We performed DEER, FRET and SAXS experiments to probe short distances, long distances, and molecular shapes, respectively. For the DEER and FRET experiments, we used engineered non-farnesylated hGBP1 cysteine variants (Figure 1A) labeled with MTSSL (R1) as spin label and with Alexa488-Alexa647 as FRET pair (Förster radius R₀=52 Å), respectively. In SAXS measurements, we studied native non-farnesylated hGBP1 (Figure 2A, Figure 2—figure supplement 1A). Corroborating results indicate deviations from the non-farnesylated crystal structure (PDB-ID: 1DG3). A Kratky-plot of the SAXS data (Figure 2A, middle) visualizes that the non-farnesylated hGBP1 crystal structure 1DG3 disagrees with its structure in solution, which is clearly visible in the weighted residuals in the scattering vector range between 0.05 and 0.2 Å^-1 showing a significant deviation of the theoretical SAXS curve of 1DG3 from the experimental SAXS data as well as in the large ${\chi }_r^2$ value of 9.3 that highlights the mismatch between theoretical 1DG3 SAXS curve and experimental data. Ab initio modeling of the SAXS data recorded for native non-farnesylated hGBP1 revealed a shape with an additional kink between the LG and the middle domain (Figure 2A, right, Figure 2—figure supplement 1B), which does not agree with the straight crystal structure of non-farnesylated (PDB-ID: 1DG3) and farnesylated hGBP1 (PDB-ID: 6K1Z; Figure 2A).

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DEER and FRET experiments on engineered non-farnesylated hGBP1 cysteine variants probed distances between specific labeling sites (Figure 1A) - exemplified for the dual cysteine variant Q344C/A496C (Figure 2B and C). The inter-spin distances recovered for Q344C/A496C by a model free DEER analysis are clearly shifted by ~2.5 Å towards shorter distances compared to the distances simulated for an X-ray structure of non-farnesylated hGBP1 (PDB-ID: 1DG3) using a rotamer library analysis (RLA) approach (Polyhach et al., 2011; Figure 2B, right). This shows that the protein exhibits conformations, where the spin-labels come closer to each other than suggested by the crystal structure. Overall, the experimental inter-spin distributions, p(R_SS), of all eight DEER measurements were unimodal (Figure 2—figure supplement 2) and average experimental distances, ${\displaystyle ⟨R_{SS,exp}⟩}$ , differ from the RLA-predicted distances, ${\displaystyle ⟨R_{SS,sim}⟩}$, by 1.0 Å to 3.6 Å (Appendix 1—table 1). The RLA approach does not account for protein backbone dynamics. Thus, we expected to find narrower p(R_SS) in the simulations compared to the experiments. Yet, for the variants Q344C/Q525C and Q344C/V540C the experimental p(R_SS) is narrower than the p(R_SS) predicted by RLA for the crystal structure (Appendix 1—table 1). The reduced spread of inter-spin distances is indicative for a reduced conformational freedom of the spin-labeled side chains caused for instance by a denser packing of the spin label(s) with the neighboring side chains and/or the backbone elements than predicted for the crystal structure. This can for example be the case if contacts between the molecules in the crystal reorient parts of the structure that are in contact with the label(s) in the solution ‘structure’.

FRET experiments using ensemble time-correlated single photon counting (eTCSPC) recovered inter-fluorophore distance distributions, p(R_DA). The measured data are available in a public data repository (Data availability). TCSPC data of donor fluorophore in the presence (DA) and in the absence (D0) of acceptor fluorophores are visualized by ${ϵ}_D\left(t\right)$ , the FRET-induced donor decay. ${ϵ}_D\left(t\right)$ is the ratio of the fluorescence intensity decay of the donor in the presence, $f_{DD}^{\left(DA\right)}\left(t\right)$ , and the absence, $f_{DD}^{\left(D0\right)}\left(t\right)$ , of FRET (Peulen et al., 2017). For mono-exponential $f_{DD}^{\left(D0\right)}\left(t\right)$ the position (time) and the height (amplitude) of steps in ${ϵ}_D\left(t\right)$ correspond to DA distances and species fractions, respectively. The variant Q344C/A496C revealed two distances. This is a hallmark for conformational heterogeneity. (Figure 2C, center). A model free analysis by the maximum-entropy method (MEM) resolved a bimodal distance distribution p(R_DA) (Figure 2C, right) with a major and minor subpopulation. The associated conformational states are referred to by M₁, and M₂ (Figure 2C, right). The distances of the states of all 12 data sets (Figure 1) were recovered by a joint/global analysis of all measured datasets. In this analysis, we consider distance uncertainty estimates, 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 (Appendix 2). We find at room temperature a relative population of 0.61 for M₁ and 0.39 for M₂ (Appendix 1—table 1). A qualitative inspection of fluorescence decay curves can be misleading. Thus, models (see Materials and methods) were selected based on ${\chi }^2$ and Durbin-Watson tests and posterior model parameters densities were sampled in a Bayesian software framework (ChiSurf) as previously described (Vöpel et al., 2014; Peulen et al., 2017; Sanabria et al., 2020).

We simulate the positional distribution of the dyes by their accessible volume (AV) (Cai et al., 2007; Muschielok et al., 2008; Sindbert et al., 2011) to compare structures and FRET experiments (Sindbert et al., 2011; Kalinin et al., 2012). In the comparison we considered uncertainty estimates of the experimental distances (Appendix 2) and accounted for interactions of the dyes with the protein by the accessible contact volume (ACV) (Dimura et al., 2016). The fraction of dyes in an ACV was calibrated by time-resolved anisotropy experiments (Figure 2—figure supplement 3B, Appendix 1—table 1). Moreover, the anisotropy was used to estimate uncertainties using experimental informed orientation factor distributions (Dale et al., 1979). The dyes are only weakly quenched to an extent that is expected for their local environment validating the used model of a mobile dye (Appendix 1—table 2). In this case, the ${ϵ}_D\left(t\right)$ approximation showed to be accurate (Peulen et al., 2017). Activity assays show that the dyes and the mutations only weakly affect the protein function (Appendix 2, Figure 2—figure supplement 3A). This provides compelling evidence that the distances can be used for structural interpretations.

