Proceedings of the National Academy of Sciences Vol. 68, No. 3, pp. 563-565, March 1971

Substrate Anchoring and the Catalytic Power of

JACQUES REUBEN Department of Biophysics and Physical , University of Pennsylvania School of Medicine, Philadelphia, Pa. 19104 Communicated by Britton Chance, October 5, 1970

ABSTRACT Evidence from published nuclear magnetic characterized by a forward rate constant k0. The same overall resonance studies of -substrate and enzyme- reaction in presence of a specific enzyme has a rate constant inhibitor systems shows that substrates are confined at the of the enzyme, have a relatively long resi- ke, and is accelerated by a factor of ke/ko. The profile of the dence time, and tumble in solution as an enzyme-sub- potential energy along the reaction coordinate (in the absence strate complex. The consequences of this "substrate of enzyme) is depicted in Fig. 1 (11). Region I corresponds to anchoring" with regard to the catalytic power of enzymes the solvated reactants. Region II characterizes the course of are considered. It appears that as a result of the relatively slow motions, the probability of existence of the "activated the potential-energy change preceding the formation of the complex" in the enzymatic reaction may be increased and "activated complex", C*, and Region III the course after the thus the reaction rate may be accelerated by factors of chemical transformation has occurred. Region IV corresponds between 106 and 109. It is estimated that the combined to the solvated products. Since the "activated complex" of effect of substrate anchoring, desolvation, and charge an enzymatic reaction is carried the compensation may lead to reaction-rate accelerations by by enzyme, parts of Re- factors of between 109 and 1018. gions II and III, on both sides of the border line between them, occur on the enzyme. In aqueous solutions (at about The main characteristic of enzymes, i.e., the fact that in their 370C) the molecular tumbling time of small is very presence reaction rates are accelerated more short, of the order of 10-11 see, and for water molecules it is specifically by even shorter than 12 and in some cases up to 20 orders of magnitude, has (about 10-12 sec). Therefore, if the "activated hitherto remained an It that complex" dissociates instead of proceeding to products, the enigma (1, 2). seems, however, reactants will be the rationalization of the catalytic power of enzymes has been rapidly solvated and reach Region I and, based on models that usually do not consider the dynamic only after a new collision, will a new "activated complex" be properties of the enzyme-substrate system and, therefore, formed. If, on the other hand, vibrational or restricted rota- some of them seem to be rather unrealistic. tional motions of the substrates at the active site of an enzyme cause a of Recently there has been a growing accumulation of data, disruption the "activated complex", the substrate obtained by nuclear magnetic resonance , which anchoring may be visualized to have the effect of keeping pertains to the dynamic characteristics of them much closer to the border line between Regions II and enzyme-substrate III and enzyme-inhibitor complexes. The most important re- and therefore the probability of formation of a new "acti- stilt of these studies appears to be the observation that the vated complex" is enhanced and the rate constant corre- correlation time for random reorientation of an internuclear spondingly increased. The shape of the potential energy profile vector in an enzyme-substrate (or inhibitor) complex is the in the presence of the enzyme is probably different than that tumbling time of the complex itself (or a shorter electron-spin shown in Fig. 1. relaxation time for complexes containing some paramagnetic The first step in reaction (1) is the formation of an AB com- labels) and that the residence time of the substrate (or inhib- plex. In solution, the rate of formation of AB is usually diffu- itor) on the enzyme is much longer than the correlation time sion controlled and is characterized by a time constant of the (3-9). In fact, residence times of the order of 10-L-10-2 sec for order of 10-11 sec.* The dissociation of the complex is caused NADH and NAD on liver can be in- by vibrational motions, which are usually characterized by a ferred from the kinetics of the enzymatic reaction (10). The possible consequences of this "substrate anchoring" by the enzyme regarding the catalytic power of enzymes are con- sidered in the next section. SUBSTRATE ANCHORING AND REACTION AB RATE ACCELERATION For convenience we will discuss the course of a reaction of the form Reaction Coordinate A +BzC (1) Fig. 1. The potential energy along the reaction path. This work was done while the author was on leave from The Weizmann Institute of Science, Rehovot, Israel, during the * Complex formation involving desolvation may introduce addi- tenure of a Career Investigator Fellowship of the American tional potential energy barriers, slowing down the diffusion-con- Heart Association. trolled process by a factor of about 102 (12). 563 Downloaded by guest on September 30, 2021 564 Biochemistry: J. Reuben Proc. Nat. Acad. Sci. USA 68 (1971)

