Integrative dynamic structural biology unveils conformers essential for the oligomerization of a large GTPase

Guanylate binding proteins (GBPs) are soluble dynamin-like proteins that undergo a conformational transition for GTP-controlled oligomerization and disrupt membranes of intracellular parasites to exert their function as part of the innate immune system of mammalian cells. We apply neutron spin echo, X-ray scattering, fluorescence, and EPR spectroscopy as techniques for integrative dynamic structural biology to study the structural basis and mechanism of conformational transitions in the human GBP1 (hGBP1). We mapped hGBP1’s essential dynamics from nanoseconds to milliseconds by motional spectra of sub-domains. We find a GTP-independent flexibility of the C-terminal effector domain in the µs-regime and resolve structures of two distinct conformers essential for an opening of hGBP1 like a pocket knife and for oligomerization. Our results on hGBP1’s conformational heterogeneity and dynamics (intrinsic flexibility) deepen our molecular understanding relevant for its reversible oligomerization, GTP-triggered association of the GTPase-domains and assembly-dependent GTP-hydrolysis.


Introduction
The biological function of proteins is directly linked to their structure, conformational heterogeneity, and their associated conformational dynamics. It is well known that structural flexibilities, heterogeneities, and polymorphisms can enable interactions among biomolecules, promote promiscuity with different binding partners, and are often essential for enzymatic activity. (1,2) For a molecular understanding of such biological processes (1) the players of the biological process need to be described by structures, and (2) the associated conformational dynamics need to be characterized in detail. However, if taken out of context the structures of individual macromolecules are often uninformative about function. X-ray crystallography and electron microscopy provide detailed insights on snapshots of conformational states revealing secondary structures of individual domains and domain arrangements. However, to relate structures with their associated function it is imperative to study their conformational dynamics and for a molecular understanding of a biological process all conformational states need to be mapped, ideally watching single molecules move along their transition paths. (3) The relevance of dynamic structural biology is most evident for motor proteins such as myosin or dynamin, where cyclic structural changes are the molecular mechanism for their function. A widespread mechanism exerting such biomolecular function is the binding and cleavage of a suitable substrate to switch between at least two distinct states. Mostly hydrolyzable substrates such as the nucleotides ATP or GTP control structural changes by introducing the substrate hydrolysis as a quasi-irreversible step. Notably, the molecular mechanisms of the functionally relevant dynamics are mostly unknown because structurally flexible intermediates cannot be crystallized. Thus, NMR spectroscopy is often employed to map conformationally excited states and intermediates. (4) For larger proteins the determination of dynamic biomolecular structures is extremely challenging, as there is no single technique that can in parallel observe conformational transitions in biomolecules and determine structures with close to atomistic resolution. To overcome the disadvantages of the individual experimental methods, we employ a new integrative approach that unveils dynamic conformers and domain motions of large multidomain proteins. (5,6) By combining multiple experimental techniques we simultaneously probe protein structures and dynamics and cover time scales from nanoseconds to seconds for dynamic structural biology.
We apply this approach to study molecular mechanisms and design principles of large GTPases, a class of soluble proteins that are important for the innate cell-autonomous immunity in multicellular organisms. These large GTPases, namely guanylate binding proteins (GBPs), belong to the dynamin superfamily and more specifically to the class of interferon-γ induced effector molecules of first cell-autonomous defense. (7) GBPs have efficient antimicrobial activity against a wide range of intracellular pathogens such as viruses (8,9), bacteria(10-12) by assembling of inflammasomes (13,14) and by directly attacking the parasites (15). In living cells GBP isoforms form polar homo-and hetero-oligomers in different subcellular localizations, (16,17) that are involved in the intracellular immune response such as: defense against the vesicular stomatitis virus and the encephalomyocarditis virus, (8) suppression of Hepatitis C virus replication, (9) promotion of oxidative killing and the delivery of antimicrobial peptides to autophagolysosomes. (18) As a prime example for a GBP we study the human guanylate binding protein 1 (hGBP1). hGBP1 is biochemically well characterized and shows nucleotide-dependent oligomerization. (19) In vitro studies demonstrated GTP regulated polymerization of hGBP1 and the formation of polar supramolecular structures. (20) Noteworthy, a homolog GBP in mice translocates from the cytosol to endomembranes and attacks the plasma membrane of eukaryotic cellular parasites by the formation of supramolecular complexes during infection. (15) An additional feature of GBPs is the GTP induced formation of multimeric complexes in mesoscopic droplet-shaped protein condensates (referred to as vesicle-like structures, VLS) and on parasite membranes. VLS potentially facilitate the controlled formation of productive and supramolecular complexes (20) that attack intra-cellular parasites in living cells (15).
X-ray crystallography on the full-length hGBP1 revealed a folded and fully structured protein with the typical architecture of a dynamin superfamily member. hGBP1 consists of a large GTPase domain (LG domain), an alpha-helical middle domain, and an elongated, also purely alpha-helical, effector domain comprising the helices α12 and α13, with an overall length of around 120 Å (Fig. 1A).(21) X-ray crystallography (19) and biochemical experiments (7) identified the LG domains as interfaces for GTP-analogue induced homo-dimerization. Like for other membrane associated dynamins that form tubular shaped condensates to fuse membranes in cells (22,23), cylindrical and tubular structure have been observed for hGBP1 (20,22). For hGBP1 neither molecular structures of these tubules nor precursor structures in solution that inform on the assembly mechanism are known. FRET and DEER experiments on the hGBP1dimer identified two conformers. In the majorly populated hGBP1 dimer, the two C-terminal α13 helices associate. (24) This is in line with live-cell experiments that highlight the relevance of helix α13 for the immune response (12,25,26). However, an association of the two α13 helices in a hGBP1 dimer requires large-scale structural rearrangements that cannot be explained by the GppNHp bound X-ray crystal structures. (19) This highlights the necessity for structural flexibility on the formation pathway of a fully bridged hGBP1 dimer (b-hGBP1:L)2, where nucleotide ligands L (GTP) are bound and the effector domains and the LG domains are both associated (Fig. 1B). On the formation pathway of the fully bridged hGBP1 dimer, there are at least two intermediates -the ligand complex hGBP1:L and the flexible dimer (f-hGBP1:L)2 (Fig. 1B).
We address the question at which step of this pathway hGBP1 becomes flexible (red arrows ,   Fig. 1B). There are three option: either hGBP1's flexibility is substrate independent (i), induced by the ligand (ii), or induced by the dimerization (iii). Consequently, three potential dimerization scenarios could describe the required structural rearrangements (Fig. 1B). In the first pathway (Fig. 1B, i) the structural flexibility is an intrinsic property of the free monomer and already in the absence of substrate; although the flexibility is only needed the dimerization at a later step. In the second pathway (Fig.1B, ii) the free monomer is predominantly stiff; the binding and/or the hydrolysis of the substrate in the complex hGBP1:L increases the flexibility needed at a later stage for the dimerization. In the third alternative pathway (Fig.1B, iii) GTP binds to hGBP1 to enable dimerization of the LG domains and the LG domain dimerization triggers an internal rearrangement for effector domains to associate. To sum up, the pathways could be distinguished if one studies the monomeric hGBP1 that has either a single (pathways ii, iii) or multiple conformations in dynamic exchange (pathway i). Otherwise, the different mechanisms are indistinguishable. Hence, to differentiate these pathways, we map the structure and dynamics of the free and the ligand bound hGBP1. The network is shown on top of the crystal structure (hGBP1, PDB-ID: 1DG3). hGBP1 consists of three domains: the LG domain (blue), a middle domain (gray) and the helices α12/13 (green/orange). The amino acids highlighted by the labels were used to attach spin-labels and fluorophores for DEER-EPR and FRET experiments, respectively. Magenta and black lines connect the DEER pairs and FRET-pairs, respectively. In hGBP1 the C-terminus is posttranslationally modified and farnesylated for insertion into parasite membranes (red). (B) Potential different pathways for the formation of a functional hGBP1 dimer where the substrate binding LG domains and the helix α13 associate. The association of the helix α13 requires flexibility (highlighted by red arrows). This flexibility could be induced at different stages of a dimerization pathway.
We employ an integrative modeling toolkit for dynamic structural biology to address two objectives: (1) mapping the motions of the monomeric hGBP1 in the absence and the presence of a ligand and (2) resolving the structures of potential hGBP1 conformers in solution. This way, we study the molecular prerequisites for hGBP1 dimerization. We use structural information from small-angle X-ray scattering (SAXS), electron paramagnetic resonance (EPR) spectroscopy by site-directed spin labeling (27), ensemble and single-molecule fluorescence spectroscopy (28) and dynamic information from neutron spin-echo spectroscopy (NSE) and filtered fluorescence correlation spectroscopy (fFCS) (5). We mapped exchange kinetics from nanoseconds to milliseconds and detected at least two new conformational states in hGBP1.
Moreover, interrogating hGBP1's conformational dynamics by a network of 12 FRET pairs ( Fig. 1A), we generated a temporal spectrum of hGBP1's internal motions. Finally, we discuss potential implications of the detected protein flexibility and conformers controlling the formation of multimers. This allows us to understand the mechanisms excreting the function of this large multi-domain system, i.e., the programmed and controlled oligomerization.
We expect that our findings on the so far unresolved intrinsic flexibility of nucleoside triphosphate processing enzymes will sharpen our view on the importance of conformational dynamics for ligand-controlled allosteric regulation of multi-domain proteins and enzymes far beyond GBPs.