Distances of M₁ agree better with the full length X-ray structure than M₂ (Figure 2C, right, Appendix 1—table 1) - the sum of uncertainty weighted squared deviations, ${\chi }_{FRET}^2$ , for M₁ is significantly smaller than for M₂ (${\displaystyle {\chi }_{FRET}^2\left(M_1,1DG3\right)\approx 17}$ vs. ${\displaystyle {\chi }_{FRET}^2\left(M_2,1DG3\right)\approx 1500}$), confirmed in an F-test with a corresponding p-value >0.999. The variants A496C/V540C and T481C/Q525C designed to test the stability of helix α12, revealed identical distances for M₁ and M₂ (Appendix 1—table 1). Thus, we corroborate that helix α12 is extended like in previous crystal structures (e.g. PDB-ID: 1DG3). N18C/Q344C and Q254C/Q344C probe distances between the middle- and the LG domain. They revealed only relatively minor differences between M₁ and M₂. In variants that interrogate motions from the middle domain and the helices α12/13 M₁ and M₂ were significantly different.

To sum up, EPR-DEER at cryogenic temperatures detected small deviations to the crystal structure. SAXS and FRET detected clear deviations at room temperature. To describe the FRET data at least two states are necessary, which are not detected in the DEER experiments most likely due to re-equilibration of the two conformations during sample freezing. Temperature-dependent measurements revealed that these states are also populated at higher physiological temperatures (Appendix 2, Figure 2—figure supplement 3C).

The distance information of the SAXS, DEER, and FRET experiments provides evidence for a motion of the middle-domain, the LG-domain, and α12/13. We probe the global and the inter-domain motion by single-molecule (sm)FRET experiments with Multiparameter Fluorescence Detection (MFD) and Neutron Spin Echo (NSE) experiments (Sisamakis et al., 2010; Biehl et al., 2011). The NSE experiments are most sensitive up to a correlation time of 200 ns. The filtered fluorescence correlation spectroscopy (fFCS) of our MFD data is most sensitive from sub-microseconds to milliseconds. Thus, by combining NSE with MFD-fFCS, we effectively probe for conformational dynamics from nano- to milliseconds.

An analysis of the NSE data is visualized in Figure 3A, which displays the effective diffusion coefficient D_eff extracted from the initial slope of the NSE spectra in dependence of the scattering vector q (Figure 3—figure supplement 1). The measured D_eff(q) agrees well with the theoretical calculations, accounting for rigid body diffusion alone. The same result was obtained by directly optimizing the parameters of an analytical model describing rigid protein-diffusion (Materials and methods, Equation 9) to the NSE spectra (Figure 3—figure supplement 1B) by ${\displaystyle \mathrm{\Delta }{D}_{eff}\approx u^2/\tau }$ with MSD $u^2$ and relaxation time $\tau$ of internal protein dynamics. Hence, a reasonably large $u^2$ -value could in principle be compensated by a long relaxation time $\tau$ of internal dynamics leading to small $\Delta D_{eff}$ -values. To test this scenario and to assess potential contributions of internal protein dynamics to rigid-body diffusion, we consider a full analytical model in Materials and methods Equation 8 and Equation 9 and examine the intermediate scattering functions $I\left(q,t\right)$ (Figure 3—figure supplement 1A). The additional contribution at short times due to internal dynamics can be estimated by a Debye-Waller argument (Biehl et al., 2008): Internal protein dynamics with a MSD of $u^2$ leading to a change in the $I\left(q,t\right)$ within the observed errors (errors ~0.007 < 0.01) can be estimated by $\frac{{-u}^2{q}^2}{3}=ln\left(1-err.\right)$ . If we consider the deviation at ${\displaystyle Q=0.5n{m}^{-1}}$ then we obtain a value of ${\displaystyle u=0.25nm}$. Compared to the size of the hGBP1 protein internal motions with such small amplitudes are not observable by NSE. A significant additional contribution of internal protein dynamics to the measured effective diffusion coefficients cannot be identified. Hence, the overall internal protein dynamics may only result in negligible amplitude, that is, minor overall shape changes, within the observation time up to 200 ns.

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To cover sub-µs to ms dynamics, we performed MFD smFRET experiments on freely diffusing molecules. We determine for every molecule the average fluorescence lifetime of the donor, 〈τ_D(A)〉_F, and the FRET efficiency, E, to create MFD-diagrams that visualize heterogeneities among the molecules. MFD diagrams correlate calibrated intensity-based observables to the fluorescence lifetimes for revealing conformational heterogeneity. For FRET efficiencies, we calibrate our instrument by DNA reference samples as previously described (Hellenkamp et al., 2018) and account for sample-specific dark-states using fluorescence decay and FCS measurement of single-labeled samples (Appendix 1—table 3). In MFD-diagrams, ‘static FRET-lines’ serve as a reference to detect fast conformational dynamics (Kalinin et al., 2010). In case of sub-millisecond hGBP1 dynamics, we expect to observe multimodal distributions (Barth et al., 2022; Opanasyuk et al., 2022). Analogous to NMR relaxation dispersion experiments, a peak shift from the static FRET line towards longer 〈τ_D(A)〉_F is evidence for conformational dynamics faster than the observation time (~ms) (Kalinin et al., 2010; Sisamakis et al., 2010). All 12 FRET variants had single FRET peaks in the 2D-histograms (Figure 3B, Figure 3—figure supplement 2). In 8 out of 12 variants the peak was significantly shifted, a clear indication of dynamics (Figure 3—figure supplement 2). An analysis of the fluorescence decays of the FRET sub-ensembles (Figure 3—figure supplement 3) by a two-component model (see Materials and methods) revealed limiting states (Appendix 1—table 5) that agree with the eTCSPC data (Appendix 1—table 1). The MFD peak positions (Figure 3—figure supplement 2) are consistent with the eTCSPC data (Figure 3B, Figure 3—figure supplement 3). This is additional evidence for conformational heterogeneity and sub millisecond dynamics.

