The rupture length and its histogram
If the single complex is formed, the AFM probe withdrawal generates bending of both interacting molecules. Then, the rupture length can be defined an unbinding distance L* calculated after the conversion of the force curve into the force versus tip-surface distance function (see Chapter 3 for details). The value of the rupture length, L, is determined from the following equation:
where kc is the cantilever spring constant, F is the unbinding force, the distance |Lk - Lc| is the distance between the moment when the cantilever starts to bend (Lc) and the moment when molecules unbind (Lk ) as it is shown at Fig. 5.22.
Figure 5.22 Example of the force curve recorded for the interaction between antigen-antibody complex. Reprinted with permission from .
The value of the rupture length L brings information about the mechanical resistance of the formed complex to the applied external force. The exemplary distribution of the rupture length obtained for the unbinding of single anti-BSA-BSA complexes is presented in Fig. 5.23.
Figure 5.23 Histogram of the rupture length obtained for the interaction between albumin molecules and monoclonal antibody against albumin. The monoclonal antibody against albumin (anti-BSA) was immobilized on a surface of the AFM probe while albumin molecules (BSA) were deposited on a mica surface. The line denotes the Gauss function. Reprinted with permission from .
The distribution shows only one peak centered at 23.7 ± 5.3 nm (the bin size reflects the experimental detection limits—the distance between two subsequent z-steps was 3 nm) and they agree with the data reported for BSA and polyclonal antibody against BSA . However, if the single molecular complex is formed between a ligand and a receptor embedded in the cell membrane, the rupture length would reflect the overall mechanical resistance of the whole system composed of these two molecules and the cell membrane at the place of the receptor anchorage. Since most receptors present on a surface of living cells are linked with actin cytoskeleton, the mechanical resistance will be also influenced by properties and structure of such a linkage.