Search

The Lande subtraction method has been widely used in Coulomb problems, but the momentum coordinate p∈(0,∞) is assumed. In past applications, a very large range of p was used for accuracy. We derive the supplementary formulation with p∈(0,p_{max}) at reasonably small p_{max} for practical calculations. With the recipe, accuracy of the hydrogenic eigenspectrum is dramatically improved compared to the ordinary Lande formula by the same momentum grids. We apply the present formulation to strong-field atomic above-threshold ionization and high-order harmonic generations. We demonstrate that the proposed momentum space method can be another practical theoretical tool for atomic strong-field problems in addition to the existing methods.

A coarse-grained off-lattice model that is not biased in any way to the native state is proposed to fold proteins. To predict the native structure in a reasonable time, the model has included the essential effects of water in an effective potential. Two new ingredients, the dipole-dipole interaction and the local hydrophobic interaction, are introduced and are shown to be as crucial as the hydrogen bonding. The model allows successful folding of the wild-type sequence of protein G and may have provided important hints to the study of protein folding.

Lattice models, for their coarse-grained nature, are best suited for the study of the "designability problem," the phenomenon in which most of the about 16 000 proteins of known structure have their native conformations concentrated in a relatively small number of about 500 topological classes of conformations. Here it is shown that on a lattice the most highly designable simulated protein structures are those that have the largest number of surface-core switchbacks. A combination of physical, mathematical, and biological reasons that causes the phenomenon is given. By comparing the most foldable model peptides with protein sequences in the Protein Data Bank, it is shown that whereas different models may yield similar designabilities, predicted foldable peptides will simulate natural proteins only when the model incorporates the correct physics and biology, in this case if the main folding force arises from the differing hydrophobicity of the residues, but does not originate, say, from the steric hindrance effect caused by the differing sizes of the residues.

Analysis of the geometric properties of a mean-field HP model on a square lattice for protein structure shows that structures with a large number of switchbacks between surface and core sites are chosen favorably by peptides as unique ground states. Global comparison of model (binary) peptide sequences with concatenated (binary) protein sequences listed in the Protein Data Bank and the Dali Domain Dictionary indicates that the highest correlation occurs between model peptides choosing the favored structures and those portions of protein sequences containing alpha helices.