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

Abstract

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 dynamic changes of their structures. Conformational flexibilities, heterogeneities, and polymorphisms are known to enable interactions among biomolecules, promote promiscuity with different binding partners, and are essential for enzymatic activity (Tompa and Fuxreiter, 2008; Hensen et al., 2012). This is most evident for motor proteins such as myosin or dynamin, where cyclic structural changes are crucial for their function. Thus, for a mechanistic molecular understanding of biological processes, the structure and the associated dynamics of the key components need to be characterized in great detail, ideally on a single-molecule level (Lerner et al., 2018; Lerner et al., 2021).

While NMR spectroscopy is an excellent tool to map conformationally excited states and intermediates (Neudecker et al., 2012) the determination of dynamic biomolecular structures of large systems is extremely challenging. To-date no individual technique fully maps structures and dynamics on all time scales and on a length scale necessary to understand large molecular systems. Thus, multiple experimental techniques need to be combined to probe different aspects and unveil structures of large multi-domain proteins (Felekyan et al., 2012; Kilic et al., 2018; Lerner et al., 2021). Here, we present and apply a framework that integrates short and long-range distances with shape information amended by time-resolved spectroscopy and molecular dynamics simulations for dynamic structures. Our framework identifies functional elements as building blocks, and balances experimental information in a meta-analysis to generate integrative dynamic structures with a small number of informative distances.

We apply our framework to study molecular mechanisms of a guanylate binding protein (GBP), a class of soluble proteins that belong to the dynamin superfamily and to the class of interferon-γ induced effector molecules (Praefcke and McMahon, 2004). GBPs are important for innate cell-autonomous immunity in mammals. GBPs form supramolecular complexes during infection and are recognized for their immune activity against a wide range of intracellular pathogens such as viruses (Anderson et al., 1999; Itsui et al., 2009), and bacteria (Kim et al., 2011; MacMicking, 2012; Li et al., 2017). Noteworthy, a GBP in mice translocates from the cytosol to endomembranes and attacks the plasma membrane of eukaryotic cellular parasites by the controlled formation of productive and supramolecular complexes (Kravets et al., 2016). As a prime example for a GBP, we study the human GBP1 (hGBP1). hGBP1 shows nucleotide-dependent dimerization (Ghosh et al., 2006), and the formation of supramolecular structures promoted by GTPase activity (Shydlovskyi et al., 2017). 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 a length of 120 Å (Prakash et al., 2000; Figure 1A). X-ray crystallography (Ghosh et al., 2006) and biochemical experiments (Ince et al., 2017) identified the LG domains as interface for GTP induced homo-dimerization. Like for other membrane-associated dynamins that form tubular shaped assemblies to fuse or divide membranes in cells (Faelber et al., 2012; Reubold et al., 2015), cylindrical and tubular structures have been observed for hGBP1 (Shydlovskyi et al., 2017). For hGBP1 neither molecular structures of these tubules nor precursor structures in solution that could inform on the assembly pathway are known (Cui et al., 2021). Previous FRET and DEER experiments on hGBP1 dimers identified two conformers. In the dominant dimer, the two C-terminal α13 helices associate (Vöpel et al., 2014). This is in line with live-cell experiments that highlight the relevance of helix α13 for the immune response (Tietzel et al., 2009; Li et al., 2017; Piro et al., 2017). Previously, we identified monomeric and dimeric forms of farnesylated hGBP1 by SEC-SAXS and ultracentrifugation (Figure 1—figure supplement 1). These experiments lead to the hypothesis that specific intramolecular interactions stabilize the GTPase and act as a safety mechanism preventing hGBP1 dimerization (Lorenz et al., 2020). Here, to unravel the conformational changes necessary for the formation of a fully bridged dimer (b-hGBP1:L)₂ (Figure 1B), we study non-farnesylated hGBP1, where nucleotide ligands L (GTP) are bound and the effector domains and the LG domains are both associated (Figure 1B). The association of two α13 helices in a dimer requires large-scale structural rearrangements that cannot be explained by known X-ray structures (Ghosh et al., 2006). On the pathway to a bridged dimer, there are at least two intermediates - the ligand complex hGBP1:L and the flexible dimer (f-hGBP1:L)₂ (Figure 1B).

Figure 1.

DEER and FRET distance network that probes structural arrangement of the human guanylate binding protein 1 (hGBP1) and potential dimerization pathways.

(A) 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 represent the DEER- and FRET-pairs, respectively. In hGBP1 the C-terminus is post-translationally modified and farnesylated for insertion into membranes (red). (B) Potential different pathways for the formation of a functional hGBP1 homodimer where the substrate binding LG domains and the helix α13 associate. The association of the helix α13 requires flexibility (red arrows). This flexibility could be induced at different stages of a dimerization pathway.

Figure 1—figure supplement 1.

Structural knowledge on hGBP1.

Crystallographic and model-free structural knowledge on hGBP1 is highlighted by solid contour lines of the domains. Model-based and indirect structural information is highlighted by dashed contour lines of the domains. (A) In the crystallographic monomer (PDB-ID: 1DG3) the LG- (blue), middle- (gray), helix α12 (green), and helix α13 (orange) of hGBP1 adopt an extended conformation where helix α12/13 attach to one side of the LG-domain (Prakash et al., 2000). (B) In crystallographic dimer data of the LG-domain (2BC9, 2B92, 2B8W) and in a crystallographic dimer of the full-length protein (PDB-ID: 1F5N) require helix α13 to be located at diastral sites of the LG:LG domain dimer (C) FRET and DEER experiments on hGBP1 verified crystallographic LG:LG domain interaction (solid lines) and identified two dimer conformations. In the minor (10% population) conformation helix α13 were separated. In the major conformation (90% population) two α13 helices associate (Vöpel et al., 2014). (D) A crystallographic structure on farnesylated hGBP1. The farnesyl anchor (red) attached to helix α13 extends along helix α12 and binds between α12 and α13. The farnesylated hGBP1 and the non-farnesylated hGBP1 crystal structures are largely consistent (RMSD 1.4 Å). (E) SEC-SAXS experiments on farnesylated hGBP1 identified a monomer and (F) two dimer conformations (Lorenz et al., 2020).

By probing hGBP1’s flexibility (red arrows, Figure 1B), we discern the different dimerization paths (black arrow, Figure 1B). Either the flexibility is substrate independent (i), induced by the ligand (ii), or induced by the dimerization (iii). In the first path (Figure 1B, i), the flexibility is an intrinsic property already present in the absence of substrate, although the flexibility is only needed for the dimerization at a later step. In the second path (Figure 1B, ii), the monomer is stiff; the binding and/or the hydrolysis of the substrate in the complex hGBP1:L increases the flexibility for the dimerization. In the third path (Figure 1B, iii), GTP binds to hGBP1 to enable the dimerization of the LG domains and the LG domain dimerization triggers a rearrangement for effector domains. The path could be distinguished if one studies the dynamics of monomeric hGBP1 in the presence and the absence of the substrate. Thus, we map the structure and dynamics of the free and the ligand bound hGBP1.

Experimentally, we map the motions of the monomeric non-farnesylated hGBP1 in the absence and in the presence of the non-hydrolysable ligand GDP-AlF_x, corroborated by GTP control experiments. By combining experimental information through integrative modeling, we also resolve hGBP1 structures that explain the molecular prerequisites for dimerization. To generate structures, we use information from small-angle X-ray scattering (SAXS), electron paramagnetic resonance (EPR) spectroscopy by site-directed spin labeling (Klare and Steinhoff, 2009), ensemble and single-molecule fluorescence spectroscopy (Hellenkamp et al., 2018). smFRET and DEER independently yield distance restraints for modeling, the former with the advantage of being a single-molecule technique that can be applied under ambient conditions, whereas the latter uses a single type of label that is smaller compared to FRET labels, simplifying treatment of the label for modeling purposes. For dynamic information, we apply neutron spin-echo spectroscopy (NSE) and filtered fluorescence correlation spectroscopy (fFCS) (Felekyan et al., 2012; Lerner et al., 2021). We resolve structures of two new conformational states by integrative modeling and mapped hGBP1’s kinetics from nanoseconds to milliseconds. Interrogating conformational dynamics by a network of 12 FRET pairs (Figure 1A), we generate 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 via an opening like a pocketknife. This allows us to understand the mechanisms excreting the function of this large multi-domain system, that is, the programmed and controlled oligomerization.

