Internal fluctuations in globular proteins

Internal packing conditions and fluctuations of amino acid residues in globular proteins

In order to investigate the environmental conditions of amino acid residues in protein molecules, four kinds of packing studies (atomic, geometric, hydrophobic and hydration) were formulated and tested on two proteins; bovine pancreatic trypsin inhibitor (BPTI) and bovine pancreatic ribonuclease S (RNase S). The inter-relationship of these packings on the fluctuations of amino acid residues was analysed by comparing the packing results with the dynamical studies, such as the root-mean-square-deviation values of atomic displacements obtained from the trajectories of molecular dynamics simulation, temperature factor information from crystal structures and residue fluctuations in proteins from continuum model. These analyses yield information about the most fluctuating and most stabilizing residue sites. Comparison of the results obtained by these methods indicate a good agreement, specifying an inverse correlation between the residue packing and fluctuations. This kind of study is helpful in identifying the specific residue sites such as nucleation, receptor binding and antigenic determining sites which in a way indirectly correlates with the functional residues in protein molecules.

Differential equation model to study dynamic behaviour of globular proteins

By regarding the globular proteins as spheroidal shaped bodies of uniform density, a differential equation model to study their low amplitude fluctuations was developed. It was then applied to the crystal structures of pancreatic trypsin inhibitor and ferrocytochrome c. The results were tested by comparing them with those of the dynamic simulation and temperature factor studies on the same proteins.

Biological functions of low-frequency vibrations (phonons). III. Helical structures and microenvironment

Low-frequency vibrations in biomacromolecules possess significant biological functions. In this paper, the alpha-helix element is compared with a mass-distributed spring. Based on this, a set of intuitive and easily handled equations are derived for predicting the fundamental frequencies of helical structures in protein molecules. As shown in the equations, the fundamental frequency depends not only on the constituents of a helix itself but also on its microenvironment. The calculated results agree with the observations. The calculations also demonstrate that the low-frequency vibrations with wave number of approximately 30 cm-1 do not necessarily arise from motions that involve either all or very large portions of the protein molecule as previously thought; a piece of helix containing more than 10 residues and surrounded by a proper microenvironment can also generate such low-frequency motions. Furthermore , we illustrate that the low-frequency motions are closely related to the native state of a protein molecule. Upon denaturation, which is accompanied by a radical change of the relevant microenvironment, the original fundamental frequency also disappears. Consequently, this kind of special frequency termed activating low frequency can serve as a dynamic criterion in identifying whether a biomacromolecule is in its native state. The energy of a phonon excited by this kind of low-frequency vibration is of the same order of magnitude as the average enthalpy value per residue measured during conformational change in some protein molecules. Therefore, there must be some intrinsic relation between the allosteric transitions of protein molecules and their low-frequency motions.