Single-molecule FRET reveals multiscale chromatin dynamics modulated by HP1α

The dynamic architecture of chromatin fibers, a key determinant of genome regulation, is poorly understood. Here, we employ multimodal single-molecule Förster resonance energy transfer studies to reveal structural states and their interconversion kinetics in chromatin fibers. We show that nucleosomes engage in short-lived (micro- to milliseconds) stacking interactions with one of their neighbors. This results in discrete tetranucleosome units with distinct interaction registers that interconvert within hundreds of milliseconds. Additionally, we find that dynamic chromatin architecture is modulated by the multivalent architectural protein heterochromatin protein 1α (HP1α), which engages methylated histone tails and thereby transiently stabilizes stacked nucleosomes. This compacted state nevertheless remains dynamic, exhibiting fluctuations on the timescale of HP1α residence times. Overall, this study reveals that exposure of internal DNA sites and nucleosome surfaces in chromatin fibers is governed by an intrinsic dynamic hierarchy from micro- to milliseconds, allowing the gene regulation machinery to access compact chromatin.

and Alexa647. (b) Chemical structure of the dye linked to a dT nucleotide. To calculate the dye accessible contact volumes for these dyes, the structure was approximated by an ellipsoid (R dye(1) , R dye (2) and R dye(3) ) connected by a linker of length (L link ) and width (w link ). Accessible contact volume dye model was used where part of AV which is closer than 3 Å from the macromolecular surface is defined to have higher dye density ρ dye 4 .
For the parameters used for the different dyes, see step 9: FRET positioning and screening calculations. (c) Molecular structure of a compact chromatin array, consisting of a stack of 3 tetranucleosomes (4-4-4, register 1) with DA1-positioned dyes in the central tetranucleosome. The model was produced by fitting nucleosomes into the electron density of the cryoEM structure of a 177-bp nucleosome array, ref. 5 . The inter-dye distance was evaluated using simulated dye accessible contact volumes (ACV) 6 . (d) Molecular structure of a chromatin array, consisting of a stack of 2 tetranucleosomes, flanked by two unstacked nucleosomes at each side (2-4-4-2, register 2) with DA1-positioned dyes on the two central tetranucleosomes and inter-dye distance from ACV-calculations. (e) Inter-dye distance for DA2 dyes in register 1 compacted arrays. (f) Inter-dye distance for DA2 dyes in register 2 compacted arrays. (g) Inter-dye distance for DA3 dyes in register 1 compacted arrays. Linker DNA was introduced extending the nucleosomal DNA connecting neighboring nucleosomes.
The distance is calculated between the phosphate groups of the modified bases (P-P distance). (h) Inter-dye distance for DA3 dyes in register 2 compacted arrays. Linker DNA was introduced extending the nucleosomal DNA connecting neighboring nucleosomes. Shown are calculated P-P distances. and dynamic mixing between (R1 mean -1and R2 mean - 2 and (R1 mean + 1 and R2 mean + 2 distributions (cyan symbols), where  i =*R i and =0.06.
[d] We computed the densities of  2 (see section 3.5 of ref. 12  [f] See step 9, Summary 9.3. [g] Calculated according to eq. (9.7).  Figures 16 -18). The model distances were calculated for the tetranucleosome model (register 1 and 2) considering the total experimental uncertainty Table 7

