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Enzymatic transition states and transition state analogues
Enzymatic transition states and transition state analogues Vern L Schramm Transition states are the balance point of catalysis. Bonds are partially made and/or broken at the transition state, and the energy of the extended system provides near-equal probability that the system forms products or reverts to reactants. Enzymatic catalytic sites provide dynamic electronic environments that increase the probability that the transition state will be formed. Alignment of reactants in the Michaelis complex and motion of the catalytic site architecture are necessary to achieve the transition state. Transition state lifetimes are a fraction of a picosecond, preventing chemical equilibrium in extended covalent systems. Thus, dynamic descriptions of enzymatic transition states are required. Stable analogues similar to the transition state capture dynamic excursions that generate the transition state and convert them into thermodynamic binding energy. These analogues bind with extraordinary affinity relative to reactants. Addresses Department of Biochemistry, Albert Einstein College of Medicine, 1300 Morris Park Avenue, Bronx, NY 10461, USA Corresponding author: Schramm, Vern L ([email protected])
Current Opinion in Structural Biology 2005, 15:604–613 This review comes from a themed issue on Catalysis and regulation Edited by William N Hunter and Ylva Lindqvist Available online 4th November 2005 0959-440X/$ – see front matter # 2005 Elsevier Ltd. All rights reserved. DOI 10.1016/j.sbi.2005.10.017
Introduction The idea of the enzymatic transition state developed from the chemical rate theory of Eyring, who formulated the transition state as a stable state to enable mathematical treatment using the thermodynamic and activated state concepts of the time [1]. The approach of Eyring dominated thinking about enzymatic transition states for decades, and led to the early concept that enzymes achieve their catalytic potential by binding tightly to the ‘activated complex’ or transition state in the same way that antibodies were known to bind with high affinity to their haptens [2,3]. Propagation of these ideas continued with the ‘lock and key’ and ‘transition state binding’ descriptions of enzyme function [4,5]. Wolfenden quantitated the concept of transition state stabilization by creating a thermodynamic box with the hypothetical construct of the binding energy between the free transiCurrent Opinion in Structural Biology 2005, 15:604–613
tion state and the enzyme (Figure 1) [5,6]. These ideas have been experimentally supported by X-ray crystallography, which shows loose complexes between enzymes and reactants (Michaelis complexes), and tighter complexes between enzymes and analogues of their transition states [7,8].
Equilibrium treatment of transition states Despite its practical utility and broad acceptance, the Eyring treatment, which assumes thermodynamically stable transition states, is physically impossible. A recent review of current developments in reaction rate theory summarizes these problems in the provocative statements: ‘‘a definite quantum transition state theory has not been formulated to date. . .’’ and ‘‘transition state theory is no longer valid and cannot even serve as a conceptual guide for understanding the critical factors which determine rates away from equilibrium’’ [9]. The opposing view with regard to modern classical transition state theory is ‘‘. . .alternative descriptions proposed as the source of enzyme catalysis are encompassed in modern transition state theory and do not require the introduction of new concepts’’ [10]. With this degree of uncertainty regarding the nature of transition states, how can we interpret the general principles of catalysis which appear empirically correct, or are experimentally useful and attractive? These include: enzymes bind tightly to their transition states; limiting values of transition state binding energy are given by kenzyme/kchemical binding energy of the Michaelis complex; chemically stable analogues of the transition state bind tightly to their cognate enzymes with a limiting value of kenzyme/ kchemical binding energy of the Michaelis complex [11]. Additionally, how can we resolve these principles with the growing evidence that dynamics play an important role in reaching the transition state in enzymatic catalysis [12,13], that dynamic excursions promote hydride tunneling [14] and that near-attack configurations (NACs) overcome most of the barrier to achieve the transition state [15]? This ‘opinion’ article will provide an intuitive approach to examining conflicting issues concerning the nature of enzymatic transition states, tight binding at the transition state, rapid release of products and enzymatic dynamics. The exploration of well-known timescales of chemical events pertaining to transition states in chemistry and in enzymatic catalytic sites will be useful for this exercise. Some of these concepts have been discussed ([16] and other reviews), and this article expands these analyses with a discussion of recent literature and adds some speculation. www.sciencedirect.com
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Figure 1
Reaction coordinate diagram and energy relationships for uncatalyzed and enzyme-catalyzed reactions, and transition state analogue binding to an enzyme (E). [Uncat]z and [EA]z are transition state barriers for the uncatalyzed and enzymatic reactions, respectively. A, I, EA and EI are substrate (reactant), transition state analogue and their complexes with the enzyme. EIz is the complex of a transition state analogue that has captured transition state dynamic motion into a stable complex, as described in the text. DDGz is the enzymatic efficiency compared to the uncatalyzed chemical reaction (kenzyme/kchemical) expressed in Gibbs free energy. DDG-Iz is the energetic difference in binding energy for a perfect transition state analogue and substrate. The upper right hand scheme is a thermodynamic box for the relative reaction rates of an uncatalyzed reaction (kchemical) or enzyme-catalyzed reaction (kenzyme). Dissociation constants for the substrate (Kd) and the substrate molecule at the transition state configuration (Kdz) predict tight binding of the transition state complex. Adapted from [43].
Timescales in chemistry and enzymology The conversion of a bond vibrational mode (stretching and restoring forces) to a bond-dissociating translational mode (an imaginary frequency) defines the transition state. Along the reaction coordinate, the transition state forms within the time span of a bond vibration, typically 1013 s for bonds of biochemical interest (Figure 2). This timescale contrasts sharply with that of typical enzyme catalytic rates of 1 to 103 s1. For the purpose of comparison, the catalytic rate of purine nucleosidase (PNP) — 20 s1 — is near the middle of this range. The capitalistic scaling of the time constants of the transition state lifetime and catalysis by PNP is the equivalent of spending a $5 billion fortune one cent at a time. Why is catalysis so slow when bond excursions and transition state lifetimes are so fast? The answer comes from the limits of diffusional capture between a substrate and enzyme (109 M1 s1), and from the relatively long times needed for enzymes to rearrange protein structure and position the substrate(s) for productive chemistry. Recent and insightful studies have measured multiple conformational changes in lactate dehydrogenase following the formation of encounter complexes of enzyme–NADH www.sciencedirect.com
[17]. A microsecond protein conformational adjustment and a millisecond catalytic site closing event are required before the enzyme–NADH complex reaches equilibrium. Therefore, chemistry is delayed by a relatively long time simply because of conformational adjustments that align reactants in the catalytic site. Similar rates have been seen for loop opening and closing events in orotate phosphoribosyltransferase (OPRTase) and triose phosphate isomerase (TIM) (Figure 2) [18,19]. Even after these adjustments, Michaelis complexes are bound weakly and the reactants require additional time to adjust flexible bond angles within the catalytic site. These pre-transition state steps are usually reversible, and substrates often diffuse in and out of the catalytic site many times before catalysis. This happens when loop motions that capture/ release the substrates in the catalytic site are faster than the time to form the transition state.
Tight binding at the transition state? The fleeting lifetime of an enzymatic transition state prevents a true (thermodynamic) equilibrium from forming a tightly bound transition state complex. Researchers have recognized this by calling the transition state a quasiCurrent Opinion in Structural Biology 2005, 15:604–613
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Figure 2
This is a hollow argument for tight binding, because the lifetime of the transition state is shorter than the time required for a water molecule to diffuse in or out of the catalytic site, or even over distances equivalent to its own diameter (Figure 2). Below, I attempt to reconcile the dynamic nature of the transition state with the extraordinary binding affinity of transition state analogues. We propose that transition state analogues capture a rare conformational event that generates the transition state.
Protein dynamic motion Computational advances have led to insights into the atomic excursions that result from thermal motion in enzyme–reactant complexes [10,20]. Dynamic motion of linked regions of the protein has been proposed to transfer vibrational energy into the catalytic site [12,21,22,23]. Domain and loop motions are responsible for the appropriate alignment of groups for catalysis in the Michaelis complex. Reaching the transition state from this complex involves a stochastic search of enzyme– substrate contact distances to achieve the transition state [16].
Nature of enzymatic transition states
Time constants of molecular dynamics, protein motion and catalysis.
equilibrium state, which we can interpret to mean ‘not in equilibrium’ [10]. A thermodynamic description of the transition state complex requires bond equilibrium to propagate through both the enzyme and reactants during the lifetime of the transition state. As protein conformational changes are slow, this is impossible during the transition state lifetime. Clearly, thermodynamic equilibrium cannot occur at the transition state. However, enzymes invariably close loops, flaps or domains over the catalytic site before reaching the transition state. Conformational changes are required to productively position reactants and to shield reactive species from solvent. The catalytic site remains closed during the lifetime of the transition state; therefore, we can say with certainty that reactants cannot diffuse from the catalytic site during this period, a definition of tight binding at the transition state.