To quantify the dynamics, we performed filtered FCS (fFCS) and jointly analyze all species cross-correlation functions (sCCF) and the species autocorrelation functions (sACF) by a single model (Figure 3—figure supplement 4) to determine characteristic times (Appendix 1—table 6). For a pure two state system (M₁ ${\displaystyle \leftrightharpoons }$ M₂), we expected to find a single characteristic time. However, at least two relaxation times with corresponding amplitude were required to describe individual fFCS datasets (36 relevant free parameters). Thus, there are more than two (kinetic) states. To compare the relaxation times across FRET variants, and to reduce the number of free parameters we performed a global analysis of the fFCS data (Materials and Methods, Equations 17–19). In global analysis, local and global parameters are simultaneously optimized (Beechem et al., 2002). Global parameters are varied parameters shared across datasets. Local parameters are varied parameters of a single dataset. In our analysis, relaxation times were global parameters (3 relaxation times, shared across FRET variants), corresponding amplitudes were local parameters (2 amplitudes per FRET pair) of FRET variants. Model parameters and uncertainties were determined by optimizing and sampling over local and global parameters using the sum of all weighted squared deviations computed for all 48 model and experimental fFCS curves as objective function. Figure 3—figure supplement 4 display the experimental fFCS and model fFCS curves computed for the global analysis result (Appendix 1—table 6). This analysis recovered three correlation times (2, 23 and 297 µs) with significantly varying amplitudes (Figure 3D, Appendix 1—table 6) and average relaxation times varied approximately (gray bars in Figure 3D). In most cases, the shortest component has the highest amplitude. This is consistent with the MFD-diagrams because we detected shifted/dynamic unimodal peaks. We mapped the average correlation times color coded to the FRET network (Figure 3E). This highlights that the fast dynamics is associated to α12/13 and the middle domain while the slow dynamics is predominantly linked to the LG domain. Referring to the sketch in Figure 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-AlF_x as a non-hydrolysable substrate that mimics the holo-state hGBP1:L. The GDP-AlF_x concentration was sufficiently high (100 µM) to fully induce dimerization of hGBP1 at µM concentrations (Kravets et al., 2016). For comparison, the affinity of hGBP1 for mant-GDP is ~3.5 μM and much higher for GDP-AlFx (Praefcke et al., 1999). MFD control experiments performed on hydrolysable GTP agree with the non-hydrolysable GDP-AlF_x (Figure 3—figure supplement 5B). Hence, in the sm-measurements GDP-AlF_x was bound to the LG domain while the non-farnesylated 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 GDP-AlF_x and GTP induced effects at higher hGBP1 concentrations because of oligomerization (Figure 3—figure supplement 5A). Surprisingly, the amplitude distribution is within errors indistinguishable from the measurements of the nucleotide-free apo forms (Figure 3D). Moreover, the FRET observables changed neither.

We found for hGBP1 in solution a conformationally heterogeneous ensemble that can be approximated by conformers M₁ and M₂ (TCSPC), no significant shape changes of non-farnesylated hGBP1 on a timescale up to 200 ns (NSE), and complex kinetics spanning the µs-range mainly associated to α12/13 and the middle domain (fFCS) that is unaffected by a nucleotide analog as a substrate. Based on the distance and the dynamic information, we propose a complex motion of α12/13 relative to the LG and the middle domain and additional intermediate conformational states, captured by fFCS through their kinetic fingerprint.

We performed molecular dynamics (MD) simulations without experimental restraints to (i) identify functional elements of non-farnesylated hGBP1 in the presence and the absence of GTP, (ii) to assess the structural dynamics of the full-length crystal structure at the atomistic level, and (iii) to capture potential motions of non-farnesylated hGBP1 (Materials and methods). The apo (PDB-ID: 1DG3) and a GTP bound holo-form of non-farnesylated hGBP1 were simulated in three replicas by conventional MD simulations for 2 µs each (Figure 4—figure supplement 1A). Additionally, accelerated molecular dynamics (aMD) simulations, which samples free-energy landscapes of a small protein approximately 2000-fold more efficiently (Pierce et al., 2012), were performed in two replicas of 200 ns each to enhance the conformational sampling. An autocorrelation analysis of the RMSD determined for the conventional MD simulations 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, respectively (Figure 4—figure supplement 1B). The amplitude of the fluctuations is, on average, below an RMSD of 3 Å, and could thus not be resolved by our NSE experiments. In the MD simulations, larger conformational changes (RMSD >7 Å) with considerable shape changes were very rare events. Consistent with previous computational observations (Barz et al., 2019; Figure 4—figure supplement 1C), a principal 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 (Figure 3F). A visual inspection of structures deviating most from the mean reveals a kink at the connector of the LG and the middle domain (Figure 3G) consistent with rearrangements required for average shape as revealed by SAXS (Figure 2).

To sum up, the MD simulations cover timescales of a few microseconds, show potential directions of motions, and identified a pivot point between the LG and the middle domain. In agreement with NSE on the simulation timescale, the overall shape is mainly 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.

