Extending the geometric build-up algorithm for the molecular distance geometry problem
Information Processing Letters
Solving molecular distance geometry problems by global optimization algorithms
Computational Optimization and Applications
An SDP-Based Divide-and-Conquer Algorithm for Large-Scale Noisy Anchor-Free Graph Realization
SIAM Journal on Scientific Computing
On the number of solutions of the discretizable molecular distance geometry problem
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
The discretizable molecular distance geometry problem
Computational Optimization and Applications
On the number of realizations of certain Henneberg graphs arising in protein conformation
Discrete Applied Mathematics
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Nuclear magnetic resonance (NMR) structure modeling usually produces a sparse set of inter-atomic distances in protein. In order to calculate the three-dimensional structure of protein, current approaches need to estimate all other ``missing'' distances to build a full set of distances. However, the estimation step is costly and prone to introducing errors. In this report, we describe a geometric build-up algorithm for solving protein structure by using only a sparse set of inter-atomic distances. Such a sparse set of distances can be obtained by combining NMR data with our knowledge on certain bond lengths and bond angles. It can also include confident estimations on some ``missing'' distances. Our algorithm utilizes a simple geometric relationship between coordinates and distances. The coordinates for each atom are calculated by using the coordinates of previously determined atoms and their distances. We have implemented the algorithm and tested it on several proteins. Our results showed that our algorithm successfully determined the protein structures with sparse sets of distances. Therefore, our algorithm reduces the need of estimating the ``missing'' distances and promises a more efficient approach to NMR structure modeling.