Dynamic excursions of enzyme-bound reactants, together with motions of enzyme sidechains, loops and domains, all change the reactant–enzyme distances and dynamic interaction energies on the timescales summarized in Figure 2. Rotation about covalent bonds, and flap and domain motions (108 to 103 s) form an alignment poised to achieve the transition state. Bruice has called this the NAC or the ‘‘turnstile to the transition state’’ [24,25]. In X-ray crystal studies of high-resolution structures of Michaelis complexes, it is clear that reactant– protein interactions are too weak to account for the formation of the transition state and the enzyme-imposed rate accelerations. Flap opening and flap closing dynamics (103 to 105 s) position specific amino acids with respect to the reactants. Superimposed on slow domain movements are higher frequency bond vibration modes from amino acid sidechains and from the reactants. Typical atomic excursions of approximately 0.5 A˚ occur on the subpicosecond timescale (Figure 3). Therefore, during the time between loop closure and opening, typically 103 s, there is time for approximately 1010 dynamic excursions of 0.5 A˚ magnitude of each atom at the catalytic site, thus ‘interrogating’ the bound reactants. Molecular dynamics (MD) or quantum mechanical/molecular mechanical (QM/MM) calculations are stymied by long timescales, because computational dynamics calculations
(Figure 3 Legend) Dynamic motion in PNP. (a) The left panel shows distances from the crystal structure of bovine PNP in complex with immucillin-H, a transition state analogue, and phosphate. The panel on the right indicates the catalytic (red) and anti-catalytic (blue) vibrational modes of the Michaelis complex. To generate these panels, the structure of the bovine PNP–inosine–SO4 complex was taken from [36], the sulfate was replaced with phosphate, inosine was replaced with guanosine and dynamic excursions were calculated by MD simulation for the human PNP–guanosine–PO4 complex [28]. (b) The distances between O50 –O40 and O40 –Ophosphate are shown during a 100 ps MD simulation. From the 0.5 A˚ distance of the atomic excursions, we see fluctuating hydrogen bond lengths and electrostatic interactions on the subpicosecond timescale, as discussed in the text. Adapted from [16]. Current Opinion in Structural Biology 2005, 15:604–613
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Figure 3
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Figure 4
Comparative structures of reactant state (Michaelis or substrate analogue) complexes and transition state analogue complexes of (a) bovine PNP, (b) human MTAP and (c) Escherichia coli MTAN. Reactant complexes are shown on the left and transition state analogue complexes are on the right. Dissociation constants are shown below each complex. Note the similarity of the contacts in Michaelis and transition state complexes. Major differences in interatomic contact distances are emphasized in color; red is tighter in the transition state analogue complex and blue is Current Opinion in Structural Biology 2005, 15:604–613
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can simulate on the nanosecond timescale, but important loop and domain motions are up to a million times slower [20]. What does this mean in terms of reaching the transition state? Hydrogen bonds are the most common chemistrypromoting force between enzyme and reactants held in the NAC configuration. A 0.5 A˚ nuclear excursion between a hydrogen bond acceptor–donor pair can convert the hydrogen bond distance from 3.1 to 2.6 A˚. At 3.1 A˚, the hydrogen bond energy is weak, typically <1 kcal/mol. However, at 2.6 A˚, the bond is highly energetic, and can be considered a ‘low barrier’ or partial covalent hydrogen bond, well suited to electron withdrawal or contribution. Short hydrogen bonds can contribute 4–6 kcal/mol (or more) toward catalysis [26,27]. Electronic rearrangements necessary for catalysis are typically made up of many such interactions, all changing distance on the subpicosecond timescale. An example of the distance fluctuations between atoms that play electronic roles in catalysis is seen in PNP (Figure 3) [8,28]. Because each atomic nucleus can, in principle, move in all directions, motions that make a hydrogen bond longer or adopt less favorable angles are anti-catalytic (blue vectors in Figure 3), and those that shorten bonds and favor electron migration (red vectors in Figure 3) are catalytic, contributing to the reaction coordinate. These excursions provide fluctuations in the instantaneous electronic environment at the enzyme–reactant interface. The transition state is achieved when each of the catalytically critical bonds moves in a coordinated excursion that adds/withdraws electrons simultaneously as needed to reach the transition state. Computational and experimental dynamics approaches to the study of enzyme function indicate that the protein architecture is designed to make catalytic motions more frequently coordinated than random (anti-catalytic) motions [12,21]. In the PNP case, when all five of the catalysis-promoting distances shorten simultaneously, the transition state is reached [16]. Note that it takes a long time (milliseconds) to accomplish this state, because the probability of five or more dynamic excursions coinciding is small. The instantaneous geometry that forms the transition state will not generate a conformational change transmitted through the protein or cause ‘clamping down’ (global protein conformational compression specific to the transition state), nor will it achieve a ‘tightly bound’ transition state, except in the dynamic sense of the fraction of a picosecond in which the transition state occurs. However, as discussed below, if we could freeze time at the instant
of the excursion that forms the transition state, keep the reactants and their instantaneous local contacts frozen at the transition state, and let the rest of protein equilibrate, we would have a tightly bound transition state complex with transition state binding energy equivalent to kenzyme/ kchemical binding energy of the Michaelis complex. The term ‘transition state stabilization’ has fostered the idea that an energy-equilibrated transition state exists. Realistic enzymatic transition states might more appropriately be expressed in terms of statistical dynamic probabilities rather than thermodynamic expressions.
Dynamics of hydride transfer and quantum mechanical tunneling In hydride transfer reactions, the dynamic motions are relatively simple; acceptor and donor are pushed together by the vibrational mode of a ‘promoting amino acid’ near either or both the acceptor or donor [14,29]. In this dynamic mode, the distance between the acceptor and donor determines the extent of quantum mechanical tunneling. The dynamic principles outlined above also hold for hydride transfer; atomic excursions that move the hydride donor–acceptor pair apart are anti-catalytic, and only when acceptor and donor move simultaneously toward each other does hydride transfer occur. Computational analysis of hydride transfer reactions has shown that the hydride has the ability to cross the transition state barrier and, with finite probability, recross (or return) to reactants before forming products [30]. The recrossing phenomenon also occurs in non-enzymatic systems [31]. Enzymes that limit transition state recrossing are said to aid catalysis by increasing the transition coefficient, the probability that reactants at (or past) the transition state will form products rather than returning to reactants [10]. Studies by the Klinman group have investigated this phenomenon as a function of temperature, by comparing thermophilic and psychrophilic enzymes, and mutagenesis of the promoting groups, with convincing results [32,33]. The coupled protein networks (elegantly described by the Benkovic and Wright groups) in dihydrofolate reductase are proposed to be responsible for increasing the probability of these specific transitionstate-promoting protein vibrational modes [34,35].
Weak binding of reactants Compared to forces imposed at the instantaneous transition state, reactants are bound weakly. The relatively weak binding of substrate to the catalytic site of bovine PNP (Michaelis constant of 28 mM) is reflected in the long hydrogen bond distances seen in crystal structures of PNP Michaelis complexes (Figures 3 and 4) [7,8,36].
(Figure 4 Legend Continued) weaker in the transition state analogue complex. Bovine PNP shows several shortened hydrogen bonds that form interactions with leaving groups. Human MTAP shows shortened hydrogen bonds to the ribosyl that are presumed to be interactions that form the ribooxacarbenium ion. In E. coli MTAN, there are some hydrogen bond losses in the MT-DADMe-ImmA complex and minimal changes to the inhibitor leaving group mimic. However, the transition state analogue forms a potential ion pair with the water (hydroxyl) nucleophile. Tight binding is likely to come from capturing a dynamic excursion that forms the ribooxacarbenium hydroxide ion pair at the transition state. MTA, MT-ImmA, MTT and MT-DADMeImmA are 50 -methylthioadenosine, methylthio-immuncillin-A, 50 -methylthiotubercidin and methylthio-DADMe-immucillin-A, respectively [42,46]. www.sciencedirect.com
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However, when immucillin-H, a transition state analogue, is crystallized in the PNP catalytic site, six new hydrogen bonds are formed and an ion pair moves closer together. If one treats these interactions as static problems in thermodynamics, and estimates the sum of the hydrogen bond and ion pair energies, it can be estimated that up to 30 kcal/mol more binding energy is present in the transition state analogue complex than in the Michaelis complex [37]. This is far more than the 10.1 kcal/mol experimentally observed for the binding of immucillin-H relative to the binding of substrate (inosine). This energetic difference is a result of both cooperativity between interaction sites on the inhibitor and protein reorganization to hold the protein statically in the configuration that it acquires only instantaneously and dynamically in the actual transition state. The transition state is therefore not a thermodynamic entity, but a dynamic mode that is improbable on the timescale of bond vibrations, taking millions to billions of excursions to find the saddle point that defines the transition state (spending the $5 billion fortune 1 cent at a time). This explains why catalysis is so slow relative to the lifetime of the transition state, and to the timescales of bond vibrations and domain motion.