Dynamic structural biology analysis:
We used a combination of experimental observables (described in detail below) for structural and kinetic analyses to establish a model for chromatin dynamics, as shown in Fig. 6. We established an 11-step workflow for dynamic structural biology (Supplementary Fig. 9), involving a sequence of steps: Step 1: Measuring FRET efficiencies over time in smTIRF we explored chromatin dynamics in the 100 ms -seconds regime. Employing cross-correlation analysis we observed that between 20-55% of fibers showed dynamics on the 50-500 ms timescale ( Fig. 2 and Supplementary Table 6).
Step 3: Sub-ensemble Time Correlated Single Photon Counting (seTCSPC) resolved the FRET efficiency levels corresponding to chromatin structural states (Supplementary Fig. 10).
Step 5: Photobleaching and photoblinking analysis was employed to confirm that the observed dynamic processes originate from structural transitions and did not contain contributions from photophysics of the dyes (Supplementary Fig. 14a).
Steps 6-11: The combined obtained data was used to formulate kinetic models and assign states and connectivity between the states (step 6). Subsequently a unified kinetic model was used in dynamic PDA analysis (step 7, Fig. 5 and Supplementary Fig. 16-18). A global fit to the experimental data yields improved FRET efficiency levels values with corresponding population fractions and exchange rate constants. Afterwards the model was judged by applying a selection of criteria (Supplementary Fig. 15) including an evaluation of goodness of fit, the stability of the fit results (step 8) as well as by determination of the parameter uncertainties (step 9) and structural validation such as atomistic models (step 9) and coarse grained simulations (step 10). The procedure finally results in a complete model of chromatin dynamics (step 11).
Step 1. smTIRF From donor-(F D ) and acceptor fluorescence emission intensity (F A ) traces FRET efficiency (E FRET ) traces were calculated, using  Table 5).
Cross-correlation analysis was performed using where F D and F states where tetranucleosome interactions are stable over time (Figure 6).

Step 2: 2D MFD plots with FRET lines and calibration of the FRET measurements
Burst selection. The bursts of all samples were identified and selected from the MFD data trace as described in ref. 16 . Double-labeled chromatin arrays with the DA pair Alexa488/647 capable for FRET (FRET-active) were selected by Pulsed Interleaved Excitation (PIE) using E FRET vs S (stoichiometry) 2D histograms. For subsequent analysis we selected bursts with 0.2 < S < 0.8 to separate double-labeled species from single dye labeled molecules and |T GX -T RR | < 1 ms to remove contributions from photophysical processes 17 (Supplementary Fig. 8a). For PIE 18 , the corrected stoichiometry S is defined as (ii) The background corrected signals I were used together with four correction factors α, β, γ, δ to compute S according to: The parameter α is a correction factor for the spectral donor fluorescence crosstalk (leakage) into the red "acceptor" detection channel.  normalizes the direct acceptor excitation rates in the FRET experiment to that in the PIE experiment defined by the acceptor excitation cross-sections [a] average values for the FRET pairs DA1-3. The determined values are compiled in the summary tables reported in step 9.

Calculation of FRET efficiencies EFRET from fluorescence signals
The corrected FRET efficiency E FRET is defined via fully corrected fluorescence intensities F: In analogy to S, E FRET can be computed by the observed intensities and corresponding correction parameters α, β, γ defined in eq. (2.3): Expanding the dynamic range of smFRET studies. We used the FRET pairs Alexa568/647 (Förster Radius R 0 = 82 Å) and Alexa488/647 (R 0 = 52 Å) to exploit different distance sensitivities (Fig. 3d,e): Alexa568/647 allows for the detection of long-range dynamics beyond 120 Å, whereas Alexa488/647 enables the investigation of sub-states and their exchange dynamics below 60 Å.
Static and dynamic FRET lines. All MFD plots (Fig. 3d,e) for DA1-3 (Alexa488/647 and Alexa568/647) are presented with static and dynamic FRET lines, to demonstrate the presence of two distinct chromatin populations (register 1 and 2). Each population exhibits kinetic exchange faster than the molecular dwell time (< 10 ms) within the bursts. The theoretical dependence between FRET efficiency and species weighted average donor fluorescence lifetime in presence of acceptor dye is described as (2.6) Here we use an empirical dependence of species weighted average donor lifetime τ x on fluorescence weighted average donor lifetime τ F as a polynomial with c i coefficients obtained by numerical simulations 12 (2.7) Here we used the following joint parameters for DA1-3 constructs, which are common for the two FRET pairs Alexa568/647 and Alexa568/647, respectively: Alexa568/647 labeling (Fig. 3d) The dynamic FRET line are described as where  F1 and  F2 are the donor fluorescence lifetimes defining the limiting FRET states of the respective line. We have assumed that the limiting states of each DA sample remain the same for all Mg 2+ concentrations.