Experimental equilibrium distributions
We combined SAXS, DEER, and FRET experiments to probe distinct structural features of hGBP1 expressed and labeled for DEER and FRET by standard procedures (Methods 1).
Size exclusion chromatography SAXS (SEC-SAXS) measurements (Methods 2) were performed at different protein concentrations (Fig. S1A). SEC-SAXS assures the data quality by discriminating aggregates and oligomeric species in the sample immediately before the SAXS data acquisition. A Kratky-plot of the SAXS data ( Fig. 2A, middle) visualizes that hGBP1's conformation in solution clearly disagrees with the crystal structure of the full-length protein (PDB-ID: 1DG3). Ab initio modeling of the SAXS data (Methods 2) revealed a shape that suggests an additional kink between the LG and the middle domain ( Fig. 2A, right).
Orthogonal information to the SAXS data were obtained by DEER (Methods 3) and FRET experiments (Methods 4), which specifically probe distances between labeling sites (Fig. 1A).
The results of the DEER and FRET measurements and analyses are exemplified for the dual cysteine variant Q344C/A496C labeled by MTSSL spin probes for DEER experiments ( Fig. 2B) and by the fluorophores Alexa488 and Alexa647 for ensemble FRET experiments bimodal distance distribution p(RDA) (Fig. 2C, right) with a major and minor subpopulation. To associated conformational states are referred to as M1, and M2, respectively (Fig. 2C, right).
For an unambiguous assignment of the experimental distances to the conformational states, all 12 datasets (Fig. 1) were analyzed by a joint/global quasi-static homogeneous FRET-model (29))for all samples with shared species fractions of M1 = 0.61 and M2 = 0.39(Tab. S1A) at room temperature.
To compare theoretical and experimental average DA distances ⟨ ⟩ and distance distributions p(RDA), we need (1) a dye model that predicts the spatial distributions of the flexibly linked dyes for given structural models (31,32) and (2)  Overall, in the FRET measurements, M1 agreed better with the X-ray structure than M2 ( Fig. 2C, right, Tab. S1A) -the sum of uncertainty weighted squared deviations, 2 , for M1 is significantly smaller than for M2 ( 2 ( 1 , 1 3)~17 vs. 2 1 (section 2), Fig. S4D). An analysis result of the NSE data is visualized in Fig. 3A, which displays the scattering vector, q, dependent effective diffusion coefficient Deff extracted from the initial slope of the NSE spectra measured up to 200 ns (Fig. S5A) Fig. 3B, Fig. S3A). In 8 out of 12 variants, we found clear indications of dynamics by a peak shift of the FRET molecules off the static FRET-line towards longer ⟨τD(A)⟩F (Fig. S3A).

