Proteins are natural modular objects usually composed of several domains, each domain bearing a specific function that is mediated through its surface, which is accessible to vicinal molecules. This draws attention to an understudied characteristic of protein structures: surface, that is mostly unexploited by protein structure comparison methods. In the present work, we evaluated the performance of six shape comparison methods, among which three are based on machine learning, to distinguish between 588 multi-domain proteins and to recreate the evolutionary relationships at the protein and species levels of the SCOPe database.The six groups that participated in the challenge submitted a total of 15 sets of results. We observed that the performance of all the methods significantly decreases at the species level, suggesting that shape-only protein comparison is challenging for closely related proteins. Even if the dataset is limited in size (only 588 proteins are considered whereas more than 160,0 0 0 protein structures are experimentally solved), we think that this work provides useful insights into the current shape comparison methods performance, and highlights possible limitations to large-scale applications due to the computational cost.

In this paper, we put forward on the drive-response synchronization in shape for four-dimensional (4-D) continuous chaotic system, using the basic theory of plane curves in classical differential geometry. For 4-D continuous system, shape synchronization means the six-response systems have the same shape of chaotic attractor as the six projective systems of driver system. Numerical simulations are given to verify the theoretical analysis, which clearly shows that the shape controllers can really make two systems achieve shape synchronization in a quite short time. Moreover, a shape synchronization encryption algorithm for color image is proposed. Simulation results reveal the superiority of the proposed approach.

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