Altogether, the SAXS, NSE, EPR, and FRET measurements give a unified and consistent view on hGBP1 conformational dynamics. As recommended in Lerner et al., 2021, the assessment of sample properties and function (effects of mutations and labeling on enzyme properties, temperature effects of the conformational equilibrium), the estimation of the uncertainty of the determined interlabel distances and the consistency check between distinct measurement methods in Appendix 2 provide confidence that our data are suitable for quantitative integrative structural modeling.

Thus, we used the obtained structural experimental information, the kinetics, the MD simulations, and the prior structural information provided by existing crystal structures to create new structures for M₁ and M₂ by experimentally guided structural modeling. Previously, we developed approaches for integrative modeling using FRET data (Sindbert et al., 2011; Kalinin et al., 2012) that could successfully resolve three short-lived conformational states of proteins in two benchmark studies: (1) For a large GTPase with synthetic simulated data (Dimura et al., 2016) and (2) the enzyme Lysozyme (T4L) of the bacteriophage T4 with experimental ensemble and single-molecule data (Dimura et al., 2020; Sanabria et al., 2020). Here, we extended this framework to incorporate DEER and SAXS data. The framework combines the experimental data in meta-analysis via their information content. A detailed description of our integrative modeling can be found in Materials and methods and Appendix 3.

In a nutshell, we generate quantitative structures in three major steps (Figure 4A): (i) ‘Data acquisition’ (steps 1–3), (ii) ‘Model generation’ (steps 4–5), and (iii) ‘Model discrimination’ (steps 6–7). In our previous benchmark study 29 optimal chosen FRET pairs achieved an accuracy and a precision below 2 Å for a similar large GTPase (Dimura et al., 2016). Here, given only 12 FRET and 8 DEER pairs we expect to recover structures with an average RMSDs of 8–15 Å. We mainly aim to resolve molecular shapes, domain arrangement, and topologies.

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We generate new structures (Figure 4A, steps 4–5) by sampling the conformational space of a coarse grained (cg) hGBP1 representation using FRET and DEER restraints. The representation (Figure 4B) is based on an order-parameter based rigidity analysis (Figure 4—figure supplement 1D), knowledge on the individual domains (Low and Löwe, 2010; Chen et al., 2017). It can reproduce the motion of the MD simulations (Figure 3F). For maximum parsimony, the DEER, FRET, and SAXS data were described by pairs of the structures (M₁, M₂) ranked by their agreement with SAXS, and DEER, FRET using ${\chi }_{SAXS}^2$ and ${\chi }_{DEER,FRET}^2$ , respectively (Figure 4C; Appendix 3). The pair best agreeing with SAXS has a middle domain kinked towards the LG domain. A SAXS ensemble analysis revealed species population fractions for M₁ between ~0.1–0.7 (Figure 4—figure supplement 1E, p-value = 0.68). A meta-analysis by Fisher’s method jointly scores pairs of structures considering all available data (Figure 4A, step 6b) and estimates for the effective degrees of freedom (dof) of the representation and the experiments (Figure 4C). A stability test demonstrates that varying the dofs has a minor influence on the structure (Figure 4—figure supplement 2A). A combined p-value of 0.68 discriminates 95% of all (M₁, M₂) pairs (Figure 4C, red area; Figure 4—figure supplement 2B) leaving models with average RMSDs of 11.2 Å and 14.5 Å for M₁ and M₂, respectively. The uncertainties are largest for α12/13 (Figure 4E). The pair of structures are validated for DEER and FRET comparing experimental and modeled average distances (Figure 4D, left). This comparison identified initial assignment outliers (Appendix 2, Figure 2—figure supplement 3). For SAXS, pairs of structures are compared by computed scattering curves (Figure 4D, right). This comparison demonstrates that the integrative structures capture the essential features of the experiments and that the data recorded on non-farnesylated hGBP1 cysteine variants for FRET/DEER is consistent with SAXS data recorded on native non-farnesylated hGBP1.

The standard deviation of pairwise C_α distances, ${\displaystyle SD\left(R_{C_{\alpha }}\right)}$ , reveals alignment free regions of low and high variability (Figure 4E, lower triangles). To check if the variability exceeds the expectances based on experimental precision, ${\displaystyle SD\left(R_{C_{\alpha }}\right)}$ is normalized by computing a weighted (normalized) precision, ${\displaystyle SD\left(R_{C_{\alpha }}\right)/SD{\left(R_{C_{\alpha }}\right)}_{ref}}$ (Figure 4E upper triangles). The reference ${\displaystyle SD{\left(R_{C_{\alpha }}\right)}_{ref}}$ is the precision of "ideal and perfect" model ensembles, determined using the experimental uncertainties under the assumption, that the best experimental determined model is the ground truth. For M₁, this procedure yields a distribution for the weighted precision of the recovered structural models that fluctuates around unity, the theoretical optimum (Figure 4E, left). The weighted precision for M₂ close to the C-terminus (end of helix α12 and α13) is lower than expected (Figure 4E, right), presumably due to granularity of the model or systematic experimental errors. The heterogeneity of the structural ensembles judged by their root-mean-squared-fluctuations (RMSF) is in the expected range of ~7 and~9 Å, for M₁ and M₂ respectively (Figure 4F). We deposited the conformational ensemble with all meta data at the prototype archiving system PDB-Dev with the ID: PDBDEV_00000088.