Results

Experimental equilibrium distributions

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).

Figure 2.

Probing the structure of hGBP1 in solution experimentally.

The left panels illustrate the characteristic properties probed by the experiments: (A) small angle X-ray scattering (SAXS), (B) double electron-electron resonance spectroscopy (DEER), and (C) Förster resonance energy transfer spectroscopy (FRET). In general, all middle panels display representations of the experimental data (dark yellow curves). The right panels show model-free analysis (red). Predicted experimental data based on a full-length X-ray crystal structure (PDB-ID: 1DG3) are shown in blue. To the top of the experimental curves, either data noise weighted, w.res., or unweighted residuals, res., are shown (middle panels). DEER and FRET experiments sense distances between labels that are flexibly coupled to specific labeling sites (exemplified for the double cysteine variant Q344C/A496C). The time-dependent responses of the sample (middle) inform on the inter-label distance distributions (right panels). The recovered distance distributions are compared to structural models by simulating the spatial distribution of the labels around their attachment point (left panels). The spatial distributions of the MTSSL-labels (B, left), as well as the donor and acceptor dye (C, left), are shown in magenta, green, and red, respectively. All distances resolved by EPR and FRET are compiled in Appendix 1—table 1 (A) Left: In SAXS the scattered intensity I(q) is measured as a function of the scattering vector q. Middle: For better illustration, I(q) is presented in a Kratky-plot. The data are deposited in SASBDB (ID: SASDDD6). Right: SAXS ab initio bead modeling determines an average shape of hGBP1 in solution. (B) Left: The DEER experiments measured the dipolar coupling between two MTSSL spin-labels (magenta). Middle: DEER-traces, F(t), analyzed by Tikhonov regularization (red curve). Right: Recovered inter-spin distance distributions, p(R_SS). (C) Left: FRET experiments measure the energy transfer from a donor fluorophore (Alexa488, green) to an acceptor fluorophore (Alexa647, red). Middle: Fluorescence intensity decays of the donor analyzed by the maximum entropy method (MEM) recover donor-acceptor distance distributions, p(R_DA). The inset displays the L-curve criterion of the MEM reconstruction for the presented data set. The FRET-induced donor decay, ε_D(t), represents the fluorescence decays (Peulen et al., 2017). ε_D(t) is corrected for the fraction of FRET-inactive molecules, x_DOnly. The shape of ε_D(t) reveals characteristic times (labeled M₁ and M₂) that correspond to peaks in p(R_DA). Right: Recovered inter-label distance distributions for FRET.

Figure 2—figure supplement 1.

Small-angle X-ray scattering measurements on the nucleotide-free hGBP1.

(A) Measured SAXS data of hGBP1 at different protein concentrations. The scattering curves are not normalized by the protein concentration. (B) Structure factor of the 29.9 mg/mL solution extracted from the SAXS data. The structure factor is obtained by the background corrected SAXS curves at highest concentration scaled through division by the form factor (empty circles). The fitted structure factors according to the Percus-Yevik structure factor include the correction for the protein asymmetry factor beta (full line) (Wertheim, 1963; Kotlarchyk and Chen, 1983). For comparison, the uncorrected structure factor without asymmetry factor is given (stitched line). Data are averaged at larger wave vectors to reduce noise.

Figure 2—figure supplement 2.

DEER-spectroscopy on a network of MTSSL spin-labeled pairs of the hGBP1 resolves pairwise inter-label distance distributions.

(A) At the top, the network of spin-labeled hGBP1 is shown superposed to a crystal structure of hGBP1. A rotamer library analysis (RLA) simulates for the crystal structure (PDB-ID: 1DG3), the FRET major state (M₁), the minor state (M₂) inter-spin distance distributions. To the left, experimental background corrected DEER-traces and simulated DEER-traces based on a RLA of different structural models; to the right, inter-spin distance distribution as determined by Tikhonov regularization of the experimental DEER-trace. (B) Parametrization of the EPR-MTSSL label for accessible volume calculations. Top the distance distributions for the spin-pair N18C/Q577C of the hGBP1 crystal structure (PDB-ID: 1DG3) as calculated by the MTSSL-Wizard (Hagelueken et al., 2012) 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 (Hagelueken et al., 2012) and MMM (Polyhach, Bordignon et al.). 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.

Figure 2—figure supplement 3.

Quality controls for labeling based methods.

(A) Assessment of the labeling on the protein activity by comparison of the GTPase activity (left) and the self-oligomerization of hGBP1 (right). The effect of labeling on GTPase activity of hGBP1 as measured by the specific activities of 1µM single cysteine hGBP1 mutants at 25°C, either unlabeled or modified by Alexa488 or MTSSL at their free cysteines. Specific activities of the hGBP1 variants labeled by Alexa488 and Alexa647. The effect of the labels on the oligomerization of hGBP1 was assessed by size exclusion chromatography of 20 µM of unlabeled (top, right) and double labelled hGBP1 Cys9 (bottom, right) in the presence of 150–200 µM GppNHp or GDP AlF_x or in the absence of any nucleotide. (B) The fluorescence properties of the dye were studied by time-resolved anisotropies and dynamic quenching. The donor Alexa488 was predominantly freely rotating. This is highlighted by the fast-initial decay of the time-resolved anisotropy, r(t). (C) Temperature dependent FRET measurements: (i) apparent FRET efficiency ${\displaystyle E_{app}=1/\left(1+S_G/S_R\right)}$ (${\displaystyle S_G}$ and ${\displaystyle S_R}$ are the measured (uncorrected) green and red fluorescence intensities) as measured on a steady-state fluorometer. (ii) Time-resolved fluorescence decay of the hGBP1 variant Q254C/Q540C for a temperature of 35°C. (iii) Temperature dependence of the population of the state M1 for the variant Q254C/Q540C as determined by an analysis of the associated time-resolved fluorescence decays. (iv) Normalized changes of the fluorescence observables in dependence of the temperature. (D) A consistency analysis reveals that two DEER datasets (encircled in yellow) resolve M₁ instead of an averaged state of the two states, ${\displaystyle ⟨M_1,M_2⟩}$. The deviation between the simulated and the experimental observables beyond the noise of the other measurements identify two distances assigned to M₂ as misassignment.

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).

Identification and quantification of molecular kinetics

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.

Figure 3.

Conformational dynamics of hGBP1 studied by neutron spin echo (NSE), single molecule (sm) FRET with multi-parameter fluorescence detection (MFD), and molecular dynamics (MD) simulations.

(A) Effective diffusion coefficients of hGBP1, D_eff, determined by NSE and dynamic light scattering (DLS) compared to a model describing only the rigid body translational and rotational diffusion as a function of the scattering vector, q. The agreement of the experimental and calculated diffusion coefficients demonstrates insignificant shape changes on fast time scales up to 200 ns. (B) Two-dimensional single-molecule histogram of the absolute FRET-efficiency, E, and the average fluorescence weighted lifetimes of the donor in the presence of FRET, 〈τ_D(A)〉, of the double cysteine variant Q344C/V540C. One-dimensional histograms are projections of the 2D histogram. The color of the variant’s name indicates the location of the donor (green) and acceptor (red) determined by limited proteolysis and time-resolved anisotropies. The static-FRET line (blue) relates E and 〈τ_D(A)〉 for static proteins. The dynamic FRET line (magenta) describes molecules that change their conformation from M₁ to M₂ (brown circle) and vice-versa while being observed. The 〈τ_D(A)〉- E diagrams of all variants are compiled in Figure 3—figure supplement 2. M₁ and M₂ were identified by eTCSPC (Appendix 1—table 1) and sub-ensemble TCSPC (Figure 3—figure supplement 3, Appendix 1—table 5). Molecules in M₂ with bleaching acceptors are described by a bleaching line (dark yellow) that describes the transitions from M₂ to the donor only population (DOnly). Photons of molecules in the H and L area (H - high FRET, L - low FRET) were used to generate filters for filtered FCS (fFCS). (C) fFCS species autocorrelation functions (sACF) and species cross-correlation function (sCCF) of the variant Q344C/T540C (semitransparent lines) and corresponding model functions (solid lines) (Materials and Methods, Equation 17). The fFCS model parameters were determined by a global analysis of all 12 FRET-pairs (Figure 3—figure supplement 4) and revealed three correlation times (vertical dotted lines). The weighted residuals are shown to the top. The filter setting for fFCS of all samples and the fit results are compiled in Appendix 1—table 6. (D) Amplitudes of the fitted fFCS correlation times of the GTP free apo- (orange circles) and GDP-AlF_x bound holo-state (violet triangles) (values see Appendix 1—table 6). The average correlation times for the variants are shown as gray vertical lines. The gray boxes highlight the minimum and maximum of the average correlation times. (E) The average correlation times of the apo-state are mapped color-coded to a crystal structure (PDB-ID: 1DG3). Sections of the five rigid elements are displayed by cyan dashed lines. (F) Principle components analysis (PCA) of molecular dynamics (MD) and accelerated molecular dynamics (aMD) simulations (Materials and methods). The LG domain, the middle domain, and α12, and α13 are colored in blue, gray, green, and orange, respectively. The red arrows indicate the direction of the motion (scaled by a factor of 1.5 for better visibility). The semi-transparent cyan circle corresponds to a pivot point. The first five principal components (PCs), sorted by the magnitude of the eigenvalues, contribute to 60% of the total variance of all simulations. (G) Superposition of a MD trajectory frame (gray) deviating the most in RMSD (~8 Å) from the crystal structure (green). Both structural models were aligned to the LG domain.

