Comparison with experimental kinetics

From an energetic point of view, the Gibbs free energy barriers, $\Delta G^{\ddagger }$, corresponding to a one-step process that would proceed with the experimental rate constant $k_{cat}$, and our theoretical potential energy barriers, $\Delta V^{\ddagger }$, taken as the highest energy along the QM/MM potential energy profiles, are shown in table 2.3.

Table 2.3: Comparison between the $k_{cat}$ determined experimentally and the Gibbs free energy barriers, $\Delta G^{\ddagger }$ calculated from them, and the theoretical potential energy barriers, $\Delta V^{\ddagger }$ for the three mechanisms I, II, III

$k_{cat}/s^{-1}$

$\Delta G^{\ddagger }$

$(kcal/mol)$

$\Delta V^{\ddagger }$
I	II	III

(S)-Propargyl

79[220]

14.96

30.1

28.1

21.9

(S)-Vinyl

250$\pm$20[219]

14.27

26.7

20.8

20.8

(S)-Mandelate

350$\pm$5[214]

14.07

27.2

28.1

19.3

(R)-Propargyl

37[220]

15.41

26.8

24.8

18.7

(R)-Vinyl

240$\pm$30[219]

14.29

24.1

18.2

17.7

(R)-Mandelate

500$\pm$10[214]

13.85

20.5

21.4

15.4

Our results indicate that the reaction proceeds at least through three different mechanisms, in such a way that the effective potential energy barrier attributed to the overall reaction would indeed be lower than the particular potential energy barriers associated to each mechanism. It can be seen that in both S$\to$R and R$\to$S directions mec II and mec III are faster than mec I for vinylglycolate and propargylglycolate. For mandelate, mec III and mec I are more favorable than mec II.

In spite of the approximations used, there is a good qualitative agreement when comparing the Gibbs free energy barriers deduced from the experimental $k_{cat}$ for the (S)-enantiomers (from 14.96 kcal/mol to 14.07 kcal/mol) with the value of the potential energy maximum of the most favorable mechanism (mec III) that goes from 21.9 kcal/mol to 19.3 kcal/mol. In addition, mec III is the only one that gives the experimental trend of $k_{cat}$ with respect to the substrate. That is, mandelate, which is the substrate that undergoes racemization by the enzyme at the highest rate, has the lowest potential energy barrier of the three substrates in the two directions (S$\to$R and R$\to$S). Vinylglycolate has been found to be an excellent substrate of Mandelate Racemase with kinetic parameters comparable to those of mandelate. In the second column of table 2.3 it can be verified that (S)-vinylglycolate and (S)-mandelate are racemized by MR enzyme at a similar rate although vinylglycolate is somewhat slower. In agreement, the global potential energy barriers for mandelate are around 1 kcal/mol lower than for vinylglycolate in the forward and reverse reactions.

Propargylglycolate is the substrate that undergoes racemization at the lowest rate and it is also the one that presents the highest potential energy barriers in both the S-to-R and the R-to-S directions. On the other hand, the reaction with mandelate turns out to be experimentally faster from R to S than from S to R, but when the substrates are (R)-vinylglycolate or (R)-propargylglycolate the interconversion is slower than in the S to R direction. In agreement with the experimental results, we obtain a smaller potential energy barrier for the reaction with (R)-mandelate than with (S)-mandelate. However, in disagreement with the experimental values, (R)-vinylglycolate and (R)-propargylglycolate present lower potential energy barriers than the corresponding (S)-enantiomers.