# Relation between the unbinding force and the number of ruptured bonds

When multiple peaks are observed in a force histogram, they are usually attributed to the rupture of more than one single complex present within the contact area of the AFM probe and the surface. Thus, the first peak corresponds to the unbinding event involving the rupture of one single complex; the second one is related to the simultaneous unbinding of two single complexes (thus, the force value at the second maximum is doubled), etc. Such force histogram can be translated into the relationship of the unbinding force determined for each consecutive peak and the peak number (i.e., number of ruptured single complexes), and the linear dependence is expected if only one type of interaction is present (Fig. 5.21). The peak number is equal to the number of ruptured single complexes when the center of the first force peak agrees with the force value obtained from the slope. The unbinding force for a given individual lectin-glycan complex, i.e., ConA-mannose-type glycans, determined from the slope of the fitted line, was of 105 ± 15 pN. This value is in agreement with those obtained to unbinding ConA from the same glycan type probed on the prostate cells (115 ± 72 pN) [50]. Therefore, the position of the first peak (~200 pN) can be attributed to the simultaneous rupture of two single complexes, which was confirmed by the large number of mannose-type glycans.

Figure 5.21 Linear regression fitted to the unbinding force as a function of the number of succeeding peaks observed in the histogram (Fig. 5.20b) obtained for melanoma WM35 cells probed with lectin ConA. Data points correspond to centers of Gaussians fitted to each single peak present in force histogram while error bars represent their standard deviations. The 95% confidence bands are marked as grey lines. Reprinted with permission from [2].

In order to statistically evaluate the obtained differences between cell lines, for each fitted line the confidence bands of 95% were calculated. They estimate the certainty of the shape of the fitted line and the assumed confidence level implies a 95% chance that the true regression line fits within these bands (grey lines in Fig. 5.21). This approach works reasonably well when the regression curve is calculated basing on more points, which in our studies corresponds to cases where histograms were composed of five maxima.