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A number of recently discovered protein structures incorporate a rather unexpected structural feature: a knot in the polypeptide backbone. These knots are extremely rare, but their occurrence is likely connected to protein function in as yet unexplored fashion. Our analysis of the complete Protein Data Bank reveals several new knots which, along with previously discovered ones, can shed light on such connections. In particular, we identify the most complex knot discovered to date in human ubiquitin hydrolase, and suggest that its entangled topology protects it against unfolding and degradation by the proteasome. Knots in proteins are typically preserved across species and sometimes even across kingdoms. However, we also identify a knot which only appears in some transcarbamylases while being absent in homologous proteins of similar structure. The emergence of the knot is accompanied by a shift in the enzymatic function of the protein. We suggest that the simple insertion of a short DNA fragment into the gene may suffice to turn an unknotted into a knotted structure in this protein.
We study the space of all compact structures on a two-dimensional square lattice of size $N=6times6$. Each structure is mapped onto a vector in $N$-dimensions according to a hydrophobic model. Previous work has shown that the designabilities of struc
This chapter describes gene expression analysis by Singular Value Decomposition (SVD), emphasizing initial characterization of the data. We describe SVD methods for visualization of gene expression data, representation of the data using a smaller num
We analyze the complex networks associated with brain electrical activity. Multichannel EEG measurements are first processed to obtain 3D voxel activations using the tomographic algorithm LORETA. Then, the correlation of the current intensity activat
Recent literatures reported blue-green emission from amyloid fibril as exclusive signature of fibril formation. This unusual visible luminescence is regularly used to monitor fibril growth. Blue-green emission has also been observed in crystalline pr
We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer how they