Farnesylation of human guanylate-binding protein 1 as safety mechanism preventing structural rearrangements and uninduced dimerization

Human guanylate-binding protein 1 (hGBP1) belongs to the family of dynamin-like proteins and is activated by addition of nucleotides, leading to protein oligomerization and stimulated GTPase activity. In vivo, hGBP1 is post-translationally modiﬁed by attachment of a farnesyl group yielding farn-hGBP1. In this study, hydrodynamic differences in farn-hGBP1 and unmodiﬁed hGBP1 were investigated using dynamic light scattering (DLS), analytical ultracentrifugation (AUC) and analytical size-exclusion


Introduction
GTP-binding proteins are found in all three kingdoms of life and are mainly involved in regulatory functions of cellular processes like membrane deformation and signal transduction [1]. According to Gasper et al. [2], GTP-binding proteins can further be divided into conventional G proteins like Ras proteins with high nucleotide affinity and the necessity for nucleotide exchange factors for activation and signalling, and into G proteins that are activated by nucleotide-dependent dimerization (GADs). GADs are structurally characterized by the presence of large GTPase domains, a low intrinsic nucleotide affinity and cooperative GTPase activity upon self-assembly [2]. Furthermore, many members of this family are able to interact with lipid membranes [3]. Dynamin is a prominent member of the GAD family, which upon GTP binding and hydrolysis is able to catalyse scission of vesicles [4] from membranes by forming long helical oligomers [5].
Human guanylate-binding protein 1 (hGBP1) belongs to the family of dynamin-related large GTPbinding proteins [6]. The crystal structure of full-length hGBP1 consists of three domains (Fig. 1A), a N-terminal large GTPase domain (LG), a middle domain consisting of a-helices and a GTPase effector domain. Overall, the crystal structure (Fig. 1A) is elongated with the globular N-terminal LG domain on one side and a long a-helix 12 spanning back from the middle domain to the LG domain over a range of approximately 130 A. This helix is followed by the very short a-helix 13, which runs antiparallel and closely packed to a-helix 12. The three members hGBP1, hGBP2 and hGBP5 of the hGBP family possess a C-terminal prenylation motif (CaaX) that leads to post-translational attachment of a C-15 or C-20 isoprenyl group [7]. In the case of hGBP1, it was shown that the C-15 farnesyl moiety is covalently attached to the cysteine of the CaaX-binding motif (Fig. 1A). This modification is essential for intracellular formation of vesiclelike structures [7]. Moreover, it was shown in vitro that vesicle association is dependent on farnesylation [8].
Oligomerization properties of hGBP1 after nucleotide addition were reported first from size-exclusion chromatography (SEC) and dynamic light scattering (DLS) experiments. Without nucleotides, hGBP1 was proposed to be monomeric, whereas after addition of nonhydrolyzable GTP analogues like GppNHp, it was classified as a dimer [6,9]. Dimerization of hGBP1 is most prominently mediated by the formation of headto-head dimers that are facing each other via the LG domain interfaces, as it was suggested from crystal structures of the isolated LG domains in the presence of nucleotides and other biochemical assays like mutational studies [9,10]. A potential hGBP1 dimer model based on the crystallographic LG domains and the monomer crystal structure is shown in Fig. 1B. More recently, in a study by V€ opel et al. [11] based on FRET and EPR distance measurements, the crystal dimer model has been challenged. It has been suggested that in addition to the crystallographic dimer model there exists a distorted and more opened hGBP1 dimer in solution as well. In the opened hGBP1 dimer, helices 13 can interact with each other forming a coiled-coil structure, which is not possible in the crystallographic dimer model due to structural constraints. Moreover, interaction of helices 13 in the dimer would allow to bring the farnesyl groups of two proteins in close contact as the farnesyl group is attached to the C-terminal CaaX motif of helix 13. In the first description of farn-hGBP1 purification by Fres et al. [8], it was proposed that hGBP1 undergoes structural changes after farnesylation as the protein surface is less hydrophobic compared to the nonfarnesylated protein, which was observed during purification on a hydrophobic interaction chromatography column [8]. It was proposed that the C terminus with its hydrophobic amino acids is internally hidden after farnesylation [8].
In this study, we investigated the structural differences between the ground states (inactive/nucleotide free) of the unmodified and farnesylated hGBP1 (farn-hGBP1) in solution. In addition, we investigated the effect of GppNHp binding on unmodified hGBP1. GppNHp is a nonhydrolyzable analogue mimicking the nucleotide-bound state in solution. For that purpose, we have performed a set of experiments using DLS, SEC and analytical ultracentrifugation (AUC). After observation of differences in their hydrodynamic properties, we have used small-angle X-ray scattering (SAXS) to clarify the structural origin of the hydrodynamic differences. We found a monomer-dimer equilibrium with a dimer fraction of around 10-20% of the commonly used nonmodified hGBP1 even in nucleotide-free solution and in the presence of GppNHp under standard conditions (2 mgÁmL À1 or 30 lM hGBP1 in Tris buffered solution at pH 7.9). Moreover, we observed strong structural perturbations of the hGBP1 monomer in the presence of GppNHp. The hGBP1 dimer was found to be structurally distorted and the obtained solution structures agree with an opened solution structure, which might be relevant for oligomerization of farn-hGBP1 as described in recent electron microscopy and fluorescence studies [12]. The combination of the different techniques led us to the conclusion that farnesylation of hGBP1 is needed to prevent oligomerization and to stabilize the inactive ground state before activation of hGBP1 by nucleotides in solution occurs ensuring a controlled signal transduction mechanism.