Identification and quantification of molecular kinetics
Analogous to relaxation dispersion experiments in NMR, such shifts confirm that M1 and M2 are in an exchange faster than the integration time of the molecules (~milliseconds). (35,36) A detailed analysis of the fluorescence decays of the FRET sub-ensembles (Fig. S3B) by a twocomponent model revealed limiting states (Tab. S1C) agreeing with the eTCSPC measurements (Tab. S1A). Hence, the peak positions in the MFD histograms are consistent with the eTCSPC analysis and are captured by dynamic FRET-lines, which describe the mixing of the two states (Fig. 3B, Fig. S3A). the species autocorrelation functions (sACF) determined by fFCS (Fig. S3C) and displayed the results as relaxation time spectra, where the normalized amplitudes are plotted versus the correlation time (Fig. 3D). Surprisingly, each individual set of sCCF and sACF of the 12 FRET pairs required at least two correlation times to be fully described. This is an indication for more complex kinetics or more (kinetic) states, which are unresolved by the analysis of the fluorescence decays. In a global analysis of all 12 variants (eq. 17), where we treat all 48 fFCS curves (two SACF and SCCF per variant) as a single dataset and we recovered three joint correlation times of 2, 23 and 297 µs (Fig. 3C). However, the amplitudes of the relaxation times differ significantly so that the average relaxation time varies approximately by one order of magnitude (gray bars in Fig. 3D). Intriguingly, this global analysis reveals a variant-specific amplitude distribution of correlation times and highlights significant differences among the variants (Fig. 3D, Fig. S3C, Tab. S2). In most cases, the shortest correlation time has the highest amplitude. This is consistent with the MFD histograms, because we detected shifted/dynamic unimodal peaks. To visualize the dynamics detected by fFCS, we mapped the average correlation times color coded to the FRET network shown on top of a protein X-ray structure (Fig. 3E). This visualization highlights that the fast dynamics is mainly associated with the helices α12/13 and the middle domain, while the slow dynamics is predominantly linked to the LG domain.
Referring to the sketch in Fig. 1B, we hypothesize that the states M1 and M2 and the transition among them are of functional relevance (pathway i). Therefore, we studied the effect on the dynamics exerted by the ligand GDP-AlFx as a substrate that mimics the holo-state hGBP1:L.
The GDP-AlFx concentration was sufficiently high (100 µM) to fully induce dimerization for hGBP1 at µM concentrations. (15) For comparison, the affinity of hGBP1 for mant-GDP is ~3.5 μM and much higher for GDP-AlFx. (37) Hence, in the sm-measurements GDP-AlFx was bound to the LG domain while hGBP1 (20 pM) was still monomeric. We refer to this as the holo-form of the protein and selected a set of variants (N18C/Q577C, Q254C/V540C, Q344C/V540C) for   which we found large substrate induced effects at higher hGBP1 concentrations due to oligomerization. Surprisingly, the amplitude distribution of the correlation times is within errors indistinguishable from the measurements of the nucleotide-free apo forms (Fig. 3D). Moreover, the FRET observables did not change either.
In conclusion, our integrative study on the structure and dynamics yielded the four major

Essential motions determined by molecular dynamics simulations
We performed molecular dynamics (MD) simulations without experimental restraints to assess the structural dynamics of the full-length crystal structure at the atomistic level and to capture potential motions of hGBP1 (Methods 6, Supplementary Note 2). The apo (PDB-ID: 1DG3) and a GTP bound holo-form of hGBP1 were simulated in three replicas by conventional MD simulations for 2 µs each (Fig. S6A). Additionally, accelerated molecular dynamics (aMD) simulations, which proved to sample the free-energy landscape of a small protein (58 amino acids) 2000-fold more efficiently (38), were performed in two replicas of 200 ns each.
Autocorrelation analysis of the RMSD vs. the average structure of the MD simulations reveals fast correlation times. The average correlation time in the presence and the absence of GTP were 11 ns and 17 ns (Fig. S6B). However, note that the amplitude of the fluctuations is, on average, below an RMSD of 3 Å, which is below the resolution limit of our NSE measurements.
In the MD simulations, larger conformational changes (RMSD > 7 Å) with considerable shape changes were very rare events. A principle component analysis revealed kinking motions of the middle domain and helix α12/13 around a pivot point as most dominant motions in the MD simulations (Fig. 3F). A visual inspection of structures deviating most from the mean reveals a kink at the connector of the LG and the middle domain ( Fig. 3G) consistent with rearrangements required for average shape as recovered by SAXS (Fig. 2).
To sum up, the MD simulations cover only time-scales of a few microseconds. Nevertheless, they indicated potential directions of motions and identified a pivot point between the LG and the middle domain. In agreement with NSE on the simulation time-scale, the overall shape is majorly conserved, and large conformational changes are rare events. The helices α12/13 were mobile and exhibited a limited "rolling" motion along the LG and middle domain that could connect the conformers M1 and M2 as suggested by our FRET studies.

Experimentally guided structural modeling
We integrate the experimental evidence for alternative conformations beyond the crystal structure into structural models of hGBP1 (Methods 7). Considering the specific requirements of label-based methods (31,32) we previously demonstrated using synthetic data the reliability of MFD measurements for resolving short-lived conformational states by structural models of a large GTPase. (33) Here, we additionally integrate DEER and SAXS data in a joined framework for an unbiased meta-analysis (Methods 7) and generate quantitative structural models for hGBP1 in three major steps: (i) "Data acquisition", (ii) "Model generation", and (iii) "Model discrimination" (Fig. 4A). In a previous in silico benchmark study on the GTPase Alastin, we needed only 29 optimal chosen FRET pairs to achieve an accuracy vs. the target structures and a precision below 2 Å.(33) For the given set of 12 FRET and 8 DEER pairs of hGBP1 we expect to recover low-resolution models with an average RMSDs in the range of 8-15 Å, and aim to resolve hGBP1's shape, domain arrangement, and topology.  are sums of weighted squared deviations and rank the pairs of structural models. To the right, a meta-analysis (eq. 25) fuses the probabilities derived from Data acquisition. We initially assumed as prior knowledge that the crystal structure of hGBP1 corresponded to the solution structure and designed the above experiments to test this assumption (Fig. 4A, steps 1-3). Model generation. As we disproved this initial assumption, we employed the experimental data to generate new structural models by modifying our initial model (Fig. 4A, steps 4-5). For that, we sampled the experimentally allowed conformational space as vastly as possible by combining simulations of different granularity and computational complexity (Methods 7). First, we identify a set of rigid bodies (RBs) (Fig. 4B, Supplementary Note 4) using the information on the motions observed in the MD simulations ( Fig. 3F), an order-parameter based rigidity analysis (Fig. S6C), knowledge on the individual domains within the dynamin family (40,41), position dependence of FRET and DEER properties (Tab. S1A) and SAXS experiments suggesting a kink in hGBP1's middle domain.
To this RB assembly, we applied DEER and ensemble FRET restrains for guided rigid body , which capture deviations between the model and the data for SAXS and for the combined DEER and FRET datasets, respectively (Methods 7). For maximum parsimony with respect to the modelled conformational states, the DEER, FRET and SAXS measurements were described by two states M1 and M2. Theoretical SAXS curves for all structural models of M1 and M2 were calculated using the computer program CRYSOL. Using the theoretical SAXS curves all possible combinations of structural models for M1 and M2 were ranked by their agreement with the SAXS data in an ensemble analysis (Fig. 4A, step 6a; Fig. 4C, eq. 21). Like in the model free bead modeling of the SAXS data (Fig. 2), for the pair of structural models best agreeing with SAXS the middle domain is kinked towards the LG domain (Fig. S1C). The SAXS ensemble analysis reveals species population fractions for M1 in the range of ~0.1-0.7 (Fig. S1D and analysis to rank and discriminate the generated structural models in a statistically meaningful manner (Fig. 4A, step 6b). In this step, the meta-analysis considers estimates for the degrees of freedom (dof) of the model and the data (Methods 7). This way, we select wellbalanced structural models and fully avoid fudge factors equalizing experimental contributions to the model (Fig. 4C, Combined screening). A stability test demonstrates that reasonably chosen dofs have only a minor influence on the results (Fig. S6D). In the final analysis, a pvalue of 0.68 discriminated more than 95% of all structural models (Fig. 4C, red area; upper triangles). The weighting reference ( ) is the expected precision of "ideal and perfect" model ensembles, determined using the experimental uncertainties under the assumption, that the best experimentally determined model is the ground truth.
For M1, this procedure yields a rather uniform distribution for the weighted precision of the recovered structural models that fluctuates around unity, the theoretical optimum (Fig. 4E, left).
The distribution of the weighted precision for M2 looks also fine, except close to the C-terminus (end of helix α12 and α13) where the precision of the ensemble is worse than expected (Fig. 4E, right), presumably due to granularity of the model or systematic experimental errors. The heterogeneity of the structural ensembles is judged by their root mean square fluctuations (RMSF) (Fig. 4F). The RMSF values of both conformers M1 and M2 depend on the residue number and fluctuate around the expected range of ~ 7 and ~ 9 Å, respectively. To visualize differences among the structural models, we aligned the selected conformers to the LG domain.
This demonstrates that in M1 and M2 α12/13 binds at two distinct regions of the LG domain

