Graphical method for force analysis: macromolecular mechanics with atomic force microscopy.

We present a graphical method for a unifying, quantitative analysis of molecular bonding-force measurements by atomic force microscopy (AFM). The method is applied to interpreting a range of phenomena commonly observed in the experimental AFM measurements of noncovalent, weak bonds between biological macromolecules. The analysis suggests an energy landscape underlying the intermolecular force and demonstrates that many observations, such as "snaps-on," "jumps-off," and hysteresis loops, are different manifestations of a double-well energy landscape. The analysis gives concrete definitions for the operationally defined "attractive" and "adhesive" forces in terms of molecular parameters. It is shown that these operationally defined quantities are usually functions of the experimental setup, such as the stiffness of the force probe and the rate of its movement. The analysis reveals a mechanical instability due to the multistate nature of molecular interactions and provides new insight into macromolecular viscosity. The graphical method can equally be applied to a quantitative analysis of multiple unfolding of subunits of the giant muscle protein titin under AFM.