Verification of monodispersity and quality control by DLS
Dynamic light scattering was measured to verify the required sample quality for AUC and SAXS experiments and to determine the hydrodynamic radius R h of the protein at infinite dilution. Nucleotide-free solutions of hGBP1 and farn-hGBP1 as well as hGBP1 solution containing 1 mM GppNHp were measured using DLS. Intensity-weighted size distributions of all investigated samples show only one peak demonstrating the absence of protein aggregation at all measured protein concentrations. Illustratively, the fitted time correlation data and intensity-weighted size distributions obtained from 1 mgÁmL À1 protein solutions are shown in Fig. 2. Hydrodynamic radii were calculated from the DLS correlation functions and the R h values were linearly extrapolated for c ? 0 mgÁmL À1 . R h values at infinite dilution of the investigated samples are given in Table 1. Theoretical R h values were calculated from the monomer crystal structure (1DG3) and the dimer model (1F5N -2BC9) using the computer programs HYDROPRO and SOMO, see Table 1.
The calculated R h values of the monomer crystal structure are 4.0/3.8 nm (HYDROPRO/SoMo) and 5.7/5.3 nm for the dimer model. All experimentally determined diffusion coefficients lie between the theoretical values of monomer and dimer. The measured hydrodynamic radius of farn-hGBP1 with 4.74 nm is smaller than that of nucleotide-free hGBP1 with 5.73 nm, although hGBP1 in nucleotide-free solution was proposed to be monomeric. As described earlier [13], we observe an increase in the measured R h value of hGBP1 upon addition of GppNHp. That observation would be in agreement with assumed dimerization of hGBP1 in the presence of GppNHp [13].
Our DLS experiments point out that farn-hGBP1 has similar hydrodynamic properties compared to the crystal structure of hGBP1, whereas hGBP1 in nucleotide-free solution and in the presence of GppNHp has a larger apparent hydrodynamic radius lying in between that of the theoretical values of monomer and dimer. DLS does not allow to separate an eventually occurring monomer-dimer equilibrium. A mixture of monomer and dimer would result in a higher apparent hydrodynamic radius. A structural expansion of monomeric hGBP1 would also result in a larger hydrodynamic radius possibly approaching that of the hGBP1 dimer model. Therefore, the larger hydrodynamic radii of hGBP1 in nucleotide-free and in the presence of GppNHp could be either caused by a monomer-dimer equilibrium or due to structural expansion of monomeric hGBP1. Hence, we investigated the oligomeric distribution further using SEC and AUC experiments that allow to distinguish monomers and dimers in solution.

