Proton Bridges in Enzyme Catalysis BY J. P. ELROD,R. D. GANDOUR, J. L. HOGG,M. KISE G. M. MAGGIORA AND K. s. VENKATASUBBAN R.L. SCHOWEN* Departments of Chemistry and Biochemistry University of Kansas Lawrence Kansas 66045 U.S.A. Received 28th April 1975 Chains of two hydrogen bonds (charge-relay systems) exist in the active sites of serine proteases and may be catalytic entities. It is shown theoretically that the coupling of the motions of the two protons in such arrays (and thus the efficiency with which they can relay charge) is a critical function of the distances across the hydrogen bonds ; long distances favour uncoupled motion short distances coupled motion. Rate measurements in mixtures of light and heavy water show that the serine proteases chymotrypsin trypsin and elastase function as one-proton catalysts one proton of the chain presumably bridging as in ordinary general catalysis.On the other hand three enzymes of the amidohydrolase class a glutaminase and two asparaginases show two-proton catalysis. This may arise from a charge-relay chain although evidence for such a structure has not yet been advanced for these enzymes or from some other catalytic entity involving two coupled proton bridges. Thirty-four years ago R. P. Bell’s Acid-Base Catalysis laid out the foundations on which he and several generations of scientists have build today’s edifice of under- standing in this field. While the importance of acid-base interactions for the catalytic power of enzymes has been clear for a long time,’ the recent growth of information on the three-dimensional structure of enzymes has led to the discovery of active-site entities of particular catalytic potential.Among these is the charge-relay chain (eqn (I)) found in the active sites of such serine proteases as chymotrypsin trypsin and elastase and recognized by Blow Birktoft and Hartley as a possible source of catalysis. As negative charge is relayed to the hydroxyl oxygen as in eqn (l) its (asp) (his) (ser) (asp) (his) (ser) nucleophilicity is increased and increased to an unusual extent because the protonic positive charge is transferred out to the carboxyl group rather than merely to the neighbouring imidazole. Conversely relay of the proton (reverse of eqn (1)) to the hydroxyl oxygen (or to another group occupying its position) can greatly increase the leaving-group reactivity of this centre because the negative charge is removed to a correspondingly large distance.Charge-relay chains should be encountered only rarely in non-enzymic systems (excepting the special case of solvent bridging) because of the entropic difficulties of assembling and orienting the composite group^.^ To function most effectively in the manner just described the charge-relay chain must require some degree of coupZing of the motions of the two protons in its com- ponent hydrogen bonds. In this way a smooth relay of charge is accomplished while only an ordinary catalytic advantage would be derived from independent shifts of the protons. In this paper we describe a theoretical demonstration of the impor- 145 PROTON BRIDGES tance of geometry for the coupling of proton motions in hydrogen-bond chains and experimental tests of the degree of coupling in some enzymic activated complexes which potentially involve multiple-proton bridges.COUPLING OF PROTON MOTIONS IN HYDROGEN-BOND CHAINS In an array such as the charge-relay chain the potential energy E may be described as a function of two variables Arl and Ar2 representing the displacements of the two protons from their equilibrium positions with all other coordinates of the system being either relaxed to their minimum-energy values or constrained to some desired values (e.g. to the known positions of groups in an enzyme active site). This permits construction of a three-dimensional potential-energy surface E(Arl Arz) and its representation by a contour map of the familiar sort.In discussing coupling of the two motions it is convenient to plot energy as a function of normalized coordinates p1 = (Arl/Art) and p2 = (Ar2/Ari),where Arf represents the total displacement of the proton which occurs in the overall reaction. The coordinates p1 and p2 are dimensionless quantities which vary from zero to one as the reaction proceeds from reactants to products. Fig. 1 illustrates a schematic contour map E(pl,p2) and shows I I / c / I I / / I / 0 P2 FIG.1 .