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The Moderately Efficient Enzyme

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The Moderately Efficient Enzyme Current Topic pubs.acs.org/biochemistry The Moderately Efficient Enzyme: Futile Encounters and Enzyme Floppiness Arren Bar-Even,† Ron Milo,‡ Elad Noor,∥ and Dan S. Tawfik*,§ † Max Planck Institute of Molecular Plant Physiology, Am Mühlenberg 1, 14476 Potsdam-Golm, Germany ‡ § Department of Plant & Environmental Sciences and Department of Biological Chemistry, The Weizmann Institute of Science, Rehovot 76100, Israel ∥ Institute of Molecular Systems Biology, ETH Zurich, Auguste-Piccard-Hof 1, CH-8093 Zurich, Switzerland ABSTRACT: The pioneering model of Henri, Michaelis, and Menten was based on the fast equilibrium assumption: the substrate binds its enzyme reversibly, and substrate dissociation is much faster than product formation. Here, we examine this assumption from a somewhat different point of view, asking what fraction of enzyme−substrate complexes are futile, i.e., result in dissociation rather than product formation. In Knowles’ notion of a “perfect” enzyme, all encounters of the enzyme with its substrate result in conversion to product. Thus, the perfect enzyme’s ffi ff catalytic e ciency, kcat/KM, is constrained by only the di usion on-rate, and the fraction of futile encounters (defined as φ) approaches zero. The available data on >1000 different enzymes suggest that for ≥90% of enzymes φ > 0.99 and for the “average enzyme” φ ≥ 0.9999; namely, <1 of 104 encounters is productive. Thus, the “fast equilibrium” assumption holds for the vast majority of enzymes. We discuss possible molecular origins for the dominance of futile encounters, including the coexistence of multiple sub-states of an enzyme’s active site (enzyme floppiness) and/or its substrate. Floppiness relates to the inherent flexibility of proteins, but also to conflicting demands, or trade-offs, between rate acceleration (the rate-determining chemical step) and catalytic turnover, or between turnover rate and accuracy. The study of futile encounters and active-site floppiness may contribute to a better understanding of enzyme catalysis, enzyme evolution, and improved enzyme design. ichaelis and Menten formalized Henri’s model in what the macroscopic kinetic parameters of many hundreds of M has become known as the Michaelis−Menten equation, enzymes have been measured, the data regarding the or model.1 Their model assumed a simplified scenario whereby microscopic parameters remain limited. It is thus impossible the product concentration is essentially zero. Under such to directly assess how widely valid the Henri−Michaelis− ≫ conditions, product inhibition and the reversible reaction could Menten assumption of k2 k3 was. Here, we apply a simple ffi both be ignored, resulting in the following mechanism: model that compares the enzyme catalytic e ciency, kcat/KM,to the diffusion-limited collision rate and thereby allows the k1 k E +⇄SESE →+3 P macroscopic-based assessment of the fraction of futile − k2 (1) substrate enzyme encounters. We found that for the average enzyme, <1 of 104 encounters is productive. We subsequently The model was also based on the assumption of a fast address the molecular origins of futile encounters and their − ≫ enzyme substrate equilibrium, namely of k2 k3, and thereby relation to the coexistence of multiple enzyme sub-states, or ≈ the Michaelis constant KM k2/k1 = KS. Later, Briggs and enzyme floppiness. Haldane used a steady-state model, which assumes only that the concentration of ES does not change over time (i.e., with no ■ THE APPLIED MODEL assumptions regarding the relation of k3 to k2,orofKM to KS), − In the Michaelis Menten equation, k1 represents the and obtained the same rate equation in which KM =(k2 + k3)/ 3 2 “ ” association rate leading to the enzyme−substrate complex. k1. An interesting implication of the fast equilibrium ≫ − However, the experimentally measured k1 values may refer to assumption (k2 k3) is that the majority of enzyme substrate ff complexes dissociate rather than go forward to yield the di erent steps along the trajectory leading eventually to the − product, and also to enzymes whose mechanisms and rate- product. In other words, most enzyme substrate encounters ff are futile. determining steps widely di er. In some cases, k1 is measured Shortly after the Michaelis−Menten model was devised, the macroscopic kinetic parameters (KM and kcat) of a few enzymes Received: June 5, 2015 became known, but their microscopic kinetic constants Revised: July 22, 2015 remained unknown. To date, more than a century later, while Published: July 28, 2015 © 2015 American Chemical Society 4969 DOI: 10.1021/acs.biochem.5b00621 Biochemistry 2015, 54, 4969−4977 Biochemistry Current Topic by coupling to catalysis, and in others, it is measured directly, and the substrate.15 Considering all collisions, the diffusion e.g., by fluorescence quenching upon substrate binding. In the limit