Hydrodynamic properties investigated by SEC and AUC
Size-exclusion chromatography experiments of hGBP1 were already performed in earlier studies [6,14,15] with the aim to determine the oligomeric state of hGBP1 in solution. An important recent finding was that the elution properties of hGBP1 are not only dependent on the presence or absence of nucleotides but also on the salt concentration. Therefore, we ensured that the chosen buffer composition in our study is the same buffer condition as described in the previous work [15]. Molecular mass calibration of SEC columns is routinely performed for globular proteins, which obey a linear correlation of R h 3 / M m . For the case of  The discrepancy is more pronounced for the second elution peak of the dimer fraction. There we obtain molecular masses of 236.40 kDa for hGBP1 and 274.72 kDa in the presence of GppNHp, which is in the range of trimers to tetramers. The dimeric nature of this second species is corroborated from the following AUC experiments and will further be discussed from the SEC-SAXS results where scattering intensity and concentration measurement in-line can confirm the dimeric nature of this eluting species. This information leads to the conclusion that for hGBP1, the standard molecular weight calibration of SEC elution volumes is not suitable. Therefore, we performed a calibration of the SEC column based on the hydrodynamic radius of reference proteins calculated using the program SOMO as  Table 2. The separation based on hydrodynamic properties on the SEC column in nucleotide-free solution shows pronounced differences between farnesylated and unmodified hGBP1 similar to the previous DLS results. Whereas farn-hGBP1 elutes as one peak from the column with a hydrodynamic radius of 3.77 nm, two elution peaks with R h values of 3.82 and 5.01 nm for nucleotide-free hGBP1 are visible. In the presence of GppNHp, hGBP1 shows a similar elution profile compared to nucleotide-free condition with the monomer as the main elution fraction and the dimer giving a secondary peak corresponding to shifted R h values of 4.01 and 5.22 nm respectively. Apparently, the SEC column used in our study shows a higher separation capacity than that used in a previous study [15], where SEC peaks due to hGBP1 dimers only appeared as broad shoulders. The lower separation capacity of the column used by Ince et al. [15] is most likely due to ageing of the column (personal communication).
The SEC results affirm the initial observation by DLS that farn-hGBP1 appears always monodisperse in the most compact conformation corresponding to a pure monomer fraction. Moreover, the hydrodynamic radius of 3.77 nm is in excellent agreement with the theoretical R h of the crystal structure conformation of the monomeric hGBP1 (R h = 3.79 nm calculated with SoMo of pdb ID 1DG3). Without the farnesylation,  the main peak of hGBP1 is also in the radius range of a monomer, but slightly larger than farn-hGBP1. In the presence of GppNHp, the R h values of 4.01 and 5.22 nm are shifted and indicative of a structural expansion of hGBP1 upon GppNHp binding. Additionally, a small third fraction due to higher oligomers or aggregates is visible in the elution profiles (volume fraction of less than 2%) that we have neglected in our analysis and discussion. For further analysis of the oligomeric state of hGBP1 in solution, we performed AUC experiments. Using AUC, we obtain physical parameters calculated from hydrodynamic measurements, for example, the sedimentation coefficient s 20,W , which gives additional information on conformational changes. The frictional ratio f/f 0 is informative on protein globularity and is used to calculate the molecular mass of the separated species based on f/f 0 which was assumed to be equal for all fitted species. Sedimentation velocity analysis of hGBP1 confirms the observed distribution of different oligomeric states even in the absence of nucleotides for hGBP1. The AUC experimental data are evaluated as described before, importantly they are resolved into up to three different species, which are present in solution during the AUC run. Measured AUC absorption data of nucleotide-free hGBP1 and in the presence of GppNHp are shown in Fig. 4. The results of the c(s) distribution analysis with a weight averaged f/f 0 ratio are depicted in Fig. 3A. Sedimentation coefficients, frictional ratios and molecular masses obtained from the distribution analysis are reported in Table 3 together with theoretical values of the monomer (pdb ID 1DG3) and dimer model (1F5N-2BC9) calculated with SoMo.
As in the case of SEC profiles, we observe a single distribution peak of farn-hGBP1, while two distinct peaks are found for nonmodified hGBP1 in the presence and absence of GppNHp (Fig. 3). A third minor peak is found for the nonmodified hGBP1. The two main peaks correspond to the monomeric and dimeric forms of the protein with molecular masses of 59.0-61.6 kDa for the monomer and 106.0-110.0 kDa for the dimer, see Table 3. The third minor AUC distribution peak is always around 9.2-9.6 S corresponding to a molecular weight of around 225 kDa under the assumption of the same f/f 0 value for all three species.
The obtained c(s) distribution for farn-hGBP1 always consists of only one peak (100% peak 1 as shown in Fig. 3A) corresponding to the monomeric protein for all measured conditions. The theoretical sedimentation coefficient of the monomeric crystal structure (pdb ID 1DG3) as calculated using SoMo is 3.96 S being almost identical with experimentally determined sedimentation coefficients of the  monomeric farn-hGBP1 and hGBP1 in the absence of nucleotide with 4.11 and 4.05 S respectively. The measured sedimentation coefficient of hGBP1 in the presence of GppNHp is 4.22 S being larger than that of the crystal structure, which indicates a modified conformation or altered hydration shell of the hGBP1 monomer due to GppNHp binding. The theoretical sedimentation coefficient of the hGBP1 dimer model 1F5N-2BC9 is 5.61 S. The experimentally determined sedimentation coefficients of the hGBP1 dimers in the absence and presence of nucleotide are larger than the theoretical value of the dimer model indicative of a different shape of the hGBP1 dimer in solution. The experimental value of the hGBP1 dimer in the presence of GppNHp appears to be larger than that in nucleotide-free solution indicative of structural rearrangements induced by GppNHp binding as well.
The frictional ratio f/f 0 reflects both the shape and hydration of the protein molecule and can be considered as an approximate measure of the protein globularity. Here, a similar frictional ratio with 1.35 of farn-hGBP1 and 1.30 of nucleotide-free hGBP1 is observed, while GppNHp results with 1.14 in a smaller f/f 0 value of hGBP1. The smaller ratio could be due to the weight averaging of f/f 0 in the c(s) analysis and is, therefore, not further discussed.

Structural investigations by SAXS
Small-angle X-ray scattering experiments were performed to gain structural information of farn-hGBP1 and hGBP1 in solution at low resolution. We performed SEC-SAXS experiments, where monomers, dimers and higher order oligomers are separated on a SEC column that is directly connected to the SAXS instrument. SEC elution profiles of the monomer and dimer fractions overlaid with fitted radii of gyration R g and forward scattering I(0) from each recorded SAXS frame in the peak regions are shown in Fig. 5. Resulting SAXS data of hGBP1 and farn-hGBP1 monomers and dimers are presented in Fig. 6. Primary physical parameters were calculated from the SEC-SAXS data of the hGBP1 and farn-hGBP1 monomers and the hGBP1 dimers as described in Material and Methods. Radii of gyration R g , maximal protein dimensions D max , Porod volumes V Porod , volumes of correlation V c and experimental molecular masses M m determined from V Porod and V c as well as the   Tables 4 and 5.