Transition state analogues If the enzymatic transition state is a dynamic mode, then what are transition state analogues and why do they bind so tightly? Transition state analogues capture the simultaneous molecular excursions that generate the dynamic transition state. This state is linked to the dynamic path of protein conformational change that the enzyme has evolved to favor. In the presence of a transition state analogue, the protein structure collapses around the analogue into a static, thermodynamically equilibrated potential energy well. Release of the analogue requires the slow and energetically unfavorable expansion of the protein. Release rates of transition state analogue inhibitors are very slow, from minutes to days, resulting in tight binding. Dissociation constants in the picomolar range (1012 M) are not uncommon [37,38,39,40] and analogues in the femtomolar range (1015 M) have been described [41]. Studies of transition state analogue inhibitors with picomolar and femtomolar dissociation constants bound to their cognate enzymes reveal that the difference between substrate binding and transition state analogue binding is subtle, and transition-statepromoting conformational changes are frequently within the range of dynamic excursions of enzymatic sidechains at the catalytic site (Figure 4) [8,39,42]. When presented with a chemically stable mimic of the transition state, thermodynamically stable tight binding occurs. All of the improbable statistical dynamic motions that lead to the transition state, including protonation, hydrogen bond formation and ion pair formation, now become energetically favorable thermodynamic interactions. This causes the classical conversion of DDGz from Current Opinion in Structural Biology 2005, 15:604–613
barrier lowering at the transition state to DDG-Iz binding of the transition state analogue (Figure 1) [16,43]. The protein conformation present at the transition state is closely related to that of the Michaelis complex after all adjustments have been made to reach the NAC (or EA0 of Figure 1). In catalysis, the conversion of EA0 into the transition state is a dynamic search for coincident interactions for the fraction of a picosecond that leads to transition state formation. But when a transition state analogue is bound, the favorable, fleeting and dynamic interactions of the transition state are converted into stable interactions, and the protein undergoes a major conformational change driven by the conversion of dynamic interactions around the catalytic site into stable, thermodynamic interactions. This gives rise to the stable, compressed state of enzyme complexes with transition state analogues. Hydrogen/deuterium exchange into the protein peptide bonds is decreased in this state relative to any other complex [44]. This condensed state of the enzyme is not formed during catalysis and is a stable state only in the presence of the transition state analogue. Bond breaking following normal transition state formation causes a rapid return to an open enzyme conformation, facilitating product release. Enzymes have evolved to form exquisite vibrationally linked structures that exhibit dynamic excursions leading to the transition state, followed by loop/domain opening to complete the catalytic cycle. Thus, an electrostatic mimic of the transition state draws the protein into a conformation that is related to but is off the normal reaction path. This is illustrated in Fig. 1 by the blue potential energy well for the complex with transition state analogues.
Limits of transition state analogue binding
It has been proposed that a 1011 M dissociation constant is the practical limit of binding energies for ligand–protein interactions [45]. However, transition state analogues commonly violate this limit, with numerous femtomolar dissociation constants (10–15 M) having been described (e.g. [46]). These are easily within the limits of the transition state thermodynamic box of Wolfenden (Figure 1) and remain valid estimates of the affinity of analogues of the transition state. Other analogues, made by ‘click chemistry’, have also reached the femtomolar range and are not necessarily related to the transition states of these enzymes [47]. The 1011 M limit of binding energy has led to proposals that any ligand, including transition states or transition state analogues, that exceeds 1011 M binding energy must have covalent character between protein and ligand [48,49]. Covalency is neither necessary nor desirable for most enzymatic transition states, as it necessarily involves multiple transition states and slows catalysis by requiring multiple statistical dynamic searches, as described above. In addition, transition state analogues with picomolar and femtomolar affinity have been rigorously explored, and show no evidence of covalency. Three examples of enzyme– www.sciencedirect.com
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transition state analogue complexes and their contacts are shown for PNP, 50 -methylthioadenosine phosphorylase (MTAP) and 50 -methylthioadenosine/S-adenosylhomocysteine nucleosidase (MTAN) (Figure 4).
Conclusions Enzymes reach their transition states through dynamic stochastic searches. Binding equilibrium does not exist at the transition state. The transition state complex exists only for the duration of bond breaking. Thermodynamic binding forces between enzyme and reactant are instantaneously altered as all groups required for catalysis are synchronized in a dynamic excursion towards the reactant. This dynamic excursion involves local motion at the catalytic site linked to larger scale dynamic modes of the protein that favor transition state formation. Transition state analogues form stable complexes by capturing and stabilizing the local dynamic modes at the catalytic site; these trigger conformational collapse of the linked dynamic modes throughout the protein. Transition state analogues capture the dynamic networks of protein structure that have evolved to produce dynamic transition states and convert the dynamic modes into thermodynamically stable protein complexes.
References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted as: of special interest of outstanding interest 1.
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22. Wolf-Watz M, Thai V, Henzler-Wildman K, Hadjipavlou G, Eisenmesser EZ, Kern D: Linkage between dynamics and catalysis in a thermophilic-mesophpilic enzyme pair. Nat Struct Mol Biol 2004, 11:945-949. 23. Antoniou D, Abolfath MR, Schwartz SD: Transition path sampling of classical rate-promoting vibrations. J Chem Phys 2004, 121:6442-6447. Attempts were made to explain enzymatic proton transfer reactions that include quantum tunneling. An equivalent classical chemical problem was evaluated, and dynamic atomic motion was found to contain slow and fast oscillations optimal for catalysis but outside current concepts of transition state theory. 24. Bruice TC: A view at the millennium: the efficiency of enzymatic catalysis. Acc Chem Res 2002, 35:139-148. 25. Luo J, Bruice TC: Anticorrelated motions as a driving force in enzyme catalysis: the dehydrogenase reaction. Proc Natl Acad Sci USA 2004, 101:13152-13156. 26. Gerlt JA, Kreevoy MM, Cleland W, Frey PA: Understanding enzymic catalysis: the importance of short, strong hydrogen bonds. Chem Biol 1997, 4:259-267. 27. Neidhart D, Wei Y, Cassidy C, Lin J, Cleland WW, Frey PA: Correlation of low- barrier hydrogen bonding and oxyanion binding in transition state analogue complexes of chymotrypsin. Biochemistry 2001, 40:2439-2447. 28. Nu´n˜ez S, Antoniou D, Schramm VL, Schwartz SD: Promoting vibrations in human purine nucleoside phosphorylase. A molecular dynamics and hybrid quantum mechanical/ molecular mechanical study. J Am Chem Soc 2004, 126:15720-15729. Classical and mixed quantum/classical MD simulations were performed to assess the existence of protein-facilitated promoting vibrations. The hybrid QM/MM methods were used to consider whether an enzymatic vibration that pushes oxygens of PNP together is coupled to the reaction coordinate. The calculations revealed the existence of promoting vibrations coupled to the reaction coordinate. 29. Soudackov A, Hatcher E, Hammes-Schiffer S: Quantum and dynamical effects of proton donor-acceptor vibrational motion in nonadiabatic proton-coupled electron transfer reactions. J Chem Phys 2005, 122:14505. 30. Hammes-Schiffer S: Quantum-classical simulation methods for hydrogen transfer in enzymes: a case study of dihydrofolate reductase. Curr Opin Struct Biol 2004, 14:192-201. 31. Pritchard HO: Recrossings and transition-state theory. J Phys Chem 2005, 109:1400-1404. Computational chemistry using simple chemical isomerization demonstrates transition state recrossings. Some reacting molecules cross the transition state ‘balance point’ but return to reactant before going to product, making the transmission coefficient near 0.5. 