# Molecular distance geometry methods: from continuous to discrete

@article{Liberti2011MolecularDG, title={Molecular distance geometry methods: from continuous to discrete}, author={Leo Liberti and Carlile Lavor and Antonio Mucherino and Nelson Maculan}, journal={Int. Trans. Oper. Res.}, year={2011}, volume={18}, pages={33-51} }

Distance geometry problems (DGP) arise from the need to position entities in the Euclidean K-space given some of their respective distances. Entities may be atoms (molecular distance geometry), wireless sensors (sensor network localization), or abstract vertices of a graph (graph drawing). In the context of molecular distance geometry, the distances are usually known because of chemical properties and nuclear magnetic resonance experiments; sensor networks can estimate their relative distance…

## 114 Citations

Recent advances on the Discretizable Molecular Distance Geometry Problem

- Computer ScienceEur. J. Oper. Res.
- 2012

DISCRETE APPROACHES FOR SOLVING MOLECULAR DISTANCE GEOMETRY PROBLEMS USING NMR DATA

- Computer Science
- 2010

This paper focuses on protein backbones and presents a methodology for computing their full-atom conformations starting from NMR data by solving two MDGPs by exploiting the coordinates of the hydrogens and known bond lengths and bond angles.

Feasibility check for the distance geometry problem: an application to molecular conformations

- Computer ScienceInt. Trans. Oper. Res.
- 2017

The main motivation to this work is to derive new pruning devices within branch and prune algorithms for instances occurring in real applications related to determination of molecular conformations, which is a particular case of the DGP.

Energy-based pruning devices for the BP algorithm applied to Distance Geometry

- Computer Science2013 Federated Conference on Computer Science and Information Systems
- 2013

Computer experiments show that the newly added pruning devices are able to improve the performance of the BP algorithm, as well as the quality (in terms of energy) of the conformations in the solution set.

Clifford Algebra and the Discretizable Molecular Distance Geometry Problem

- Computer Science
- 2015

The results suggest that a master equation might exist, what is generally not believed by many researchers, based on polyspherical coordinates which depends on di−3, i.

Polynomial cases of the Discretizable Molecular Distance Geometry Problem

- Computer Science, MathematicsArXiv
- 2011

This work discusses assumptions that bound the search tree width to a polynomial size and exploits the natural vertex order to show that the search space for feasible embeddings is discrete.

The i BP algorithm for the discretizable molecular distance geometry problem with interval data

- Computer Science, Mathematics
- 2011

This paper shows that a discretization is still possible and proposes the iBP algorithm to solve the Distance Geometry Problem in three dimensions, where some of the edge weights are subject to uncertainty within a given nonnegative interval.

Calculating the possible conformations arising from uncertainty in the molecular distance geometry problem using constraint interval analysis

- ChemistryInf. Sci.
- 2017

Modeling the Molecular Distance Geometry Problem Using Dihedral Angles

- Computer ScienceISBRA
- 2017

An alternative formulation based on dihedral angles to the molecular distance geometry problem with imprecise distance data is presented, which reduces by 2/3 the number of variables of the problem and allows us to calculate the derivatives of the standard Cartesian coordinates representation with respect to the dihedral angle.

The interval Branch-and-Prune algorithm for the discretizable molecular distance geometry problem with inexact distances

- Computer Science, MathematicsJ. Glob. Optim.
- 2013

The case where the full-atom representation of the protein backbone and some of the edge weights are subject to uncertainty within a given nonnegative interval is discussed and it is shown that a discretization is still possible and the iBP algorithm is proposed to solve the problem.

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