Problema de Steiner Euclidiano aplicado a moléculas de interesse biológico

Abstract

An old problem and of great application in the Applied Mathematics is known as problem of Steiner, with consists of the determination of a point that minimizes certain distances, problem this that was studied by famous mathematical as Fermat and Torricelli. A fundamental result in biochemistry and molecular modelling is the determination of the configurations of minimum energy (MECs) for structures such macromoleculares like proteins and DNA. The Steiner minimal trees (SMT) are seen as a useful algorithm paradigm to model these structures. In this work, we will examine how SMTs and the value of the ratio Steiner (½) compared with the MSTs are correlated with the energies MECs in a way physically significant. We verified that carbon and nitrogen atoms are Steiner points in the proteins minimal Steiner trees.