32. Liang ZX, Tsigos I, Lee T, Bouriotis V, Resing KA, Ahn NG, Klinman JP: Evidence for increased local flexibility in psychrophilic alcohol dehydrogenase relative to its thermophilic homologue. Biochemistry 2004, 43:14676-14683. 33. Liang ZX, Lee T, Resing KA, Ahn NG, Klinman JP: Thermalactivated protein mobility and its correlation with catalysis in thermophilic alcohol dehydrogenase. Proc Natl Acad Sci USA 2004, 101:9556-9561. 34. Venkitakrishnan RP, Zaborowski E, McElheny D, Benkovic SJ, Dyson HJ, Wright PE: Conformational changes in the active site loops of dihydrofolate reductase during the catalytic cycle. Biochemistry 2004, 43:16046-16055. 35. Sikorski RS, Wang L, Markham KA, Rajagopalan PT, Benkovic SJ, Kohen A: Tunneling and coupled motion in the Escherichia coli dihydrofolate reductase catalysis. J Am Chem Soc 2004, 126:4778-4779. 36. Mao C, Cook WJ, Zhou M, Federov AA, Almo SC, Ealick SE: Calf spleen purine nucleoside phosphorylase complexed with substrates and substrate analogues. Biochemistry 1998, 37:7135-7146. 37. Kicska GA, Tyler PC, Evans GB, Furneaux RH, Shi W, Fedorov A: Atomic dissection of the hydrogen bond network for Current Opinion in Structural Biology 2005, 15:604–613
transition-state analogue binding to purine nucleoside phosphorylase. Biochemistry 2002, 41:14489-14498. 38. Lewandowicz A, Taylor Ringia EA, Ting LM, Kim K, Tyler PC, Evans GB, Zubkova OV, Mee S, Painter GF, Lenz DH et al.: Energetic mapping of transition state analogue interactions with human and Plasmodium falciparum purine nucleoside phosphorylases. J Biol Chem 2005, 280:30320-30328. The binding of different transition state analogues (derived from specific atomic alterations of immucillin-H) was measured at the catalytic sites of human and malarial PNP. This study demonstrates remarkable differences in the binding of transition state analogues among PNP isozymes. Energetic mapping of PNP–immucillin-H binding energy gives 30 kcal/ mol, whereas the catalytic rate enhancement of PNP is 18 kcal/mol. Binding interactions are strongly cooperative. 39. Singh V, Shi W, Evans GB, Tyler PC, Furneaux RH, Almo SC, Schramm VL: Picomolar transition state analogue inhibitors of human 50 -methylthioadenosine phosphorylase and X-ray structure with MT-immucillin-A. Biochemistry 2004, 43:9-18. Based on the ribooxacarbenium ion character of N-ribosyltransferase transition states, transition state analogues were designed, synthesized as described in [40] and co-crystallized with human MTAP. Differences in catalytic site contacts between substrate-bound and transition state complexes are modest. 40. Evans GB, Furneaux RH, Lenz DH, Painter GF, Schramm VL, Singh V, Tyler PC: Second generation transition state analogue inhibitors of human 50 - methylthioadenosine phosphorylase. J Med Chem 2005, 48:4679-4689. 41. Singh V, Evans GB, Lenz DH, Mason JM, Clinch K, Mee S, Painter GF, Tyler PC, Furneaux RH, Lee JE et al.: Femtomolar transition state analogue inhibitors of 50 -methylthioadenosine/S-adenosylhomocysteine nucleosidase from Escherichia coli. J Biol Chem 2005, 280:18265-18273. The transition state structure described in [46] was used to design transition state analogue inhibitors. This study reports ten transition state analogue inhibitors with equilibrium dissociation constants between 47 and 900 fM (1015 M). 42. Lee JE, Singh V, Evans GB, Tyler PC, Furneaux RH, Cornell KA, Riscoe MK, Schramm VL, Howell PL: Structural rationale for the affinity of pico- and femtomolar transition state analogues of Escherichia coli 50 - methylthioadenosine/Sadenosylhomocysteine nucleosidase. J Biol Chem 2005, 280:18274-18282. Crystal structures of MTAN complexed with transition state analogues were determined to 2.2 A˚ resolution, and compared with other MTAN– inhibitor complexes. These are among the tightest binding enzyme– ligand complexes ever described; analysis of their mode of binding provides extraordinary insight into the structural basis of their affinity. The MTAN–inhibitor complex reveals the presence of a new ion pair, between the 40 -iminoribitol atom and the nucleophilic water (WAT3), that captures key features of the transition state. 43. Schramm VL: Enzymatic transition states and transition state analog design. Annu Rev Biochem 1998, 67:693-720. 44. Wang F, Shi W, Nieves E, Angeletti RH, Schramm VL, Grubmeyer C: A transition-state analogue reduces protein dynamics in hypoxanthine-guanine phosphoribosyltransferase. Biochemistry 2001, 40:8043-8054. 45. Kuntz ID, Chen K, Sharp KA, Kollman PA: The maximal affinity of ligands. Proc Natl Acad Sci USA 1999, 96:9997-10002. 46. Singh V, Lee JE, Nu´n˜ez S, Howell PL, Schramm VL: Transition state structure of 50 -methylthioadenosine/Sadenosylhomocysteine nucleosidase from Escherichia coli and its similarity to transition state analogues. Biochemistry 2005, 44:11647-11659. The transition state structure of MTAN was solved using kinetic isotope effects (KIEs) and matching the KIEs to Gaussian03 models of the transition state. The transition state is characterized by near-fully dissociated ribooxacarbenium ion character, with low or no participation of the water nucleophile at the transition state. The methylthio group is surrounded by a hydrophobic pocket, as revealed by the crystal structure described in [42]. The transition state structure was used in [41] to design transition state analogues. 47. Krasin´ski A, Radic´ Z, Manetsch R, Raushel J, Taylor P, Sharpless KB, Kolb HC: In situ selection of lead compounds by click chemistry: target-guided optimization of www.sciencedirect.com
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acetylcholinesterase inhibitors. J Am Chem Soc 2005, 127:6686-6687. Using tacrine and phenylphenanthridinium reagent libraries, reactions occur preferentially within the catalytic site of acetylcholinesterase to tailor-fit two halves of extended hydrophobic cations into the catalytic site. Dissociation constants as low as 33 fM are obtained. 48. Houk KN, Leach AG, Kim SP, Zhang X: Binding affinities of host guest, protein-ligand and protein-transition-state complexes. Angew Chem Int Ed Engl 2003, 42:4872-4897. The binding affinity of complexes, including Michaelis complexes, is roughly equivalent to the surface area buried upon complex formation. Enzyme–transition state analogue complexes bind more tightly than
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predicted from the area because of close contacts within the complex, but explaining the transition state analogue binding energy ‘‘remains a significant challenge’’. 49. Zhang X, Houk KN: Why enzymes are proficient catalysts: beyond the Pauling paradigm. Acc Chem Res 2005, 38:379-385. Catalytic proficiency is explained by the ‘covalent hypothesis’, which proposes that all proficient enzymes have covalent interactions between enzyme and the transition state. Only modestly proficient enzymes are proposed to operate by non-covalent transition state binding mechanisms. This surprising proposal requires a new definition of covalent bonds before it becomes useful for enzymology.
Current Opinion in Structural Biology 2005, 15:604–613
Current Opinion in Structural Biology 2005, 15:604–613 This review comes from a themed issue on Catalysis and regulation Edited by William N Hunter and Ylva Lindqvist Available online 4th November 2005 0959-440X/$ – see front matter # 2005 Elsevier Ltd. All rights reserved. DOI 10.1016/j.sbi.2005.10.017
Introduction The idea of the enzymatic transition state developed from the chemical rate theory of Eyring, who formulated the transition state as a stable state to enable mathematical treatment using the thermodynamic and activated state concepts of the time [1]. The approach of Eyring dominated thinking about enzymatic transition states for decades, and led to the early concept that enzymes achieve their catalytic potential by binding tightly to the ‘activated complex’ or transition state in the same way that antibodies were known to bind with high affinity to their haptens [2,3]. Propagation of these ideas continued with the ‘lock and key’ and ‘transition state binding’ descriptions of enzyme function [4,5]. Wolfenden quantitated the concept of transition state stabilization by creating a thermodynamic box with the hypothetical construct of the binding energy between the free transiCurrent Opinion in Structural Biology 2005, 15:604–613
tion state and the enzyme (Figure 1) [5,6]. These ideas have been experimentally supported by X-ray crystallography, which shows loose complexes between enzymes and reactants (Michaelis complexes), and tighter complexes between enzymes and analogues of their transition states [7,8].