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 (Figure 5A, red spheres). In M₁, α12/13 binds to the same side of the LG domain as in the known crystal structure (PDB-ID: 1DG3). In M₂, α12/13 binds to the opposing side of the LG domain. In a global alignment of the M₁ and M₂ structures, the best representatives of the ensembles visualize the transition between M₁ and M₂. A rearrangement of residues 306–312 results in a rotation of the middle domain around a pivot point (Figure 5B, cyan circle) and describes the experimental data. The relocation of α12/13 agrees well with global motions identified by PCA of the MD simulations (Hamelberg et al., 2004). In the transition from M₁ to M₂ α12/13 ‘rolls’ along the LG domain, while the middle domain rotates and kinks towards the LG domain. M₁ is comparable to the crystal structure except for a kink of the middle towards the LG domain, the movement of α12/13 stops on the opposite side of the LG domain.

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SAXS experiments were performed on the beamlines X33 at the Doris III storage ring, DESY and at the BM29, ESRF (Pernot et al., 2013) 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) was coupled to the SAXS beamline (SEC-SAXS). The scattering vector q is defined as $q=4\pi /\lambda \cdot sin\left(\theta /2\right)$ 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 0.006–0.49 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). (Svergun et al., 1995) F(q) informs about the electron distribution in the protein, while S(q) contains q-dependent modulations due to protein-protein interactions occurring at higher protein concentration. At sufficiently low protein concentrations (in the limit of c → 0) the structure factor converges towards unity. A concentration series (non-farnesylated hGBP1 concentrations of 1.1, 2.1, 5.0, 11.5, and 29.9 mg/mL) was recorded on X33 (Figure 2—figure supplement 1A), whereas on BM29 two SEC-SAXS runs have been performed using non-farnesylated protein concentrations of 2 mg/mL and 16 mg/mL that were loaded on the SEC column. The same buffer was used for both SAXS and SEC-SAXS experiments: 50 mM TRIS, 5 mM MgCl₂, 150 mM NaCl at pH 7.9. The SEC-SAXS data were averaged over the elution peak. The obtained SEC-SAXS data of the used high and low protein solutions were overlapping validating the infinite dilution limit. Therefore, the SEC-SAXS data recorded at the high protein concentration were used for further data analysis. An automated sample changer was used for sample loading and cleaning of the sample cell on X33. The storage temperature of the sample changer and the temperature during X-ray exposure in the sample cell were 10 °C. The buffer was measured before and after each protein sample as a check of consistency. For each sample, eight frames with an exposure time of 15 s each were recorded to avoid radiation damage. The absence of radiation damage was verified by comparing the measured individual frames. The frames without radiation damage were merged. On BM29 X-ray frames with exposure time of 1 s were continuously recorded. The scattering contribution of the buffer and the sample cell was subtracted from the measured protein solutions. Measured background corrected SAXS intensities I(q,c) of the non-farnesylated hGBP1 solutions are shown in Figure 2—figure supplement 1A. I(q,c) were scaled by the protein concentration c and extrapolated (c → 0) to determine the form factor I(q,0) of the protein at infinite dilution. At larger q-values, where the structure factor equals unity, the extrapolated form factor overlapped with the SAXS data of the highest protein concentration within the error bars. Therefore, for better statistics the extrapolated form factor at small q-values and the data of the 29.9 mg/mL solution at larger scattering vectors were merged. The structure factor S(q,c) (Figure 2—figure supplement 1B) was extracted by S(q,c)=I(q,c) / (c·I(q,0)) and fitted by a Percus-Yevik structure factor including the correction of Kotlarchyk and Chen, 1983 for asymmetric particles resulting in an effective hard sphere radius of 2.2 nm (Wertheim, 1963). Size exclusion chromatography SAXS (SEC-SAXS) measurements were performed at different protein concentrations (Figure 2—figure supplement 1A). SEC-SAXS assures the data quality by discriminating a sample purification step immediately before the SAXS data acquisition.

SAXS data was analyzed using the ATSAS software package (Petoukhov et al., 2012). Theoretical scattering curves of the crystallographic and the simulated structures of the monomer were calculated and fitted to the experimental SAXS curves using the computer program CRYSOL. 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.

Experiments were performed and are described by Vöpel et al., 2014. Briefly, experiments were carried out at X-band frequencies (~9.4 GHz) with a Bruker Elexsys 580 spectrometer equipped with a split-ring resonator (Bruker Flexline ER 4118X-MS3) in a continuous flow helium cryostat (CF935; Oxford Instruments) controlled by an Oxford Intelligent Temperature Controller ITC 503S adjusted to stabilize a sample temperature of 50 K. Sample conditions for the EPR experiments were 100 µM protein in 100 mM NaCl, 50 mM Tris-HCl, 5 mM MgCl₂, pH 7.4 dissolved in D₂O with 12.5% (v/v) glycerol-d₈. DEER inter spin-distance measurements were performed using the four-pulse DEER sequence (Martin et al., 1998; Pannier et al., 2000):

with observer pulse (ν_obs) lengths of 16 ns for π/2 and 32 ns for π pulses and a pump pulse (ν_pump) length of 12 ns. A two-step phase cycling (+ ‹x›, - ‹x›) was performed on π/2(ν_obs). 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 υ_pump was set to the center of the resonator dip coinciding with the maximum of the EPR absorption spectrum. The observer frequency ν_obs was set ~65 MHz higher, at the low field local maximum of the EPR spectrum. Deuterium modulation was averaged by adding traces recorded with eight different τ₁ values, starting at τ_1,0 = 400 ns and incrementing by Δτ₁ = 56 ns. Data points were collected in 8 ns time steps or, if the absence of fractions in the distance distribution below an appropriate threshold was checked experimentally, in 16 ns time steps. The total measurement time for each sample was 4–24 h.

