GENERAL DISCUSSION Dr. W. J. Albery (Oxford University) said In using the solvent isotope curve to draw conclusions about the transition state one has to be very careful. Fig. 1 shows a typical solvent isotope curve. Information is contained in the overall magnitude of the effect (the value at x = 1) and in the shape of the curve (the value at x = 3). Unfortunately all curves that pass through the same values at x = + and x = 1 are so close to each other at x = t and x = 3 that even rate ratios precise to several parts in a thousand cannot distinguish between the different curves corresponding to different models of the transition state. Hence it is better to concentrate experi- ments at x = 3 and x = 1. The extra information obtained for experiments at x = 3can be described by the curvature parameter which describes how far the point at x = 3 lies off the line joining the points at x = 0 and x = 1 as shown in fig.1 ; y is normalised so that y = 0 for the straight line A in fig. 1 y = 1 for the curve B which corresponds to a linear variation of k,/ko with x and y = + for curve C the " quadratic " case discussed by Schowen. When one has obtained a value of y instead of carrying out an " inventory of protons " one can carry out an inventory of the possible transition states which will fit the data and which have expressions of the form (1 -x+ (1 -x +&x)~. In this expression if a and b are both positive the fractionation refers to the transition state. Reactant fractionation can be considered by either a or b being negative.FIG.1.-Typical solvent isotope curve plotted as In (k,/k,) against x where x is the atom fraction of deuterium. The curvature parameter y measures how far the observed curve deviates at x = 3 from the straight line A. To carry out the inventory values of ay are plotted on a diagram of the type shown in fig. 2. Each parabola is labelled with the ratio a/b and where the line representing ay crosses a parabola we have a possible transition state. For instance in fig. 2 where the line representing y crosses the parabola labelled 1we have a = b = I. The parabola labelled 0 represents a model with the 4Aprotons singled out and a differential medium effect (b 3 a),where lots of & protons each contribute a little. The position of the intersection allows one to read off the values of AA and A,.These parameters describe the relative contributions of the 4Aand 4Bprotons to the overall effect and from these values of 4Aand 4Bcan be calculated. The two particular transition states discussed by Schowen are represented by S for a single proton in flight with no contribution from cbs and by Q for two protons contributing W. J. Albery Proton Transfer Reactions (Chapman and Hall London 1975) p. 272. 160 GENERAL DISCUSSION equally. From the data in Schowen’s paper we obtain the values of y in table 1. It can be seen that for systems (3) and (5) no conclusions can be drawn. For system (4) and probably less certainly system (2) the single proton model is correct. System (1) is plotted in fig.2 and the solvent isotope effect does not allow us to decide between FIG.2.-Plot of y for chymotrypsin acylation reaction to find possible transition states with fraction- ation of the form (1 -x+ $AX)(1 -x+ $BX)~. The parabolas are labelled with a/b = 6-1for a = 1. Each intersection corresponds to a possible transition state and AA and AB describe the relative importance of the $A and $B factors to the overall solvent isotope effect. The broken lines are one standard deviation for the value of y. An intersection at S corresponds to a transition state with a single proton in flght and no other significant factors ; an intersection at Q corresponds to a transition state with two protons in flight with +A = $B. the single or the quadratic model. Systems (6) and (7) have low values of y which arise from the “quadratic ” shape discussed by Schowen.However values of the fractionation factors for different possible transition states for system (6) are collected in table 2. The models with b = 10 correspond to a medium effect. Although TABLE 1 .-VALUES OF y no. system chymotrypsin acylation 0.65+ 0.13 chymotrypsin deacetylation 1.3 k0.3 trypsin 1.4 kO.9 elastase 1.10_+0.04 glutaminase -0.3 kO.9 asparaginase E. Coli 0.31+0.09 asparaginase Erwinia 0.36f 0.15 TABLE 2.-vALUES OF FRACTIONATION FACTORS FOR POSSIBLE TRANSITION STATES FOR SYSTEM 6 a 1 1 2 2 4~ 0.60 0.54 0.66 0.65 b 3 10 3 10 $B 0.82 0.95 0.92 0.98 this effect or the secondary effect for b = 3 are closer to unity for the model with two protons in flight (a = 2) the models with one proton in flight (a = 1) cannot be completely ruled out.Furthermore the values of 4Afor the two proton model are rather large for protons in flight. Remembering that for the fractionation in L30+ 162 GENERAL DISCUSSION 1 = 0.69 it might be that the low values of y for systems 6 and 7 are caused by changing -NH2 to -N+H3 and there are no protons in flight at all. Prof. R. L. Schowen (University of Kansas) said Albery’s method of representing acceptable mechanistic models for interpreting rates in mixed light and heavy water is very admirable