Our study was based on DNA extension changes under tension induced by the docking of a single IHF protein to an H′ sequence inserted to the middle of a 445 bp (~150 nm in contour length) DNA that does not contain any other high-affinity site based on the known consensus sequence for IHF (SM-Text “DNA constructs”) (Fig. 1a). The extension change was measured by magnetic tweezers with a spatial resolution of ~2 nm and a sampling rate of 100 Hz23. To ensure the specificity of the binding, parallel experiments were performed on a control DNA of the same sequence but lacking the H′ site (SM-Text “DNA constructs”). In E. coli, the MgCl 2 concentration is tightly regulated in a narrow range of 1–4 mM24. Therefore, in all our experiments of the specific interaction between IHF and H′ DNA sequence, 2.5 mM MgCl 2 was included to mimic the physiological condition.

Figure 1 Two conformational states of DNA-IHF complex. (a). A sketch of the principle of the measurement. The H′ DNA bending by IHF binding reduces the DNA extension, which is detected by the resulting change of the height of the bead. (b). Dynamic fluctuations between two extensions in 10 nM IHF, 50 mM KCl, 2.5 mM MgCl 2 , 10 mM Tris (pH 7.4) and 21°C at different forces (0.5–1 pN) indicated by different colors. The red line represents extension steps detected a noise-beating step-finding algorithm (SM-Text “Noise-beating step-finding algorithm”). (c). The probability densities of the two extension states, which were produced by the double Gaussian fitting of the normalized histogram of smoothed data at different forces (0.4–1 pN, represented by different colors) using a bin size of 1 nm. A statistics of 40 distributions gave a step size of 17.34 ± 0.08 (mean ± s.d.) nm and R2 = 0.96 ± 0.022 (mean ± s.d.). Note, only 13 fitting lines from 5 DNA molecules were shown in figure for clarity. Full size image

Fig. 1b shows representative time traces recorded in 10 nM IHF, 50 mM KCl, 2.5 mM MgCl 2 , 10 mM Tris (pH 7.4) and 21 ± 1°C at force range from 0.5–1 pN. Clear two-state fluctuations between a shorter DNA extension (bent DNA) and a longer DNA extension (unbent DNA) were observed. The two-state fluctuations were filtered with fast Fourier transformation, followed by two-state digitizing using a noise-beating step-finding algorithm similar to that developed by Cui et al25. (red data in Fig. 1b) (see details in supplementary materials). Such two-state fluctuations were not seen before IHF was introduced (Fig. S1). It was also absent with the control DNA construct of the same sequence but lacking the H′ site in the presence of IHF (Fig. S2). In addition, the force extension curves of a 48,502 bp long λ-DNA in the presence of 10 nM IHF were indistinguishable from that of the naked λ -DNA in 50 mM KCl (Fig. S3a), which suggested that non-specific binding of IHF does not play an observable role in this condition (note that on lambda DNA there are four high affinity consensus sites26, but their contributions to the force-extension curves of the vast lambda DNA is negligible27). Thus, we conclude that the two-state fluctuation was both IHF and H′ sequence dependent.

Fig. 1c shows the normalized histogram of DNA extension distributions, which are apparently bimodal with two extension species, fitted with double Gaussian distributions at different forces (Fig. 1c). The distance between the two peaks calculated based on 40 such distributions is 17.34 ± 0.08 nm (mean ± s.d.) represented the extension difference of the two conformational states at the force range. Remarkably, a small force change of sub-pN switched the lower extension state from more probable to less probable, suggesting that the balance between the two states can be fine-tuned by adjusting force over a narrow range.