Figure 3—figure supplement 1.

Neutron spin echo spectroscopy (NSE) on the hGBP1 resolves internal dynamics on the nanosecond timescale.

(A) Intermediate scattering function as measured by NSE with fits according to the rigid body models. The numbers to the right show the respective wave-vectors from top down with q in nm^-1. (B) Effective diffusion coefficients determined by NSE together with rigid body diffusion calculated from the protein structure. Circles and black line correspond to values derived from the initial slope of the NSE spectra and for rigid body diffusion at infinite dilution. The strong q-dependent increase is entirely due to the elongated shape of the protein. Triangles and red line correspond values obtained from exponential fits to the NSE spectra and to theoretical curves (Materials and Methods, Equation 9) without internal dynamics for t>25 ns. It is evident that rigid body diffusion includes a fast component that is visible at short times below 25 ns.

Figure 3—figure supplement 2.

Single-molecule fluorescence measurements.

Multi-parameter fluorescence detection histograms of different variants of Alexa488 and Alexa647 labeled human guanylate binding protein 1. The dashed blue lines are either static FRET-lines (see Materials and methods) considering linker broadening (top panels) or Perrin-equations for a dye with two rotational correlation times (Appendix 2, Equations 21 and 22). x₁ and x₂ refer to the fraction of fast and slow rotating dyes, respectively. For variants with states of different FRET efficiencies, dynamic FRET-lines connecting these states are shown as magenta solid line. The dark-yellow lines describe the acceptor bleaching from high-FRET states. The data are displayed in histograms of the donor-acceptor fluorescence intensity-ratio, F_D/F_A, the steady-state transfer-efficiency, E_S, and the mean fluorescence averaged lifetime of the donor in the presence of the acceptor ⟨τ_D(A)⟩_F. The variance of the donor-acceptor lifetime var(τ_DA) was calculated for every detected fluorescence burst. The color of the FRET-pair name indicated the most probable position of the donor (green) and acceptor dye (red); as inset the fluorescence quantum yield of the acceptor Φ_F,A and the donor Φ_F,D are shown. The fraction of the acceptor Alexa647 in trans-conformation, a_trans, was determined by FCS and is shown as inset.

Figure 3—figure supplement 3.

Sub-ensemble fluorescence decays ${\displaystyle {\mathit{f}}_{\mathit{E}\mathit{m}.|\mathit{E}\mathit{x}\mathit{c}.}^{\left(\mathit{s}\mathit{p}\mathit{e}\mathit{c}\mathit{i}\mathit{e}\mathit{s}\right)}}$ of single-molecule FRET measurements on different FRET-labeled (Alexa488, Alexa647) variant of hGBP1.

Considering the distinct fluorescence species and acquired data, the fluorescence decays of the 12 samples are display in the following colors: Green (${\displaystyle {\mathit{f}}_{\mathit{D}|\mathit{D}}^{\left(\mathit{D}0\right)}}$, donor fluorescence of the donor-only population D0 of the respective sample, the donor-only population was selected by the acceptor intensity); Orange (${\displaystyle {\mathit{f}}_{\mathit{D}|\mathit{D}}^{\left(\mathit{D}\mathit{A}\right)}}$, donor fluorescence of the FRET population DA, that is donor in the presence of the acceptor); Magenta (${\displaystyle {\mathit{f}}_{\mathit{A}|\mathit{D}}^{\left(\mathit{D}\mathit{A}\right)}}$, FRET-sensitized acceptor of the FRET population DA). The fluorescence decays were jointly analyzed by model (Materials and methods, Equations 10–15) with a weighted combination of normal distributed donor-acceptor distances. The mean and the fractions of the normal distributions are reported by the insets, for example, the variant Q254C/Q577C was described by two normal distributions, with average distances of 53 Å and 71 Å with fractions of 0.16 and 0.84, respectively. All fit results are compiled in Appendix 1—table 5.

Figure 3—figure supplement 4.

Global analysis of filtered fluorescence correlation spectroscopy of FRET-labeled variants for the hGBP1 probing its internal dynamics from µs to ms.

The model function (red) line is a global (single) model for all depicted fFCS curves. In the MFD histograms high FRET, H, and low FRET, L, species were identified to generate a variant specific set of filters, that are compiled in Appendix 1—table 6. These filters were used to calculate two species cross-correlation functions, sCCFs, and two species autocorrelation functions, sACFs (Materials and methods). For every variant the sCCFs and the sACFs are shown to the top and bottom, respectively. The sACFs and the sCCFs of all variants were analyzed by a global model (red lines, Materials and methods, Equations 17–19) with three correlation times. The weighted residuals of the model and the data are shown to the top of the sACFs and the sCCFs. The displayed correlation curves correspond to the fluorescence intensity weighted average correlation curves obtained by subsetting the measurement. The fluorescence intensity weighted averages correspond to the displayed mean correlation amplitudes of the individual correlation channels. The fit results are compiled in Appendix 1—table 6.

Figure 3—figure supplement 5.

Single-molecule fluorescence measurements under dimer conditions and in the presence of nucleotides.

(A) Multiparameter single-molecule fluorescence measurements of a set of comparable hGBP1 variants that is weakly affected in their GTP hydrolysis to different extent by the introduced mutations and labels. The labeling positions N18C and Q254C are on opposing sites of the molecule. LP and UP refer to labeled protein and unlabeled protein, respectively. In the presence of UP (10 µM) and GDP-AlF_x (100 µM) 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. (B) Control measurements of the variant N18C/Q577C to study the effect of GTP binding on hGBP1. Under single-molecule conditions (pM concentration) the intensity-based FRET indicators (F_D/F_A and the FRET efficiency, E) are independent on the presence of the substrate GTP. In the presence of GTP and hGBP1 at micromolar concentration oligomerization / dimerization occurs and hGBP1 undergoes a conformational change highlighted by a change of the FRET indicators.

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.

Essential motions determined by molecular dynamics simulations

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.

Experimentally guided structural modeling

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.

Figure 4.

Integrative modeling workflow and structure validation.

