damage to the probe. We used a cantilever (Biolever mini, Olympus, Japan) whose nominal spring constant was 60 pN/nm.

3. Data Analysis

3.1. Conversion of Force-Displacement Curves to Force-Separation Curves

First, force-piezo displacement curves were converted to force-separation curves by using the obtained deflection sensitivity [35] . In this work, the zero separation was defined by the x-positions at the triggering force of 150 pN.

3.2. Detection of Streptavidin-Biotin Interaction from Force-Separation Curves

In this work, we employed two methods to extract the force of streptavidin-biotin interaction from force-separation curves. One is a subtraction of the minimum value in the force curve from the baseline [Figure 1(a)]. The base line was defined by the average of 10 points at the separation of 60 nm in the curve.

The other approach was a method based on fuzzy logic algorithm developed by the Kasas et al. In this approach, the events of the rupture of the streptavidin-biotin bond was detected with the shape of the peak. The detection was based on three criteria, which were a V-shape, vertical steep segment, and right angle [Figure 1(b)]. Three vectors to calculate scores were set same as the parameters used by Kasas et al. We eliminated that force curves with multiple rupture events, because the loading force was shared by multiple bonds resulting in a lowering of the loading rate. Considering the population of such curves (less than 1%), the effect on the overall statistics is negligible.

Considering our design of the tip [biotin immobilized via 10 nm of PEG chain and streptavidin (around 5 nm) fixed on the surface via 2 nm of PEG chain], rupture events with longer rupture separation may involve other molecular events such as unfolding of streptavidin, stretching of contaminants. Therefore, we discuss the rupture events with rupture separations shorter than 30 nm for the both cases.

4. Results & Discussion

Our analysis using the fuzzy logic algorithm method revealed that the rupture events were detected in only 11% of the total force curves. The MFOF was observed at 27 pN [Figure 2(a)], in agreement with the previously reported results [13] , indicating that single-molecule events were dominant, and that there is a small contribution of events for rupturing of double or higher multiple bonds to the total statistic.

Figure 2. Histograms of (a) force and (b) distribution of all detected rupture events by conventional and fuzzy logic algorithm methods.

The histograms clearly exhibit the difference in the statistics of rupture forces [Figure 2(a)]. The MFOF values are significantly different, i.e., 10 and 27 pN from the conventional and fuzzy logic algorithm methods, respectively. The overall comparison is shown in Figure 2(b) revealed that the false detection of rupture event in weak rupture force region (<15 pN) distributes in the overall range of the rupture separation.

The conventional method returns one “rupturing” force value from each force-separation curve even without any rupturing event. It picked up the minimum value even from the noise, generating the increase in the number of rupture force comparable to the magnitude of the thermal noise as shown in Figure 3(a) (in this work around 10 pN in peak-to-peak). These results show in the increase of the population in the region of small rupture forces [Figure 2(a)].

Next, we discuss several examples of false detections that were avoided by the fuzzy logic algorithm. Figure 3(a) exhibits a typical false detection of thermal noise of cantilever from force curves without any rupture events. The fuzzy logic algorithm perfectly succeeded in eliminating this kind of data from the statistics. As to the case of Figure 3(b), the stretching of contaminants seemed confined between the tip and surface. In this case, a strong adhesion with a long rupture separation was observed. The long-separation peeling-off process exhibited a long plateau shape and dull peaks before the rupture in the negative force. The fuzzy logic algorithm rejected similar cases because of the low scores for the V-shape.

Finally, we discuss the artifact on the potential landscape evaluated based on the Bell-Evans theory. As we discussed, the conventional method tends to overestimate the population of weak rupture force by picking up the thermal noise, resulting in the decrease in the MFOF. The overall change in the force-loading rate profile, which is used to estimate the xb and τ0, depends on the combination of ligands and receptors and the design of the tip and surface. Here, we display two examples of the artifact of the conventional method on plots of

Figure 3. Examples of false-detected rupture events by the conventional method (a) thermal noise, (b) non-specific interaction probably due to hydrophobic contaminant confined between the tip and surface.

force-loading rate and potential landscapes (Figure 4). The main artifact, an overall lowering of the rupture force in every loading rate results in the shorter τ0 (the inverse of the intersection of the plot and the x-axis), indicating the lower potential barrier than the real barrier height. Even small changes in a slope of the plot lead to the change in both in xb and in particular τ0 [Equation (1)], since x-axis is in a logarithmic scale and the position of the intersection drastically changes.

5. Conclusion

We investigated statistics of single-molecule interaction forces of the streptavidin-biotin ligand-receptor system. To effectively extract single molecular events from 22,500 force-separation curves obtained from AFM measurements, we employed two different ways. One is a conventional way that is built in major commercial AFM systems. It calculates the difference between the minimum value in the curve and baseline. The other is a method based on fuzzy logic algorithm initially proposed by Kasas et al. In this method, the rupture events in the force-separation curves were recognized by the scoring of characteristic shape. We found that the obvious difference in the obtained histograms of the rupture force. The conventional way frequently exhibited false detection, which picked up the thermal noise as a rupturing event. This false detection contributed to the increase in the population of the force weaker than 20 pN, resulting in the lowering of the most frequently observed rupture force, which is an important factor to illustrate potential landscapes of ligand-receptor systems based on the Bell-Evans theory. The conventional way also undesirably detected the non-specific interaction as the rupturing event. We found that this also provides undesirable effects on histograms in an overall range. Therefore, we concluded that the effective selection of force curves for data analyses using approaches of shape recognition is important for the quantitative analyses of various force measurements (adhesion, deformation, protein-stretching, etc.).

Figure 4. Schematic illustrations of the artifact on (a) force-loading rate plots (note that x-axis is in a logarithmic scale) and (b) the resulting potential landscapes evaluated by the Bell-Evans theory.

Acknowledgements

A part of this work was performed under the Cooperative Research Program of “NJRC Mater. & Dev.” This work is also supported by JST-PRESTO and MEXT KAKENHI (17K20095 and 15KK0184).

NOTES

*Equally contributed authors.

Cite this paper
Tahara, H. , Nyu, T. , Mondarte, E. , Maekawa, T. and Hayashi, T. (2018) Application of Fuzzy Logic Algorithm to Single-Molecule Force Spectroscopy of the Streptavidin-Biotin System. Advances in Materials Physics and Chemistry, 8, 217-226. doi: 10.4236/ampc.2018.85014.
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