The nano-scale viscoelasticity using atomic force microscopy in liquid environment

We measured viscoelasticity of two nanoscale systems, single protein molecules and molecular layers of water confined between solid walls. In order to quantify the viscoelastic response of these nanoscale systems in liquid environment, the measurements are performed using two types of atomic force microscopes (AFMs), which employ different detection schemes to measure the cantilever response. We used a deflection detection scheme, available in commercial AFMs, that measures cantilever bending and a fibre-interferometer based detection which measures cantilever displacement. The hydrodynamics of the cantilever is modelled using Euler-Bernoulli equation with appropriate boundary conditions which accommodate both detection schemes. In a direct contradiction with many reports in the literature, the dissipation coefficient of a single octomer of titin I27₈ is found to be immeasurably low. The upper bound on the dissipation coefficient is 5 × 10^-7 kg s^-1, which is much lower than the reported values. The entropic stiffness of single unfolded domains of protein measured using both methods is in the range of 10 mN m^-1. We show that in a conventional deflection detection measurement, the phase of the bending signal can be a primary source of artefacts in the dissipation estimates. It is recognized that the measurement of cantilever displacement, which has negligibly small phase lag due to hydrodynamics of the cantilever at low excitation frequencies, is better suited for ensuring artefact-free measurement of viscoelasticity compared to the measurement of the cantilever bending. Further, it was possible to measure dissipation in molecular layers of water confined between the tip and the substrate using fibre interferometer based AFM with similar experimental parameters. It confirms that the dissipation coefficient of a single I27₈ is below the detection limit of AFM. The results shed light on the discrepancy observed in the measured diffusional dynamics of protein collapse measured using Force spectroscopic techniques and single-molecule optical techniques.