A detailed description and the used data can be found in Appendix 3. (A) The workflow combines rigid body docking (RBD), structural refinements, and molecular dynamics (MD) simulations. Rigid bodies (RBs) are identified by MD simulations and principal components analysis (PCA) (Materials and methods). (B) RBD representation of hGBP1: LG-domain (blue), the middle domain (gray), helix α12 (green), helix α13 (orange). The numbers correspond to the RB amino acid ranges. The crosses mark the FRET (black) and the EPR (magenta) labeling positions. The RBD considers the label distribution illustrated for a FRET pair by semi-transparent green (donor) and red (acceptor) surfaces. (C) Left: outline of ${\chi }_{SAXS}^2$ (Appendix 3, Equation 27) and ${\chi }_{DEER,FRET}^2$ (Appendix 3, Equation 28) for all (M₁, M₂) pairs of structures (left). Confidence levels of the meta-analysis (Materials and methods, Equation 20) that discriminates (M₁, M₂) pairs (right). Red and dark yellow regions correspond to p-values smaller than 0.68 and 0.95, respectively. (D) Experimental validation of the best pair of structures. Comparison of experimental ${\displaystyle R_{LL,exp}}$ (for DEER ${\displaystyle ⟨R_{SS,exp}⟩}$ and for FRET ${\displaystyle {\overline{R}}_{DA,exp}}$) and modeled label distances ${\displaystyle R_{LL,sim}}$ (for DEER ${\displaystyle ⟨R_{SS,sim}⟩}$ and FRET ${\displaystyle {\overline{R}}_{DA,sim}}$). Specific symbols display label distances ${\displaystyle R_{LL,exp}}$ for label pairs with distinct (▲) and equal (●) values for M₁ and M₂, respectively (see Appendix 1—table 1). For SAXS the scattering curve (black line) of the structure pair (M₁, M₂) is compared to the experimental data (orange line) by the weighted residuals to the top. (E) The standard deviation, SD, of the pairwise C_α-C_α distance ${\displaystyle SD\left(R_{\alpha }\right)}$ of the experimental ensemble with a p-value <0.68 (lower triangles) highlights the structural uncertainty. ${\displaystyle SD\left(R_{\alpha }\right)}$ normalized by the ${\displaystyle SD{\left(R_{\alpha }\right)}_{ref}}$ computed by the experimental uncertainty validates the structures. (F) Root mean square fluctuations (RMSF) of the C_α atoms of structures with a p-value <0.68 are displayed for the globally aligned ensemble.

Figure 4—figure supplement 1.

Analysis of molecular dynamics simulations, conformational space, identification of flexible regions, ensemble selection.

(A) Root mean squared deviation (RMSD) vs. the average structure of three repeats of 2 µs MD simulations in the presence and absence of GTP bound to the binding pocket of the LG domain. (B) Autocorrelation analysis of the RMSDs. The autocorrelation function of the RMSD vs. the average structure of the MD simulations in the presence (red) and absence (blue) of GTP are shown as light-colored thick lines. t_c is the correlation time. The darker colored red and blue lines correspond to a multiexponential model (${\displaystyle \sum _{i=1}^4{a}_{i}exp\left(\frac{-t_c}{{\tau }_i}\right)+b}$). The amplitudes a_i and the characteristic times ${\tau }_i$ are given in the table shown as an inset. (C) Assessment of the conformers within the conformational space covered by MD simulations using FRET- and EPR-data (Appendix 1—table 1). 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., 2019 using our FRET positioning and screening (FPS) toolkit (Kalinin et al., 2012) to compute the quality parameter ${\chi }_{DEER,FRET}^2$ (Appendix 3, Equation 28). The structural features of the conformers are described by the measure, RMSD_Cα 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 (Figure 5). (D) To the top the crystallographic B-factors of the Cα atoms (PDB-ID: 1DG3) and the NH S² 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 S² order parameter. (E) Ensemble selection. The fitted fractions of the conformer M₂, x_M2, for all combinations (M₁, M₂) generated by rigid body docking (RBD) using the DEER and FRET constraints are shown in dependence of the reduced sum of the squared deviation, ${\chi }_r^2$, in a 2D histogram. The red line corresponds to a p-value of 0.68. Pairs of structural models above the red line are discriminated.

Figure 4—figure supplement 2.

Analysis of structure generation and discrimination.

(A) 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 (dof_d,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 (${\displaystyle x={\chi }^2/min({\chi }^2)}$) and an estimate of dof_m ~10 for the degrees of freedom of the model (Appendix 3, Equation 29). The dof_d,SAXS was varied to assess the influence of the relative weights of DEER, FRET and SAXS (Materials and methods, Equation 20). (B) Fraction of discriminated structures vs. p-value of discriminating a pair of structure from the best structure.

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.

Figure 5.

Selected conformers and corresponding dimer models based on integrative modeling structures using of DEER, FRET, and SAXS data.

(A) All structures for M₁ and M₂ were aligned to the LG domain and are represented by orange and gray dots, indicating the C_α atoms of the amino acids F565 and T481, respectively. The structures best agreeing with all experiments are shown as cartoon representation (ribbon presentation see Figure 5—figure supplement 1). Non-rejected structures (p-value = 0.68, Figure 4—figure supplement 1E) represented by red spheres. The ensemble has been at deposited at PDB-Dev with the ID: PDBDEV_00000088. (B) Global alignment of all selected structures (p-value = 0.68). In the center, the structures best representing the average of the selected ensembles are shown. The transition from M₁ to M₂ (average correlation times 10–150 µs) can be described by a rotation around the region connecting the LG with the ligand binding site (magenta cross) and the middle domain (cyan circle). (C) Potential hGBP1:hGBP1 dimer structures constructed by superposing the head-to-head interface of the LG domain (PDB-ID: 2B92) to the full-length crystal structure (1DG3). The LG and middle domain are colored in blue and gray, respectively. Helices α12 and α13 are colored in green and orange, respectively.

Figure 5—figure supplement 1.

Selected conformers models based on integrative modeling structures using of DEER, FRET, and SAXS data.

(A) The pair of structural models (M₁, M₂) selected from the structural ensemble generated by DEER- and FRET-measurements best corresponding to the SAXS scattering data is shown in a cartoon representation. Both structural models are aligned to the LG domain.

Discussion

In non-farnesylated hGBP1 we found two conformations (M₁ and M₂), determined corresponding structures by integrative modeling, and mapped the M₁/M₂ exchange dynamics by NSE spectroscopy and fFCS. NSE showed no shape changes on the ns-timescale up to 200 ns. fFCS on a network of FRET-pairs revealed considerable dynamics on slower time scales (2–300 µs, Figure 3). The distribution of dynamics over such a wide range is indicative of a frustrated/rugged potential energy landscape with several substates and multiple kinetic barriers. Structural models for M₁ and M₂ based on SAXS, DEER, and FRET data revealed that the middle domain kinks towards the LG domain and that the helices α12/13 are bound on opposite sides of the LG domain. Notably, largest relative changes in DA distances are correlated with the fastest relaxation time (Figure 3D, Appendix 1—table 6). These findings are self-consistent, as the conformational transition from M₁ to M₂ and vice versa is complex and may cause a distribution of relaxation times, indicating a rough energy landscape with several intermediates, and the dynamics is mainly associated to α12/13. Analogous to protein folding, where (Chung et al., 2012) monitored the transition from the unfolded to the folded state and defined a transition path time, it would be intriguing to define an effective time for the conformational transition from M₁ to M₂. The conformational transition time would be a convolute of all observed relaxation times (Figure 3, Appendix 1—table 6) that is expected to be in the sub-millisecond time range. To sum up, the experiments can be described by two conformational states separated by a rugged energy landscape, resulting in slow transition invisible on the NSE timescale. The smFRET measurements demonstrate that this transition is an intrinsic property of non-farnesylated hGBP1 that does not depend on the presence of substrate (pathway (i) in Figure 1B).

