Abstract
Since the advent of Molecular Dynamics (MD) in biopolymers science with the study by Karplus et al. on protein dynamics, MD has become the by foremost well established, computational technique to investigate structure and function of biomolecules and their respective complexes and interactions. The analysis of the MD trajectories (MDTs) remains, however, the greatest challenge and requires a great deal of insight, experience, and effort. Here, we introduce a new class of invariants for MDTs based on the spatial distribution of Mean-Energy values ξ(k) (L) on a 2D Euclidean space representation of the MDTs. The procedure forces one MD trajectory to fold into a 2D Cartesian coordinates system using a step-by-step procedure driven by simple rules. The ξ(k) (L) values are invariants of a Markov matrix ((1) Π), which describes the probabilities of transition between two states in the new 2D space; which is associated to a graph representation of MDTs similar to the lattice networks (LNs) of DNA and protein sequences. We also introduce a new algorithm to perform phylogenetic analysis of peptides based on MDTs instead of the sequence of the polypeptide. In a first experiment, we illustrate this algorithm for 35 peptides present on the Peptide Mass Fingerprint (PMF) of a new protein of Leishmania infantum studied in this work. We report, by the first time, 2D Electrophoresis isolation, MALDI TOF Mass Spectroscopy characterization, and MASCOT search results for this PMF. In a second experiment, we construct the LNs for 422 MDTs obtained in DNA-Drug Docking simulations of the interaction of 57 anticancer furocoumarins with a DNA oligonucleotide. We calculated the respective ξ(k) (L) values for all these LNs and used them as inputs to train a new classifier with Accuracy = 85.44% and 84.91% in training and validation respectively. The new model can be used as scoring function to guide DNA-Drug Docking studies in drug design of new coumarins for PUVA therapy. The new phylogenetics analysis algorithms encode information different from sequence similarity and may be used to analyze MDTs obtained in Docking or modeling experiments for any classes of biopolymers. The work opens new perspective on the analysis and applications of MD in polymer sciences.