A correlation force spectrometer for single molecule measurements under tensile load

Abstract

The dynamical-mechanical properties of a small region of fluid can be measured using two closely spaced thermally stimulated micrometer-scale cantilevers. We call this technique correlation force spectroscopy (CFS). We describe an instrument that is designed for characterizing the extensional properties of polymer molecules that straddle the gap between the two cantilevers and use it to measure the stiffness and damping (molecular friction) of a dextran molecule. The device is based on a commercial atomic force microscope, into which we have incorporated a second antiparallel cantilever. The deflection of each cantilever is measured in the frequency range dc–1 MHz and is used to generate the cross-correlation at equilibrium. The main advantage of cross-correlation measurements is the reduction in thermal noise, which sets a fundamental noise limit to force resolution. We show that the thermal noise in our cross-correlation measurements is less than one third of the value for single-cantilever force microscopy. The dynamics of the cantilever pair is modeled using the deterministic motion of a harmonic oscillator initially displaced from equilibrium, which yields the equilibrium auto and cross-correlations in cantilever displacement via the fluctuation-dissipation theorem. Fitted parameters from the model (stiffness and damping) are used to characterize the fluid at equilibrium, including any straddling molecules.