The force-dependent probability of the bent DNA state, P bent , can be calculated by the relative area of the two species in the bimodal extension distribution. This probability is related to the free energy difference between the two states through the Boltzmann distribution:

where ΔG is the Gibbs free energy difference between the unbent and bent DNA conformations in the absence of force, Δz is the step size of two-state fluctuation and f is the force applied to the DNA. While ΔG describes the stability of the interaction between IHF and H′, it depends on the protein concentration C. The intrinsic stability of the interaction is described by the dissociation constant K d , which is a concentration independent quantity and is related to ΔG through: K d = C × Exp(−ΔG/k B T). A lower value of K d indicates a stronger interaction. Substituting ΔG with K d and C, Eq. (1) becomes:

This equation explicitly expresses the dependence of P bent on both force and protein concentration, as well as the dissociation constant of the specific interaction between H′ and IHF. In our experiments, C and f were given as experimental parameters and the resulting P bent and Δz were measured; therefore K d is the only free parameter that can be determined by fitting the experimental data to Eq. (2). As the fluctuation step size Δz is narrowly distributed around its average, for simplicity Δz was set to be a constant at its average value (17.34 nm) in our fitting.

Fig. 2 shows the fitting at two different temperatures 21 ± 1°C (dark gray) and 31 ± 1°C (red) in 50 mM KCl, which yielded the average values of K d associated with fitting standard errors of 0.44 ± 0.06 nM and 1.54 ± 0.08 nM, respectively, using data from multiple (≥3) independent experiments under respective temperatures. The results showed that the bent DNA state in an IHF-H′ complex became less stable as temperature increased.

Figure 2 The effects of temperature, KCl concentration and IHF concentration on H′ DNA bending. The bending probability as a function of force in 2.5 mM MgCl 2 , 10 mM Tris (pH 7.4), at 10 nM IHF, 50 mM KCl, 21° (dark gray symbols), 10 nM IHF, 50 mM KCl, 31°C (red symbols), 100 nM IHF, 200 mM KCl, 21°C (blue symbols), 500 nM IHF, 200 mM KCl, 21°C (orange symbols) and 1000 nM IHF, 200 mM KCl, 21°C (wine symbols). Data for each solution condition were obtained from multiple (≥3) independent DNA molecules. Error bars for each data points (symbols) were standard deviations from multiple (≥3) repeating measurements for the same DNA molecules. The bending probabilities were calculated by the relative area of the two species in the bimodal extension distribution. Under each solution condition, data obtained were fitted by the two-state model (Eq.(2)) to obtain K d and the standard error of K d (fitting error), which are indicated in figure panels by corresponding colors. The goodness of the fitting (R2) are 0.84, 0.98, 0.94, 0.93, 0.99, respectively. The purple dot line is the theoretical calculation of the bending probability in 10 nM IHF, 200 mM KCl, 2.5 mM MgCl 2 , based on the two-state model with an averaged K d = 28.5 nM. Full size image

At a higher salt concentration of 200 mM KCl containing 2.5 mM MgCl 2 , two-state fluctuation was not observed at 21°C, indicating that the unbent DNA state dominated in the force range in the presence of 10 nM IHF (Fig. S4). We reasoned that this could be due to reduced binding affinity at higher salt concentration; therefore, we investigated IHF binding at higher IHF concentrations of 100, 500 and 1000 nM, where two-state fluctuations were observed (Fig. S4). Fig. 2 shows the resulting force dependent bending probabilities (symbols), the corresponding two-state theoretical fitting based on Eq. (2) (lines), indicated by blue, orange and wine colors, respectively. K d estimated from the three different IHF concentrations at 200 mM KCl were overall consistent with each other, with a value of 28.5 ± 3.9 nM (mean ± s.d.). Based on the K d estimated at 200 mM KCl, the bending probability at 10 nM IHF in the force range of 0.5–1 pN was predicted to be lower than 5%, which explained why we did not observe two-state fluctuations in 10 nM IHF at 200 mM KCl.

Here we note that the salt dependence of IHF binding to DNA is rather complex, related to release of counterions when IHF initially weakly binds to DNA and further release of counterions which is countered by simultaneous release of water molecules in the following tightly bending process. As a result, the first step is sensitive to KCl concentration while the second is less sensitive28,29. Increasing KCl concentration will reduce the first step of binding; therefore higher IHF concentration is needed to observe the two-state IHF dependent fluctuation in our experiments.

