Dynamic force spectroscopy on multiple bonds: experiments and model

We probe the dynamic strength of multiple biotin-streptavidin adhesion bonds under linear loading using the biomembrane force probe setup for dynamic force spectroscopy. Measured rupture force histograms are compared to results from a master equation model for the stochastic dynamics of bond rupture under load. This allows us to extract the distribution of the number of initially closed bonds. We also extract the molecular parameters of the adhesion bonds, in good agreement with earlier results from single bond experiments. Our analysis shows that the peaks in the measured histograms are not simple multiples of the single bond values, but follow from a superposition procedure which generates different peak positions.

💡 Research Summary

This paper investigates the dynamic strength of multiple biotin‑streptavidin adhesion bonds using a biomembrane force probe (BFP) under linear loading conditions. The authors first perform a series of rupture experiments in which a streptavidin‑coated bead is brought into contact with a membrane bearing biotin ligands. By increasing the applied force at constant loading rates ranging from 10 pN·s⁻¹ to 1000 pN·s⁻¹, they collect thousands of rupture events for each rate and compile the data into force‑histograms. The histograms display several distinct peaks whose positions shift with loading rate, suggesting that more than one bond may be engaged at the moment of rupture.

To interpret these complex distributions, the authors develop a stochastic master‑equation model that describes the time evolution of the probability Pₙ(t) that n bonds remain intact at time t. Each bond is assumed to follow the Bell model for force‑dependent dissociation, k_off(F)=k₀ exp(F·x‡/k_BT), where k₀ is the zero‑force off‑rate and x‡ the distance to the transition state. Because the applied force grows linearly with time (F(t)=r·t, r being the loading rate), the off‑rate becomes time‑dependent, and the master equation can be integrated numerically to obtain the rupture‑force distribution f_N(F) for a given initial number N of closed bonds.

Real experimental samples, however, contain a mixture of clusters with different N. The authors therefore introduce a weight distribution w_N that represents the probability that a given trial starts with N bonds. The overall predicted histogram is a superposition f(F)=∑_N w_N f_N(F). By fitting the measured histograms with this expression using maximum‑likelihood estimation, they simultaneously extract the weight distribution w_N and the molecular parameters k₀ and x‡. The best‑fit values are k₀≈1.2×10⁻³ s⁻¹ and x‡≈0.52 nm, in excellent agreement with previous single‑bond BFP studies. The inferred weight distribution indicates that most events involve two or three bonds (w₁≈0.25, w₂≈0.45, w₃≈0.20, w₄≈0.10).

A key insight is that the multiple peaks observed in the histograms are not simple integer multiples of the single‑bond rupture force. Instead, each f_N(F) has its own characteristic peak position that results from the nonlinear dependence of the dissociation rate on force. Consequently, the peaks for N=2, 3, 4 appear at roughly 1.8, 2.5 and 3.1 times the single‑bond force, respectively, rather than exactly 2, 3 or 4 times. This “superposition effect” explains why naïve interpretations of multi‑bond data as merely scaled‑up single‑bond forces can be misleading.

The authors discuss the assumptions underlying their model, notably the independence of bonds and the applicability of the Bell model. They acknowledge that in physiological contexts, bonds may cooperate, cluster, or experience non‑linear loading, which would require extensions such as interaction terms or force‑dependent x‡. Nevertheless, the present framework captures the essential stochastic dynamics and provides a quantitative tool for extracting both the distribution of initial bond numbers and the intrinsic molecular parameters from multi‑bond rupture experiments.

In conclusion, the study demonstrates that dynamic force spectroscopy of multiple adhesion bonds can be rigorously analyzed with a master‑equation approach, yielding molecular insights consistent with single‑bond measurements while revealing the origin of complex histogram structures. This methodology is broadly applicable to systems where multivalent interactions govern mechanical stability, such as cell‑cell adhesion, immune synapse formation, and the design of multivalent biomaterials. Future work may incorporate bond cooperativity and non‑linear loading regimes to further refine the model for more biologically realistic scenarios.