The DEER data was analyzed using the software DeerAnalysis which implements a Tikhonov regularization (Jeschke et al., 2006). Background correction of the DEER signal dipolar evolution function V(t) (normalized to unity at the time t=0)

was performed assuming an isotropic distribution of the spin-labeled hGBP1 molecules in frozen solution that is described by

Briefly, the resulting form factor ${\displaystyle F(t)}$ is modulated with the dipolar frequency

that is proportional to the cube of the inverse of the inter-spin distance R_SS (µ_B: Bohr magneton; µ₀: magnetic field constant; θ: angle between the external magnetic field and the vector connecting the two spins, for nitroxide spin labels the g values of both spins can be approximated with the isotropic value g ≈ 2.006). Analysis of the form factor ${\displaystyle F(t)}$ in terms of a distance distribution ${\displaystyle p(R_{SS})}$ was performed by a Tikhonov regularization. A simulated time domain signal

from a given distance distribution ${\displaystyle p(R_{SS})}$ was calculated by means of a kernel function

with ${\displaystyle {\omega }_{DD}(R_{SS})=\frac{2\pi \cdot 52.04MHzn{m}^{-3}}{R_{SS}^3}}$ for nitroxide spin labels. The optimum p(R_SS) was found by minimizing the objective function

The regularization parameter $\alpha$ was varied to find the best compromise between smoothness, that is, the suppression of artifacts introduced by noise, and resolution of $p\left(R_{SS}\right)$. The optimum regularization parameter was determined by the L-curve criterion, where the logarithm of the smoothness ${‖\frac{d^2}{d{r}^2}p\left(R_{SS}\right)‖}^2$ of $p\left(R_{SS}\right)$ is plotted against the logarithm of the mean square deviation ${‖S\left(t\right)-V_{local}\left(t\right)‖}^2$, allowing to choose the distance distribution with maximum smoothness representing a good fit to the experimental data.

Theoretical inter spin label distance distributions for MTSSL spin labels attached to structural models have been calculated using the rotamer library analysis (RLA) implemented in the freely available software MMM (Polyhach et al., 2011).

Neutron spin echo (NSE) was measured on IN15 at the Institut Laue-Langevin, Grenoble, France. The NSE data were described by rigid body diffusion of non-farnesylated hGBP1 to detect intra-molecular dynamics. Four incident neutron wavelengths with 8, 10, and 12.2, and 17.5 Å were used. The buffer composition for NSE experiments was 50 mM TRIS, 5 mM MgCl₂, 150 mM NaCl at pD 7.9 in heavy water (99.9 atom % D). The protein concentration was 30 mg/mL. The measured NSE spectra are shown in Figure 3—figure supplement 1. Effective diffusion coefficients D_eff were determined from the initial slope of the NSE spectra by using a cumulant analysis $\frac{I\left(q,t\right)}{I\left(q,0\right)}=exp\left(K_{1t}+\frac{1}{2}{K}_2{t}^2\right)$ with $D_{eff}=\frac{-K_1}{q^2}$.

The rigid body diffusion D₀(q) of a structural model at infinite dilution was calculated according to Biehl et al., 2011:

where ${\displaystyle \hat{D}}$ is the 6x6 diffusion tensor, which was calculated using the HYDROPRO program (Ortega et al., 2011). 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 Inoue et al., 2010:

with ${\displaystyle S_l\left(q\right)=\sum _m{\left|\sum _i{b}_i{j}_l\left(q{r}_i\right)Y_{l,m}\left({\mathrm{\Omega }}_i\right)\right|}^2}$

where D_t and D_r are the calculated scalar translational and rotational diffusion coefficients found in the trace of ${\displaystyle \hat{D}}$ of the rigid protein at infinite dilution from the structural models. Rotational diffusion of the rigid protein were expressed in spherical harmonics with spherical Bessel functions j_l(qr_i), spherical harmonics Y_l,m and scattering length densities b_i of atoms at positions r_i. Here, the crystal structure was used as a base. D_t and D_r were chosen according to the mixture of crystal structure and best representing M₂ structure. Direct interaction and hydrodynamic interactions were accounted for by the corrections $D_{t,eff}\left(q\right)=D_t{H}_t/S\left(q\right)$ and $D_{r,eff}=H_r{D}_r$. Interparticle interactions were considered by the structure factor S(q) as measured by SANS. H_t and H_r, reduce the effective translational and rotational diffusion coefficients. H_t is related to the intrinsic viscosity [η] by H_t =1-c[η] and H_r can be approximated by 1-H_r=(1-H_t)/3 for spherical particles (Degiorgio et al., 1995), which might underestimate H_r for large asymmetric particles. Internal protein dynamics was described by an exponential decay with a q-independent rate Γ, and a q-dependent contribution A(q) of internal dynamics to the NSE spectra.

The parameters H_t, H_r, the relaxation time λ, and the amplitudes A(q) (Materials and methods, Equation 9) were simultaneously optimized to all NSE spectra (Figure 3—figure supplement 1). 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 (Figure 3—figure supplement 1) with H_t = 0.61 ± 0.01 and H_r = 0.72 ± 0.03 as the only fitting parameters.

Dynamic light scattering was measured on a Zetasizer Nano ZS instrument (Malvern Instruments, Malvern, United Kingdom) in D₂O buffer identical to that used in the NSE experiment. Autocorrelation functions were analyzed by the CONTIN like algorithm (Provencher, 1982) to obtain the translational diffusion coefficient D_T need for analysis. The diffusion coefficient of a single protein increases from the translational diffusion D_T measured at low q (DLS) due to contributions from rotational diffusion D_R(q) and contributions related to internal protein dynamics D_int(q) as the observation length scale 2π/q covers the protein size. The translational and rotational diffusion coefficients D_T and D_R(q) were calculated and corrected for hydrodynamic interactions and interparticle effects to result in the expected D₀(q) for a rigid body (Figure 3A, black line, Materials and methods, Equation 9).

