Effects of Viscoelastic Cantilever - Sample Interaction on Laser Beam Deflection in MAC Mode MRFM

Abstract

Amplitude and phase of a laser beam reflected from an oscillating cantilever tip in Magnetic AC (MAC) mode of Molecular Recognition Force Microscopy (MRFM) are theoretically investigated by taking into account both the spring constant of the tip/crosslinker/antibody/antigen complex and hydrodynamical cantilever - sample interaction. Analytical results are obtained based on some geometrical specifications of a typical cantilever - sample MRFM system. For high frequencies of the driving magnetic field the laser beam deflection is mainly due to the cantilever deformation and the amplitude of the tip oscillations is strongly damped. Therefore high frequencies are not favourable for biologically relevant studies. At low frequencies, a specific effect of apparent oscillation damping is predicted at a certain relation between the spring constants of the cantilever (kc) and the tip/crosslinker/antibody/antigen complex (ka). In this specific regime characterized by a critical ratio ka/kc = 8, the cantilever tip oscillates preserving constant zero slope, so that the amplitude of the beam deflection is zero. With growing frequencies the amplitude of the beam deflection increases. It also grows at a constant frequency if ka/kc deviates from its critical value 8. Since comparable values of ka and kc and low frequencies are desirable for better accuracy of the measurements, the effect of apparent damping has to be always taken into account when interpreting the experimental data. A Matlab movie demonstrates the simulation of the MRFM experimental setup in different regimes characterized by the values of the magnetic field frequency and γ = 3 ka/kc (www.welcome.to/biophysics).