Fig. 2: Kinetic heterogeneity is tuned by Mg²⁺ and the nucleic acid strand type.

a Representative single-molecule traces of EBS1*/IBS1* (blue) and EBS1*/dIBS1* (orange) displaying different residence times in the zero and high FRET state in response to gradual changes in the composition of the ionic environment. The traces are selected to reflect the overall histogram shown in Fig. 1f. The discretized state sequence is depicted by alternating backgrounds (white: zero FRET; gray: high FRET) for the top left trace and omitted elsewhere for clarity. Only dynamic molecules were used for the analysis. b The molecule-to-molecule variability is visualized by correlating the mean dwell times in the bound, 〈t_high〉, and unbound state, 〈t_zero〉, for every time trace. There are no distinct kinetic subspecies, but rather a single stretched cluster. Data is shown for 100 mM K⁺ and 10 mM Mg²⁺. c The cluster center is calculated by k-means and depicted as a circle in different shades of blue or orange for every Mg²⁺ concentration (10 mM Mg²⁺ is highlighted with a thick, black edge). Contact formation under high ionic strength (1 M K⁺) in the absence of Mg²⁺ (100 μM EDTA) is indicated by a blue or orange square. d Cumulative K_d,n histograms (10 mM Mg²⁺) are fitted to a logistic function (Supplementary Eq. 13). e Stability constants of EBS1*/IBS1* and EBS1/dIBS1 as a function of Mg²⁺ are quantified by the transition point, K_d, from fits in c. Error bars are drawn as mean ± 2 s.d. of 100 bootstrap samples. f Heterogeneity within the bound state is evaluated by computing cumulative dwell time histograms of the bound state. The presence of multiple decays is a characteristic of kinetic heterogeneity. The weighting factors (mean ± s.d.) of the dissociation rate coefficients k_off,1 and k_off,2 are indicated alongside the decay. The ion dependence of the prefactor is displayed on the right for EBS1*/IBS1*. g Rate coefficients and average weighting factors (mean ± s.d.) over the whole Mg²⁺ titration. The star (*) indicates the degree of heterogeneity. The latter is largest if the rate coefficients are far apart and equally populated (weighting factor ≈0.5). Source data are provided as a Source Data file.