THE SOLUTION OF THE DISTANCE GEOMETRY PROBLEM IN PROTEIN MODELING VIA GEOMETRIC BUILDUP

A well-known problem in protein modeling is the determination of the structure of a protein with a given set of inter-atomic or inter-residue distances obtained from either physical experiments or theoretical estimates. A general form of the problem is known as the distance geometry problem in mathematics, the graph embedding problem in computer science, and the multidimensional scaling problem in statistics. The problem has applications in many other scientific and engineering fields as well such as sensor network localization, image recognition, and protein classification. We describe the formulations and complexities of the problem in its various forms, and introduce a geometric buildup approach to the problem. Central to this approach is the idea that the coordinates of the atoms in a protein can be determined one atom at a time, with the distances from the determined atoms to the undetermined ones. It can determine a structure more efficiently than other conventional approaches, yet without requiring more distance constraints than necessary. We present the general algorithm and its theory and review the recent development of the algorithm for controlling the propagation of the numerical errors in the buildup process, for determining rigid vs. unique structures, and for handling problems with inexact distances (distances with errors). We show the results from applying the algorithm to some of the model problems and justify the potential use of the algorithm in protein modeling.