Energetics of activation

Another important aspect of electrocatalysis is the study of dispersed high specific area and supported, both metal and non-metal, electrocatalysts. A high degree of dispersion brings about enhancement of the catalytic activity because of the specific area and energetics of active sites [140] and decrease of susceptibility of poisoning because of the improved ratio of catalyst area to impurities in solution. 

One of the most important questions for a conformational search strategy is, When have I found all of the energetically interesting con formers This is an area of active research and the ideal answer seems to be, When you find all of the local minima. However, this answer is not always reasonable, because medium to large molecules have a large number of minima (see Complexity of Potential Energy Surfaces on page 14). 

Jaroniec, M., Gilpin, R. K., Kaneko, K. and Choma, J., Evaluation of energetic heterogeneity and microporosity of activated carbon fibers on the basis of gas adsorption isotherms, Langmuir, 1991, 7(1 1), 2719 2722. 

After the somewhat tedious parametrization procedure presented above you are basically an expert in the basic chemistry of the reaction and the questions about the enzyme effect are formally straightforward. Now we only want to know how the enzyme changes the energetics of the solution EVB surface. Within the PDLD approximation we only need to evaluate the change in electrostatic energy associated with moving the different resonance structures from water to the protein-active site. 

FIGURE 6.10. Comparing the energetics of the EVB configurations in solution and in the active site of lysozyme. The calculations were done by using the PDLD and related models (Refs. 6 and 7) and they represent a study of a stepwise mechanism. The energetics of a more concerted pathway (e.g., that of Fig. 6.9) is almost identical to that of the stepwise mechanism and correlated in a similar way with the electrostatic effect of the protein. 

The actual calculations that compare the energetics of the EVB configurations in the protein-active site and solutions are summarized in Fig. 6.10. 

The considerations presented above were based on the specific assumption that the catalytic reaction of the serine proteases involves mechanism a of Fig. 7.2. However, one can argue that the relevant mechanism is mechanism b (the so-called charge-relay mechanism ). In principle the proper procedure, in case of uncertainty about the actual mechanism, is to perform the calculations for the different alternative mechanisms and to find out which of the calculated activation barriers reproduces the observed one. This procedure, however, can be used with confidence only if the calculations are sufficiently reliable. Fortunately, in many cases one can judge the feasibility of different mechanisms without fully quantitative calculations by a simple conceptual consideration based on the EVB philosophy. To see this point let us consider the feasibility of the charge-relay mechanism (mechanism b) as an alternative to mechanism a. Starting from Fig. 7.2 we note that the energetics of route b can be obtained from the difference between the activation barriers of route b and route a by... 

With the valence bond structures of the exercise, we can try to estimate the effect of the enzyme just in terms of the change in the activation-free energy, correlating A A g with the change in the electrostatic energy of if/2 and i/r3 upon transfer from water to the enzyme-active site. To do this we must first analyze the energetics of the reaction in solution and this is the subject of the next exercise. 

Calculations of the actual dependence of the activation barrier, Ag, on the metal size in the active site of SNase are summarized in Fig. 8.10. The results reflect mainly the energetics of i//2 and ij/3, since the dependence on the ionic radius in is found to be rather small. 

Exercise 9.1. Evaluate the energetics of the reaction of Fig. 9.2 in a nonpolar enzyme-active site. 

It should be born in mind, however, that the activation parameters calculated refer to the sum of several reactions, whose enthalpy and/or entropy changes may have different signs from those of the decrystalUzation proper. Specifically, the contribution to the activation parameters of the interactions that occur in the solvent system should be taken into account. Consider the energetics of association of the solvated ions with the AGU. We may employ the extra-thermodynamic quantities of transfer of single ions from aprotic to protic solvents as a model for the reaction under consideration. This use is appropriate because recent measurements (using solvatochromic indicators) have indicated that the polarity at the surface of cellulose is akin to that of aliphatic alcohols [99]. Single-ion enthalpies of transfer indicate that Li+ is more efficiently solvated by DMAc than by alcohols, hence by cellulose. That is, the equilibrium shown in Eq. 7 is endothermic ... 

In any case, one might expect that the rate of the Ca -pump is rather slow relative to the processes unleashed by muscle activation. This is certainly tme for the Na -K -pump, and if it is tme for the Ca -pump as well, then the significance of the amount of charge which may or may not be transported concomitantly with Ca becomes rather unimportant. In short, the rate at which the pump works is more important for contraction than the detailed energetics of the transport reaction. How much of the variability of smooth muscle responsivity is in fact determined by transients in the Ca distribution, e.g., in smooth muscle myocytes, remains to be discovered. 

The second group of studies tries to explain the solvent effects on enantioselectivity by means of the contribution of substrate solvation to the energetics of the reaction [38], For instance, a theoretical model based on the thermodynamics of substrate solvation was developed [39]. However, this model, based on the determination of the desolvated portion of the substrate transition state by molecular modeling and on the calculation of the activity coefficient by UNIFAC, gave contradictory results. In fact, it was successful in predicting solvent effects on the enantio- and prochiral selectivity of y-chymotrypsin with racemic 3-hydroxy-2-phenylpropionate and 2-substituted 1,3-propanediols [39], whereas it failed in the case of subtilisin and racemic sec-phenetyl alcohol and traws-sobrerol [40]. That substrate solvation by the solvent can contribute to enzyme enantioselectivity was also claimed in the case of subtilisin-catalyzed resolution of secondary alcohols [41]. 

The importance of solvation on reaction surfaces is evident in striking medium dependence of reaction rates, particularly for polar reactions, and in variations of product distributions as for methyl formate discussed above and of relative reactivities (18,26). Thus, in order to obtain a molecular level understanding of the influence of solvation on the energetics and courses of reactions, we have carried out statistical mechanics simulations that have yielded free energy of activation profiles (30) for several organic reactions in solution (11.18.19.31. ... 

According to the Lindemann-Christiansen hypothesis, formulated independently by both scientists in 1921, all molecules acquire and lose energy by collisions with surrounding molecules. This is expressed in the simplified form of the Lindemann mechanism, in which we use an asterisk to indicate a highly energetic or activated molecule, which has sufficient energy to cross the barrier towards the product side, and M is a molecule from the surroundings M may be from the same type as A ... 

The kinetic factor is proportional to the energetic state of the system and (for heterogeneous catalytic systems) the number of active sites per unit volume (mass) of catalyst. The driving-force group includes the influence of concentration and distance from chemical equilibrium on the reaction rate, and the hindering group describes the hindering effect of components of the reaction mixture on the reaction rate. The kinetic factor is expressed as the rate constant, possibly multiplied by an equilibrium constant(s) as will be shown later. 

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