FIGURE 3. Biotin–streptavidin bond strengths.

a, Force histograms from tests of single biotin–streptavidin bonds demonstrate shift in peak location and increase in width with increase in loading rate. Gaussian fits used to determine the most frequent rupture force or bond strength are shown. Governed ideally by the thermal force f, standard deviations _f of the distributions also reflected uncertainties in position x and video sampling time t_v, that is, _f [ f² + (k_f x)² + (r_ft _v)²]^1/2. As _f increased from 1 pN at the slowest rate to 60 pN at the fastest rate, the standard error in mean force (the statistical measure for error in strength) ranged from 0.3 pN to 5 pN. b, Dynamic strength spectra for biotin–streptavidin (circles) and biotin-avidin (triangles) bonds. Defined as thermal energy k_B T ÷ distancex, the slopes (f ) of the solid lines in the biotin–streptavidin spectrum map activation barriers at x 0.5 nm and 0.12 nm along the direction of force based on values of 8 pN and 34 pN. Merging with biotin–streptavidin above 85 pN, the high-strength regime for biotin–avidin also maps an inner barrier at x 0.12 nm but the slope f 13–14 pN of the intermediate strength regime (dashed line) between 38 pN and 85 pN indicates that the next barrier maps to x 0.3 nm. Slight curvature and reduction in slope between 38 pN and 11 pN suggests that the barrier extends to 0.5 nm. Below 11 pN, the biotin–avidin spectrum exhibits a low-strength regime (dashed line) with a slope of f 1.4 pN that maps to x 3 nm. Consistent with the high-strength regime is the biotin–streptavidin strength (_AFM) measured recently by atomic-force microscopy (AFM) using a carbon nanotube as the tip²⁴ and the biotin–avidin strength (not shown) measured previously⁴ by AFM.