Step 3: Sub-ensemble TCSPC
For defining the limiting states for dynamic FRET lines indicated by FRET efficiency levels (Fig. 3e orange, wine and gray lines), we performed sub-ensemble Time Correlated Photon Counting (seTCSPC) analysis of DA1-3 (Alexa488/647), which were selected from the sample as double-labeled species by PIE (Supplementary Fig.   8a). Characteristic populations for each respective limiting state are analyzed for bursts with a low FRET efficiencies (0< E FRET <0.199) of the low FRET population (LF) and for bursts with higher FRET efficiencies (0.2< E FRET <1.0) of the dynamic FRET population (dynF). To retrieve the required information about the limiting states, we analyzed bursts of each population separately. The specific fluorescence decays were analyzed by a fit model described previously 19 . The fluorescence decay of the donor reference (DOnly, in the absence of FRET) was approximated by a single fluorescence lifetime, τ D(0) : Hence, the FRET-rate (k FRET ) is only determined by the donor-acceptor distance and their relative orientation.
In the presence of FRET, the donor fluorescence decay can be expressed using the donor-acceptor distance distribution p(R DA ): Here we assumed Gaussian distribution of donor-acceptor distances (p(R DA )) with a mean of R DA  and a halfwidth of DA  which is expressed as: In addition, a fraction of Donor-only molecules (x DOnly ) and a constant offset c was considered to describe the experimentally observed fluorescence decay f(t): We refer to this ratio as the FRET-induced donor decay, ε D (t), as it quantifies the quenching of the donor by FRET (see Main Text, Fig. 3f) with rate constant k FRET . ε D (t) allows us to directly display the underlying interdye distances that correspond to a characteristic time for the FRET species j (where j can be the species A, B, C and D, respectively) (eq. (3.6)).
Note that each Förster Radius R 0 has been computed with a specific fluorescence quantum yield of the donor and DA3, respectively) were analyzed in joint fit as described in detail in ref. 10 to determine the FRET species specific inter-dye distances R DA,j . The DA1 Alexa488/647 subpopulation (E FRET > 0.065, dynF, see also Figure   3f) and subpopulation with E FRET < 0.065, LF) at 1 mM Mg 2+ was fitted by eq.  Supplementary Fig. 10. This analysis yielded a good estimate of the FRET parameters of the structural states underlying the dynamic populations (register 1 and 2). Note, that it is difficult to resolve distances of this FRET pair above 90 Å by seTCSPC.

Step 4: Burst-ID FCS
To perform an unbiased check for the presence of exchange kinetics detected by FRET 3 , we computed the color correlation functions (auto-(green-green (G,G) and red-red (R,R))-and cross-(green-red (G,R) and redgreen (R,G)) functions, respectively) for the signal of those bursts, which were selected from the sample as double-labeled species by PIE (Supplementary Fig. 8a). These burst-ID cross-correlation functions G G,R and G R,G together with auto-correlation functions G G,G and G R,R were globally fitted by eq. 4.1 with three relaxation times t Rj . To fit the color auto(i=m)-and cross(i≠m)-correlation functions in a global approach, we have used a set of equations previously presented 5,20 where t Rj are the relaxation times that correspond to the exchange times between selected color signals (i=G,R and m=G,R) with corresponding absolute amplitudes of the auto-correlation function (4.2) A 3-dimensional Gaussian shaped volume element with parameters  0 and z 0 is considered. We assume that    Fig. 11).
Step photobleaching and/or photoblinking were present. However, as shown in Supplementary Fig. 14a, significant photobleaching and photoblinking was not present under our measurement conditions, because the |T GX -T RR | distribution is symmetric and narrow. Additionally, we checked for the presence of potentially weak photobleaching and photoblinking processes by applying the macro time filter |T GX -T RR |< 1 ms threshold criterion for burst selection (Supplementary Fig. 14b, left panel). The influence of the presence and absence of this selection criterion on the shape of the FRET efficiency distribution is demonstrated for double labeled bursts of DA1 (Alexa488/647) in 0.5 mM Mg 2+ . We fitted two FRET efficiency E FRET histograms with and without applied macro time filter (Supplementary Fig. 14b) by Photon Distribution Analysis (PDA, see step 7) for a 3 ms time window. The obtained FRET distributions and means with (left panel) and without (right panel) burst selection did not significantly differ from each other which proves the absence of marked acceptor photobleaching and photoblinking processes.
Steps 6-11. Establishing a dynamic model for chromatin dynamics

