energy profiles have not been determined for the incremental steps in the in vitro design and evolution of novel enzymes so that the importance of the uniform binding, differential binding, and selective binding of transition states proposed by Albery and Knowles can be assessed. Hilvert, Houk, Baker and coworkers demonstrated the success of directed evolution to improve initial computational design of a “Kemp eliminase” that catalyzes the irreversible ring-opening of 5-nitro-benzisoxazole to 2-cyano-4-nitrophenol48–51 and, also, of retro-aldolases that catalyze multistep reactions with an active site Lys involving imine formation, carbon-carbon bond cleavage, and regeneration of the Lys amino group, with the various steps requiring proton-transfer reactions45–47, 52, 53. In both cases, the efficiencies of the initial computational designs could be significantly improved. However, the irreversibility of the Kemp eliminase and the multistep mechanism of the retro-aldolase preclude the experimental determination of the free-energy profile.

Computational (QM/MM) studies of the energetics of evolutionary pathways for directed evolution of catalytic efficiency have been reported. For evolved Kemp eliminases, ground state destabilization and transition state stabilization have been suggested for two independent evolutionary pathways54. For evolved retro-aldolases, the rate-determining step is a chemical step involving decomposition of an eneamine intermediate55. Computational analyses of the structures and reaction coordinates may facilitate the identification of additional designed substitutions that may further enhance efficiency by altering the stabilities of stable complexes and/or transition states.

Irrespective of the future directions of enzymology, elucidation of the free-energy profile for the triosephosphate isomerase-catalyzed reaction provides both 1) a high standard of rigor for investigating reaction mechanisms and 2) the intellectual foundation for understanding Nature’s strategies for the evolution of catalytic efficiency.

ACKNOWLEDGMENT

The author thanks Professor Ronald T. Raines for insightful comments about the manuscript as well as providing reprints of the articles. The author also thanks Nicholas Vasi in the Institute for Genomic Biology for his assistance in preparing the figures from the reprints.

FUNDING INFORMATION

This work was supported by P01GM118303 from the National Institutes of Health.

Footnotes

The author declares no competing financial interest.

