One of the main methods for experimentally determining protein structure is nuclear magnetic resonance (NMR) spectroscopy. The advantage of using NMR compared to other methods is that the molecule may be studied in its natural state and environment. However, NMR is limited in its facility to analyze multi-domain molecules because of the scarcity of inter-atomic NMR constraints between the domains. In those cases it might be possible to dock the domains based on long range NMR constraints that are related to the molecule's overall structure.

We present two computational methods for rigid docking based on long range NMR constraints. The first docking method is based on the overall alignment tensor of the complex. The docking algorithm is based on the minimization of the difference between the predicted and experimental alignment tensor. In order to efficiently dock the complex we introduce a new, computationally efficient method called PATI for predicting the molecular alignment tensor based on the three-dimensional structure of the molecule. The increase in speed compared to the currently best-known method (PALES) is achieved by re-expressing the problem as one of numerical integration, rather than a simple uniform sampling (as in the PALES method), and by using a convex hull rather than a detailed representation of the surface of a molecule. Using PATI, we derive a method called PATIDOCK for efficiently docking a two-domain complex based solely on the novel idea of using the difference between the experimental alignment tensor and the predicted alignment tensor computed by PATI. We show that the alignment tensor fundamentally contains enough information to accurately dock a two-domain complex, and that we can very quickly dock the two domains by pre-computing the right set of data.

A second new docking method is based on a similar concept but using the rotational diffusion tensor. We derive a minimization algorithm for this docking method by separating the problem into two simpler minimization problems and approximating our energy function by a quadratic equation.

These methods provide two new efficient procedures for protein docking computations.