Modeling of Biomolecular Systems Interactions, Dynamics, and Allostery: Bridging Experiments and Computations - September 10-14, 2014, Istanbul, Turkey

Modeling of Biomolecular Systems Interactions, Dynamics, and Allostery Session VIII Abstracts

Fractal Structure of Interaction Pathways in Proteins and Prediction of Allosteric Paths Burak Erman . Koc University, Sariyer Istanbul, Turkey. Information from one point to another in a protein proceeds along fractal paths. The problem is that of a random walk on fractal structures. We propose a simple computational method to determine the minimum number of steps to move between two distant points in the protein, which leads to the Hausdorff dimension of interaction pathways. The magnitude of the dimension depends on the range of interactions. We define the range of interaction as the radius of a sphere in which a central residue interacts with other residues inside this sphere. At short interaction length scales the Hausdorff dimension approaches 2.0 which is below the fractal dimension 2.55 of a liquid just above the glass transition temperature. At length scales above 6.8 Angstroms, the fractal dimension of interaction pathways in proteins exhibits a constant universal value around 1.3. The fractal path problem in a protein is equivalent to the bond percolation problem. We propose a step by step method, based on the successive powers of the contact matrix of a protein, to determine percolation clusters and the residues on the most probable fractal path between two points. The problem is of special interest for studying allosteric paths in proteins. Sample calculations on several proteins show that residues on most probable paths determined by the present model are mostly conserved residues.

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