Using a Distributed SDP Approach to Solve Simulated Protein Molecular Conformation Problems

This chapter presents various enhancements to the DISCO algorithm (originally introduced by Leung and Toh(SIAM J. Sci. Comput. 31:4351–4372, 2009) for anchor-free graph realization in $${\mathbb{R}}^{d}$$ ) for applications to conformation of protein molecules in $${\mathbb{R}}^{3}$$ . In our enhanced DISCO algorithm for simulated protein molecular conformation problems, we have incorporated distance information derived from chemistry knowledge such as bond lengths and angles to improve the robustness of the algorithm. We also designed heuristics to detect whether a subgroup is well localized and significantly improved the robustness of the stitching process. Tests are performed on molecules taken from the Protein Data Bank. Given only 20% of the interatomic distances less than 6Åthat are corrupted by high level of noises (to simulate noisy distance restraints generated from nuclear magnetic resonance experiments), our improved algorithm is able to reliably and efficiently reconstruct the conformations of large molecules. For instance, given 20% of interatomic distances which are less than 6Åand are corrupted with 20% multiplicative noise, a 5,600-atom conformation problem is solved in about 30min with a root-mean-square deviation (RMSD) of less than 1Å.