A polynomial time algorithm for computing the area under a GDT curve.
BACKGROUND
Progress in the field of protein three-dimensional structure prediction depends on the development of new and improved algorithms for measuring the quality of protein models. Perhaps the best descriptor of the quality of a protein model is the GDT function that maps each distance cutoff θ to the number of atoms in the protein model that can be fit under the distance θ from the corresponding atoms in the experimentally determined structure. It has long been known that the area under the graph of this function (GDT_A) can serve as a reliable, single numerical measure of the model quality. Unfortunately, while the well-known GDT_TS metric provides a crude approximation of GDT_A, no algorithm currently exists that is capable of computing accurate estimates of GDT_A.


METHODS
We prove that GDT_A is well defined and that it can be approximated by the Riemann sums, using available methods for computing accurate (near-optimal) GDT function values.


RESULTS
In contrast to the GDT_TS metric, GDT_A is neither insensitive to large nor oversensitive to small changes in model's coordinates. Moreover, the problem of computing GDT_A is tractable. More specifically, GDT_A can be computed in cubic asymptotic time in the size of the protein model.


CONCLUSIONS
This paper presents the first algorithm capable of computing the near-optimal estimates of the area under the GDT function for a protein model. We believe that the techniques implemented in our algorithm will pave ways for the development of more practical and reliable procedures for estimating 3D model quality.
Department of Computer Science, University of Northern Iowa, 305 ITTC, Cedar Falls, Iowa, 50613 USA.
Aleksandar
A
Poleksic
Model quality; Protein structure; Structure modeling; Structure prediction