Graph theory from theoretical informatics is applied in this work in the context of recognizing, following in time, and statistically analyzing conformations in Molecular Dynamics (MD) trajectories.<br/>At the granularity level chosen in this work, our algorithm converts the cartesian coordinates of atoms of snapshots along trajectories, into mixed graphs such that vertices represent atoms of the molecular system and directed/undirected edges represent the bonds formed between these atoms (covalent bond, hydrogen bonds, intermolecular electrostatic interactions, etc., depending on the system). In order to identify a conformational change, the algorithm applies an isomorphism test that allows decide if two graphs are identical or not. In our case, a conformational change is characterized by a change either in the covalent bonds or/and in the intermolecular bonds. These bond dynamics (forming/breaking) represent, in the graph terminology, a change of the edge sets.<br/>The exploration of different conformations can be seen as an exploration of different graph topologies. Hence, two conformations are identical if and only if their corresponding graphs are isomorphic, i.e., the two graphs have the same set of bonds (edges) connected to the same set of atoms type (vertices with the same color).<br/>The use of graph theory methods does not only provide a direct and fast methodology to identify conformers, but also allows provide all transitions (interconversion reactions) that have been observed between the different conformers.<br/>Our algorithm has been tested and validated on DFT-MD and QM-MM trajectories of gas phase molecules and clusters. We will in particular illustrate results for peptides of increasing size and complexity. The immediate transferability of the algorithm is furthermore demonstrated on more complex air/liquid water interface. We designed our algorithm in a way that it can be extended and can take into account any types of bonds and parameters and then can be applied to any molecular system. Hence, ongoing work is currently analyzing reaction networks along (de)hydrogenation catalysis, this will be illustrated here as well.

Combining graph theory and molecular dynamics simulations: Automatic analyses of the molecular conformations and their changes over time

ACS Spring Meeting 2021

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