To understand the functional relevance of M₁ and M₂, various observations and existing experimental information on farnesylated hGBP1 must be considered. We previously speculated that the farnesyl anchor acts as a ‘safety latch’ that attaches α12/13 to the LG domain. Nevertheless, we identified monomeric as well as dimeric forms of farnesylated and non-farnesylated hGBP1 by SEC-SAXS that both require large structural rearrangements (Lorenz et al., 2020). Thus, the dimerization, as the first step in oligomerization of hGBP1, is a feature that demands flexibility of the structure as deduced from major structural rearrangements described so far (Vöpel et al., 2014; Ince et al., 2017; Shydlovskyi et al., 2017). In particular, large movements of the LG, the middle domain and helices α12/13 against each other are required to establish the elongated building blocks of the polymer (Shydlovskyi et al., 2017). It is also most conceivable that multiple dynamically interchanging configurations of the sub-domains need to be sampled to assemble the highly ordered protein. Dynamins and farnesylated hGBP1 form highly ordered oligomers (Shydlovskyi et al., 2017) 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 (Vöpel et al., 2014) in the presence of a GTP analog. This finding is inconsistent with non-farnesylated nucleotide free (PDB-ID: 1DG3), nucleotide bound (PDB-ID: 1F5N) and farnesylated nucleotide free (PDB-ID: 6K1Z) full-length crystal structures. In dimers formed by two hGBP1s in a 1DG3, 1F5N, or 6K1Z conformation the helices α13 are on opposite sides and thus could not be associated (Figure 5). Similar findings were recently published for hGBP5 (Cui et al., 2021), showing that the middle domain undergoes a drastic movement after GTP binding, forming a closed dimer. 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, GTP binding likely leads to dimerization because of the increased affinity between the LG domain. In the formed dimer the low affinity between the α12/13 helices and the middle domain suffices to induce opening like a pocket knife which is the prerequisite for oligomerisation. In line with previous studies, which identified preferred pathways to increase the association yield of protein-protein complexes (Kozakov et al., 2014), we suggest dimerization path (i) as mechanism for dimerization of non-farnesylated hGBP1 (Figure 1B), that is, owing to the substrate independent 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 Figure 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 towards the LG domain as found for other dynamins (Low and Löwe, 2010; Chen et al., 2017). Moreover, our data supports two conformations with distinct binding sites of helix α12/13 that can be explained by major rearrangements of the region connecting the middle and the LG domain. Prakash et al., 2000 described already the interconnecting region of LG and middle domain, which comprise residues 279–310 including a small β-sheet and α-helix 6. The packing of helix α6 (residues 291–306) against α1/β1 of the LG domain and against helix α7 of the middle domain was hypothesized to stabilize the relative location of LG and middle domain against each other. Most intriguingly, the Sau group reported on the importance of helix α6 for full catalytic activity of hGBP1 and for oligomer formation. They could also clearly establish the relationship between oligomer formation and defensive activity against hepatitis C virus showing that impairing catalytic activity and oligomer formation by mutations leads also to a decreased antiviral activity (Pandita et al., 2016). These observations support our conclusions as to the importance of the movements around the pivot point located close to α-helix 6. Similar movements have been reported for other dynamin-like proteins, where the GTPase domain rearranges with respect to the middle domain along the catalytic cycle (Faelber et al., 2012; Kalia et al., 2018; Cui et al., 2021).

Previous data revealed two hGBP1 dimer conformations. In the major populated D₂ conformation two α13 helices dimerize while in the minor D₁ conformation helix α13 are separated (Kravets et al., 2012; Vöpel et al., 2014; Kravets et al., 2016; Shydlovskyi et al., 2017). 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 (Figure 6). We found that M₁ is the prevailing conformation in solution. Thus, even though hGBP1 is flexible it likely first dimerizes via the LG domain to form a stable D₂ dimer. 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 can bind to another protomer, whilst the conformational dynamics appear to remain unchanged (Vöpel et al., 2014) which agrees with our current findings. When two GTP-bound hGBP1s associate, a head-to-head dimer is formed either in a M₁:M₁, M₂:M₂ or a M₁:M₂ configuration. As the M₁:M₂ dimer has a higher stability, the α13 helices of the two subunits associate and the equilibrium is shifted towards the M₁:M₂ dimers (Vöpel et al., 2014).

Figure 6.

Potential oligomerization pathways of the human guanylate binding protein 1 (hGBP1) summarizing current experimental findings (Kravets et al., 2012, Vöpel et al., 2014; Kravets et al., 2016; Shydlovskyi et al., 2017).

In the presence and absence of a nucleotide, hGBP1 is in a conformational exchange with a Pivot point between LG and middle domain resulting in at least two conformational states M₁ and M₂ with a correlation time of 2–300 µs. Binding of a nucleotide to the LG domain activates hGBP1 for dimerization. After hGBP1 dimerization via the LG domains conformational changes of the middle domains and the helices α12/13 lead to an association of both helices α13. The species fractions for respective populations are given as numbers on top of the wells of a schematic energy landscape (black line). The substrate GTP lowers the activation barrier (red line). Under turn-over of GTP, farnesylated hGBP1 further self-assembles to form highly ordered, micelle-like polymers.

Figure 6 highlights the capability of hGBP1 to form networks during phase separation. Notably, hGBP1 shares these features with other proteins that also undergo phase separation. As observed in this work, conformational flexibility, multivalent interactions and amphiphilicity were reported as important factors for phase separation (Banani et al., 2017; Cui et al., 2021). Moreover, directionality is introduced because hGBP1’s interaction sites have distinct affinities that define the polarity of the formed molecular assembly. The high affinities of LG domains ensure formation of a dimeric encounter complex already at low concentrations in the first step. The conformational flexibility of hGBP1’s effector domain promotes the second key step for multimerization - the association of helices α13 that makes the dimer amphiphilic.

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, Figure 1B). 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 GTP, substrates and other proteins, respectively. Considering, for example, the movement of the substrate-dependent conformational transitions in the finger subdomain of a DNA polymerase (Rothwell et al., 2013), these opening and closing movements are essential for catalyzing polymerization under ambient conditions. The rule that functionally relevant conformational equilibria may be pre-defined by protein design also applies to other steps in protein function. In future, when considering additional quantitative live-cell, single-molecule and kinetic studies on farnesylated hGBP1, such integrative approaches may provide a molecular picture of complex biological processes like intracellular immune response.

In a broader perspective, this work and further experimental studies Hellenkamp et al., 2017; Borgia et al., 2018; Lerner et al., 2018; Dimura et al., 2020; Sanabria et al., 2020; Lerner et al., 2021; Agam et al., 2022, Hamilton et al., 2022 demonstrate the great capabilities of integrative label-based studies in combination with other experimental techniques to resolve the structure and dynamics of proteins under native conditions. This information on the promiscuous nature of proteins can contribute to shape a dynamic view on these macromolecules that links structural states and conformational dynamics with function. In case of hGBP1, the intrinsic flexibility is crucial for oligomerization (Figure 1 and Figure 6). Moreover, the obtained knowledge paves the way toward dynamic structural biology where structural models and kinetic information can be archived and disseminated in databases such as the prototype archiving system PDB-Dev (Berman et al., 2019).

Materials and methods

Protein expression and labeling

Expression and purification

SAXS experiments were performed on native non-farnesylated hGBP1 variants. Cysteine non-farnesylated variants for EPR and fluorescence experiments are based on cysteine-free hGBP1 (C12A/ C82A/ C225S/ C235A/ C270A/ C311S/ C396A/ C407S/ C589S) and were constructed in a pQE80L vector (Qiagen, Germany) following the instructions of the QuikChange site-directed mutagenesis kit (Stratagene, USA) according to Vöpel et al., 2009; Vöpel et al., 2014. Neither amino acid positions in direct proximity to the nucleotide binding pocket nor inside the G domain dimerization interface nor charged amino acids on the protein surface were taken into consideration for labeling (Tsodikov et al., 2002). All chosen positions had an accessible surface area (ASA) value higher than 60 Ų. Previously, these mutations were shown to only weakly affect non-farnesylated hGBP1’s function (Vöpel et al., 2009; Vöpel et al., 2014). New cysteines were introduced at various positions of interest (N18C, Q254C, Q344C, T481C, A496C, Q525C, V540C, Q577C). The GTPase activity of the labeled and unlabeled non-farnesylated hGBP1 variants was quantified by an assay as previously described (Kunzelmann et al., 2006) (Appendix 2). The mutagenesis was verified by DNA sequencing with a 3130xl sequencer (Applied Biosystems, USA). hGBP1 was expressed in BL21-CodonPlus(DE3)-RIL (Supplier Agilent) and purified following the protocol described previously (Praefcke et al., 1999). A Cobalt-NTA-Superflow was used for affinity chromatography. No glycerol was added to any buffer as it did not make any detectable differences. To not interfere with the following labeling reactions, the storage buffer did not contain DTT or DTE. Protein concentrations were determined by absorption at 280 nm according Gill and Hippel using an extinction coefficient of 45,400 M^–1 cm^–1. Tests of enzyme activity and function demonstrate that the effect of mutations and labeling on non-farnesylated hGBP1’s function is small (Appendix 2).

