Network theory approach for data evaluation in the dynamic force spectroscopy of biomolecular interactions

Investigations of molecular bonds between single molecules and molecular complexes by the dynamic force spectroscopy are subject to large fluctuations at nanoscale and possible other aspecific binding, which mask the experimental output. Big efforts are devoted to develop methods for effective selection of the relevant experimental data, before taking the quantitative analysis of bond parameters. Here we present a methodology which is based on the application of graph theory. The force-distance curves corresponding to repeated pulling events are mapped onto their correlation network (mathematical graph). On these graphs the groups of similar curves appear as topological modules, which are identified using the spectral analysis of graphs. We demonstrate the approach by analyzing a large ensemble of the force-distance curves measured on: ssDNA-ssDNA, peptide-RNA (system from HIV1), and peptide-Au surface. Within our data sets the methodology systematically separates subgroups of curves which are related to different intermolecular interactions and to spatial arrangements in which the molecules are brought together and/or pulling speeds. This demonstrates the sensitivity of the method to the spatial degrees of freedom, suggesting potential applications in the case of large molecular complexes and situations with multiple binding sites.