Electrostatic properties of disordered regions control transcription factor search and pioneer activity

Domain: neuroscience
Published: 2026-02-08
Editorial outcome: major_revision

Abstract
Transcription factors (TFs) search for and bind specific DNA target sites to control gene expression. However, eukaryotic TF target search within the chromatinized genome is poorly characterized. Here, we combine in vivo and in vitro single-molecule imaging to dissect the role of differentially-charged DNA-binding domain flanking regions in the target search of Sox TFs. We demonstrate that the flanking region of Sox2 markedly enhances search efficiency compared to the negatively-charged flanking region of Sox17. The involved mechanisms are distinct for naked DNA compared to chromatin. On DNA, the enhanced search of Sox2 is driven by an increased target recognition rate during 1D sliding, despite reduced sliding speed. Conversely, enhanced nonspecific interactions between the Sox2’s DNA-binding domain flanking region and nucleosomes facilitate binding to compact chromatin and reinforce pioneer activity. These findings provide critical insights into biophysical mechanisms governing TF target search within the chromatinized genome.

Introduction
Transcription factors (TFs) are central regulators of gene expression in all living organisms. They identify and bind target DNA sites in a sequence-specific manner via their DNA-binding domains (DBDs) (specific interactions), navigating a vast landscape of nonspecific DNA (nonspecific interactions). An efficient target search is crucial to allow a limited number of TFs (103–106 molecules per cell1,2) to locate and discriminate tens of thousands of target sites identified by chromatin immunoprecipitation sequencing (ChIP-seq)3–6 from millions of nonspecific decoy sites within the complex nuclear environment7–11.

The mechanisms by which TFs maximize their target search efficiency within chromatin remain poorly understood. The facilitated diffusion model, formulated for free DNA, states that TFs enhance search efficiency by engaging in nonspecific DNA interactions, alternating between 1D diffusion along DNA and 3D diffusion within the nucleoplasm12–15. This dimensionality-reduced diffusion is believed to substantially increase search efficiency compared to free diffusion alone, although the magnitude of this effect is still debated16. Pioneering experiments showed directly that the bacterial TF LacI follows the facilitated diffusion model in live E. coli17 and in vitro18–20. However, in eukaryotes chromatin acts as a barrier to TF-DNA interactions, potentially impairing TF target search and site recognition21–24. Eukaryotic TFs contain intrinsically disordered regions (IDRs) outside of their DBDs. How these regions influence target search remains unclear. Recent findings indicate that IDRs play an important role in defining the binding specificity of TFs in vivo25. TFs with identical DBDs but distinct IDRs recognize the same motifs in vitro, but often bind distinct genomic subsets in vivo, highlighting the role of DBD-proximal IDRs in modulating target selection. While IDRs can mediate protein-protein interactions26–29, they can also play a key role in determining chromatin binding and diffusion behavior, even in the absence of interaction partners30–34.

A subset of eukaryotic TFs, known as pioneer TFs (pTFs), can bind nucleosomal DNA and initiate local chromatin opening, facilitating access to previously inaccessible regulatory elements35–38. Sox TFs, which includes several pTFs24,39, bind their targets through their high mobility group box DBD, either alone or as heterodimers with other TFs. We previously observed that individual Sox TFs show markedly different degrees of association with mitotic chromosomes, a property that correlates with nonspecific DNA binding. We also showed that a higher content of positively charged amino acids promotes TF association to mitotic chromosomes40. Sox TFs exhibit a broad charge distribution in regions outside the DBD, going from −9z to +9z, while their net charge within the DBDs is comparable (Fig. 1a). The overall charge in these DBD-flanking IDRs is positively correlated with their ability to bind mitotic chromosomes (Fig. 1b).

Among the Sox TFs, Sox2 exhibited the most positively-charged DBD flanking region (DFR), which correlated with the highest fraction of TF molecules associated with mitotic chromosomes40. This has been proposed to reflect its superior ability to nonspecifically bind chromatinized DNA and to efficiently search the genome. Indeed, Sox2 functions as a potent pTF5,41 and is a core pluripotency TF42,43, heterodimerizing with Oct444,45. In contrast, the DFR of another Sox TF, Sox17, was found to carry the most negative charges, and Sox17 only showed weak mitotic binding, potentially indicating a lower ability to nonspecifically scan chromatin, which may limit its pTF function. Sox17 is expressed during differentiation towards extraembryonic endoderm46,47, and can also heterodimerize with Oct448,49. Importantly, Sox2 and Sox17 alone bind to a virtually identical motif50 due to their similar DBD, which allows a direct comparison between the two TFs. Still, upon heterodimerization with Oct4, they bind a slightly distinct composite motif because of differences in their heterodimerization interface located within the DBD.

Here, we investigate the role of differentially-charged DBD-flanking IDR stretches of the Sox2 and Sox17 TFs (DFR and DFR , respectively) in regulating their ability to search for their binding sites on naked DNA and chromatin, using both in vivo and in vitro single-molecule approaches.

Results
Sox2 and Sox17 mutants to study the DFR impact on target search
We defined the DFRs (Supplementary Fig. 1a) as the segment C-terminal to the DBD, starting at the residue that immediately follows the prominent positive charge peak in each TF’s respective charge distribution (Fig. 1c). The DFR length (116 amino acids) was determined to achieve a large charge difference between DFR (+1z) and DFR (−9.5z) while limiting the total number of amino acids included (Supplementary Fig. 1b). We then generated two DFR-swapped constructs: (i) Sox2 carrying the acidic DFR (Sox2a) and (ii) Sox17 carrying the DFR (Sox17b) (Fig. 1d). Additionally, constructs containing only the DBDs of Sox2 and Sox17 (Sox2D and Sox17D) were produced to isolate the influence of the DFRs on Sox-DNA binding dynamics.

We engineered mouse embryonic stem cell (mESC) lines containing HaloTag (Halo) fusions to either Sox2, Sox2a, Sox17, Sox17b, Sox2D or Sox17D stably integrated under the control of a doxycycline (dox)-inducible promoter, enabling their expression at low levels for single-molecule imaging51 (Fig. 1e). We then characterized their genome-wide binding profiles by ChIP-seq (Supplementary Fig. 1c). Motif enrichment analysis of ChIP-seq peaks indicated that all Sox TFs bound to nearly identical motifs, including their respective canonical motifs for Sox2 and Sox17 (Supplementary Fig. 1d). Therefore, although Sox17 is not expressed endogenously in mESCs, Sox17 and its mutant Sox17b can still recognize their target sites in this context. Notably, Sox2a bound to motifs that are more similar to those bound by Sox2 than Sox17, confirming that Sox2a still retains the DNA-binding specificity of Sox2. Since Sox2 is crucial for maintaining pluripotency in mESCs, we also determined whether Sox2a can fulfill this role. To this end, we performed a pluripotency rescue assay by using the 2TS22C cell line52, which allows us to fully deplete endogenous Sox2 upon dox addition within 48 h. These cells were also engineered to express Halo-Sox2 or Halo-Sox2a at the same level. We then treated these cell lines with dox for 5 days and quantified the percentage of undifferentiated cell colonies and NANOG expression levels by immunofluorescence (IF) (Supplementary Fig. 1e, f). Halo-Sox2a was able to rescue ESC colony morphology and NANOG expression, even though less potently than Halo-Sox2, demonstrating that Sox2a can partially replace Sox2 in maintaining pluripotency of mESCs.

DFRs impact the residence times of TFs on DNA in vivo
Single-molecule tracking (SMT) allows direct observation of the TF search process within living cells51. We expressed our six different TFs at a low level and labeled them with JF54953. To visualize chromatin, we used SNAP-H2B labeled with silicon rhodamine (SiR)54. We then quantified TF-DNA interaction dynamics using single-molecule highly inclined and laminated optical sheet (smHILO) microscopy. We used four different imaging conditions by fixing the illumination time per frame at 60 ms, and interspersing variable dark times to obtain frame intervals of 120, 240, 480, and 960 ms (Supplementary Fig. 2a). This approach allows us to determine TF binding behavior over a broad temporal range (Fig. 1f).

Most individual molecules were confined within nuclei (Fig. 1e, f). We then reconstructed trajectories for individual molecules using TrackIt55 and plotted the reverse cumulative density function (1-CDF) of bound times. Sox2 and Sox17b exhibited slower 1-CDF decays compared to Sox2a and Sox17 or their DBD alone (Fig. 1g, Supplementary Fig. 2b), indicating slightly longer residence times.

We employed the genuine rate identification (GRID)56 method to resolve the populations of bound molecules in an unbiased manner, categorizing them into distinct bound states. For all TFs, we identified six populations of bound states (Supplementary Fig. 2c) from a distribution of residence times ranging from 0.1 to 1000 s (Supplementary Table 1). While the residence time distributions for Sox2 and Sox17b were narrow and well defined, Sox2a and Sox17 exhibited broader distributions (Fig. 1h), suggesting complex interactions associated with a continuum of binding energies. We note that the uncertainty on the duration and amplitudes of extremely long-lived states in GRID analysis is inherently high, as the determination of these bound times approaches is limited by dye lifetimes. Moreover, the amplitudes of the extremely long-lived states are very low in the spectra. We therefore interpret the slowest components as indicative of rare, very stable binding events rather than precisely quantified lifetimes.

The mean frequency of long-lived binding events (>10 s) in GRID spectra was higher for Sox2 (0.042) compared to either Sox2a (0.018) or Sox17 (0.025) (Supplementary Fig. 2d, Supplementary Table 2). We also calculated fractional occupancies55–58, i.e., the fraction of total bound time spent in each state (Supplementary Fig. 2e; see the “Methods” section). This revealed that Sox2 (0.66) and Sox17b (0.60) spend more time in long-lived states (>10 s) than Sox2a (0.47) and Sox17 (0.47) (Supplementary Fig. 2f, Supplementary Table 2). Overall, these results suggest that DFRs have an impact on Sox TF-DNA residence times.

DFRs regulate in vivo target search efficiency
Next, we dissected the target search process of the different Sox TFs. We first performed continuous imaging using a 10 ms exposure time to observe both diffusing and bound molecules (Fig. 2a, b). In 2D HILO imaging, fast-diffusing molecules often appear motion-blurred or leave the focal plane, leading to their under-detection59,60. To make sure that this limitation does not bias our results, we applied the state array (SA) method61, which estimates diffusion coefficients and localization error variances on a per-trajectory basis while also correcting for defocalization biases. We obtained diffusion coefficient distributions spanning 10−3 to 102 μm2 s−1 (Fig. 2c, d; see the “Methods” section). Strikingly, swapping the DFRs between Sox2 and Sox17 led to a reciprocal swap in their diffusion profiles (Fig. 2d), indicating that the electrostatic properties of the DFRs modulate the diffusion landscape of Sox TFs.

Notably, the peak of the diffusion spectrum displayed a pronounced left-skewed tail, suggesting the presence of at least one intermediate state in addition to the bound and freely diffusing populations. Consistent with previous observations for Sox259,62, we modeled the diffusion behavior of all Sox TFs using a three-state diffusion model encompassing fast-diffusing, slow-diffusing, and bound states (Fig. 2b, Supplementary Fig. 3a). Spot-On analysis of jump distance distributions59 revealed that Sox2 and Sox17b generally exhibited lower diffusion coefficients for fast and slow diffusing populations (Fig. 2e–g, Supplementary Table 2).

To quantify the bound population, we defined molecules with diffusion coefficients < 0.01 μm2 s−1 as chromatin-bound63–65. Under this criterion, Sox2 and Sox17b exhibit higher bound fractions than Sox2a and Sox17 (Fig. 2h), which was also in line with Spot-On analysis (Supplementary Fig. 3b, Supplementary Table 2). Furthermore, Sox2 compared to Sox2a, and Sox17b compared to Sox17 spend less time in fast and slow diffusing modes, respectively, and also transition to a bound state more rapidly (Supplementary Fig. 3c). Taken together, this suggests that individual Sox2 and Sox17 molecules spend less time in a diffusing state before transitioning to a bound state.

Next, we investigated whether the set of TFs differs in their association rate to genomic targets. We measured their pseudo on-rate (k )40, defined as the time-averaged binding frequency of TFs to the whole genome, as determined by the number of immobilized molecules per imaging frame (see the “Methods” section). We defined 1 s as a minimal trajectory length to separate nonspecific and specific interactions to determine k . Sox2 (k = 1.00 ± 0.53) and Sox17b (k = 0.89 ± 0.45) displayed a higher nonspecific k than Sox2a (k = 0.66 ± 0.22) and Sox17 (k = 0.68 ± 0.39) (Fig. 2i), in line with the previous diffusion analysis. This suggests that the DFR leads to a higher frequency of nonspecific DNA-binding events for Sox2 and Sox17b. Importantly, Sox2 (k = 1.00 ± 0.62) exhibits a faster specific k than the other TFs (k = 0.40 ± 0.24 for Sox2a, 0.59 ± 0.46 for Sox17, 0.28 ± 0.19 for Sox17b) (Fig. 2j). In summary, our in vivo data demonstrate that TFs containing a DFR interact more frequently with DNA and display enhanced target search efficiency compared to TFs containing DFR .

DFRs do not impact 3D diffusion-mediated association to naked DNA and residence times in vitro
A limitation of in vivo measurements is that specific and nonspecific binding events can only be inferred from residence times, and the chromatin context in which they occur is unknown. Therefore, we performed in vitro studies to examine how the DFRs impact DNA binding dynamics of Sox TFs on naked and chromatinized DNA, focusing mainly on Sox2, Sox2a, and Sox17.

We employed a fluorescence colocalization approach37 (Fig. 3a) using single-molecule total internal reflection fluorescence (smTIRF) microscopy. Here, Alexa Fluor 647 (AF647)-labeled DNA or chromatin substrates are immobilized in a flow channel, and their positions are detected. Subsequently, Sox TFs carrying a JF549-dye are introduced. When bound to DNA, they appear as fluorescent spots colocalizing with immobilized DNA molecules. Recording movies enables us to directly determine on-rates and residence times for specific DNA or chromatin environments.

We produced recombinant Halo-containing Sox2, Sox2a, and Sox17 in insect cells (Supplementary Fig. 4a–c; see the “Methods” section) and validated their DNA-binding ability by electrophoretic mobility shift assays (EMSA), which allowed us to estimate nanomolar DNA affinities for the Sox TFs (Fig. 3b, Supplementary Fig. 4d), consistent with published values41. We also measured the salt dependency of Sox-DNA binding via EMSA by varying NaCl concentrations. Sox2a and Sox17 dissociated from DNA at lower NaCl concentrations (EC = 14.6 ± 2.1 mM NaCl, EC = 27.6 ± 3.8 mM NaCl) than Sox2 (EC = 38.4 ± 5.4 mM NaCl) (Fig. 3c, Supplementary Fig. 4e, f). Therefore, Sox2 binds its consensus site at higher ionic strength, suggesting a charge-dependent effect of the DFRs on the binding mechanism.

We then investigated how charged DFRs influence TF target search on naked DNA. We designed DNA substrates of 25, 50, 100, and 250 bp length, based on the 601 Widom sequence (601WS)66 (Fig. 3d). Each DNA substrate contained a single Sox motif (5’-CTTTGTT-3’) at the center (DNA+), except for a 50 bp control DNA without motif (DNA-). The DNA molecules were immobilized in a flow cell, and the binding dynamics of Sox TFs were monitored using smTIRF imaging. We recorded 10-min movies in the JF549 channel at a frame rate of 5 Hz with a 100 ms illumination time to monitor TF-DNA binding events by colocalization detection (Fig. 3a). Fluorescence time-traces were extracted from the JF549 channel, where high intensity indicates bound states (Fig. 3e). This revealed that the frequency of binding events for all Sox TFs increased with longer DNA, particularly for short binding events (Fig. 3f).

We next determined the on-rates (k ) of Sox TFs by fitting a monoexponential decay to the 1-CDF of unbound times (Supplementary Fig. 5a). This revealed that Sox2, Sox2a, and Sox17 display comparable k values that increased with DNA length (Supplementary Fig. 5b, Supplementary Table 3).

k exhibited a nonlinear relationship with DNA length in bp (Supplementary Fig. 5c). The collision radius of two molecules in solution is proportional to their radius of gyration, and this becomes particularly important for DNA lengths above the DNA persistence length of 45 nm67–69. Indeed, k scaled directly with the calculated radii of gyration of the DNA templates (Supplementary Fig. 5d; see the “Methods” section). This relationship allowed us to extrapolate to short DNA lengths and determine a nanoscopic association rate (k), defined as the association rate to a single site on DNA. We found similar values for all TFs, with k = 2.14 ± 0.11 × 105 M−1 s−1 bp−1, k = 1.93 ± 0.21 × 105 M−1 s−1 bp−1, and k = 1.85 ± 0.13 × 105 M−1 s−1 bp−1 (Supplementary Fig. 5e). This indicates that neither the DFR nor the DFR impacts the overall probability of interactions between freely diffusing TFs and naked DNA.

Next, we quantified TF residence times by analyzing the distribution of bound times. The 1-CDFs (Supplementary Fig. 5f) were well-described by a biexponential decay, indicating two distinct binding modes of Sox TFs with DNA+ (Supplementary Fig. 5g–j, Supplementary Table 3): a short-lived (τ = 1.1 ± 0.3 s, τ = 0.8 ± 0.3 s, τ = 1.1 ± 0.4 s) and a long-lived interaction mode (τ = 14.9 ± 4.5 s, τ = 12.4 ± 5.2 s, τ = 10.2 ± 4.5 s). Conversely, the binding of Sox TFs to DNA lacking a motif (DNA-) was characterized by a single short-lived population (τ = 0.5 ± 0.01 s, τ = 0.6 ± 0.05 s, τ = 0.6 ± 0.06 s). This indicates that the long-lived populations, characterized by τ , correspond to specific, on-target binding. The average specific residence times and bound fractions for all DNA lengths and the three TFs (Supplementary Fig. 5k, l) aligned well with a previously reported value for Sox2 measured by in vitro SMT70. Moreover, for each DNA length, we observed similar specific residence times τ for the Sox TFs.

In contrast, it was not possible to directly relate τ to nonspecific interactions. Previous measurements using fluorescence correlation spectroscopy in mouse embryos revealed that such nonspecific DNA interactions for Sox2 at individual random sites are extremely short-lived, with microscopic nonspecific residence times of 10 ms71, which is well below the time resolution of our experiment (5 Hz). Similarly, the nonspecific residence time of LacI in E. coli has been reported as less than 5 ms using SMT72, whereas other TFs, such as TetR or p53, exhibited longer nonspecific residence times (158 and 900 ms, respectively)60,73. This suggests that the short-lived interactions we measured as τ likely represent the extreme tail of the nonspecific residence time distribution, and may involve numerous transient events of Sox TFs, such as hopping12,19, where TFs repeatedly re-associate and dissociate within a local regime before fully dissociating.

DFR facilitates target search by increasing the target recognition probability
The overall DNA binding rate (k ) is determined by the intervals between all binding events, regardless of interaction type. Because it encompasses both specific and nonspecific interactions, k does not directly reflect the efficiency in locating a specific target site. Target search efficiency, in contrast, is defined solely by the intervals between specific interactions, which we refer to as the search time.

To quantify target search efficiency, we introduce a new rate constant: the specific on-rate (k ). We used a residence-time threshold of τ > 1 s to identify specific binding events and determined search times (as illustrated in Fig. 3e). We fitted the search time distributions (Fig. 3g) with a monoexponential decay to determine k for the Sox TFs interacting with the different DNA substrates. This analysis revealed that k increased with DNA length for Sox TFs (Supplementary Fig. 5m, Supplementary Table 3). We interpret this increased search efficiency on longer DNA as evidence that 1D sliding facilitates target search. This is consistent with direct experimental evidence for TF sliding for both prokaryotic and eukaryotic TFs and DNA binding proteins19,74–77. Sox2 consistently exhibited about 1.5 times higher k values compared to both Sox2a and Sox17, suggesting that DFR enhances target search efficiency over DFR .

Furthermore, the nearly identical k values of Sox2a and Sox17 strongly indicate that the DFR plays a key role in enhancing 1D diffusion-mediated target search.

We then implemented a theoretical formulation of the facilitated diffusion model describing the target search of a TF on DNA containing a single target site12,17 (Fig. 3h). Here, the target search process involves three steps. First, a TF binds nonspecifically to a random DNA site. Second, it slides along the DNA to the target until it either dissociates or recognizes and specifically binds the target site. The model is thus defined by four parameters: (i) the nanoscopic association rate (k), previously determined as about 2 × 105 M−1 s−1 bp−1 for the three Sox TFs (Supplementary Fig. 5e); (ii) the 1D diffusion coefficient on DNA (D ); (iii) the target recognition rate (k), which determines the probability of the TF recognizing the specific DNA site when sliding over it; and iv) the nonspecific residence time τ , reporting on the probability of the TF dissociating from nonspecific DNA sites, and set to 10 ms for both TFs71. Since τ sets the intrinsic timescale of the search process, we defined both the sliding and target recognition processes as a function of τ , introducing an average sliding length (s = 2∙D ∙τ ) and a target recognition constant (K = k ∙τ ) to reduce the number of parameters (Fig. 3h; see the “Methods” section).

