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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.
