Entropic cost

The greater the number of unfolded conformations of a protein, tbe higher the entropic cost of folding that protein into its single native state (see Chapter 6). Reducing the number of unfolded conformations therefore increases... 

The final ingredient that enters the calculation is the density factor pw. This is the actual density of water appropriate to the thermodynamic state intended in the calculation. For the usual case of 1 atm. pressure and 298K, this is I gem 3. The reference density in the electronic structure calculations is p° = 1 atm//metal-water complexes, the free energies should be adjusted by —mRT In (pi 2o/p ) = —mRTIn (1354). With these inputs the excess chemical potential is readily composed as per (9.50), provided the optimal value of m is known. This is found by composing the excess chemical potential for different assumed m values and identifying the most stable case. For the dication transition metals studied, this is found to be six, consistent with experiment [12]. 

The cyclotrimer products are liberated in subsequent, consecutive substitution steps with new butadiene, which is an exothermic reaction (AH) for expulsion of all-t-CDT by three /ran.v-butadienes along 8b —> l b. This process, however, is endergonic by 7 kcal mol-1 (AG) after entropic costs are taken into account. Therefore, 7b and 8b (stabilized by donors) are indicated to be likely candidates for isolable intermediates of the catalytic process, while the active catalyst l b, the intermediate species 2b, in particular, and other species will not be present in a sufficient concentration, since they are either too reactive or thermodynamically too unfavorable, for experimental characterization. Overall, the cyclotrimerization process is driven by a strong thermodynamic force with an exothermicity of —44.6 kcal mol-1 (AH for the process without a catalyst) for the fusion of three trans-butadiene to afford the favorable all-t-CDT. 

Desolvation of the reacting polar groups is also a mechanism by which enzymes achieve rate accelerations. The desolvation of functional groups takes places during the inclusion of the reactants within the catalytic apparatus of the active site. This is another way of looking at the selective stabilization of the TS, in terms of a specific solvation of the reactants by the enzyme residues of the active site, which replaces the random solvation by the solvent molecules and the inherent enthalpic and entropic cost associated with their reorganization in the TS. 

With the above simple examples we wish to emphasize that the synthetic use of hydrogen bonding assemblies in the effective formation of supramolecular macrocycles relies on high EM values and on the establishment of stable intermolecular arrays of hydrogen bonds capable of affording a high enthalpic gain to compensate for the entropic cost of the assembly. 

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