Free energy intramolecular interaction

Fig. 11.4. The free energy of interaction of two flat plates sterically stabilized by tails of molecular weight 6 000 according to the theory of Hesselink, Vrij and Overbeek (1971). Three different intramolecular expansion factors are shown (after Hesselink, 1977).

A thermodynamically stable conformation arises from the minimization of the overall free energy of interaction resulting from all intramolecular and intermolecular contributions. Whatever the control of the folding process may be, thermodynamic or kinetic, the conformation must be thermodynamically stable with respect to small perturbations of the molecular geometry. Of course, it is also stable relatively to the unfolded state. In spite of controversies, the thermodynamic hypothesis represents a necessary working hypothesis for all current attempts of a theoretical analysis of protein stability and for determination of the allowed conformations of a polypeptide chain. 

Fig. 2.5. Possible applications of a coupling parameter, A, in free energy calculations, (a) and (b) correspond, respectively, to simple and coupled modifications of torsional degrees of freedom, involved in the study of conformational equilibria (c) represents an intramolecular, end-to-end reaction coordinate that may be used, for instance, to model the folding of a short peptide (d) symbolizes the alteration of selected nonbonded interactions to estimate relative free energies, in the spirit of site-directed mutagenesis experiments (e) is a simple distance separating chemical species that can be employed in potential of mean force (PMF) calculations and (f) corresponds to the annihilation of selected nonbonded interactions for the estimation of e.g., free energies of solvation. In the examples (a), (b), and (e), the coupling parameter, A, is not independent of the Cartesian coordinates, x. Appropriate metric tensor correction should be considered through a relevant transformation into generalized coordinates...

An alternative approach to calculating the free energy of solvation is to carry out simulations corresponding to the two vertical arrows in the thermodynamic cycle in Fig. 2.6. The transformation to nothing should not be taken literally -this means that the perturbed Hamiltonian contains not only terms responsible for solute-solvent interactions - viz. for the right vertical arrow - but also all the terms that involve intramolecular interactions in the solute. If they vanish, the solvent is reduced to a collection of noninteracting atoms. In this sense, it disappears or is annihilated from both the solution and the gas phase. For this reason, the corresponding computational scheme is called double annihilation. Calculations of... 

For intramolecular reactions the situation is different. Here the free-energy contribution from the non-reacting part of the molecule can be, and quite often is, most significant. Moreover, steric restrictions due to the intervening chain can significantly alter the way in which the end-groups interact in the... 

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