Step 6. Evaluation of kinetic networks between FRET species compatible with experimental data
The detected FRET species, which correspond to structurally meaningful chromatin conformers, form a kinetic network. Using the above presented observations from the various experiments (TIRF, seTCSPC, burst-ID FCS, MFD) kinetic and structural models for chromatin dynamics were formulated (Supplementary Fig.   15). The models to be evaluated involved four kinetic states (A-D) in two exchanging dynamic populations (register 1 and 2), corresponding to different tetranucleosome interactions.
In an iterative process, we used dynamic PDA (step 7) to refine the parameters and fit the experimental data using the developed kinetic models, followed by model validation (step 8). From the obtained, refined parameters, combined with structural molecular modeling (steps 9-10), a global model for chromatin conformational change was formulated (step 11, Fig. 5). The model encompasses a locally dynamic fiber which fluctuates between different tetranucleosome stacking registers on the millisecond timescale. Associations between tetranucleosomes are loose and exchange in the microsecond region. Finally, tetranucleosome open on the millisecond timescale and couple to static locked states, which persist structured over 50-500 ms. The individual steps 7-11 for this analysis are described below.

Step 7. General description of PDA analysis
Each sample with a specific FRET dye configuration (DA1, DA2 or DA3) was measured at various Mg 2+ concentrations under single-molecule conditions. The signals of the selected FRET bursts (Supplementary Fig.   8a) were split into equal time windows (TW). The  (Supplementary Fig. 16-18). The fundamental idea in PDA is computing the distribution of the chosen FRET indicator for a given FRET efficiency (or FRET-averaged donor-acceptor distance, R DA  E ) 4,14 taking into account photon shot-noise. Due to the flexibility of the dye linker, FRET pairs exhibit a distribution of FRET efficiencies or apparent distances even on rigid molecules, which is caused by distinct acceptor brightnesses 21 . This distance distribution is well approximated by a Gaussian distribution with a half width  ~6 Å.

Calculation of donor acceptor distances from fluorescence signals
The FRET-averaged distance R DA E between the dyes could be calculated from the mean FRET efficiency defined in eq. (2.4) In this work we calculated R DA E directly from the observed intensities and corresponding correction parameters α, β, γ, δ defined in Step 2:  Supplementary Fig. 14c). A global fit of both TWs using a joint models with static Gaussian distributions indicates that a model without dynamic exchange terms cannot describe both data sets appropriately, because the exchange dynamics influences the width of the distributions in each TW differently. Therefore Thus, in order to simulate dynamics between two Gaussian distributed species and to reduce computational cost, the model distribution can be approximated with the sum of two dynamic distributions between (R1 mean -1and R2 mean -2and (R1 mean +1and R2 mean +2) (Supplementary Fig. 14d).
MFD data were then globally fitted using dynamic PDA and assuming a kinetic model 14 Supplementary Fig. 15) was used to globally fit the group of histograms for each FRET dye configuration over all Mg 2+ concentrations ( Fig.   5a-c and final models in Supplementary Fig. 16-18). Thirdly, the dynamics of exchanging molecules was described by models with a series of two-state kinetic exchange terms connecting the quasi-static populations.
Final models are shown in Fig. 5d-f and Supplementary Fig. 16-18. Importantly, global fits were employed to evaluate the Mg 2+ dependencies, assuming a linear relationship between the logarithms of the rate constants and the ionic strength: 3) similar to observations in protein folding 22 .
Step 8: Validation of kinetic models.
Based on the model-free FCS analysis (Supplementary Fig. 11), yielding 3 relaxation times, at least four kinetically relevant species are expected. As our dye configurations (DA1-3) are not equally sensitive to all structural exchanges processes and states (Fig. 4a)  A number of different models were tested and based on criteria i-vi (Supplementary Fig. 15). The models shown in Fig. 3d were deemed to be the most probable to describe the experimental data. Finally, from the static and dynamic fractions, weighted by the associated rate constants, the relative populations of each state were calculated ( Fig. 5g- where P i denotes the population of state i, P s i is the static fraction, P d ij is the dynamic fraction between states i and j and k ij , k ji are the associated rate constants.

