Weighted and unweighted network of amino acids within protein

The information regarding the structure of a single protein is encoded in the network of interacting amino acids. Considering each protein as a weighted and unweighted network of amino acids we have analyzed a total of forty nine protein structures that covers the three branches of life on earth. Our results show that the probability degree distribution of network connectivity follows Poisson's distribution; whereas the probability strength distribution does not follow any known distribution. However, the average strength of amino acid node depends on its degree (k). For some of the proteins, the strength of a node increases linearly with k. On the other hand, for a set of other proteins, although the strength increases linaerly with k for smaller values of k, we have not obtained any clear functional relationship of strength with degree at higher values of k. The results also show that the weight of the amino acid nodes belonging to the highly connected nodes tend to have a higher value. The result that the average clustering coefficient of weighted network is less than that of unweighted network implies that the topological clustering is generated by edges with low weights. The ratio of average clustering coefficients of protein network to that of the corresponding classical random network varies linearly with the number (N) of amino acids of a protein; whereas the ratio of characteristic path lengths varies logarithmically with N. The power law behaviour of clustering coefficients of weighted and unweighted network as a function of degree k indicates that the network has a signature of hierarchical network. It has also been observed that the network is of assortative type

Mean-field theory for scale-free random networks

Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study the scaling properties of the recently introduced scale-free model, that can account for the observed power-law distribution of the connectivities. We develop a mean-field method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the scaling exponents. The mean-field method can be used to address the properties of two variants of the scale-free model, that do not display power-law scaling.Comment: 19 pages, 6 figure

Quantum Dot and Hole Formation in Sputter Erosion

Recently it was experimentally demonstrated that sputtering under normal incidence leads to the formation of spatially ordered uniform nanoscale islands or holes. Here we show that these nanostructures have inherently nonlinear origin, first appearing when the nonlinear terms start to dominate the surface dynamics. Depending on the sign of the nonlinear terms, determined by the shape of the collision cascade, the surface can develop regular islands or holes with identical dynamical features, and while the size of these nanostructures is independent of flux and temperature, it can be modified by tuning the ion energy

Quantum Dot and Hole Formation in Sputter Erosion

Recently it was experimentally demonstrated that sputtering under normal incidence leads to the formation of spatially ordered uniform nanoscale islands or holes. Here we show that these nanostructures have inherently nonlinear origin, first appearing when the nonlinear terms start to dominate the surface dynamics. Depending on the sign of the nonlinear terms, determined by the shape of the collision cascade, the surface can develop regular islands or holes with identical dynamical features, and while the size of these nanostructures is independent of flux and temperature, it can be modified by tuning the ion energy

Nanowire formation on sputter eroded surfaces

Rotated ripple structures (RRS) on sputter eroded surfaces are potential candidates for nanoscale wire fabrication. We show that the necessary condition for RRS formation is that the width of the collision cascade in the longitudinal direction has to be larger than that in the transverse direction, which can be achieved by using high energy ion beams. By calculating the structure factor for the RRS we find that they are more regular and their amplitude is more enhanced compared to the much studied ripple structure forming in the linear regime of sputter erosion.Comment: 3 pages, 5 figures, 2 column revtex format, submitted to Appl. Phys. Let