There are approximately 43,000 proteins whose tertiary structures have been experimentally determined and deposited in the Protein Data Bank. A large number of these protein structures have been determined through X-ray crystallography techniques, which relies on the crystallization of the protein, gathering diffraction data, and fitting a protein model to an electron density map. Solution NMR techniques are also used for protein structure determination. Unlike X-ray crystallography techniques, NMR produces a large number of distance and torsion angle constraints, which can be used to generate an ensemble of models that best satisfies both the data and the physical interactions among atoms. The goal of NMR structure refinement approaches is to achieve higher quality structure models that approach the resolution of structures determined through crystallography techniques.

The problem of protein structure prediction is a well-studied problem in computational biology. Three general classes of algorithms have emerged, based on the techniques of comparative modeling, fold recognition, and first principles methods. Knowledge-based first principles methods incorporate distance constraints from known structures into statistical models. These approaches can be contrasted with physics-based first principles approaches, which try to predict protein structure based solely upon the primary sequence and the application of detailed force fields and energy models. For a detailed summary of protein structure prediction methods, the reader is directed to recent reviews[1,2,3].

First principles protein structure prediction approaches can be applied to the problem of NMR structure refinement. A novel physics-based first principles approach, ASTRO-FOLD[4], has several merits that make it well suited to problems of this type. The NMR structure refinement problem is a heavily constrained nonlinear minimization problem when atomistic-level energy functions are used. These problems require powerful global search strategies to identify the best structures. The ASTRO-FOLD tertiary structure prediction approach combines torsion angle dynamics with a deterministic global optimization technique (αBB) and a strochastic optimization technique (conformational space annealing) to minimize a detailed atomistic-level energy function. Further improvements to this approach include constrained rotamer optimization, improved torsion angle dynamics routines, and a streamlined parallel implementation. This results of applying this approach to several test proteins will be presented.

[1] Floudas CA, Fung HK, McAllister SR, Mönningmann M, and Rajgaria R. Advances in Protein Structure Prediction and De Novo Protein Design: A Review. Chem Eng Sci. 2006;61: 966-988.

[2] Floudas CA. Research Challenges, Opportunities and Synergism in Systems Engineering and Computational Biology. AIChE J. 2005;51:1872-1884.

[3] Floudas CA. Computational Methods in Protein Structure Prediction. Biotech Bioeng, 2007, in press.

[4] Klepeis JL and Floudas CA. ASTRO-FOLD: A Combinatorial and Global Optimization Framework for Ab Initio Prediction of Three-dimensional Structures of Proteins from the Amino Acid Sequence. Biophys J, 2003;85:2119-2146.