Decarboxylation reactions free energies

Alternatively one can make use of No Barrier Theory (NBT), which allows calculation of the free energy of activation for such reactions with no need for an empirical intrinsic barrier. This approach treats a real chemical reaction as a result of several simple processes for each of which the energy would be a quadratic function of a suitable reaction coordinate. This allows interpolation of the reaction hypersurface a search for the lowest saddle point gives the free energy of activation. This method has been applied to enolate formation, ketene hydration, carbonyl hydration, decarboxylation, and the addition of water to carbocations. ... 

The carboxylation of pyruvate supplies a significant portion of the thermodynamic push for the next step in the sequence. This is because the free energy change for decarboxylation of /3-keto carboxylic acids such as oxaloacetate is large and negative. The oxaloacetate formed from pyruvate by carboxylation is converted to phosphoenolpyruvate in a reaction catalyzed by phosphoenolpyruvate carboxyki-nase. In many species, including mammals, this reaction involves a GTP-to-GDP conversion. 

Fig. 1 Computed free energy reaction profiles for the decarboxylation of OMP in water and in the wild-type enzyme ODCase. Reprinted with permission from Reference 66. Copyright 2000 National Academy of Sciences.

Table 11 Observed and calculated free energies of activation for decarboxylation reactions ...

The barriers just described were calculated with 1-methylorotic acid (11) as a reference point to model the uncatalyzed reaction in solution. However, the computed free-energy barriers for decarboxylation of zwitterions 4b and 6b are 8.4 and 7.6 kcal mol-1, respectively. This difference of 0.8 kcal mol-1 is significantly smaller than the 6 kcal mol-1 difference calculated by Lee and Houk for the 2-protonation and 4-protonation pathways. This discrepancy arises from an internal hydrogen bond (12) between the Nl-H and the carboxylate that artificially stabilizes the 02-protonated zwitterion 4a, and renders its corresponding decarboxylation barrier too high. When the Nl-H is replaced by a methyl, the hydrogen bond is removed, and the ylide and carbene mechanisms become closer in energy nonetheless, 4-protonation is still favored. 

Gao and coworkers used QM/MM calculations74 to map out the reaction coordinate and predict the activation free energies for OMP decarboxylation by ODCase and for the decarboxylation of the 1-methylorotate anion (lb) in water.22 Free energies of binding were then computed for structures involved in the decarboxylation using FEP methods.71... 

After performing ab initio and solvation calculations to examine the decarboxylation reaction in water, the free energy surface of the enzyme-catalyzed reaction was explored. An initial ODCase-OMP complex was constructed from the structure of the ODCase-6-azaUMP complex reported by Pai and coworkers,22... 

The successive carboxylation and decarboxylation reactions are both close to equilibrium (they have low values of their standard free energies) as a result, the conversion of pyruvate to phosphoenolpyruvate is also close to equilibrium (AG° = 2.1 kj mol = 0.5 kcalmoh ). A small in crease in the level of oxaloacetate can drive the equilibrium to the right, and a small increase in the level of phosphoenolpyruvate can drive it to the left. A concept well known in general chemistry, the law of mass action, relates the concentrations of reactants and products in a system at equilibrium. Changing the concentration of reactants or products causes a shift to reestablish equilibrium. A reaction proceeds to the right on addition of reactants and to the left on addition of products. 

For ODCase, non-covalent mechanisms have often been proposed, as reflected in three of the mechanisms shown in Fig. 2. This is the crux of the attention showered on ODCase how can this enzyme achieve its rate acceleration without the use of cofactors, metals, or acid-base catalysis From Wolfenden s measurements of the uncatalyzed reaction of 1-methylorotic acid in water, he calculated the rate enhancement (kcat/kun) in the enzyme to be 1.4x10, corresponding to a reduction of AG of 24 kcal/mol [1]. He also reported the catalytic proficiency to be 2x10 meaning that the enzyme-transition state complex is an impressive 32 kcal/mol more stable than the fi-ee enzyme and transition state in water (i.e., the effective binding free energy of the transition state out of water is 32 kcal/mol) [1] The experimental free energy of activation is 15 kcal/mol for this decarboxylation in ODCase. 

Using the EVB approach, which was calibrated to the aqueous reaction [28], Warshel et al. also reproduced the experimental free energy of activation for the catalyzed (OMP) reaction in ODCase. The EVB energy profile and barrier for the decarboxylation reaction in the gas phase was not reported. Although the computed barrier heights for the enzyme reaction are similar in the two computational studies [16, 28], a major difference is that the... 

In analyzing the origin of enzyme catalysis, Warshel and others have advocated the importance of comparing the enzymatic reaction with a reference reaction in water [32]. In addition, it is also necessary to study the reference reaction in the gas phase in order to understand the intrinsic reactivity and the effect of solvation. Thus, to understand enzyme catalysis fully, we must compare results for the same reaction in the gas phase (intrinsic reactivity), in aqueous solution (solvation effects), and in the enzyme (catalysis). This is not possible when there is no model reaction for the uncatalyzed process in the gas phase and in water, or if the uncatalyzed reaction is a bimolecular process as opposed to a unimolecular reaction in the enzyme active site. None of these problems apply to the ODCase reaction. Furthermore, OMP decarboxylation is a unimolecular process, both in water and the enzyme, providing an excellent opportunity to compare directly the computed free energies of activation [1] this is the approach that we have undertaken [16]. Warshel et al. used an ammonium ion-orotate ion pair fixed at distances of 2.8 or 3.5 A as the reference reaction in water to mimic an active site lysine residue [32]. 

TABLE 5.7 Observed and Calculated Free Energies of Activation for Decarboxylation Reactions"... 

Figure 10 Free energy profiles for the decarboxylation reaction of 3-carboxy-benzisoxazole in the gas phase and aqueous solution. The reaction coordinate is illustrated by the C—C distance.

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