BackgroundBiomolecules or other complex macromolecules undergo conformational transitions upon exposure to an external perturbation such as ligand binding or mechanical force. To follow fluctuations in pairwise forces between atoms or residues during such conformational changes as observed in Molecular Dynamics (MD) simulations, we developed Time-Resolved Force Distribution Analysis (TRFDA).ResultsThe implementation focuses on computational efficiency and low-memory usage and, along with the wide range of output options, makes possible time series analysis of pairwise forces variation in long MD simulations and for large molecular systems. It also provides an exact decomposition of pairwise forces resulting from 3- and 4-body potentials and a unified treatment of pairwise forces between atoms or residues. As a proof of concept, we present a stress analysis during unfolding of ubiquitin in a force-clamp MD simulation.ConclusionsTRFDA can be used, among others, in tracking signal propagation at atomic level, for characterizing dynamical intermolecular interactions (e.g. protein-ligand during flexible docking), in development of force fields and for following stress distribution during conformational changes.
Previous Atomic Force Microscopy (AFM) experiments found single layers of defect-free graphene to rupture at unexpectedly high loads in the micronewton range. Using molecular dynamics simulations, we modeled an AFM spherical tip pressing on a circular graphene sheet and studied the stress distribution during the indentation process until rupture. We found the graphene rupture force to have no dependency on the sheet size and a very weak dependency on the indenter velocity, allowing a direct comparison to experiment. The deformation showed a non-linear elastic behavior, with a two-dimensional elastic modulus in good agreement with previous experimental and computational studies. In line with theoretical predictions for linearly elastic sheets, rupture forces of non-linearly elastic graphene are proportional to the tip radius. However, as a deviation from the theory, the atomic stress concentrates under the indenter tip more strongly than predicted and causes a high probability of bond breaking only in this area. In turn, stress levels decrease rapidly towards the edge of the sheet, most of which thus only serves the role of mechanical support for the region under the indenter. As a consequence, the high ratio between graphene sheets and sphere radii, hitherto supposed to be necessary for reliable deformation and rupture studies, could be reduced to a factor of only 5-10 without affecting the outcome. Our study suggests time-resolved analysis of forces at the atomic level as a valuable tool to predict and interpret the nano-scale response of stressed materials beyond graphene.
We present a computationally efficient pairwise potential for use in molecular dynamics simulations of large graphene or carbon nanotube systems, in particular, for those under mechanical deformation, and also for mixed systems including biomolecules. Based on the Morse potential, it is only slightly more complex and computationally expensive than a harmonic bond potential, allowing such large or mixed simulations to reach experimentally relevant time scales. By fitting to data obtained from quantum mechanics (QM) calculations to represent bond breaking in graphene patches, we obtain a dissociation energy of 805 kJ mol(-1) which reflects the steepness of the QM potential up to the inflection point. A distinctive feature of our potential is its truncation at the inflection point, allowing a realistic treatment of ruptured C-C bonds without relying on a bond order model. The results obtained from equilibrium MD simulations using our potential compare favorably with results obtained from experiments and from similar simulations with more complex and computationally expensive potentials.
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