# Other Theoretical Models for Single Molecule Interactions

The Bell-Evans approach is the oldest and most widely applied model describing the unbinding of single molecular complexes [27]. However, the data collected so far show that for certain cases this model does not provide satisfactory description of the unbinding of single molecular complexes. The more realistic models like the Dudko-Hummer-Szabo [28, 29] or the Friddle-Noy-De Yoreo [30] ones have been developed.

## Dudko-Hummer-Szabo model

In the Dudko-Hummer-Szabo model [28, 29], the single molecular complexes unbinding is described by a harmonic free-energy potential with a single sharp energy barrier. The molecular complex is pulled apart at constant velocity by the external force representing a harmonic spring. The relations for the most probable unbinding force and the probability distributions are very similar to those obtained on a basis of the Bell-Evans model. However, to describe the unbinding process more efficiently, an additional parameter, i.e., energy barrier height, has been introduced in the equation for the unbinding rate:

where *a* corresponds to the shape of the free-energy potential. It is equal either to 3/2 or to 1/2, i.e., assumes either linear-cubic or cusp-like shape of the energy barrier, respectively.

In the Dudko-Hummer-Szabo model, the relation between the most probable unbinding force and the loading rate is the following:

where *g* = 0.5772 is the Euler-Mascheroni constant.

The introduction of the energy barrier height *E _{b}* allows to interpret cases with multiple energy barriers characterized by widths x

_{b}of less than 1 A such as for avidin-biotin [15] or individual Fv fragments of anti-lysozyme antibodies [31].

## Friddle-Noy-De Yoreo model

In the Friddle-Noy-De Yoreo model, when two molecules are pulled apart, two cases are considered, namely, (i) an equilibrium one at lower loading rates that enables for rebinding of molecules and (ii) a so-called kinetic phase observed at higher loading rates where molecules can unbind reversibly. The most probable unbinding force is approximated by the equation

where *g* = 0.5772 is the Euler-Mascheroni constant, *f _{eq}* is the force value at which dissociation and association rates are equaled to

where *k _{c}* is the cantilever spring constant.