Equilibrium treatment of transition states Despite its practical utility and broad acceptance, the Eyring treatment, which assumes thermodynamically stable transition states, is physically impossible. A recent review of current developments in reaction rate theory summarizes these problems in the provocative statements: ‘‘a definite quantum transition state theory has not been formulated to date. . .’’ and ‘‘transition state theory is no longer valid and cannot even serve as a conceptual guide for understanding the critical factors which determine rates away from equilibrium’’ [9]. The opposing view with regard to modern classical transition state theory is ‘‘. . .alternative descriptions proposed as the source of enzyme catalysis are encompassed in modern transition state theory and do not require the introduction of new concepts’’ [10]. With this degree of uncertainty regarding the nature of transition states, how can we interpret the general principles of catalysis which appear empirically correct, or are experimentally useful and attractive? These include: enzymes bind tightly to their transition states; limiting values of transition state binding energy are given by kenzyme/kchemical binding energy of the Michaelis complex; chemically stable analogues of the transition state bind tightly to their cognate enzymes with a limiting value of kenzyme/ kchemical binding energy of the Michaelis complex [11]. Additionally, how can we resolve these principles with the growing evidence that dynamics play an important role in reaching the transition state in enzymatic catalysis [12,13], that dynamic excursions promote hydride tunneling [14] and that near-attack configurations (NACs) overcome most of the barrier to achieve the transition state [15]? This ‘opinion’ article will provide an intuitive approach to examining conflicting issues concerning the nature of enzymatic transition states, tight binding at the transition state, rapid release of products and enzymatic dynamics. The exploration of well-known timescales of chemical events pertaining to transition states in chemistry and in enzymatic catalytic sites will be useful for this exercise. Some of these concepts have been discussed ([16] and other reviews), and this article expands these analyses with a discussion of recent literature and adds some speculation. www.sciencedirect.com
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Figure 1
Reaction coordinate diagram and energy relationships for uncatalyzed and enzyme-catalyzed reactions, and transition state analogue binding to an enzyme (E). [Uncat]z and [EA]z are transition state barriers for the uncatalyzed and enzymatic reactions, respectively. A, I, EA and EI are substrate (reactant), transition state analogue and their complexes with the enzyme. EIz is the complex of a transition state analogue that has captured transition state dynamic motion into a stable complex, as described in the text. DDGz is the enzymatic efficiency compared to the uncatalyzed chemical reaction (kenzyme/kchemical) expressed in Gibbs free energy. DDG-Iz is the energetic difference in binding energy for a perfect transition state analogue and substrate. The upper right hand scheme is a thermodynamic box for the relative reaction rates of an uncatalyzed reaction (kchemical) or enzyme-catalyzed reaction (kenzyme). Dissociation constants for the substrate (Kd) and the substrate molecule at the transition state configuration (Kdz) predict tight binding of the transition state complex. Adapted from [43].
Timescales in chemistry and enzymology The conversion of a bond vibrational mode (stretching and restoring forces) to a bond-dissociating translational mode (an imaginary frequency) defines the transition state. Along the reaction coordinate, the transition state forms within the time span of a bond vibration, typically 1013 s for bonds of biochemical interest (Figure 2). This timescale contrasts sharply with that of typical enzyme catalytic rates of 1 to 103 s1. For the purpose of comparison, the catalytic rate of purine nucleosidase (PNP) — 20 s1 — is near the middle of this range. The capitalistic scaling of the time constants of the transition state lifetime and catalysis by PNP is the equivalent of spending a $5 billion fortune one cent at a time. Why is catalysis so slow when bond excursions and transition state lifetimes are so fast? The answer comes from the limits of diffusional capture between a substrate and enzyme (109 M1 s1), and from the relatively long times needed for enzymes to rearrange protein structure and position the substrate(s) for productive chemistry. Recent and insightful studies have measured multiple conformational changes in lactate dehydrogenase following the formation of encounter complexes of enzyme–NADH www.sciencedirect.com
[17]. A microsecond protein conformational adjustment and a millisecond catalytic site closing event are required before the enzyme–NADH complex reaches equilibrium. Therefore, chemistry is delayed by a relatively long time simply because of conformational adjustments that align reactants in the catalytic site. Similar rates have been seen for loop opening and closing events in orotate phosphoribosyltransferase (OPRTase) and triose phosphate isomerase (TIM) (Figure 2) [18,19]. Even after these adjustments, Michaelis complexes are bound weakly and the reactants require additional time to adjust flexible bond angles within the catalytic site. These pre-transition state steps are usually reversible, and substrates often diffuse in and out of the catalytic site many times before catalysis. This happens when loop motions that capture/ release the substrates in the catalytic site are faster than the time to form the transition state.
Tight binding at the transition state? The fleeting lifetime of an enzymatic transition state prevents a true (thermodynamic) equilibrium from forming a tightly bound transition state complex. Researchers have recognized this by calling the transition state a quasiCurrent Opinion in Structural Biology 2005, 15:604–613
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Figure 2
This is a hollow argument for tight binding, because the lifetime of the transition state is shorter than the time required for a water molecule to diffuse in or out of the catalytic site, or even over distances equivalent to its own diameter (Figure 2). Below, I attempt to reconcile the dynamic nature of the transition state with the extraordinary binding affinity of transition state analogues. We propose that transition state analogues capture a rare conformational event that generates the transition state.
Protein dynamic motion Computational advances have led to insights into the atomic excursions that result from thermal motion in enzyme–reactant complexes [10,20]. Dynamic motion of linked regions of the protein has been proposed to transfer vibrational energy into the catalytic site [12,21,22,23]. Domain and loop motions are responsible for the appropriate alignment of groups for catalysis in the Michaelis complex. Reaching the transition state from this complex involves a stochastic search of enzyme– substrate contact distances to achieve the transition state [16].
Nature of enzymatic transition states
Time constants of molecular dynamics, protein motion and catalysis.
equilibrium state, which we can interpret to mean ‘not in equilibrium’ [10]. A thermodynamic description of the transition state complex requires bond equilibrium to propagate through both the enzyme and reactants during the lifetime of the transition state. As protein conformational changes are slow, this is impossible during the transition state lifetime. Clearly, thermodynamic equilibrium cannot occur at the transition state. However, enzymes invariably close loops, flaps or domains over the catalytic site before reaching the transition state. Conformational changes are required to productively position reactants and to shield reactive species from solvent. The catalytic site remains closed during the lifetime of the transition state; therefore, we can say with certainty that reactants cannot diffuse from the catalytic site during this period, a definition of tight binding at the transition state.
Dynamic excursions of enzyme-bound reactants, together with motions of enzyme sidechains, loops and domains, all change the reactant–enzyme distances and dynamic interaction energies on the timescales summarized in Figure 2. Rotation about covalent bonds, and flap and domain motions (108 to 103 s) form an alignment poised to achieve the transition state. Bruice has called this the NAC or the ‘‘turnstile to the transition state’’ [24,25]. In X-ray crystal studies of high-resolution structures of Michaelis complexes, it is clear that reactant– protein interactions are too weak to account for the formation of the transition state and the enzyme-imposed rate accelerations. Flap opening and flap closing dynamics (103 to 105 s) position specific amino acids with respect to the reactants. Superimposed on slow domain movements are higher frequency bond vibration modes from amino acid sidechains and from the reactants. Typical atomic excursions of approximately 0.5 A˚ occur on the subpicosecond timescale (Figure 3). Therefore, during the time between loop closure and opening, typically 103 s, there is time for approximately 1010 dynamic excursions of 0.5 A˚ magnitude of each atom at the catalytic site, thus ‘interrogating’ the bound reactants. Molecular dynamics (MD) or quantum mechanical/molecular mechanical (QM/MM) calculations are stymied by long timescales, because computational dynamics calculations
(Figure 3 Legend) Dynamic motion in PNP. (a) The left panel shows distances from the crystal structure of bovine PNP in complex with immucillin-H, a transition state analogue, and phosphate. The panel on the right indicates the catalytic (red) and anti-catalytic (blue) vibrational modes of the Michaelis complex. To generate these panels, the structure of the bovine PNP–inosine–SO4 complex was taken from [36], the sulfate was replaced with phosphate, inosine was replaced with guanosine and dynamic excursions were calculated by MD simulation for the human PNP–guanosine–PO4 complex [28]. (b) The distances between O50 –O40 and O40 –Ophosphate are shown during a 100 ps MD simulation. From the 0.5 A˚ distance of the atomic excursions, we see fluctuating hydrogen bond lengths and electrostatic interactions on the subpicosecond timescale, as discussed in the text. Adapted from [16]. Current Opinion in Structural Biology 2005, 15:604–613
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Figure 3
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Figure 4
Comparative structures of reactant state (Michaelis or substrate analogue) complexes and transition state analogue complexes of (a) bovine PNP, (b) human MTAP and (c) Escherichia coli MTAN. Reactant complexes are shown on the left and transition state analogue complexes are on the right. Dissociation constants are shown below each complex. Note the similarity of the contacts in Michaelis and transition state complexes. Major differences in interatomic contact distances are emphasized in color; red is tighter in the transition state analogue complex and blue is Current Opinion in Structural Biology 2005, 15:604–613
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can simulate on the nanosecond timescale, but important loop and domain motions are up to a million times slower [20]. What does this mean in terms of reaching the transition state? Hydrogen bonds are the most common chemistrypromoting force between enzyme and reactants held in the NAC configuration. A 0.5 A˚ nuclear excursion between a hydrogen bond acceptor–donor pair can convert the hydrogen bond distance from 3.1 to 2.6 A˚. At 3.1 A˚, the hydrogen bond energy is weak, typically <1 kcal/mol. However, at 2.6 A˚, the bond is highly energetic, and can be considered a ‘low barrier’ or partial covalent hydrogen bond, well suited to electron withdrawal or contribution. Short hydrogen bonds can contribute 4–6 kcal/mol (or more) toward catalysis [26,27]. Electronic rearrangements necessary for catalysis are typically made up of many such interactions, all changing distance on the subpicosecond timescale. An example of the distance fluctuations between atoms that play electronic roles in catalysis is seen in PNP (Figure 3) [8,28]. Because each atomic nucleus can, in principle, move in all directions, motions that make a hydrogen bond longer or adopt less favorable angles are anti-catalytic (blue vectors in Figure 3), and those that shorten bonds and favor electron migration (red vectors in Figure 3) are catalytic, contributing to the reaction coordinate. These excursions provide fluctuations in the instantaneous electronic environment at the enzyme–reactant interface. The transition state is achieved when each of the catalytically critical bonds moves in a coordinated excursion that adds/withdraws electrons simultaneously as needed to reach the transition state. Computational and experimental dynamics approaches to the study of enzyme function indicate that the protein architecture is designed to make catalytic motions more frequently coordinated than random (anti-catalytic) motions [12,21]. In the PNP case, when all five of the catalysis-promoting distances shorten simultaneously, the transition state is reached [16]. Note that it takes a long time (milliseconds) to accomplish this state, because the probability of five or more dynamic excursions coinciding is small. The instantaneous geometry that forms the transition state will not generate a conformational change transmitted through the protein or cause ‘clamping down’ (global protein conformational compression specific to the transition state), nor will it achieve a ‘tightly bound’ transition state, except in the dynamic sense of the fraction of a picosecond in which the transition state occurs. However, as discussed below, if we could freeze time at the instant
of the excursion that forms the transition state, keep the reactants and their instantaneous local contacts frozen at the transition state, and let the rest of protein equilibrate, we would have a tightly bound transition state complex with transition state binding energy equivalent to kenzyme/ kchemical binding energy of the Michaelis complex. The term ‘transition state stabilization’ has fostered the idea that an energy-equilibrated transition state exists. Realistic enzymatic transition states might more appropriately be expressed in terms of statistical dynamic probabilities rather than thermodynamic expressions.
