**Figure 5)** so that the precision of the obtained corresponded to our experimental one. In this way, we obtained a $dof_{d,DEER/FRET} = 22$ (Figure 4—figure supplement 2A) - a value that is close to the number of independent label-pair positions of 23. For SAXS measurements the number of Shannon channels is typically in the range of 10–23. For our measurements, the number of Shannon channels approximately 18–22 (Moore, 1980; Mertens and Svergun, 2017). We used the number of Shannon channels as an initial estimate for the dof of the SAXS measurements, $dof_{d,SAXS}$, and we varied $dof_{d,SAXS}$ in the range of 10–24. We found only minor effects of $dof_{d,SAXS}$ on $\alpha_{SAXS}$, the SAXS discrimination power of the models, and used $dof_{d,SAXS} = 17$ to discriminate structural models (Figure 4—figure supplement 2A). Using these estimates of $dof_m$ and $dof_d$, $\alpha$ for DEER/FRET, $\alpha_{DEER,FRET}$, and SAXS, $\alpha_{SAXS}$, were calculated for all pairs (M₁, M₂). Next, $\alpha_{DEER,FRET}$ and $\alpha_{SAXS}$ were combined in a meta-analysis to a joint probability of discriminating a pair.

$\alpha_{DEER,FRET}$ and $\alpha_{SAXS}$ measure how likely a pair (M₁, M₂) is dissimilar from the best pair for DEER/FRET and SAXS, respectively. To combine DEER/FRET and SAXS we used the probability $p$ that a pair is similar, $p=1-\alpha$. Note, $p$ for DEER/FRET, $p_{DEER,FRET}$, and for SAXS, $p_{SAXS}$, considers the degrees of freedom for the system and data. Moreover, $p_{DEER,FRET}$ and $p_{SAXS}$ are independent. Thus, Fisher's method was applied to fuse datasets in a meta-analysis. Fisher's method combines probabilities of $k$ independent tests (here $k=2$) into a combined $\chi^2_{2k}$ with 2 $k$ degrees of freedom. For $p_{DEER,FRET}$ and $p_{SAXS}$, the combined probability is

$$ \begin{aligned} \chi^2_{2k} & \sim -2 \cdot \sum_{i=1}^{k} \ln(p_i) = -2 \cdot \ln\left(\prod_{i=1}^{k} p_i\right) \quad (30) \\ & = -2 \cdot \ln(p_{DEER,FRET} \cdot p_{SAXS}) \end{aligned} $$

Thus, $\chi^2_{2k}$ is chi-squared distributed with 4 combined degrees of freedom. In this way a $\chi^2_{2k}$ value was determined for every (M₁, M₂), and pairs (M₁, M₂) were discriminated by a chi-squared test with 4 degrees of freedom.

## Assessment of model precision and quality

To assess the local quality of the models, the inter-residue distances between all $C_\alpha$ atoms, $R_{C_\alpha}$, and the standard deviation, $SD(R_{C_\alpha})$, of the distribution of $R_{C_\alpha}$ were calculated for all models as a measure for the experimental model precision (Figure 4E, lower triangles). Next, we checked if these variabilities are larger than statistically expected. For this, we compared the experimental precision $SD(R_{C_\alpha})$ to the precision $SD(R_{C_\alpha})_{ref}$ of a ground truth model ensemble as an 'ideal and perfect' reference by computing the weighted (normalized) precision, $SD(R_{C_\alpha})/SD(R_{C_\alpha})_{ref}$. Due to (i) the incomplete experimental information on the model, (ii) the uncertainties of the experiments, and (iii) imprecisions of the model, we anticipate a limited resolution of the model even for ideal experiments. We calculated the reference precision of the ground truth ensembles in two steps. At first, we use the models for M₁ and M₂ of the experimental ensemble that describe our FRET and EPR data best. Next, we use the distances corresponding to the best models and our experimental errors in Appendix 3—table 1 to generate the ideal reference ensemble by our structural modeling pipeline (Figure 4A) so that we could compute the theoretical inter-residue distance distributions and precisions. The finally computed distributions of the weighted precisions, $SD(R_{C_\alpha})/SD(R_{C_\alpha})_{ref}$ allow us to test whether the modeled conformational ensemble approaches the theoretical optimum ratios around unity or whether systematic deviations indicate problems in the modelling.