-Schematic potential-energy surface E(pl pz) in which energy contours would be plotted as functions of the normalized coordinates pl = Ar,/Ari and pz = Two possible pathways representing the longest (L = 2) and shortest (L = 2+),are shown.two possible minimum-energy reaction paths from reactants (0 0) to products (1 1). The diagonal pathway represents the most direct way of accomplishing the reaction with both proton motions proceeding in perfect synchrony (thus exactly coupled). The dimensionless length of this pathway (projected onto the plane E = 0) is 2*. The other pathway represents the most indirect reaction scheme-a perfectly stepwise or uncoupled path. Its dimensionless length (projected on E = 0) is 2. Thus the length L of the projected reaction path across E (pl p2) is a quantitative measure of the overall (dynamical coupling during reaction. In fact we can define a degree of coupling oby eqn (2) so that ovaries from zero for perfectly uncoupfed processes to unity for perfectly coupled processes.(The extension to other processes and to spaces of higher dimensionality is straightforward with the limits of L being N and N3 where N is the number of coordinates 5b) 0= (2-L)/(2-23). (2) ELROD GANDOUR HOGG KISE MAGGIORA SCHOWEN VENKATASUBBAN 147 DETERMINANTS OF COUPLING IN PROTON BRIDGES It seems initially reasonable that the chemical constitution of a hydrogen-bond chain ought to influence the degree of coupling exhibited by a hydrogen-bond chain; this has been confirmed the~retically.~~ The same study showed that a second factor of great and perhaps dominant importance was the distance across each hydrogen bond. Long distances favoured uncoupled reactions while shorter distances led to ever greater coupling.This finding may hold particular significance for the hydrogen- bond arrays of enzymes where the distances are effectively fixed by the three- dimensional structure (thus by molecular evolution) but may also be to some degree adjustable for example by the binding of substrate or through conformation changes of the enzyme. rFH FIG.2.-Potentialenergy surface for the conversion of +H3N-H.. .F-H.. .OHz (lower left corner) to H3N...H-F.. .H-OH; (upper right corner). Energy contours are labelled in kcal/mol. The N-F and F-0 distances are constrained to 3.00 A. The ordinate is ~NH and abscissa is ~FH. Since A&H = 0.90 8,and A& = 0.96 A a rough transformation to normalized coordinates was performed by setting ArhH-ArkHd.93 A.Then L = 1.74 (w = 0.44) for the “ northwest ” reaction path and L = 1.77 (w = 0.39) for the “southeast ” reaction path. Calculations to illustrate the effect of hydrogen-bond length on coupling are shown in fig. 2 and 3. Both calculations are for the reaction of eqn (3) with the distance R held constant at 3.00A in fig. 2 and at 2.75A in fig. 3. A discussion of the computational method and the basis for choice of the chemical constituents in eqn (3) can be found in an earlier publi~ation.~~ As is clearly seen in fig. 2 and 3 the surfaces change character completely when R is altered by only 0.25 A. At the longer distance seen in fig. 2 there are two minimum energy paths (“ northwest” and “ southeast ”) with low degrees of coupling.For the northwest route o = 0.44 and for the southeast o = 0.39. On the other hand when the system is made shorter as in fig. 3 there is a single highly coupled path (o= 0.94). Thus compres- sion of the chain converts a very poorly coupled system into one which is nearly perfectly coupled. PROTON BRIDGES tR+cR+ tR+tR+ +HSN-H.. .F-H.. .OH,+ H3N...H-F...H-OHl (3) This behaviour is entirely consistent with expectations from the component hydrogen-bond potential functions. A long hydrogen bond should have a high barrier between its two potential-energy minima because a centrally-located proton will be weakly bound by both bases. In the shorter system acentral proton can occupy the overlapping region of the potential fields of the two bases decreasing the barrier.Coupled motion of the two protons in a chain leads these effects for the individual hydrogen bond to reinforce producing a high central region for the surface of a long system and a lower central region for the shorter system. rFH FIG.3.