Solution structures of hGBP1 and farn-hGBP1 monomers
At first glance, the measured SEC-SAXS monomer scattering curves of farn-hGBP1 and hGBP1 are of similar shape for all conditions, see Fig. 6. The black crosses in the normalized Kratky plots of hGBP1 monomer and dimer at the position ( ffiffi ffi 3 p , 1.104)see middle panels in Fig. 6 indicate the position at which a globular monodomain protein that fulfils the Guinier approximation would have its maximum in a normalized Kratky plot [16]. The deviation of the peak positions of the hGBP1 monomer and dimer from that ideal value are related to the asymmetry of the protein and potentially also due to the intrinsic flexibility of hGBP1 [16]. Subtle structural differences are observed when considering the experimentally determined R g and D max values. The Guinier analysis confirms the earlier result by SEC and AUC that farn-hGBP1 has the most compact shape with a real space R g of 3.85 nm of the monomer. The nucleotide-free hGBP1 monomer has a R g derived from Guinier analysis of 3.89 nm, which is in a similar range as the farn-hGBP1 radius. The hGBP1 monomer in the presence of GppNHp, however, is more extended with a R g of 4.49 nm. That observation is also visible in the determined D max values. The SEC-SAXS data of the monomeric structures confirm the previous observations by SEC and AUC of similar shapes of the farn-hGBP1 and nucleotide-free hGBP1 monomer, whereas GppNHp-bound hGBP1 monomer is more extended and structurally perturbed. Another hint for structural rearrangements next to the enlarged R g in the presence of GppNHp is the volume of correlation change (Table 4). With 547. 17 A 2 for farn-hGBP1 and 570.21 or 610. 35 A 2 for hGBP1 without nucleotide or with GppNHp, respectively, V c deviates by 4% or 12% from the most compact conformation, which is the farn-hGBP1 monomer.
To investigate, whether the farn-hGBP1 and hGBP1 monomers are similar to the reported crystal structure (pdb ID 1DG3), we first calculated the theoretical SAXS pattern of the monomeric crystal structure using the program CRYSOL and fitted the theoretical scattering curve to the measured SEC-SAXS data of the different monomers (Fig. 7A). Concerning farn-hGBP1 in nucleotide-free solution, the fit yields a good agreement with the experimental data (v 2 = 2.61). In comparison to farn-hGBP1, nucleotide-free hGBP1 has a larger v 2 value of 15.06 showing that the conformation in solution is different from the rigid crystal structure. Concerning hGBP1 in the presence of GppNHp, the fit quality is very poor (v 2 = 636.12) and the residuals shown in Fig. 7A at the bottom reveal significant deviations between the theoretical curve and the measured SAXS data. Structural perturbation of GppNHpbound monomeric hGBP1 is also visible in the larger R G and R h values (see Tables 1, 2 and 4). The analysis of the molecular mass of the monomers for all conditions shows a deviation from the expected theoretical value of 69.17 kDa by 5-8%, which is an expected range for small-angle scattering data analysis [17] and underlines the correct classification of this species as monomer.
EOM modelling was performed as a next step. Good fits to the SEC-SAXS in the q-range up to 0.2 A À1 were obtained (v 2 = 1.10 for farn-hGBP1, v 2 = 1.69 for hGBP1, and v 2 = 46.35 for hGBP1+GppNHp). Experimental SEC-SAXS data with EOM fits are shown in Fig. 8A. From EOM conformational ensemble  Fig. 9. For farn-hGBP1 and hGBP1, the best structural models are found in two clusters with R G around 35 and 45 A, whereas in the presence of GppNHp the clusters are shifted to higher R G values. In the D max distribution, the values of farn-hGBP1 and hGBP1 are single peaked, while the D max distribution hGBP1+GppNHp is significantly broadened demonstrating a larger conformational flexibility of hGBP1+GppNHp as compared to farn-hGBP1 and nucleotide-free hGBP1. EOM additionally provides a parameter R flex to allow a quantitative characterization of the distributions. R flex is coupled with the entropy of the protein and, therefore, to the flexibility of the system. A low entropy content corresponds to a low R flex value. Highly flexible proteins on the other hand have high R flex values. A theoretical protein having Gaussian-like chain statistics would have R flex = 100% [18]. Moreover, R flex parameters calculated by (Ensemble Optimization Method) EOM allow to quantify the flexibility of the proteins in comparison to the generated structural pool. The obtained R flex parameters are 76.2% for farn-hGBP1, 80.6% for nucleotide-free hGBP1 and 81.5% for hGBP1+GppNHp, while the corresponding value of the structural pool is 91.3%. As stated before, R flex of 100% would correspond to a Gaussian-like distribution of structural parameters with randomly aligned regions in solution. Those R flex values are indicative of a less flexible farn-hGBP1 and significantly more flexible hGBP1 monomers without the farnesyl group being attached [18]. Structural rigid-body modelling using SASREF was performed as well and gave excellent fits up to q = 0.3 A À1 based on the residual deviation of the fit from the experimental data (v 2 = 3.02 for farn-hGBP1, v 2 = 1.39 for hGBP1, but v 2 = 41.48 for hGBP1+GppNHp). Experimental SEC-SAXS data of the monomers and SASREF fits are shown in Fig. 10. Using SASREF, only a single structure is refined against the SEC-SAXS data, while for EOM analysis a conformational ensemble is generated. However, SASREF models allow to visualize the measured SEC-SAXS data as average structural models. Rigid-body modelling fails for larger q-ranges due to local structural perturbations that cannot be modelled using only rigid-body domains. Obtained structural SASREF models are shown in Fig. 10 as well. While for farn-hGBP1, a structure is obtained that is very similar to the crystal structure, the obtained models for nucleotide-free hGBP1 and hGBP1+GppNHp show the structural perturbation of the protein directly. The conformational flexibility of hGBP1 monomer is due to a reorientation of helices 12 and 13 that is more pronounced in the presence of GppNHp.