rate constant is ∼1010 s−1 M−1.6,11,12 This value can be ff latter case, k1 may represent the rate constant for the formation derived from the di usion equation using characteristic of an encounter complex (including nonproductive ones) or parameters of the diffusion constants of metabolites (D ∼ more advanced complexes leading to catalysis. Thus, to assess 10−5 s−1 cm2)16,17 and the average physical radius of proteins (r what fraction of substrate−enzyme encounters result in product = 2 nm)18 being substituted in the expression for the diffusion formation, we use a generic definition that is derived from the limit on rate, 4πDr.16 perfect enzyme notion and is independent of the experimental By a more conservative estimate, only collisions with the fi “ ’ determination of k1. We therefore consider a modi ed black enzyme s active-site patch are considered as being potentially box” formalism of the Michaelis−Menten mechanism in which productive, and the rest of the protein surface is taken as being ∼ the k parameters are modified such that k corresponds to the inert toward the substrate. Using characteristic patch sizes, 1 ff ∼ 9 −1 −1 6,11,12 diffusion-limited enzyme−substrate collision rate and ÉS di usion on-rates of 10 s M have been calculated. represents the initial substrate−enzyme encounter complex: Overall, as a benchmark for evaluating enzymes, we consider ∼ fi ∼ k1 to be the range de ned by the two cases mentioned above, k1 k͠ 9 10 −1 −1 É +⇄SESÉ →3 ́ + P namely between 10 and 10 s M . ͠ k2 (2) “ ” ffi ■ THE PERFECT ENZYME In a so-called perfect enzyme , the catalytic e ciency, kcat/ ff The title of “perfect” has been applied to many enzymes, but in KM, is equal to the di usion on-rate, i.e., to the rate constant for the occurrence of substrate−enzyme encounters.4,5 Drawing fact, only few so-called perfect enzymes, having kcat/KM values ff from this notion, in our “black box” formalism, we indicate well within the range of the di usion limit mentioned above (109−1010 s−1 M−1), have been described. For example, the every initial encounter of a substrate with any enzyme molecule 10 −1 −1 kcat/KM of carbonic anhydrase is 10 s M or possibly regardless of its state is counted, and those that do not lead to 19 6 fi ∼ higher, and the kcat/KM values of fumarase and of superoxide product are de ned as futile encounters. Thus, k1 corresponds dismutase are very close to 1010 s−1 M−1.20 The value of a to the diffusion-limited enzyme−substrate collision rate, and 10 −1 −120 ́ mutant of the latter has been shown to exceed 10 s M thus, ES represents the initial substrate−enzyme encounter ff (kcat/KM may exceed the di usion rate limit because of complex. We thus refer here to the initial encounter complex as electrostatic steering, as discussed below). Other reported the complex whose rate of occurrence is limited only by ff “ ” examples include a prolyl 4-hydroxylase with -X-Pro-Gly- di usion (what is considered as the initial encounter complex , substrates,21 acyl-CoA dehydrogenase (and its F105L mutant in and the corresponding models for estimating the diffusion rate, 22 ́ particular) accepting 2-methylbutanoyl-CoA, and 3-phospho- is discussed below). We also denote the enzyme by E, instead glycerate kinase accepting 1,3-bisphosphoglycerate.23 Triose- of E, as the former corresponds to the total enzyme phosphate isomerase, the first enzyme proclaimed “perfect”,4 concentration rather than the free enzyme: a random collision × 8 −1 −1 was reported to have a kcat/KM of 4 10 s M , less than half by a substrate can occur with the enzyme molecule, including of our lower limit for the diffusion rate. those with occupied active sites (such a case will also count as a What does a k /K that equals the diffusion rate constant ́ ͠ cat M futile encounter because there is already an ES formed). k3 mean? encompasses all downstream steps leading to product (1) All steps following the formation of the initial encounter formation, including the formation of a substrate−enzyme complex, namely, formation of the enzyme−substrate complex complex (denoted ES, which may be a more advanced stage (the classic ES complex) from the initial encounter complex ́ than the initial ES encounter complex) in which the substrate is (ÉS), chemical transformation, product release, etc., occur at ͠ rates much faster than the diffusion rate. productively bound within the active site. Similarly, k2 ́ encompasses all dissociation rates that result in substrate (2) The rates of dissociation of the ES encounter complex, as fi release, including the dissociation of the initial encounter well as of the subsequent complexes, are signi cantly lower complex and of any other downstream complex (ES, etc.). than the rate of product formation. In other words, in a perfect − It therefore follows that the fraction of futile encounters enzyme, every substrate enzyme collision results in conversion between an enzyme and its substrate can be defined as to product.
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