-PotentiaLenergy surface for the conversion of +H3N-H.. .F-H.. .OHz to H3N...H-F.. . H-OH; with N-F and N-0 distances constrained to 2.75A. Energy contours are labelled in kcal/mol. The ordinate is ~NHand the abscissa ~FH. Since A~&H= 0.56A,arb^ = 0.61 A a rough transformation to normalized coordinates was made with Arh~-Arb~-0.58A. This yields L = 1.45 for the reaction path and w = 0.94. PROTON INVENTORIES OF ENZYMIC TRANSITION STATES It is also desirable to investigate experimentally the degree to which coupled motion of the protons in enzymic charge-relay chains contributes to catalysis.Since each proton should produce a kinetic isotope effect if its binding state is altered on formation of the catalytic transition state the information wanted is a list of" active protons" (those generating isotope effects) and the isotope effect for each a "proton inventory ". Such an inventory is in principle accessible by studies in mixtures of protium and deuterium oxides?. According to the well-established relationship of eqn (4) k, the rate constant in a solvent mixture with atom fraction n of deuterium is related to ko (for pure protium oxide) through the reactant-state isotopic fractionation factors 47 and the transition-state isotopic fractionation factors 4:.If as eqn (4b) ELROD GANDOUR HOGG KISE MAGGIORA SCHOWEN,VENKATASUBBAN 149 emphasizes the entire reactant-state contribution RSC(n) is known the relationship becomes a polynomial in n the order of which (v) specifies k = kon(1-n+n4T) 1 V k,RSC(n) = ko n(1-n +n#T) (4b) i the number of " active " protons and the coefficients of which allow the calculation of the +T,i.e. the isotope effect for each proton. Thus k,(n) along with some measure or hypothesis concerning RSC (n),can yield the proton inventory. Since only those protons which change state on activation will contribute to RSC(n) and since exchangeable protons of proteins (except those of sulphydryl groups) are expected to have 4 -1 we set RSC(n) equal to unity for the cases to be considered here.There can be some dangers in this procedure. Kresge has shown that small reactant contributions may conspire under cover of strong coincidence and experimental error to conceal a transition-state contribution to k,(n). Although it is desirable to be alert to this possibility it is unlikely that Nature will haunt a system from case to case producing exactly the appropriate cancellation conditions in each event. Thus a similar result with different substrates or under different conditions ought generally to lay this ghost. For the particular case of double-hydrogen-bond chains such as the charge-relay chain one can distinguish two extreme situations and a continuum of intermediate cases.If the system is totally uncoupled but with one of its components still acting as a one-proton catalytic bridge (v = 1 in eqn (4b),analogously to common general catalysis lo) then k,,(n)should be linear in tz. If the system is perfectly coupled with both hydrogens generating equal kinetic isotope effects (v = 2 4; = $;) then k,(n) should be quadratic and [k,(n)]%should be linear in n. Between these extremes there should be a continuum of imperfectly coupled cases in which k,(n) is quadratic but 4; # 6;. These and the perfectly coupled case correspond to the two-proton catalytic bridge or true charge-relay. ONE-PROTON BRIDGES IN SERINE PROTEASES Proton inventories for two reactions of a-chymotrypsin are shown in fig. 4. The filled circles in fig.4 are data for removal of an acetyl group attached to the serine hydroxyl of the charge-relay chain. The measurements are those of Pollock Hogg and Schowen," enriched by some later points obtained by Elrod. The dependence of k on n is clearly linear corresponding to a single-proton bridge with isotope effect kH/kD = 2.4. Two objections may be raised to this experiment. First coincidental cancellation of factors from RSC(n) with the contribution of a second trmsition- state proton can conceal its effe~t.