Comparing protein structures and inferring functions with a novel three-dimensional Yau–Hausdorff method

Abstract

Structures and functions of proteins play various essential roles in biological processes. The functions of newly discovered proteins can be predicted by comparing their structures with that of known-functional proteins. Many approaches have been proposed for measuring the protein structure similarity, such as the template-modeling (TM)-score method, GRaphlet (GR)-Align method as well as the commonly used root-mean-square deviation (RMSD) measures. However, the alignment comparisons between the similarity of protein structure cost much time on large dataset, and the accuracy still have room to improve. In this study, we introduce a new three-dimensional (3D) Yau–Hausdorff distance between any two 3D objects. The (3D) Yau–Hausdorff distance can be used in particular to measure the similarity/dissimilarity of two proteins of any size and does not need aligning and superimposing two structures. We apply structural similarity to study function similarity and perform phylogenetic analysis on several datasets. The results show that (3D) Yau–Hausdorff distance could serve as a more precise and effective method to discover biological relationships between proteins than other methods on structure comparison.

Communicated by Ramaswamy H. Sarma

Keywords:

• Three-dimensional Yau–Hausdorff distance
• structure comparison
• classification
• protein function
• phylogenetic analysis

Acknowledgements

The authors wish to thank the Department of Mathematical Science at Tsinghua University for providing the work space and library facilities.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This study is supported by the National Natural Sciences Foundation of China [91746119], Tsinghua University startup fund. The funders did not take part in study design; in collection and analysis of data; in the writing of the manuscript; and in the decision to publish this manuscript.