Persistent similarity for biomolecular structure comparison

Biomolecular structure comparison not only reveals evolutionary relationships, but also sheds light on biological functional properties. However, traditional ways to calculate structure or sequence similarity, which always involve superposition or alignment, are computationally inefficient. In this paper, we propose a new method called persistent similarity, which is based on a newly-invented method in algebraic topology, known as persistent homology. Different from all previous topological methods, persistent homology is able to embed a geometric measurement into topological invariants, thus provides a bridge between geometry and topology. After that, the topological information derived from the persistent homology analysis can be uniquely represented by a series of one-dimensional (1D) persistent Betti functions (PBFs). In this way, any complicated biomolecular structure can be represented as several 1D PBFs, and persistent similarity is defined as the quotient of intersect areas and union areas of any two PBFs. If structures have no significant topological properties, a pseudo-barcode is introduced to insure a better comparison. Further, a multiscale biomolecular representation is introduced through the multiscale rigidity function. It naturally induces a multiscale persistent similarity. The multiscale persistent similarity enables an objectiveoriented comparison. Stated differently, it facilitates the comparison of structures at any particular scale of interest. Finally, the proposed method is validated by four different cases. It is found that the persistent similarity can be used to describe the intrinsic similarities and differences between the structures very well. Particularly, it delivers one of the best results for isomer total curvature energy prediction.

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Published 26 November 2018