Structure and domain dynamics of human lactoferrin in solution and the influence of Fe(III)-ion ligand binding
© The Author(s). 2016
Received: 19 May 2016
Accepted: 25 October 2016
Published: 4 November 2016
Human lactoferrin is an iron-binding protein of the innate immune system consisting of two connected lobes, each with a binding site located in a cleft. The clefts in each lobe undergo a hinge movement from open to close when Fe3+ is present in the solution and can be bound. The binding mechanism was assumed to relate on thermal domain fluctuations of the cleft domains prior to binding. We used Small Angle Neutron Scattering and Neutron Spin Echo Spectroscopy to determine the lactoferrin structure and domain dynamics in solution.
When Fe3+ is present in solution interparticle interactions change from repulsive to attractive in conjunction with emerging metas aggregates, which are not observed without Fe3+. The protein form factor shows the expected change due to lobe closing if Fe3+ is present. The dominating motions of internal domain dynamics with relaxation times in the 30–50 ns range show strong bending and stretching modes with a steric suppressed torsion, but are almost independent of the cleft conformation. Thermally driven cleft closing motions of relevant amplitude are not observed if the cleft is open.
The Fe3+ binding mechanism is not related to thermal equilibrium fluctuations closing the cleft. A likely explanation may be that upon entering the cleft the iron ion first binds weakly which destabilizes and softens the hinge region and enables large fluctuations that then close the cleft resulting in the final formation of the stable iron binding site and, at the same time, stable closed conformation.
Lactoferrin (Lf) is an iron-binding globular protein found in milk and many other secretory fluids like saliva, tears and mucosal secretions of bronchial, nasal, lachrymal, and genitourinary passages of the body . Because of its antibacterial, antiviral and antifungal activity it belongs to the innate immune system. Human lactoferrin (hLf) is a monomeric protein consisting of a single polypeptide chain of 691 amino acid residues and shares the main structure with other proteins from the transferrin family. The transferrin family proteins have two main lobes connected by a short linker (for hLf an alpha helix) and each of the lobes possesses a binding site for an iron ion located in a cleft between two domains [2, 3]. The C-terminal lobe and the N-terminal lobe share a sequence identity of about 40 % and the binding site is equally structured in all transferrins of higher organisms.
The binding of Fe3+-ions is accompanied with an intense red coloration of hLf. Iron is bound reversibly, but with a very high binding affinity (K ~ 1022 M, [3, 4]) which is about 300 times stronger than the binding affinity of the main iron transport protein transferrin, with which it shares 60 % sequence identity [5, 6]. The high binding affinity is the cause for the main antibacterial activity as it removes the essential iron for bacteria growth beside a variety of other functions [3, 7].
An overview of the crystal structures of human lactoferrin available today in the protein data bank shows that the issue of the C-terminal binding cleft remains unresolved. The PDB structures can be classified in two groups: both binding clefts are closed (“closed-closed”): 1b0l (recombinant Fe(III)2-Lf), 1fck (Ce(IV)2-Lf), 1lfg (apo-Lf), 1lfi (Cu(II)2-Lf), 1sqy (Cu(II)2-Lf). The structures in the second group have a closed C-terminal cleft and an open N-terminal cleft (“closed-open”): 1lfh (apo-Lf), 1cb6 (apo-Lf). The distances of corresponding Cα-atoms for all PDB structures in each group deviate only for 5 out of 691 residues by more than 1.5 Å, which is the typical spatial resolution of crystallography, showing that only two major conformations were observed.
It has been suggested from small angle X-ray scattering, that both binding clefts of iron free Lf are open in solution , however at present there is no such structure available in the protein data bank.
Tight iron binding by domain closure with the ability for release in an open configuration requires a mechanism of configurational change.
Relating to a binding mechanism it was suggested by Baker et al. that the iron binds in the open configuration first to one domain and then the cleft closes leading to an attractive interaction of the iron ion with both sides of the binding site, thus locking the closed conformation . Gerstein and Baker assumed that in the open configuration thermal fluctuations are sufficient to close the cleft and if an iron was bound, the closed form is stabilized [2, 11, 16]. Gerstein assumes a similar energy between open and closed states, moreover Baker constrains to transient visits of the closed conformation - which contradicts the similar energy assumption, assuming a Boltzmann factor- to justify solution scattering results of Grossmann et al. . In this context electrostatic interaction cannot cause the domain closure from the open configuration, because the distance of iron to the other domain would be too large (>10 Å, equivalent to 19.3 Å for the Cα distance in Fig. 1). Iron release is then triggered mainly by pH change through a destabilization of the cleft.
Recently Neutron Spin Echo Spectroscopy (NSE) was used to examine the domain dynamics of multidomain proteins as phosphoglycerate kinase and alcohol dehydrogenase [17, 18]. With its space-time resolution on the molecular scale, NSE is sensitive to internal protein dynamics on the nanometer and nanosecond scale. A detailed normal mode analysis allows the description of main domain movements and a determination of their motion amplitudes and timescales .
The goal of this work is to investigate the mechanism of domain closure induced by iron binding in solution. According to the proposed mechanism domain movements should be observed in the open configuration without bound iron, while with bound iron the corresponding movements should be suppressed. From the comparison between both, a picture of the underlying mechanisms will be developed.