Please note that the above procedure provides only an estimate for the reference model precision and corresponding variability of $R_{C_\alpha}$. For a correctly estimated model precision with the corresponding $SD(R_{C_\alpha})_{ref}$, the weighted precision $SD(R_{C_\alpha})/SD(R_{C_\alpha})_{ref}$ theoretically has the meaning of an F-value. Such an F-value for pair-wise estimates of the model precision as $SD(R_{C_\alpha})$ could be used for estimating the probability that the model insufficiently describes the data within their experimental noise. This procedure could yield such estimates for residue pairs that facilitate the detection of the model defects and limitations.
Rigid body docking (RBD)

Identification of rigid domain and rigid body decomposition

The first step for RBD is the segmentation of hGBP1 into rigid domains that can represent the essential motions of the protein (Figure 3F). Moreover, the segmentation should introduce sufficient degrees of freedom to fulfil the experimental constraints. The substrate free (PDB-ID: 2B92) and a substrate bound form of the LG domain (PDB-ID: 2B92) differ by only 1.1 Å RMSD, and the distance network (Figure 1A) for the label-based measurements were designed to probe distance changes between the LG, the middle domain, and α12/13. Hence, the LG domain (residue 1–309) was modeled as a single RB. In the MD simulations α12/13 moved relative to the middle and the LG domain while the middle domain changes its orientation relative to the LG domain. The DEER measurement on the variant A551C/Q577 informs on the position of α13 relative to helix α12. Consequently, α12 (residue 482–563) and α13 (residue 564–584) were treated as separate RBs. We note that we treated helix α12 in this work as rigid, because we had no experimental evidence for unfolding or kinking of this helix. Without a rearrangement of the middle domain the motion of α12/13 is highly restricted in a RBD framework. To allow for more flexibility the middle domain was represented by two bodies (residue 310–373 and residue 374–481). Overall, hGBP1 was decomposed into the LG domain, two RBs for the middle domain, helix α12, and helix α13. Therefore, to capture hGBP1’s motions and fulfil the experimentally probed degrees of freedom hGBP1 was described by five RBs. Experimental evidence for such a decomposition is the FRET measurements on the variants A496C/V540C, T481C/Q525C, and Q344C/T481C which probe the conformation of α12 and the middle domain. An analysis of the protein mechanics by the S² order parameters of the NH bond determined by analysis of the MD simulations and the B-factors of the full-length protein revealed sets of characteristic spikes (Figure 4—figure supplement 1D). These spikes rationalize the rigid body decomposition and identify flexible regions of the protein, which mainly correspond to flexible loops connecting individual helices. They indicate that the middle domain, helix α12, and helix α13 are flexibly linked.

Definition of restraints

As next step of RBD, a set of restraints needs to be defined. The RBD procedure uses for model generation experimental restraints, a repulsion potential as a penalty function for atomic overlaps, and bonds between the RBs. The experimental restraints, bonds connecting the bodies, and the repulsive clash are considered by the terms χ²ₚₐ₉₄,ₐ₉₄ (Appendix 3, Equation 28), χ²ₚₐ₉₄,ₚₐ₉₄, and, χ²ₚₐ₉₄, respectively. The overall RBD potential χ²ₚₐ₉₄ is

$$ \chi_{RBD}^2 = \chi_{DEER/FRET}^2 + \chi_{bonds}^2 + \chi_{clash}^2 \quad (31) $$

The bond term was a combination of quadratic potentials

$$ \chi_{bonds}^2 = \sum_{i,j} \left( \frac{R_{ij} - R_{eq,ij}}{k_{ij,\pm}} \right)^2 \quad (32) $$

where $R_{ij} = |\vec{r}_j - \vec{r}_i|$ is the distance between the vectors $\vec{r}_j$ and $\vec{r}_i$, defined by the arrangement of the RBs, $R_{eq,ij}$ is the equilibrium distance of the distance pair, and $k_{ij,\pm}$ is a constant which depends on the sign of $R_{ij} - R_{eq,ij}$.