Solution structures of dimeric hGBP1
The second SEC-SAXS elution peak, which was further analysed, is in the range of 1.32-1.40 V e /V o eluting from the SEC column and only appears for nonfarnesylated hGBP1 in nucleotide-free buffer or in the presence of GppNHp. The analysis of the molecular mass by Porod volume and the volume of correlation confirms that this is a dimeric species of hGBP1 with a deviation from the expected theoretical dimer weight of 138.34 kDa by 5-18% (Table 5). Another hint for the dimeric nature of this species is the comparison of absorption to forward scattering intensity (Fig. 5) where I(0) is always higher by approximately a factor of 2 in this region compared to absorption at 280 nm when both are normalized to 1 at the maximum peak position. The absorption is indicative for the total number of proteins in solution, hence a bulk property. The forward scattering I(0), however, is proportional to the number of electrons contained in a scattering volume. This means that the molecular mass is higher in this eluting species by approximately a factor of 2 compared to the first monomer peak, to which the chromatogram is normalized. Considering the hGBP1 dimers, we find similar radii of gyration and maximal dimensions indicative of similar dimer structures in the presence and absence of nucleotide.
As a first step, we calculated the theoretical scattering function of the dimer model (see Fig. 1B) using the program CRYSOL and compared the theoretical fits to the measured SEC-SAXS data of the hGBP1 dimers, shown in Fig. 7B. From a visual inspection of the fits, it is already clear that the dimer model does not reproduce the measured SEC-SAXS data. This is particularly clear for the double peak structure visible in the Kratky plot (middle panel of Fig. 7B) that is not reproduced at all by the theoretical model. That observation is corroborated by the obtained v 2 values EOM analysis was performed as a next step and the experimental SEC-SAXS data with EOM-based fits are shown in Fig. 8B in the q-range up to 0.2 A À1 . Obtained Rflex-values are 0.85 and 1.49 for hGBP1 and hGBP1+GppNHp dimers, respectively, indicative of good fits to the data. Obtained R g and D max distributions are presented in Fig. 9B and D. Two differently occupied clusters of dimer conformations are obtained indicative of two distinct structural states. For hGBP1+GppNHp, the major peak is significantly broadened, indicative of enhanced structural flexibility as compared to the nucleotide-free hGBP1 dimer. The obtained R flex -values corroborate the larger structural plasticity of the hGBP1+GppNHp dimer with R flex = 74.1% and 80.6% for nucleotide-free and GppNHp solution, respectively, while R flex = 90.4% corresponds to the flexibility of the generated structural pool.
Using the rigid-body modelling approach from SAS-REF, dimeric hGBP1 constructs are calculated and presented in Fig. 11 together with the experimental SEC-SAXS data in the q-range up to 0.3 A À1 . During SAS-REF modelling the structural constraint was considered that the helices 13 remain in contact with each other, which is based on the previous FRET and EPR study by V€ opel et al. [11]. The v 2 -values of the fits are 0.91 and 6.40 for hGBP1 and hGBP1+GppNHp dimers, respectively, indicative of good fits to the data as well. The theoretical curves represent the characteristic double peak of the Kratky plots very well. Obtained structural models of both hGBP1 dimers are shown in Fig. 11B. Both models show a perturbed and flexible dimer structure with opened middle domains.

Validation of structural rigid-body models by their hydrodynamic properties
To validate the obtained rigid-body models that have been obtained by SAXS, we calculated their  Tables 6  and 7. Good and reasonable agreement between calculated R h and R g values and corresponding experimental parameters is found for all monomer and dimer models. Calculated sedimentation coefficients of hGBP1 and farn-hGBP1 monomers are systematically underestimated. For hGBP1, the calculated dimer structure shows similar hydrodynamic properties compared to the earlier SEC and AUC experiments. In the presence of GppNHp, the parameters of the calculated dimer systematically deviate from the experimentally determined sedimentation coefficient.

