Figure 3. Analytical theory compared with simulations.

Using a single set of model parameters, our theory (equation (17), solid lines) provides an accurate global approximation to both slow (a) and fast (c) external force protocols (as compared with the intramolecular relaxation timescale, in our case), apart from a narrow range (b) close to a critical loading rate (_c≈10⁵ pN s⁻¹ for our choice of parameters). The ‘experimental’ rupture force histograms have been generated by direct stochastic integration (see Methods section), using =10 × k_BT, T=300 K, x_b=1 nm, D=1,000 nm² s⁻¹ and =1…10¹¹ pN s⁻¹. Our best-fit parameters obtained with equation (17) are =10.15 × k_BT, x_b=0.98 nm, D=976 nm² s⁻¹. Since the mean rupture force varies by orders of magnitude at large loading rates, we use double-logarithmic scaling for >10⁷ pN s⁻¹ (c).