Overlaps of rigid bodies we penalized by the atomic overlaps in the repulsion potential χ²ₚₐ₉₄:

$$ \chi_{clash}^2 = \sum_{i,j} \begin{cases} 0, & R_{ij} \ge R_{wi} + R_{wj} \\ \left( \frac{R_{wi} + R_{wj} - R_{ij}}{R_{ctol}} \right)^2, & R_{ij} < R_{wi} + R_{wj} \end{cases} \quad (33) $$

Here $R_{ij}$ is the distance between the atoms with the index i and j belonging to different subunits, $R_{wi}$ and $R_{wj}$ are their van der Waals radii, and $R_{ctol}$ is a constant defining the “clash tolerance”.

The restraints defining χ²ₚₐ₉₄,ₐ₉₄ for M₁ and M₂ are listed in the Appendix 3—table 1. Parameters defining contributions to χ²ₚₐ₉₄,ₚₐ₉₄, namely the connection of the N- and C-termini and a set of weak bonds based on a crystal structure (PDB-ID: 1DG3) to stabilize the middle domain, are listed in
**Appendix 3—table 2.** The rigid body model does not allow for bending. Therefore, a very weak repulsion potential was used for $\chi_{clash}^2$ ($R_{ctol}$ = 6 Å).

Rigid body docking procedure

The final docking step generates structural models fulfilling the constraints summarized by the energy function (Appendix 3, Equation 31). Starting from a random initial arrangement of the RBs, forces drive the RB assembly towards a configuration with a minimum energy (Kalinin et al., 2012). For fast calculations, the forces are applied between the average label position and optimizes the distance between the average label positions $R_{mp}$.

$$R_{mp} = \left| \left\langle \vec{r}_{L1}^{(i)} \right\rangle - \left\langle \vec{r}_{L2}^{(j)} \right\rangle \right| = \left| \frac{1}{n} \sum_{i=1}^{n} \vec{r}_{L1}^{(i)} - \frac{1}{m} \sum_{j=1}^{m} \vec{r}_{L2}^{(j)} \right| \quad (34)$$

Here $\vec{r}_{L1}^{(i)}$ and $\vec{r}_{L2}^{(j)}$ are the coordinates of the two labels in the conformation (i) and (j). Using the mean position of the dyes instead of the full spatial distribution of the dyes reduces the complexity of the RBD and increases its speed (Kalinin et al., 2012). DEER and fluorescence decays measurements recover inter-label distance distributions, $p(R_{LL})$, and not the distance between the label positions. For a uniformly populated AV

$$\langle R_{LL} \rangle = \left| \left\langle \vec{r}_{L1}^{(i)} \right\rangle - \left\langle \vec{r}_{L2}^{(j)} \right\rangle \right| = \frac{1}{nm} \sum_{i=1}^{n} \sum_{j=1}^{m} \left| \vec{r}_{L1}^{(i)} - \vec{r}_{L2}^{(j)} \right| \quad (35)$$

To use average distances $\langle R_{LL} \rangle$ during RBD a transfer function converted the experimental average inter label distance $\langle R_{LL} \rangle$ to $R_{mp}$ (Kalinin et al., 2012). After docking, the spatial distribution of the labels were simulated for the generated structural models to calculate average distances $\langle R_{LL} \rangle$ as a set of model distances, $\{R_{model}\}$.

**Appendix 3—table 1.** Experimental restraints for rigid body docking.

Analysis results of DEER-EPR and FRET eTCSPC. The labels Alexa488, Alexa647, and MTSSL are referred to by D, A, and R1, respectively. The names of the labeling sites report on the location of the dyes and the introduced mutation. For DEER, average inter-label distances $\langle R_{LL,exp} \rangle$ and the widths of the inter-spin distance distribution $w_+$ and $w_-$ are reported (Appendix 1—table 1). For FRET, mean distances $\bar{R}_{DA,exp}$ (Appendix 1—table 1) and uncertainties of the mean are reported ($\Delta_+$ and $\Delta_-$) (Appendix 1—table 4). The measurements are grouped into three classes. Class (I) informs on $M_1$ and $M_2$ by two distinct distances. Class (II) informed on $M_1$. In class (III) measurements $M_1$ and $M_2$ were not resolved into separate states. The simulated average label-to-label distances correspond to the distances of the pair of structures (M1, M2) best agreeing with SAXS, DEER, and FRET combined (Figure 5—figure supplement 1).

