Entropy loss

V (the potential) is identified with the enthalpy, i.e. the number n of base pairings (contacts), and T corresponds to the entropy. At each stage in the folding process, as many as possible new favourable intramolecular interactions are fonned, while minimizing the loss of confonnational freedom (the principle of sequential minimization of entropy loss, SMEL). The entropy loss associated with loop closure is (and the rate of loop closure exp... 

Fernandez A and Cendra H 1996 in vitro RNA folding the principle of sequential minimization of entropy loss at work Biophys. Chem. 58 335-9... 

FIGURE 16.2 The intrinsic binding energy of the enzyme-snbstrate (ES) complex (AGi ) is compensated to some extent by entropy loss dne to the binding of E and S (TAS) and by destabilization of ES (AGt) by strain, distortion, desolvation, and similar effects. If AGi, were not compensated by TAS and AG, the formation of ES would follow the dashed line. 

FIGURE 16.3 (a) Catalysis does not occur if the ES complex and the transition state for the reaction are stabilized to equal extents, (b) Catalysis will occur if the transition state is stabilized to a greater extent than the ES complex right). Entropy loss and destabilization of the ES complex ensure that this will be the case. 

Clearly, proximity and orientation play a role in enzyme catalysis, but there is a problem with each of the above comparisons. In both cases, it is impossible to separate true proximity and orientation effects from the effects of entropy loss when molecules are brought together (described the Section 16.4). The actual rate accelerations afforded by proximity and orientation effects in Figures 16.14 and 16.15, respectively, are much smaller than the values given in these figures. Simple theories based on probability and nearest-neighbor models, for example, predict that proximity effects may actually provide rate increases of only 5- to 10-fold. For any real case of enzymatic catalysis, it is nonetheless important to remember that proximity and orientation effects are significant. 

Part (a) is the driving force for the adsorption. If only (a) were present, adsorbed chains would lie flat on the surface. Parts (b) and (c) are the opposing forces (b) accounts for the entropy loss of a bond on the surface as compared to the solution, (c) represents the separation into a concentrated surface phase and a dilute solution. Part (d) arises from polymer-polymer, solvent-solvent and polymer-solvent interactions, which usually favour accumulation of segments. At equili-... 

It is well known that native collagen containes tripeptide sequences, which alone are not capable of building up a triple helix (e.g. Gly-Pro-Leu, Gly-Pro-Ser) when they exist as homopolypeptides. The synthesis of threefold covalently bridged peptide chains opens up the possibility of investigating the folding properties of such weak helix formers, because the bridging reduces the entropy loss during triple-helix formation and thereby increases the thermodynamic stability of the tertiary structure. Therefore, we have... 

Sutoh and Noda154 succeeded in proving, by synthesizing block copolymers of the structure (Gly-Pro-Pro)n(Gly-Ala-Pro)m-(Gly-Pro-Pro)n, that with increasing imino add content, AS° changes to higher positive values. They do, however, not relate this to lower entropy losses of conformation but to hydrophobic interactions of the proline residues in the helical state. 

All results, except those of Sutoh and Noda, seem to confirm that the higher thermostability with increasing imino acid content is caused by an enthalpy overcompensation of the entropy losses. AH° and also AS° are obviously caused by different effects. This is shown by Eq. (10) and Fig. 38... 

Hence, according to the transition state theory, adsorption becomes more likely if the molecule in the mobile physisorbed precursor state retains its freedom to rotate and vibrate as it did in the gas phase. Of course, this situation corresponds to minimal entropy loss in the adsorption process. In general, the transition from the gas phase into confinement in two dimensions will always be associated with a loss in entropy and the sticking coefficient is normally smaller than unity. 

In any state preceding the onset of crystallization at T < To we assume that bundle stability is favored by localized attractive interactions between contacting (short) stems, some enthalpy advantage being balanced by a corresponding entropy loss (see Fig. 3). Depending upon the core structure of the crystalline stems, various bundle models were examined [8,9]. In the present... 

In order to understand the thermodynamic issues associated with the nanocomposite formation, Vaia et al. have applied the mean-field statistical lattice model and found that conclusions based on the mean field theory agreed nicely with the experimental results [12,13]. The entropy loss associated with confinement of a polymer melt is not prohibited to nanocomposite formation because an entropy gain associated with the layer separation balances the entropy loss of polymer intercalation, resulting in a net entropy change near to zero. Thus, from the theoretical model, the outcome of nanocomposite formation via polymer melt intercalation depends on energetic factors, which may be determined from the surface energies of the polymer and OMLF. 

Now we can readily deduce the stability/instability conditions from Figure 6. For < J the attraction is too weak to overcome the particle entropy loss and the dispersion is stable. 

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