REFERENCES

  • [1].Albery WJ, and Knowles JR (1976) Deuterium and tritium exchange in enzyme kinetics, Biochemistry 15, 5588–5600. [DOI] [PubMed] [Google Scholar]
  • [2].Herlihy JM, Maister SG, Albery WJ, and Knowles JR (1976) Energetics of triosephosphate isomerase: the fate of the 1(R)-3H label of tritiated dihydroxyacetone phsophate in the isomerase reaction, Biochemistry 15, 5601–5607. [DOI] [PubMed] [Google Scholar]
  • [3].Maister SG, Pett CP, Albery WJ, and Knowles JR (1976) Energetics of triosephosphate isomerase: the appearance of solvent tritium in substrate dihydroxyacetone phosphate and in product, Biochemistry 15, 5607–5612. [DOI] [PubMed] [Google Scholar]
  • [4].Fletcher SJ, Herlihy JM, Albery WJ, and Knowles JR (1976) Energetics of triosephosphate isomerase: the appearance of solvent tritium in substrate glyceraldehyde 3-phosphate and in product, Biochemistry 15, 5612–5617. [DOI] [PubMed] [Google Scholar]
  • [5].Fisher LM, Albery WJ, and Knowles JR (1976) Energetics of triosephosphate isomerase: the nature of the proton transfer between the catalytic base and solvent water, Biochemistry 15, 5621–5626. [DOI] [PubMed] [Google Scholar]
  • [6].Leadlay PF, Albery WJ, and Knowles JR (1976) Energetics of triosephosphate isomerase: deuterium isotope effects in the enzyme-catalyzed reaction, Biochemistry 15, 5617–5620. [DOI] [PubMed] [Google Scholar]
  • [7].Albery WJ, and Knowles JR (1976) Free-energy profile of the reaction catalyzed by triosephosphate isomerase, Biochemistry 15, 5627–5631. [DOI] [PubMed] [Google Scholar]
  • [8].Albery WJ, and Knowles JR (1976) Evolution of enzyme function and the development of catalytic efficiency, Biochemistry 15, 5631–5640. [DOI] [PubMed] [Google Scholar]
  • [9].Belasco JG, and Knowles JR (1980) Direct observation of substrate distortion by triosephosphate isomerase using Fourier transform infrared spectroscopy, Biochemistry 19, 472–477. [DOI] [PubMed] [Google Scholar]
  • [10].Raines RT, Sutton EL, Straus DR, Gilbert W, and Knowles JR (1986) Reaction energetics of a mutant triosephosphate isomerase in which the active-site glutamate has been changed to aspartate, Biochemistry 25, 7142–7154. [DOI] [PubMed] [Google Scholar]
  • [11].Raines RT, and Knowles JR (1987) Enzyme relaxation in the reaction catalyzed by triosephosphate isomerase: detection and kinetic characterization of two unliganded forms of the enzyme, Biochemistry 26, 7014–7020. [DOI] [PubMed] [Google Scholar]
  • [12].Blacklow SC, Raines RT, Lim WA, Zamore PD, and Knowles JR (1988) Triosephosphate isomerase catalysis is diffusion controlled. Appendix: Analysis of triose phosphate equilibria in aqueous solution by 31P NMR, Biochemistry 27, 1158–1167. [DOI] [PubMed] [Google Scholar]
  • [13].Nickbarg EB, Davenport RC, Petsko GA, and Knowles JR (1988) Triosephosphate isomerase: removal of a putatively electrophilic histidine residue results in a subtle change in catalytic mechanism, Biochemistry 27, 5948–5960. [DOI] [PubMed] [Google Scholar]
  • [14].Lodi PJ, and Knowles JR (1993) Direct evidence for the exploitation of an alpha-helix in the catalytic mechanism of triosephosphate isomerase, Biochemistry 32, 4338–4343. [DOI] [PubMed] [Google Scholar]
  • [15].Sampson NS, and Knowles JR (1992) Segmental motion in catalysis: investigation of a hydrogen bond critical for loop closure in the reaction of triosephosphate isomerase, Biochemistry 31, 8488–8494. [DOI] [PubMed] [Google Scholar]
  • [16].Sampson NS, and Knowles JR (1992) Segmental movement: definition of the structural requirements for loop closure in catalysis by triosephosphate isomerase, Biochemistry 31, 8482–8487. [DOI] [PubMed] [Google Scholar]
  • [17].Richard JP (2012) A paradigm for enzyme-catalyzed proton transfer at carbon: triosephosphate isomerase, Biochemistry 51, 2652–2661. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [18].Zhang Z, Sugio S, Komives EA, Liu KD, Knowles JR, Petsko GA, and Ringe D (1994) Crystal structure of recombinant chicken triosephosphate isomerase-phosphoglycolohydroxamate complex at 1.8-A resolution, Biochemistry 33, 2830–2837. [DOI] [PubMed] [Google Scholar]