Protein labeling

FRET labeling was performed in two steps. To start the first labeling reaction, a solution with a hGBP1 concentration 100–300 µM in labeling buffer containing 50 mM Tris-HCl (pH 7.4), 5 mM MgCl₂, 250 mM NaCl was gently mixed with a 1.5-fold molar excess of Alexa647. After 1 hour incubation on ice, the unbound dye was removed using a HiPrep 26/20 S25 desalting column (GE Healthcare, Germany) with a flow rate of 0.5 ml/min. After this first labeling step, double, single, and unlabeled proteins were separated based on the charge difference introduced by the coupled dyes using anion exchange chromatography on a ResourceQ column (GE Healthcare, Germany) and a salt gradient running from 0 to 500 mM NaCl over 120 ml at a pH of 7.4 and flow rate of 2.0 ml/min. The peaks in the elugram were analyzed for their degree of labeling (dol) by measuring their absorption by UV/Vis spectroscopy at a wavelength of 280 nm and 651 nm. The fraction with the highest, single-acceptor labeled protein amount was labeled with a fourfold molar excess of Alexa488 C5 maleimide (Alexa488). The unreacted dye was separated as described for the first labeling step. Finally, the degrees of labeling (dol) for both dyes were determined (usually 70–100% for each dye). The dol was determined by absorption using 71,000 M^–1 cm^–1 and 265,000 M^–1 cm^–1 as extinction coefficients for Alexa488 and Alexa647, respectively. The labeled proteins were aliquoted into buffer containing 50 mM Tris-HCl (pH 7.9), 5 mM MgCl₂, 2 mM DTT, shock-frozen in liquid nitrogen and stored at –80 °C. We determined a Förster radius R₀=52 Å for the FRET-pair Alexa488 - Alexa647.

The spin labeling reactions were conducted at 4 °C for 3 hr using an 8-fold excess of (1-Oxyl-2,2,5,5-tetramethylpyrroline-3-methyl) methanethiosulfonate (MTSSL) as a spin label (Enzo Life Sciences GmbH, Germany). The reaction was performed in 50 mM Tris, 5 mM MgCl₂ dissolved in D₂O at pH 7.4. Unbound spin labels were removed with Zeba Spin Desalting Columns (Thermo Fisher Scientific GmbH, Germany) equilibrated with 50 mM Tris, 5 mM MgCl₂ dissolved in D₂O at pH 7.4. Concentrations were determined as described before. Labeling efficiencies were determined by double integration of CW room temperature (RT) 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

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.

Pulse EPR (DEER) experiments

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):

(1)

$\frac{\pi }{2}\left({\nu }_{obs}\right)-{\tau }_1-\pi \left({\nu }_{obs}\right)-t\prime -\pi \left({\nu }_{pump}\right)-\left({\tau }_1+{\tau }_2-t\prime \right)-\pi \left({\nu }_{obs}\right)-echo$

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)

(2)

$V\left(t\right)=F\left(t\right)\cdot V_{background}\left(t\right),$

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

(3)

$V_{background}\left(t\right)=exp\left(-k\cdot t\right).$

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

(4)

${\omega }_{DD}\left(R_{SS},\theta \right)=\frac{1}{4\pi }\cdot \frac{g^2{\mu }_B^2{\mu }_0}{\hslash }\cdot \frac{1}{R_{SS}^3}\cdot \left(3{\cos }^2\theta -1\right),$

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

(5)

$S(t)=K(t,R_{SS})\cdot p(R_{SS})$

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

(6)

$K(t,R_{SS})={\int }_0^{1}cos[(3x^2-1)\cdot {\omega }_{DD}\cdot t]dx$

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

(7)

$G_{\alpha }(P)=\Vert S(t)-V_{local}(t){\Vert }^2+\alpha \cdot {\Vert \frac{d^2}{d{r}^2}p\left(R_{SS}\right)\Vert }^2.$

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

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:

(8)

${\displaystyle D_0\left(q\right)=\frac{1}{q^{2}F\left(q\right)}\sum _{j,k}⟨b_{j}exp(-i\overrightarrow{q}{\overrightarrow{r}}_j)\left(\begin{array}{c}\overrightarrow{q}\\ \overrightarrow{q}\times {\overrightarrow{r}}_j\end{array}\right)\hat{D}\left(\begin{array}{c}\overrightarrow{q}\\ \overrightarrow{q}\times {\overrightarrow{r}}_k\end{array}\right)b_{k}exp(i\overrightarrow{q}{\overrightarrow{r}}_k)⟩}$

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:

(9)

${\displaystyle \begin{array}{l}I\left(q,t\right)/I\left(q,0\right)=\left[\left(1-A\left(q\right)\right)+A\left(q\right)exp\left(-\mathrm{\Gamma }t\right)\right]\cdot \\ exp\left(-q^2{D}_t\frac{H_t}{S\left(q\right)}t\right)\left(\sum _{l=0}^{15}{S}_l\left(q\right)exp\left(-l\left(l+1\right)D_r{H}_{r}t\right)\right)/\sum _{l=0}^{15}{S}_l\left(q\right)\end{array}}$

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).

Fluorescence spectroscopy

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.

Burst-wise single molecule analysis

Briefly, as the first step in the burst-wise analysis, fluorescence bursts were discriminated from the background signal of 1–2 kHz of the single-molecule measurements by applying an intensity threshold criterion. Next, the anisotropy and the fluorescence averaged lifetime, ${\displaystyle ⟨{\tau }_{D\left(A\right)}{⟩}_F}$, were determined for each burst. Moreover, the background, the detection efficiency-ratio of the ‘green’ and ‘red’ detectors, and the spectral cross-talk were considered to determine the FRET efficiency, E, of every burst (Sisamakis et al., 2010). Absolute FRET efficiencies require calibrated instruments (Hellenkamp et al., 2018) and considerations of the excitation power and FRET-dependent photophysics (Widengren et al., 2001). The species averaged fluorescence lifetime of the donor in the absence of an acceptor ${\displaystyle ⟨{\tau }_{D\left(0\right)}{⟩}_x}$, ${\displaystyle ⟨{\tau }_{D\left(A\right)}{⟩}_F}$, and the FRET efficiency estimate the mean, ${\displaystyle ⟨{\tau }_{D\left(A\right)}{⟩}_x=\left(1-E\right)\cdot ⟨{\tau }_{D\left(0\right)}{⟩}_x}$, and variance, ${\displaystyle var\left({\tau }_{D\left(A\right)}\right)=⟨{\tau }_{D\left(A\right)}{⟩}_F\cdot ⟨{\tau }_{D\left(A\right)}{⟩}_x-⟨{\tau }_{D\left(A\right)}{⟩}_x^2}$, of the burst averaged fluorescence lifetimes distribution. This highlights conformational dynamics by a non-zero variance (Figure 3—figure supplement 2). For a detailed analysis of the sub-ensemble, the fluorescence photons of multiple bursts were integrated into joint fluorescence decay histograms (seTCSPC, Figure 3—figure supplement 3).

FRET-lines

By relating fluorescence parameters, FRET lines serve as a visual guide to interpret histograms of MFD parameters determined for individual molecules. The fluorescence weighted lifetime of the donor, 〈τ_D(A)〉_F, and the FRET efficiency, E, were related by FRET-lines by a methodology similar as previously described (Kalinin et al., 2010). First, FRET-rate constant distributions, p(k_RET), were calculated for a given set of model parameters. Next, p(k_RET) was converted to the averages 〈τ_D(A)〉_F and E. This results in a parametric relation between 〈τ_D(A)〉_F and E called FRET-line. We use two types of FRET-lines: dynamic and static FRET-lines. Dynamic FRET-lines describe the mixing of typically two states. A static FRET-line relates 〈τ_D(A)〉_F to E for all molecules that are static within their observation time (the burst duration). Static molecules are identified by populations in a MFD histogram located on the static FRET-line. The FRET-lines were calculated using the scripting capability of ChiSurf assuming states with normal distributed distance and are calibrated for sample-specific fluorescence properties, that is, donor and acceptor fluorescence quantum yields, the fraction of acceptor in power dependent dark states (cis-state in Alexa647), and complex fluorescence decays of the donor in the absence of FRET.

