Practical Protein Chemistry - A. Darbre 1989

Prediction of Peptide and Protein Conformation
Initial Prerequisites for Calculations
Testing of Potential Functions Derived from Structural Data Using More Precise Methods

The easiest answer to the question posed above is to assume that calculating physical properties using potential function data is invalid. However, a more appropriate approach is to analyze whether the overestimation of barriers stems from some unjustified simplification, even when correct potential Functions are used. Indeed, such a simplification does occur: the assumption of a Rigid Geometry. It is well known that Bond Lengths and valence angles in molecules are not constant, and variations in valence angles can be crucial in preventing atomic collisions. For instance, in a four-atom system with an A-B-C-D bond configuration, slightly increasing the A-B-C and B-C-D angles is important to mitigate the A...D interaction.

A suitable method that accounts for the relaxation of particle interactions in this manner is the valence force field approximation—a set of potential functions in which the energy depends on both bond lengths and valence angles for a given type of chemical bond. One of the first valence force fields was calculated by Hagler and Stern (unpublished work) using vibrational frequency and geometry data for N-methylacetamide. The solution of the inverse problem demonstrated that valence angles possess sufficient flexibility to achieve the required lowering of energy barriers. Introducing the valence force field imparted significant flexibility to peptide molecules [67]. For example, characteristic distances in Polypeptides can be reduced from 19 to 5, which corresponds to the lower bound of the experimental range. This proved that METABOLISM/2.html">THE CONCEPT OF flexible geometry plays a vital role in refining calculations and must be taken into account. Through further investigation and optimization of the valence force field properties using an extended-basis quantum mechanical method, optimal values for all necessary parameters were determined [24]. The resulting valence force field exhibited slightly lower flexibility of the peptide group compared to the empirical force field; consequently, valence angles could only vary within ±5°, which was nevertheless sufficient to retain the primary advantages of the new approximation.

Implementing the concept of flexible geometry requires no special effort to calculate the Free energy as a function of an expanded set of internal degrees of freedom. To estimate the additional contribution arising from flexible geometry, calculations were performed for hexapeptide molecules [20] containing Alanine, Methionine, and Glycine residues (for which experimental data are available). It turned out that the entropic contribution to the free energy is comparable in magnitude to the potential energy and cannot be neglected in precise calculations.

If the vibrational degrees of freedom of biological molecules provide such a significant contribution to the conformational free energy, evaluating the effect introduced by the solvent is equally important. Indeed, it is well known that the stability of Globular Proteins is largely governed by hydrophobic interactions, the entropic contribution of which depends on The Nature of the solvent. Furthermore, major roles are also played by the solvation energy contribution, The formation of Hydrogen Bonds involving solvent molecules, and The Influence of polar solvent groups on Electrostatic Interactions within the protein molecule.

The Monte Carlo Method was used to calculate the positions of Water molecules in hydrated crystals of Lysozyme and A number of cyclic Peptides [16]. The conformation of the protein and peptide molecules in these calculations was assumed to be the same as in the crystals. Satisfactory agreement was demonstrated between the calculated and experimental locations of the water molecules. Therefore, the results obtained by the same method regarding The Study of solutions of other peptides [22]—for which corresponding experimental data were lacking—deserve confidence. In any case, The most significant Conclusions of the latter work should not depend on the specific form of the potential functions or the Nature of the approximation used in the Monte Carlo method. For instance, it was found that the solvent's influence on the Conformational Energy of small peptides correlates with the potential energy of the isolated molecule. Thus, studies performed at a higher level of approximation yielded a somewhat unexpected result: earlier "quantitative" calculations are no longer of great value. It is also evident that THE CONTRIBUTION OF potential energy, calculated in the conventional manner, is comparable in magnitude to other contributions to the system's free energy. Of course, the Specific characteristics of the system under study are also of great importance; for example, in the case of a nonpolar solvent, neglecting its influence does not distort the results. It should also be noted that more accurate calculations, which currently require prohibitively large amounts of computer time, are always a possibility, and the rapid advancement of computing technology will increasingly facilitate such research. Finally, the refinement of theoretical concepts should help develop more appropriate computational approximations. For instance, the assumption that the "reaction field" plays a decisive role in solute-solvent interactions appears very promising, especially since it allows for an analytical representation of the corresponding dependencies. Moreover, such interactions can be restricted to the scale of the first solvation shell, as was demonstrated in simulations of protein self-assembly [33, 62].