Dynamics of hydride transfer and quantum mechanical tunneling In hydride transfer reactions, the dynamic motions are relatively simple; acceptor and donor are pushed together by the vibrational mode of a ‘promoting amino acid’ near either or both the acceptor or donor [14,29]. In this dynamic mode, the distance between the acceptor and donor determines the extent of quantum mechanical tunneling. The dynamic principles outlined above also hold for hydride transfer; atomic excursions that move the hydride donor–acceptor pair apart are anti-catalytic, and only when acceptor and donor move simultaneously toward each other does hydride transfer occur. Computational analysis of hydride transfer reactions has shown that the hydride has the ability to cross the transition state barrier and, with finite probability, recross (or return) to reactants before forming products [30]. The recrossing phenomenon also occurs in non-enzymatic systems [31]. Enzymes that limit transition state recrossing are said to aid catalysis by increasing the transition coefficient, the probability that reactants at (or past) the transition state will form products rather than returning to reactants [10]. Studies by the Klinman group have investigated this phenomenon as a function of temperature, by comparing thermophilic and psychrophilic enzymes, and mutagenesis of the promoting groups, with convincing results [32,33]. The coupled protein networks (elegantly described by the Benkovic and Wright groups) in dihydrofolate reductase are proposed to be responsible for increasing the probability of these specific transitionstate-promoting protein vibrational modes [34,35].
Weak binding of reactants Compared to forces imposed at the instantaneous transition state, reactants are bound weakly. The relatively weak binding of substrate to the catalytic site of bovine PNP (Michaelis constant of 28 mM) is reflected in the long hydrogen bond distances seen in crystal structures of PNP Michaelis complexes (Figures 3 and 4) [7,8,36].
(Figure 4 Legend Continued) weaker in the transition state analogue complex. Bovine PNP shows several shortened hydrogen bonds that form interactions with leaving groups. Human MTAP shows shortened hydrogen bonds to the ribosyl that are presumed to be interactions that form the ribooxacarbenium ion. In E. coli MTAN, there are some hydrogen bond losses in the MT-DADMe-ImmA complex and minimal changes to the inhibitor leaving group mimic. However, the transition state analogue forms a potential ion pair with the water (hydroxyl) nucleophile. Tight binding is likely to come from capturing a dynamic excursion that forms the ribooxacarbenium hydroxide ion pair at the transition state. MTA, MT-ImmA, MTT and MT-DADMeImmA are 50 -methylthioadenosine, methylthio-immuncillin-A, 50 -methylthiotubercidin and methylthio-DADMe-immucillin-A, respectively [42,46]. www.sciencedirect.com
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However, when immucillin-H, a transition state analogue, is crystallized in the PNP catalytic site, six new hydrogen bonds are formed and an ion pair moves closer together. If one treats these interactions as static problems in thermodynamics, and estimates the sum of the hydrogen bond and ion pair energies, it can be estimated that up to 30 kcal/mol more binding energy is present in the transition state analogue complex than in the Michaelis complex [37]. This is far more than the 10.1 kcal/mol experimentally observed for the binding of immucillin-H relative to the binding of substrate (inosine). This energetic difference is a result of both cooperativity between interaction sites on the inhibitor and protein reorganization to hold the protein statically in the configuration that it acquires only instantaneously and dynamically in the actual transition state. The transition state is therefore not a thermodynamic entity, but a dynamic mode that is improbable on the timescale of bond vibrations, taking millions to billions of excursions to find the saddle point that defines the transition state (spending the $5 billion fortune 1 cent at a time). This explains why catalysis is so slow relative to the lifetime of the transition state, and to the timescales of bond vibrations and domain motion.
Transition state analogues If the enzymatic transition state is a dynamic mode, then what are transition state analogues and why do they bind so tightly? Transition state analogues capture the simultaneous molecular excursions that generate the dynamic transition state. This state is linked to the dynamic path of protein conformational change that the enzyme has evolved to favor. In the presence of a transition state analogue, the protein structure collapses around the analogue into a static, thermodynamically equilibrated potential energy well. Release of the analogue requires the slow and energetically unfavorable expansion of the protein. Release rates of transition state analogue inhibitors are very slow, from minutes to days, resulting in tight binding. Dissociation constants in the picomolar range (1012 M) are not uncommon [37,38,39,40] and analogues in the femtomolar range (1015 M) have been described [41]. Studies of transition state analogue inhibitors with picomolar and femtomolar dissociation constants bound to their cognate enzymes reveal that the difference between substrate binding and transition state analogue binding is subtle, and transition-statepromoting conformational changes are frequently within the range of dynamic excursions of enzymatic sidechains at the catalytic site (Figure 4) [8,39,42]. When presented with a chemically stable mimic of the transition state, thermodynamically stable tight binding occurs. All of the improbable statistical dynamic motions that lead to the transition state, including protonation, hydrogen bond formation and ion pair formation, now become energetically favorable thermodynamic interactions. This causes the classical conversion of DDGz from Current Opinion in Structural Biology 2005, 15:604–613
barrier lowering at the transition state to DDG-Iz binding of the transition state analogue (Figure 1) [16,43]. The protein conformation present at the transition state is closely related to that of the Michaelis complex after all adjustments have been made to reach the NAC (or EA0 of Figure 1). In catalysis, the conversion of EA0 into the transition state is a dynamic search for coincident interactions for the fraction of a picosecond that leads to transition state formation. But when a transition state analogue is bound, the favorable, fleeting and dynamic interactions of the transition state are converted into stable interactions, and the protein undergoes a major conformational change driven by the conversion of dynamic interactions around the catalytic site into stable, thermodynamic interactions. This gives rise to the stable, compressed state of enzyme complexes with transition state analogues. Hydrogen/deuterium exchange into the protein peptide bonds is decreased in this state relative to any other complex [44]. This condensed state of the enzyme is not formed during catalysis and is a stable state only in the presence of the transition state analogue. Bond breaking following normal transition state formation causes a rapid return to an open enzyme conformation, facilitating product release. Enzymes have evolved to form exquisite vibrationally linked structures that exhibit dynamic excursions leading to the transition state, followed by loop/domain opening to complete the catalytic cycle. Thus, an electrostatic mimic of the transition state draws the protein into a conformation that is related to but is off the normal reaction path. This is illustrated in Fig. 1 by the blue potential energy well for the complex with transition state analogues.
