Recent advances on the interval distance geometry problem

Douglas Gonçalves (1) , Antonio Mucherino (2) , Carlile Lavor (3) , Leo Liberti (4)

1 UFSC - Universidade Federal de Santa Catarina = Federal University of Santa Catarina [Florianópolis]
2 MIMETIC - Analysis-Synthesis Approach for Virtual Human Simulation
3 IMECC - Instituto de Matemática, Estatística e Computação Científica [Brésil]
4 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

We discuss a discretization-based solution approach for a classic problem in global 1 optimization, namely the distance geometry problem (DGP). We focus our attention on a par-1 2 ticular class of the DGP which is concerned with the identification of the conformation of 3 biological molecules. Among the many relevant ideas for the discretization of the DGP in 4 the literature, we identify the most promising ones and address their inherent limitations 5 to application to this class of problems. The result is an improved method for estimating 2 6 3D structures of small proteins based only on the knowledge of some distance restraints 7 between pairs of atoms. We present computational results showcasing the usefulness of the 8 new proposed approach. Proteins act on living cells according to their geometric and chem-9 ical properties: finding protein conformations can be very useful within the pharmaceutical 10 industry in order to synthesize new drugs.

Mots clés: Distance geometry; Molecular conformation; Discretization

Domaines: Recherche opérationnelle [math.OC]; Géométrie algorithmique [cs.CG]; Mathématique discrète [cs.DM]

Douglas Gonçalves, Antonio Mucherino, Carlile Lavor, Leo Liberti. Recent advances on the interval distance geometry problem. Journal of Global Optimization, 2017, 69 (3), pp.525-545. ⟨10.1007/s10898-016-0493-6⟩. ⟨hal-02105295⟩