Discussion
Our experimental findings on the structure of hGBP1 in solution can be approximated by two major conformations M1 and M2, which are in dynamic exchange. We mapped the dynamics of hGBP1 by NSE spectroscopy and fFCS. NSE showed that hGBP1 is a protein without significant detectable shape changes on the ns-timescale up to 200 ns. However, fFCS that analyzed a network of FRET-pairs revealed considerable dynamics on slower time scales (2-  To understand the potential functional relevance of M1 and M2, various observations should be considered. First, the oligomerization of hGBP1 is an important feature that demands flexibility of the structure as deduced from major structural rearrangements described so far. (20,24,44) In particular, large movements of the LG, the middle domain and helices 12/13 against each other are required to establish the elongated building blocks of the polymer. (20) It is also most conceivable that various dynamically interchanging configurations of the sub-domains need to be sampled to assemble the highly ordered polymer. Dynamins and farnesylated hGBP1 are known to form highly ordered oligomers (20) requiring at least two binding sites. We previously showed that non-farnesylated hGBP1 forms dimers via the LG domains (in a head-to-head manner) and via helix α13 (24) in the presence of a GTP analog. This finding is inconsistent with the crystal structures of the full-length protein (PDB-ID: 1DG3 and 1F5N) and for dimers formed by two hGBP1s in the same conformations, as within such dimers the helices α13 are on opposite sides and thus could not associate (Fig. 5). However, in a dimer formed of two distinct conformers (M1:M2), the helices α13 are located on the same side of their LG domains.
Thus, in line with previous studies, which identified preferred pathways to increase the association yield of protein-protein complexes, (45) we suggest that, owing to the conformational flexibility, precursors necessary for oligomerization are already formed spontaneously before binding of the oligomerization-inducing substrate GTP. Remarkably, we detected virtually no substrate induced differences in the amplitude distribution of the correlation times demonstrating that the flexibility is independent of the bound nucleotide.
Overall, the findings strongly suggest that the GTP induced dimerization of the GTPase domains and a substrate independent flexibility are needed for a dimerization of the effector domains (pathway i in Fig. 1B). The substrate solely facilitates hGBP1 association by increasing the affinity of the LG domain as a hub for dimerization.
Structure-wise, we found that the middle domain is kinked with respect to the LG domain as found for other dynamins (40,41). Moreover, our data supports two conformations with distinct binding sites of helix a12/13 that can be explained by major rearrangements of the region connecting the middle and the LG domain. Prakash et al. Previous data (15,17,20,24) and our new findings in this work lead to a common model which describes the reaction pathway of hGBP1 from a monomer to the formation of mesoscale droplets in vitro and living cells (Fig. 6). All structural requirements for this multi-step conformational rearrangement for positioning the two interaction sites and defining the molecular polarity are already predefined in the monomeric hGBP1 molecule. In the absence of substrate and other GBP molecules, hGBP1 adopts at least two distinct conformational states.
Upon addition of GTP the LG domain is capable of binding to another protomer, whilst the conformational dynamics appear to remain unchanged. When two GTP bound hGBP1s associate, a head-to-head dimer either in a M1:M1, M2:M2 or a M1:M2 configuration is formed.
As the M1:M2 dimer has a higher stability, in M1:M2 the α13 helices of the two subunits associate, the equilibrium is shifted towards the M1:M2 dimers. (24) Notably, in vivo helix α13 is farnesylated at the end of a "CaaX" motif (7). Thus, hGBP1 provides a membrane anchor and now, hGBP1 dimers supposedly act as amphiphilic particles in the build-up of supramolecular structures. (20) This suggests, in line with the common knowledge that amphiphilic Janus particles can form liquid phases (48), that hGPB1 forms protein condensates and droplets, also referred to as vesicle like structures (VLS) in living cells. In a more general view, our results on hGBP1 demonstrate that the exchange between distinct protein conformations is usually encoded in its design (pathway i, Fig. 1A). Thus, the conformational flexibility of a protein can already be a characteristic of the apo form although this property is only relevant for a later stage of the protein's functional cycle, for example in a complex with its ligand, substrates and other proteins, respectively. Considering, for example, the movement of the substrate-dependent conformational transitions in the finger subdomain of a DNA polymerase, (52) it is obvious that these opening and closing movements are essential for catalyzing polymerization under ambient conditions. The rule that functionally relevant conformational equilibria may be predefined by protein design also applies to other steps in protein function. In future, when considering additional quantitative live-cell studies such integrative approaches may provide a molecular picture on complex biological processes like intracellular immune response. Labeling efficiencies were determined by double integration of CW room temperature (RT)

Protein expression and labeling
EPR spectra by comparison of the EPR samples to samples of known concentration. In all cases, the labeling efficiencies were ~90-100%.

Small angle X-ray scattering
Experimental methods. Small-angle X-ray scattering (SAXS) was measured on the beamlines X33 at the Doris III storage ring, DESY and on BM29 at the ESRF(54) using X-ray wavelengths of 1.5 Å and 1 Å, respectively. On BM29 a size exclusion column (Superdex 200 10/300 GL, GE Healthcare) coupled to the SAXS beamline was used (SEC-SAXS). The scattering vector q is defined as = 4 / ⋅ sin ( /2) with the incident wavelength λ and the scattering angle θ.
The measurements cover an effective q range from 0.015 to 0.40 Å -1 for X33 data and 0.006 to 0.49 Å -1 for BM29 data.
SAXS allows determining the shape and low-resolution structure of proteins in solution by the measured scattering intensity I(q), which is proportional to the form factor F(q) multiplied by the structure factor S(q). (55)  The distance distribution function P(r) was determined using the program DATGNOM. Ab initio models were generated using the program DAMMIF. In total 20 ab initio models were generated, averaged and the filtered model was used. Normalized spatial discrepancy (NSD) values of the different DAMMIF models were between 0.8 and 0.9 indicative of good agreement between generated ab initio models. The resolution of the obtained ab initio model is 29±2 Å as evaluated by the resolution assessment algorithm.