The 1D target search model, now a function of two free parameters, K and s , was subsequently applied to fit the k dependence on DNA length (Fig. 3i, Supplementary Table 4). The specific binding probabilities during 1D sliding (p ) were 0.049 ± 0.036 for Sox2, 0.011 ± 0.007 for Sox2a, 0.009 ± 0.010 for Sox17 (Fig. 3j), confirming that DFR facilitates the TF target search more effectively. Accordingly, K , which was determined to be 2.3-fold higher for Sox2 (Fig. 3k), resulted in a higher target recognition rate for Sox2 (k = 2.70 ± 0.99 × 104 s−1) over Sox2a and Sox17 (k = 1.15 ± 0.16 × 104 s−1, k = 1.03 ± 0.17 × 104 s−1) (Fig. 3l). Conversely, s was around 1.4-fold greater for Sox2a and Sox17 (Fig. 3m), corresponding to D = 2.63 ± 1.09 × 105 bp2 s−1, D = 5.03 ± 2.34 × 105 bp2 s−1, and D = 5.55 ± 5.14 × 105 bp2 s−1 (Fig. 3n), in agreement with values reported for LacI19.

Together, this indicates that the DFR facilitates target recognition of Sox2 during 1D sliding, whereas the DFR leads to more frequent bypassing of the target site. The slower Sox2 sliding may reflect a trade-off between scanning speed and recognition efficiency78,79.

Sox TFs interact specifically and nonspecifically with nucleosomes
As Sox2 can bind to nucleosomes in vivo, we dissected the impact of DFR on TF-DNA interactions in the context of chromatin by comparing Sox2 and Sox2a. To examine their binding dynamics to single nucleosomes (Fig. 4a), we constituted three different mononucleosomes (MNs), using a 250 bp DNA sequence based on the 601 WS and recombinant human histone octamers, resulting in MNs flanked by 50 bp linker DNA. One MN contained a Sox motif positioned at superhelical location −6 (SHL-6), a position close to the nucleosome entry site (MN-6), where Sox2 can bind with Oct444. A second MN had the motif positioned at SHL+2 (MN+2), an internal position where Sox2 can bind and locally distort DNA39 (Fig. 4b; see the “Methods” section).

We also reconstituted an MN devoid of any binding motif (MN-). Using the smTIRF colocalization approach, we measured binding kinetics and constructed 1-CDFs of bound times from the resulting fluorescence time-traces (Fig. 4c, Supplementary Fig. 6a–c).

A triexponential function, associated with three residence times τ, τ , and τ , was required to adequately describe the binding kinetics of both Sox2 and Sox2a on motif-containing MNs (Supplementary Fig. 6d). In contrast, binding kinetics to MN-, lacking a TF binding site, were well-described by a biexponential decay with two residence times τ and τ . The shortest residence time (τ = 0.8 ± 0.1 s) was observed across all MNs, and given its similarity to τ in naked DNA, could be attributed to nonspecific DNA interactions (Fig. 4d). In contrast, the intermediate residence time (τ = 3.4 ± 0.4 s) was not identified in free DNA and is thus specific for MNs. As it appeared in both motif-containing and motif-absent MNs, we attribute it to TF-histone interactions (Fig. 4d). Finally, the longest residence time (τ = 9.3 ± 0.6 s) was unique to motif-containing MNs, confirming its correspondence to specific interactions (Fig. 4d).

We then compared Sox2 binding to the motifs within MNs at SHL+2 and SHL−6. While the residence times were comparable for the two positions (Fig. 4e), the fraction of specific binding events was higher in MN+2 compared to MN−6, indicating that Sox2 has a higher probability of binding to the internal position at SHL+2 (Fig. 4f). This can be explained by the rotational positioning of the motif, which faces outward in MN+2 but inward in MN-6, consistent with previous reports70. Finally, a comparison between Sox2 and Sox2a (Fig. 4e–h, Supplementary Table 5) showed similar residence times across all tested MNs.

DFR increases the fraction of specifically bound molecules on chromatin
We next used single-molecule imaging to assess whether the nature of the DFR is critical for the chromatin invasion ability of Sox237 (Fig. 5a). We assembled chromatin fibers (CFs) on DNA templates containing 10 tandem repeats of the 601 WS separated by 30 bp linker DNA, either containing a Sox motif at the entry site (SHL−6) of the fifth nucleosome (CF+) or in the absence of any target motif (CF−) (Supplementary Fig. 7a–c; see the “Methods” section).

We then imaged Sox2 and Sox2a binding dynamics to these chromatin fibers. Of note, under our imaging buffer conditions, corresponding to an ionic strength of 120 mM monovalent cations, chromatin is partially compacted37,80. With CF+, Sox2 exhibited more frequent long binding events compared to Sox2a (Fig. 5b). Similar to the MN results, both Sox TFs showed three different residence times on CF+, while they displayed only two nonspecific binding populations on CF− (Supplementary Fig. 7d–h). These residence times closely matched the ranges identified in the MN dataset (Supplementary Table 5). On chromatin fibers, nonspecific interactions predominate because of their large size and the consequent challenge for a TF to locate its embedded target site. However, Sox2 exhibited significantly more long binding events (7.0 ± 1.6%) (Supplementary Fig. 7f) compared to Sox2a (1.2 ± 0.3%) (Supplementary Fig. 7h). This suggests that DFR enhances Sox2’s ability to access and recognize motifs within chromatin.

We next determined k for Sox2 and Sox2a on MNs and CFs, using a residence time threshold (3.8 s for MNs, 3.4 s for CFs) to select specific binding events, and generated 1-CDF curves of interspaced search times (Supplementary Fig. 7i, j). We found k to be markedly higher for Sox2 than for Sox2a on all substrates (Fig. 5c). This was especially pronounced for MN+2 compared to MN-6, highlighting Sox2’s superior ability to interact with internal target sites. Of note, we detected a lower frequency of binding events with residence times above the threshold in the absence of the motif, which originate from the tail of the τ lifetime distribution and could be assigned as a background on-rate (shown in gray in Fig. 5c).

In general, a target site within chromatin is expected to be less accessible than on a nucleosome because of nucleosomes stacking in a tetranucleosome conformation81–83. However, the effective k of Sox2 increased from MN-6 to CF+ by 1.3-fold (Fig. 5c), suggesting that 1D diffusion along the chromatin, or a higher local TF concentration due to the availability of many nonspecific binding sites, might facilitate target search. In contrast, no such increase in effective k was detected for Sox2a (Fig. 5c). Finally, when including nonspecific binding events (Supplementary Fig. 7k, l), Sox2 exhibited approximately three times higher k with all the nucleosome constructs than Sox2a (Fig. 5d). As the nature of the DFR did not impact the on-rate for naked DNA (Supplementary Fig. 5c–e), this suggests that the nonspecific interactions of DFR increase the on-rate specifically on nucleosomes.

In summary, our on-rate results demonstrate that DFR promotes prevalent nonspecific binding from 3D diffusion to nucleosomes, enabling Sox2 to invade chromatin more effectively.

DFR enhances in vivo pioneer activity by facilitating closed chromatin binding and initiation of chromatin opening
We next asked how the different DFRs control chromatin invasion of Sox TFs in cells. We induced Sox2 and Sox2a expression in engineered mESC lines, and subsequently performed fluorescence-activated cell sorting (FACS) to select cells with near-identical TF expression levels (Fig. 6a, Supplementary Fig. 8a; see the “Methods” section). We validated the genome-wide binding profiles of exogenously-expressed Halo-Sox2 against endogenously expressed Sox2 via ChIP-Seq3 (Supplementary Fig. 8b, c).

To quantitatively compare the genomic occupancy of Sox2 and Sox2a, we applied a spike-in normalization approach using Drosophila chromatin (see the “Methods” section). We merged regions enriched for one or both Sox TFs (Sox-enriched regions) (Fig. 6b). Sox2a enrichment was well-correlated to Sox2 ChIP scores across Sox-enriched regions, although the occupancy level was lower compared to Sox2 (Fig. 6c, Supplementary Fig. 8d). To analyze genome-wide binding patterns, we identified the commonly occupied regions (CORs) containing ChIP-seq peaks for both Sox2 and Sox2a (Fig. 6b). We then plotted the log2-fold change of the COR ChIP scores for Sox2 over Sox2a in descending order. CORs were further sub-clustered into three groups (Fig. 6d) defined by (i) higher Sox2 binding; (ii) higher Sox2a binding; (iii) equal binding of Sox2 and Sox2a within a ±10% margin. The larger number of Sox2-enriched CORs (Fig. 6d) and higher ChIP enrichment of Sox2 across CORs (Supplementary Fig. 8e) confirmed that Sox2 exhibited greater genomic occupancy compared to Sox2a. Besides, motif analysis across CORs and exclusive regions revealed comparable binding specificity of Sox2 and Sox2a (Supplementary Fig. 8f).

To assess the ability of Sox2 and Sox2a to open compact regions, we generated ATAC-seq data for the same cell lines. We aligned ATAC-seq profiles with ChIP log2-fold changes to assess chromatin accessibility across CORs. CGR8 cells expressing only H2B-SNAP (Ctrl) served as a control of initial chromatin accessibility (Fig. 6e). mESCs overexpressing Sox2 exhibited higher chromatin accessibility at CORs than those overexpressing Sox2a (Supplementary Fig. 8g). However, Ctrl ATAC-seq revealed that Sox2-enriched CORs were initially 1.7-fold more closed compared to Sox2a-enriched CORs (Fig. 6f). This confirms that DFR enhances chromatin invasion of Sox2, as we observed in vitro. We then computed the log2-fold change of ATAC scores for Sox2 and Sox2a over Ctrl. Sox2 increased chromatin accessibility across CORs more than Sox2a (Fig. 6g, Supplementary Fig. 8h).

Finally, we determined changes in chromatin accessibility in regions with comparable Sox2 and Sox2a occupancy (within a range of ±10%) and initial chromatin accessibility (Fig. 6h). Chromatin accessibility increased more for Sox2 than for Sox2a (Fig. 6i). Altogether, this data indicates that DFR allows Sox2 to bind to poorly accessible chromatin and to open bound regions more effectively, which endows Sox2 with superior pioneering activity.

Methods
mESC culture
mESCs were routinely cultured on 0.1% gelatin-coated (Sigma, G9391) 100 mm Petri dishes at 37°C with 5% CO in GMEM (Sigma, G5154-500ML), supplemented with 10% ESC-qualified fetal bovine serum (Gibco, 16141-079), 1% nonessential amino acids (Gibco, 11140-050), 2 mM L-glutamine (Gibco, 25030-024), 2 mM sodium pyruvate (Sigma, S8636-100ML), 100 μM 2-mercaptoethanol (Sigma, 63689-25), 1% penicillin–streptomycin (BioConcept, 4-01F00-H), in-house produced leukemia inhibitory factor (LIF), CHIR99021 (Merck, 361559-5MG) at 3 μM and PD184352 (Sigma, PZ0181-25MG) at 0.8 μM. Cells were passaged every 2–3 days using trypsinization (Sigma, T4049-100ML). Once cells reached 60–70% confluency, one-sixth to one-tenth of the culture was used for the next passage.

For imaging, one day prior to measurement, 170 μm glass-bottom 35 mm Petri dishes were pre-coated with a 1:10 dilution of Biolaminin (BioLamina, LN511-0202) in DPBS containing magnesium and calcium ions (Gibco, 14040117). Cells were then plated on the dishes in FluoroBrite DMEM (Thermo Fisher, A18967-01) supplemented with 10% ESC-qualified fetal bovine serum, 1% nonessential amino acids, 2 mM L-glutamine, 2 mM sodium pyruvate, 100 μM 2-mercaptoethanol (Sigma-Aldrich, 63689-25ML-F), 1% penicillin/streptomycin, LIF, CHIR99021 at 3 μM, and PD184352 at 0.8 μM.

Lentiviral vector production
Lentiviral vectors were produced by transfection of HEK 293T cells with the envelope (psPAX2, Addgene, 12260), packaging (pMD2.G, Addgene 12259), and the lentiviral construct of interest using calcium phosphate transfection106,107. The HEK293T cells were cultured in GlutaMAX-containing DMEM (Gibco, 31966021) with 10% fetal bovine serum (Gibco, 10270106) and 1% penicillin–streptomycin (BioConcept, 4-01F00-H). At 2 days post-transfection, when the cells reached 80% confluency, the virus-containing medium was harvested and cleared of cell debris by centrifugation. Viral vectors were concentrated 120-fold by ultracentrifugation at 20,000 × g for 120 min at 4°C. 50,000 cells in 1 mL of medium in a 12-well plate were transduced with 50 μL of concentrated lentiviral vector particles to generate stable cell lines.

Generation of dox-inducible Halo-SoxTF-expressing mESCs
SoxTF-expressing embryonic stem (SES) cell lines in Supplementary Table 6 are mESC derivatives of CGR8 cells engineered to express Halo-Sox TFs upon doxycycline induction. Three transgenes were inserted into the genome using a lentiviral vector approach. The lentiviral plasmids (pLV-TRE3G-Halo-Sox) were generated using the pLV-TRE3G-Halo-Sox2 plasmid108 and the cDNA sequence of Sox1740, which were sourced from the laboratory. Using the In-fusion cloning technique (Takara Bio, 638947), we generated lentiviral plasmids containing transgenes for every Halo-Sox TF. The obtained products were transformed into HB101 competent cells. Clones were sequenced to verify the presence of the sequence of interest.

CGR8 cells (Sigma, 07032901-1VL) were transduced to constitutively express rtTA3G, Halo-Sox TFs, or H2B-SNAP. The genes encoding the recombinant proteins, Halo-Sox TFs (sequences in Supplementary Table 7), regulated by seven Tet operators, and H2B-SNAP driven by an hPGK promoter, were integrated into the mouse genome of SES cells as indicated in Supplementary Table 6. To select SES cells containing the transgene of interest, cells were treated with 2 μg/mL of puromycin (Gibco, A11138-03) for the TRE3G-Halo-Sox2 transgene and/or 1 μg/mL of blasticidin for PGK-rtTA3G for a week. PGK-H2B-SNAP positive SES cells were sorted by FACS based on SNAP-SiR647 intensity after 30 min incubation of SNAP-labeling SiR647 dye (NEB, S9102S) in the cells.

Generation of 2TS22C cells expressing Halo-Sox2 or Halo-Sox2a
The 2TS22C cell line52 enables knockdown of endogenous Sox2 upon dox treatment. Similar to the dox-inducible Halo-Sox expressing mESCs (Supplementary Table 6), 2TS22C cells expressing Halo-Sox2 (SES13) or Halo-Sox2a (SES14) were generated using lentiviral vector transduction. To generate pLV-EF1α-Halo-Sox plasmids, mCherry in the pLV-EF1α-mCherry plasmid fragment was exchanged with Halo-Sox2 or Halo-Sox2a using restriction cloning. Finally, SES13 and SES14 were sorted by FACS based on Halo-SiR647 intensity after a 30 min incubation with 50 nM of Halo-SiR647 dye at 37°C.

Pluripotency maintenance assay
To ensure similar expression levels of Halo-Sox2 and Halo-Sox2a, SES13 and SES14 were incubated with Halo-labeling SiR647 dye for 30 min at 37°C followed by FACS using the intensity gate, resulting in the same mean fluorescence intensity between SES13 and SES14 samples. Immediately after FACS, 1000 cells were seeded on gelatin-coated, 170 μm glass-bottom 35 mm Petri dishes in GMEM (Sigma, G5154-500ML), supplemented with 10% ESC-qualified fetal bovine serum (Gibco, 16141-079), 1% nonessential amino acids (Gibco, 11140-050), 2 mM L-glutamine (Gibco, 25030-024), 2 mM sodium pyruvate (Sigma, S8636-100ML), 100 μM 2-mercaptoethanol (Sigma, 63689-25), 1% penicillin–streptomycin (BioConcept, 4-01F00-H), LIF, CHIR99021 (Merck, 361559-5MG) at 3 μM and PD184352 (Sigma, PZ0181-25MG) at 0.8 μM. Following this, 1 μg/mL of dox was added to induce knockdown of endogenous Sox2. The medium supplemented with dox was changed on the third and fifth day after seeding.

On the sixth day after the first dox addition, cells were fixed with 4% formaldehyde (Thermo Fisher, 28908) for 10 min at room temperature, gently washed with DPBS (Gibco, 14040091), and stored at 4°C in 2 mL of DPBS. Since differentiation of mESCs leads to colony flattening and loss of regular edges109–111, colony morphology serves as a metric of the pluripotency status. The shape of cell colonies was assessed using phase-contrast microscopy (Zeiss LSM700 UP2, BIOP, EPFL) with a ×10 air objective (Objective EC Plan-Neofluar ×10/0.3 Ph1 M27) on an inverted Zeiss Axio Observer Z1 microscope.

For NANOG IF imaging, on the fifth day after the first dox addition, 170 μm glass-bottom 35 mm Petri dishes were pre-coated with a 1:10 dilution of Biolaminin (BioLamina, LN511-0202) in DPBS containing magnesium and calcium ions (Gibco, 14040117). 600 cells were seeded on the dishes with fresh medium supplemented with dox. After cell fixation on day 6 using 4% formaldehyde (Thermo Fisher, 28908), cells were permeabilized with 0.5% Triton (AppliChem, A1388,0500) at room temperature, followed by multiple washes using DPBS (Gibco, 14040091). Blocking was performed with 1% BSA solution (Sigma-Aldrich, A7906; in DPBS) for 30 min. Subsequently, a rabbit anti-NANOG antibody (CST, 8822) was diluted 1:500 in 1% BSA and incubated with the cells overnight at 4°C. After washing the antibody off with DPBS, cells were incubated for 1 h at room temperature with AF647-conjugated secondary Chicken anti-Rabbit IgG antibody (Invitrogen, A-21443) at a 1:500 dilution in 1% BSA solution. The cells were washed gently twice with 0.1% Tween-20 (Fisher Scientific, 10113103; in DPBS) and once with DPBS. Finally, Fluoromount G with DAPI (SouthernBiotech, 0100-20) was applied to the samples, and cells were incubated for at least 10 min before imaging.

IF imaging was performed on an Inverted Nikon Eclipse Ti2-E motorized microscope using confocal microscopy (Nikon-CSU-W1, BIOP, EPFL) with a ×60 oil objective (Objective CFI Plan Apo Lambda ×60/1.40). 638 and 405 nm diode lasers were used to excite AF647 dye and DAPI, respectively. For quantification, the StarDist plugin112 in Fiji113 was employed to detect nuclei based on DAPI signals. AF647-NANOG IF intensity was then measured within the nuclei of each cell.

In vivo SMT sample preparation
One day prior to imaging, approximately 105 cells were plated on a 170 μm glass-bottom 35 mm Petri dish in FluoroBrite DMEM (Thermo Fisher, A18967-01) supplemented with 10% ESC-qualified fetal bovine serum (Gibco, 16141-079), 1% nonessential amino acids (Gibco, 11140-050), 2 mM L-glutamine (Gibco, 25030-024), 2 mM sodium pyruvate (Sigma, S8636-100ML), 100 μM 2-mercaptoethanol (Sigma, 63689-25), 1% penicillin–streptomycin (BioConcept, 4-01F00-H), LIF, CHIR99021 (Merck, 361559-5MG) at 3 μM and PD184352 (Sigma, PZ0181-25MG) at 0.8 μM. The dishes were already pre-coated with a 1:10 dilution of Biolaminin (BioLamina, LN511-0202) in DPBS containing magnesium and calcium ions (Gibco, 14040117).

The specific concentrations of dyes and dox to visualize Halo-Sox molecules were optimized for each Halo-Sox TF. Cells were incubated overnight with dox to induce Halo-Sox TF expression. Before the measurement, we performed Halo-labeling with the JF549 dye (Promega, GA1110) to measure the residence times and diffusing dynamics. Dox and Halo-JF549 concentrations are indicated in Supplementary Table 8. For all cell lines and conditions, 1–2 nM of SNAP-labeling SiR647 (NEB, S9102S) was applied. Cells were incubated with the dyes for 30 min at 37°C to visualize Halo-Sox TFs and SNAP-H2B, respectively, before imaging. Excess dye was gently washed out using the imaging medium.

In vivo smHILO microscopy setup
An inverted Nikon Eclipse Ti2-E fluorescence microscope equipped with a ×100 oil immersion NA 1.49 objective (SRHP Apo TIRF) was employed. Fluorophore excitation was achieved using the N-STORM Direct Point illuminator. Two-color imaging was performed with a 30 mW 561 nm diode laser for Halo-JF549 excitation, and a 50 mW 638 nm diode laser for SNAP-SiR647 excitation, with a 405/488/568/647 DM wheel and DM 568 LP emission filter. Dye emission was detected using two Photometrics Prime 95B sCMOS cameras with a physical pixel size of 11 × 11 μm2.

