Discussion

At first, the very low bond-forces and the two maxima may look a little dubious, but after a thorough investigation it is clear that they fit very well to the investigations of other groups.

Figure 4.9: Bond-Force dependency on the loading rate for the streptavidin-biotin bond. The values for the atomic force microscopy (AFM) are from [97] and the values for the dynamic force spectroscopy (DFS) are from [91].

Figure 4.10: Bond-Force dependency on the loading rate for the avidin-biotin bond. The values for the atomic force microscopy (AFM) are from [44] and the values for the dynamic force spectroscopy (DFS) are from [91].

Other experimental [91,28,39,40,109,134,15] and theoretical publications [59,70,65,121] already showed that the bond-force of ligand-receptor bonds is highly dependent on the loading-rate (i.e. the rate of force increase $F'$). Figures 4.9 and 4.10 present graphs of the streptavidin-biotin and avidin-biotin bond-forces in dependency of the corresponding loading-rate. The values for the bond-forces are from AFM measurements [97,23], DFS measurements [91] and the results in this thesis. The bond-force is plotted against the logarithm of the loading-rate, because it is proportional to the logarithm of the loading-rate. As it was already shown by MERKEL et al.  in 1999 [91], the streptavidin-biotin bond can be divided in two linear regions, and the avidin-biotin bond can be divided into three linear regions. These different force regimes can be attributed to the behaviour of a one (or more) state energy potential that experiences an outer force (confer section 1.1.4 for the transition-state-theory and Kramers model). The bond-forces measured in this thesis extend the lower linear region for about 2 (avidin-biotin) to 3 (streptavidin-biotin) orders of magnitude down. At an extremely low loading-rate of only 1fN/sec, the streptavidin-biotin bond-force is only $\approx$245fN, and the avidin-biotin bond-force is only $\approx$58fN. So the logarithmic dependence between bond-force and loading-rate is still valid for loading-rates down to 1fN/sec.

Together with the low force events from [91], a linear fit can be applied to the measurements and the off rate $k_{\rm off}$ can be calculated. From equation 1.1 we can derive for the off rate: $k_{\rm off} = \frac{x_\beta\cdot r_0}{k_{\rm B}T}$. Using this equation, we get for the avidin-Biotin bond $k_{\rm off-Avidin} = 1.3\cdot 10^{-3}$sec$^{-1}$ and for streptavidin-biotin bond $k_{\rm off-Strept} = 4.8\cdot 10^{-4}$sec$^{-1}$, which is much higher than calorimetric measurements of GREEN in 1975 [57] ( $k_{\rm off-Avidin}^{\rm Green} = 4\cdot 10^{-8}$sec$^{-1}$ and $k_{\rm off-Strept}^{\rm Green} = 3\cdot 10^{-6}$sec$^{-1}$). However, recent measurements [134], using label exchange experiments, showed an off rate for streptavidin-biotin between $k_{\rm off-Strept}^{\rm Williams} = 1\cdot 10^{-5}$sec$^{-1}$ and $8.7\cdot 10^{-7}$sec$^{-1}$ which is only a little bit higher than our measurements. Using only AFM measurements, all rupture events are quite far away from the natural off rate and that is the reason for the wide range. Because our measurements are much closer to the natural off rate the result of the linear regression is more precise.

While measuring very low bond-forces at very low loading-rates, another particular feature of the ligand-receptor bonds can be seen in the measurements. The fact that the second bond-force maxima for both investigated bonds is 4 times higher than the first maxima substantiates the theory of positive cooperativity for these ligand-receptor bonds. The affinity of these bonds, and with it the bond-force, only changes when the protein binds four ligands. There is no difference between one, two and three ligands bound to the protein. But with four ligands, a structural change in the protein induces a change of the affinity of the bond [133]. Only then, all four ligands add to the bond-force that is then four times higher than a single bond. For a more comprehensive explanation of the cooperativity in ligand-receptor bonds, see section 1.1.4. Even the single high force event for the streptavidin-biotin bond at 457fN supports the cooperativity, because it is approximately twice the second maxima (244,7fN with $\sigma_{\bar x} = 64,5$fN), and, therefore, corresponds to a full double bond with two streptavidin proteins and eight biotin ligands.

Section 4.3 presented a dependency between the concentration of the biotin on the sample surface and the number of breakable and unbreakable ligand-receptor bonds. For concentrations above 1000nM, no bonds could be ruptured in this setup. This is a clear indication for two or more full bonds, so the cumulated bond-force is higher than the highest bond-force that can be applied in this setup.

Several bonds per marker were very likely another problem for the examination of sulfur-gold bonds (confer section 4.1). Because the magnetic SH-markers can bind everywhere on the gold conducting line, there are most likely two or more bonds between the marker and the surface. And because it is not so easily possible to adjust the concentration of the gold atoms on the surface, as it is with biotinylated oligonucleotides, the sulfur-gold system is not really feasible.

In summary, this new method opens up the possibility for new ultra low force measurements with extremely low loading-rates. It is a very interesting tool to examine biological bonds, because it has several advantages. First of all, the maximum applied forces are strong enough for nearly all biological bonds (streptavidin-biotin is the strongest known non-covalent bond). But in contrast to e.g. AFM experiments, the loading-rate is very low. This means that the experimental conditions are more similar to the in vivo conditions of the ligand-receptor pair, although it is an in vitro experiment. This method can give more insights on the bond behaviour for near equilibrium conditions of biological bonds, and may add to new developments [105] in this research area.