<table><thead><tr><th rowspan="2">#</th><th rowspan="2">Technique</th><th colspan="3">Experiment</th><th colspan="2">Experiment</th><th colspan="2">Simulation</th><th rowspan="2">Class</th></tr><tr><th>Labelling site<sup>(a)</sup></th><th>M<sub>1</sub></th><th>M<sub>2</sub></th><th>M<sub>1</sub></th><th>M<sub>2</sub></th><th>M<sub>1</sub></th><th>M<sub>2</sub></th></tr><tr><th></th><th></th><th>1</th><th>2</th><th>R&#773;<sub>DA,exp</sub> / Å</th><th>(Δ<sub>+</sub>; Δ<sub>−</sub>) / Å</th><th>R&#773;<sub>DA,exp</sub> / Å</th><th>(Δ<sub>+</sub>; Δ<sub>−</sub>) / Å</th><th>R&#773;<sub>DA,sim</sub> / Å</th><th></th></tr></thead><tbody><tr><td>1</td><td>FRET</td><td>Q344C<sup>D</sup></td><td>N18C<sup>A</sup></td><td>73.6</td><td>(8.9; 8.3)</td><td>67.0</td><td>(5.6; 5.4)</td><td>73.9</td><td>62.3</td><td>(I)</td></tr><tr><td>2</td><td>FRET</td><td>V540C<sup>D</sup></td><td>N18C<sup>A</sup></td><td>57.8</td><td>(3.6; 3.6)</td><td>36.6</td><td>(2.7; 2.7)</td><td>63.9</td><td>40.3</td><td>(I)</td></tr><tr><td>3</td><td>FRET</td><td>N18C<sup>D</sup></td><td>Q577C<sup>A</sup></td><td>64.2</td><td>(4.7; 4.7)</td><td>47.4</td><td>(2.8; 2.8)</td><td>62.3</td><td>54.8</td><td>(I)</td></tr><tr><td>4</td><td>FRET</td><td>Q344C<sup>D</sup></td><td>Q254C<sup>A</sup></td><td>81.3</td><td>(17.9; 15.1)</td><td>72.3</td><td>(8.0; 7.6)</td><td>78.0</td><td>79.8</td><td>(I)</td></tr><tr><td>5</td><td>FRET</td><td>V540C<sup>D</sup></td><td>Q254C<sup>A</sup></td><td>63.6</td><td>(4.6; 4.5)</td><td>36.8</td><td>(2.7; 2.7)</td><td>63.2</td><td>41.3</td><td>(I)</td></tr><tr><td>6</td><td>FRET</td><td>Q344C<sup>D</sup></td><td>T481C<sup>A</sup></td><td>37.9</td><td>(2.6; 2.6)</td><td>54.4</td><td>(3.3; 3.3)</td><td>49.2</td><td>57.3</td><td>(I)</td></tr><tr><td>7</td><td>FRET</td><td>A496C<sup>D</sup></td><td>Q344C<sup>A</sup></td><td>48.0</td><td>(2.9; 2.9)</td><td>23.5</td><td>(8.2; 8.2)</td><td>43.4</td><td>38.3</td><td>(I)</td></tr><tr><td>8</td><td>FRET</td><td>Q344C<sup>D</sup></td><td>Q525C<sup>A</sup></td><td>46.7</td><td>(2.8; 2.8)</td><td>20.7</td><td>(13.3; 13.3)</td><td>43.6</td><td>28.0</td><td>(I)</td></tr></tbody></table>