Our multi-time interval approach interleaves 60 ms illumination with dark periods of 60, 180, 420, and 900 ms. This design creates overlapping observation windows that capture both fast off-rates and long-lived binding events, ensuring comprehensive sampling of all intermediate lifetimes. This multi-time interval measurement also enabled correction for photobleaching, since the time-lapse imaging conditions only affect the photobleaching rate without altering residence times. The number of cells per time interval and Sox TF is indicated in Supplementary Table 9. SNAP-H2B was imaged with a 60 ms exposure time once every 9–10 frames of Halo-JF549.

To measure diffusion dynamics, we recorded continuous time-lapse movies for 30 s with a 100 Hz frame rate (cell numbers are indicated in Supplementary Table 9). Prior to capturing Sox TF kinetics, a snapshot of SNAP-H2B was taken with a 100 ms exposure. We used the same microscope settings as for diffusion analysis, except for the laser power for JF549 activation, which was increased to 110 mW.

Expression, labeling, and purification of Sox TFs
Each Halo-Sox TF construct contained a twin-Strep tag at the C-terminus and an 8× His tag at the N-terminus, and was cloned into the donor plasmid pACEBac1 (bearing a gentamicin resistance marker and a YFP reporter gene). Baculovirus production from Sf9 cells and subsequent Halo-Sox TF expression in Hi5 cells were performed by the Protein Production and Structure Core Facility at EPFL. For purification, the cell pellet harvested from 300 mL of cell culture was suspended in a lysis buffer (100 mM KCl, 150 mM NaCl, 50 mM Tris, 10 mM HEPES at pH 7.6, 2 mM DTT, 1 mM EDTA, protease inhibitor cocktail, 0.2 mM PMSF, 0.1% IGEPAL, 20–30 U/mL DNase I, 5 mM MgCl , and 5 mM CaCl ). The suspension was lysed by sonication at 30% amplitude (750 W/20 kHz) with 3/27 son/off pulses for 5 cycles on ice. The lysate was clarified by three rounds of centrifugation at 16,000–21,000 × g for 15–30 min each.

Twin-Strep affinity purification was performed on ice using 1 mL of Strep-Tactin Superflow high-capacity resin (IBA Lifesciences, 2-1208-010-20ML) according to the standard gravity-flow protocol. The resin was first washed with 2 mL of buffer W (100 mM Tris, pH 7.6, 150 mM NaCl, 2 mM DTT, 1 mM EDTA) and preincubated in cold lysis buffer. After loading the lysate, the column was washed with 7 mL of W buffer and then eluted with 12 mL of E buffer (100 mM Tris, pH 7.6, 150 mM NaCl, 2 mM DTT, 1 mM EDTA, 10 mM desthiobiotin). Elution progress was monitored by SDS–PAGE gel electrophoresis (Supplementary Fig. 4a–c). The eluted sample was incubated overnight on ice with a 1.1 molar equivalent of Halo ligand-JF549 (Promega, GA1110) in buffer S (100 mM KCl, 150 mM NaCl, 10 mM HEPES at pH 7.6, 2 mM DTT). After size-exclusion chromatography on a Superdex 200 Increase 10/300 GL column (Cytiva, 28990944) (Supplementary Fig. 4a–c), the Halo-Sox TFs were assessed for labeling efficiency (92–99%) and for concentration (1–2 μM) by UV–Vis spectroscopy (Supplementary Fig. 4a–c; Supplementary Table 10).

Electrophoretic mobility shift assays (EMSA)
The protein concentration was titrated from 0.8 to 50 nM while maintaining a constant concentration (2 nM) of AF647-labeled DNA substrate. Sdna6 (Sox motif: 5’-CATTGTG-3’; Supplementary Fig. 4d) and Sdna4 (Sox motif: 5’-CTTTGTT-3’; Fig. 3b) in Supplementary Table 11 were used as motif-containing DNA substrates. Especially, Sdna6 sequence corresponds to a region (−483 to −454)89 of the human miR302 gene. Additionally, five-fold excess (10 nM) of poly(deoxyinosinic-deoxycytidylic) acid (poly dI-dC, Thermo Fisher, 20148E) was added to reduce nonspecific interactions between Sox TFs and DNA114. The EMSA buffer consisted of 20 mM HEPES, 20 mM Tris, 1 mM DTT, 50 mM KCl, 0.5 mg/mL BSA, 0.02% Tween-20, 10% glycerol, 3.2% glucose, and 2 mM Trolox, at pH 7.5. After 30 min of incubation at room temperature, the reactions were separated by native PAGE using a 5% Tris base, boric acid, EDTA (TBE) gel, run in 0.5x TBE buffer, at 120 V for 50 min on ice. Dissociation constants were estimated by quantifying the proportion of bound versus unbound DNA in each lane as the Sox TF concentration increased, based on AF647 fluorescence emission.

To determine the ionic strength sensitivity of Sox TFs to DNA binding via EMSA, NaCl was titrated from 12.5 to 400 mM into the mixture of 1 nM fluorescently-labeled DNA substrate (Sdna6 in Supplementary Table 11; Sox motif: 5’-CATTGTG-3’), 10 nM Sox TFs in 20 mM HEPES, 20 mM Tris, 1 mM DTT, 12.5 mM KCl, 0.5 mg/mL BSA, 0.02% Tween-20, 10% glycerol, at pH 7.5. After 60 min of incubation at room temperature, the reactions were separated by native PAGE (5% TBE gel, 0.5× TBE buffer, 50 min at 120 V on ice). EC values were estimated by quantifying the proportion of bound versus unbound DNA in each lane as the NaCl concentration increased, based on AF647 fluorescent emission.

Oligonucleotide labeling
Synthetic oligonucleotides containing amino-modified C6 at their 5’-end were subjected to two rounds of ethanol precipitation prior to labeling. To initiate the labeling reaction, 10–20 nmol of oligonucleotide were dissolved in 50 μL of 0.1 M sodium tetraborate buffer (pH 8.5). A two molar-equivalent amount of the NHS ester-functionalized fluorophore (AF647 (Invitrogen, A20006) or XFD647 (AAT bio, 1833), which are chemically identical) was then added to the solution. The mixture was incubated in the dark at room temperature and agitated at 300 rpm overnight. After ethanol precipitation to eliminate unreacted dye, RP-HPLC purification was performed via RP-HPLC on an InertSustain C18 column (GL Sciences, 5020-07445) under a 20-min gradient from 0% to 70% Solvent B (100 mM triethylammonium acetate, pH 7, mixed with acetonitrile), with a flow rate of 1 mL/min and detection at 260 and 640 nm. The labeled oligonucleotides were resuspended in Milli-Q water at a final concentration of 0.1–1 mM and stored at −20°C.

Generation of naked and mononucleosome DNA
For DNA substrates shorter than 200 bp (Sdna3, Sdna4, Sdna5, Sdna6, Sdna8, in Supplementary Table 11), two complementary oligonucleotides that are either biotinylated or AF647-conjugated (4–40 μM each) were annealed in 50–200 μL of 1× Phusion HF buffer. The mixture was heated to 95°C and then cooled to 20°C at a rate of −1°C/min, followed by a 1-h incubation at 55°C to ensure complete strand hybridization. For double-stranded DNA longer than 200 bp (Sdna9, Sdna10, Sdna11, Sdna16, in Supplementary Table 11), PCR amplification was performed. Each 50 μL reaction in 1× Phusion HF buffer contained 100–600 nM of a fluorescently labeled primer, a 1.1–1.2 molar equivalent of a second primer, 200 μM dNTPs (NEB, N0447S), and 1–2 U of Phusion DNA polymerase (NEB, M0530S). The two primers were either conjugated with AF647 or biotinylated. Template DNA (1–5 ng) was typically used, except for Sdna4. For Sdna4, both primers were used at 3 μM to generate primer dimers during amplification. The thermocycling program included an initial denaturation at 95°C for 1 min, followed by 25–30 cycles of 95°C for 30 s, 60–68°C for 15 s, and 72°C for 30 s, with a final 5-min extension at 72°C. 8–48 parallel reactions were conducted to increase DNA yield. Both the annealed and PCR-amplified products were then purified using QIAquick PCR purification kit (QIAGEN, 28104) and verified by native polyacrylamide gel electrophoresis.

Preparation of 1x MMTV buffer DNA
MMTV buffer DNA (Sdna19 in Supplementary Table 11) for chromatin reconstitution was derived from a plasmid carrying eight tandem repeats of the MMTV sequence (8× MMTV DNA). After growing large-scale plasmid cultures (100 mL), DNA was purified using a midiprep kit (QIAGEN, 12943), digested overnight at 37°C with EcoRV-HF (NEB, R3195L) and Quick CIP (NEB, M0525L), followed by incubating the digest at 80°C for 20 min to inactivate the enzymes. The resulting 1× MMTV fragments (151 bp) were purified from the plasmid backbone using PEG6000 precipitation. Residual PEG was removed through PCR purification kits (QIAGEN, 28104), ensuring a clean preparation of the MMTV DNA fragments.

Generation of plasmids containing 10-mer 601WS nucleosome arrays
To obtain a 10× 601WS array featuring 30-bp linkers and incorporating a Sox motif at the SHL-6 position of the fifth nucleosome (Supplementary Fig. 7a; Sdna17 in Supplementary Table 11), we adopted a plasmid-based strategy for precision and reproducibility. The final plasmid, Spla38 was assembled through a two-step molecular cloning workflow using RecP1115 and Spla37. Their relevant sequence blocks used in this work are marked below:
RecP1: pWM531-EcoRI-DraIII-1×601WS-BamHI-4×601WS-BglII-BsaI
Spla37: pMARQ-BglII-Sox601WS-DraIII
First, the 5× 601WS plasmid (Spla42), which contains a Sox motif at the fifth nucleosome position, was generated. The BamHI-4×601WS-BglII segment from RecP1 was inserted into Spla37 (pMARQ-BglII-Sox601WS) by BamHI/BglII restriction cloning. Before digestion, Spla37 was PCR-linearized using a reverse primer (Soli179 in Supplementary Table 12) containing 5’-BamHI-EcoRI-3’ restriction sites. The resulting construct, Spla42 is summarized below:
Spla42: pMARQ-EcoRI-BamHI-4×601WS-BglII-Sox601WS-DraIII
Second, the 10× 601WS plasmid (Spla38) containing a Sox motif at the fifth nucleosome was cloned. The EcoRI-4×601WS-Sox601WS-DraIII segment from Spla42 was transferred back into RecP1 (pWM531-EcoRI-DraIII-5×601WS) by EcoRI/DraIII restriction cloning, yielding the final plasmid, Spla38 shown below:
Spla38: pWM531-4×601WS-Sox601WS-5×601WS-BsaI
To generate a Sox motif-free 10× 601WS control plasmid (Sdna18 in Supplementary Table 11), Spla37 was replaced with Spla36 (pMARQ-BglII-601WS-DraIII) and the same cloning workflow was applied. The intermediate and final plasmids are:
Spla43: pMARQ-EcoRI-5×601WS-DraIII
Spla35: pWM531-10×601WS-BsaI
Restriction enzymes used in this workflow included BamHI-HF, BglII, EcoRI-HF, and DraIII-HF (NEB). Both Spla38 and Spla35 were validated by Sanger sequencing and by diagnostic digests (EcoRI-HF, EcoRV-HF, BsaI-v2-HF, and HindIII-HF; NEB). Validated plasmids were expanded in 200 mL cultures of DH5α E. coli and purified using the QIAquick midiprep kits (QIAGEN, 12943) followed by QIAquick PCR purification kits (QIAGEN, 28104).

Purification of chromatin DNA
To purify chromatin DNA for the assembly of CF+ or CF− (Sdna17 and Sdna18, respectively; sequences in Supplementary Table 11), a standard digestion reaction was set up with 1000–2500 pmol of plasmid DNA (Spla38 or Spla35) in a final volume of 1.4 mL of 1× γCutSmart buffer. The reaction was supplemented with 1200 units of EcoRI-HF (NEB, R3101L), 2000 units of EcoRV-HF (NEB, R3195L), and 500 units of Quick CIP (NEB, M0525L), and incubated at 37°C for 20 h. The enzymes were then inactivated by heating to 80°C for 30 min.
To generate a BsaI overhang 3’-end, 1000 units of BsaI-HFv2 (NEB, R3733S) were added in a final volume of 1.46 mL of 1× γCutSmart buffer, followed by incubation at 37°C for 20 h.
The digested DNA was then purified through multiple rounds of 4–7.5% PEG6000 precipitation to remove plasmid backbone fragments. After adjusting the NaCl concentration to 500 mM, samples were incubated on ice for 30 min and centrifuged at 21,000 × g for 30 min at 4°C to pellet short DNA fragments. The supernatant was retained at each step, while the PEG6000 concentration was increased in 0.5% increments. Gel electrophoresis of both the supernatant and the pellet at each step monitored the purification progress. Once the target DNA fragments reached high purity, remaining PEG was removed using QIAquick PCR purification kits (QIAGEN, 28104).
To generate the biotinylated adapter oligo (Sanc1 in Supplementary Table 11) as described previously116, a biotin-labeled oligonucleotide was annealed in 1× T4 DNA ligase buffer to its complementary strand (Soli176 and Soli175, respectively, in Supplementary Table 12), which carries a 5′-phosphorylated BsaI overhang and an AF647 fluorophore introduced via an NHS-ester labeling protocol. Next, 800–1600 pmol of chromatin DNA possessing a BsaI overhang (previously purified by PEG precipitation) were mixed with a 2.5-fold molar excess of Sanc1. The mixture was ligated overnight at 16°C in the dark using 8000 units of T4 DNA ligase (NEB, M0202S). Excess Sanc1 was removed by PEG precipitation, and the resulting ligated DNA (Sdna17 or Sdna18 in Supplementary Table 11) was further purified with the QIAquick PCR purification kit (QIAGEN, 28104).

Octamer refolding
To refold histone octamers, equimolar ratios of recombinant, purified human H3.2 containing the C110A substitution and wild-type human H4 were combined in an unfolding buffer (6 M Guanidine–HCl, 20 mM Tris–HCl, 5 mM DTT, pH 7.5) alongside 1.1 equivalents of wild-type human H2A and human H2B. The final protein concentration was adjusted to 0.5–1 mg/mL. Refolding proceeded via dialysis in a Slide-A-Lyzer Dialysis Cassette (Thermo Fisher, 66332) against a refolding buffer (2 M NaCl, 10 mM Tris, 1 mM EDTA, 1 mM DTT, pH 7.5). Any aggregates were removed by centrifugation at 2500 × g for 20 min at 4°C. The resulting octamers were purified by size-exclusion chromatography on a Superdex 200 Increase 10/300 GL column (Cytiva, 28990944) and analyzed by SDS–PAGE and RP-HPLC. Fractions containing pure octamers were pooled and concentrated to ~40 μM. Glycerol was then added to a final concentration of 50%, and these octamer stocks were stored at −20°C until use.

Nucleosome assembly
Mononucleosomes (MN−6, MN+2, and MN−) and chromatin fibers (CF+ and CF−) containing up to 10× 601WS nucleosome positioning sequences (NPSs) with 30 bp linkers were assembled through high-salt to low-salt dialysis (from 2 M to 10 mM NaCl) (Supplementary Fig. 7a). In a high-salt buffer (10 mM Tris, 1 mM EDTA, 2 M NaCl), histone octamers were mixed with DNA (Sdna10, Sdna11, Sdna16, Sdna17, or Sdna18 in Supplementary Table 11) at NPS-to-octamer ratios ranging from 1:1 to 1:2.5. To avoid excessive octamer binding to the fibers, 0.25 equivalents of MMTV DNA, which has lower affinity for mononucleosome formation compared to 1× 601 DNA, were added exclusively to the chromatin assembly reaction. The mixture was dialyzed overnight at 4°C, while the salt concentration was gradually changed using a peristaltic pump from high-salt to low-salt buffer (10 mM Tris, 1 mM EDTA, 10 mM NaCl). After dialysis, any aggregates were removed by centrifugation (21,000 × g, 10 min, 4°C). The dialyzed sample concentrations were determined by UV using a NanoDrop spectrophotometer (Thermo Fisher), and nucleosome assembly efficiency was evaluated by native PAGE performed on ice.

The integrity of the chromatin fibers was assessed by ScaI digestion of the fibers, resulting in individual mononucleosomes (Supplementary Fig. 7b). 80 ng of chromatin fibers were incubated with ScaI-HF (NEB, R3122S) at 37°C for 3 h in the dark. The digested products were then analyzed by native PAGE to confirm nucleosome quality and ensure full nucleosome occupancy as inferred from the absence of free DNA (Supplementary Fig. 7b). Once octamer saturation was verified, magnesium precipitation using 6 mM MgCl was used to further purify the chromatin fibers (Supplementary Fig. 7c).

The imaging buffer IB3 contained 100 mM KCl and 20 mM HEPES (with Na+ as the counterion), yielding 120 mM monovalent cations. Under these conditions, chromatin adopts a partially compacted state, as revealed by single-molecule FRET37,80.

Slide and cover glass cleaning and flow-channel assembly
Coverslips (24×40 mm2, 1.5 mm thick) and glass slides (76×26 mm2), containing holes to access flow channels after assembly, underwent multiple cleaning steps: First, they were sonicated for 20 min in a 10% (w/v) Alconox detergent solution, followed by successive sonication in ethanol and acetone. Between each solvent step, Milli-Q water sonication ensured the removal of the previous solvent. The slides were then cleaned for 2–4 h in a Piranha solution (3 M sulfuric acid and 60% hydrogen peroxide at a 3:1 ratio) and thoroughly rinsed in Milli-Q water. Next, they were sonicated in acetone for 10 min, then silanized for 10 min in 2% (3-aminopropyl)triethoxysilane prepared in acetone. Afterward, they were quenched in Milli-Q water and dried under nitrogen gas.

To assemble flow channels, we cut channel spacers from a 0.12 mm thickness double-sided adhesive sheet (GraceBio, 620001) using previously reported designs37,115,117. Each set of prepared coverslips and slides was assembled into a “sandwich” configuration, with the printed adhesive sheet sandwiched between the silanized coverslip and glass slide. The assembled devices were subsequently vacuum-sealed and stored at −20°C until use.

Microfluidic channel preparation
To prepare measurement chambers, assembled coverslip-microscopy slide devices were warmed to room temperature. 10-µL pipette tips were glued into the prepared holes using epoxy glue. The individual flow-channels were then passivated by PEGylation: A PEG solution was prepared by dissolving 1 mg of biotinylated PEG-bis-succinimidyl valerate (SVA) (5 kDa) and 20 mg of methoxy PEG-SVA (5 kDa) in 200 µL of 100 mM sodium tetraborate buffer (pH 8.5). This solution was injected into the pre-formed channels and incubated for 2–3 h at room temperature before use in single-molecule experiments.

smTIRF microscopy setup
For single-molecule colocalization imaging, we used a Nikon Ti-E inverted microscope equipped with a Nikon TIRF illuminator and a ×100 oil immersion objective (NA 1.49). For illumination, two lasers were used: a Coherent OBIS 640LX (640 nm, 40 mW) to image AF647-labeled DNA and an OBIS 532LS (532 nm, 50 mW) to image JF549-labeled Halo-Sox TFs. These lasers were coupled into the microscope via an optical fiber, and an acousto-optic tunable filter was used for wavelength selection. Laser power densities at the objective were 44 W/cm2 for 532 nm and 11 W/cm2 for 640 nm. Nikon’s Perfect Focus system was used to compensate for axial fluctuations in the field of view (FOV). Emissions were detected over an 800×800 px2 FOV by a Photometrics Prime 95B sCMOS camera, with a physical pixel size of 11×11 μm2. Some movies acquired on bare DNA substrates were recorded using an ANDOR iXon EMCCD camera with a 256×256 px² FOV and 16×16 μm2 pixel size.

In vitro single-molecule colocalization measurements
Prior to imaging, all buffers were degassed. An oxygen-scavenging system was prepared by dissolving 1 mg catalase in 100 µL of 50 mM phosphate buffer (pH 7.0), and 10 mg glucose oxidase was dissolved in a mixture of 40 µL catalase solution and 60 µL of T50 buffer (Gloxy). This mixture was centrifuged at 21,000 × g for 3 min, and the supernatant was taken for use. All DNA and protein samples used for in vitro SMT were spun down at 21,000 × g for 10 min at 4°C to clear aggregates and were transferred to DNA low-binding (Eppendorf, 0030108051) or protein low-binding tubes (Eppendorf, 0030108116), respectively.

Prior to imaging, each PEGylated flow-channel was rinsed with ultra-pure water (ROMIL, H950L) and equilibrated with T50 buffer (10 mM Tris, 50 mM NaCl, pH 8). A peristaltic pump was used for the injection into the microfluidic channel. 30 μL of 0.2 mg/mL neutravidin in the T50 buffer was injected to facilitate DNA-substrate tethering and then washed with the T50 buffer. BSA (5 mg/mL) was incubated for 10 min, followed by washing with T50. Finally, the channels were equilibrated with imaging buffer (IB3), which included 20 mM HEPES, 20 mM Tris, 1 mM DTT, 3 mM EDTA, 100 mM KCl, 2 mg/mL BSA, 0.02% Tween-20, 10% glycerol, 3.2% glucose, Gloxy, and 2 mM Trolox at pH 7.5.