Fluorescence decay analysis

Fluorescence decay analysis was performed using ChiSurf, an open-source software tailored for the global analysis of multiple fluorescence experiments. Fluorescence intensity decays of the donor in the presence, ${\displaystyle f_{D|D}^{\left(DA\right)}\left(t\right)}$, and the absence of FRET, ${\displaystyle f_{D|D}^{\left(D0\right)}\left(t\right)}$ , inform on DA distance distributions, p(R_DA) (Peulen et al., 2017). However, the local environment of the dyes may result in complex fluorescence decays of the donor ${\displaystyle f_{D|D}^{\left(D0\right)}\left(t\right)}$ and the acceptor ${\displaystyle f_{A|A}^{\left(AD\right)}\left(t\right)}$ even in the absence of FRET. Such sample-specific fluorescence properties were accounted for by donor and acceptor reference samples using single cysteine variants. ${\displaystyle f_{D|D}^{\left(D0\right)}\left(t\right)}$ and ${\displaystyle f_{A|A}^{\left(A0\right)}\left(t\right)}$ were formally described by multi-exponential model functions:

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$\begin{array}{l}{f}_{D|D}^{\left(D0\right)}\left(t\right)=\sum _i{x}_D^{\left(i\right)}exp\left(\frac{-t}{{\tau }_D^{\left(i\right)}}\right)\\ f_{A|A}^{\left(DA\right)}\left(t\right)=\sum _i{x}_A^{\left(i\right)}exp\left(\frac{-t}{{\tau }_A^{\left(i\right)}}\right)\end{array}$

Here, D|D refers to the donor fluorescence under the condition of donor excitation and A|A refers to the acceptor fluorescence under acceptor excitation. Species fractions $x_D^{\left(i\right)}$ and $x_A^{\left(i\right)}$ and lifetimes of the donor ${\tau }_D^{\left(i\right)}$ and the acceptor ${\tau }_A^{\left(i\right)}$ are summarized in Appendix 1—table 2.

We assume that the same distribution of FRET-rate constants quenches all fluorescent states of the donor (quasi-static homogeneous model Peulen et al., 2017). Thus, ${\displaystyle f_{D|D}^{\left(DA\right)}\left(t\right)}$ can be expressed by:

(11)

${\displaystyle f_{D|D}^{\left(DA\right)}\left(t\right)=f_{D|D}^{\left(D0\right)}\left(t\right)\cdot \sum _i{x}_{RET}^{\left(i\right)}exp\left(-t\cdot k_{RET}^{\left(i\right)}\right)=f_{D|D}^{\left(D0\right)}\left(t\right)\cdot {ϵ}_D\left(t\right),}$

where ${\displaystyle {ϵ}_D(t)}$ is the FRET-induced donor decay. The MFD measurements demonstrate that the major fraction of the dyes is mobile (Appendix 2). Therefore, we approximate κ² by 2/3 and relate ${\displaystyle {ϵ}_D(t)}$ to p(R_DA) by:

(12)

${ϵ}_D\left(t\right)={\int }_{R_{DA}}p\left(R_{DA}\right)\cdot exp\left(-t\cdot k_0\cdot {\left(\frac{R_0}{R_{DA}}\right)}^6\right)d{R}_{DA}+x_{DOnly}.$

Here, R₀ is the Förster radius (R₀=52 Å) and k₀=1/τ₀ is the radiative rate constant of the unquenched dye (τ₀ = 4 ns). In ε_D(t) incomplete labeled molecules lacking an acceptor and molecules with bleached acceptors are considered by the fraction of FRET-inactive, x_DOnly.

For rigorous uncertainty estimates p(R_DA) was modeled by a linear combination of normal distributions. Overall, a superposition of two normal distributions with a central distance ${\displaystyle {\overline{R}}_{DA}^{\left(1,2\right)}}$ and a width w_DA was sufficient to describe the data:

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$p\left(R_{DA}\right)=\frac{1}{\sqrt{\frac{\pi }{2}}\cdot w_{DA}}\left[x_1{e}^{-{\left(\frac{2\left(R_{DA}-{\overline{R}}_{DA}^{\left(1\right)}\right)}{w_{DA}}\right)}^2}+\left(1-x_1\right)e^{-{\left(\frac{2\left(R_{DA}-{\overline{R}}_{DA}^{\left(2\right)}\right)}{w_{DA}}\right)}^2}\right]$

In the analysis of the seTCSPC data, the FRET-sensitized emission of the acceptor, ${\displaystyle f_{A|D}^{(DA)}\left(t\right)}$ , was considered to reduce the overall photon noise and a typical width of 12 Å was consistent with the data. ${\displaystyle f_{A|D}^{\left(DA\right)}\left(t\right)}$ was described by the convolution of ${\displaystyle f_{A|A}^{\left(DA\right)}\left(t\right)}$ , and ${\displaystyle f_{D|D}^{\left(DA\right)}\left(t\right)}$ :

(14)

$f_{A|D}^{\left(DA\right)}\left(t\right)=f_{D|D}^{\left(D0\right)}\left(t\right)\cdot {ϵ}_D\left(t\right)\otimes f_{A|A}^{\left(DA\right)}\left(t\right)$

All f(t)s were fitted by model functions using the iterative re-convolution approach (Straume et al., 2002). Here, the parameters of a model function g(t) were optimized to the data by using the modified Levenberg–Marquardt algorithm. The model function g(t) considers experimental nuisances as scattered light and a constant background:

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$g\left(t\right)=N_F\cdot f\left(t\right)\otimes IRF\left(t\right)+N_{BG}\cdot IRF\left(t\right)+bg$

N_F is the number of fluorescence photons, N_BG is the number of background photons due to Rayleigh or Raman scattering and bg is a constant offset attributed to detector dark counts and afterpulsing. In seTCSPC, the fraction of scattered light and the constant background was calculated by the experimental integration time and the buffer reference measurements. In eTCSPC, the fraction of scattered light and the constant offset were free fitting parameters. Finally, g(t) was scaled to the data by the experimental number of photons and fitted to the experimental data. Statistical errors were estimated by sampling the parameter space (Foreman-Mackey et al., 2013) and applying an F-test at a confidence level of 95% in addition to support plane analysis of the parameters (Straume et al., 2002).

Filtered species cross-correlation functions

Filtered fluorescence correlation spectroscopy of the acquired MFD data was performed as previously described (Felekyan et al., 2012). In a global analysis, all 48 fFCS curves (two SACF and SCCF per variant) are treated as a single dataset. Filtered FCS increases the contrast by a set of state-specific filters applied to the recorded photon stream. For every FRET pair, a specific set of filters, $w_j^{\left(i\right)}$ , was generated using experimental fluorescence bursts for high (H) and low (L) FRET states as previously described and listed in Appendix 1—table 6 (Felekyan et al., 2012). Using these filters species cross-correlation functions $G^{\left(n,m\right)}\left(t_c\right)$ were calculated by weighted signal intensities S_j(t):

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${\displaystyle G^{\left(n,m\right)}\left(t_c\right)=\frac{⟨F^{\left(n\right)}\left(t\right)\cdot F^{\left(m\right)}\left(t+t_c\right)⟩}{⟨F^{\left(n\right)}\left(t\right)⟩\cdot ⟨F^{\left(m\right)}\left(t+t_c\right)⟩}\text{ with }{F}^{\left(n\right)}\left(t\right)=\left(\sum _{j=1}^{d\cdot L}{w}_j^{\left(n\right)}\cdot S_j\left(t\right)\right)}$

Herein n and m are the two species (either H or L), d is the number of detectors, L is the number of TAC channels, and S_j(t) is the signal recorded in the TAC-channel j. The choice of n and m defines the type of the correlation function. If n equals m, G^(n,n)(t_c) is a species autocorrelation function (sACF), otherwise G^(n,m)(t_c) is a species cross-correlation function (sCCF) (Felekyan et al., 2012). Overall four correlation curves were generated per sample: two species auto - sACF^H,H(t_c), sACF^L,L(t_c) and two species cross - sCCF^H,L(t_c), sCCF^L,H(t_c) correlation curves. All curves were fitted by a model which factorizes G^(n,m)(t_c) into a diffusion-, $G_{diff}^{\left(n,m\right)}\left(t_c\right)$ , and a kinetic- term $G_{kin}^{\left(n,m\right)}\left(t_c\right)$ :

(17)

$G_{}^{\left(\text{n,m}\right)}\left(t_c\right)=1+\frac{1}{N_{eff}^{\left(\text{n,m}\right)}}\cdot G_{\text{Diff}}^{\left(\text{n,m}\right)}\left(t_c\right)\cdot G_{\text{kin}}^{\left(\text{n,m}\right)}\left(t_c\right)$

Here, N_eff^(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 $G_{diff}^{\left(n,m\right)}\left(t_c\right)$ is

(18)

$G_{\text{Diff}}={\left(1+\frac{t_c}{t_{\text{Diff}}}\right)}^{-1}{\left(1+{\left(\frac{{\omega }_0}{z_0}\right)}^2\left(\frac{t_c}{t_{\text{diff}}}\right)\right)}^{-1/2}$

where t_diff 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/e² of the maximum’s intensity.