EPR spectroscopy
with observer pulse (νobs) lengths of 16 ns for π /2 and 32 ns for π pulses and a pump pulse (νpump) length of 12 ns. A two-step phase cycling (+ ‹x›, -‹x›) was performed on π/2(νobs). Time t' was varied with fixed values for τ1 and τ2. The dipolar evolution time is given by t = t' -τ1.
Data were analyzed only for t > 0. The resonator was overcoupled to Q ~ 100. The pump frequency υpump was set to the center of the resonator dip (coinciding with the maximum of the EPR absorption spectrum. The observer frequency νobs was set ~65 MHz higher, at the low field local maximum of the EPR spectrum. Deuterium modulation was averaged by adding traces was performed assuming an isotropic distribution of the spin-labeled hGBP1 molecules in frozen solution that is described by Briefly, the resulting form factor ( ) is modulated with the dipolar frequency that is proportional to the cube of the inverse of the inter-spin distance RSS (µB: Bohr magneton; for nitroxide spin labels. The optimum p(RSS) was found by minimizing the objective function The regularization parameter was varied to find the best compromise between smoothness, i.e., the suppression of artifacts introduced by noise, and resolution of ( ). The optimum Here We assume that the same distribution of FRET-rate constants quenches all fluorescent states of the donor (quasi-static homogeneous model (29)). Thus, | ( ) ( ) can be expressed by: Where εD(t) is the FRET-induced donor decay. The MFD measurements demonstrate that the major fraction of the dyes is mobile (Supplementary Note 1). Therefore, we approximate the κ 2 by 2/3 and relate εD(t) to the p(RDA) by: Here, R0 is the Förster-radius (R0 = 52 Å) and k0=1/0 is the radiative rate constant of the unquenched dye (0= 4 ns). In εD(t) incomplete labeled molecules lacking an acceptor and molecules with bleached acceptors are considered by the fraction of FRET-inactive, xDOnly.
For rigorous uncertainty estimates p(RDA) was modeled by a linear combination of normal distributions. Overall, a superposition of two normal distributions with a central distance ̅ (1,2) and a width wDA was sufficient to describe the data: In the analysis of the seTCSPC data, the FRET-sensitized emission of the acceptor, | ( ), was considered to reduce the overall photon noise and a typical width of 12 Å was consistent with the data. | ( ) ( ) was described by the convolution of | ( ) ( ), and | ( ) ( ): All f(t)s were fitted by model functions using the iterative re-convolution approach.
Here, N (n,m) is the effective number of molecules. The sACFs were fitted by individual effective numbers of molecules. The two sCCFs shared a single effective number of molecules.
We assume that the same diffusion term can describe all correlation curves of a sample and that the molecules diffuse in a 3D Gaussian illumination/detection profile. Under these assumptions where tdiff the characteristic diffusion time and ω0 and z0 are the radii of the focal and the axial plane, respectively, where the intensity decayed to 1/e 2 of the maximum's intensity.
The kinetic terms of the sACF and the sCCF were formally described by: Here, A0 defines the amplitude of the anti-correlation; Ab accounts for acceptors bleaching in The rigid body diffusion D0(q) of a structural model at infinite dilution was calculated according to (34): where ̂ is the 6x6 diffusion tensor, which was calculated using the HYDROPRO program. (63) D0(q) was calculated for the hGBP1 crystal structure (PDB-ID: 1DG3) and the best representing M2 structure. The population values have been determined from fits to the SAXS data with 69% best representing M2 structure and 31% crystal structure at the temperature of 10°C.
The full NSE spectra were described by rigid body diffusion and internal protein dynamics according to (64): where asymmetric particles. Internal protein dynamics was described by an exponential decay with a q-independent rate , and a q-dependent contribution A(q) of internal dynamics to the NSE spectra.
The parameters Ht, Hr the relaxation time λ and the amplitudes A(q) (eq. 19) were simultaneously optimized to all NSE spectra (Fig. S5). The fits show a small contribution of internal dynamics with amplitudes close to the error bars and seemingly long relaxation times, but not strong enough to be determined unambiguously. Fitting the spectra without additional internal dynamics shows an excellent description of the data (Fig. S5)

Integrative modeling
The generation of structural models follows the workflow (Fig. 4A) presented in the main text.
A key prerequisite for integrative modeling is the simulation of experimental observables for a given set of structural models. To generate an integrative structural model, the degrees of freedom, i.e., the model needs to be defined, structural models need to be generated, the structural models need to be ranked, i.e., evaluated against the experimental data, and experiments need to be combined in a meta-analysis.

Simulation of experimental parameters
Theoretical SAXS scattering curves for the structural models were calculated using the established software CRYSOL.(55) DEER and the FRET inter-label distance distributions ( , ) were simulated by accessible volume (AV) simulations. The experimental interlabel distances were compared to the simulated average distances (Fig. 4D). For a given protein conformation M the average simulated distance for all label linker conformations ⟨ ,sim ⟩ is Because of the different meaning of the experimental DEER and FRET inter-label distances, the modeled average inter-spin distances ⟨ , ⟩ and the center to center inter-dye distances  (Fig. S2B).
The analysis of the fluorescence data provided per variant two central distances ̅ that were assigned based on their relative population to the identified conformations M1 and M2 (eq. 11) while the model free DEER analysis yields distance distributions (eqs. 5, 6) that were considered by their average distance 〈 , 〉. Note, contrary to the simulated average distance, the experimental average is a linear combination of the distances of the two co-existing conformations.
The N-to the C-terminal parts of the rigid bodies were connected via bonds with a weak quadratic potential. Such reduced model does not allow for bending of the individual domains.
Therefore, we used a very soft clash-potential (Supplementary Note 4).

