# Distance Geometry in Protein Modeling

**Dr. Attila Sit / Eastern Kentucky University**

A well-known problem in protein modeling is the determination of protein structures with a given set of interatomic distances obtained from either physical experiments or theoretical estimates. A more general form of this problem is known as the distance geometry problem in mathematics. The problem can be solved in polynomial time if a complete set of exact distances is given, but is generally intractable for sparse data. We investigate the solution of the problem within a geometric buildup framework using special least-squares approximation techniques. in protein NMR, however, distances can only be measured with their rough ranges, and hence an ensemble of solutions satisfying the given constraints becomes critical to find. The structure determination problem can be formulated as an optimization problem to find the equilibrium positions and maximal possible fluctuation radii for the atoms in the protein, subject to the condition that the fluctuations should be within the given distance bounds. the formulation of the optimization problem is given. The algorithm for solving the problem is described. the test results on model proteins are presented.