Ensemble and single-molecule FRET experiments were performed at room temperature in 50 mM Tris-HCl buffer (pH 7.4) containing 5 mM MgCl₂ and 150 mM NaCl. All ensemble measurements were performed at concentrations of labeled protein of approximately 200 nM. The single-molecule (sm) measurements were performed at concentrations of labeled protein of approximately 20 pM to assure that only single-molecules were detected. All sm MFD-measurements probing the hGBP1 apo state were performed under two conditions: (i) without unlabeled protein, and (ii) with 7.5 µM unlabeled protein to minimize the loss of labeled molecules due to adsorption in the measurement chamber. Both conditions gave comparable results. Due to the higher counting statistics, all results of the apo state reported in this work have been obtained for condition ii. To study also the ligand-bound non-farnesylated holo state hGBP1:L (Figure 1B) by fFCS (Figure 4D), we used the ligand GDP-AlF_x as a non-hydrolysable substrate. The ligand GDP -AlF_x is formed in situ by diluting a stock solution with 30 mM AlCl₃ and 1 M NaF by 1:100 in the standard buffer containing 100 µM GDP and 20 pM labeled protein without unlabeled protein (condition i).

Ensemble fluorescence time-correlated single-photon-counting (TCSPC) measurements of the donor fluorescence decay histograms were either performed on an IBH-5000U (HORIBA Jobin Yvon IBH Ltd., UK) equipped with a 470 nm diode laser LDH-P-C 470 (Picoquant GmbH, Germany) operated at 8 MHz or on a EasyTau300 (PicoQuant, Germany) equipped with an R3809U-50 MCP-PMT detector (Hamamatsu) and a BDL-SMN 465 nm diode laser (Becker & Hickl, Germany) operated at 20 MHz. The donor fluorescence was detected at an emission wavelength of 520 nm using a slit-width that resulted in a spectral resolution of 16 nm in the emission path of the machines. A cut-off filter (495 nm) in the detection path additionally reduced the contribution of the scattered light. All measurements were conducted at room temperature under magic-angle conditions. Typically, 14·10⁶–20·10⁶ photons were recorded at TAC channel-width of 14.1 ps (IBH-5000U) or 8 ps (EasyTau300). When needed, the analysis considers differential non-linearities of the instruments by multiplying the model function with a smoothed and normalized instrument response of uncorrelated room light. The fits cover the full instrument response function (IRF) and 99.9% of the total fluorescence. The IRFs had typically FWHM of 254 ps (IBH-5000U) or 85 ps (PicoQuant EasyTau300).

Single-molecule fluorescence spectroscopy data was acquired on a custom MFD setup with polarized excitation and detection in the ‘green’ and ‘red’ detection channels (Sisamakis et al., 2010). Briefly, a beam of linearly polarized pulsed argon-ion laser (Sabre, Coherent) was used to excite freely diffusing molecules through a corrected Olympus objective (UPLAPO 60X, 1.2 NA collar (0.17)). The laser was operated at 496 nm and 73.5 MHz. An excitation power of 120 µW at the objective has been used during experiments. The fluorescence light was collected through the same objective and spatially filtered by a 100 µm pinhole which defines an effective confocal detection volume of ~3 fl. A polarizing beam-splitter divided the collected fluorescence light into its parallel and perpendicular components. Next, the fluorescence light passed a dichroic beam splitter that defines a ‘green’ and ‘red’ wavelength range (below and above 595 nm, respectively). After passing through band pass filters (AHF, HQ 520/35 and HQ 720/150) single photons were detected by two ‘green’ (either τ-SPADs, PicoQuant, Germany or MPD-SPADs, Micro Photon Devices, Italy) and two ‘red’ detectors (APD SPCM-AQR-14, Perkin Elmer, Germany). Two SPC 132 single photon counting boards (Becker & Hickel, Berlin) have recorded the detected photons stream. Thus, for each detected photon the arrival time after the laser pulse, the time since the last photon and detection channel number (so, polarization and color) were recorded.

A detailed description of our integrative modeling with all steps can be found in Appendix 3. In short, DEER, FRET (eTCSPC), and the SAXS data were used to generate integrative structure for the states M₁ and M₂. Based on the experimental data and the MD simulations, the protein was decomposed into a set of rigid bodies. The assembly of the rigid bodies was sampled using DEER and FRET restraints and refined by NMSim (Ahmed and Gohlke, 2006) and MD simulations. All pairs of structures for M₁ and M₂ were enumerated and scored against the DEER, FRET and SAXS data. The probability for a pair of structures for the DEER and FRET, p_DEER,FRET, and SAXS, p_SAXS, are combined in a meta-analysis using Fishers’s method.

The probability $p_{DEER,FRET}$ and $p_{SAXS}$ take the data information content into account. For SAXS the number of Shannon channels was used. For DEER and FRET, the information content was estimated using a greedy backward elimination feature selection algorithm to assess the effective number of informative measurements (Dimura et al., 2016). The estimates for the information content were varied to assess the impact on the resulting structures. Finally, an F-test on ${\chi }_{2k}^2$ is used to discriminate pairs.