for its simplicity clarity and economy. It should be particularly useful in cases where only a few data are available. Our customary method of treating such results is more conventional.We first fit the data for k to a polynomial in n by least-squares polynomial regression evaluating by Fisher’s F test the statistical significance of each term in the polynomial equation. This specifies the number of “active” protons which are required by the data. Thus if only the linear term is significant a one-proton system is indicated if the quadratic term is significant two protons are required etc. Having thus found the number of protons required and thus the number of factors needed on the r.h.s. of eqn (4b) of our paper we then fit k to the appropriate form of this equation by a general least-squares technique. This provides the best-fit values of the fractionation factors. Other things being equal one should obtain similar results from Albery’s method and the method just described.ERWlNlA L -ASNASE (V,/V,) = 2.52( I-n+n/ 1.62) SL’BSTFIPTE I-ASN 0 0.5 1 n FIG.1.-Ratio of maximum velocity V in mixed isotopic solvent to V for deutzrium oxide as a function of n for hydrolysis of asparagine (upper curve) and glutamine (lower curve) by asparaginase of Erwiniu curotovuru. The conditions are the same as for fig. 6 of our paper. If we use the numbering for the different systems given in Albery’s table 1 our treatment finds the linear term for all systems (1 to 7 inclusive) significant at the 0.999 level and the cubic term not significant above the 0.8 level (systems 2 and 4) or the 0.9 level (systems 1 3 5 6 and 7). This shows either one or two protons to be GENERAL DISCUSSION 163 required by all the systems studied.For systems 2 and 3 the quadratic term is not significant at the 0.8 level confirming the conclusion of one-proton catalysis. If one attempts nevertheless to fit a two-proton form of eqn (4b) to the data for system 2 for example the fractionation factors found correspond to isotope effects of 2.53 and 0.96 for the two protons further showing that only one proton is effectively responsible for the solvent isotope effect. For system 1 the quadratic term is significant at the 0.95 level and for system 4 at the 0.99 level. However the best-fit fractionation factors for the two-proton model yield isotope effects of 1.69 and 1.14 (system 1) and 2.50 and 0.98 (system 4). Thus once again it is a single proton in effect which produces the entire solvent isotope effect.For the amidohydrolase systems (5 to 7 inclusive) the quadratic term is significant at the 0.999 level in all cases. The best-fit fractionation factors are in reasonable agreement with the square- root dependencies shown in our paper. For these reactions therefore two-proton catalysis is indicated. Thus our usual method of data treatment indicates that for systems 2 3 and 4 no contribution beyond a few percent is to be ascribed to a second proton while system 1 can tolerate a second-proton isotope effect of about 1.14 (versus 1.69 for the first proton). For the amidohydrolases (systems 5-7) two-proton catalysis is fully confirmed. The discrepancies between these conclusions and Albery’s perhaps arise from the use of the entire data set in the method of treatment just discussed.The models discussed by Albery with 3-10 reactant-state contributing protons are closely related to models used earlier by Kresge and are best discussed below in connection with Kresge’s remarks. It can however be noted here that the involvement of ammonium functional groups is unlikely to product unusual effects \ \ \ since the fractionation factors for /N-H and -N-N+ both appear to be unity.’ / In the period following submission of our paper some support for the view expressed in its last sentence has been obtained by Mr. Daniel M. Quinn Mr. Mark Patterson and Mr. Robert Jarvis. If the two-proton catalytic entity of the amido- hydrolases exhibits coupled proton motion because its overall length in the catalytic transition state is just correct for the natural substrates studied (glutamine with glutaminase and asparigine with aspariginases) this length might be altered and the coupling destroyed if unnatural substrates were employed.Fig. 1 shows data for Erwinia asparaginase with the natural substrate asparagine (showing two-proton catalysis) and the unnatural substrate glutamine. For the latter (which reacts more slowly by a factor of about 30) the solvent isotope effect is reduced and VJn)becomes linear. Thus alteration of the substrate structure converts Erwinia asparaginase from a two-proton catalyst (with asparagine) to a one-proton catalyst (with glutamine). It is notable that only a very modest acceleration factor (maximally 30-fold) is associated with the coupling.Dr. W. J. Albery (Oxford) (communicated) First let me emphasise that in calculating the value of y I did use the complete data set for each system. Second I would like to comment on Schowen’s statement that the cubic term is insignificant and “ this shows either one or two protons to be required by all the systems studied ”. It is tempting to conclude that a