GreMuTRRR: A Novel Genetic Algorithm to Solve Distance Geometry Problem for Protein Structures

Nuclear Magnetic Resonance (NMR) Spectroscopy is a widely used technique to predict the native structure of proteins. However, NMR machines are only able to report approximate and partial distances between pair of atoms. To build the protein structure one has to solve the Euclidean distance geometry problem given the incomplete interval distance data produced by NMR machines. In this paper, we propose a new genetic algorithm for solving the Euclidean distance geometry problem for protein structure prediction given sparse NMR data. Our genetic algorithm uses a greedy mutation operator to intensify the search, a twin removal technique for diversification in the population and a random restart method to recover stagnation. On a standard set of benchmark dataset, our algorithm significantly outperforms standard genetic algorithms.Comment: Accepted for publication in the 8th International Conference on Electrical and Computer Engineering (ICECE 2014

Euclidean distance geometry and applications

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure

Double Variable Neighbourhood Search with Smoothing for the Molecular Distance Geometry Problem

We discuss the geometrical interpretation of a well-known smoothing operator applied to the Molecular Distance Geometry Problem (MDGP), and we then describe a heuristic approach based on Variable Neighbourhood Search on the smoothed and original problem. This algorithm often manages to find solutions having higher accuracy than other methods. This is important as small differences in the objective function value may point to completely different 3D molecular structures

Double variable neighbourhood search with smoothing for the molecular distance geometry problem

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We discuss the geometrical interpretation of a well-known smoothing operator applied to the Molecular Distance Geometry Problem (MDGP), and we then describe a heuristic approach based on Variable Neighbourhood Search on the smoothed and original problem. This algorithm often manages to find solutions having higher accuracy than other methods. This is important as small differences in the objective function value may point to completely different 3D molecular structures.4341700207218Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

On The Number Of Solutions Of The Discretizable Molecular Distance Geometry Problem

The Discretizable Molecular Distance Geometry Problem is a subset of instances of the distance geometry problem that can be solved by a combinatorial algorithm called "Branch-and-Prune". It was observed empirically that the number of solutions of YES instances is always a power of two. We perform an extensive theoretical analysis of the number of solutions for these instances and we prove that this number is a power of two with probability one. © 2011 Springer-Verlag.6831 LNCS322342Lavor, C., Liberti, L., Maculan, N., Computational experience with the molecular distance geometry problem (2006) Global Optimization: Scientific and Engineering Case Studies, pp. 213-225. , Pintér, J. (ed.) Springer, BerlinLiberti, L., Lavor, C., Maculan, N., Marinelli, F., Double variable neighbourhood search with smoothing for the molecular distance geometry problem (2009) Journal of Global Optimization, 43, pp. 207-218Saxe, J., Embeddability of weighted graphs in k-space is strongly NP-hard (1979) Proceedings of 17th Allerton Conference in Communications, Control and Computing, pp. 480-489Huang, H.X., Liang, Z.A., Pardalos, P., Some properties for the Euclidean distance matrix and positive semidefinite matrix completion problems (2003) Journal of Global Optimization, 25, pp. 3-21Hendrickson, B., The molecule problem: Exploiting structure in global optimization (1995) SIAM Journal on Optimization, 5, pp. 835-857Eren, T., Goldenberg, D., Whiteley, W., Yang, Y., Morse, A., Anderson, B., Belhumeur, P., Rigidity, computation, and randomization in network localization (2004) IEEE Infocom Proceedings, pp. 2673-2684Krislock, N., Wolkowicz, H., Explicit sensor network localization using semidefinite representations and facial reductions (2010) SIAM Journal on Optimization, 20, pp. 2679-2708Gunther, H., (1995) NMR Spectroscopy: Basic Principles, Concepts, and Applications in Chemistry, , Wiley, New YorkSchlick, T., (2002) Molecular Modelling and Simulation: An Interdisciplinary Guide, , Springer, New YorkSantana, R., Larrañaga, P., Lozano, J., Combining variable neighbourhood search and estimation of distribution algorithms in the protein side chain placement problem (2008) Journal of Heuristics, 14, pp. 519-547Lavor, C., Mucherino, A., Liberti, L., Maculan, N., Discrete approaches for solving molecular distance geometry problems using NMR data (2010) International Journal of Computational Biosciences, 1 (1), pp. 88-94Lavor, C., Liberti, L., Maculan, N., Mucherino, A., The discretizable molecular distance geometry problem Computational Optimization and Applications, , doi: 10.1007/s10589-011-9402-6Liberti, L., Lavor, C., Maculan, N., A branch-and-prune algorithm for the molecular distance geometry problem (2008) International Transactions in Operational Research, 15, pp. 1-17Mucherino, A., Lavor, C., Liberti, L., The discretizable distance geometry problem Optimization Letters, , To appear inLavor, C., Lee, J., John, A.L.S., Liberti, L., Mucherino, A., Sviridenko, M., Discretization orders for distance geometry problems Optimization Letters, , doi: 10.1007/s11590-011-0302-6Lavor, C., Mucherino, A., Liberti, L., Maculan, N., On the computation of protein backbones by using artificial backbones of hydrogens (2011) Journal of Global Optimization, 50, pp. 329-344Liberti, L., Lavor, C., Mucherino, A., Maculan, N., Molecular distance geometry methods: From continuous to discrete (2010) International Transactions in Operational Research, 18, pp. 33-51Lavor, C., Liberti, L., Maculan, N., Mucherino, A., Recent advances on the discretizable molecular distance geometry problem European Journal of Operational Research, , accepted / invited surveyBlumenthal, L., (1953) Theory and Applications of Distance Geometry, , Oxford University Press, OxfordConnelly, R., Generic global rigidity (2005) Discrete Computational Geometry, 33, pp. 549-563Brady, T., Watt, C., On products of Euclidean reflections (2006) American Mathematical Monthly, 113, pp. 826-829Lavor, C., Liberti, L., Maculan, N., (2006) The Discretizable Molecular Distance Geometry Problem, , Technical Report q-bio/0608012, arXivDong, Q., Wu, Z., A geometric build-up algorithm for solving the molecular distance geometry problem with sparse distance data (2003) Journal of Global Optimization, 26, pp. 321-333Coope, I., Reliable computation of the points of intersection of n spheres in Rn (2000) Australian and New Zealand Industrial and Applied Mathematics Journal, 42, pp. C461-C47