Steps 9-11. Assignment of the states
For a structural interpretation of the detected inter-dye distances from MFD and PDA, we determined the uncertainties in our analysis and subsequently applied structural modeling, using both available structures and coarse grained modeling, in combination with modeling of the conformational distributions of the dyes.
Step 9: Relating measured R DA distances to structural models of compact chromatin states Here, first we define the uncertainties in the measured parameters, followed by the construction of molecular models for the compact states. Here r i denotes the depolarization fractions related to order parameters, and  i the corresponding depolarization times mainly by dye rotation. In the r(t) analysis we applied the fundamental anisotropies r 0 = 0.38 for Alexa488 and Alexa647, respectively. We used the amplitude of the longest depolarization time r i to approximate the residual anisotropy r inf for computing the dye and position specific fraction of trapped dyes using eq. (9.2).
The fraction of trapped dyes is needed to parametrize the contact volume for improving the accuracy of the estimated spatial dye density in ACV simulations described in step 9, section FRET positioning and screening calculations below.
Summary of dye properties of the donor Alexa488. In the tables below the fluorescence lifetimes and anisotropy contributions of this donor dye are compiled. [a] The fit values with using eq. (9.1) are averages for measurements at 0.0, 0.5, 1.0 and 4 mM Mg 2+ .

Summary of acceptor dye properties.
In the tables below the fluorescence lifetimes and anisotropy contributions of the acceptor dye Alexa647 is summarized. In practice, as all cyanine based dyes, Alexa647 can have several dye populations in distinct environments with specific brightnesses when coupled to biomolecules referred to as acceptor heterogeneity, A het . This typical behavior is also seen in nucleosome arrays (see Summary 9.3). In this case a fixed DA distance is usually not sufficient to describe FRET species, and a Gaussian distance distribution with a mean apparent distance  R  and an apparent distribution half width (hw app ) has to be used instead. As shown by Kalinin and colleagues 21  R  is slightly biased towards longer distances as compared to R DA  E (eq. (9.3)).
where Ф FA is the acceptor fluorescence quantum yield. Note that the fraction of fluorescent trans states a (usually a = 0.8) cancels out in eq. (9.3)-(9.4). In this work, the correction factors Ф FA  1/6 Ф FA -1/6  are very close to unity (Summary 9.3) and thus can be disregarded for the calculation of interdye distances (i.e. in this . Applying the rules for error propagation for the function R ( FA ), one obtains also an relation for the variance and half width () of the apparent DA distance (eq. 9.4).
The fact that relative experimental half widths (R DA ) (Supplementary Figures 16-18 surprising. Note that the difference is the smallest (less than factor 2) for DA3. Summary 9.3. Fluorescence lifetimes and other dye parameters of the acceptor dye Alexa647 with a= 0.8.
Contributions to the uncertainty ΔR 0 . The overall uncertainty for the Förster radius, ΔR 0 , is estimated by the uncertainties of the local refractive index, n, the exact donor fluorescence quantum yield,  F,D , spectral overlap integral, J, and the FRET orientations factor,  2 , ref. 11 (eq. (9.8)). Contributions to the uncertainty ΔR DA (R DA ) by noise. We have to determine the precision of the dynamic PDA fits, ΔR DA (R DA ) caused by statistical noise. Here, we performed a subsampling analysis, where the dynamic PDA fit procedure was repeated three times using a 70% subsample of the total dataset. The standard deviations from these three fits are reported in Supplementary Figures 16-18, and determine the precision of our fitting procedure. The overall precision in R DA , ΔR DA (R DA ), from dynamic PDA is reported in Supplementary They are then propagated using eq. (9.7), to estimate the total uncertainty of the determined distances.
Together, these analyses result in a total uncertainty for R DA for DA1 of 9%, for R DA for DA2 of 9% and R DA for DA3 of 8% (Supplementary Table 7).
