It has recently been shown that in proteins the atomic mean-square displacement (or B-factor) can be related to the number of the neighboring atoms (or protein contact number), and that this relationship allows one to compute the B-factor profiles directly from protein contact number. This method, referred to as the protein contact model, is appealing, since it requires neither trajectory integration nor matrix diagonalization. As a result, the protein contact model can be applied to very large proteins and can be implemented as a high-throughput computational tool to compute atomic fluctuations in proteins. Here, we show that this relationship can be further refined to that between the atomic mean-square displacement and the weighted protein contact-number, the weight being the square of the reciprocal distance between the contacting pair. In addition, we show that this relationship can be utilized to compute the cross-correlation of atomic motion (the B-factor is essentially the auto-correlation of atomic motion). For a nonhomologous dataset comprising 972 high-resolution X-ray protein structures (resolution <2.0 A and sequence identity <25%), the mean correlation coefficient between the X-ray and computed B-factors based on the weighted protein contact-number model is 0.61, which is better than those of the original contact-number model (0.51) and other methods. We also show that the computed correlation maps based on the weighted contact-number model are globally similar to those computed through normal model analysis for some selected cases. Our results underscore the relationship between protein dynamics and protein packing. We believe that our method will be useful in the study of the protein structure-dynamics relationship.

Recently, we have developed a method (Shih et al., Proteins: Structure, Function, and Bioinformatics 2007;68: 34-38) to compute correlation of fluctuations of proteins. This method, referred to as the protein fixed-point (PFP) model, is based on the positional vectors of atoms issuing from the fixed point, which is the point of the least fluctuations in proteins. One corollary from this model is that atoms lying on the same shell centered at the fixed point will have the same thermal fluctuations. In practice, this model provides a convenient way to compute the average dynamical properties of proteins directly from the geometrical shapes of proteins without the need of any mechanical models, and hence no trajectory integration or sophisticated matrix operations are needed. As a result, it is more efficient than molecular dynamics simulation or normal mode analysis. Though in the previous study the PFP model has been successfully applied to a number of proteins of various folds, it is not clear to what extent this model will be applied. In this article, we have carried out the comprehensive analysis of the PFP model for a dataset comprising 972 high-resolution X-ray structures with pairwise sequence identity or=0.5. Our result shows that the fixed-point model is indeed quite general and will be a useful tool for high throughput analysis of dynamical properties of proteins.

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Carbon nanoparticles, like nanocones and nanodiscs, can be obtained by mechanical treatment of carbon nanofilaments. Microstructural studies suggest that in nanocones the conical graphene stacking with progressively increasing apex (cone) angles does not fully agree with current theoretical geometry models, such as a closed cones model and a cone-helix model. The unusual stacking form of nanocones was taken into account in a modified cone-helix model. The formation mechanism of the distinctive microstructure is attributed to the inclined anchoring effect, and the relaxation of internal stresses, which were induced by the confined pyrolysis process, resulting in easier disintegration by sonication the nanofilaments. This is disclosed for the first time in literature regarding the attainment of uniform carbon nanoparticles.