For immobilization, 10–50 pM of AF647-labeled, biotin-conjugated DNA constructs, mononucleosomes, or chromatin fibers in IB3 buffer were injected into the channel, with the degree of immobilization measured by single-molecule imaging. Excess DNA constructs, mononucleosomes, or chromatin fibers were washed away with 200 μL of IB3 buffer. Finally, 2 nM of JF549-labeled Halo-Sox2 or Halo-Sox2a was flowed at 0.5 μL/min.

After injection, Sox TF interaction dynamics with immobilized DNA, nucleosome, and chromatin substrates were recorded using a 10-min acquisition at a 200 ms frame interval. AF647-labeled DNA was excited and imaged once every 200 frames for drift correction and DNA localization, whereas JF549-labeled Halo-Sox TFs were recorded continuously (100 ms illumination + 100 ms dark time per frame).

ChIP-seq
Under the mESC culture conditions described above, SES4.1, SES5.1, SES7.1, and SES9.1 cells (Supplementary Table 6) were incubated for 20 h in the presence of 300, 70, 1000, and 1000 ng/mL dox, respectively, to induce expression of Halo-conjugated Sox2, Sox2a, Sox17, and Sox17b. The Halo-Sox TFs were then labeled with 50 nM Halo-SiR dye. Two biological replicates were processed for Sox2 and Sox2a, while Sox17 and Sox17b were profiled using one biological replicate each.

Fixation was performed in a PBS-based buffer, first with 2 mM of disuccinimidyl glutarate (Thermo Fisher, 20593) for 50 min at room temperature, followed by 1% formaldehyde (Thermo Fisher, 28908) for 10 min. Fixation was quenched by incubating the samples in 200 mM Tris–HCl (pH 8.0) for 10 min. Fixed cells were pelleted at 600 × g for 4 min at 4°C and resuspended in 1% ESC-qualified fetal bovine serum (Gibco, 16141-079). Cells were sorted by FACS at 4°C, using the intensity gate adjusted to yield equivalent mean Halo-SiR intensities between SES4.1 and SES5.1 FACS samples (Fig. 6a, Supplementary Table 13), and similarly between SES7.1 and SES9.1 FACS samples.

Sorted cells were resuspended in LB1 buffer (50 mM HEPES–KOH pH 7.4, 140 mM NaCl, 1 mM EDTA, 0.5 mM EGTA, 10% Glycerol, 0.5% NP-40, 0.25% Triton X-100, supplemented with Protease inhibitor cocktail (Sigma, P8340-1ML) at 1:100 dilution), incubated on ice for 10 min, and centrifuged at 1700 × g for 5 min at 4°C. This step was repeated once more. Pellets were then resuspended in LB2 buffer (10 mM Tris–HCl pH 8.0, 200 mM NaCl, 1 mM EDTA, 0.5 mM EGTA, supplemented with Protease inhibitor cocktail (Sigma, P8340-1ML) at 1:100 dilution), incubated for 10 min on ice, and centrifuged again. Pellets were washed twice with SDS shearing buffer (10 mM Tris–HCl pH 8.0, 1 mM EDTA, 0.15% SDS, supplemented with Protease inhibitor cocktail (Sigma, P8340-1ML) at 1:100 dilution)), taking care not to disturb them, and finally resuspended in SDS shearing buffer on ice. Chromatin was sheared using a Covaris E220 (200 cycles, 5% duty cycle, 140 W, 20 min). Lysates were clarified at 10,000 × g for 5 min at 4°C, and supernatants were collected.

ChIP and DNA purification were performed using the ChIP-IT High Sensitivity kit (Active Motif, 53040) according to the manufacturer’s instructions. Input chromatin amounts were 20 μg for Sox2 and Sox2a, and 30 μg for Sox17 and Sox17b. Drosophila spike-in chromatin (Active Motif, 53083) was added at 1 ng per 1 μg of target chromatin. Spike-in antibody (anti-H2Av; Active Motif, 61686) was added at 0.5 μg per 10 ng spike-in chromatin and processed together with 40 μL Halo-Trap agarose beads (ChromoTek, ota-20) per reaction. ChIP reactions were incubated overnight at 4°C on a rotating platform (30 rpm). Sequencing libraries were prepared using the NEBNext Ultra II DNA Library Prep Kit (NEB, E7645), size-selected using AMPure XP beads (Beckman Coulter, A63880), and sequenced on an Illumina NextSeq 500 using 75-nucleotide read-length paired-end sequencing.

ATAC-seq
SES4.1 and SES5.1 cells were treated with dox under the same conditions used for ChIP-seq and labeled with 50 nM Halo-SiR647 dye. Cells were FACS-sorted at 4°C using the same intensity gates as in the ChIP-seq workflow (Supplementary Table 13).

ATAC-seq was performed following established methods118. Approximately 50,000 cells were lysed in 50 μL of ATAC–lysis buffer (10 mM Tris–HCl, 10 mM NaCl, 3 mM MgCl , 0.1% NP-40, pH 7.4), and nuclei were pelleted at 800 × g for 5 min. The transposition reaction was carried out by resuspending nuclei in 50 μL of TAPS-DMF buffer (10 mM TAPS, 5 mM MgCl , 10% DMF, pH 8.5) and 2.5 μL of Tn5 transposase (Illumina, 20034197) at 37°C for 30 min. DNA was eluted in 10 μL of nuclease-free water, using the DNA Clean & Concentrator kit (Zymo Research, D4004) with a 5:1 binding buffer-to-sample ratio.

For library preparation, transposed DNA was PCR-amplified using NEBNext High-Fidelity 2× PCR Master Mix (NEB, M0541L), 0.5 μM Ad1.1 universal primer, 0.5 μM Ad2.X indexing primer, and 0.6× SYBR Green I (Thermo Fisher, S7585) in a 65 μL reaction. Thermocycling proceeded as follows: 72°C for 5 min; 98°C for 30 s; then 5 cycles of 98°C for 10 s, 63°C for 30 s, and 72°C for 60 s.

A 10 μL aliquot was analyzed by qPCR to determine the optimal total number of amplification cycles, using the fluorescence signal at one-third saturation to avoid over-amplification. The remaining DNA was amplified for the required number of cycles, purified (Zymo, D4004), size-selected with AMPure XP beads (Beckman Coulter, A63880), and sequenced on an Illumina NextSeq 500 using 75-nucleotide read-length paired-end sequencing.

Electrical charge distribution generation
Along a protein sequence, the average charge of the amino acids within a sliding five-amino-acid window was calculated. The residues Aspartic acid (D) and Glutamic acid (E) were assigned a charge of −1, Histidine (H) a charge of +0.5, and Lysine (K) and Arginine (R) a charge of +1. These calculations were performed using EMBOSS Pepinfo120.

In vivo SMT imaging data processing
Nuclei were detected using the StarDist plugin in Fiji113. Based on these nuclear ROIs, single-cell movies in the JF549 channel were cropped. Using TrackIt55, individual Sox TF molecules within the nuclear ROIs were detected using the detection thresholds listed in Supplementary Table 14. Detected spots were linked across consecutive frames using the nearest-neighbor algorithm to construct the single-molecule trajectories. The tracking-loss probability (due to molecules moving laterally out of the imaging plane or out of focus) was set to 0.005. Considering the input parameters (Supplementary Table 14) and the loss probability, the tracking radii were automatically computed for different dark time conditions (Supplementary Table 15). For the continuous movies with 100 Hz of frame rate, the tracking radius for all Sox TFs was set to 8.1312 pixels with respect to 894 nm of the maximum jump distance.

GRID analysis
GRID is restricted to superimposed exponential reactions with positive amplitudes and converts the inverse Laplace transformation into a minimization problem, exploring a discrete set of potential outcomes56. In the off-rate domain, 200 possible dissociation rates (k) were logarithmically spaced from log(k)=–3 to log(k)=0.85. Bulk GRID analysis yielded a single photobleaching rate for the pooled trajectories of all the Sox TFs. This photobleaching rate (0.028 s−1) was then applied uniformly to all Sox TF constructs, regardless of the specific TF. The regularization weight parameter was set to 0.1, the default value in the GRID implementation.

For each Sox TF, 100 resampling iterations were performed. In each iteration, 80% of single cells were randomly selected using a custom MATLAB code, and a GRID spectrum was computed. GRID-determined dissociation rates with amplitudes below 0.1% were excluded. The remaining rates from all 100 iterations were combined into a relative frequency histogram using 100 equally spaced bins (Fig. 1h). To compute the fractional occupancy spectrum (F) (Supplementary Fig. 2e), each GRID-determined state’s amplitude (A) was weighted by its residence time (τ), and the resulting products were normalized by their total sum:

State array analysis
The State array method61, for which the code is openly accessible, was used with the following settings: likelihood_type=RBME, pixel_size_μm=0.11, frame_interval=0.01, focal_depth=0. The diffusion coefficient grid was defined on a logarithmic scale from 10−3 to 102 µm2 s−1 (150 bins) while all the other parameters were kept as default in constant.py. The state occupations marginalized on the diffusion coefficient for individual cells were computed in Fig. 2c and per TF, the single-cell state occupations were averaged in Fig. 2d.

Spot-On analysis
The MATLAB version of Spot-On59 was used in this analysis. To generate the Spot-On data from single-cell analysis, the entire trajectories were used. In the 3-state model, the range of each diffusion coefficient was set to be 1×10−5–5×10−2 µm2 s−1 for the bound state, 5×10−2–5×100 µm2 s−1 for the slow diffusing state, and 1×100–5×101 µm2 s−1 for the fast diffusing state. For the jump length distribution parameters, the number of time points and max jump distance were set as 8 and 2 µm. To correct localization and defocalization errors, for z-correction, an axial resolution of 0.7 µm was applied, and the localization error fitted from data was allowed. The CDFs of jump lengths were fitted globally across all the time points in 3 iterations.

Pseudo on-rate analysis
The pseudo on-rate (k ) was calculated according to Eq. (2)

where n is the number of considered frames, TI is a time interval between movie frames, C is the concentration of target TFs per frame (i), and N τ is the number of selected molecules lasting the given bound time (τ), which appear first at the frame i.

For nonspecific k , molecules detected in 100 Hz continuous movies were used and τ < 1 s was applied. During trajectory reconstruction in TrackIt, the maximum allowed jump distance was constrained by a diffusion coefficient of 0.08 µm2 s−1, yielding a tracking radius of 0.5243 µm. The total number of bound or diffusing trajectories was used as a proxy for the relative nuclear concentration of each Sox TF.

For specific k , molecules detected in 120 ms time interval movies were considered and τ was set to > 1 s. Here, the nuclear concentration of Sox TFs was estimated from the mean Halo-JF549 nuclear intensity after background subtraction. Photobleaching effects were accounted for by measuring the fluorescent intensity per frame over time.

Following the initial phase during which most molecules are detected, a series of consecutive empty frames—where no molecules are detected—could artificially lower the average molecule count, leading to an underestimation of k . Such empty frames often occur due to photobleaching or during long recordings with prolonged periods without signal. To correct for this bias, we defined an idle time (5 s for nonspecific k and 10 s for specific k ). When an idle period is detected, n is set to the first frame of that period, and the summation for the average is terminated. This approach excludes empty frames from the calculation, ensuring a more accurate measurement of the k . Custom MATLAB scripts were used to perform this calculation.

For statistical analysis in OriginPro 2022, the single-cell distributions of k across Sox TFs were first assessed for normality using the Shapiro–Wilk test, with normality rejected at a significance level of 0.05. Consequently, a Kruskal–Wallis ANOVA was performed, followed by Dunn’s test for multiple comparisons.

In vitro single-molecule colocalization data processing
ND2 raw images were converted to TIFF format, followed by background subtraction using a rolling ball filter with a radius of 50 pixels. This process was done in Fiji113. Further data extraction was performed using custom MATLAB codes. The analysis consisted of six main steps. First, the loci of anchored DNA/MN/CF on the FOV were identified. Second, colocalization of Sox TFs with immobilized DNA/MN/CF was determined using 2D-Gaussian fitting of detected single-molecule emitters to determine the shape of the point spread function (PSF) as well as the exact position of each detection. Third, we extracted fluorescence time-traces of JF549-labeled Sox TFs from each DNA/MN/CF location. Fourth, each time-trace was segmented based on the information from the JF549 emission, i.e., sections of the trace were excluded from the analysis: Detections where the PSF exceeded 300 nm at its full width at half maximum were excluded. Moreover, JF549 detections that did not colocalize with DNA/MN/CF positions (as determined by a 300 nm threshold) were excluded from the traces. Lastly, detections that showed multiple stepwise changes in fluorescence intensity or exceeded a threshold value were excluded from the trace, as they arose from multiple TFs or aggregates. If more than 80% of traces from a movie were excluded during trace selection, the entire movie was discarded. Fifth, traces were fitted using a stepfit algorithm121. Finally, bound states were identified using an intensity threshold derived from the fitted trace, and the corresponding bound, unbound, and search times were determined.

Statistical analysis for residence times, on-rates and specific on-rate
The bound, unbound, and search times from each movie (Fig. 3e) were used to generate the corresponding 1-CDF curves (Fig. 3g, Supplementary Fig. 5a, f). First, a cumulative histogram was constructed with a bin size of 0.2 s—matching the movie frame interval. Then, the histogram was normalized to range from 0 to 1.

To estimate the residence times of Sox TFs, we applied multi-exponential decay fits to the 1-CDF curves of bound times. For naked DNA substrates, a biexponential model (n=2 in Eq. (3) was used, while for nucleosomes, a triexponential model (n=3 in Eq. (3) was employed.

In these models, the inverse of each decay rate, k, corresponds to a residence time, τ.

The on-rate (k ) and specific on-rate (k ) were determined by fitting the 1-CDF curves of unbound and search times, respectively, with a monoexponential model (n=1 in Eq. (3); here, k and k were calculated by dividing the decay rate k by the Sox TF concentration (2 nM). All fitting procedures were carried out using the Levenberg–Marquardt algorithm in OriginPro 2022.

To generate the fractional occupancies (F) (Fig. 4f, h, Supplementary Figs. 5j, 7f, h), each bound fraction (A) was weighted by its residence time (τ), and the resulting products were normalized by their total sum:

DNA coiling model
DNA, as a polymer, will coil when its length exceeds its persistence length (l ), which is ~45 nm67–69—roughly equivalent to 132 bp. For naked DNA of length 2L, the gyration radius (R ) is expressed as follows:

The on-rate (k ) may depend on the overall size of the DNA encountered by a TF. Because DNA coils, k is proportional to the DNA’s gyration radius (R ) multiplied by the nanoscopic association rate (k), which is defined as the rate at which a TF binds to a unit-length DNA segment (2L ).

Nonlinear fitting of the k curve (Supplementary Fig. 5c) using Eq. (6) was performed with the Levenberg–Marquardt algorithm, employing the standard deviation of each data point as the weighting factor. The standard errors of the fitting parameters k and L were calculated with OriginPro 2022. In this fitting, the persistence length (l ) was fixed at 132 bp. L was assumed to be the same among Sox TFs, which was obtained as 5.8 bp.

1D target search model
A 1D search model has been previously introduced by Berg et al.12 and Hammar et al.17. It describes the behavior of a TF on bare DNA containing a single binding site at its center. We can use this model to describe the Sox TF target search for a motif located at the center of a stretch of naked DNA (Fig. 3h). The model involves four parameters: the nanoscopic association rate (k), nonspecific residence time (τ ), the 1D diffusion coefficient (D ), and the target recognition rate (k). A TF binds to any sites on DNA at k, slides with D and then recognizes the target with k upon encounter. During this process, the TF resides on DNA nonspecifically for τ .

In this model, the specific on-rate (k ) was defined as the association rate to the target site on bare DNA, via 1D diffusion as well as 3D diffusion. Consequently, k depends on L, the length of flanking DNA as below:

Although k cannot be measured directly at present, it can be indirectly estimated (Fig. 3l) by determining the specific on-rate (k ) in a defined system under various conditions (Fig. 3i).

To fit the measured k curve (Fig. 3i) with the 1D target search model, we considered the sliding length (s ), which was previously introduced as below:

Furthermore, we defined a target recognition constant (K ) as below, since the target recognition process would occur before it dissociates from the site:

Using Eqs. (8) and (9), k s,on in Eq. (7) becomes as a function of L with three parameters of k, K , and s , as below:

Accordingly, the recognition probability p bind is expressed as below:

Then the nonlinear fitting on the k curve (Fig. 3i) with Eq. (10) was conducted based on the Levenberg–Marquardt algorithm using the SD of each data point as the weighting factor. The standard errors of fitting parameters or derived parameters of k and D (from Eqs. (8) and (9) considering τ = 10 ms71) were also calculated in OriginPro 2022. In the fitting, k was fixed to measured values of k = 2.14 M−1 s−1 bp−1, k = 1.93 × 105 M−1 s−1 bp−1, and k = 1.85 × 105 M−1 s−1 bp−1 as listed in Supplementary Table 4.

ChIP-seq analysis
ChIP-sequencing libraries were mapped (BAM format) to mm10 version of Mus musculus genome or BDGP6 version of Drosophila melanogaster genome, using STAR122 with parameters --alignMatesGapMax 2000 --alignIntronMax 1 --alignEndsType EndtoEnd --outFilterMultimapNmax 1. Duplicated reads and reads not mapping to chromosome 1–19 and X or Y, were removed using SAMTools123. For the Spike-in normalization, normalization factors were calculated to equalize the total read counts across all Drosophila BAM files. These normalization factors were then applied to downsample the mouse-genome alignment files using SAMTools123. Besides, between replicates, the ratio of their sequencing depths was used to normalize alignment files mapped on the mouse genome using SAMTools123. For score comparisons across samples, the replicate BAM files were merged using SAMTools123. Scores were determined from these merged BAM files using the bamCoverage function from DeepTools v3.3.0124 with setting --normalizeUsing RPKM.

Peak calling was performed on the normalized BAM files using MACS2 v3.0.0a7 with settings -f BAMPE -g mm, and regions listed in the ENCODE mm10 blacklist were excluded. ChIP peaks between replicates were consolidated using a specific combining protocol (https://ro-che.info/articles/2018-07-11-chip-seq-consensus), employing lower=1 and rangesOnly=T in the slice() function from the GenomicRanges library.

These merged peak files were used to generate Sox-enriched regions following the same procedure. Starting from the replicate-merge BED files, CORs were defined via the same protocol, but with lower=2 and rangesOnly=T in slice(). To quantify enrichment across CORs, two approaches were used: (i) multiBigwigSummary in DeepTools124 or (ii) bigWigToBedGraph from the UCSC genome toolkit. Log2-fold changes in Sox2 scores relative to Sox2a scores were computed for each COR, and regions were classified as Sox2-enriched or Sox2a-enriched based on the sign of the log2-fold values. For exclusive region analysis, each replicate-merged BED file (Sox2 or Sox2a) was processed with the subtract function in BEDTools125 to remove CORs. The resulting intervals were then merged again using the same ChIP peak consolidation protocol. Genome tracks were viewed using Integrated Genome Browser126.

Next, these replicate-merged BED files were input into HOMER2’s findMotifsGenome.pl127 to discover motifs. The search was restricted to 200 bp regions around the peaks, on bigWig files that were generated from merged BAM files spanning the replicates.

ATAC-seq analysis
ATAC-Seq libraries were mapped and filtered as described for ChIP-Seq. Accessible peaks were then called, and scores were computed as described above for ChIP-Seq.

Statistical analysis
Most results are presented as means ± SD unless stated otherwise. Two-group comparisons were conducted using two-tailed, heteroscedastic t-tests. For multiple comparisons, distributions were first evaluated for normality using the Shapiro–Wilk test; When normality was rejected, a nonparametric, one-way Kruskal–Wallis ANOVA was performed, followed by Dunn’s test for pairwise comparisons. When normality was confirmed, one-way parametric ANOVA was used. A p-value ≤ 0.05 was considered statistically significant. All statistical analyses were performed using OriginPro 2022. Statistical significance is indicated in the figures using standard asterisk ranges, while all exact p-values are fully reported in the Source Data.

Reporting summary
Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability
All single-molecule data are available from Zenodo: https://doi.org/10.5281/zenodo.14948338 (Fig. 1, Supplementary Fig. 2); https://doi.org/10.5281/zenodo.14948340 (Fig. 2, Supplementary Fig. 3); https://doi.org/10.5281/zenodo.14948308, https://doi.org/10.5281/zenodo.16954952, https://doi.org/10.5281/zenodo.16954984 (Fig. 3, Supplementary Fig. 5); https://doi.org/10.5281/zenodo.14948298, https://doi.org/10.5281/zenodo.16955046 (Figs. 4, 5, Supplementary Fig. 6-7). Biochemical gel assay data are available in Zenodo: https://doi.org/10.5281/zenodo.16955178. All sequencing data were deposited at NCBI Gene Expression Omnibus (GEO), accession numbers GSE290873 and GSE290874: https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE290873, https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE290874. Source Data are provided with this paper. Additional imaging data, detailed protein purification protocols, and plasmid maps of expression vectors are available upon request. Further information and requests for resources and reagents should be directed to and will be fulfilled by Beat Fierz (beat.fierz@epfl.ch) or David Suter (david.suter@epfl.ch). Source data are provided with this paper.

