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Open Access Research article

Using diffusion distances for flexible molecular shape comparison

Yu-Shen Liu123*, Qi Li1, Guo-Qin Zheng1, Karthik Ramani4 and William Benjamin4

Author Affiliations

1 School of Software, Tsinghua University, Beijing 100084, China

2 Key Laboratory for Information System Security, Ministry of Education of China, Beijing, China

3 Tsinghua National Laboratory for Information Science and Technology, Beijing, China

4 Purdue University, West Lafayette, IN, USA

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BMC Bioinformatics 2010, 11:480  doi:10.1186/1471-2105-11-480

Published: 24 September 2010



Many molecules are flexible and undergo significant shape deformation as part of their function, and yet most existing molecular shape comparison (MSC) methods treat them as rigid bodies, which may lead to incorrect shape recognition.


In this paper, we present a new shape descriptor, named Diffusion Distance Shape Descriptor (DDSD), for comparing 3D shapes of flexible molecules. The diffusion distance in our work is considered as an average length of paths connecting two landmark points on the molecular shape in a sense of inner distances. The diffusion distance is robust to flexible shape deformation, in particular to topological changes, and it reflects well the molecular structure and deformation without explicit decomposition. Our DDSD is stored as a histogram which is a probability distribution of diffusion distances between all sample point pairs on the molecular surface. Finally, the problem of flexible MSC is reduced to comparison of DDSD histograms.


We illustrate that DDSD is insensitive to shape deformation of flexible molecules and more effective at capturing molecular structures than traditional shape descriptors. The presented algorithm is robust and does not require any prior knowledge of the flexible regions.