Model building. We built models using the cryo-EM structure of a 12-mer nucleosomal array with 177 bp nucleosome repeat length 5 . We then modeled the accessible contact volume (ACV) for dyes in the DA1, DA2 or DA3 configuration and employed these distance distributions to calculate an average, conformationweighted inter-dye distance (see below, FRET positioning and screening calculations). Importantly, we considered two possible fiber structures: The 12-mer array could exist as a stack of three tetranucleosome (TN) units (TN1(N1-N4); TN2(N5-N8); TN3(N9-N12), 4-4-4, register 1) as observed in the cryoEM structure (see Fig.   1a). Alternatively, tetranucleosomes could stack in a different register (TN1(N3-N6); TN2(N7-N10), with four unstacked nucleosomes at both ends, 2-4-4-2, register 2). This would put the DA1-3 dye pairs into neighboring tetranucleosomes. Finally, if the nucleosome-nucleosome interactions are local and fiber compaction is not fully cooperative, both registers are expected to be populated. We thus produced models for both registers and calculated the expected inter-dye distances for DA1-3 in register 1 and 2 ( Supplementary Fig. 12 and Supplementary Table 8). The observed deviations for DA2 can be rationalized by rotational motions between two nucleosomes (see Supplementary Fig. 13 e,f). A "clamshell" motion by ~10° would be sufficient to explain the experimental data of DA2 (488/647). Note that DA1 is relatively insensitive to these motions.
FRET positioning and screening calculations. The dye distribution was modeled by the accessible contact volume approach (ACV) 4 which is similar to the accessible volume (AV) 6 , but additionally defines an area close to the surface as contact volume. Here donor and acceptor fluorophores are approximated by a ellipsoid with an empirical radius R dye(i) and where central atom of the dye is connected via flexible linkage with effective length L link and width w link to the C 5 atom in the dT nucleotide. All geometric parameters for the dyes were: Alexa488: L link =20 Å, w link =4.5 Å, R dye(1) =5 Å, R dye(2) =4.5 Å, R dye(3) =1.5 Å, Alexa568: L link =22 Å, w link =4.5 Å, Supplementary Fig. 12). In the ACV model the part of AV which is closer than 3 Å from the macromolecular surface (referred to as contact volume) is defined to have a distinct spatial dye density ρ dye . In this model, where a dye freely diffuses within the AV and its diffusion is hindered close to the surface, the spatial density ρ dye along R is approximated by a step function: ρ dye (R < 3 Å) = θ CV,dye •ρ dye (R ≥ 3 Å). Here θ CV,dye corresponds to the relative dye density in the contact volume relative to outer volume. θ CV,dye is adjusted such that fraction of trapped dyes, determined by the residual anisotropy (see [a] computed by eq. 9.2 with values from the Summary 9.2 (donor) and Summary 9.4 (acceptor).
Step  Fig. 13a). We then measured inter-dye distances for all nucleosomes in these structures for DA1-3 and produced distance distribution histograms (Supplementary Fig.   13b,c,d). These histograms showed that expected peak inter-dye distances were 110 Å (and a smaller fraction of structures with 190 Å) for DA1, 80 Å and 120 Å for DA2 and 90 Å for DA3. These distances match distances expected for states D in the PDA (Fig. 4a).
Finally, to understand the intra-tetranucleosome dynamics observed for DA2 (Fig. 4a,b) we employed the tetranucleosome X-ray structure 13 to test how structural distortions affect inter-dye distances for DA1 and DA2 (Supplementary Fig. 13e,f) and DA3 (Supplementary Fig. 13g). DA2 was found to be more sensitive to tetranucleosome distortions, and distances observed for state C could be modeled by a 30 o change in the tetranucleosome interaction angle (Supplementary Fig. 13e) or by a 30 o rotation of one nucleosome relative to its neighbor (Supplementary Fig. 13f). Importantly, these conformations still allow interactions at the H2B and H2A four-helix bundle 5 to persist. To illustrate the effect of nucleosome structural motions on each of FRET dye configurations (DA1, DA2, DA3), we plot FRET-average inter-dye distance as a function of the motion coordinate (Supplementary Fig. 13e,f). We used tetranucleosome structural models 13 as a starting point for our illustrations. First we tested, how the DA1 and DA2 inter-dye distances change with respect to the clamshell-like opening angle between the two nucleosome units (N5, N7, Supplementary Fig. 13e). To define the clamshell rotation coordinate, we chose an axis going through the phosphorous atom of the unit N7, chain B, residue 55 and the phosphorous atom of the unit N7, chain A, residue -30. Thus, clamshell motion is the rotation of the unit N7 around the specified axis with the origin at the phosphorous atom of N7, chain B, residue 55. Second, we tested the DA1 and DA2 distance change with respect to the in-plane nucleosome rotation. To define this second rotational motion coordinate we chose the rotation axis between the centers of mass of the nucleosome units N5 and N7. Thus N7 is rotated around the specified axis with the origin at the center of mass of N7.
As the result we have observed that DA2 distance senses nucleosome clamshell motion while DA1 does not (Supplementary Fig. 13e). R DA  E for DA2 changes from 69 Å to 48 Å in the angular range of -30° to 0°.
DA1 is not sensitive to this motion and varies only from 47 to 50 Å. In the case of in-plane rotation, R DA  E for DA2 drops from 70 Å to 50 Å, when angle ranges from -30° to 30°. R DA  E for DA1 is also sensitive to this motion and shows an increase of R DA  E from 45 Å to 58 Å.

