Effects of multiple-bond ruptures on kinetic parameters extracted from force spectroscopy measurements: revisiting biotin-streptavidin interactions

Abstract

Force spectroscopy measurements of the rupture of the molecular bond between biotin and streptavidin often results in a wide distribution of rupture forces. We attribute the long tail of high rupture forces to the nearly simultaneous rupture of more than one molecular bond. To decrease the number of possible bonds, we employed hydrophilic polymeric tethers to attach biotin molecules to the atomic force microscope probe. It is shown that the measured distributions of rupture forces still contain high forces that cannot be described by the forced dissociation from a deep potential well. We employed a recently developed analytical model of simultaneous rupture of two bonds connected by polymer tethers with uneven length to fit the measured distributions. The resulting kinetic parameters agree with the energy landscape predicted by molecular dynamics simulations. It is demonstrated that when more than one molecular bond might rupture during the pulling measurements there is a noise-limited range of probe velocities where the kinetic parameters measured by force spectroscopy correspond to the true energy landscape. Outside this range of velocities, the kinetic parameters extracted by using the standard most probable force approach might be interpreted as artificial energy barriers that are not present in the actual energy landscape. Factors that affect the range of useful velocities are discussed.

FIGURE 1

Schematic diagram of the rupture of two parallel tethered biotin molecules from streptavidin.

FIGURE 2

The PMF tilted by the applied force. Labels indicate position of the integration limits.

FIGURE 3

Expected PD functions (solid lines) calculated using Eqs. 1–4 and 6 and the PMF from molecular dynamics simulations (shown in the inset) for different probe velocities and parameters given in the graph. Dashed lines show the PD functions calculated using the Bell-Evans kinetic model combined with the eFJC tether model. The kinetic parameters are shown in the graph. The Bell-Evans model calculations were performed for velocities spanning the range available in typical AFM experiments.

FIGURE 4

PD calculated according to the two-bond rupture model. Calculations use the Bell-Evans kinetic model and the FJC tether model. Other model parameters are shown in the graph. The dash-dotted line shows the single-bond PD. Different values of used in the calculations are shown next to the corresponding lines. Calculations were performed using the numerical solution of Eq. 8 (shaded dashed lines) and by the approximate analytical solution given by Eqs. 9 and 10 (solid black lines). Lines closely overlap, and the difference between numerical and analytical solutions cannot be seen in this graph.

FIGURE 5

Typical force plots exhibiting the rupture events at the tip sample separation that corresponds to the tether length. The fit with the eFJC model to one of the stretching events is also included. The inset shows the contour length distribution obtained from fitting the force curves to the eFJC model.

FIGURE 6

Fits of the rupture force histograms by the model given by Eq. 6 that uses the Bell-Evans model for the dissociation rate and the eFJC tether model. Histograms are arranged according to the mean apparent loading rate (ALR) shown in the graphs. The corresponding probe velocities (PV) are also shown in the graphs. The line plots shown in each panel indicate the fit function, the single- and two-bond contributions to the distribution, and the limiting window function. The legend in the top left panel identifies different curves.

FIGURE 7

(A) MPF versus loading rate dependences from the individual bond rupture model (circles) and from the simulated experiment (squares). Straight lines show fits of the apparent linear regions to the Bell-Evans model. The resulting fit parameters are shown in the legend. (B–D) Calculated histograms of rupture forces at different probe velocities, corresponding to the points indicated in A. Lines show the Gaussian fits, the noise threshold limits, and the one- and two-bond components, as indicated by the legend. Kinetic parameters obtained from the MPF versus loading rate dependence are significantly modified by the noise at the low and high velocities.

FIGURE 8

Dependence of the velocity limits (A) on the tether stiffness and (B) on the PEG tether length. Calculations performed for several dissociation rates k₀ that are indicated in the corresponding area. Other parameters are the same as in Fig. 7.