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. Introduction. – It has been recognized recently [1] that the signals generated at a single molecule (or another nano-size object) differ from signals obtained in large-scale systems consisting of ensemble of molecules. In particular, enhanced fluctuations, randomness and irreproducibility of the signals are observed in single-molecule measurements. A representative example is the mechanical signal generated in the dynamic force spectroscopy (DFS) of molecular bonds [2, 3]. The force spectroscopy of single molecules and molecular complexes has become a leading methodology for measuring biomolecular unbinding forces, which form the bases of biologically relevant molecular processes [4]. For instance, some recently studied examples include measurements of fundamental biomolecular forces in DNA unzipping [5], ALCAM-ALCAM [6], peptideantibody [7], RNAprotein [8] interactions, etc. In a typical pulling experiment in DFS based on the Atomic Force Microscopy, the ligand and receptor molecule are attached via polymer linkers on the AFM tip and the solid support (e.g glass, mica, goldsurface). The molecules are brought close to each other for certain contact time allowing them to form a bond and then pulled away until the bond breaks. The process is repeated many times. In each pulling event, changes in the deflection of the AFM cantilever as a function of distance are measured. Knowing the spring constant of the cantilever, this data can be calculated into distance dependent forces, resulting in so called force-distance curves. From these curves different parameters can be obtained, such as force needed to break a certain bond and the force loading rate. Further quantitative analysis of these data sets requires an elaborated theoretical framework [2] in order to extract the parameters of binding potential, the bond strength and the survival time. The applied force reduces the barrier between the bound and dissociated states of the binding molecules, allowing to estimate the force at which the barrier disappears and to measure the dissociation rate λ(F ). Then the natural dissociation rate at vanishing force is ex-