Appendix 3—table 1 Continued on next page
<table><caption>Appendix 3—table 1 Continued</caption><thead><tr><th rowspan="3">#</th><th rowspan="3">Technique</th><th colspan="6">Experiment</th><th colspan="2">Simulation</th><th rowspan="3">Class</th></tr><tr><th colspan="2">Labelling site<sup>(a)</sup></th><th colspan="2">M<sub>1</sub></th><th colspan="2">M<sub>2</sub></th><th>M<sub>1</sub></th><th>M<sub>2</sub></th></tr><tr><th>1</th><th>2</th><th>R&#773;<sub>DA,exp</sub> / Å</th><th>(Δ<sub>+</sub>; Δ<sub>-</sub>) / Å</th><th>R&#773;<sub>DA,exp</sub> / Å</th><th>(Δ<sub>+</sub>; Δ<sub>-</sub>) / Å</th><th>R&#773;<sub>DA,sim</sub> / Å</th><th>R&#773;<sub>DA,sim</sub> / Å</th></tr></thead><tbody><tr><td>9</td><td>FRET</td><td>Q344C<sup>D</sup></td><td>V540C<sup>A</sup></td><td>59.3</td><td>(3.8; 3.8)</td><td>45.5</td><td>(2.8; 2.8)</td><td>53.1</td><td>45.5</td><td>(I)</td></tr><tr><td>10</td><td>FRET</td><td>Q577C<sup>D</sup></td><td>Q254C<sup>A</sup></td><td>70.8</td><td>(9.2; 9.0)</td><td>52.9</td><td>(7.4; 7.4)</td><td>75.2</td><td>35.4</td><td>(I)</td></tr><tr><td>#</td><td>Technique</td><td>1</td><td>2</td><td>⟨R<sub>ss,exp</sub>⟩ / Å</td><td>(w<sub>+</sub>; w<sub>-</sub>) / Å</td><td colspan="4">⟨R<sub>ss,sim</sub>⟩ / Å</td><td></td></tr><tr><td>11</td><td>DEER</td><td>C225C<sup>R1</sup></td><td>K567C<sup>R1</sup></td><td>12.0</td><td>(5.5; 5.5)</td><td>-<sup>(b)</sup></td><td>-</td><td>16.4</td><td>58.1</td><td>(II)</td></tr><tr><td>12</td><td>DEER</td><td>C225C<sup>R1</sup></td><td>Q577C<sup>R1</sup></td><td>22.9</td><td>(6.0; 6.0)</td><td>-<sup>(b)</sup></td><td>-</td><td>29.6</td><td>50.1</td><td>(II)</td></tr><tr><td></td><td></td><td colspan="2">M<sub>1</sub> &amp; M<sub>2</sub></td><td>M<sub>1</sub> &amp; M<sub>2</sub></td><td colspan="4">M<sub>1</sub></td><td>M<sub>2</sub></td><td></td></tr><tr><td></td><td></td><td colspan="2">R&#773;<sub>DA,exp</sub> / Å</td><td>(Δ<sub>+</sub>; Δ<sub>-</sub>) / Å</td><td colspan="4">R&#773;<sub>DA,sim</sub> / Å</td><td></td><td></td></tr><tr><td>13</td><td>FRET</td><td>T481C<sup>D</sup></td><td>Q525C<sup>A</sup></td><td>69.6</td><td>(6.6; 6.3)</td><td>(4.6; 4.6)</td><td></td><td>68.6</td><td>72.7</td><td>(III)</td></tr><tr><td>14</td><td>FRET</td><td>A496C<sup>D</sup></td><td>V540C<sup>A</sup></td><td>63.6</td><td></td><td></td><td></td><td>71.7</td><td>70.7</td><td>(III)</td></tr><tr><td>#</td><td>Technique</td><td>1</td><td>2</td><td>⟨R<sub>SS,exp</sub>⟩ / Å</td><td>(w<sub>+</sub>; w<sub>-</sub>) / Å</td><td colspan="4">⟨R<sub>SS,sim</sub>⟩ / Å</td><td></td></tr><tr><td>15</td><td>DEER</td><td>N18C<sup>R1</sup></td><td>Q344C<sup>R1</sup></td><td>64.6</td><td>(12.2; 12.2)</td><td></td><td></td><td>73.3</td><td>60.9</td><td>(III)</td></tr><tr><td>16</td><td>DEER</td><td>N18C<sup>R1</sup></td><td>Q577C<sup>R1</sup></td><td>53.2</td><td>(7.6; 7.6)</td><td></td><td></td><td>63.9</td><td>51.6</td><td>(III)</td></tr><tr><td>17</td><td>DEER</td><td>A551C<sup>R1</sup></td><td>Q577C<sup>R1</sup></td><td>20.5</td><td>(7.7; 7.7)</td><td></td><td></td><td>33.0</td><td>20.5</td><td>(III)</td></tr><tr><td>18</td><td>DEER</td><td>Q344C<sup>R1</sup></td><td>A496C<sup>R1</sup></td><td>40.0</td><td>(9.6; 9.6)</td><td></td><td></td><td>38.8</td><td>35.8</td><td>(III)</td></tr><tr><td>19</td><td>DEER</td><td>Q344C<sup>R1</sup></td><td>Q525C<sup>R1</sup></td><td>32.0</td><td>(2.7; 2.7)</td><td></td><td></td><td>36.7</td><td>25.0</td><td>(III)</td></tr><tr><td>20</td><td>DEER</td><td>Q344C<sup>R1</sup></td><td>V540C<sup>R1</sup></td><td>46.6</td><td>(6.8; 6.8)</td><td></td><td></td><td>51.4</td><td>47.9</td><td>(III)</td></tr><tr><td></td><td></td><td colspan="2">x<sub>r</sub><sup>2</sup></td><td colspan="4"></td><td>2.07</td><td>1.89</td><td></td></tr></tbody></table>