product of the form n(1-x+4,x). . . (I -x+4,x) I R.L.Schowen. Progr. Phys. Org. Chem.. 1972 9 275. GENERAL DISCUSSION will yield a significant term in x“. But alas this is not the case. This can be demon- strated by considering the following particular example 53 15 (1-x++43 = 1-54~2+~ where A = X( 1 -X)(X -9/27.Now for all values of x (0 < x Q l) 1A1 is smaller than 2 x and thus compared to the normal experimental scatter A is insignificant. Hence it is not surprising that in fitting a solvent isotope curve to a polynomial the cubic term is insignificant. This will be true whatever the number of terms in the fractionation product. All solvent isotope curves can be satisfactorily fitted with just the linear and the quadratic terms. Thus one cannot find the number of “active protons” by evaluating the statistical significance of terms in a polynomial. This is the reason why the extra information from measurements in H20/D,0 mixtures can be described by the single curvature parameter y. It is also the reason why it is better to concentrate the mixture measurements at x = 3.Returning to Schowen’s systems the two different methods of analysis agree about systems 2 and 4. With respect to systems 3 and 5 the y treatment shows that the experimental scatter is too large to discriminate between the different models; it is true that the single proton model fits system 3 better than the two proton model and vice versa for system 5 but the alternative models cannot be ruled out. Incidentally one advantage of the y treatment is that one can imagine a Gaussian curve constructed on the y plot and this allows one to visualise how tentative or otherwise one’s con- clusions must be. Systems 6 and 7 are similar to each other. Table 1 shows for TABLE 1.-VALUES OF (kx/kl,-,bs)FOR DIFFERENT TRANSITION STATES^ FOR SYSTEM 6 a 1 1 2 2 3 0.602 0.543 0.658 0.649 0.702 4A b 3 10 3 10 3 0.821 0.952 0.917 0.977 0.987 4B T obs 0.00 2.92 2.93 2.93 2.93 2.93 2.93 0.10 2.66 2.67 2.67 2.67 2.67 2.67 0.20 2.47 2.42 2.42 2.42 2.42 2.42 0.30 2.18 2.19 2.19 2.19 2.19 2.19 0.40 1.97 1.97 1.98 1.97 1.97 1.97 0.50 1.77 1.77 1.78 1.77 1.77 1.77 0.60 1.58 1.59 1.59 1.59 1.59 1.59 0.70 1.42 1.42 1.42 1.42 1.42 1.41 0.80 1.27 1.26 1.26 1.26 1.26 1.25 0.90 1.07 1.11 1.11 1.11 1.11 1.11 1.00 1.00 0.98 0.98 0.98 0.98 0.97 S.D.0.023 0.024 0.023 0.023 0.023 a The transition state fractionation is (I -x+ $AX)’(l -x+ $BX)~; b S.D. is the standard deviation. system 6 the fit obtained by the y treatment for the different transition states.As always the different models give the same solvent isotope curve. (The models with b = 3 and b = 10 do not describe reactant fractionation but transition state fractiona-tion). In considering models of this type one is not suggesting any chance cancelling of factors. On the contrary the models with b = 10 correspond to a medium effect GENERAL DISCUSSION 165 or to small contributions from a large number of sites which do not cancel. The data in table 1 confirm the earlier conclusion that as good a fit to the data can be found for the single proton model as for the double proton model. I have conducted a similar analysis of system 1. Possible models with associated fractionation factors are given in table 2.Again all the different models give virtually the same solvent TABLE 2.-POSSIBLE TRANSITION STATES FOR SYSTEM 1 U 1 1 1 2 2 4A 0.608 0.599 0.597 0.695 0.694 b 1 3 10 3 10 $I3 0.868 0.958 0.988 1.030 1.009 103(s.~.) 9.3 9.3 9.4 9.2 9.2 isotope curve and for each model I have given in table 2 the standard deviation between the calculated curve and the experimental curve. The model in the left-hand column (a = 1 b = 1) is the same model found by Schowen (4A1 = 1.64 and & = 1.15) ; however as the two right-hand columns show models with two protons and a very modest medium effect will fit the data equally well. Finally the results given by Schowen in his last paragraph are most interesting and suggest that the alteration of y with substrate may be the best way to investigate the two proton mechanism.Prof. R.L. Schowen (University of Kansas) (communicated):Polynomial regression is capable of accurately measuring the number of active protons when the requisite precision is available and it always indicates the number of active protons required by the data. Models having more active protons cannot then derive support from the data (see below). The precision needed to establish a given term is a sensitive function of the isotope effect. In Albery’s example with 4 = 0.67 the third proton requires precision of a few tenths of a percent and the second proton about three percent. At 4 = 0.57 one percent suffices for the third proton and at 4 = 0.47 two percent. Albery has also given further detail on many-proton fits to system 6 (numbering of Albery’s original table l) for which polynomial regression shows linear (confidence level 0.999) and quadratic (0.999) terms to be highly significant and the cubic term (0.9) much less so.We accordingly interpret the results in terms of two-proton catalysis. Albery shows in his new table 1 that there exist many proton models according to which he