time constant of the order of 10-13 sec. Due to substrate been rather arbitrarily made. Thus, e.g., an unexplained fac- anchoring, however, the mean lifetime of the AB complex on tor of 10 accounts for the formation of a covalent intermediate an enzyme is much longer. From nuclear magnetic resonance and a factor of 10-2 (rate decrease) has been allowed to account data, the mean lifetime of an enzyme-substrate complex may for the proximity effect in a hydrolytic reaction (see ref. 2, be estimated to be of an order of magnitude between 10-7 Table II). and 10-4 sec (3-9). From the following argument the prob- Not only are the enzymes carriers of the substrates (sub- ability for the reaction to proceed may be expected to increase strate anchoring), but, by virtue of their properties, they pro- correspondingly. The probability of forming an "activated vide a suitable medium for the reaction to occur with much complex" may be assumed to obey a simple exponential law higher probability. The question of desolvation with regard to and the ratio of the probabilities in the two cases to be given enzymatic reactions involving acid-base has re- by P(ti)/P(t2) = (1 - e-wtl),(1-e- W212). If we consider the cently been discussed in some detail by Cohen, Vaidya, and reactions to proceed via a similar pathway, i.e., wi = w2, and if Schultz in their study of the active site of a-chymotrypsin the rate constants are such that wit, and w2t2 << 1, then P(tl)/ (19). They reached the conclusion that desolvation alone may P(t2) = t1/t2. lead to rate accelerations by a factor of 103 or more (19). To If the formation of an ABEnz complex is also diffusion con- emphasize this point, one should consider the water trolled, the rate acceleration due to substrate anchoring may as a reactant. For a water molecule to react, it has to be dis- be by factors of between 106 and 109. It may appear from the engaged from at least some of the four hydrogen bonds in suggested model that slow relative movements will result in which it serves both as proton donor and proton acceptor. higher probabilities for reaction and, since the characteristic The effects of desolvation in this case may be even more pro- times involved are expected to obey a simple exponential law nounced. Also (for a reaction between substrates of similar (r = Toe -E/RT), the rate should increase with lowering of the charge), charge compensation due to binding of charged sub- temperature. The observability of such "negative" tempera- strates on oppositely charged groups at the active site of the ture behavior depends on the energies of all the enzyme may reduce the potential energy of the "activated processes taking place along the reaction coordinate. For complex" and lead to rate accelerations by factors of up to movements of low activation energy, the net result will be a 3 X 10".t Combined with the effects of substrate anchoring decrease in the apparent activation energy of the enzyme- and desolvation, the anticipated factors for rate accelerations catalyzed reaction, which is indeed often observed (1, 2, 13, by enzymes are thus estimated to be between 109 and 1018. 14). From the above considerations, and the vast amount of The effect of substrate anchoring is entropic in origin since knowledge on enzymes (1, 2, 13, 14), the following it does not assume a change in the energy levels available to general model for the catalytic power of enzymes emerges. the system but rather a shift in the fraction of time spent at The enzymes provide chemically- and sterically-specific sites each of the energy states (11) (see also ref. 13). A favorable for substrate binding. As a result of the binding to the enzyme, change of the energy states, e.g., by desolvation and charge the substrates are desolvated, the charges of some of their compensation, should also lead to rate acceleration (see Dis- ionized groups are compensated, their rotational and transla- cussion). tional motions relative to each other, as well as relative to The effect of substrate anchoring may appear to be similar the enzyme "surface", are greatly restricted, and the reacting to the so-called proximity effect (15); however, here we have groups are precisely oriented, thus enabling the reaction considered the duration of the proximity. As shown above, to proceed with high probability and minimal activation the long residence time of substrates at the active site of an energy. In addition, for some enzymes, the catalytic power enzyme and in the vicinity of each other may lead to rate may be further enhanced by formation of stable intermedi- accelerations by factors of between 106 and 109. The rate ac- ates, nucleophilic catalysis, and by specific acid-base catal- celeration observed by going from inter- to intra-molecular ysis in which the enzyme provides the catalytic groups (1, 2, reactions of the same mechanism (see ref. 1, chap. 1) seems to 13, 14). The flexible structure of the enzyme molecule allows strongly support the point made here. for conformational changes to occur due to binding of sub- It may be instructive to consider as an example the differ- ences between liver and yeast alcohol dehydrogenases. The t The repulsion energy between two similar unit charges, 10-A apart, can exceed 10 kcal/mol, depending on the dielectric con- mean residence time of the coenzyme NADH on the liver is is stant of the medium. The potential energy of repulsion given enzyme is about 0.32 sec and the rate of hydride transfer = z by Eq = q2/er. For e 4, Eq = 6 X 10-13 erg 10 kcal/mol,

