Multivalency: influence of the residence time and the retraction rate on rupture forces measured by AFM

The Bell-Evans theory relative to rupture forces between non-covalently interacting molecules predicts that the rupture force increases linearly with the logarithm of the force loading rate. Here we investigate by force spectroscopy performed with an atomic force microscope (AFM) the rupture forces between surfaces covered by beta-cyclodextrin (beta-CD) molecules and AFM tips coated with adamantane (AD) groups. The beta-CD molecules are either deposited through a self-assembled monolayer (SAM) or grafted on poly(allylamine hydrochloride) chains (PAH-CD) that are adsorbed on the substrate. The AD groups are fixed covalently on the AFM tip through either a one-AD or a four-AD platform linked to the tip though a PEO chain. It is found that while the rupture forces between AFM tips covered with tetravalent AD molecules and SAM-CD surfaces do not exceed twice those found with tips covered by monovalent AD molecules, the rupture forces increase by a factor of 20 on PAH-CD substrates for a tetravalent AD covered tip compared to a monovalent one. Thus, there seems to exist a synergistic effect between the molecule multivalence and the polymeric nature of the CD-covered substrate. As found in the literature, we observe an increase of the intensity of the rupture forces between the AD-covered AFM tip and the beta-CD covered substrate with the contact time over timescales up to several seconds. Finally, we find that when the host-guest system involves the multivalency of the AD guest and/or the polymeric nature of the host the mean rupture force decreases with the loading rate in contrast to what is predicted by the Bell-Evans theory. We tentatively explain this "anti-Bell-Evans" behavior by the possibility of rebinding during the rupture process. This effect should have important implications in the understanding of forces at the cellular level.