Publisher Summary This chapter deals with the recent developments regarding the description and nature of the conformation of proteins and polypeptides with special reference to the stereochemical aspects of the problem. This chapter considers the parameters that are required for an adequate description of a polypeptide chain. This chapter focuses the attention on what may be called “internal parameters”—that is, those which can be defined in terms of the relationships among atoms or units that form the building blocks of the polypeptide chains. This chapter also provides an account of the mathematical method of utilizing these parameters for calculating the coordinates of all the atoms in a suitable frame of reference, so that all the interatomic distances, and bond angles, can be calculated and their consequences worked out. This chapter observes conformations in amino acids, peptides, polypeptides, and proteins.

Conformation of Polypeptides and Proteins

A theoretical study is made of the equations of state of argon and nitrogen, at high temperatures and densities. The intermolecular potential used is of the Lennard‐Jones form, with an adjustable rigid sphere cutoff. A perturbation theory is developed, by which the thermodynamic properties of one system may be related to those of a slightly different system and to the difference in the intermolecular potentials of the two systems. In this article, the unperturbed system is a rigid sphere fluid, and the Lennard‐Jones potential is the perturbation. The results are in fair agreement with experiment, and also lead to an experimental test of the theoretical rigid sphere equation of state.

High‐Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases

Correlating the structure and action of biological molecules requires knowledge of the corresponding relation between structure and energy. Probably the most important factors in such a structure– energy correlation are associated with electrostatic interactions. Thus the key requirement for quantative understanding of the action of biological molecules is the ability to correlate electrostatic interactions with structural information. To appreciate this point it is useful to compare the electrostatic energy of a charged amino acid in a polar solvent to the corresponding van der Waals energy. The electrostatic free energy, ΔGel, can be approximated (as will be shown in Section II) by the Born formula (ΔGel = –(166Q2/ā) (I – I/E)). Where ΔGel is given in kcal/mol, Qis the charge of the given group, in units of electron charge, āis the effective radius of the group, and E is the dielectric constant of the solvent. With an effective radius of charged amino acids of approximately 2 A, Born's formula gives about – 80 kcal/mol for their energy in polar solvents where E is larger than 10. This energy is two orders of magnitude larger than the van der Waals interaction of such groups and their surroundings.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0033583500005333

Calculations of electrostatic interactions in biological systems and in solutions.

Computer simulation calculations on liquid water, aqueous solutions and biological interfaces have been made almost universally assuming pair-additive interactions. Experimental and theoretical evidence implies this is a serious oversimplification. The development and testing of a different approach is reviewed in which many-body forces are specifically taken into account through molecular polarisation. Solution and interfacial properties of aqueous systems are particularly sensitive to such forces.

Cooperative effects in simulated water

The study of polar fluids begun in a previous paper is continued. Calculations for the Stockmayer potential are extended to include the term of order μ6, where μ is the dipole moment. The effects of higher-order terms are then approximated by means of a simple Pade extrapolation procedure, and the liquid-gas coexistence curve is located in this approximation. An orientation-independent but temperature-dependent potential that is thermodynamically equivalent to an arbitrary orientation-dependent potential is introduced and used to assess the lowest-order thermodynamic effects that result from the presence of quadrupole and octupole terms in the pair-potential. Several values of quadrupole and octupole moments representative of a dipolar molecule (HCl) as well as linear molecules (N2, O2 and CO2, for which μ=0) are considered.

Thermodynamic perturbation theory for simple polar fluids. II

An equation is given for the classical second virial coefficient of a polar gas in terms of the parameters appearing in an intermolecular potential energy which includes London and dipole attraction and inverse‐power repulsion. The equation is successfully fitted to the data for H2O and NH3 with allowance for the small quantum correction, and the derived values of the London constant are in good accord with theoretical estimates. The defects of the model and its relation to the concept of the hydrogen bond are briefly discussed.

W. H. Stockmayer

Papers

Second Virial Coefficients of Polar Gases