~ Second the deacetylation of the acetyl-enzyme is rather remote from the physiological process for which evolution designed chymo- trypsin and therefore even if the charge-relay chain is uncoupled in this reaction it is possible that the full structure of a physiological substrate would call the coupled chain into action.Both objections are met by the open circles of fig. 4 for the acylation of the enzyme (nucleophilic attack by the serine hydroxyl) by a close analog of the natural peptide substrates N-acetyl-L-tryptophanamide (ATA). Since this quite different process again produces a hear k,(n) with kH/kDnow 1.9 it is most unlikely that fortuitous cancellations are at work. Further this substrate fills all the binding PROTON BRIDGES n FIG.4.-Ratio of maximum velocity Vn in mixed isotopic solvent to Vl for deuterium oxide as a function of n for deacetylation of acetyl-a-chymotrypsin (25.00k 0.05" pH 7.5 and equivalent filled circles) and for acylation of a-chymotrypsin by N-acetyl-L tryptophanamide (ATA 25.00 & 0.5" ; pH 8.10 and equivalent open circles).positions of the active site and ought to simulate well the physiological situation. Nevertheless the charge-relay chain appears uncoupled and the enzyme is employing a one-proton catalytic bridge. Studies concerned with two other members of the serine-protease family appear in fig. 5. The open circles of fig. 5 are for the deacetylation of acetyltrypsin (quite analogous to the chymotrypsin reaction of fig. 4) which exhibits a linear k,(n) with n FIG.5.-Ratio of maximum velocity V in niixed isotopic solvent to Vl for deuterium oxide as a function of n for deacetylation of acetyltrypsin (25.00+0.10" pH 7.54 and equivalent open circles) and of acetylelastase (25.Ook 0.10"; pH 7.54 and equivalent filled circles).ELROD GANDOUR HOGG KISE MAGGIORA SCHOWEN VENKATASUBBAN 151 kH/kD= 1.4. Again one would prefer to add results for a physiological substrate but our studies in this regard are incomplete. However although details have not been published Mason and Ghiron l2 have reported the rates of deacylation of N-benzoyl-L-arginyltrypsinin mixed isotopic solvents. Their values for k,(n) generate a linear plot (not shown) with kH/k,= 2.6. Therefore it seems clear that trypsin also employs a one-proton catalytic bridge. Finally the results for deacetyl- ation of acetylelastase a third member of the family seen as the filled circles of fig. 5 are also indicative of the one-proton catalytic bridge. The isotope effect is kH/kD= 2.2.Results for a physiological substrate of elastase are not yet in hand. The serine proteases seem not to employ charge-relay as a catalytic factor but rather a one-proton bridge of the type familiar in general catalysis. The small magnitudes of the isotope effects (k,/k = 1.4-2.6) suggest to us that the proton in these bridges is not "in flight " but is a non-reaction-coordinate proton engaged in "solvation catalysis ''.lo? l3 TWO-PROTON CATALYSIS BY AMIDOHYDROLASES Other enzymes in addition to the serine proteases have as their physiological task the catalytic hydrolysis of the amide linkage. Among these are the aspara- ginases and glutamina~es,~ which catalyze the hydrolysis of asparagine (eqn (5) x = 1) and glutamine (eqn (9,x = 2) respectively.These enzymes are larger and more complex than the serine proteases detailed X-ray crystallographic structures are not available and mechanistic investigations are at a more primitive stage. Thus we have no indication as yet whether a charge-relay chain exists at the active sites of l-i'l \ GLUTAMINASE 1.01 L \x ASPARAGINASE, 1 1 ERWIN;\ 0 0.5 1 n FIG.6.