Proton inventory curves

Fig. 11.7 Proton inventory curves (plots of k(n)/k(H) vs. n (or x) = atom fraction D) for overall isotope effects of 2 (upper plot) and 10 (lower plot). In each, the three curves (reading from top to bottom) are for single site, two site, and multi-site isotope effects. Error bars of 3% middle curves) are shown in each case. For ko/ki = 2 the technique is unable to distinguish between the curves at this level of precision (3%), but is more than adequate for ko/ki = 10 (Schowen, R. L., J. Label Compd Radiopharm. 50, 1052 (2007), with permission Wiley Interscience)...

It must be appreciated that the selection of the best model—that is, the best equation having the form of Eq. (6-97)—may be a difficult problem, because the number of parameters is a priori unknown, and different models may yield comparable curve fits. A combination of statistical testing and chemical knowledge must be used, and it may be that the proton inventory technique is most valuable as an independent source capable of strengthening a mechanistic argument built on other grounds. 

Many rate constants in aqueous solutions are pH or pD sensitive. In particular, enzyme catalyzed reactions often show maxima in plots of pH(pD) vs. rate. The example in Fig. 11.5 is constructed for a reaction with a true isotope effect, kH/kD = 2, and with maxima in the pH(pD)/rate dependences as shown by the bell shaped curves. These behaviors are typical for enzyme catalyzed reactions. When the isotope effect is obtained (incorrectly) by comparing rates at equal pH and pD, the values plotted along the steep dashed curve result. If, however, the rate constants at corresponding pH and pD (pD = pH + 0.5) are employed, a constant and correct value is obtained, kH/kD = 2. Thus for accurate measurements of the isotope effects one must control pH and pD at appropriate values (pD = pH + 0.5 in our example) using a series of buffers. In proton inventory experiments (see below) buffers should be employed to insure equivalent acidities across the entire range of solvent isotope concentration (0 < xD < 1), xD is the atom fraction of deuterium [D]/([H] + [D]). 

Interestingly, FKBP12 does not show diffusion control of kc J Km, and proton inventory does not show a bulging down curve. This case underlines the idea that a distinct catalytic mechanism exists for FKBP compared with cydophilins and parvulins. 

We had invoked a simultaneous two proton transfer mechanism rather than a sequential mechanism - in which one catalytic group followed the other in the overall process - and were able to test this with a technique called proton inventory." We examined the original cyclodextrin fcfv-imidazole in mixtures of water and D2O and saw that the rate constant as a function of deuterium concentration followed a curved line, indicating that the isotope effect involved two different protons rather than a single one. To validate this, we also examined the same kind of plot with the cyclodextrin mono-imidazole, in which only one proton would be expected to be moving in the transition state, and this indeed followed a linear plot supporting a single proton motion in the isotope effect. 

Figure lo. Proton inventory for alcohol dehydrogenase-catalyzed oxidation of ethamd with NAD. The data points are the measni A carvahi (lc ) and die curve was drawn according to q. (17.7a, assuming that Jto=i50 s r=o.37, and =0.73 (Chandra Sekhar Plapp, 1990). 

Here ( )i and ( )j are isotopic fractionation factors for isotopically exchangeable hydrogen sites in the transition state (TS) and reactant state (RS) respectively. Plots of k n vs n are curves in the present case, which clearly shows that the process involves a single proton of H-D exchange in the reaction sequence from the hydroxide ion. This proton exchange can be shown by a comparison with standard proton inventory plots reported in the literature[13]. Hence, the participation of hydroxide ion in the formation of trasition state is inferred. 

The pH vs rate profile showed a bell-shaped curve indicating that this catalyst uses both B and BH+ in a bifunctional mechanism. As with the enzyme, the bis-imidazole catalyst can perform its bifunctional catalysis by a simultaneous mechanism, not the sequential mechanism of simple buffer catalysis. We saw that this was indeed the case, as revealed by the tool called "proton inventory." In this technique the reaction is performed in D2O, in H2O, and in mixtures of the two. If only one proton that can exchange with D2O is moving in the transition state, the points all lie on a straight line between the H2O and slower D2O points. If two (or more) protons are moving, the line is curved. It had been found for the enzyme ribonuclease A [10] that a curved line was seen corresponding to the movement of two protons, and we also saw a curved plot—with very similar data— for our cyclodextrin-6A,6B-bisimidazole catalyst 6 [11]. Controls established that indeed this was a reliable indication that our system is performing simultaneous bifunctional catalysis, just as the enzyme does. In particular, the... 

Each (p is the fractionation factor for a given proton that is moving—that is, the inverse of the isotope effect for each proton that is moving. If only one proton moves, a plot of n versus k /kii is linear if two protons move, the plot is quadratic in tr, and if three protons move, the plot is cubic in n, etc. Hence, the term proton inventory is applied to such an experiment and plot. The shape of the curve allows us to inventory the number of protons that are moving, and fitting the curve can extract the individual fractionation factors. 

Draw two curves associated with proton inventory studies where two protons are "in flight" in the rate-determining step. In the first case each proton has an associated isotope effect of 2, while in the second case one isotope effect is 1.5 and the other is 2.5. Using a proton inventory analysis, can you differentiate the two possibilities ... 

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