Optimal sensitivity for molecular recognition MAC-mode AFM

Molecular recognition force microscopy (MRFM) using the magnetic AC mode (MAC mode) atomic force microscope (AFM) was recently investigated to locate and probe recognition sites. A flexible crosslinker carrying a ligand is bound to the tip for the molecular recognition of receptors on the surface of a sample. In this report, the driving frequency is calculated which optimizes the sensitivity (S). The sensitivity of MRFM is defined as the relative change of the magnetically excited cantilever deflection amplitude arising from a crosslinker/antibody/antigen connection that is characterized by a very small force constant. The sensitivity is calculated in a damped oscillator model with a certain value of quality factor Q, which, together with load, defines the frequency response (unloaded oscillator shows resonance at Q > 0.707). If Q < 1, the greatest value of S corresponds to zero driving frequency omega (measured in units of eigenfrequency). Therefore, for Q < 1, MAC-mode has no advantage in comparison with DC-mode. Two additional extremes are found at omegaL = (1 - 1/Q)(1/2) and omegaR = (1 + 1/Q)(1/2), with corresponding sensitivities S(L) = Q2/(2Q - 1), S(R) = Q2/(2Q + 1). The L-extreme exists only for Q > 1, and then S(L) > S(R), i.e. the L-extreme is the main one. For Q > 1, S(L) > 1, and for Q > 2.41, S(R) > 1. These are the critical Q-values, above which selecting driving frequency equal to sigmaL or sigmaR brings advantage to MAC mode vs. DC mode. Satisfactory quality of the oscillator model is demonstrated by comparison of some results with those calculated within the classical description of cantilevers.