-Square root of the ratio of maximum velocity V, in mixed isotopic solvent to VI for deuterium oxide as a function of n for amidohydrolase reactions. The upper plot is for glutamine hydrolysis catalyzed by glutaminase of E. coli at 37.0*0.2" pH 5.50 and equivalent. The lower plot is for hydrolysis of asparagine by asparaginase of E. coli (37.00+0.2" pH 7.12 and equivalent open circles) and by asparaginase of Erwinia carotoooru (37.00i-0.02" pH 7.12 and equivalent filled circles).PROTON BRIDGES these enzymes. Nevertheless it seems that like the serine proteases they form an intermediate acyl-enzyme and it is of interest to inquire to what extent they share the same proton-bridging properties in their catalytic transition states. -0,c 0 -0,c \ // \ -b CH(CH2)XC CH(CH,),CO +NH (5) / \ / HiN NH H;N Fig. 6 displays results from three enzymes a glutaminase of Escherichia coli an asparaginase of Escherichia coli and an asparaginase of Erwinia carotovora. All are catalyzing the hydrolysis of their natural substrates glutamine or asparagine at 37”. In this figure the square-root [kn(n)]*is plotted and is a linear function in all three cases.Thus all three enzymes are employing two-proton catalytic bridges with k,/k = 1.33 (glutaminase) 1.71 (asparaginase E. coli) and 1.62 (asparaginase Erwinia carotouora) for each proton and thus overall solvent isotope effects of 1.80 2.93 and 2.62 respectively. It then appears that in the amidohydrolases two protons are coupled in the catalytic transition state. The structural nature of the catalytic bridge(s) remains unknown a charge-relay chain a bifunctional catalytic entity or some other apparatus may be at work. It is tempting to speculate that a charge-relay chain exists here and that it has in these enzymes been brought to such an overall length through structural factors that its proton motions are now closely coupled.APPENDIX EXPERIMENTAL DETAILS The INDO potential surfaces for the asymmetric hydrogen-bond chains +H3N-H.. . F-H.. .OH2,were calculated in the manner described for symmetrical systems by Gandour Maggiora and Sch~wen.~~ Rate measurements were generally made spectrophotometrically employing a Cary 16 spectrophotometer interfaced to a Hewlett-Packard 2100A computer. The output of the photomultiplier consisting of a 60 Hz train of alternating sample and reference pulses was conveyed to an analogue-to-digital converter through a synchronizer which identified the pulses. Fifteen measurements of the height of both sample and reference pulses were averaged across each cycle and a value of the absorbance calculated from the logarithm of the ratio of these averages.Reaction times were divided into 1000 segments and absorbances were then time-averaged across each segment. Zero-order rate constants were calculated from a linear least-squares fit of absorbance to time. For some glutaminase runs ammonium-ion concentrations were determined by a Beckman cation-sensitive electrode (39137) interfaced to the same computer. Enzymes with one exception were commercial materials obtained from Sigma Chemical Company [chymotrypsin trypsin elastase glutaminase and asparaginase (E.coli)] or Worthington Biochemicals (chymotrypsin). The asparaginase of Erwinia carotovora was a generous gift of Dr. H. E. Wade of the Microbiological Research Establishment Porton Down Salisbury U.K. Deuterium oxide was obtained from various sources (Diaprep Biorad and Stohler Isotope Companies) and was either distilled or used as supplied; in all cases rates were shown to be independent of the method of purification.Tris buffer components were also obtained from Sigma and were used for pH control near pH 8. Acetate buffers were used near pH 5. Constant buffer ratios in mixed isotopic solvents were maintained in order to hold the pL at a corresponding point on the pL/rate profiles (an “ equivalent pH ”). In a typical experiment 3 ml of buffer solution was placed in a cuvet in the thermostatted cell-holder of the spectrophotometer and allowed to attain thermal equilibrium with the ELROD GANDOUR HOGG KISE MAGGIORA SCHOWEN VENKATASUBBAN 153 bath as indicated by a glass-covered thermistor probe.Then 0.1 ml of the enzyme stock solution was introduced by micropipet. After five minutes 0.1 ml of substrate stock solution was injected the solution was shaken and the absorbance monitored at 215 nm (amide substrates) or 400 nm (p-nitrophenyl acetate). It is a pleasure to acknowledge the support of this work by the National Institutes of Health and National Science Foundation (U.S.A.) the kind gift of Erwinia asparaginase from Dr. H. E. 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