can split the contribution of the second proton into three parts (or equally well into lo) with a standard deviation of 1-2 % or that he can pare away factors of up to around 1.2 and split these into numerous parts or that he can build on the less significant cubic term. Again I will have to refer to my reply to Kresge there seems to me little profit in constructing enormously complex models on the basis of data which justify only the simple two-proton picture.Similar comments apply to system 1 (Albery’s new table 2) interpreted by us as a one-proton case because of the low significance of the quadratic (0.95) and cubic (0.8) terms in the polynomial. As Albery has noted the two-proton model in the leftmost column of this table is that to which I referred above in saying “ . . it is a single proton in effect which produces the entire solvent isotope effect ”. At the right end of this table are examples in which “ complex cancellation of contributions . . . so chosen as not to perturb the linearity of v,(n) to an easily detectable extent” are again adduced as previously by Kresge.This Symposium page 160. GENERAL DISCUSSION As I mentioned before the y-method and polynomial regression ought to give similar results and I speculated that use of the whole data set in polynomial regression might explain the discrepancies. From the more detailed presentation I now see that the whole data set is used in both methods. The apparent discrepancies I now suppose to correspond to the allowance by the y-method of models which would produce terms with low confidence limits (say less than 0.8-0.9) in the polynomial regression. These are indeed possible models which greater precision might later justify. Finally I completely agree with the burden of Albery's last comment that investigation of structural and other effects on the shapes of solvent isotope effect curves represents the most promising avenue of pursuit of the questions in this field.Prof. A. J. Kresge (Urziuersityof Toronto)said It is well known that enzymes have many labile hydrogens which exchange rapidly with an aqueous solvent and con- formational and other changes in the enzyme that occur during catalysis could produce secondary isotope effects at these labelled positions which might combine to mark the isotope effect due to proton transfer.' To investigate this matter we have begun measuring solvent isotope effects on certain reactions of cycloamyloses. These substances are cyclic glucopyranosides with central cavities-" active sites "-which mimic the catalytic action of some enzymes remarkably closely ; they are at the same time relatively small molecules (6-8 glucose residues) with a manageable number of exchangeable sites (3 per glucose residue).We have found so far that dissociation of the cyclohexylamylose-p-nitrophenylate inclusion complex gives an overall solvent isotope effect of 0.72 (KD/KH) and an effect of 0.91 (Kx/KH)in a 50 50 H20-D20 mixture (X= 3). This curved depend- ence of isotope effect on solvent deuterium content has just the form needed to convert the behaviour expected for two-proton transfer catalysis into that for a one-proton transfer mechanism. Prof. R.L. Schowen (Uniuersity of Kansas) said Kresge's interesting investigation confirms that small solvent isotope effects may be generated by molecular association processes. This is to be expected and one can hope that complete elucidation of these effects will lead to an improved understanding of the detailed structural changes which accompany association processes including the association of substrates with enzymes.However I do not consider that these observations suggest any changes in the interpretation of our results for serine proteases. In the paper to which he has referred Kresge proposed an alternative interpreta- tion of our data for system 2 of Albery's table 1. Whereas we ascribed the linear character of v,(n) to the generation of the entire solvent isotope effect by a single transition-state proton Kresge proposed models in which 75-80 % of the solvent isotope effect arose from a single transition-state proton and the remainder of the effect from a complex cancellation of contributions of up to 21 other reactant and transition-state protons.These contributions were so chosen as not to perturb the linearity of u,(n) to an easily detectable extent. As is explained in our paper such a complex cancellation might conceivably account for a single case of linear u,(n) but to believe that a similar cancellation (involving different magnitudes and different physical processes) should hold for various substrates enzymes and rate-determining steps would require an extraordinary act of faith. It also happens that none of the A. J. Kresge J. Amer. Chem. SOC.,1973 95 3065. D. W. Griaths and M.L.Bender Adu. Catalysis 1973 23,209. GENERAL DISCUSSION 167 cases for which we report a linear v,(n) (all being maximum-velocity studies) involves a molecular association process.Since the submission of our paper we have completed a few further investigations of serine proteases. For example linear zI,(n) with linear term significant at 0.999 