Discussion
Previous studies have reported that hGBP1 is a flexible molecule that can undergo large conformational changes upon activation by nucleotides. This was proven, for example, with biochemical assays like amino acid accessibility on the surface by V€ opel et al. [19]. In that study by V€ opel et al., it has been shown that in the presence of GppNHp, the buried cysteines are better accessible compared to the control condition in the presence of GMP or nucleotide-free solution, which is indicative of higher flexibility in the protein in the presence of GppNHp. Moreover, in the presence of GTP, the authors proposed that a cysteine becomes accessible, which is located on helix 4 0 (see Fig. 1) and is usually buried between LG domain and C-terminal helices 12/ 13. This movement of helix 4 0 was also indicated from the crystallographic dimer structures of the LG domains as helix 4 0 would clash with helix 12/13 when the full- length crystallographic structure is aligned to it. Therefore, it has been proposed that the LG domain and helices 12/13 move away from each other in the course of GTP hydrolysis. In later studies using FRET and EPR, it was shown that helix 13 detaches from helix 12, which allows helix 13 to establish a second dimer interface of two hGBP1 proteins [11]. Recent studies on farn-hGBP1as found under physiological conditions illustrate that farn-hGBP1 can build up large polymeric structures that are relevant for membrane interactions [12]. For the mechanism of polymerization of farn-hGBP1, it was suspected that a large rearrangement by opening and particularly releasing the a12/13 domain upon GTP binding is necessary [11,13,19] and a nucleotide-dependent release of the farnesyl anchor mediates the opening of hGBP1 and allows hydrophobic interactions [12]. Our study on hydrodynamic and structural differences between farn-hGBP and hGBP shows that farn-hGBP1 under nucleotide-free conditions is present as monomer only, while hGBP1 both under nucleotidefree and GppNHp solution conditions is present as a monomer-dimer equilibrium. The solution structure of farn-hGBP1 monomer is in a compact crystal-like conformation as seen by its hydrodynamic behaviour and its solution structure. Without the farnesyl moiety, the hGBP1 monomer shows structural perturbations as compared to the crystal structure with increased conformational flexibility, which is strongly enhanced upon GppNHp binding. Rigid-body models of nonmodified hGBP1 derived from SAXS data suggest that observed structural plasticity is caused by a-helices 12 and 13 that detach from the rest of the protein being significantly more flexible for the GppNHp-bound hGBP1 monomer. The solution structures of hGBP1 and farn-hGBP1 determined by SAXS are cross-validated with their experimentally determined hydrodynamic properties as measured by DLS and AUC, see Tables 7 and 8.
A further novel result that we report in our study is the fact that a dimeric hGBP1 structure is found for nonmodified hGBP1 in the absence and presence of GppNHp. Up to now, it has been assumed that nonmodified nucleotide-free hGBP1 is entirely monomeric in solution, while hGBP1 in the presence of GppNHp forms purely dimers. Our experimental results demonstrate that this is not the case, the monomer-dimer equilibrium of hGBP1 is established independently of the presence of nucleotides. Solution structures of dimeric hGBP1 are not in agreement with the dimer model that is based on available crystal structures (see Fig. 1B). Instead, the hGBP1 dimer in solution shows structural perturbations similar to its monomeric state: a-helices 12/13 are detached from the protein and rigid-body modelling agrees with a dimerization interface formed by two a13 helices of two hGBP1. The double peak of dimeric hGBP1 visible in the Kratky peak is the characteristic feature of the protein in solution. It can only be reconstructed by structurally perturbed and opened hGBP1 dimer models. Furthermore, structural flexibility of hGBP1 dimer in the presence of GppNHp is increased as compared to the nucleotide-free state, which is also observed for the hGBP1 monomer. As the appearance of dimers is completely vanished in the presence of farnesylation, this post-translational modification seems to be important as a safety mechanism to prevent uninduced signal transduction under biological conditions in cells. The earlier described dimers formed via the LG interface can already occur under nucleotide-free conditions of nonmodified hGBP1. This observation underlines and confirms the earlier proposed dimerization mechanism of the previously described domain movements of a12/13 domain upon GTP binding. The dimeric fractions of hGBP1 are surprisingly already present under nucleotide-free conditions in the chosen concentration range that is appropriate for SEC, AUC and SAXS measurements. The high flexibility of the dimer as shown from EOM analysis could be very important to mediate further oligomerization and demonstrate the first molecular steps that occur during the supramolecular assembly process of farn-hGBP1 in the presence of GTP and GDP AlFx as already observed before. This principle of conformational flexibility for signal transduction has been observed for light-sensitive signalling proteins as well [20,21]. Opened hGBP1 dimer structures would enable the formation of circular nucleation discs of farn-hGBP1 with fully extended hGBP1 and LG domains pointing at the outside of the oligomer, while the farnesyl group is located in the centre of the disc as previously suggested based on cryo-TEM images [12]. Future work will be directed to investigate the occurrence of structural perturbations induced by nucleotides during the assembly process of farn-hGBP1 to the observed supramolecular structures.

Expression and purification of unmodified and farnesylated hGBP1
Unmodified and farnesylated hGBP1 were purified as described earlier [8,22]. In short, for expression of farnesylated  -hGBP1), the plasmid containing the hGBP1 gene was coexpressed with a plasmid coding for human farnesyltransferase subunits a/b. The plasmids were obtained from G. Praefcke as a friendly gift and are the same as used in earlier publications and as the full-length protein used for crystallization [6,23]. Plasmids containing hGBP1 (pQE80L) and/or farnesyltransferase subunits (pRSF-DUET1) were transformed in Escherichia coli BL21(DE3)-RIL cells using the heat shock method, cultivated in Terrific Broth (TB) medium supplemented with 100 lgÁmL À1 ampicillin and/or 50 lgÁmL À1 kanamycin, respectively, and expression was induced by the addition of 100 lM isopropyl-D-thiogalactopyranoside. After 16 h at 22°C, cells were harvested by centrifugation at 5000 g for 20 min at 4°C.

Purification of hGBP1
Cells were resuspended in buffer containing 50 mM Tris-HCl (pH 7.9), 5 mM MgCl 2 , 500 mM NaCl and 10% glycerol (v/v) and disrupted using a tip sonicator (Bandelin-Sonoplus, Berlin, Germany) or a French pressure cell (Thermo Scientific, Waltham, MA, USA) with a maximum pressure of 1.7 kbar at 4°C. After centrifugation at 15 000 g for 60 min at 4°C, the supernatant was subjected to His 6 -tag affinity chromatography (HisPur Cobalt Resin, Thermo Scientific, or TALON superflow, GE Healthcare, Chicago, IL, USA). hGBP1 containing fractions were combined and ammonium sulphate was added to a final concentration of 3 M. After 10 min of stirring at room temperature, the precipitate was separated by centrifugation at 7140 g for 15 min at 4°C. The pellet was either stored at À80°C or directly resuspended in buffer C [50 mM Tris-HCl (pH 7.9), 5 mM MgCl 2 , 150 mM NaCl] and applied onto a Superdex 200 26/60 column. All fractions containing monomeric hGBP1 were combined, concentrated to a final concentration of about 100 mgÁmL À1 and frozen in liquid nitrogen for storage at À80°C. The protein purity was analysed by SDS/PAGE (4-20% gradient gel, Expedeon).