Limits of transition state analogue binding
It has been proposed that a 1011 M dissociation constant is the practical limit of binding energies for ligand–protein interactions [45]. However, transition state analogues commonly violate this limit, with numerous femtomolar dissociation constants (10–15 M) having been described (e.g. [46]). These are easily within the limits of the transition state thermodynamic box of Wolfenden (Figure 1) and remain valid estimates of the affinity of analogues of the transition state. Other analogues, made by ‘click chemistry’, have also reached the femtomolar range and are not necessarily related to the transition states of these enzymes [47]. The 1011 M limit of binding energy has led to proposals that any ligand, including transition states or transition state analogues, that exceeds 1011 M binding energy must have covalent character between protein and ligand [48,49]. Covalency is neither necessary nor desirable for most enzymatic transition states, as it necessarily involves multiple transition states and slows catalysis by requiring multiple statistical dynamic searches, as described above. In addition, transition state analogues with picomolar and femtomolar affinity have been rigorously explored, and show no evidence of covalency. Three examples of enzyme– www.sciencedirect.com
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transition state analogue complexes and their contacts are shown for PNP, 50 -methylthioadenosine phosphorylase (MTAP) and 50 -methylthioadenosine/S-adenosylhomocysteine nucleosidase (MTAN) (Figure 4).
Conclusions Enzymes reach their transition states through dynamic stochastic searches. Binding equilibrium does not exist at the transition state. The transition state complex exists only for the duration of bond breaking. Thermodynamic binding forces between enzyme and reactant are instantaneously altered as all groups required for catalysis are synchronized in a dynamic excursion towards the reactant. This dynamic excursion involves local motion at the catalytic site linked to larger scale dynamic modes of the protein that favor transition state formation. Transition state analogues form stable complexes by capturing and stabilizing the local dynamic modes at the catalytic site; these trigger conformational collapse of the linked dynamic modes throughout the protein. Transition state analogues capture the dynamic networks of protein structure that have evolved to produce dynamic transition states and convert the dynamic modes into thermodynamically stable protein complexes.
References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted as: of special interest of outstanding interest 1.
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8.
Fedorov A, Shi W, Kicska G, Fedorov E, Tyler PC, Furneaux RH, Hanson JC, Gainsford GJ, Larese JZ, Schramm VL, Almo SC: Transition state structure of purine nucleoside phosphorylase and principles of atomic motion in enzymatic catalysis. Biochemistry 2001, 40:853-860.
9. Pollak E, Talkner P: Reaction rate theory: where it was, where is it today, and where is it going? Chaos 2005, 15:26116. A trip through the history of rate theory, including the proposals of Arrhenius (1889), Wigner (1932), Eyring (1935), Kramers (1940), Pechukas (1976), Chandler (1978) and Pollock (1986). Current problems are posed together with a summary of new directions for rate (transition state) theory. 10. Garcia-Viloca M, Gao J, Karplus M, Truhlar DG: How enzymes work: analysis by modern rate theory and computer simulations. Science 2004, 303:186-195. Transition state theory, as applied by computer simulations, is explored in the context of enzymatic catalytic power. Using examples, it is proposed www.sciencedirect.com
that all enzymatic rate enhancements can be explained by existing theory — lowering the free energy of activation and increasing the transmission coefficient. The ‘quasi-thermodynamic free energy of activation’ is used to indicate that equilibrium is not established at the transition state. 11. Wolfenden R: Thermodynamic and extrathermodynamic requirements of enzyme catalysis. Biophys Chem 2003, 105:559-572. A review of the proposal that the transition state binding energy of enzymatic catalysis is kcat/Km rate for the uncatalyzed reaction in water. Of specific interest here is a thorough discussion of the remote binding interactions that contribute to catalysis and transition state stabilization. Classic examples of transition state structures are reviewed. 12. Benkovic SJ, Hammes-Schiffer S: A perspective on enzyme catalysis. Science 2003, 301:1196-1202. Dihydrofolate reductase is exemplified as an enzymatic scaffold for coupled dynamic networks of conserved residues that foster the formation of the transition state. Protein dynamic motion is shown to be central to catalysis, and the need for additional experimental and theoretical studies is emphasized. 13. Wong KF, Selzer T, Benkovic SJ, Hammes-Schiffer S: Impact of distal mutations on the network of coupled motions correlated to hydride transfer in dihydrofolate reductase. Proc Natl Acad Sci USA 2005, 102:6807-6812. 14. Liang ZX, Klinman JP: Structural bases of hydrogen tunneling in enzymes: progress and puzzles. Curr Opin Struct Biol 2004, 14:648-655. Hydrogen tunneling is highlighted by three enzyme systems, including soybean lipoxygenase-1, thermophilic alcohol dehydrogenase and dihydrofolate reductase. Particular attention has been devoted to the issues of whether protein dynamics modulate hydrogen tunneling probability and whether the tunneling process contributes to the catalytic power of enzymes. 15. Zhang X, Zhang X, Bruice TC: A definitive mechanism for chorismate mutase. Biochemistry 2005, 44:10443-10448. Computational chemistry is used to conclude that the formation of the NAC by the enzyme is the major contributor to catalysis. Computed transition state structures are similar in vacuum, in water or in the enzyme. 16. Schramm VL: Enzymatic transition states: thermodynamics, dynamics and analogue design. Arch Biochem Biophys 2005, 433:13-26. The short lifetime of the transition state is emphasized to demonstrate that the dynamic nature of enzymatic transition states cannot be adequately described in thermodynamic terms, including transition state binding energy. It is proposed that transition states are reached by stochastic dynamic excursions of protein groups that participate in transition state formation. Transition state analogues capture dynamic energy and convert it into thermodynamic energy. 17. McClendon S, Zhadin N, Callender R: The approach to the Michaelis complex in lactate dehydrogenase: the substrate binding pathway. Biophys J 2005, 89:2024-2032. Binding of NADH to lactate dehydrogenase occurs via an encounter complex followed by two unimolecular conformational adjustments on the microsecond to millisecond timescale, including the closure of the catalytic site loop. Thermodynamic analysis suggests that transient melting of 10–15% of the protein is involved in this structural alteration to align NADH in the catalytic site. 18. Wang GP, Cahill SM, Liu X, Girvin ME, Grubmeyer C: Motional dynamics of the catalytic loop in OMP synthase. Biochemistry 1999, 38:284-295. 19. Desamero R, Rozovsky S, Zhadin N, McDermott A, Callender R: Active site loop motion in triosephosphate isomerase: T-jump relaxation spectroscopy of thermal activation. Biochemistry 2003, 42:2941-2951. Temperature-jump analysis with a hinge tryptophan as the reporter shows the rate of catalytic site loop opening to be 2500 s1 and loop closing to be 47 ms1. Loop opening is correlated with product release and therefore kcat. This work confirms earlier NMR work by the McDermott group. 20. Karplus M, McCammon J: Dynamics of proteins: elements and functions. Annu Rev Biochem 1983, 52:263-300. 21. Yang LW, Bahar I: Coupling between catalytic site and collective dynamics: a requirement for mechanochemical activity of enzymes. Structure 2005, 13:893-904. Current Opinion in Structural Biology 2005, 15:604–613