Code availability
Analysis scripts are available in Zenodo: https://doi.org/10.5281/zenodo.16955257 (related to In vivo assay); https://doi.org/10.5281/zenodo.16954687 (related to In vitro assay).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Sakong et al. investigate how charged regions, adjacent to canonical DNA binding domains in SOX2, affect target search in the context of chromatin. To this end, they combine single-molecule imaging in vitro with imaging and genomics analyses in stem cells. They find that the ability of pioneer factors to invade chromatin is affected by their charged regions, adjacent to the canonical DNA binding domains (referred to here as DFRs, for DBD flanking regions). Overall, the manuscript is well written, interesting, and the science is rigorous, with only a few exceptions that are specified below. The topic is very important and timely, given strong interest in how pioneer factors access their target sites within chromatin, and how unstructured/charged regions participate in this process. The only serious issue is with the quantification of equilibrium dissociation constants (point 1). There is also a lack of evidence for the expression level and stability of transcription factors in cells (point 2). Some of the statements made based on the in vitro assays are not supported by the data, which can be addressed mainly textually by statement moderation (points 3-4). I believe that all these issues would be reasonably easy to correct, after which the manuscript should be appropriate for publication in Nature Communications.\n\nMajor points\n1. Figure 3b: The quantification of the affinity of transcription factors for DNA using EMSA is invalid, and the resulting equilibrium dissociation constants (Kd) are likely wrong. Specifically, based on the EMSA in Fig. 3b, the authors concluded that the EMSA “allowed us to estimate dissociation constants of 1.6 nM for Sox2 and 2.3 nM for Sox2a.” Yet, in this EMSA, the authors used a DNA probe concentration of 2 nM, meaning that they could not physically detect Kd values under 2 nM. Practically, under these conditions, the authors are unlikely to reliably detect Kd values below 20 nM (i.e., <10-fold the DNA probe concentration). This is because under these conditions, the protein is at the “titration regime”, where Kd concentration is too close to the probe concentration. Hence, what the authors quantified was likely the concentration of the probe in each of these experiments, not Kd. If the authors wish to quantify dissociation constants using this experimental system, they could attempt to use conditions that reduce the affinity of the transcription factors for DNA (i.e., increase Kd to >10-fold above the probe concentration). This can usually be done by adding monovalent salt to the binding buffer and/or adding competitor DNA. A recommended reading on how to measure and evaluate equilibrium dissociation constants can be found in [PMID: 32758356].\n2. Figure 6: Based on the ChIP-seq and ATAC-seq data in Fig. 6, the authors conclude that the DFR allows Sox2 to bind to poorly accessible chromatin and open it more effectively. Could the authors exclude the possibility that Sox2 is superior to Sox2a in recruiting cofactors that might facilitate chromatin opening? Given that most of the binding sites of Sox2 and Sox2a are non-overlapping, isn’t it fair to say that the DFR has a large effect on binding specificity, beyond what could be explained by the in vitro experiments? These aspects could be discussed, even if they cannot be reasonably addressed experimentally. More importantly, the authors should carry out immunoblotting on both lines to demonstrate that the expression level and stability of the ectopically expressed transcription factors are the same in both cell lines. This is necessary for showing that the results in Figure 6 cannot be explained by a higher expression or stability of Sox2 compared to Sox2a.\n3. Fig 5. Nucleosome arrays are an inadequate model for inaccessible chromatin when assayed under the experimental conditions used here. Specifically, the authors set up some of the rationale for experiments in Fig 5 by saying that \"...a target site within chromatin is expected to be less accessible than on a nucleosome because of nucleosomes stacking in a tetranucleosome conformation [REF 67-69]\" (L337). Yet, this statement does not seem to be relevant for the experiments that were carried out here: nucleosome stacking is often observed in vitro in the presence of H1 histones [REF 67] or magnesium [REF 68], which were not used here. In the absence of magnesium or H1 histones, 601 arrays are largely open (e.g. see Fig 1A in Li et al 2016 [REF 67]). For the same reason, the chromatin cartoons in Fig 5 are misleading, as the 601 array is unlikely to be folded into a compact state under the conditions used. Based on data in Fig 5, the authors concluded that DFR \"...enabling Sox2 to invade chromatin more effectively\" (L349). But is this the result of chromatin “invasion”, rather than more binding sites that enhance scanning? If the authors wish to avoid H1 or magnesium cations in their experimental system, they should minimally avoid statements regarding chromatin folding, such as interactions between nucleosomes, \"compact chromatin\" (from the abstract), \"invasion\" into chromatin in vitro, or even a chromatin “fiber”. Such characteristics are unlikely to have a substantial relevance under the experimental conditions used.\n4. Fig 4-5. All the experiments with nucleosomes (Fig 4) and chromatin (Fig 5) were done using 601 sequences that strongly position nucleosomes. This is in contrast to native sequences, where nucleosomes can slide more readily. As a result, could it be possible that some of the derived constants were overestimated or underestimated? If the authors can carry out some of the experiments without strong positioning sequences, that would be ideal; otherwise, they should at a minimum discuss this as a potential limitation.\n\nMinor points\n5. Figure 1c: Since ChIP-seq was done here, it would be appropriate to present a ChIP-seq heatmap or minimally show some sample genome tracks, as was done in Fig 6, so the reader can appreciate the quality of the data.\n6. Extended Data Fig. 3: Since Sox2 and Sox2a are compared in vitro, it would be appropriate to present also the size-exclusion chromatography profile and SDS-PAGE analysis for Sox2a, as was done for Sox2. This would help exclude the possibility that variations in the apparent DNA-binding activity are attributed to differences in protein purity and solubility. Moreover, it is recommended to check the ratio between absorbance at 260 and 280 for both proteins to exclude the possibility that variations in nucleic acid contamination contributed to the differences in DNA-binding activities in vitro.\n7. Line 215: “This indicates that DFRs do not impact the overall probability of interactions between freely diffusing TFs and naked DNA.” This is a rather strong and broad statement, given that only two DFRs were tested on one TF within the context of Extended Data Fig 3h. Unless the authors wish to test additional TFs and DFRs, it would seem appropriate to minimally moderate this statement to avoid the impression that they are referring to a general principle that would apply to every TF and every DFR.\n\nPresentation\n8. Extended Data Fig. 3d-e: A colour key is needed to explicitly indicate DNA length.\n9. Extended Data Fig. 3g: Check if the x-axis unit should be in nm rather than bp.\n10. Extended Data Fig. 3h: When referring to this figure, the text in Line 214 quotes different units than those indicated on the y-axis.\n11. Figure 3i: Consider specifying in the legend what each of the constants in the figure refers to, so readers do not have to refer back to the main text every time they look at this model figure", "reviewer_2": "Pls see attached PDF file", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_4": "The present paper from Saking, Fierz, and Suter focuses on understanding the target search of the SOX transcription factor family.\nThis is a key and long-standing question that dates back to the landmark 1970 paper by Riggs (author Ref13), who observed that the kON of LacI was about two orders of magnitude higher than the Smoluchowski limit. Since then, the TF field has been trying to understand how the ON-rates of TFs can be so high. 2 major models have been proposed. First, electrostatics. This is the model originally favored by Riggs and also others like Halfon (see https://portlandpress.com/biochemsoctrans/article/37/2/343/64235/An-end-to-40-years-of-mistakes-in-DNA-protein ). Second is the model of facilitated diffusion, where a mix of 1D DNA sliding and 3D diffusion can accelerate the search. These two are not mutually exclusive. The second model forms the framework for this paper.\nThe problem of TF search is therefore a foundational textbook-level question, but it remains unsolved. In my opinion the present paper takes several important steps in the direction towards solving it and very much expands our understanding of TF search. There are lots of interesting observations in this paper that I won’t attempt to summarize all of them, but among the things I found impressive were: 1) the nice focus on a family of SOX and the role of DFR regions, showing clearly how DFRs can affect the ON-rate; 2) the comprehensiveness of the investigation. A major strength of this paper is that it is very focused on the SOX factors and then comprehensively investigates these using a combination of genomics, in-cell single-molecule tracking, in vitro-single-molecule tracking, looking at both naked DNA and chromatinized templates, and careful modeling; 3) the findings are quite interesting and illuminating.\nOverall, this is in my view an excellent paper. The comprehensiveness of the studies and the range of approaches is truly impressive, yet they are well-integrated, resulting in comprehensive insights from the orthogonal approaches. In my view, this paper is likely to be of quite general interest to a wide readership. Nevertheless, there are some issues that need to be addressed and I think there are some technical errors and problems in the present paper. However, these are all highly addressable as far as I can tell and will not overturn the major conclusions, they will just be required for correctness. I list my comments below.\n\nCOMMENTS:\n1. DATA AND CODE IS MISSING: the authors provide Zenodo links to the data which is great but the links do not work. The whole point is to make the data available to the reviewer. Please correct this. Also it says the code and analysis scripts are available upon request. These need to be available as well, can you put on GitHub or Zenodo?\n2. I too am convinced by facilitated diffusion, but I think the authors overstate it. They say it increases search efficiency by orders of magnitude, which sounds like >100x-1000x. This is probably not true. Theory says that if search is 50:50 3D:1D, then acceleration is half the sliding length and Hammar estimated sliding length to be 45 bp, resulting in a max acceleration of 20x. This is still significant and important, but it is not “orders of magnitude”. Please correct. I would also suggest having a sentence on the slight controversy about facilitated diffusion https://portlandpress.com/biochemsoctrans/article/37/2/343/64235/An-end-to-40-years-of-mistakes-in-DNA-protein\n3. Along these lines, where they estimate kON rates, can they compare directly to the Smoluchowski limit?\n4. Line numbers would have helped\n5. Page 2, 2nd paragraph, a “DFR-like” region also accelerates the CTCF target search by 2.5-fold in cells and is relevant for the discussion here https://www.nature.com/articles/s41589-019-0422-3\n6. REF2 is an important early paper, but the key conclusions from this paper are now well-known to be wrong and has been disproven in several other papers, so probably makes sense to remove this from the reference section, since there are plenty of other papers on Sox2 that could also be cited like https://elifesciences.org/articles/22280\n7. Small thing, but in Fig 2d, it is a little unclear if the proteins include the N- and C-terminal segments. It looks like Sox2 is only DBD and DFR, but there are other regions. Can you clarify if those domains are included.\n8. I understand the math behind GRID, but I am skeptical of the 6-well-resolved residence times. Fitting 6 exponentials with 6 fractions involves 11 free parameters (N-1 fractions, 6 rates) from limited and noisy data does not strike me as statistically robust. Moreover, the in-cell rates are completely consistent with the in vitro rates. Lots of things can go wrong inside cells, like a Halodye getting stuck somewhere. I am not saying they should remove the GRID analysis, but they should at least include a few sentences about the uncertainty and difficulty, the limited statistical power, and the disagreement with the in vitro measurements.\na. Along these lines, a res-time of 1000s correspond a kOFF of 0.001 sec^-1. But their photobleaching rate is stated to be 0.028 s^-1. I.e. the photobleaching rate is 28x faster than the slow residence times. Which means that the error on the photobleaching rate estimation must be <2-3%. It seems completely unrealistic to get such a low error on the photobleaching estimate and therefore, it does not seem statistically robust to me to try to estimate residence times that are much much lower than the photobleaching rate.\nb. It would be essential to acknowledge this and tone this down. Ideally the very slow residence times should be cross-validated with orthogonal assays.\nc. The in vitro residence times are ~1 sec and ~14 sec and this is reported on page 10. The authors should compare and contrast this with the in-cell residence times.\n9. DIFFUSION analysis: they fit 3 Brownian subpopulations to 1-CDFs and then they make an arbitrary threshold of 0.1 um2/s in Fig 2c and call everything below for “bound”. But we know 0.1 um2/s is too high because people have done histone tracking and found the diffusion coefficient of bound chromatin to be 10x-100x slower that this. My question is why do the analysis like this, because while this is the right direction, but the analysis – unless I misunderstood in which case I do apologize – ignores several known and solved problems. Most notably defocalization and localization error. As best I can tell, the analysis ignores localization error. While eq2 is theoretically correct, it is practically incorrect. It ignores localization error and motion blur and such. Motion blur may not be huge, but localization error must be accounted for. Defocalization is a serious issue as well, which if not taken into account will give you the wrong numbers. But this is now a solved problem. Mazza-2012 and Hansen-2018 showed how to account for both defocalization and localization error. So in short, the authors should adopt a rigorous analysis that takes into account both localization error and defocalization.\n10. In eq2, the authors show an alpha on time, but this is lot in eq 3. Do the authors try to fit alpha? If so, how subdiffusive are things?\n11. When the authors do the pseudo-ON-rate analysis, they do not clearly describe where the equations come from. Notably, REF2 did such an analysis but the equations in that paper are wrong. The incorrect math of REF 2 from fixed in Loffreda et al. https://www.nature.com/articles/s41467-017-00398-7 Can you specify where the equations come from?\n12. The in vitro experiments are extremely comprehensive and well-done. I think this is such a major strength of this paper. All their analysis and modeling assumes that they see sliding, but if I am not mistaken, they never directly observe sliding? Sliding has been directly observed in prior work. Maybe the DNA is too short here to observe it. If they cannot directly observe sliding, they should comment on it in the main text and make clear that prior work has observed it but here it is just assumed to be true.\n13. The presentation is in general well-done and comprehensive. The SI tables are great and the methods well-described for the most part. That said, the kinetic parameters for the GRID analysis appear to be missing and seem like a full SI table for the in-cell SMT parameters would be required.\n14. Top of page 11, where they discuss non-specific binding times, here they may want to compare to https://www.nature.com/articles/ncomms8357 which nicely studied this.\n15. Page 11, can they directly compare to the Smoluchowski limit for kON rates here? The whole reason to suggest facilitated diffusion is the higher than Smoluchowski, so this seems like a great place to calculate what they expect and compare it here.\n16. I love Fig 3i. Strongly consistent with 1D sliding and facilitated diffusion.\n17. Fig 4e, but more generally, when you do residence time fitting of multiple populations, you will undercount slow ones and overcount fast ones. Suppose you have 2 TFs in a nucleus. One TF binds for 1000 sec. The other TF binds for 0.5 sec ON and then diffuses and then back ON for 0.5, and does this 500 times over the 1000 sec. Then in the 1000sec movie, one TF gave 1 binding event and the other TF gave 500 binding event trajectories, giving apparent fractions of 1/501 vs. 500/501, but in reality it was 50:50. Do you correct for this? If not, the equation to do so can be found in https://www.sciencedirect.com/science/article/pii/S2589004222020521#sec4 under section “Analysis of trajectories from slow 2 Hz SPT movies”\n18. A bit more discussion of how 1D sliding works on nucleosomal DNA could be nice."}, "author_response": "1 REVIEWER COMMENTS\n4 domains in SOX2, affect target search in the context of chromatin. To this end, they\n5 combine single-molecule imaging in vitro with imaging and genomics analyses in stem\n6 cells. They find that the ability of pioneer factors to invade chromatin is affected by their\n7 charged regions, adjacent to the canonical DNA binding domains (referred to here as\n10 a few exceptions that are specified below. The topic is very important and timely, given\n11 strong interest in how pioneer factors access their target sites within chromatin, and\n12 how unstructured/charged regions participate in this process. The only serious issue is\n13 with the quantification of equilibrium dissociation constants (point 1). There is also a\n14 lack of evidence for the expression level and stability of transcription factors in cells\n15 (point 2). Some of the statements made based on the in vitro assays are not supported\n16 by the data, which can be addressed mainly textually by statement moderation (points\n17 3-4). I believe that all these issues would be reasonably easy to correct, after which the\n18 manuscript should be appropriate for publication in Nature Communications.\n20 1. Figure 3b: The quantification of the affinity of transcription factors for DNA using EMSA is\n21 invalid, and the resulting equilibrium dissociation constants (Kd) are likely wrong. Specifically,\n22 based on the EMSA in Fig. 3b, the authors concluded that the EMSA “allowed us to estimate\n23 dissociation constants of 1.6 nM for Sox2 and 2.3 nM for Sox2a.” Yet, in this EMSA, the\n24 authors used a DNA probe concentration of 2 nM, meaning that they could not physically\n25 detect Kd values under 2 nM. Practically, under these conditions, the authors are unlikely to\n26 reliably detect Kd values below 20 nM (i.e., <10-fold the DNA probe concentration). This is\n27 because under these conditions, the protein is at the “titration regime”, where Kd\n28 concentration is too close to the probe concentration. Hence, what the authors quantified was\n29 likely the concentration of the probe in each of these experiments, not Kd. If the authors wish\n30 to quantify dissociation constants using this experimental system, they could attempt to use\n31 conditions that reduce the affinity of the transcription factors for DNA (i.e., increase Kd to\n32 >10-fold above the probe concentration). This can usually be done by adding monovalent salt\n33 to the binding buffer and/or adding competitor DNA. A recommended reading on how to\n34 measure and evaluate equilibrium dissociation constants can be found in [PMID: 32758356].\nd\n36 values as \"estimated.\" However, we recognize that even with this qualification, the text may\n37 imply a level of precision that is not supported under the experimental conditions used. We\n38 have therefore revised the sentence to read:\n39 “… to estimate nanomolar DNA affinities for the Sox TFs (Fig. 3b,\n42 the functionality of the recombinant transcription factors, not to obtain precise dissociation\n43 constants. More accurate quantification of binding affinities is provided by the single-molecule\n44 data presented later in the manuscript.\n1\n45 2. Figure 6: Based on the ChIP-seq and ATAC-seq data in Fig. 6, the authors conclude that\n46 the DFR allows Sox2 to bind to poorly accessible chromatin and open it more effectively.\n48 that might facilitate chromatin opening? Given that most of the binding sites of Sox2 and\n50 specificity, beyond what could be explained by the in vitro experiments? These aspects could\n51 be discussed, even if they cannot be reasonably addressed experimentally. More importantly,\n52 the authors should carry out immunoblotting on both lines to demonstrate that the expression\n53 level and stability of the ectopically expressed transcription factors are the same in both cell\n54 lines. This is necessary for showing that the results in Figure 6 cannot be explained by a\n55 higher expression or stability of Sox2 compared to Sox2a.\n58 fluorescence intensity after Halo-labeling) to ensure comparable expression levels of Sox2\n59 and Sox2a across the two cell lines. This sorting strategy provides precise, quantitative\n60 control of transcription factor expression. We explain this strategy more clearly in the main\n61 text, an updated Fig. 6a, Supplementary Fig. 8a, and Table S13:\n62 “... and subsequently performed fluorescence-activated cell sorting (FACS) to\n63 select cells with near-identical TF expression levels (Fig. 6a, Supplementary Fig.\n64 8a, Table S13; see Methods).”\n65 “ Cell sorting strategy for ChIP-seq and ATAC-seq: mESCs expressing Halo-\n67 indicated gating windows (black) corresponding to near-identical TF expression\n68 levels (see also Table S13).”\n70 recruitment as the origin for differential binding dynamics. While we cannot fully exclude the\n71 possibility that the DFR contributes to differential cofactor engagement, our interpretation is\n72 that the DFR primarily enhances chromatin target search efficiency rather than altering\n73 sequence specificity. This view is supported by the motif analysis (Supplementary Fig. 1d),\n74 which shows similar motif preferences for Sox2 and Sox2a, and by the single-molecule\n75 assays in vitro, which demonstrate enhanced search dynamics DFR , in the absence of\nSox2\n76 any additional cofactors. Nevertheless, we acknowledge that DFR-mediated effects in vivo\n77 could extend beyond search kinetics to include cofactor interactions.\n79 “Of note, our experiments focused solely on interactions of individual TFs with\n81 changes in protein-protein interactions, in particular potential differences in\n82 cofactor recruitment, were not evaluated in our work, and we cannot fully\n83 exclude that such effects might contribute to the observed differences between\n84 the Sox TF variants in vivo.”