level is observed for deacylation of a-N-benzoyl-L-arginyltrypsin(quadratic and cubic terms not significant at level of 0.8) and a-N-benzoyl-L-arginylthrombin (quadratic term significant only at 0.9 cubic not significant at 0.8 level) and for acylation of elastase by a-N-carbobenzyloxy-L-alanine p-nitrophenyl ester (quadratic term not significant at level of 0.8 cubic only at 0.8). The former two cases do not involve association processes while the last case does. In my opinion to pursue a model in which exact cancellation between reactant- state and transition-state contributions occurs in each of these cases is quite unlikely to prove fruitful.The current finding of one-proton catalysis does not of course mean that if the physiological substrate structure is approached more closely for the serine proteases no coupling will be observed. Indeed the amidohydrolase results suggest that coupling could occur with proper choice of substrate. If so we may expect to observe non-linear v,(n) with the serine proteases. Prof. R. P. Bell (University of Stirling) said Schowen has made theoretical calculations of the relation between the lengths of hydrogen bonds and the occurrence of coupling between the motion of two protons and has used the results to draw conclusions about the nature of such motion in enzyme reactions.I would like to ask whether this relation has been tested in model systems with known hydrogen bond lengths or whether such tests are feasible. Prof. R. L. Schowen (University of Kansas) said The only attempt of which I know to simulate the charge-relay system in a small molecule is the effort of Rogers and Bruice which has been discussed together with other pertinent information by Bruice.2 The hydrogen-bond lengths in this molecule are not known. Although there should in-principle be no barrier to the construction of suitable model com- pounds it may emerge that enzymes (for which structures are now rapidly becoming available) offer the best field for testing the calculations.Dr. R. A. More O’Ferrall (University College Dublin) said It was first shown some years ago in the general base catalysed cyclisation of chlorobutanol that ACO-H-o-c-c1 proton transfers between oxygen atoms at least when concerted with bond-making or bond-breaking to carbon may be characterised by primary hydrogen isotope effects abnormally close to unity. I am not sure that this finding has been fully explained but I wonder if it is relevant to the interpretation of Knowles and Albery’s result ? G. A. Rogers and T. C. Bruice J. Amer. Chem. SOC.,1974 96,2473. T. C. Bruice Ann. Rev. Biochem. 1974. C. G. Swain D. A. Kuhn and R. L. Schoweo J. Amer. Chem. SOC.,1965,87 1553. GENERAL DISCUSSION Prof. R. L. Schowen (Uniuersity of Kansas) said The conclusion reached in the paper which More O’Ferrall has cited is that the proton is not “ in flight ” in the transition state for reorganization of the heavy-atoms ; that is it has no significant amplitude in the reaction coordinate.I still hold this view and suspect that it applies both to the kind of case observed by Fisher Albery and Knowles in which the fractionation factor for the critical proton is near unity and to a large number of cases in which the fractionation factor is around 0.5. Even if this is so no inter- mediate structure (in the usual sense of a stable species) is necessarily required between the transition state and the product in which the proton has been transferred. Instead as Choi and Thornton have explained the reaction path from the heavy- atom reorganization transition state may lead directly down into the proton-transfer transition state entering at a right angle to the proton-transfer reaction path.Dr. W. J. AIbery (Oxford University) and Prof. J. R. Knowles (Harvard University) (communicated) Although the fractionation factor for a proton transfer that is concerted with other covalency changes may be close to unity in our case the proton transfer from the carboxylate base would be a simple single step. Thus the factor for this type of transfer one would still expect to be less than 0.3. Prof. R. A. Marcus (University of Illinois) said Did you consider the possibility of investigating the effect of added molecules that might more readily accept a proton? Prof.J. R. Knowles (Harvard University) said No. I have considerable doubts about doing enzyme-catalyzed reactions in anything but buffered solutions in IH2O. I am even prejudiced against 2H20(pace Professor Schowen) since the effects upon such things as the apparent pK,-values of ionising groups on the enzyme the con- formation of the proton and effects upon the exact constellation of active-site function- alities are largely unknown and are very hard to assess. [Professor W. P. Jencks communicated the possibility that the proton transfer could be dependent on the buffer (in our case triethanolamine). Our data cannot rule this out though the steric constraints of the enzyme’s active site make direct transfer to buffer unlikely even though Grotthus-type transfer via the solvent is undoubtedly possible.] M. Choi and E. R. Thornton J. Amer. Chem. Suc. 1974 96 1428.