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22. Wolf-Watz M, Thai V, Henzler-Wildman K, Hadjipavlou G, Eisenmesser EZ, Kern D: Linkage between dynamics and catalysis in a thermophilic-mesophpilic enzyme pair. Nat Struct Mol Biol 2004, 11:945-949. 23. Antoniou D, Abolfath MR, Schwartz SD: Transition path sampling of classical rate-promoting vibrations. J Chem Phys 2004, 121:6442-6447. Attempts were made to explain enzymatic proton transfer reactions that include quantum tunneling. An equivalent classical chemical problem was evaluated, and dynamic atomic motion was found to contain slow and fast oscillations optimal for catalysis but outside current concepts of transition state theory. 24. Bruice TC: A view at the millennium: the efficiency of enzymatic catalysis. Acc Chem Res 2002, 35:139-148. 25. Luo J, Bruice TC: Anticorrelated motions as a driving force in enzyme catalysis: the dehydrogenase reaction. Proc Natl Acad Sci USA 2004, 101:13152-13156. 26. Gerlt JA, Kreevoy MM, Cleland W, Frey PA: Understanding enzymic catalysis: the importance of short, strong hydrogen bonds. Chem Biol 1997, 4:259-267. 27. Neidhart D, Wei Y, Cassidy C, Lin J, Cleland WW, Frey PA: Correlation of low- barrier hydrogen bonding and oxyanion binding in transition state analogue complexes of chymotrypsin. Biochemistry 2001, 40:2439-2447. 28. Nu´n˜ez S, Antoniou D, Schramm VL, Schwartz SD: Promoting vibrations in human purine nucleoside phosphorylase. A molecular dynamics and hybrid quantum mechanical/ molecular mechanical study. J Am Chem Soc 2004, 126:15720-15729. Classical and mixed quantum/classical MD simulations were performed to assess the existence of protein-facilitated promoting vibrations. The hybrid QM/MM methods were used to consider whether an enzymatic vibration that pushes oxygens of PNP together is coupled to the reaction coordinate. The calculations revealed the existence of promoting vibrations coupled to the reaction coordinate. 29. Soudackov A, Hatcher E, Hammes-Schiffer S: Quantum and dynamical effects of proton donor-acceptor vibrational motion in nonadiabatic proton-coupled electron transfer reactions. J Chem Phys 2005, 122:14505. 30. Hammes-Schiffer S: Quantum-classical simulation methods for hydrogen transfer in enzymes: a case study of dihydrofolate reductase. Curr Opin Struct Biol 2004, 14:192-201. 31. Pritchard HO: Recrossings and transition-state theory. J Phys Chem 2005, 109:1400-1404. Computational chemistry using simple chemical isomerization demonstrates transition state recrossings. Some reacting molecules cross the transition state ‘balance point’ but return to reactant before going to product, making the transmission coefficient near 0.5. 32. Liang ZX, Tsigos I, Lee T, Bouriotis V, Resing KA, Ahn NG, Klinman JP: Evidence for increased local flexibility in psychrophilic alcohol dehydrogenase relative to its thermophilic homologue. Biochemistry 2004, 43:14676-14683. 33. Liang ZX, Lee T, Resing KA, Ahn NG, Klinman JP: Thermalactivated protein mobility and its correlation with catalysis in thermophilic alcohol dehydrogenase. Proc Natl Acad Sci USA 2004, 101:9556-9561. 34. Venkitakrishnan RP, Zaborowski E, McElheny D, Benkovic SJ, Dyson HJ, Wright PE: Conformational changes in the active site loops of dihydrofolate reductase during the catalytic cycle. Biochemistry 2004, 43:16046-16055. 35. Sikorski RS, Wang L, Markham KA, Rajagopalan PT, Benkovic SJ, Kohen A: Tunneling and coupled motion in the Escherichia coli dihydrofolate reductase catalysis. J Am Chem Soc 2004, 126:4778-4779. 36. Mao C, Cook WJ, Zhou M, Federov AA, Almo SC, Ealick SE: Calf spleen purine nucleoside phosphorylase complexed with substrates and substrate analogues. Biochemistry 1998, 37:7135-7146. 37. Kicska GA, Tyler PC, Evans GB, Furneaux RH, Shi W, Fedorov A: Atomic dissection of the hydrogen bond network for Current Opinion in Structural Biology 2005, 15:604–613
transition-state analogue binding to purine nucleoside phosphorylase. Biochemistry 2002, 41:14489-14498. 38. Lewandowicz A, Taylor Ringia EA, Ting LM, Kim K, Tyler PC, Evans GB, Zubkova OV, Mee S, Painter GF, Lenz DH et al.: Energetic mapping of transition state analogue interactions with human and Plasmodium falciparum purine nucleoside phosphorylases. J Biol Chem 2005, 280:30320-30328. The binding of different transition state analogues (derived from specific atomic alterations of immucillin-H) was measured at the catalytic sites of human and malarial PNP. This study demonstrates remarkable differences in the binding of transition state analogues among PNP isozymes. Energetic mapping of PNP–immucillin-H binding energy gives 30 kcal/ mol, whereas the catalytic rate enhancement of PNP is 18 kcal/mol. Binding interactions are strongly cooperative. 39. Singh V, Shi W, Evans GB, Tyler PC, Furneaux RH, Almo SC, Schramm VL: Picomolar transition state analogue inhibitors of human 50 -methylthioadenosine phosphorylase and X-ray structure with MT-immucillin-A. Biochemistry 2004, 43:9-18. Based on the ribooxacarbenium ion character of N-ribosyltransferase transition states, transition state analogues were designed, synthesized as described in [40] and co-crystallized with human MTAP. Differences in catalytic site contacts between substrate-bound and transition state complexes are modest. 40. Evans GB, Furneaux RH, Lenz DH, Painter GF, Schramm VL, Singh V, Tyler PC: Second generation transition state analogue inhibitors of human 50 - methylthioadenosine phosphorylase. J Med Chem 2005, 48:4679-4689. 41. Singh V, Evans GB, Lenz DH, Mason JM, Clinch K, Mee S, Painter GF, Tyler PC, Furneaux RH, Lee JE et al.: Femtomolar transition state analogue inhibitors of 50 -methylthioadenosine/S-adenosylhomocysteine nucleosidase from Escherichia coli. J Biol Chem 2005, 280:18265-18273. The transition state structure described in [46] was used to design transition state analogue inhibitors. This study reports ten transition state analogue inhibitors with equilibrium dissociation constants between 47 and 900 fM (1015 M). 42. Lee JE, Singh V, Evans GB, Tyler PC, Furneaux RH, Cornell KA, Riscoe MK, Schramm VL, Howell PL: Structural rationale for the affinity of pico- and femtomolar transition state analogues of Escherichia coli 50 - methylthioadenosine/Sadenosylhomocysteine nucleosidase. J Biol Chem 2005, 280:18274-18282. Crystal structures of MTAN complexed with transition state analogues were determined to 2.2 A˚ resolution, and compared with other MTAN– inhibitor complexes. These are among the tightest binding enzyme– ligand complexes ever described; analysis of their mode of binding provides extraordinary insight into the structural basis of their affinity. The MTAN–inhibitor complex reveals the presence of a new ion pair, between the 40 -iminoribitol atom and the nucleophilic water (WAT3), that captures key features of the transition state. 43. Schramm VL: Enzymatic transition states and transition state analog design. Annu Rev Biochem 1998, 67:693-720. 44. Wang F, Shi W, Nieves E, Angeletti RH, Schramm VL, Grubmeyer C: A transition-state analogue reduces protein dynamics in hypoxanthine-guanine phosphoribosyltransferase. Biochemistry 2001, 40:8043-8054. 45. Kuntz ID, Chen K, Sharp KA, Kollman PA: The maximal affinity of ligands. Proc Natl Acad Sci USA 1999, 96:9997-10002. 46. Singh V, Lee JE, Nu´n˜ez S, Howell PL, Schramm VL: Transition state structure of 50 -methylthioadenosine/Sadenosylhomocysteine nucleosidase from Escherichia coli and its similarity to transition state analogues. Biochemistry 2005, 44:11647-11659. The transition state structure of MTAN was solved using kinetic isotope effects (KIEs) and matching the KIEs to Gaussian03 models of the transition state. The transition state is characterized by near-fully dissociated ribooxacarbenium ion character, with low or no participation of the water nucleophile at the transition state. The methylthio group is surrounded by a hydrophobic pocket, as revealed by the crystal structure described in [42]. The transition state structure was used in [41] to design transition state analogues. 47. Krasin´ski A, Radic´ Z, Manetsch R, Raushel J, Taylor P, Sharpless KB, Kolb HC: In situ selection of lead compounds by click chemistry: target-guided optimization of www.sciencedirect.com
Enzymatic transition states and transition state analogues Schramm 613
acetylcholinesterase inhibitors. J Am Chem Soc 2005, 127:6686-6687. Using tacrine and phenylphenanthridinium reagent libraries, reactions occur preferentially within the catalytic site of acetylcholinesterase to tailor-fit two halves of extended hydrophobic cations into the catalytic site. Dissociation constants as low as 33 fM are obtained. 48. Houk KN, Leach AG, Kim SP, Zhang X: Binding affinities of host guest, protein-ligand and protein-transition-state complexes. Angew Chem Int Ed Engl 2003, 42:4872-4897. The binding affinity of complexes, including Michaelis complexes, is roughly equivalent to the surface area buried upon complex formation. Enzyme–transition state analogue complexes bind more tightly than
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predicted from the area because of close contacts within the complex, but explaining the transition state analogue binding energy ‘‘remains a significant challenge’’. 49. Zhang X, Houk KN: Why enzymes are proficient catalysts: beyond the Pauling paradigm. Acc Chem Res 2005, 38:379-385. Catalytic proficiency is explained by the ‘covalent hypothesis’, which proposes that all proficient enzymes have covalent interactions between enzyme and the transition state. Only modestly proficient enzymes are proposed to operate by non-covalent transition state binding mechanisms. This surprising proposal requires a new definition of covalent bonds before it becomes useful for enzymology.
Current Opinion in Structural Biology 2005, 15:604–613