Purification of farn-hGBP1
The purification strategy was the same as described for hGBP1, with an additional hydrophobic interaction chromatography (HIC, HiTrap Butyl HP, GE Healthcare) step for separation of unmodified from farnesylated hGBP1 after His 6 -tag affinity chromatography. The HIC column was equilibrated with buffer containing high salt concentration (50 mM Tris-HCl (pH 7.9), 5 mM MgCl 2 and 1.2 M (NH 4 ) 2 SO 4 ) and eluted with low salt buffer (50 mM Tris-HCl (pH 7.9), 5 mM MgCl 2 ). After His 6 -tag affinity as well as after HIC chromatography, the protein containing fractions were precipitated using 3 M (NH 4 ) 2 SO 4 as described for the unmodified hGBP1 before.

Sample preparation for AUC, DLS and SAXS measurements
All buffers were degassed before usage and samples were freshly prepared directly before the respective measurements. Protein concentration was determined on a Nano-Drop 2000c Spectrophotometer (Thermo Scientific) using an extinction coefficient of 46 340 M À1 Ácm À1 (calculated with full-length amino acid sequence of hGBP1 with His 6tag using ProtParam on the ExPASy server).
The concentrated protein stock solution was diluted in buffer C to desired concentrations. Possible higher aggregates were removed by centrifugation at 13 400 g for 22 min at room temperature and the supernatant was used for measurements. For measurements in the presence of GppNHp, the nucleotide was added directly before the measurement at the desired concentration as indicated in the results part (either 0.2, 1.0 or 1.5 mM final nucleotide concentration) and samples were incubated 10-30 min at room temperature.

Dynamic light scattering
Translational diffusion coefficients (D trans ) of the different samples were measured using dynamic light scattering experiments on a Malvern Zetasizer Nano ZS instrument (4 mW He-Ne laser, k = 633 nm, h = 173°). At least three different protein concentrations between 0.2 and 5 mgÁmL À1 were measured with at least 15 runs per measurement to extrapolate the translational diffusion coefficient to zero concentration D trans (conc ? 0). D trans and Stokes radii were calculated using the standard protein analysis mode of the instrument's software which is a non-negative least squares (NNLS) analysis followed by L-curve regularizer calculation.

Analytical size-exclusion chromatography
Samples of hGBP1 were prepared as described before to final protein concentrations of 2 or 13 mgÁmL À1 in buffer C. The samples were incubated for 30 min at room temperature before injection on the gel filtration column (Superdex 200 10/300 GL, GE Healthcare). The elution profile was monitored by absorption at 280 nm using an € Akta Purification system (FPLC, GE Healthcare). The calibration of the system was done using commercially available standard proteins (blue dextran, ferritin, catalase, conalbumin, ovalbumin) as well as BSA (monomers/dimers with 66/132 kDa) and farn-hGBP1 (monomer with 69 kDa) under the same running and buffer conditions. The calibration runs were used to determine the column-specific calibration curve. As the crystal structure of hGBP1 exists in an elongated shape, the assumption of globular eluting particles does not hold and, therefore, the molecular weight calibration is error prone (Eq. 2). We preferred to calculate The oligomeric distribution was estimated by peak area integration of each peak divided by the total peak area of all peaks.

Analytical ultracentrifugation
All samples were freshly prepared for centrifugation experiments as described earlier. Sedimentation experiments were performed using a Beckman Coulter ultracentrifuge equipped with an absorption optical scanner (Optima XL-A) at 10°C with 116,272 g. The detection wavelength was chosen between 290 and 300 nm in order to keep the signal contribution from the added nucleotide small. An 8-hole titanium rotor loaded with titanium double sector cells (1.2 cm optical path length) with quartz windows had been used for the measurements. Data recording was performed after thorough thermal equilibration in intensity mode with a radial step size of 0.002 cm.
Partial specific volume m of the protein was estimated using Sednterp [24] for the protein sequence of hGBP1 with attached His-tag (0.73627 cm 3 Ág À1 at 22°C, 0.73754 cm 3 Ág À1 at 20°C and 0.73117 cm 3 Ág À1 at 10°C). Buffer viscosity and density were measured for all buffers with or without added nucleotide (Anton Paar DMA5000, Anton Paar Microviscosimeter Lovis 2000 M), see Table 8. The AUC data were analysed using the software SEDFIT with continuous c(s) distribution model. The minimal chosen resolution was 0.1 S with at least s min = 1 S and s max = 15 S and applying a logarithmic s-space for all samples. The conventional c(s) distribution as described by Schuck [25] is confined to a single frictional ratio, which is determined as a weight-average frictional ratio f/f 0 of all sedimenting material from nonlinear optimization of this parameter [26]. To simplify the comparison of the results, the obtained sedimentation coefficients are transformed to standard solvent conditions of water at 20°C [27]. s 20;w ¼ s exp g exp g 20;w 1 À m 20;w Á q 20;w 1 À m exp Á q exp ð3Þ Oligomer distribution was determined from the obtained c(s 20,w ) distributions. Peak maxima are determined with a threshold of 1% of the distributions maximum peak height. The peak limits are chosen by reaching a local minimum or 20% of the peak's height. The peak area is then calculated with Simpson's rule integration. For estimation of the oligomeric fraction m, integrated peak areas of each peak are divided by the total sum of all peaks.