\n85 3. Fig 5. Nucleosome arrays are an inadequate model for inaccessible chromatin when\n86 assayed under the experimental conditions used here. Specifically, the authors set up some\n87 of the rationale for experiments in Fig 5 by saying that \"...a target site within chromatin is\n88 expected to be less accessible than on a nucleosome because of nucleosomes stacking in a\n89 tetranucleosome conformation [REF 67-69]\" (L337). Yet, this statement does not seem to be\n90 relevant for the experiments that were carried out here: nucleosome stacking is often\n91 observed in vitro in the presence of H1 histones [REF 67] or magnesium [REF 68], which\n92 were not used here. In the absence of magnesium or H1 histones, 601 arrays are largely\n2\n93 open (e.g. see Fig 1A in Li et al 2016 [REF 67]). For the same reason, the chromatin\n94 cartoons in Fig 5 are misleading, as the 601 array is unlikely to be folded into a compact state\n95 under the conditions used. Based on data in Fig 5, the authors concluded that DFR\n96 \"...enabling Sox2 to invade chromatin more effectively\" (L349). But is this the result of\n97 chromatin “invasion”, rather than more binding sites that enhance scanning? If the authors\n98 wish to avoid H1 or magnesium cations in their experimental system, they should minimally\n99 avoid statements regarding chromatin folding, such as interactions between nucleosomes,\n100 \"compact chromatin\" (from the abstract), \"invasion\" into chromatin in vitro, or even a\n101 chromatin “fiber”. Such characteristics are unlikely to have a substantial relevance under the\n102 experimental conditions used.\n104 concentration of Mg2+ or inclusion of H1. However, in our experiments, the imaging buffer\n105 contained 100 mM KCl and 20 mM HEPES (with Na+ as the counterion), yielding a total\n106 monovalent ion concentration of 120 mM. Under these conditions, chromatin adopts a\n107 partially compacted state, as demonstrated by single-molecule FRET measurements that\n108 monitor nucleosome stacking (see e.g. Fig. 5C from Mivelaz et al., Mol. Cell 2020, or Fig. 1\n109 from Korolev et al., Biophys J. 2010). Thus, nucleosome stacking is present in our conditions\n110 (albeit to a lesser degree compared to high Mg2+ conditions), and chromatin invasion can\n111 take place. Moreover, our statements about chromatin invasion are also supported by results\n112 obtained in living cells, where we observe higher propensity of Sox2 to bind chromatin with\n113 low accessibility, compared to Sox2a.\n115 composition, and we have clarified this point in the Results and Methods sections with the\n116 following additions:\n117 “We then imaged Sox2 and Sox2a binding dynamics to these chromatin fibers.\n119 of 120 mM monovalent cations, chromatin is partially compacted [ref 37,79].”\n120 “The imaging buffer IB3 contained 100 mM KCl and 20 mM HEPES (with Na+ as\n121 the counterion), yielding 120 mM monovalent cations. Under these conditions,\n122 chromatin adopts a partially compacted state, as revealed by single-molecule\n124 4. Fig 4-5. All the experiments with nucleosomes (Fig 4) and chromatin (Fig 5) were done\n125 using 601 sequences that strongly position nucleosomes. This is in contrast to native\n126 sequences, where nucleosomes can slide more readily. As a result, could it be possible that\n127 some of the derived constants were overestimated or underestimated? If the authors can\n128 carry out some of the experiments without strong positioning sequences, that would be ideal;\n129 otherwise, they should at a minimum discuss this as a potential limitation.\n131 positioning and are generally less uniformly phased or saturated compared to those formed\n132 on 601 sequences. This could, in principle, influence the derived kinetic constants under\n133 native chromatin conditions.\n135 the ability to precisely control nucleosome positions and densities. This level of control is\n136 essential for dissecting the mechanistic aspects of the target search process in a\n137 reproducible manner. Notably, the key findings from our in vitro assays align well with in vivo\n138 observations, suggesting that the conclusions remain robust despite the use of strongly\n139 positioning sequences.\n3\n141 “We note that the 601WS positioning sequences, while providing precise\n142 nucleosome placement, cannot recapitulate the heterogeneity of native\n143 chromatin, where nucleosome positioning, stability and occupancy varies.\n145 conclusions extend beyond the reconstituted system.”\n147 5. Figure 1c: Since ChIP-seq was done here, it would be appropriate to present a ChIP-seq\n148 heatmap or minimally show some sample genome tracks, as was done in Fig 6, so the\n149 reader can appreciate the quality of the data.\n151 data, but shows charge distributions across the Sox2 and Sox17 sequences. We thus\n152 improved the figure legend to clarify the methods used to generate this plot.\n154 interpretation and allow readers to assess data quality, we have included representative\n155 genome browser tracks in Supplementary Fig. 1c, corresponding to the data shown in\n157\n158 6. Supplementary Fig. 3: Since Sox2 and Sox2a are compared in vitro, it would be\n159 appropriate to present also the size-exclusion chromatography profile and SDS-PAGE\n160 analysis for Sox2a, as was done for Sox2. This would help exclude the possibility that\n161 variations in the apparent DNA-binding activity are attributed to differences in protein purity\n162 and solubility. Moreover, it is recommended to check the ratio between absorbance at 260\n163 and 280 for both proteins to exclude the possibility that variations in nucleic acid\n164 contamination contributed to the differences in DNA-binding activities in vitro.\n166 profiles, SDS-PAGE analyses, and UV absorbance spectra for Sox2a alongside those for\n168 solubility across all proteins. In addition, the 260/280 absorbance ratios (Table S10) are\n169 within the expected range, excluding the possibility that nucleic acid contamination\n170 contributed to the observed differences in DNA-binding activity.\n171 7. Line 215: “This indicates that DFRs do not impact the overall probability of interactions\n172 between freely diffusing TFs and naked DNA.” This is a rather strong and broad statement,\n173 given that only two DFRs were tested on one TF within the context of Supplementary Fig 3h.\n175 minimally moderate this statement to avoid the impression that they are referring to a general\n176 principle that would apply to every TF and every DFR.\n178 on a limited set of constructs. We have therefore revised the sentence to refer specifically to\nSox2 Sox17\n180 “This indicates that neither the DFR nor the DFR impact the overall\nSox2 Sox17\n181 probability of interactions between freely diffusing TFs and naked DNA.”\n183 for Sox17, showing that Sox17 exhibits target search behavior on naked DNA similar to that\n184 of Sox2a (which carries DFR ). These results further support our conclusion and\nSox17\n4\n185 demonstrate its consistency across two distinct DFRs. Accordingly, Fig. 3, and\n188\n189 8. Supplementary Fig. 3d-e: A colour key is needed to explicitly indicate DNA length.\n190\n193 9. Supplementary Fig. 3g: Check if the x-axis unit should be in nm rather than bp.\n194\n197 10. Supplementary Fig. 3h: When referring to this figure, the text in Line 214 quotes different\n198 units than those indicated on the y-axis.\n199\n201 now correctly includes bp-1.\n203 11. Figure 3i: Consider specifying in the legend what each of the constants in the figure\n204 refers to, so readers do not have to refer back to the main text every time they look at this\n205 model figure.\n206\n208 updated the caption to read:\n209 “h, Scheme of the 1D target search model: initially, a TF binds nonspecifically to\na 1D d\n211 until it dissociates from DNA. Upon reaching the target site, the TF either\n212 recognizes the target with k, or bypasses it. s : sliding length. K : target\nr L R\n213 recognition constant.”\n5\n218 differentially charged DFRs lead to distinct target search efficiency, as well as distinct search\n219 mechanisms between naked DNA and chromatinized DNA. These findings are significant not\n220 only in providing novel insights into the target search process of Sox TFs beyond the well-\n221 established facilitated diffusion model (which might very well be applicable to other TFs as\n222 well), but also sheds fundamental insights into the biophysical underpinnings of IDR-\n223 mediated TF-chromatin interactions in general.\n225 experimental evidence (comprising of single-molecule imaging, biochemical and genomic\n226 data) are solid and nicely complement each other, and the conclusions are convincingly\n227 supported by the data. I did not spot any major issue regarding logic, experimental design or\n228 data interpretation/argumentation. I, however, have a few issues concerning some of the\n229 experimental details, data analyses, further elaboration of the significance of certain findings,\n230 as well as several presentation-related issues, for the authors’ consideration.\n231 1. In the time-lapse imaging experiments where a 60-ms illumination is interspersed with\n232 varying dark times to obtain imaging intervals of 120, 240, 480 and 960 ms, it is unclear how\n233 the authors ensured that a certain bound molecule detected after a time-lapse is still the\n234 same molecule as before the light was switched off? Could it be that the original molecule\n235 unbinds and another molecule binds to the same binding site during the dark time, which\n236 would affect the subsequent analysis of the binding dynamics. An explanation on how this is\n237 avoided would be needed. Also, it might be useful to provide illustrative schematics for the\n238 various time-lapse illumination patterns, indicating the durations of each “on” and “off ”\n239 intervals.\n241 single-molecule imaging. We agree that, in isolation, a long imaging interval (e.g., 960 ms)\n242 could raise the concern that a molecule detected after a dark interval might not be the same\n243 one observed before the interval. However, this is precisely why we employed multiple time-\n244 lapse conditions with increasing intervals (120, 240, 480, and 960 ms), each interleaving a\n245 60-ms illumination with a dark period. These conditions were carefully designed to yield\n246 overlapping time windows across which binding events could be sampled.\n248 ensure comprehensive temporal coverage. Shorter intervals (e.g., 120 ms) are sensitive to\n249 fast off-rates and minimize the chance of missed unbinding/rebinding events. Longer\n250 intervals (e.g., 960 ms) allow us to detect longer-lived events that would be underestimated in\n251 high-frame-rate acquisition due to photobleaching. Crucially, the datasets from each tl-\n252 condition overlap in their effective observational time windows, which ensures that any event\n253 falling within an intermediate lifetime range is sampled by at least one of the tl-settings.\n256 “Our multi-time interval approach interleaves 60 ms illumination with dark periods\n257 of 120, 240, 480, and 960 ms. This design creates overlapping observation\n258 windows that capture both fast off-rates and long-lived binding events, ensuring\n259 comprehensive sampling of all intermediate lifetimes.”\n6\n261 nearest-neighbour algorithm for trajectory reconstruction. The probability of a different\n262 molecule rebinding to the same location in the next frame is highly unlikely given our\n263 parameters across all the movies: the effective area of each spot is 17 px2, while the\n264 average nucleus area is 12,100 px2, with an average of 17 spots appearing per frame.\n266 the time-lapse illumination patterns, indicating the durations of the “on” and “off”\n267 periods for each condition (new Supplementary Fig. 2a).\n268 2. The SMT measurements, coupled with GRID analysis, identified 6 well-resolved\n269 bound states for the TFs studied, with residence times ranging from 100s of ms all the\n270 way up to 1000 s. This is substantially more than the 2-4 binding modes that are\n271 commonly observed for many other types of DNA-binding proteins, and could\n272 potentially represent something significant as a consequence of the complex\n273 chromatin-interaction landscape of Sox TFs. However, this significance is not\n274 adequately explained or elaborated on in either the Results or Discussion sections.\n276 significance of the six distinct binding states observed in our SMT-GRID analysis in the\n278 “In vivo GRID analysis revealed six Sox TF–chromatin binding states spanning\n279 from 0.18 s to 380 s in line with recent studies investigating TF binding dynamics\n280 that also revealed complex residence time distributions [ref 34,58,96-98]. As\n281 supported by our in vitro measurements, intermediate residence times (10-20 s)\n282 likely correspond to specific DNA binding, while shorter-lived states (sub-second\n283 to a few seconds) reflect transient nonspecific interactions with DNA,\n284 nucleosomes, or higher-order chromatin. The longest-lived states (>50 s) are\n285 consistent with previously reported extended TF residence on regulatory\n286 chromatin [ref 99,100] and may involve cofactor binding, transcriptional complex\n287 formation, or chromatin remodeling.”\n288 3. The two main parameters used for quantifying DNA-binding from SMT\n289 measurements are the residence time and bound fraction. While these are certainly\n290 two commonly adopted and useful parameters, their utilities are not without limitations.\n292 lasting a short duration) might end up being bound for a similar total duration as\n293 another molecule that undergoes only a few but long-lived binding events. In such\n294 situations, a useful alternative parameter would be the total fraction of time the\n295 molecule stays bound under each mode, which can simply be calculated as the\n296 product of residence time and the corresponding bound fraction, normalized against\n297 the total time the molecule spends in all binding modes (see a recent e.g. in Engl et al.,\n299 of the TF molecules among the different binding modes, which might add a useful\n300 dimension to the binding landscape characterized in the work.\n302 alternative metric, ‘fractional occupancy’, to capture the total time a molecule spends in\n303 each binding mode. Fractional occupancy is defined as the product of the residence\n304 time and the GRID amplitude for each state, normalized by the sum across all states.\n306 occupancy of short-lived (<1 s) and long-lived (>10 s) binding events in Supplementary\n7\n309 “We also calculated fractional occupancies [ref 55-57], i.e. the fraction of total\n310 bound time spent in each state (Supplementary Fig. 2e; see Methods). This\n311 revealed that Sox2 (0.66) and Sox17b (0.60) spend more time in long-lived\n312 states (>10 s) than Sox2a (0.47) and Sox17 (0.47) (Supplementary Fig. 2f, Table\n315 follows:\n316 “To generate the fractional occupancy spectrum (𝐹) (Supplementary Fig. 2e),\n𝑖\n317 each GRID-determined state’s amplitude (𝐴 ) was weighted by its residence time\n𝑖\n318 (𝜏 ), and the resulting products were normalized by their total sum:\n𝑖\n319 𝐹 = 𝐴 ⋅𝜏 /∑100𝐴 ⋅𝜏 (Eq. 1)”\n𝑖 𝑖 𝑖 𝑗=1 𝑗 𝑗\n321 • Pg. 2 and 3: The acronym DFR was defined twice in the main text (in addition to that\n322 in the Abstract), whereas the terms DBD and mESC were not defined.\n324 once in the main text, and we have removed the redundant definition. Similarly, DBD is\n325 now defined upon first use in the main text. As noted by the reviewer, mESC was\n326 already defined in the main text as “mouse embryonic stem cells (mESCs).”\n327 • Pg. 2: “Among Sox TFs, Sox2 exhibited the most positively charged DFR and the highest\n328 mitotic chromosome binding.” Please specify what does “chromosome binding” refers to\n329 here, e.g. binding affinity, residence time, fraction of molecules bound, etc.\n331 in accordance with prior work, specifically Raccaud et al., 2019, where the Mitotic Bound\n333 chromosome binding refers to is the fraction of TF molecules associated with mitotic\n334 chromosomes. In Raccaud et al., this was calculated by dividing the fluorescence intensity of\n335 the TF molecules on mitotic chromosomes by the total fluorescence intensity in the cell. To\n336 remain consistent with the established terminology in the field, we have retained the original\n337 wording. To ensure clarity for readers, we now explicitly cite Raccaud et al., 2019 at the first\n338 mention of “mitotic chromosome binding” in the main text. We have now included the\n339 following in the text:\n340 “Among the Sox TFs, Sox2 exhibited the most positively-charged DFR, which\n341 correlated with the highest fraction of TF molecules associated with mitotic\n342 chromosomes [ref 40].”\n343 • Pg. 11: “…the nanoscopic association rate (ka), previously determined as about 2×105 M-\n344 1s-1bp-1…” A reference is needed here.\n346 the corresponding data in the manuscript:\n347 “…the nanoscopic association rate (k ), previously determined as about 2×105 M-\na\n348 1s-1bp-1 for the three Sox TFs (Supplementary Fig. 5e);”\n8\n350 molecule tracking measurements.\n351 • Pg. 14: “…both Sox TFs showed three different residence times on CT+, while they\n352 displayed only two nonspecific binding populations on CT- (Supplementary Fig. 5d-h).”\n354 main text. Please check and reconcile.\n356 text was inadvertently swapped. We have corrected this in the revised manuscript.\n357 • Fig. 1: The vertical axis labels for both Fig. 1a and 1c are “charge”, but they clearly denote\n358 different things; consider changing 1a to “Net charge” to distinguish it from 1c? Moreover, in\n360 position takes on multiple fractional values between -1 and 1. However, according to the\n361 designation in Supplementary Fig. 1a, the charges assigned to individual residues can only\n362 take on values of +1 z (K & R), +0.5 z (H), or -1 z (E & D). In that case, how could the\n363 charges shown in Fig. 1c have values other than these values (especially various fractional\n364 values other than +/- 0.5 z)? Lastly, in Fig. 1h, log (res. time) is plotted on the horizontal axis,\n365 therefore its unit should not be “s”, but rather “log s”. A better way to label the axis would be\n366 “log10 (res. time / s)”.\n368 it from the vertical axis in Fig. 1c. In Fig. 1h, we also corrected the x-axis label to: log10(res.\n369 time) (log s) to more accurately reflect the logarithmic scale.\n10\n371 described in the Methods section (“Electrical charge distribution generation”), the plotted\n372 values represent sliding-window averages of the assigned residue charges, using a window\n373 of five amino acids. Therefore, the charge at each position reflects the average of up to five\n374 neighboring residues, which results in fractional values between -1 and +1 (beyond the\n375 discrete residue values of +1, +0.5, or -1). This calculation was performed using EMBOSS\n377 “c, Charge distributions for Sox2 (top) and Sox17 (bottom), calculated as sliding-\n378 window averages of residue charges over five-amino-acid segments (see\n380 • Fig. 2c: Please define the vertical dotted line in the figure caption.\n382 “The dashed vertical line denotes the diffusion coefficient threshold at D=0.1\n383 μm2/s.”\n384 • Supplementary Figure 5d: The gray curves in the plots are not labeled, contrary to those in\n385 panels i-l (which indicate whether each curve denotes CT+ or CT-, etc.).\n386\n389 discovered that panels i–l were mislabeled: the bottom subpanels were incorrectly labeled as\n391 and revised the figure legend to reflect these changes.\n392\n393 • Lastly, a few typos/language-related issues:\n9\n397 mm2” should be 11×11 µm2?\n2\n400 formatting on ‘mESC culture’ in Methods section, the pixel size unit on ‘In vivo smHILO\n401 microscopy setup’ in Methods section (now correctly stated as 11×11 µm2), and ensured that\n402 “E. coli” is properly italicized throughout the manuscript.\n10\n405 search of the SOX transcription factor family.\n407 by Riggs (author Ref13), who observed that the kON of LacI was about two orders of\n408 magnitude higher than the Smoluchowski limit. Since then, the TF field has been trying\n409 to understand how the ON-rates of TFs can be so high. 2 major models have been\n410 proposed. First, electrostatics. This is the model originally favored by Riggs and also\n411 others like Halfon (see\n412 https://portlandpress.com/biochemsoctrans/article/37/2/343/64235/An-end-to-40-years-\n413 of-mistakes-in-DNA-protein ). Second is the model of facilitated diffusion, where a mix\n414 of 1D DNA sliding and 3D diffusion can accelerate the search. These two are not\n415 mutually exclusive. The second model forms the framework for this paper.\n417 remains unsolved. In my opinion the present paper takes several important steps in the\n418 direction towards solving it and very much expands our understanding of TF search.\n420 summarize all of them, but among the things I found impressive were: 1) the nice focus\n421 on a family of SOX and the role of DFR regions, showing clearly how DFRs can affect\n422 the ON-rate; 2) the comprehensiveness of the investigation. A major strength of this\n423 paper is that it is very focused on the SOX factors and then comprehensively\n424 investigates these using a combination of genomics, in-cell single-molecule tracking, in\n425 vitro-single-molecule tracking, looking at both naked DNA and chromatinized\n426 templates, and careful modeling; 3) the findings are quite interesting and illuminating.\n428 and the range of approaches is truly impressive, yet they are well-integrated, resulting\n429 in comprehensive insights from the orthogonal approaches. In my view, this paper is\n430 likely to be of quite general interest to a wide readership. Nevertheless, there are some\n431 issues that need to be addressed and I think there are some technical errors and\n432 problems in the present paper. However, these are all highly addressable as far as I\n433 can tell and will not overturn the major conclusions, they will just be required for\n434 correctness. I list my comments below.\n436 1. DATA AND CODE IS MISSING: the authors provide Zenodo links to the data which\n437 is great but the links do not work. The whole point is to make the data available to the\n438 reviewer. Please correct this. Also it says the code and analysis scripts are available\n439 upon request. These need to be available as well, can you put on GitHub or Zenodo?\n441 2. I too am convinced by facilitated diffusion, but I think the authors overstate it. They\n442 say it increases search efficiency by orders of magnitude, which sounds like >100x-\n443 1000x. This is probably not true. Theory says that if search is 50:50 3D:1D, then\n444 acceleration is half the sliding length and Hammar estimated sliding length to be 45 bp,\n445 resulting in a max acceleration of 20x. This is still significant and important, but it is not\n446 “orders of magnitude”. Please correct. I would also suggest having a sentence on the\n447 slight controversy about facilitated diffusion\n448 https://portlandpress.com/biochemsoctrans/article/37/2/343/64235/An-end-to-40-years-\n449 of-mistakes-in-DNA-protein\n11\n451 magnitude” overstated the acceleration effect of facilitated diffusion. We have revised\n452 the text to more accurately reflect theoretical and experimental estimates and also\n453 acknowledge differing views in the field:\n454 “This dimensionality-reduced diffusion is believed to substantially increase\n455 search efficiency compared to free diffusion alone, although the magnitude of\n456 this effect is still debated [ref 16].”\n457 3. Along these lines, where they estimate kON rates, can they compare directly to the\n460 at the Smoluchovski limit, both due to experimental constraints, and because Sox2 and\n461 related factors might encounter barriers upon DNA binding and thus might not follow\n462 purely diffusion-controlled association kinetics.