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Topology of proteins

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Classification of Molecular Structures

Proteins are the main building blocks and functional units in the organism. A protein is a linear macromolecule composed of amino acids connected by peptide bonds. The linear structure does not however manifest itself as the protein folds into a complicated 3-dimensional shape.

The function of a protein is determined by its shape. However, current methods of determining a protein’s function use its amino acids sequence rather than its shape. The most natural way of modeling protein’s structure is via 3-dimensional simplicial complexes, as follows. Each atom is a point in space and a vertex in the complex. If the distance between two atoms is less that the sum of their van der Waals radii they share electrons and are connected by a bond which is represented as an edge of the complex. If three atoms share electrons they are connected into a triangle. Thus the simplicial complex is a combination of vertices, edges and triangles.

We classify proteins by computing the number of “tunnels” and “voids” in their structure. We apply the persistent homology algorithm to discover important, large-scale, features of the molecule. The very first fact about a given protein established by our algorithm is whether it is ring-like or hand-like. Second, we measure, indirectly, the dimensions of these features. In particular, such a computation will tell us if the protein can hold a DNA molecule. Further, we apply this approach to discover other types of docking sites such as ones of protein-protein interactions. The significance of these techniques lies in our ability to use computers to process newly discovered as well the thousands of known proteins in order to determine their function with a high degree of confidence. The algorithms will also apply to inorganic molecules, as well as synthetic molecules, drugs, etc.


See also Applications of Computational Topology by Christopher Johnson.