Systematic conformational search with constraint satisfaction

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Includes bibliographical references (p. 170-177).Determining the conformations of biological molecules is a high scientific priority for biochemists and for the pharmaceutical industry. This thesis describes a systematic method for conformational search, an application of the method to determining the structure of the formyl-Met-Leu-Phe-OH (fMLF)peptide by solid-state NMR spectroscopy, and a separate project to determine the structure of a protein-DNA complex by X-ray crystallography. The purpose of the systematic search method is to enumerate all conformations of a molecule (at a given level of torsion angle resolution) that satisfy a set of local geometric constraints. Constraints would typically come from NMR experiments, but applications such as docking or homology modelling could also give rise to similar constraints. The molecule to be searched is partitioned into small subchains so that the set of possible conformations for the whole molecule may be constructed by merging the feasible conformations for the parts. However, instead of using a binary tree for straightforward divide-and-conquer, four innovations are introduced: (1) OMNIMERGE searches a subproblem for every possible subchain of the molecule. Searching every subchain provides the advantage that every possible merge is available; by choosing the most favorable merge for each subchain, the bottleneck subchain(s) and therefore the whole search may be completed more efficiently. (2) A cost function evaluates alternative divide-and-conquer trees, provided that a preliminary OMNIMERGE search of the molecule has been completed. Then dynamic programming determines the optimal partitioning or "merge-tree" for the molecule; this merge-tree can be used to improve the efficiency of future searches.(cont.) (3) PROPAGATION shares information by enforcing arc consistency between the solution sets of overlapping subchains. By filtering the solution set of each subchain, infeasible conformations are discarded rapidly. (4) An A* function prioritizes each subchain based on estimated future costs. Subchains with sufficiently low priority can be skipped, which improves efficiency. A common theme of these four ideas is to make good choices about how to break the large search problem into lower-dimensional subproblems. These novel algorithms were implemented and the effectiveness of each is demonstrated on a well-constrained peptide with 40 degrees of freedom.by Lisa Tucker-Kellogg.Ph.D

OmniMerge: A Systematic Approach to Constrained Conformational Search

OmniMerge performs a systematic search to enumerate all conformations of a molecule (at a given level of torsion-angle resolution) that satisfy a set of local geometric constraints. Constraints would typically come from NMR experiments, but applications such as docking or homology modeling could also give rise to similar constraints. The molecule to be searched is partitioned into small subchains so that the set of possible conformations for the whole molecule may be constructed by merging the feasible conformations for the subchain parts. However, instead of using a binary tree for straightforward divide-and-conquer, OmniMerge defines a sub-problem for every possible subchain of the molecule. Searching every subchain provides a counter-intuitive advantage: with every possible subdivision available for merging, one may choose the most favorable merge for each subchain, particularly for the bottleneck chain(s). Improving the bottleneck step may therefore cause the whole search to be completed more quickly. Finally, to discard infeasible conformations more rapidly, OmniMerge filters the solution set of each subchain based on compatibility with the solutions sets of all overlapping subchains. These two innovations—choosing the most favorable merges and enforcing consistency between overlapping subchains—yield significant improvements in run time. By determining the extent of structural variability permitted by a set of constraints, OmniMerge offers the potential to aid error analysis and improve confidence for NMR results on peptides and moderate-sized molecules.Singapore-MIT Alliance (SMA

Systematic Conformational Search with Constraint Satisfaction

Throughout biological, chemical, and pharmaceutical research,conformational searches are used to explore the possiblethree-dimensional configurations of molecules. This thesis describesa new systematic method for conformational search, including anapplication of the method to determining the structure of a peptidevia solid-state NMR spectroscopy. A separate portion of the thesis isabout protein-DNA binding, with a three-dimensional macromolecularstructure determined by x-ray crystallography.The search method in this thesis enumerates all conformations of amolecule (at a given level of torsion angle resolution) that satisfy aset of local geometric constraints, such as constraints derived fromNMR experiments. Systematic searches, historically used for smallmolecules, generally now use some form of divide-and-conquer forapplication to larger molecules. Our method can achieve a significantimprovement in runtime by making some major and counter-intuitivemodifications to traditional divide-and-conquer:(1) OmniMerge divides a polymer into many alternative pairs ofsubchains and searches all the pairs, instead of simply cutting inhalf and searching two subchains. Although the extra searches mayappear wasteful, the bottleneck stage of the overall search, which isto re-connect the conformations of the largest subchains, can be greatlyaccelerated by the availability of alternative pairs of sidechains.(2) Propagation of disqualified conformations acrossoverlapping subchains can disqualify infeasible conformations veryrapidly, which further offsets the cost of searching the extrasubchains of OmniMerge.(3) The search may be run in two stages, once at low-resolutionusing a side-effect of OmniMerge to determine an optimalpartitioning of the molecule into efficient subchains; then again athigh-resolution while making use of the precomputed subchains.(4) An A* function prioritizes each subchain based onestimated future search costs. Subchains with sufficiently lowpriority can be omitted from the search, which improves efficiency.A common theme of these four ideas is to make good choices about howto break the large search problem into lower-dimensional subproblems.In addition, the search method uses heuristic local searches withinthe overall systematic framework, to maintain the systematic guaranteewhile providing the empirical efficiency of stochastic search.These novel algorithms were implemented and the effectiveness of eachinnovation is demonstrated on a highly constrained peptide with 40degrees of freedom