Generation of structural models
We use in a first step coarse-grained rigid-body (RB) models and experimental constraints from DEER and FRET, to sample the experimentally allowed conformational space as vast as possible. As first step to generate structural models we use RB docking (RBD) with DEER and FRET restrains. Here, average distances between the labels were determined by modeling their spatial distribution of the labels around their attachment point by accessible volume (AV) simulations. (32) Deviations between the modeled and the experimental FRET and DEER distances were minimized by driving initial random configurations the rigid-body assembly towards an optimal conformation (Supplementary Note 4). The restraints are compiled in the supplement (Tab. S3). This docking procedure was repeated 20,000 times for M1 and M2 to generate structural models refined by subsequent NMSim and MD simulations (Fig. 4A).
Next, the structural models generated by RBD were refined by the computationally more demanding normal mode based all-atom multiscale NMSim. NMSim generates representations with stereochemical accurate conformations by a three-step protocol and incorporates information about preferred directions of protein motions into a geometric simulation algorithm. (39) We used the RBD structures as a target for NMSim to optimize the stereochemistry. In targeted NMSim the conformational change vector is formulated as a linear combination of the modes calculated for the starting structure (the crystal structure) weighted by the proximity to the target structure (the RBD structure). This way, the normal modes that overlap best with the direction of conformational change contribute more to the direction of motion in NMSim.
Next, the structural models refined by NMSim were clustered into 343 and 414 groups by their Cα RMSD for the states M1 and M2, respectively, using hierarchical agglomerative clustering with complete linkage and distance threshold of 5 Å. As final step, conventional MD simulations on the group representatives were performed for 2 ns (Methods 6). The MD trajectories were clustered using hierarchical agglomerative clustering with complete linkage and distance threshold of 2 Å into 3395 and 3357 groups for M1 and M2, respectively.

Individual ranking of structural models
To filter (screen) structural models, the calculation of probabilities, the (dis)agreement of the model with the data needs to be measured. Here, the disagreement of the simulated and To determine the initially unknown fraction of molecules in the M1 state, xM1, the sum of weighted squared deviations between the experiment and the data 2 to the measured data, exp( ) was minimized.
Above, (qi) is the noise of the experimental scattering curve and N is the number of detection channels.

Model discrimination & quality assessment
The experimental technique assesses different structural aspects with uncertainties thereof, e.g. ).
Here, I is the regularized incomplete beta function. To relate the F-value x to a probability α, for given 1 2 and 2 2 and significantly different d1, and d2, we must compute the inverse of the cumulative F distribution.
Here, we compare the 2 value of all possible combinations of structural models (M1, M2) and experimental techniques DEER/FRET and SAXS F-values to the 2 value of best pair of structures ( = 2 /min ( 2 )). These models have the same dofs ( 1 = 2 = dof  Fig. 5) so that the precision of the obtained corresponded to our experimental one. In this way, we obtained a dofd,DEER/FRET = 22 (Fig. S6D) -a value that is close to the number of independent label-pair positions of 23. For SAXS measurements the number of Shannon channels is typically in the range of 10 to 23. For our measurements, the number of Shannon channels approximately 18-22 (71,72). We used the number of Shannon channels as an initial estimate for the dof of the SAXS measurements, dofd,SAXS, and we varied dofd,SAXS in the range of 10 to 24. We found only minor effects of dofd,SAXS on , the SAXS discimination power of the models, and used dofd,SXAS =17 to discriminate structural models (for details see Thus, 2 2 is chi-squared distributed with 4 combined degrees of freedom. In this way a 2 2 value was determined for every (M1, M2), and pairs (M1, M2) were discriminated by a chisquared test with 4 degrees of freedom.

Assessment of model precision & quality in Fig 4E
To assess the local quality of the models, the inter-residue distances between all atoms, , and the standard deviation, ( ), of the distribution of were calculated for all models as a measure for the experimental model precision (Fig. 4E, lower triangles). Next, we checked if these variabilities are larger than statistically expected.

Data availability
The following material is available at Zenodo (doi 10

Additional information
Supplementary Information accompanies this paper.     (43) is overlaid by the distance distribution as calculated by accessible volume calculations with the parameter set as provided below. For visual comparison, the rotamers are overlaid with the accessible volume calculated for the labeling position N18C. To parameterize the MTSSL-label we used the variant N18C/Q577C as reference and optimized the simulated linker-length, the label-radius and the linker-width until the distance distribution as determined by the AV-calculations agrees best with the distance distributions as determined by the MTSSL-Wizard (43) and MMM (30). The best agreement was found using a linker-length of 8.5 Å, a linker-width of 4.5 Å and a label-radius of 4.0 Å. All rigid body dockings were performed using this parameter set.    LP and UP refer to labeled protein and unlabeled protein, respectively. In the presence of UP and GDP-AlFx hGBP1 forms a dimer and undergoes significant conformational changes. These conformational changes were detected for the variants with weakly (N18C/Q577C) and variants stronger affected in their GTP hydrolysis (Q254C/Q540C) & (N18C/Q577C). The mutation Q577C has for the labeled and the unlabeled hGBP1 no effect on the specific activity. The mutation Q540C affects GTP hydrolysis activity of the labeled and the unlabeled hGBP1 equally strong. The mutation Q254C affects the GTP hydrolysis activity only the presence of a dye. (E) A consistency analysis reveals that two DEER datasets (encircled in yellow) resolve M1 instead of an averaged state of the two states, 〈 , 〉. The deviation between the simulated and the experimental observables beyond the noise of the other measurements identify two distances assigned to M2 as a mis-assignment. ). The amplitudes ai and the characteristic times are given in the table shown as an inset.

Integrative dynamic structural biology unveils conformers essential for the oligomerization of a large GTPase
(C) To the top the crystallographic B-factors of the Cα atoms (PDB-ID: 1DG3) and the NH S 2 order parameters calculated from the MD simulations are shown. The bottom graph illustrated the product of the B-factor normalized to the range of (0,1] and the NH S 2 order parameter. (D) Cumulative probability α that for a given F-value a proposed structural model is significantly worse than the best-found structural model. The experimental degrees of freedom (dofd,SAXS) for SAXS was varied from 11 to 24 taking the values 11,12,13,14,15,16,17,18,20,22,24 with colors varying from blue to yellow. The cumulative probabilities were calculated using the best model as a reference ( = 2 /min ( 2 )) and an estimate of dofm ~ 10 for the degrees of freedom of the model (eq. 24). The dofd,SAXS was varied to asses the influence of the relative weights of DEER, FRET and SAXS in eq. 25. (E) Fraction of discriminated structures vs. p-value of discriminating a pair of structure from the best structure.  Table 3A). We evaluated the conformers obtained by multi-resolution MD simulations (all-atom MD and coarse-grained MD with the Martini force field of Barz et al (39) using our FRET positioning and screening (FPS) toolkit (32) to compute the quality parameter χ , 2 (eq. 23). The structural features of the conformers are described by the measure, RMSDCα versus the hGBP1 crystal structure (PDB-ID: 1DG3). For comparison, we added the parameters of the best representative conformers for M1 and M2 obtained by our integrative structural modeling (Fig. 5).

