To explore the analytic relevance of unbinding force measurements between complementary DNA strands with an atomic force microscope, we measured the forces to mechanically separate a single DNA duplex under physiological conditions by pulling at the opposite 5-ends as a function of the loading rate (dynamic force spectroscopy). We investigated DNA duplexes with 10, 20, and 30 base pairs with loading rates in the range of 16-4,000 pN͞s. Depending on the loading rate and sequence length, the unbinding forces of single duplexes varied from 20 to 50 pN. These unbinding forces are found to scale with the logarithm of the loading rate, which is interpreted in terms of a single energy barrier along the mechanical separation path. The parameters describing the energy landscape, i.e., the distance of the energy barrier to the minimum energy along the separation path and the logarithm of the thermal dissociation rate, are found to be proportional to the number of base pairs of the DNA duplex. These single molecule results allow a quantitative comparison with data from thermodynamic ensemble measurements and a discussion of the analytic applications of unbinding force measurements for DNA.The direct measurement of forces between individual biological ligand receptor pairs is an emerging field. With the atomic force microscope (AFM), it has been possible to measure unbinding forces between single ligand receptor pairs, which are typically in the pico-Newton range (1-5). These sensitive force measurements can be performed with a high spatial resolution (5). However, the relevance of the force measurements as an (local) analytical tool depends on the understanding of the relationship between the measured forces and thermodynamic data characterizing the complex (6).The measured unbinding forces are not a fundamental property of a ligand-receptor pair but depend on the loading rate that is applied to the complex: If the load on the complex increases sufficiently slowly, there is time for thermal fluctuations to drive the system over the energy barrier, and the unbinding force will be small (7). A scaling of the force with the logarithm of the loading rate is expected for a single energy barrier along the unbinding path (8) and was found in AFM experiments on unfolding of protein domains (9, 10) and on rupture force measurements of the P-selectin͞ligand complex (11). With a different force probe technique, it has been possible to measure the loading rate dependence of the unbinding forces of biotin͞(strept)avidin complexes (12). In this system the loading rate dependence of the force is more complicated, indicating that more than one energy barrier is present along the separation path.The aim of our paper is to present a deeper understanding of the forces that arise if one separates the two strands of a DNA duplex by pulling at both 5Ј-ends. For this purpose, we have measured the loading rate dependence of the unbinding forces between complementary DNA strands to get information about the energy profile of the separation...

We discuss models for the force-induced dissociation of a ligand-receptor bond, occurring in the context of cell adhesion or single molecule unbinding force measurements. We consider a bond with a structured energy landscape which is modeled by a network of force dependent transition rates between intermediate states. The behavior of a model with only one intermediate state and a model describing a molecular zipper is studied. We calculate the bond lifetime as a function of an applied force and unbinding forces under an increasing applied load and determine the relationship between both quantities. The dissociation via an intermediate state can lead to distinct functional relations of the bond lifetime on force. One possibility is the occurrence of three force regimes where the lifetime of the bond is determined by different transitions within the energy landscape. This case can be related to recent experimental observations of the force-induced dissociation of single avidin-biotin bonds.

Scanning force microscopy (SFM) has been used to measure the strength of bonds between biological receptor molecules and their ligands.Here we report the measurement of the unbinding forces between avidin and biotin a model of the receptor-ligand interactions used in earlier studies-as a function of the loading rate. We have explored the unbinding force over three orders of magnitude in loading rate, and find that the force increases from ~20 pN to ~80 pN with increasing loading rate. We argue that the unbinding forces are connected to the bond lifetime as a function of an applied force. This allows to estimate thermal off-rates from measurements at finite forces. The deduced behavior of the bond lifetime of avidin-biotin in dependence of the force indicates that the dissociation proceeds via an intermediate state. Our data thus also allows to estimate the rate of an intermediate transition of the dissociation process.

Scanning force microscopy (SFM) has been used to measure the strength of bonds between biological receptor molecules and their ligands.Here we report the measurement of the unbinding forces between avidin and biotin a model of the receptor-ligand interactions used in earlier studies-as a function of the loading rate. We have explored the unbinding force over three orders of magnitude in loading rate, and find that the force increases from ~20 pN to ~80 pN with increasing loading rate. We argue that the unbinding forces are connected to the bond lifetime as a function of an applied force. This allows to estimate thermal off-rates from measurements at finite forces. The deduced behavior of the bond lifetime of avidin-biotin in dependence of the force indicates that the dissociation proceeds via an intermediate state. Our data thus also allows to estimate the rate of an intermediate transition of the dissociation process. 286 Single Molecules

The loading rate dependence of the unbinding force of a single ligand/receptor complex is determined by the rate of dissociation (off-rate) in function of applied force. Because the energy barrier for dissociation is lowered proportional to an applied force the off-rate increases exponentially with the force. This leads to a linear dependence of the unbinding force on the logarithm of the loading rate and allows to determine the thermal off-rate by extrapolating to zero force from measurements at finite forces, where the off-rates are much faster [1][2][3].However, at larger applied forces the dissociation kinetics might not be determined by the energy barrier that determines the thermal off-rate. To understand what determines the dissociation kinetics in such a case we discussed a simple model which consists of two barriers along the ligand/receptor separation path, i.e. the dissociation proceeds via an intermediate state. It turns out that at small applied force the off-rate is in fact determined by the thermal barrier (independent of the location of the intermediate state). At larger forces however, a cross-over to a regime occurs where the off-rate is either determined by the transition from the ground to the intermediate state or from the intermediate to the dissociated state (depending on the location of the intermediate state). A change of the rate dominating dissociation step with increasing force is possible in this regime. In consequence, an energy landscape with two barriers can show up to three force intervals with a different (exponential) dependence of the off-rate on the force. The unbinding force of the avidinbiotin complex shows three intervals where its loading rate dependence is different [2]. This can be attributed to the presence of at least one intermediate state along the mechanical separation path.