  • [19].Lodi PJ, and Knowles JR (1991) Neutral imidazole is the electrophile in the reaction catalyzed by triosephosphate isomerase: structural origins and catalytic implications, Biochemistry 30, 6948–6956. [DOI] [PubMed] [Google Scholar]
  • [20].Lodi PJ, Chang LC, Knowles JR, and Komives EA (1994) Triosephosphate isomerase requires a positively charged active site: the role of lysine-12, Biochemistry 33, 2809–2814. [DOI] [PubMed] [Google Scholar]
  • [21].Richard JP (1984) Acid-Base Catalysis of the Elimination and Isomerization Reactions of Triose Phosphates, J Am Chem Soc 106, 4926–4936. [Google Scholar]
  • [22].Richard JP (1985) Reaction of Triosephosphate Isomerase with L-Glyceraldehyde 3-Phosphate and Triose 1,2-Enediol 3-Phosphate, Biochemistry 24, 949–953. [DOI] [PubMed] [Google Scholar]
  • [23].Hall A, and Knowles JR (1975) Uncatalyzed rates of enolization of dihydroxyacetone phosphate and of glyceraldehyde 3-phosphate in neutal aqueous solution. Quantitative assesment of an effectiveness of an enzyme catalyst, Biochemistry 14, 4348–4352. [DOI] [PubMed] [Google Scholar]
  • [24].Richard JP, and Amyes TL (2001) Proton transfer at carbon, Curr Opin Chem Biol 5, 626–633. [DOI] [PubMed] [Google Scholar]
  • [25].Thibbllin A, and Jencks WP (1979) Unstable Carbanion. General Acid Catalysis of the Cleavage of 1-Phenylcyclopropanol and 1-Phenyl-2-arylcyclopropanol Anions, J. Am. Chem. Soc 101, 4963–4973. [Google Scholar]
  • [26].Gerlt JA, Kozarich JW, Kenyon GL, and Gassman PG (1991) Electrophilic Catalysis Can Explain the Unexpected Acidity of Carbon Acids in Enzyme-Catalyzed Reactions, Journal of the American Chemical Society 113, 9667–9669. [Google Scholar]
  • [27].Landro JA, Kallarakal AT, Ransom SC, Gerlt JA, Kozarich JW, Neidhart DJ, and Kenyon GL (1991) Mechanism of the reaction catalyzed by mandelate racemase. 3. Asymmetry in reactions catalyzed by the H297N mutant, Biochemistry 30, 9274–9281. [DOI] [PubMed] [Google Scholar]
  • [28].Richard JP, Williams G, O’Donoghue AC, and Amyes TL (2002) Formation and stability of enolates of acetamide and acetate anion: an Eigen plot for proton transfer at alpha-carbonyl carbon, J Am Chem Soc 124, 2957–2968. [DOI] [PubMed] [Google Scholar]
  • [29].Toney MD (2013) Common enzymological experiments allow free energy profile determination, Biochemistry 52, 5952–5965. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [30].Toney MD (2019) Carbon Acidity in Enzyme Active Sites, Front Bioeng Biotechnol 7, 25. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [31].Kulkarni YS, Liao Q, Petrovic D, Kruger DM, Strodel B, Amyes TL, Richard JP, and Kamerlin SCL (2017) Enzyme Architecture: Modeling the Operation of a Hydrophobic Clamp in Catalysis by Triosephosphate Isomerase, J Am Chem Soc 139, 10514–10525. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [32].Kulkarni YS, Amyes TL, Richard JP, and Kamerlin SCL (2019) Uncovering the Role of Key Active-Site Side Chains in Catalysis: An Extended Bronsted Relationship for Substrate Deprotonation Catalyzed by Wild-Type and Variants of Triosephosphate Isomerase, J Am Chem Soc 141, 16139–16150. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [33].Hawkinson DC, Eames TC, and Pollack RM (1991) Energetics of 3-oxo-delta 5-steroid isomerase: source of the catalytic power of the enzyme, Biochemistry 30, 10849–10858. [DOI] [PubMed] [Google Scholar]
  • [34].Hawkinson DC, Eames TC, and Pollack RM (1991) Kinetic competence of an externally generated dienol intermediate with steroid isomerase, Biochemistry 30, 6956–6964. [DOI] [PubMed] [Google Scholar]
  • [35].Bar-Even A, Noor E, Savir Y, Liebermeister W, Davidi D, Tawfik DS, and Milo R (2011) The moderately efficient enzyme: evolutionary and physicochemical trends shaping enzyme parameters, Biochemistry 50, 4402–4410. [DOI] [PubMed] [Google Scholar]
  • [36].Radzicka A, and Wolfenden R (1995) A proficient enzyme, Science 267, 90–93. [DOI] [PubMed] [Google Scholar]