Supplementary Tables
Supplementary Table 1A | Inter-label distance analysis of DEER measurements, ensemble fluorescence decays (eTCSPC), and residual donor fluorescence anisotropies. Average distances between the spin-labels are referred to as ⟨ , ⟩. The width of the inter-spin distance distribution is w. The center values of the donor-acceptor distance distribution correspond to ̅ , ( 1 ) and ̅ , ( 2 ) for the states, M1 and M2, respectively. The average donor-acceptor distance and the inter-spin distance simulated for the full-length crystal structure of hGBP1 (PDB-ID: 1DG3) are ̅ , and ⟨ , ⟩, respectively, with corresponding distribution widths w. The uncertainty estimates of central distance of a state determined by FRET is ∆( {1,2} ). .0 (a) DEER distance distributions for calculation of average inter-spin distances and width were determined by Tikhonov regularization of the experimental DEER-traces (eq. 7). (b) The ensemble fluorescence decays were jointly analyzed by a quasistatic homogeneous model (29) with two FRET species with the species fractions x1 and x2 as well as a D-only species (eqs. 10, 13) using the donor properties in Tab. S1B and a Förster Radius R0 = 52 Å. Moreover, the model accounted for the distance distribution with a typical width of 12 Å caused by the flexible dye-linkers (eq. 11). The reported uncertainty estimates, indicated by ±, include statistical uncertainties, potential systematic errors of the references, uncertainties of the orientation factor determined by the anisotropy of donor samples, and uncertainties of the AVs due to the differences of the donor and acceptor linker length (Note S1 section 5). The individual components are listed in Tab. S1D. Reference measurements of single D and A labeled variants are summarized in Tab. S1B, respectively. (c) For EPR-DEER the inter-spin distance distribution was calculated by a rotamer library analysis (see Methods 7). (d) The inter-fluorophores distance distribution and the corresponding average distance and width were calculated by accessible volume simulations.(32) (e) Residual anisotropies of Alexa488 in FRET labeled (Alexa488, Alexa647) variants of the human guanylate binding protein 1 determined by an analysis of the MFD histograms using a Perrin equation for a bio-exponential anisotropy decay (Fig. S3) Supplementary is the fluorescence quantum yield of the fluorescent dye species estimated by the species averaged fluorescence lifetime 〈 〉 , using 〈 〉 , and of the free dyes as a reference; (Alexa647, 〈 〉 =1.0 ns, = . ) (Alexa488, 〈 〉 =4.1 ns, = . ).  Figure 3B) for different FRET labeled (Alexa488, Alexa647) hGBP1 variants. The donor and acceptor fluorescence decays were described by a combination of two normal distributed distances with the central distances of ̅ of a state. The fractions x1 and x2 correspond to the fraction of the distance ̅ ( 1 ) and ̅ ( 2 ) , respectively. xDOnly is the fraction of molecules with no energy transfer to an acceptor. The distances recovered by eTCSPC (Tab. 1A) and seTCSPC, respectively, agree nicely within the distinct precision of each data set.   24). (e) The uncertainty of the distance due to the orientation factor was estimated using a wobbling in a cone model of the dyes using the experimental anisotropies (see Tab. S1A). [a] The names of the labelling sites report on the most likely position of the donor and the acceptor dyes. The distribution among the labelling sites was determined by an analysis of the time-resolved anisotropy decay, anisotropy PDA, and limited proteolysis of the labelled protein.

Supplementary
[b] A consistency analysis identifies that M2 must have long distances (〈 , 〉 > 5 nm) beyond the DEER detection limit for this measurement setting (see Supplementary Note 1 (section 6) and Fig. S4E). To address these general concerns we: (1) select potential labeling sites based on biochemical pre-knowledge, e.g., we avoid active/catalytic sites, (2)    to only weakly affect hGBP1's function (24,55). Before introduction of new cysteines for sitespecific labelling the GTPase activity and nucleotide binding behavior were characterized. The

Supplementary
GTPase activity of the labeled and unlabeled hGBP1 variants was quantified by an assay as previously described. (77) (Fig. S4A). The assay for measuring the protein activity has an error smaller than 10%.
However, besides the relative activity the absolute uncertainty in determining the (active) protein concentration needs to be considered. Hence, the overall uncertainty in determining the absolute protein activities is ~30%. Except of A496C and Q344C/A496C, all mutants produced more GMP than GDP, as known for the wildtype hGBP1. (78) (ii) Labelling. To check if the fluorophores bound to cysteines in hGBP1 have an impact on the oligomerization behavior an unlabeled and a labeled construct were analyzed by analytical gel filtration in the presence and the absence of a nucleotide, which induces oligomerization ( Fig. S4A). For this analysis, the variant N18C/Q577C was chosen, because N18C and Q577C are localized in proximity to dimerization interfaces of the LG and helix α13, respectively. The fluorophores are attached to the sulfhydryl group of the cysteines via a linker of ~20 Å in length.
Thus, they potentially interfere with the self-oligomerization of hGBP1. However, the elugrams of the labeled and unlabeled N18C/Q577C did not show any differences (Fig. S4A). This indicates that, at least for this mutant, the labels do not influence for hGBP1 assembly. As shown for hGBP1 Cys9, no dimer formation was observed in the presence of 200 µM GppNHp independent of being labelled or not.
In addition to the biochemical activity assays that report on the hydrolytic activity of the GTPase domain, we performed single-molecule FRET measurements of the labeled protein (LP) in the presence of excess unlabeled protein (UP) and GDP-AlFx as a substrate. Under these conditions, hGBP1 forms a dimer and undergoes significant conformational changes as seen by the significant changes of the FRET indicator FD/FA in Fig. S4C. We found minor differences among three comparable hGBP1 variants, which are affected in the hydrolysis activity to a different degree by the presence of a fluorescent dye. Hence, we conclude that a fluorescent dye, which affects the hydrolysis activity due to its proximity to hGBP1's GTP binding site has only minor influence on the global domain arrangement that is of interest in this study (Fig. S4C).
(iii) Temperature. Using a steady-state fluorometer, we measured the variants T481C/Q525C, N18C/V540C, and N18C/Q577C. As anticipated, we found a larger change in the FRET efficiency in dependency of the temperature for the variants N18C/V540C and N18C/Q577C as compared to the variant T481C/Q525C (Fig. S4D (i)). For T481C/Q525C M1 and M2 are merely indistinguishable (see distances). For these measurements, we found that the largest relative change of the populations happens between 10 °C and 25 °C. From these measurements, no absolute populations can be determined. Hence, we performed after we acquired a temperature-controlled time-resolved fluorescence spectrometer a temperature series. One measurement out of this set of measurements is shown below in Fig. S4D (ii). For this variant, we only found minor changes of the relative population of the states M1 and M2 (Fig. S4D (iii)).
We compared the different measured variants by normalizing the observed changes ( Fig. S4D (iv)). We found an average midpoint for all the variant of ~15°C. Hence, the relative population of the states at higher temperatures as found in a living cell resembles the measurements at room temperature.