\n464 relationship between the Smoluchowski limit, k , and k . \non s,on\n465 4. Line numbers would have helped\n467 5. Page 2, 2nd paragraph, a “DFR-like” region also accelerates the CTCF target search\n468 by 2.5-fold in cells and is relevant for the discussion here\n469 https://www.nature.com/articles/s41589-019-0422-3\n471 in the main text as ‘ref 34’, in the sentence:\n472 “…they can also play a key role in determining chromatin binding and diffusion\n473 behavior, even in the absence of interaction partners [ref 30-34].”\n474 6. REF2 is an important early paper, but the key conclusions from this paper are now\n475 well-known to be wrong and has been disproven in several other papers, so probably\n476 makes sense to remove this from the reference section, since there are plenty of other\n477 papers on Sox2 that could also be cited like https://elifesciences.org/articles/22280\n479 (https://elifesciences.org/articles/22280).\n481 important contribution for establishing single-molecule imaging particularly for studies\n482 of Sox2 in mouse embryonic stem cells. However, we now cite it in the Discussion,\n483 specifically in the context of Sox2 SMT in living cells, along with other relevant papers\n484 (https://doi.org/10.1016/j.celrep.2023.112748, https://doi.org/10.7554/eLife.04236.001\n485 and https://elifesciences.org/articles/22280).\n486 7. Small thing, but in Fig 1d, it is a little unclear if the proteins include the N- and C-\n487 terminal segments. It looks like Sox2 is only DBD and DFR, but there are other\n488 regions. Can you clarify if those domains are included.\n490 domain has been suggested to reside in the C-terminus for most Sox TFs. However,\n491 the precise boundaries and definitions of these regions remain unclear. For this\n12\n492 reason, we chose not to include additional domain annotations in Fig. 1d to avoid\n493 implying a level of structural definition that is not yet established.\n494 8. I understand the math behind GRID, but I am skeptical of the 6-well-resolved\n495 residence times. Fitting 6 exponentials with 6 fractions involves 11 free parameters (N-\n496 1 fractions, 6 rates) from limited and noisy data does not strike me as statistically\n497 robust. Moreover, the in-cell rates are completely consistent with the in vitro rates. Lots\n498 of things can go wrong inside cells, like a Halodye getting stuck somewhere. I am not\n499 saying they should remove the GRID analysis, but they should at least include a few\n500 sentences about the uncertainty and difficulty, the limited statistical power, and the\n501 disagreement with the in vitro measurements.\n503 inverse Laplace transform to a grid of invariable decay rates with fixed spacing but\n504 variable amplitudes. This approach is thus distinct from simply fitting 6 exponential\n505 functions, as GRID makes no a priori assumptions about lifetime distributions.\n507 to determining residence time distributions of Sox TFs in cells. First, we thus analyzed\n508 a large number of cells, averaging 180 cells per TF and collecting ~300’000 trajectories\n509 per TF. Second, for every TF, we performed 100 independent GRID analyses, each\n510 time using data from a random subset of 80% of the cells.\n512 rates (<10% difference) into single rates (‘effective GRID rates’), and discarding rates\n513 associated with low amplitude (below 0.1%). This resulted in 6 effective GRID rates\n514 consistently determined for most subsamples (see new Supplementary Fig. 2c)\n516 bound states (Fig. 1h). The widths of the peaks in the GRID spectra provide an\n517 estimate of the uncertainty associated with each state and the robustness of the\n518 approach.\n520 of Fig. 1h as follows:\n521 “h, Residence time distributions obtained from GRID analysis of 100 resampling\n522 iterations (randomly selected 80% subset of the full dataset shown in g),\n523 assembled into histograms (see Methods). The GRID amplitude indicates the\n524 bound fraction per unit of time for the corresponding residence times.”\n526 description of our data analysis:\n527 “For each Sox TF, 100 resampling iterations were performed. In each resampling\n528 iteration, a subset of 80% of single cells was randomly selected using a custom\n530 and any GRID-determined dissociation rate with an amplitude below 0.1% was\n531 excluded. The remaining rates from all 100 resamplings were combined into a\n532 relative frequency histogram using 100 equally spaced bins (Fig. 1h)”\n534 in vitro, align with previously reported extended transcription factor residence times at\n535 regulatory chromatin sites are consistent with previously reported extended TF\n536 residence on regulatory chromatin [ref 99,100] and may involve cofactor binding,\n13\n537 transcriptional complex formation, or chromatin remodeling. We have now discussed\n538 this further in the discussion section of the manuscript (see also below).\n539 a. Along these lines, a res-time of 1000s corresponds to a kOFF of 0.001 sec^-1. But\n540 their photobleaching rate is stated to be 0.028 s^-1. I.e. the photobleaching rate is 28x\n541 faster than the slow residence times. Which means that the error on the\n542 photobleaching rate estimation must be <2-3%. It seems completely unrealistic to get\n543 such a low error on the photobleaching estimate and therefore, it does not seem\n544 statistically robust to me to try to estimate residence times that are much much lower\n545 than the photobleaching rate.\n547 combination of 60 ms illumination followed by a defined dark time (60, 180, 420 or 900 ms),\n548 resulting in 120, 240, 480, and 960 ms imaging intervals. Our dye photobleaching rate was\n549 determined to be 0.028 s-1 (~36 s) under continuous illumination. Under stroboscopic\n550 imaging, the effective photobleaching rate is reduced, due to the inserted dark times. In\n551 particular, for the 960 ms interval movies, the effective photobleaching rate effectively\n552 reached 1.75 x 10-3s-1 (i.e. a dye lifetime of ~570 s). This is the relevant parameter for\n553 determining the upper limit of resolvable residence times.\n555 within the resolvable range set by this effective photobleaching rate.\n557 2.63 x 10-3s-1 using an effective photobleaching rate of 1.75 x 10-3s-1. Assuming a 3% error\n558 in both photobleaching and measured off-rates, the resulting error in the corrected off-rate\n559 would be ~6%, below the uncertainty resulting from GRID analysis and subsampling (as\n560 described above). Together, we thus feel that photobleaching is not a major source of\n561 uncertainty in our results.\n562 b. It would be essential to acknowledge this and tone this down. Ideally the very slow\n563 residence times should be cross-validated with orthogonal assays.\n565 within a restricted range, as GRID is an unbiased approach that samples across a\n566 large space of possible rates. Importantly, in other studies where imaging was\n567 performed under similar conditions on different DNA-binding proteins, GRID did not\n568 detect such very long residence times (Engl et al., Nat. Commun., 2024; Tollenaere et\n569 al., bioRxiv, 2025). This supports that the detection of long-lived states is not an\n570 inherent artifact of the GRID method. Moreover, similarly long residence times have\n571 been reported for other TFs using alternative approaches, such as for glucocorticoid\n572 receptors using power-law fitting (Garcia et al., 2021, ref 98).\n574 confidence with which they can be characterized. In particular, for Sox2a and Sox17,\n575 the GRID spectra appear more broadened and continuous. This is reflected in the\n576 manuscript where we described:\n577 “While the residence time distributions for Sox2 and Sox17b were narrow and\n578 well defined, Sox2a and Sox17 exhibited broader distributions (Fig. 1h),\n579 suggesting complex interactions associated with a continuum of binding\n580 energies.”\n582 manuscript, changing “six well-resolved populations of bound states” to “six\n14\n583 populations of bound states” and “six distinct Sox TF–chromatin binding states” to “six\n585 c. The in vitro residence times are ~1 sec and ~14 sec and this is reported on page 10.\n589 “In vivo GRID analysis revealed six Sox TF–chromatin binding states spanning\n590 from 0.18 s to 380 s in line with recent studies investigating TF binding dynamics\n591 that also revealed complex residence time distributions [ref 34,58,96-98]. As\n592 supported by our in vitro measurements, intermediate residence times (10-20 s)\n593 likely correspond to specific DNA binding, while shorter-lived states (sub-second\n594 to a few seconds) reflect transient nonspecific interactions with DNA,\n595 nucleosomes, or higher-order chromatin. The longest-lived states (>50 s) are\n596 consistent with previously reported extended TF residence on regulatory\n597 chromatin [ref 99,100] and may involve cofactor binding, transcriptional complex\n598 formation, or chromatin remodeling.”\n599 9. DIFFUSION analysis: they fit 3 Brownian subpopulations to 1-CDFs and then they\n600 make an arbitrary threshold of 0.1 um2/s in Fig 2c and call everything below for\n601 “bound”. But we know 0.1 um2/s is too high because people have done histone\n602 tracking and found the diffusion coefficient of bound chromatin to be 10x-100x slower\n603 that this. My question is why do the analysis like this, because while this is the right\n604 direction, but the analysis – unless I misunderstood in which case I do apologize –\n605 ignores several known and solved problems.\n607 ignores localization error. While eq2 is theoretically correct, it is practically incorrect. It\n608 ignores localization error and motion blur and such. Motion blur may not be huge, but\n609 localization error must be accounted for. Defocalization is a serious issue as well,\n610 which if not taken into account will give you the wrong numbers. But this is now a\n611 solved problem. Mazza-2012 and Hansen-2018 showed how to account for both\n612 defocalization and localization error. So in short, the authors should adopt a rigorous\n613 analysis that takes into account both localization error and defocalization.\n615 careful validation. In our initial analysis (Fig. 2c), we adopted a threshold of 0.1 µm²/s,\n616 in line with previous studies on chromatin-associated proteins, including ref 30\n617 (https://doi.org/10.7554/eLife.75064), ref 61\n618 (https://doi.org/10.1016/j.celrep.2023.112748), ref 62 (https://doi.org/10.1186/s13072-\n619 016-0093-1) and additional papers (https://doi.org/10.1371/journal.pcbi.1005136 added\n620 as ref 63, https://doi.org/10.7554/eLife.17667). These studies report diffusion\n621 coefficients for bound chromatin populations in the range of 0.01–0.1 µm²/s, supporting\n622 our choice as a conservative upper bound. In particular, ref 30 used the same\n623 thresholding to categorize bound fractions.\n625 performed Spot-On analysis (Hansen et al., eLife, 2018, ref 59), which accounts for\n626 axial defocalization in estimating diffusion coefficients and bound fractions. This\n627 analysis is presented in Supplementary Fig. 2, and its results are consistent with our\n628 threshold-based analysis, supporting the robustness of our findings. We initially\n629 decided to show less processed results in main figures.\n15\n632 taken into account:\n633 “In 2D HILO imaging, fast-diffusing molecules often appear motion-blurred or\n634 leave the focal plane, leading to their under-detection [ref 59,64]. To make sure\n635 that this limitation does not bias our results, we also performed Spot-On analysis\n636 of jump distance distributions, which accounts for defocalization and localization\n637 errors [ref 59].”\n638 10. In eq2, the authors show an alpha on time, but this is lost in eq 3. Do the authors\n639 try to fit alpha? If so, how subdiffusive are things?\n642 values for all investigated TFs as the new Supplementary Fig. 3b. In particular, we\n643 sorted tracks into three bins depending on their diffusion coefficient values\n644 (0.01 < D < 0.1; 0.1 < D < 1; 1 < D < 10 µm2/s). Each dot represents the average alpha\n645 within each bin for a given cell. The majority of molecules exhibit subdiffusive behavior\n646 with alpha ~ 0.8. Overall, Sox2 and Sox17b show somewhat stronger subdiffusive\n647 behavior than Sox17 and Sox2a, possibly resulting from stronger nonspecific DNA\n648 interactions.\n650 “Additionally, we determined the anomalous diffusion exponent α, to be ~0.8 for\n651 all the Sox TFs (Supplementary Fig. 3b; see Methods), suggesting a subdiffusive\n652 behavior. Notably, Sox2 and Sox17b exhibited slightly lower α than Sox17 and\n654 11. When the authors do the pseudo-ON-rate analysis, they do not clearly describe\n655 where the equations come from. Notably, REF2 did such an analysis but the equations\n656 in that paper are wrong. The incorrect math of REF 2 from fixed in Loffreda et al.\n657 https://www.nature.com/articles/s41467-017-00398-7 Can you specify where the\n658 equations come from?\npn\n660 frequency of TFs to the whole genome, determined by the number of immobilized\n661 molecules per imaging frame (see Methods). This approach follows the method\n662 described in Raccaud et al., 2019, which is cited in the text as ref 40. To further clarify,\n663 we have updated the equation from the original version, which is described in the\n665 12. The in vitro experiments are extremely comprehensive and well-done. I think this is\n666 such a major strength of this paper. All their analysis and modeling assumes that they\n667 see sliding, but if I am not mistaken, they never directly observe sliding?\n670 make clear that prior work has observed it but here it is just assumed to be true.\n672 dissociation from the DNA, but we acknowledge that this movement is not directly\n673 resolvable under our experimental conditions.\n16\n675 “We interpret this increased search efficiency for both Sox TFs on longer DNA as\n676 evidence that 1D sliding facilitates target search. This is consistent with direct\n677 experimental evidence for TF sliding for both prokaryotic and eukaryotic TFs and\n679 13. The presentation is in general well-done and comprehensive. The SI tables are\n680 great and the methods well-described for the most part. That said, the kinetic\n681 parameters for the GRID analysis appear to be missing and seem like a full SI table for\n682 the in-cell SMT parameters would be required.\n684 spectra values from Fig. 1h as Table S1 in the SI to provide a complete overview of the\n685 in-cell SMT parameters. The SMT input parameters were already included in Table\n687 14. Top of page 11, where they discuss non-specific binding times, here they may want\n688 to compare to https://www.nature.com/articles/ncomms8357 which nicely studied this.\n690 “Similarly, the nonspecific residence time of LacI in E. coli has been reported as\n691 less than 5 ms using SMT [ref 71], whereas other TFs, such as TetR or p53\n692 exhibited longer non-specific residence times (158 ms and 900 ms, respectively)\n693 [ref 64,72].”\n694 15. Page 11, can they directly compare to the Smoluchowski limit for kON rates here?\n696 seems like a great place to calculate what they expect and compare it here.\n698 reactions take place on a passivated glass surface, our observed rate constants are\n699 generally below the theoretical limit for diffusion controlled association for homogeneous\n700 systems. Moreover, Sox2 variants may have to overcome energy barriers, such as adopting\n701 the correct conformation or positioning, to bind DNA upon collision. Sox2 might thus not\n702 follow solely diffusion controlled kinetics.\n704 estimate how facilitated diffusion contributes to the target search process, using the DNA\n705 length-dependent increase in nonspecific (Supplementary Fig. 5c,d) and specific on-rate (Fig.\n706 3i).\n708 the absence of sliding, this represents an upper limit for site recognition under our conditions.\n710 specific on-rate, most likely due to facilitated diffusion (see also Eq. 12).\n711 16. I love Fig 3i. Strongly consistent with 1D sliding and facilitated diffusion.\n713 17. Fig 4e, but more generally, when you do residence time fitting of multiple\n714 populations, you will undercount slow ones and overcount fast ones. Suppose you\n715 have 2 TFs in a nucleus. One TF binds for 1000 sec. The other TF binds for 0.5 sec\n17\n717 sec. Then in the 1000sec movie, one TF gave 1 binding event and the other TF gave\n718 500 binding event trajectories, giving apparent fractions of 1/501 vs. 500/501, but in\n719 reality it was 50:50. Do you correct for this? If not, the equation to do so can be found\n720 in https://www.sciencedirect.com/science/article/pii/S2589004222020521#sec4 under\n721 section “Analysis of trajectories from slow 2 Hz SPT movies”\n723 text, we however discuss ‘fraction of binding events’ (which again are potentially fewer for\n724 long binders).\n726 thus determined ‘true fractions’ by scaling the exponential amplitude value by its associated\n727 time constant, as described in the mentioned paper. The new plots are shown in\n729 18. A bit more discussion of how 1D sliding works on nucleosomal DNA could be nice.\n731 section:\n732 “We propose that Sox2 can diffuse along chromatin by exploiting nucleosome\n733 architecture. The close spatial proximity of the two DNA gyres on the\n734 nucleosome surface allows Sox2 to bypass extensive wrapped regions, while\n735 steric occlusion of the inward-facing gyre restricts sampling to exposed turns.\n737 buried DNA segments. Consequently, TFs with high nonspecific chromatin-\n738 binding ability, like Sox2, may exploit these fleeting openings to outcompete\n739 histones and invade compact chromatin more efficiently.”\nReviewer #4 (Remarks to the Author):\nAs I wrote in my first review, this is an excellent paper that addresses a long-standing and\ndeeply interesting question using new approaches and it very effectively applies a live-cell SMT,\nin vitro SMT, and genomics integrated approach. The results are compelling and make sense.\nAs I wrote in my first review, Fig 3i is especially compelling. I have reviewed many papers for\nNat Comm over the last 5 years and among the ones that were eventually published, I think the\npresent paper is near the top. I really think it is an excellent and compelling study that is likely to\nbe of wide interest.\nBut it does have a significant weakness, which is the rigor of the live-cell SMT analysis. I\npointed these out in my first review, but the authors have chosen to largely ignore them. This is\ndisappointing and the issues will be obvious to experts in the field and turn them off what is\notherwise an outstanding paper.\nAs far as I can tell from the authors response, they agree with my concerns (e.g. diffusion\nanalysis is not correct), but rather than correcting it, they chose to keep the problematic analysis\nin the main figures and then more correct analyses to the SI. Likewise, we know from dozens of\n“chromatin dynamics studies” (e.g. using H2B tracking) that the diffusion coefficient of chromatin\nis not 0.1 um^2/s/.\nSo I would like to ask the authors to do one of two things: 1) Maybe I am wrong, in which case,\nplease run reaction-diffusion simulations, add defocalization and localization noise, and\ndemonstrate that the diffusion analysis works well. Or 2) replace it with more correct analyses.\nRegarding my comments in the last round.\nComments 1-7 have been addressed.\nComment 8 has not really been addressed. I remain skeptical of the 6 states and my request\nwas to discuss the uncertainty in one sentence in the main text, which the authors have not\ndone. They have added some discussion to the discussion section but they have not really\naddressed my concern.\nIn 8a, the authors misunderstand my concern about relative error. I do not think you can\naccurately fit a residence time with a photobleaching rate being similar. I remain extremely\nskeptical about the GRID results and the authors have chosen not to explicitly discuss the\nuncertainty in the main text which is disappointing.\nWe have now explicitly acknowledged the uncertainty of the longest-lived GRID states in the\nmain text. The revised text is in line 126 to 130. This clarification makes clear that the slowest\nGRID components are interpreted qualitatively due to their proximity to the photobleaching limit.\nThe authors have also chosen not to address Comment 9.\nIn comment 9 I pointed out that eqn 2 (now eqn 3) is incorrect for data. MSD should be\n4st^alpha + loc error + motion blur. This is a solved issue. Why do it incorrectly?\nThe authors report an alpha of 0.8 for the DNA bound fraction. Again, we know this is incorrect.\nIs there a realistic polymer model with an exponent of 0.8? Rouse says 0.5. Fractal globule says\n0.4. Recent work, spanning several orders of magnitude suggests the exponent is more like 0.3-\n0.4 https://www.biorxiv.org/content/10.1101/2025.05.10.653248v1.full and another paper says\nsomething similar https://www.biorxiv.org/content/10.1101/2025.09.24.678119v1\nAgain, why do this incorrectly in the main text and correctly in the SI (Fig S3d).\nIt is true that there are several papers that use 0.1 um^2/s as the cut-off for the chromatin\ndiffusion, but we know this is a short-hand and we know this is incorrect. If you do not account\nfor localization error, you will dramatically overestimate the bound Diff Coef.\nIt does the field a disservice to propagate incorrect approaches and it also makes the paper look\nbad. This is an extremely impressive paper, but since you open with the in vivo SMT and do\nthese analyses incorrectly, it will turn off expert readers from what is otherwise a fantastic paper.\nThe “fit diffusion coefficients from each trajectory, then fit the distribution of coefficients” was\nbenchmarked in Figure 3 of https://elifesciences.org/articles/33125 and the performance is\nterrible For example, it can easily get the Bound fraction wrong by 30-55 percentage points.\nI would like to insist that the authors either remove the currently incorrect diffusion analysis, or\nvalidate that their approach is indeed correct and accurate by performing reaction-diffusion\nsimulations, adding localization noise to their simulated data, applying their analysis\nmethodology to it, and demonstrating what they are doing is indeed correct. It is possible that I\nam missing something and I would be happy to be persuaded that I am, but in its current form,\nthe analysis appears to be the “distribution of diffusion coefficient analysis” that was shown in\n2018 to not work at all. Given that alternative more accurate approaches are in Fig S3d, it is\nreally difficult to understand why they want to keep doing it incorrectly?\nWe agree that diffusion analyses should properly account for localization error, motion blur, and\ndefocalization. We agree that the MSD-based diffusion coefficient (D) distribution analysis is\nsuboptimal given that the trajectories are too short to resolve subdiffusing behaviors and tends\nto overestimate D values, although originally we believed that it would provide a minimally\nprocessed comparison of relative bound fractions across Sox TFs.\nWe have now removed this analysis from the Main Figure 2, and instead present a State Array\n(SA) analysis (Heckert et al., 2022; https://pubmed.ncbi.nlm.nih.gov/36066004/), which explicitly\nmodels localization and defocalization errors while jointly inferring trajectory-level diffusion\ncoefficients and uncertainty estimates on a diffusion-error grid using an RBME likelihood. This\napproach allows us to obtain diffusion coefficient distributions for each movie, capturing the\nlandscape of D-values that reflect DFR-dependent effects on TF diffusive behavior. Spot-On\nanalyses are retained in the main and supplementary figures as an orthogonal validation and\nespecially to minimally resolve overlapping diffusive states (D > 0.05) by separating them into\ntwo components. Note that we have now restricted the ‘time-point’ parameter to 8 (previously\n25), as this is the conventional and recommended setting for 100 Hz SMT acquisitions and 10\nframes of mean trajectory length. With this setting, we avoid over-weighting long trajectories and\nensure sufficient sampling of out-of-focus or short-lived molecules in jump length histograms.