The kinetic terms of the sACF and the sCCF were formally described by:

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$\begin{array}{l}{G}_{kin}^{L,H}(t_c)=\left(1-A_0^{LH}\cdot (A_1\cdot e^{-t_c/t_{c,1}}+A_2\cdot e^{-t_c/t_{c,2}}+A_3\cdot e^{-t_c/t_{c,3}})\right)\\ G_{kin}^{H,L}(t_c)=\left(1-A_0^{HL}\cdot (A_1\cdot e^{-t_c/t_{c,1}}+A_2\cdot e^{-t_c/t_{c,2}}+A_3\cdot e^{-t_c/t_{c,3}})\right)\cdot \left(1-A_b^{HL}\cdot e^{-t_c/t_b}\right)\\ G_{kin}^{L,L}(t_c)=\left(1+A_1^{LL}\left(e^{-t_c/t_{c,1}}-1\right)+A_2^{LL}\left(e^{-t_c/t_{c,2}}-1\right)+A_3^{LL}\left(e^{-t_c/t_{c,3}}-1\right)\right)\\ G_{kin}^{H,H}(t_c)=\left(1+A_1^{HH}\left(e^{-t_c/t_{c,1}}-1\right)+A_2^{HH}\left(e^{-t_c/t_{c,2}}-1\right)+A_3^{HH}\left(e^{-t_c/t_{c,3}}-1\right)\right)\cdot \left(1+A_b^{HH}(e^{-t_c/tb}-1)\right)\end{array}$

Here, A₀ defines the amplitude of the anti-correlation; A_b accounts for acceptors bleaching in the high-FRET state; t_b is the characteristic bleaching time of the acceptor (under the given conditions typically 5–10ms); A₁, A₂ and A₃ together with t_c,1, t_c,2 and t_c,3 define the anti-correlation time spectrum of the H to L and L to H transitions. The sum of A₁, A₂ and A₃ was constrained to unity. The correlation times t_c,1, t_c,2 and t_c,3 were global parameters shared among all samples. A₁, A₂ to A₃ were sample specific. The amplitudes $A_1^{HH},A_2^{HH},A_3^{HH}$ and ${\displaystyle A_1^{LL},A_2^{LL},A_3^{LL}}$ of the sACFs were non-global parameters optimized for every curve individually. Overall, 48 correlation curves of 12 samples were analyzed as a joint dataset. The uncertainties of the amplitudes and correlation times were determined by support plane analysis that considers the mean and the standard deviation of the individual correlation channels. Estimates for the mean and the standard deviation of the correlation channels were determined by splitting individual measurements. The global data analysis of the FCS curves was performed using ChiSurf.

MD simulations and principal component analysis

MD simulations

We performed molecular dynamics (MD) and accelerated MD (aMD) (Hamelberg et al., 2004) simulations to identify collective degrees of freedom, essential movements, and correlated domain motions of hGBP1 by Principal Component Analysis (PCA) (Hamelberg et al., 2004). Molecular dynamics simulations were performed using the Amber14 package (Case et al., 2015) and the ff14SB force field. The simulations were started from a known crystal structure of the full-length non-farnesylated protein (PDB code: 1DG3) protonated with the program PROPKA (Bas et al., 2008) at a pH of 7.4, neutralized by adding counter ions and solvated in an octahedral box of TIP3P water (Jorgensen et al., 1983) with a water shell of 12 Å around the solute. The obtained system was used to perform unbiased MD simulations and aMD simulations (Hamelberg et al., 2004). Five unrestrained all-atom MD simulations were performed. Three of the five simulations were conventional MD (2 µs each) and two aMD simulations (200 ns each). The ‘Particle Mesh Ewald’ method (Darden et al., 1993) was utilized to treat long-range electrostatic interactions; the SHAKE algorithm (Ryckaert et al., 1977) was applied to bonds involving hydrogen atoms. For all MD simulations, the mass of solute hydrogen atoms was increased to 3.024 Da and the mass of heavy atoms was decreased respectively according to the hydrogen mass repartitioning method (Hopkins et al., 2015). The time step in all MD simulations was 4 fs 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, 10,000, 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 (Pierce et al., 2012).

Principal components analysis (PCA)

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 (Figure 4—figure supplement 1A). A correlation analysis of these RMSD trajectories reveals that the dynamics is complex (non-exponential) and predominantly in the 10–100 ns regime (Figure 4—figure supplement 1B). Structures deviating the most from the X-ray structure kink at the connector of the LG and the middle domain (Figure 3G). A PCA reveals that the first five principal components describe overall more than 60% of the variance of the MD and aMD simulations (Figure 3F). 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 (Figure 3F). The first component (1) describes a motion of the middle domain towards the LG domain. In the second component (2) the middle domain and α13 move in opposite directions. The third component (3) is like the first component with a two times smaller eigenvalue. Component (4) is like the second component, except that the middle domain and α12/13 move in the same direction. Component (5) captures a similar directionality of motion for the middle domain and α12/13 as the second component. In component (5) however, the movement of α12/13 describes a breathing motion of the catalytic LG domain. The major motions of the PCA can be described by a rotation of the middle domain relative to the GTPase domain (Figure 3F, cyan sphere).

Integrative modeling

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.

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${\displaystyle {\chi }_{2k}^2\sim -2\cdot \sum _{i=1}^{k}ln\left(p_i\right)=-2\cdot ln\left(\prod _{i=1}^k{p}_i\right)=-2\cdot ln\left(p_{DEER,FRET}\cdot p_{SAXS}\right)}$

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).

Data availability

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):

Folder	Content
EPR_data.zip	double electron-electron resonance (DEER) EPR data
FRET_data.zip	eTCSPC FRET data including fit results. Sample name includes labeled aa and used dyes
NSE.zip	neutron spin echo data
SMD_hGBP1-[sample].tgz	raw single molecule FRET data used for filter FCS and MFD analysis and calibration measurements. Sample name includes labeled aa

Subfolders for an eTCSPC FRET measurement contain the following files:

File	Content
decay.dat	FRET or donor only decay
prompt.txt	IRF
whitelight.txt	Used to create linearization table for tac gates to do full correlation

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

File	Content
fit_data.txt	Fitted data
fit_fit.txt	Fit curve
fit_info.txt	Fit results
fit_wr.txt	Residuals of the fit

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

Folder Name	Content
‘Al488_Al647’	Describes the used dyes, contains the measurement of one sample under various conditions including all files
‘Sample’	Raw data and burst analysis, including info file on burst selection under info-folder
‘BID’	Subfolder in burst analysis describing selected bursts used to create filters for fFCS
‘fFCS’	Subfolder in burst analysis, contains used lifetime filters, correlation curves and fits
‘LP’	Labeled protein, including all measurement files
‘LP_nucleotide_UP’	Labeled protein with a nucleotide and additional unlabeled protein, including all measurement files
‘LP_UP’	Labeled protein and additional unlabeled protein, including all measurement files
‘buffer’	Buffer measurement for background
‘H2O’	Water measurement for IRF
‘Rh110’	Free dye measurements for g-factor calibration
Rh101	Free dye measurements for g-factor calibration
DNA	Calibration measurement for detection efficiency

Code availability

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.