The structure generation follows the workflow (Figure 4A). Starting from the crystal structure (Figure 4A, steps 1–3), we generate new structures (Figure 4A, steps 4–5). A set of rigid bodies (RBs) (Figure 4B, Appendix 3) was defined based on the motions observed in the MD simulations (Figure 3F) taking the following information into account: (1) An order-parameter based rigidity analysis (Figure 4—figure supplement 1D); (2) Knowledge on the individual domains within the dynamin family (Low and Löwe, 2010; Chen et al., 2017); (3) Position dependent FRET and DEER properties (Appendix 1—table 1); and (4) The SAXS experiments that suggest a kink in hGBP1’s middle domain (Appendix 3, Structure representation). To this RB assembly, we applied DEER and ensemble FRET restrains for guided RB docking (RBD) (Appendix 3) (Kalinin et al., 2012). In RBD, the DEER and FRET restraints were treated by AV and ACV simulations, respectively (Appendix 3, Simulation of experimental parameters). AVs for DEER restraints were calibrated (Figure 2—figure supplement 2) against established simulation approaches (Polyhach et al., 2011; Hagelueken et al., 2012).The RBD structures were corrected for their stereochemistry (Appendix 3, Generation of structures) and were clustered into 343 and 414 groups for the states M₁ and M₂, respectively. Group representatives were used as seeds for short (1–2 ns) MD-simulations. The MD trajectories were clustered into 3395 and 3357 groups for M₁ and M₂, respectively, before being ranked by the DEER, FRET, and SAXS individually (Appendix 3, Individual ranking of structures). For well-balanced structures and equalized experimental contributions Fisher’s method fused the experimental data in a meta-analysis (Figure 4A, step 6b) considering estimates for the degrees of freedom (dof) of the protein representation and the data (Moore, 1980; Mertens and Svergun, 2017) (Appendix 3, Model discrimination and quality assessment; Figure 4C, Combined screening). In the meta-analysis a p-value of 0.68 discriminates 95% of all structural models (Figure 4C, red area; Figure 4—figure supplement 2B). The quality of the selected structures is judged by comparison to the experiments and making use of the data uncertainty. The local quality of the structures was assessed by checking if their variabilities is above the statistically expectation. Reference structure ensembles are computed to normalize the experimental model precision to a reference precision (Appendix 3, Assessment of model precision and quality).

The following material is available at Zenodo in two locations: Experimental data (https://doi.org/10.5281/zenodo.6534557): (i) fluorescence decays recorded by eTCSPC used to compute the distance restraints in Appendix 1—table 1 and Appendix 3—table 1, (ii) single-molecule multiparameter fluorescence data: all raw data, burst selection and calibration measurements, fFCS (filters and generated correlation curves) (iii) double electron-electron resonance (DEER) EPR data used for structural modeling, (iv) neutron spin-echo data and SAXS structure factor of non-farnesylated hGBP1. Scripts for structural modeling of conformational ensembles through integrative/hybrid methods using FRET, DEER and SAXS together with the initial and selected structural ensembles (https://doi.org/10.5281/zenodo.6565895). The experimental SAXS data and the ab initio analysis thereof are available in the SASBDB (ID SASDDD6). Structure models of hGBP1 based on experimental restraints were deposited to PDB-Dev (PDB-Dev ID: PDBDEV_00000088) using the FLR-dictionary extension (developed by PDB and the Seidel group) available on the IHM working group GitHub site (https://github.com/ihmwg/flrCIF; IHM Working Group, 2022). Further data sets generated during and/or analyzed during the current study are available from the corresponding author on request.

Detailed description of the experimental files available on Zenodo (doi 10.5281/zenodo.6534557):

Subfolders for an eTCSPC FRET measurement contain the following files:

Subfolder for eTCSPC FRET measurement ‘Fit_results’ contains the following files:

Subfolders for a single molecule FRET measurement are structured the following:

Most general custom-made software is directly available from http://www.mpc.hhu.de/en/software. The software ChiSurf is available at https://github.com/Fluorescence-Tools/ChiSurf (Peulen et al., 2021). General algorithms and source code are published under https://github.com/Fluorescence-Tools. Additional computer code custom-made for this publication is available upon request from the corresponding authors.

For comparison of an experimentally derived distance to the distances of a structural model different sources of uncertainties of an inter-dye distance need to be combined. Here, the reported estimates of the distance uncertainties consider relative uncertainties, $\delta$, of the accessible volume model (AV), ${\delta }_{AV}$ , the orientation factor, ${\delta }_{{\kappa }^2}$ , the reference, ${\delta }_{Reference,\pm }$ , and the statistical noise of the data, ${\delta }_{stat,\pm }$ . These uncertainties were combined to ${\delta }_{R_{DA},\pm }$ , a relative uncertainty of the distance:

${\displaystyle {\delta }_{AV}}$ 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 ${\displaystyle \mathrm{\Delta }{R}_{DA,AV}\approx 1\AA }$. This uncertainty was considered by ${\delta }_{AV}^2=R_{DA}/\Delta R_{DA,AV}$ (Peulen et al., 2017). The uncertainty ${\delta }_{{\kappa }^2}^2$ of orientation factor ${\kappa }^2$ was determined as previously described using a wobbling in a cone model considering the residual anisotropies of the dyes (Kalinin et al., 2012). The asymmetric uncertainty ${\delta }_{Reference,\pm }$ considered potential reference errors, propagating to systematic errors of an experimentally determined distance R_DA,exp.

The fluorescence rate constant of the donor in the absence of FRET, k_D, serves as reference to recover experimental distances, R_DA,exp, in the analysis of fluorescence decays. An inaccurate reference for k_D propagates to systematic errors of R_DA,exp. We estimate the contribution of an inaccurate reference to ${\delta }_{R_{DA},\pm }$ by ${\delta }_{Reference,\pm }$

Here, R₀ is the Förster radius and ${\delta }_{k_D}$ is the relative deviation of the experimentally determine k_D from the correct (true) k_D. To estimate ${\delta }_{k_D}$ we use the sample-to-sample variation of the donor fluorescence lifetimes (Appendix 1—table 2). The contribution of the statistical error ${\delta }_{stat,\pm }$ was estimated by support plane analysis and a Monte-Carlo sampling algorithm determining distributions of parameters in agreement with the experimental data (Straume et al., 2002). Using the relative uncertainty estimates the absolute uncertainties of the distances were calculated and compiled in Appendix 1—table 4.