For the = greater than 3.5 X 105 sec- (at pH 7.0) (10, 16). and for e = 80, E6 0.5 kcal/mol and exp(E,/RT) is approxi- yeast enzyme, the enzyme-coenzyme complex is of much mately 3 X 106, and 2, respectively. shorter lifetime, less than 0.002 sec and, as a result, the hydride T Recently the concept of "orbital steering" has been advanced transfer is much slower, being about 5 X 102 sec-' (at pH with regard to the catalytic power of enzymes (20). It is unclear 7.15) (17, 18). from its formulation (20) whether it means a precise orientation of the reacting groups and atoms or an actual perturbation of the DISCUSSION molecular orbitals of the substrates. In the latter case, a mani- The catalytic power of enzymes festation of the effect should be spectroscopically observable. The proposed effect of substrate anchoring regarding the In particular, nuclear magnetic resonance chemical shifts are very sensitive to relatively small perturbations. Chemical shifts catalytic power of enzymes is by no means a single factor (of substrates, substrate analogs, and inhibitors) due to binding governing the rate accelerations observed in enzymatic reac- to enzymes have hitherto been found to be of the order of magni- tions. Other mechanisms that have previously been considered tude of, or smaller than, -induced shifts (3-6, 21). It lead to catalytic factors of up to 1010 (see ref. 2, Table II). should be noted, however, that these are shifts of nuclei not It seems, however, that some of the previous estimates have directly involved in the enzymatic reaction. Downloaded by guest on September 30, 2021 Proc. Nat. Acad. Sci. USA 68 (1971) Catalytic Power of Enzymes 565

strates and allosteric effectors (2), which may in turn affect 1. Jencks, W. P., Catalysis in Chemistry and Enzymology (McGraw Hill Book Co., New York, 1969). one or more of the static and dynamic characteristics of the 2. Koshland, D. E., Jr., and K. E. Neet, Annu. Rev. Biochem., "activated complex" and thereby control the reaction rate. 37, 359 (1968). While the enzyme-catalyzed reaction undoubtedly proceeds 3. Gerig, J. T., J. Amer. Chem. Soc., 90, 2681 (1968). according to the same laws as govern chemical reactions in 4. Gerig, J. T., and J. D. Reinheimer, J. Amer. Chem. Soc., 92, general, the mechanism of the reaction may be different, 3147 (1970). 5. Sykes, B. D., J. Amer. Chem. Soc., 91, 949 (1969). (within the framework of these laws) than that of the uncata- 6. Sykes, B. D., P. D. Schmidt, and G. R. Stark, J. Biol. lyzed reaction. Chem., 245, 1180 (1970). The effects of desolvation, proximity, and restriction of 7. Marshall, A. G., Biochemistry, 7, 2450 (1968). movements on reaction rates have recently been demonstrated 8. Mildvan, A. S., and M. C. Scrutton, Biochemistry, 6, 2978 (1967). by Bruice and Turner in a study of model organic reactions 9. Leigh, J. S., Jr., Ph.D. dissertation, University of Pennsyl- (22). These authors (22) give also a detailed comment regard- vania, 1970. ing what they consider to be the inadequacy of the proximity 10. Theorell, H., and B. Chance, Acta Chem. Scand., 5, 1127 theory of Koshland (15). The effects of precise orientation (1951). have been emphasized by Storm and Koshland in an investiga- 11. Hill, T. L., An Introduction to Statistical Thermodynamics (Addison-Wesley Publishing Co., Reading, Mass., 1960). tion of rates of lactonization (20). In the latter case, however, 12. Eigen, M., and G. G. Hammes, Advan. Enzymol., 25, 1 (1963). the possibility of restricted movements has not been con- 13. Westheimer, F. H., Advan. Enzymol., 24, 441 (1962). sidered in the rationalization of the observed rate constants. 14. Cleland, W. W., Annu. Rev. Biochem., 36, 77 (1967). It seems that the duration of the proximity and orientation of 15. Koshland, D. E., Jr., J. Theor. Biol., 2, 75 (1962). 16. Theorell, H., and J. S. McKinley-McKee, Acta Chem. the reacting groups is of particular importance when compar- Scand., 15, 1797 (1961). ing rates of esterification. 17. Nygaard, A., and H. Theorell, Acta Chem. Scand., 9, 1300 A detailed evaluation of the mechanism for a given enzy- (1955). matic reaction and of the properties of, and the configuration 18. Sund, H., and H. Theorell, in The Enzymes, ed. P. D. Boyer, Press, and at, active site should enable one to establish H. Lardy, and K. Myrback, 2nd Ed. (Academic dynamics the New York, 1963), vol. 7, p. 25. the extent to which each of the factors governing the catalytic 19. Cohen, S. G., V. M. Vaidya, and R. M. Schultz, Proc. Nat. power of enzymes is important for the particular case. Acad. Sci. USA, 66, 249 (1970). 20. Storm, D. R., and D. E. Koshland, Jr., Proc. Nat. Acad. I benefited from the most inspiring atmosphere in the labora- Sci. USA, 66, 445 (1970). tory of Dr. Mildred Cohn and from helpful discussions with her, 21. Dahlquist, F. W., and M. A. Raftery, Biochemistry, 7, 3277 as well as with Dr. Ralph G. Yount, Dr. John S. Leigh, Jr., and (1968), and references cited therein. Mr. Alan McLaughlin. Thanks are also due to Dr. A. S. Mildvan 22. Bruice, T. C., and A. Turner, J. Amer. Chem. Soc., 92, 3422 for helpful comments. (1970). Downloaded by guest on September 30, 2021