\nImportantly, all trajectories remain included in the single-cell Spot-On analysis without restricting\nthe jump-to-consider parameter (revised Fig. 2e-g, S3b).\nThe latest study on chromatin diffusion that combined multiple imaging techniques to span\nseveral orders of magnitude in time in single-particle tracking (Mazzocca et al., 2025;\nhttps://pubmed.ncbi.nlm.nih.gov/40463058/) showed that chromatin exhibits strongly\nsubdiffusive dynamics (α ≈ 0.3), corresponding to effective diffusion coefficients in the range of\n∼10-3–10-2 µm² s-1. It is also well aligned with previously reported values\n(https://pubmed.ncbi.nlm.nih.gov/28035241/; https://pubmed.ncbi.nlm.nih.gov/27764097/).\nBased on this finding, we change the threshold as 10-2 µm² s-1 to define chromatin-bound Sox\nTFs.\nAccordingly, the manuscript is updated:\nfrom line 138 to 163 for in vivo diffusion analysis in the Results section;\nfrom line 977 to 983 for State array analysis in the Methods section;\nfrom line 984 to 992 for Spot-On analysis in the Methods section.\nComment 10: Again, I have big concerns about the statistical robustness. If you fit the alpha of\neach trajectory, you have a power law. To robustly fit a power law you need at least 2 log in\nboth dimensions https://www.science.org/doi/10.1126/science.1216142 For an alpha of 0.8, this\nwould be about 3 log in time. So trajectories should contain ca. 1000 frames, which I would\nimagine is not the case.\nWe agree with the reviewer and removed the anomalous diffusion exponent (α) data, as we are\nlacking statistical strength to determine it accurately.\nReviewer #4 (Remarks to the Author):\nThe authors have fully addressed my comments and concern and I strongly recommend the\npublication of this excellent paper without delay and without going back to reviewers.\nI appreciate the changes the authors have made, and I really think this is an unusually excellent\nand interesting paper, that I am sure will be well received by the field.\nSMALL THINGS\nFig. S3c is a bit unconventional. To my knowledge, you should use all the displacements/jumps\nunless you think you are missing fast moving ones due to motion blur. I might suggest to\nremove it but it is not a big deal.\nWe thank the reviewer for their appreciation of our work. For the diffusion coefficient analysis\nusing Spot-On (data displayed in Figure 2e-g and Supplementary Figure 3b), we used all the\ntrajectories. We decided to keep Supplementary Figure 3c in order to illustrate how state\nfractions shift when progressively incorporating longer trajectories.\nIn this manuscript, Sakong et al. investigated the effect of electrostatic interactions in the DBD\nflanking regions (DFRs) of two IDR-containing pioneer TFs, Sox2 and Sox 17, on their DNA-\n/chromatin-binding dynamics both in vivo and in vitro. Importantly, they found that the\ndifferentially charged DFRs lead to distinct target search efficiency, as well as distinct search\nmechanisms between naked DNA and chromatinized DNA. These findings are significant not\nonly in providing novel insights into the target search process of Sox TFs beyond the well-\nestablished facilitated diffusion model (which might very well be applicable to other TFs as\nwell), but also sheds fundamental insights into the biophysical underpinnings of IDR-mediated\nTF-chromatin interactions in general.\nOverall, the multi-disciplinary approaches adopted in this work are well-designed, the\nexperimental evidence (comprising of single-molecule imaging, biochemical and genomic\ndata) are solid and nicely complement each other, and the conclusions are convincingly\nsupported by the data. I did not spot any major issue regarding logic, experimental design or\ndata interpretation/argumentation. I, however, have a few issues concerning some of the\nexperimental details, data analyses, further elaboration of the significance of certain findings,\nas well as several presentation-related issues, for the authors’ consideration.\n1. In the time-lapse imaging experiments where a 60-ms illumination is interspersed with\nvarying dark times to obtain imaging intervals of 120, 240, 480 and 960 ms, it is unclear\nhow the authors ensured that a certain bound molecule detected after a time-lapse is still\nthe same molecule as before the light was switched off? Could it be that the original\nmolecule unbinds and another molecule binds to the same binding site during the dark time,\nwhich would affect the subsequent analysis of the binding dynamics. An explanation on\nhow this is avoided would be needed. Also, it might be useful to provide illustrative\nschematics for the various time-lapse illumination patterns, indicating the durations of each\n“on” and “off ” intervals.\n2. The SMT measurements, coupled with GRID analysis, identified 6 well-resolved\nbound states for the TFs studied, with residence times ranging from 100s of ms all the\nway up to 1000 s. This is substantially more than the 2-4 binding modes that are\ncommonly observed for many other types of DNA-binding proteins, and could\npotentially represent something significant as a consequence of the complex\nchromatin-interaction landscape of Sox TFs. However, this significance is not\nadequately explained or elaborated on in either the Results or Discussion sections.\n3. The two main parameters used for quantifying DNA-binding from SMT\nmeasurements are the residence time and bound fraction. While these are certainly\ntwo commonly adopted and useful parameters, their utilities are not without limitations.\nFor example, a molecule exhibiting many repeated transient binding events (each\nlasting a short duration) might end up being bound for a similar total duration as\nanother molecule that undergoes only a few but long-lived binding events. In such\nsituations, a useful alternative parameter would be the total fraction of time the\nmolecule stays bound under each mode, which can simply be calculated as the\nproduct of residence time and the corresponding bound fraction, normalized against\nthe total time the molecule spends in all binding modes (see a recent e.g. in Engl et al.,\nNature Commun. 2024). This parameter can hence more reliably report the partitioning\nof the TF molecules among the different binding modes, which might add a useful\ndimension to the binding landscape characterized in the work.\nMore minor issues:\n• Pg. 2 and 3: The acronym DFR was defined twice in the main text (in addition to that in\nthe Abstract), whereas the terms DBD and mESC were not defined.\n• Pg. 2: “Among Sox TFs, Sox2 exhibited the most positively charged DFR and the highest\nmitotic chromosome binding.” Please specify what does “chromosome binding” refers to\nhere, e.g. binding affinity, residence time, fraction of molecules bound, etc.\n• Pg. 11: “…the nanoscopic association rate (k ), previously determined as about 2×105\na\nM-1s-1bp-1…” A reference is needed here.\n• Pg. 14: “…both Sox TFs showed three different residence times on CT+, while they\ndisplayed only two nonspecific binding populations on CT- (Extended Data Fig. 5d-h).”\nHowever, Extended Data Fig. 5f and h seem to show the opposite of what is stated in the\nmain text. Please check and reconcile.\n• Fig. 1: The vertical axis labels for both Fig. 1a and 1c are “charge”, but they clearly denote\ndifferent things; consider changing 1a to “Net charge” to distinguish it from 1c?\nMoreover, in Fig. 1c which shows the charge distribution across the DFR sequence, the\ncharge at each position takes on multiple fractional values between -1 and 1. However,\naccording to the designation in Extended Data Fig. 1a, the charges assigned to individual\nresidues can only take on values of +1 z (K & R), +0.5 z (H), or -1 z (E & D). In that case,\nhow could the charges shown in Fig. 1c have values other than these values (especially\nvarious fractional values other than +/- 0.5 z)?\nLastly, in Fig. 1h, log (res. time) is plotted on the horizontal axis, therefore its unit should\nnot be “s”, but rather “log s”. A better way to label the axis would be “log\n10\n(res. time / s)”.\n• Fig. 2c: Please define the vertical dotted line in the figure caption.\n• Extended Data Figure 5d: The gray curves in the plots are not labeled, contrary to those in\npanels i-l (which indicate whether each curve denotes CT+ or CT-, etc.).\n• Lastly, a few typos/language-related issues:\n Pg. 28: Under “mESC culture” section: “…5% CO2 in GMEM…” should read “…5% CO\n2 in GMEM…”\n Pg. 32: Under “In vivo smHILO microscopy setup” section, I believe “…pixel size of\n11×11 mm2” should be 11×11 µm2?\n All species names should be italicized (e.g. E. coli)"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have sufficiently addressed the points I raised and provided reasonable explanations where they chose not to make changes. In my view, the paper is ready for publication.", "reviewer_2": "The authors have satisfactorily addressed all of my concerns. I recommend publication of this work at Nature Commun.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_4": "As I wrote in my first review, this is an excellent paper that addresses a long-standing and deeply interesting question using new approaches and it very effectively applies a live-cell SMT, in vitro SMT, and genomics integrated approach. The results are compelling and make sense. As I wrote in my first review, Fig 3i is especially compelling. I have reviewed many papers for Nat Comm over the last 5 years and among the ones that were eventually published, I think the present paper is near the top. I really think it is an excellent and compelling study that is likely to be of wide interest.\nBut it does have a significant weakness, which is the rigor of the live-cell SMT analysis. I pointed these out in my first review, but the authors have chosen to largely ignore them. This is disappointing and the issues will be obvious to experts in the field and turn them off what is otherwise an outstanding paper.\nAs far as I can tell from the authors response, they agree with my concerns (e.g. diffusion analysis is not correct), but rather than correcting it, they chose to keep the problematic analysis in the main figures and then more correct analyses to the SI. Likewise, we know from dozens of “chromatin dynamics studies” (e.g. using H2B tracking) that the diffusion coefficient of chromatin is not 0.1 um^2/s/.\nSo I would like to ask the authors to do one of two things: 1) Maybe I am wrong, in which case, please run reaction-diffusion simulations, add defocalization and localization noise, and demonstrate that the diffusion analysis works well. Or 2) replace it with more correct analyses.\nRegarding my comments in the last round.\nComments 1-7 have been addressed.\nComment 8 has not really been addressed. I remain skeptical of the 6 states and my request was to discuss the uncertainty in one sentence in the main text, which the authors have not done. They have added some discussion to the discussion section but they have not really addressed my concern.\nIn 8a, the authors misunderstand my concern about relative error. I do not think you can accurately fit a residence time with a photobleaching rate being similar. I remain extremely skeptical about the GRID results and the authors have chosen not to explicitly discuss the uncertainty in the main text which is disappointing.\nThe authors have also chosen not to address Comment 9.\nIn comment 9 I pointed out that eqn 2 (now eqn 3) is incorrect for data. MSD should be 4st^alpha + loc error + motion blur. This is a solved issue. Why do it incorrectly?\nThe authors report an alpha of 0.8 for the DNA bound fraction. Again, we know this is incorrect. Is there a realistic polymer model with an exponent of 0.8? Rouse says 0.5. Fractal globule says 0.4. Recent work, spanning several orders of magnitude suggests the exponent is more like 0.3-0.4 https://www.biorxiv.org/content/10.1101/2025.05.10.653248v1.full and another paper says something similar https://www.biorxiv.org/content/10.1101/2025.09.24.678119v1\nAgain, why do this incorrectly in the main text and correctly in the SI (Fig S3d).\nIt is true that there are several papers that use 0.1 um^2/s as the cut-off for the chromatin diffusion, but we know this is a short-hand and we know this is incorrect. If you do not account for localization error, you will dramatically overestimate the bound Diff Coef.\nIt does the field a disservice to propagate incorrect approaches and it also makes the paper look bad. This is an extremely impressive paper, but since you open with the in vivo SMT and do these analyses incorrectly, it will turn off expert readers from what is otherwise a fantastic paper.\nThe “fit diffusion coefficients from each trajectory, then fit the distribution of coefficients” was benchmarked in Figure 3 of https://elifesciences.org/articles/33125 and the performance is terrible For example, it can easily get the Bound fraction wrong by 30-55 percentage points.\nI would like to insist that the authors either remove the currently incorrect diffusion analysis, or validate that their approach is indeed correct and accurate by performing reaction-diffusion simulations, adding localization noise to their simulated data, applying their analysis methodology to it, and demonstrating what they are doing is indeed correct. It is possible that I am missing something and I would be happy to be persuaded that I am, but in its current form, the analysis appears to be the “distribution of diffusion coefficient analysis” that was shown in 2018 to not work at all. Given that alternative more accurate approaches are in Fig S3d, it is really difficult to understand why they want to keep doing it incorrectly?\nComment 10: Again, I have big concerns about the statistical robustness. If you fit the alpha of each trajectory, you have a power law. To robustly fit a power law you need at least 2 log in both dimensions https://www.science.org/doi/10.1126/science.1216142 For an alpha of 0.8, this would be about 3 log in time. So trajectories should contain ca. 1000 frames, which I would imagine is not the case."}, "author_response": "RESPONSE TO REVIEWERS’ COMMENTS\nReviewer #4 (Remarks to the Author):\nAs I wrote in my first review, this is an excellent paper that addresses a long-standing and\ndeeply interesting question using new approaches and it very effectively applies a live-cell SMT,\nin vitro SMT, and genomics integrated approach. The results are compelling and make sense.\nAs I wrote in my first review, Fig 3i is especially compelling. I have reviewed many papers for\nNat Comm over the last 5 years and among the ones that were eventually published, I think the\npresent paper is near the top. I really think it is an excellent and compelling study that is likely to\nbe of wide interest.\nBut it does have a significant weakness, which is the rigor of the live-cell SMT analysis. I\npointed these out in my first review, but the authors have chosen to largely ignore them. This is\ndisappointing and the issues will be obvious to experts in the field and turn them off what is\notherwise an outstanding paper.\nAs far as I can tell from the authors response, they agree with my concerns (e.g. diffusion\nanalysis is not correct), but rather than correcting it, they chose to keep the problematic analysis\nin the main figures and then more correct analyses to the SI. Likewise, we know from dozens of\n“chromatin dynamics studies” (e.g. using H2B tracking) that the diffusion coefficient of chromatin\nis not 0.1 um^2/s/.\nSo I would like to ask the authors to do one of two things: 1) Maybe I am wrong, in which case,\nplease run reaction-diffusion simulations, add defocalization and localization noise, and\ndemonstrate that the diffusion analysis works well. Or 2) replace it with more correct analyses.\nRegarding my comments in the last round.\nComments 1-7 have been addressed.\nComment 8 has not really been addressed. I remain skeptical of the 6 states and my request\nwas to discuss the uncertainty in one sentence in the main text, which the authors have not\ndone. They have added some discussion to the discussion section but they have not really\naddressed my concern.\nIn 8a, the authors misunderstand my concern about relative error. I do not think you can\naccurately fit a residence time with a photobleaching rate being similar. I remain extremely\nskeptical about the GRID results and the authors have chosen not to explicitly discuss the\nuncertainty in the main text which is disappointing.\nWe have now explicitly acknowledged the uncertainty of the longest-lived GRID states in the\nmain text. The revised text is in line 126 to 130. This clarification makes clear that the slowest\nGRID components are interpreted qualitatively due to their proximity to the photobleaching limit.\nThe authors have also chosen not to address Comment 9.\nIn comment 9 I pointed out that eqn 2 (now eqn 3) is incorrect for data. MSD should be\n4st^alpha + loc error + motion blur. This is a solved issue. Why do it incorrectly?\nThe authors report an alpha of 0.8 for the DNA bound fraction. Again, we know this is incorrect.\nIs there a realistic polymer model with an exponent of 0.8? Rouse says 0.5. Fractal globule says\n0.4. Recent work, spanning several orders of magnitude suggests the exponent is more like 0.3-\n0.4 https://www.biorxiv.org/content/10.1101/2025.05.10.653248v1.full and another paper says\nsomething similar https://www.biorxiv.org/content/10.1101/2025.09.24.678119v1\nAgain, why do this incorrectly in the main text and correctly in the SI (Fig S3d).\nIt is true that there are several papers that use 0.1 um^2/s as the cut-off for the chromatin\ndiffusion, but we know this is a short-hand and we know this is incorrect. If you do not account\nfor localization error, you will dramatically overestimate the bound Diff Coef.\nIt does the field a disservice to propagate incorrect approaches and it also makes the paper look\nbad. This is an extremely impressive paper, but since you open with the in vivo SMT and do\nthese analyses incorrectly, it will turn off expert readers from what is otherwise a fantastic paper.\nThe “fit diffusion coefficients from each trajectory, then fit the distribution of coefficients” was\nbenchmarked in Figure 3 of https://elifesciences.org/articles/33125 and the performance is\nterrible For example, it can easily get the Bound fraction wrong by 30-55 percentage points.\nI would like to insist that the authors either remove the currently incorrect diffusion analysis, or\nvalidate that their approach is indeed correct and accurate by performing reaction-diffusion\nsimulations, adding localization noise to their simulated data, applying their analysis\nmethodology to it, and demonstrating what they are doing is indeed correct. It is possible that I\nam\nam missing something and I would be happy to be persuaded that I am, but in its current form,\nthe analysis appears to be the “distribution of diffusion coefficient analysis” that was shown in\n2018 to not work at all. Given that alternative more accurate approaches are in Fig S3d, it is\nreally difficult to understand why they want to keep doing it incorrectly?\nWe agree that diffusion analyses should properly account for localization error, motion blur, and\ndefocalization. We agree that the MSD-based diffusion coefficient (D) distribution analysis is\nsuboptimal given that the trajectories are too short to resolve subdiffusing behaviors and tends\nto overestimate D values, although originally we believed that it would provide a minimally\nprocessed comparison of relative bound fractions across Sox TFs.\nWe have now removed this analysis from the Main Figure 2, and instead present a State Array\n(SA) analysis (Heckert et al., 2022; https://pubmed.ncbi.nlm.nih.gov/36066004/), which explicitly\nmodels localization and defocalization errors while jointly inferring trajectory-level diffusion\ncoefficients and uncertainty estimates on a diffusion-error grid using an RBME likelihood. This\napproach allows us to obtain diffusion coefficient distributions for each movie, capturing the\nlandscape of D-values that reflect DFR-dependent effects on TF diffusive behavior. Spot-On\nanalyses are retained in the main and supplementary figures as an orthogonal validation and\nespecially to minimally resolve overlapping diffusive states (D > 0.05) by separating them into\ntwo components. Note that we have now restricted the ‘time-point’ parameter to 8 (previously\n25), as this is the conventional and recommended setting for 100 Hz SMT acquisitions and 10\nframes of mean trajectory length. With this setting, we avoid over-weighting long trajectories and\nensure sufficient sampling of out-of-focus or short-lived molecules in jump length histograms.\nImportantly, all trajectories remain included in the single-cell Spot-On analysis without restricting\nthe jump-to-consider parameter (revised Fig. 2e-g, S3b).\nThe latest study on chromatin diffusion that combined multiple imaging techniques to span\nseveral orders of magnitude in time in single-particle tracking (Mazzocca et al., 2025;\nhttps://pubmed.ncbi.nlm.nih.gov/40463058/) showed that chromatin exhibits strongly\nsubdiffusive dynamics (α ≈ 0.3), corresponding to effective diffusion coefficients in the range of\n∼10-3–10-2 µm² s-1. It is also well aligned with previously reported values\n(https://pubmed.ncbi.nlm.nih.gov/28035241/; https://pubmed.ncbi.nlm.nih.gov/27764097/).\nBased on this finding, we change the threshold as 10-2 µm² s-1 to define chromatin-bound Sox\nTFs.\nAccordingly, the manuscript is updated:\nfrom line 138 to 163 for in vivo diffusion analysis in the Results section;\nfrom line 977 to 983 for State array analysis in the Methods section;\nfrom line 984 to 992 for Spot-On analysis in the Methods section.\nComment 10: Again, I have big concerns about the statistical robustness. If you fit the alpha of\neach trajectory, you have a power law. To robustly fit a power law you need at least 2 log in\nboth dimensions https://www.science.org/doi/10.1126/science.1216142 For an alpha of 0.8, this\nwould be about 3 log in time. So trajectories should contain ca. 1000 frames, which I would\nimagine is not the case.\nWe agree with the reviewer and removed the anomalous diffusion exponent (α) data, as we are\nlacking statistical strength to determine it accurately."}, {"round": 3, "reviewer_comments": {"reviewer_4": "The authors have fully addressed my comments and concern and I strongly recommend the publication of this excellent paper without delay and without going back to reviewers.\nI appreciate the changes the authors have made, and I really think this is an unusually excellent and interesting paper, that I am sure will be well received by the field.\n\nSMALL THINGS\nFig. S3c is a bit unconventional. To my knowledge, you should use all the displacements/jumps unless you think you are missing fast moving ones due to motion blur. I might suggest to remove it but it is not a big deal."}, "author_response": "We thank the reviewer for their appreciation of our work. For the diffusion coefficient analysis using Spot-On (data displayed in Figure 2e-g and Supplementary Figure 3b), we used all the trajectories. We decided to keep Supplementary Figure 3c in order to illustrate how state fractions shift when progressively incorporating longer trajectories."}]

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