  • [37].Stack TMM, and Gerlt JA (2020) Discovery of novel pathways for carbohydrate metabolism, Curr Opin Chem Biol 61, 63–70. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [38].Zallot R, Oberg N, and Gerlt JA (2021) Discovery of new enzymatic functions and metabolic pathways using genomic enzymology web tools, Curr Opin Biotechnol 69, 77–90. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [39].Gerlt JA, Babbitt PC, Jacobson MP, and Almo SC (2012) Divergent evolution in enolase superfamily: strategies for assigning functions, J Biol Chem 287, 29–34. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [40].Furnham N, Dawson NL, Rahman SA, Thornton JM, and Orengo CA (2016) Large-Scale Analysis Exploring Evolution of Catalytic Machineries and Mechanisms in Enzyme Superfamilies, J Mol Biol 428, 253–267. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [41].Zallot R, Oberg N, and Gerlt JA (2019) The EFI Web Resource for Genomic Enzymology Tools: Leveraging Protein, Genome, and Metagenome Databases to Discover Novel Enzymes and Metabolic Pathways, Biochemistry 58, 4169–4182. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [42].Weitzner BD, Kipnis Y, Daniel AG, Hilvert D, and Baker D (2019) A computational method for design of connected catalytic networks in proteins, Protein Sci 28, 2036–2041. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [43].Otten R, Padua RAP, Bunzel HA, Nguyen V, Pitsawong W, Patterson M, Sui S, Perry SL, Cohen AE, Hilvert D, and Kern D (2020) How directed evolution reshapes the energy landscape in an enzyme to boost catalysis, Science 370, 1442–1446. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [44].Zeymer C, and Hilvert D (2018) Directed Evolution of Protein Catalysts, Annu Rev Biochem 87, 131–157. [DOI] [PubMed] [Google Scholar]
  • [45].Giger L, Caner S, Obexer R, Kast P, Baker D, Ban N, and Hilvert D (2013) Evolution of a designed retro-aldolase leads to complete active site remodeling, Nat Chem Biol 9, 494–498. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [46].Obexer R, Godina A, Garrabou X, Mittl PR, Baker D, Griffiths AD, and Hilvert D (2017) Emergence of a catalytic tetrad during evolution of a highly active artificial aldolase, Nat Chem 9, 50–56. [DOI] [PubMed] [Google Scholar]
  • [47].Zeymer C, Zschoche R, and Hilvert D (2017) Optimization of Enzyme Mechanism along the Evolutionary Trajectory of a Computationally Designed (Retro-)Aldolase, J Am Chem Soc 139, 12541–12549. [DOI] [PubMed] [Google Scholar]
  • [48].Rothlisberger D, Khersonsky O, Wollacott AM, Jiang L, DeChancie J, Betker J, Gallaher JL, Althoff EA, Zanghellini A, Dym O, Albeck S, Houk KN, Tawfik DS, and Baker D (2008) Kemp elimination catalysts by computational enzyme design, Nature 453, 190–195. [DOI] [PubMed] [Google Scholar]
  • [49].Kiss G, Rothlisberger D, Baker D, and Houk KN (2010) Evaluation and ranking of enzyme designs, Protein Sci 19, 1760–1773. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [50].Khersonsky O, Rothlisberger D, Wollacott AM, Murphy P, Dym O, Albeck S, Kiss G, Houk KN, Baker D, and Tawfik DS (2011) Optimization of the in-silico-designed kemp eliminase KE70 by computational design and directed evolution, J Mol Biol 407, 391–412. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [51].Privett HK, Kiss G, Lee TM, Blomberg R, Chica RA, Thomas LM, Hilvert D, Houk KN, and Mayo SL (2012) Iterative approach to computational enzyme design, Proc Natl Acad Sci U S A 109, 3790–3795. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [52].Jiang L, Althoff EA, Clemente FR, Doyle L, Rothlisberger D, Zanghellini A, Gallaher JL, Betker JL, Tanaka F, Barbas CF 3rd, Hilvert D, Houk KN, Stoddard BL, and Baker D (2008) De novo computational design of retro-aldol enzymes, Science 319, 1387–1391. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [53].Obexer R, Pott M, Zeymer C, Griffiths AD, and Hilvert D (2016) Efficient laboratory evolution of computationally designed enzymes with low starting activities using fluorescence-activated droplet sorting, Protein Eng Des Sel 29, 355–366. [DOI] [PubMed] [Google Scholar]
  • [54].Jindal G, Ramachandran B, Bora RP, and Warshel A (2017) Exploring the Development of Ground-State Destabilization and Transition-State Stabilization in Two Directed Evolution Paths of Kemp Eliminases, ACS Catal 7, 3301–3305. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [55].De Raffele D, Marti S, and Moliner V (2019) QM/MM Theoretical Studies of a de Novo Retro-Aldolase Design, ACS Catal 9, 2482–2492. [Google Scholar]

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