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X-ray crystallography provides a wealth of information about the dynamic as well as static protein structure. A new method of dynamic structure refinement of protein X-ray crystallography, normal mode refinement, is proposed. In this method, the Debye-Waller factor is expanded in terms of the low-frequency internal normal modes and external normal modes, whose amplitudes and couplings are optimized in the process of crystallographic refinement. The internal and external contributions to the atomic fluctuations can be separated. Also, anisotropic atomic fluctuations and their inter-atomic correlations can be determined experimentally even with a relatively small number of adjustable parameters. The method is applied to the analyses of experimental data of human lysozyme and its mutant, C77A/C95A, to reveal its dynamic structure.

Normal mode analyses on the protein, bovine pancreatic trypsin inhibitor, in dihedral angle space and Cartesian coordinate space are compared. In Cartesian coordinate space it is found that modes of frequencies lower than 30 cm−1 contribute 80% of the total mean-square fluctuation and are represented almost completely by motions in the dihedral angles. Bond angle and length fluctuations dominate in modes above 200 cm−1, but contribute less than 2% to the total mean-square fluctuation. In the low-frequency modes a good correspondence between patterns of atomic displacements was found, but on average the root-mean-square fluctuations of the Cartesian coordinate modes are 13% greater than their dihedral angle counterparts. The main effect of fluctuations in the bond angles and lengths, therefore, is to allow the dihedral angles to become more flexible. As the important subspaces determined from the two methods overlap considerably, dihedral angle space analysis can be applied to proteins too large for Cartesian coordinate space analysis

An exact theorem is proved and its implication is discussed. The theorem states that, if a large molecule, typically biological macromolecules such as proteins, undergoes small-amplitude conformational fluctuations around its native conformation in such a way that within the range of conformational fluctuations at thermal equilibrium the conformational energy surface can be approximated by a multidimensional parabola, then the mass-weighted mean-square displacement of constituent atoms is given by the sum of the contributions from each normal mode of conformational vibration, which in turn is proportional to the inverse of the square of its frequency. This theorem provides a firm theoretical basis for the fact hitherto empirically recognized in the conformational dynamics of, for instance, native proteins that very-low-frequency normal modes make dominant contributions to the conformational fluctuations at thermal equilibrium. Discussion is given on the implication of this theorem, especially on the importance of the concept of the low-frequency normal modes, even in the case where the basic assumption of the harmonicity of the energy surface does not hold.

The conformation of the hydrogen-bonded complex of a trinucleoside diphosphate (anticodon bases), a nucleic acid base (discriminator base), and an amino acid is investigated. This complex has been named C4N (complex of the four nucleotides) by one of the authors. Concerning the aminoacylation of tRNA and the genetic code, it has been proposed that C4N accepts the cognate protein amino acid by the lock-and-key relationship. The purpose of the calculation is to investigate the conformational and energetic properties of C4N from the energy minimum principle. The calculation is carried out by using the empirical potential functions. Glycine, glutamine, and valine are taken as typical cases. The formation energies are estimated. It is shown that some conformational changes are induced in the anticodon trinucleoside diphosphate by the binding of the discriminator base. Conformational changes of C4N and the amino acid are also by the binding of the amino acid to C4N.

Conformational analyses on four cyclic model peptides of the β-bend, chicle( l - or d -Phe- l -Pro-ϵ-aminocaproyl(Aca)) and cyclo( l -Pro- l - or d -Phe-Aca), were carried out both experimentally and theoretically. Chicle( d -Phe- l -Pro- Aca) was shown to exist as a single conformer taking the type II′ β-bend. The comparison of its CD spectra with those of chicle ( l -Ala- l -Ala-Aca) revealed that type I and II′ β-bends, both with α-helix-like CD spectra, can be distinguished. Chicle ( l -Phe- l -Pro-Aca) was shown to exist as a single conformer with a cis l -Phe- l -Pro peptide bond, taking the type VI β-bend. Its CD spectrum has thus been observed for the first time for the bend containing a cis peptide bond. Chicle( l -Pro- l -Phe-Aca) was shown to exist as a mixture of two conformers, the major one taking the type I β-bend with a trans Aca- l -Pro peptide bond and the minor one with a cis Aca- l -Pro peptide bond. Chicle( l -Pro- d -Phe-Aca) was suggested to exist as a mixture of two conformers, the major one taking the type II β-bend with a trans Aca- l -Pro peptide bond and the minor one with a cis Aca- l -Pro peptide bond.