Small-angle X-ray scattering
Size-exclusion chromatography coupled with small-angle Xray scattering measurements were performed at beamline BM29 at the European Synchrotron Radiation Facility (ESRF) [28] with k = 0.992 A as the X-ray wavelength (corresponding to an energy of 12.5 keV) in-line with a size-exclusion column (SEC) (Superdex 200 10/300 GL, GE Healthcare) [29]. The X-ray beam size at the sample position is around 700 9 700 lm 2 and a Pilatus 1M detector was used. Photon flux at sample position of BM29 is reported to be up to 10 12 photons/s at maximal ESRF ring current [28]. Ring current of the ESRF during the SAXS experiment was 200 mA, which is the maximal current of the machine. The scattering vector q is defined as q = 4p/ kÁsin (h/2) with the incident wavelength k and scattering angle h. The measurements cover an effective q-range from 0.006 to 0.49 A À1 . All samples were prepared as described before with applied protein concentrations in the range of 2-55 mgÁmL À1 that are injected into a 100 lL loop. SAXS frames were recorded every 1 s during elution and the first 50 files of the run were automatically selected and averaged by the data analysis pipeline SmartMerge of BM29 [30]. Sample frames were chosen according to peak regions in intensity, matching radius of gyration and high similarity using COR-MAP [31]. If this automated data evaluation routine was not successful or overlapping species were merged, a manual data evaluation was performed using the software Sc atter of BIOISIS averaging frames in the region of a constant and stable R g for each elution peak to analyse. The scattering intensities at different elution concentrations were compared and the highest measured concentration with best signal-tonoise ratio without detectable structure factor effects was used for further data analysis.
Further data analysis was performed using the software available within the ATSAS [32] and SC ATTER software packages. Guinier analysis was performed in a q-range with qR g <1.3 yielding the parameters R g and I (0). The integrated scattering area of qI (q) versus q with upper limit of q max = 0.2 was used for determining the correlation volume V c defined as Ið0Þ= R qIðqÞdq yielding the parameter Q R ¼ V 2 c =R g . The mass of a protein is then obtained as M m = Q R /0.1231 according to Rambo et al. [17]. The molecular weight was additionally calculated from the Porod volume V P as described by Petoukhov et al. [33], which was empirically shown to be proportional to the M m with a factor of 0.625. Pair distribution functions P(r) were calculated using the program DATGNOM. Theoretical scattering curves of the monomer and dimer were computed from the crystallographic structure 1DG3 and crystallographic dimer model (Fig. 1B) and fitted to the measured data using the program CRYSOL [34]. The excess scattering density of the hydration layer was used as a free fitting parameter resulting in dro = 0.06 for farn-hGBP1 in nucleotidefree solution (100% monomeric). Additionally, a constant background variable was left as floating parameter.
Structural modelling of the hGBP1 monomers and dimers was performed by rigid-body modelling using the software programs SASREF and EOM from the ATSAS package [35]. For SASREF and EOM calculations, rigid-bodies were extracted from the crystallographic protein structure 1DG3 of the full-length protein with the LG domain (aa 1-308 of 1DG3), MD domain (309-478), C12 helix (479-565) and C13 helix (566-583) as rigid-domains. To construct an atomic hGBP1 dimer model, the LG domains of GppNHp-bound full-length hGBP1 [23] (1F5N) were aligned to the GppNHp-bound dimeric crystal structure 2BC9 of the truncated LG domain construct [10]. For rigid-body modelling using SASREF, specific contact information was provided to ensure the connectivity of the separated domains and contact between the C13 a-helical domains for the hGBP1 dimer, which was described to be an additional dimer interface earlier [11]. Each condition was used for 10 SASREF runs to generate rigid-body models and the best model was chosen based on the smallest v 2 and lowest accumulated penalty value. EOM modelling was performed using the rigid-body domains described above and the known amino acid sequences as input. Flexible linkers consisting of 10 amino acids were simulated by EOM as dummy beads that connect the rigid-body domains. Amino acids accounting for flexible linkers were deleted from the rigid-domains correspondingly. For EOM calculations, helices 12 and 13 were kept as found in the crystal structure. P2 symmetry conditions were used for hGBP1 dimer modelling. A pool of 10 000 different structural conformations was first generated by EOM that was subjected to the selection of the ensemble distribution. SAXS data and structural models are publicly available in the SASBDB [41].
To obtain a structural dimer model, the monomer crystal structure of hGBP1 crystallized in the presence of GppNHp (1F5N) was duplicated and each one aligned to each of the LG domains that are crystallized as dimers in the presence of GppNHp (2BC9) using PyMOL to generate a hGBP1 dimer model ('1F5N-2BC9', see Fig. 1B).
For HYDROPRO calculations of all pdb structures, the calculated buffer viscosity using the ZETASIZER software, and the average partial specific volume as described in AUC methods are used. For Solution Modeller hydrodynamic calculations [37], SoMo overlap bead models are calculated and Zeno hydrodynamics algorithm is used to calculate the hydrodynamic parameters.