Coarse grained simulations
The 12-nucleosomes chromatin fibers with 177bp repeats (~30bp linker DNAs) were treated at a coarsegrained resolution using a mesoscopic model developed and validated by Arya and Schlick 23,24 . According to this model, each nucleosome core (histone octamer plus wound DNA) is treated as a rigid body with an irregular surface described by 300 charged beads; the linker DNAs are treated as charged bead-chains with each bead representing a 3 nm-long segment of double-stranded DNA; and the histone tails (N termini of H2A, H2B, H3, and H4 and C termini of H2A) are also treated as charged bead-chains, where each bead represents five amino acid residues. The core, linker, and tail beads are assigned excluded volume potentials, to prevent them from overlapping with each other, and charges, to reproduce the electrostatic field of their corresponding atomistic counterpart at the specified salt concentration. The linker DNAs are assigned an intramolecular force field to reproduce experimentally obtained bending and torsional rigidity of DNA, and the histone tails are assigned an intramolecular force field to reproduce the configurational properties of atomistic histone tails. In this study, the nucleosome entry/exit angle was set to 130 o , compatible with the trajectory of linker DNA in the tetranucleosome structure of Song et al. 5 , and the monovalent salt concentration was set to 50 mM. The effects of Mg 2+ were treated phenomenologically, with suitably modified Debye length and persistence length of the linker DNA, as described elsewhere 23 .
To generate an equilibrium ensemble of fiber conformations at 293 K, we used a tailored Monte Carlo simulation approach as described elsewhere 24 . Briefly, the simulations employed four Monte Carlo "moves": global pivot rotation of the end portions of the fiber about a randomly picked nucleosome core or linker DNA bead, local translation and rotation of a randomly picked linker DNA bead or nucleosome core, and configurational bias regrowth of a randomly picked histone tail. The simulations were performed for 40 million steps, with the above four Monte Carlo moves implemented at a relative frequency of 0.2: 0.1: 0.1: 0.6, respectively.
We picked a total of 100 uncorrelated fiber conformations from the simulated ensemble, which were then used to generate the corresponding atomistic models of the fiber (Supplementary Fig. 13a-d).
Step 11: Final model and its validation -A unified model of chromatin dynamics Based on the analyses presented above (steps 1-10) we formulated a unified model for chromatin dynamics (Fig. 6). The model encompasses two dynamic populations, corresponding to two tetranucleosome registers (register 1 and 2). From dynPDA of DA1 -3, ranges for the exchange rate constants were determined and are given in Fig. 4i. The presented model is well supported by the whole of the experimental data and is corroborated by matching results from different analyses yielding FRET efficiency states, dynamics rate constants and populations (Steps 2 -4) and dynamic PDA (Step 6).