The lower extension state can be explained by bending of the H′ DNA sequence associated with an IHF. However, the longer extension state may have two alternative explanations: a DNA without an IHF bound at H′, or an IHF-H′ complex in a non-bent, intermediate state. The values of K d of ~1 nM for 50 mM KCl, 2.5 mM MgCl 2 and that of ~28 nM for 200 mM KCl, 2.5 mM MgCl 2 determined in our experiments agree with values determined in previous bulk experiments4,11, suggesting that the two-state fluctuations in our experiments are likely dominated by dissociation and association of IHF to the H′ sequence of DNA.

The specific structure of IHF-H′ complex was solved by X-ray crystallization, which indicated that the 34 bp H′ DNA is bent over the surface of an IHF hetero-dimer by an angle ~160°5. The H′ bending angle by IHF was also estimated by AFM imaging to be >120°12,13,14. Both of these methods determined the angles based on static conformations of the IHF-H′ complex. The DNA bending angle can also be estimated from our dynamic two-state extension fluctuation data under constant forces in solution. DNA can be described as a semi-flexible worm-like-chain (WLC) polymer model with a DNA bending persistence length of A ~ 50 nm30,31. In the WLC model, a DNA of contour length of L can be modeled as a chain of N segments, each with a segment length of b ≪ A. The bending energy cost in units of k B T of one DNA segment is described by: , where i denotes the i th vertex connecting the i th and (i + 1) th segments and is the tangent vector of the i th segment. The total bending energy is the sum of all the bending energies carried by each vertex: .

In our experiments, the 445 bp DNA contains one specific H′ site near the middle of the DNA that is subject to binding and unbinding of IHF. To estimate the level of overall extension reduction of the DNA tether under constant forces when an IHF is associated to the H′ site, we discretized our DNA by a segment length of b = 1 nm. The H′ site associated with an IHF was modeled as a point-like kinked site placed at the middle of the DNA, which has a preferred bending angle described by a parameter γ: θ = cos−1γ. The bending energy of this site is therefore modified to be: 27,32,33 where the and are the tangent vectors of the two successive segments involved in the kink; the dimensionless parameter a describes the deformability of the kinked site, which was chosen to be a large number to ensure a rigid kink (a = 50 nm was chosen in our calculation for Figure 3, but note the extension reduction versus force profiles are insensitive to the value of a as shown in Figure S6). The rest of DNA remained in the naked DNA state and follow WLC model.

Figure 3 Theoretical prediction of the effect of bending angle and force on the extension of short DNA. The extension reduction (Δz) of a DNA with a contour length of 150 nm induced by a kink placed at the middle as a function of force and bending angles θ = 90° (gray dotted line), 143° (gray solid line), 162° (black dotted line), 180° (black solid line). The shadow area represents the rough force range and Δz range measured in experiments. Full size image

The force-extension curves of the DNA tether with various values of preferred bending angle θ at the kinked H′ site were calculated using a previously developed transfer-matrix method27,32,33. The curves shift downward as θ increases (Fig. S6a), leading to an extension reduction Δz compared to DNA without the kink defect. Fig. 3 shows Δz versus force at several DNA bending angles in the range of 90–180°, converted from γ in the range of [−1,0] by θ = cos−1γ. In our experiment, the force range where the two-state fluctuations were observed was around 0.5–1 pN, which was associated with extension fluctuation step sizes (i.e, Δz) of ~17.34 nm. By comparison with the theoretical prediction in Fig. 3, these values corresponded to predictions with a preferred DNA bending angle of 140–180°. The bending angle θ was also independently estimated by an approximate analytical formula derived by Kulić et al34.: , which is valid for forces pN where the entropic DNA conformational fluctuation is suppressed. This analytical formula also gave similar estimated bending angle to that observed in our experimental force range (Fig. S6). Overall, the bending angle range estimated from our dynamic fluctuations is consistent with the large H′ DNA bending observed from previous X-ray crystallization and AFM imaging experiments5,12,13,14.