an algebro-topological description of protein domain structure一个algebro-topological蛋白质域结构的描述.pdfVIP

An Algebro-Topological Description of Protein Domain Structure 1,2 3 3,4 1 Robert Clark Penner , Michael Knudsen , Carsten Wiuf *, Jørgen Ellegaard Andersen 1 Center for the Topology and Quantization of Moduli Spaces, Department of Mathematical Sciences, Aarhus University, Aarhus, Denmark, 2 Departments of Mathematics and Physics/Astronomy, University of Southern California, Los Angeles, California, United States of America, 3 Bioinformatics Research Centre, Aarhus University, Aarhus, Denmark, 4 Centre for Membrane Pumps in Cells and Disease, Aarhus University, Aarhus, Denmark Abstract The space of possible protein structures appears vast and continuous, and the relationship between primary, secondary and tertiary structure levels is complex. Protein structure comparison and classification is therefore a difficult but important task since structure is a determinant for molecular interaction and function. We introduce a novel mathematical abstraction based on geometric topology to describe protein domain structure. Using the locations of the backbone atoms and the hydrogen bonds, we build a combinatorial object – a so-called fatgraph. The description is discrete yet gives rise to a 2- dimensional mathematical surface. Thus, each protein domain corresponds to a particular mathematical surface with characteristic topological invariants, such as the genus (number of holes) and the number of boundary components. Both invariants are global fatgraph features reflecting the interconnectivity of the domain by hydrogen bonds. We introduce the notion of robust variables, that is variables that are robust towards minor changes in the structure/fatgraph, and show that the genus and the number of boundary compon