(3) Rotational mobility of the fluorescence dyes
The rotational mobility of the dyes was probed by measuring their time-resolved anisotropy, r(t), using multiparameter fluorescence detection in single-molecule experiments. A formal analysis of r(t) by a multiexponential relaxation model reveals typically "fast" and slow rotational correlation times < 1 ns and > 20 ns (Fig. S4B, upper panel).
Above r0 is the fundamental anisotropy (fixed to r0 = 0.38), is the global rotation time, is the local rotation time, and ∞ is the residual anisotropy. The anisotropy difference ( 0 − ∞ ) relates to the fraction of freely rotating dyes.
To determine ( 0 − ∞ ) for the donor dyes, the two-dimensional single-molecule histograms of the steady-state anisotropy, rS, and the fluorescence lifetime, , were analyzed with a Perrin equation derived for dyes with a bi-exponential anisotropy decay (Fig. S4B). In this analysis, ∞ was treated as an unknown parameter, which was determined by optimizing the Perrin equation to the experimental histogram (Fig. S3A, blue lines). The Perrin equation for two components is: (2) Using the formalism described in (79), we obtain  2 uncertainties (RDA( 2 )) corresponding to each FRET distance for r ∞ . Moreover, ∞ was used as estimate for the fraction of the dyes bound to the surface of the protein, to calibrate the dye's accessible surface volume (ACV) as previously described. (33) The labeling-site specific r ∞ are compiled in Tab. S1A.

(4) Translational mobility of the fluorescence dyes
For all possible labeling sites, we simulated expected fluorescence quantum yields of dynamically quenched donor dyes Alexa488 diffusing within its accessible volume (AV) and accessible surface volume (ACV) using Brownian dynamics simulations with previously published parameters. (29) Finding no significant differences to other reference sample, we corroborate that within the model errors AV/ACVs describe the dye behavior (Fig. S4B, lower   panel).
To conclude, the introduced mutations and the labeling of the dyes has no major influences on the protein function, i.e., the GTP hydrolysis and the GTP induced self-oligomerization. The time-resolved anisotropy measurements and the dynamic quenching simulations agree with a donor dye freely rotating and diffusing within its AV/ACV.

(5) Uncertainty estimation
For comparison of an experimentally derived distance to the distances of a structural model different sources of uncertainties of an inter-dye distances need to be combined. Here, the reported estimates of the distance uncertainties consider relative uncertainties, , of the accessible volume model (AV), , the orientation factor, 2 , the reference, ,± , and the statistical noise of the data, ,± . These uncertainties were combined to ,± , a relative uncertainty of the distance: ,± = √ 2 + 2 2 + ,± 2 + ,± 2 (1) considers the fact that both dyes were conjugated to the protein by cysteines. Therefore, two FRET species, where the donor is either attached to the first amino acid (DA) or the second (AD), are present in the measured samples. As the donor and acceptor dyes have different geometries, the DA and AD species have distinct distributions of FRET rate constants. We previously demonstrated for the used dyes Alexa488 and Alexa647 well described by AVs, that differences in the FRET rate constant distribution between DA and AD species results in an uncertainty in the distance of Δ ,~1 Å. This uncertainty was considered by 2 = /Δ , .(29) The uncertainty 2 2 for the orientation factor 2 was determined as previously described using a wobbling in a cone model considering the residual anisotropies of the dyes.(32) The asymmetric uncertainty ,± considered potential reference errors, propagating to systematic errors of an experimentally determined distance RDA,exp. The Here, R0 is the Förster radius and is the relative deviation of the experimentally determine kD from the correct (true) kD. To estimate we use the sample-to-sample variation of the donor fluorescence lifetimes (Tab. S1B). The contribution of the statistical error ,± was estimated by support plane analysis and a Monte-Carlo sampling algorithm determining distributions of parameters in agreement with the experimental data.(63) Using the relative uncertainty estimates the absolute uncertainties of the distances were calculated.

(6) Consistency analysis identifies mis-assigned distances
The fluorescence decays were analyzed by a model function, which assigns distances to the states by their amplitude. The model free analysis of the DEER data (eq. 7) recovered inter-spin distance distributions, p(RLL), which reflect all conformational heterogeneities with unclear assignment to the corroborated states. The DEER analysis assigns no states to the recovered distributions. Therefore, initially all DEER constraints were assigned to M1 and M2 using the width of the distributions as uncertainty. This assignment resulted in structural models inconsistent with the data (Fig. S4E). The DEER measurements on C225C/K567C and C225C/Q577C revealed short distances, highlighted by the fast-initial drop of the form factors ( Fig. S2A, gray traces). Models consistent with M2 predicted long distances (> 5 nm) beyond the DEER detection limit at this measurement settings for these variants, Fig. S2A, green traces (for ~ 6-7 nm). Hence, C225C/K567C and C225C/Q577C were considered only to model M1 for highly valuable information on the position of the short helix α13 relative to helix α12. This assignment resulted in a consistent combined set of distances for FRET and DEER used for

MD simulations
We performed molecular dynamics (MD) and accelerated MD (aMD) (80)  with a direct-space, non-bonded cutoff of 8 Å. For initial minimization, 17500 steps of steepest descent and conjugate gradient minimization were performed; harmonic restraints with force constants of 25 kcal·mol -1 Å -2 , 5 kcal·mol -1 ·Å -2 , and zero during 2500, 10000, and 5000 steps, respectively, were applied to the solute atoms. Afterwards, 50 ps of NVT simulations (MD simulations with a constant number of particles, volume, and temperature) were conducted to heat up the system to 100 K, followed by 300 ps of NPT simulations (MD simulations with a constant number of particles, barostat and temperature) to adjust the density of the simulation box to a pressure of 1 atm and to heat the system to 300 K. A harmonic potential with a force constant of 10 kcal·mol -1 Å -2 was applied to the solute atoms at this initial stage. In the following 100 ps NVT simulations the restraints on the solute atoms were gradually reduced from 10 kcal·mol -1 Å -2 to zero. As final equilibration step 200 ps of unrestrained NVT simulations were performed. Boost parameters for aMD were chosen by the method as previously suggested. (38)

PC Analysis
In the MD simulations we found fluctuations of RMSD around the average structure of at most 8 Å RMSD for GTP bound and GTP free hGBP1 (Fig. S6A). A correlation analysis of these RMSD trajectories reveals that the dynamics is complex (non-exponential) and predominantly in the 10-100 ns regime (Fig. 6B). Structures deviating the most from the X-ray structure kink at the connector of the LG and the middle domain (Fig. 3G). A PCA reveals that the first five principal components describe overall more than 60% of the variance of the MD and aMD simulations (Fig. 3A). For PCA the GTPase domain (the least mobile domain) was superposed.
The mode vectors of the principal components mapped to a crystal structure of hGBP1 (PDB-ID: 1DG3) illustrate the amplitude and the directionality of the principal components (Fig. 3F).
The first component (1)