<table><caption>Appendix 3—table 2. Additional restraints for rigid body docking.</caption><thead><tr><th>Atom 1</th><th>Atom 1</th><th>Atom 2</th><th>Atom 2</th><th rowspan="2">R<sub>eq</sub> / Å</th><th rowspan="2">k<sub>ij+</sub> / Å</th><th rowspan="2">k<sub>ij-</sub> / Å</th><th rowspan="2">Restrain origin</th></tr><tr><th>Residue</th><th>Atom name</th><th>Residue</th><th>Atom name</th></tr></thead><tbody><tr><td>309</td><td>C</td><td>310</td><td>N</td><td>1.5</td><td>0.5</td><td>0.5</td><td>Primary sequence</td></tr><tr><td>373</td><td>C</td><td>374</td><td>N</td><td>1.5</td><td>0.5</td><td>0.5</td><td>Primary sequence</td></tr><tr><td>481</td><td>C</td><td>482</td><td>N</td><td>1.5</td><td>0.5</td><td>0.5</td><td>Primary sequence</td></tr><tr><td>563</td><td>C</td><td>564</td><td>N</td><td>1.5</td><td>0.5</td><td>0.5</td><td>Primary sequence</td></tr><tr><td>445</td><td>Cα</td><td>348</td><td>Cα</td><td>5.1</td><td>2</td><td>2</td><td>X-ray PDB-ID: 1DG3</td></tr><tr><td>391</td><td>Cα</td><td>336</td><td>Cα</td><td>8</td><td>4</td><td>4</td><td>X-ray PDB-ID: 1DG3</td></tr><tr><td>381</td><td>Cα</td><td>527</td><td>Cα</td><td>8.2</td><td>4</td><td>4</td><td>X-ray PDB-ID: 1DG3</td></tr><tr><td>323</td><td>Cα</td><td>292</td><td>Cα</td><td>9.3</td><td>4</td><td>4</td><td>X-ray PDB-ID: 1DG3</td></tr></tbody></table>

<footnote>(a) The names of the labelling sites report on the most likely position of the donor and the acceptor dyes. The distribution among the labelling sites was determined by an analysis of the time-resolved anisotropy decay, anisotropy PDA, and limited proteolysis of the labelled protein.</footnote>

<footnote>(b) Å consistency analysis (Figure 2—figure supplement 3D) identifies that M<sub>2</sub> must have long distances (⟨R<sub>SS,exp</sub>⟩ > 5 nm) beyond the DEER detection limit for this measurement setting (see Appendix 2 consistency analysis).</footnote>