Inference of Co-Evolving Site Pairs: an Excellent Predictor of Contact Residue Pairs in Protein 3D structures

Residue-residue interactions that fold a protein into a unique three-dimensional structure and make it play a specific function impose structural and functional constraints on each residue site. Selective constraints on residue sites are recorded in amino acid orders in homologous sequences and also in the evolutionary trace of amino acid substitutions. A challenge is to extract direct dependences between residue sites by removing indirect dependences through other residues within a protein or even through other molecules. Recent attempts of disentangling direct from indirect dependences of amino acid types between residue positions in multiple sequence alignments have revealed that the strength of inferred residue pair couplings is an excellent predictor of residue-residue proximity in folded structures. Here, we report an alternative attempt of inferring co-evolving site pairs from concurrent and compensatory substitutions between sites in each branch of a phylogenetic tree. First, branch lengths of a phylogenetic tree inferred by the neighbor-joining method are optimized as well as other parameters by maximizing a likelihood of the tree in a mechanistic codon substitution model. Mean changes of quantities, which are characteristic of concurrent and compensatory substitutions, accompanied by substitutions at each site in each branch of the tree are estimated with the likelihood of each substitution. Partial correlation coefficients of the characteristic changes along branches between sites are calculated and used to rank co-evolving site pairs. Accuracy of contact prediction based on the present co-evolution score is comparable to that achieved by a maximum entropy model of protein sequences for 15 protein families taken from the Pfam release 26.0. Besides, this excellent accuracy indicates that compensatory substitutions are significant in protein evolution.Comment: 17 pages, 4 figures, and 4 tables with supplementary information of 5 figure

Robust patchwork-based watermarking method for stereo audio signals

This paper presents a patchwork-based watermarking method for stereo audio signals, which exploits the similarity of the two sound channels of stereo signals. Given a segment of stereo signal, we first compute the discrete Fourier transforms (DFTs) of the two sound channels, which yields two sets of DFT coefficients. The DFT coefficients corresponding to certain frequency range are divided into multiple subsegment pairs and a criterion is proposed to select those suitable for watermark embedding. Then a watermark is embedded into the selected subsegment pairs by modifying their DFT coefficients. The exact way of modification is determined by a secret key, the watermark to be embedded, and the DFT coefficients themselves. In the decoding process, the subsegment pairs containing watermarks are identified by another criterion. Then the secret key is used to extract the watermark from the watermarked subsegments. Compared to the existing patchwork methods for audio watermarking, the proposed method does not require knowledge of which segments of the watermarked audio signal contain watermarks and is more robust to conventional attacks