Results and discussion
Structure: dependence of conformation on iron content
The small angle neutron scattering (SANS) of proteins in solution depends on the protein form factor F(Q) and on the spatial arrangement between proteins comprised in the structure factor S(Q). Both can be extracted from measurements at different concentrations as described in the Methods section. The form factor F(Q) contains the information about the shape of the protein. F(Q) can be calculated from the atomic coordinates of a protein structure e.g. from the PDB. This allows a comparison of a given three-dimensional atomistic protein structure model with the experimental findings.
For this, we used the 1b0l PDB structure  for the closed-closed and the 1lfh PDB structure  for the closed-open conformation. Since there is no structure with both binding clefts open available, we created an appropriate homologue model with the help of the SWISS-MODEL [22, 23] homologue modeling server as open-open structure. As input we used the amino acid sequence of 1lfh.pdb and the structure of 1dtz.pdb (camelus dromedarius apo-Lf ) as template, which both share a 74 % sequence similarity.
Figure 2a and b show pairwise comparison of the three structures. The ribbon representation as well as the displacement histograms in Fig. 2c show that the opening or closing of a cleft involves only about 1/4 of the amino acids: only one half of the cleft shows large displacements, the other half of this cleft and the entire other cleft stays virtually untouched.
This discrepancy can be explained, if a mixture of single proteins with small protein aggregates is assumed. This is modeled by adding a Guinier function to the calculated protein form factor: Ftot(Q) = I0,hLfFcalc(Q) + I0,aggexp(−Q2Ragg 2/3) (see Materials and Methods). The parameters I0,agg and Ragg were fitted and with I0,agg/I0,hLf = 0.3-0.33 and Ragg = 63-68 Å the experimental F(Q) is very well described at low Q. The Guinier description of the aggregates also allows to judge their contribution to the scattering intensity at higher Q relevant for later NSE measurements: for Q > 0.055 Å−1 the aggregate signal is less than 1 % of the monomer signal and negligible at higher Q (see in Additional file 1: Figure S1).
It is not possible to modify the three conformations of the monomeric molecule (e.g. by means of Normal Mode Analysis) in a way that the resulting form factor explains the discrepancy in Rg and matches the experimental F(Q) at higher Q at the same time. The reason for the aggregates is an attractive interaction as will be described later. It should be noted that the appearance of aggregates in the zero-extrapolated form factor implies that the aggregates don’t vanish with lowered concentration as may be expected. This might be a result from attractive interaction leading to a phase separation with high-density clusters even for low overall concentrations.
Fractions of the different structures to the best fitting structures
iron saturated pD = 5
iron saturated pD = 7
The previously assumed open-open conformation of apo-hLf is modeled with homology and experimentally verified in the iron free case. Contributions from iron bound states, crystal packing and dynamical ensembles seem to be negligible. The iron saturated samples seem to contain a portion of not completely closed structures due to incomplete saturation. The partially saturated sample resembles equilibrium between all 3 states with a probable majority in the closed-open structure. Overall the dependence of the Lf structure on the iron binding state is reproduced and the observed deviations correspond to the measured iron saturation of 5 %, 30 % and 85 % (see Methods). For all conditions except the iron free state we find small meta-stable aggregates of about 10 monomers in size (Ragg/RhLf =2.2–2.4). The metastable character is due to attractive interactions (see below discussion about the structure factor). Regarding equilibrium fluctuations between open and closed state in a two state system with a negligible energy difference would result in 50 % occupation of both states, resulting in a form factor similar to the closed-open structure as average between open-open and closed-closed. Assuming an energy difference of 1 kT (2 kT) results in 25 % (11 %) occupation of the higher energy state according to a Boltzmann distribution. Assuming that we can resolve about 10 % change in the form factor at the prominent Q = 0.2 Å−1 position, we may conclude that the energy difference needs to be larger than 2 kT to be compatible to the observation of negligible changes compared to the open-open configuration in the iron free sample.
Structure factor: interparticle interaction
The structure factor S(Q,c) contains information about the spatial distribution of the proteins in the solvent and therefore about the interaction potential between the molecules. It can be calculated from the scattering intensity I(Q) and the form factor F(Q): S(Q,c) = I(Q)/(c F(Q)), which is strictly valid only for identical spherical particles. For asymmetric particles or polydisperse systems an effective structure factor is obtained neglecting possible orientational correlations [25, 26]. Typically, S(Q,c) is equal to 1 for infinite dilution as well as for high Q, where the probed length scale is much smaller than the distance between proteins. In both cases, there is no interparticle correlation measured, thus S(Q,c) = 1. The experimental form factor from extrapolation contains contribution from aggregates. These aggregates are always present and also depend on concentration. For the structure factor calculation they need to be taken into account to prevent artifacts in the structure factor. This is done best by using the experimental form factor from extrapolation to c = 0 for S(Q,c) calculation and regarding the resulting structure factor as an effective structure factor between monomers and aggregates. As the number density of the aggregates is more than a factor of 300 smaller than the monomer number density (see Additional file 1: Figure S1) contributing aggregate-aggregate or aggregate-monomer partial structure factors should be close to one and contribute less due to the low cluster concentration. Thus the structure factor contains mainly information about monomer-monomer interactions. Nevertheless, the effective structure factor might contain contributions of cluster number density or size variations with concentration and smaller contribution from the partial structure factors related to cluster-cluster and cluster-monomer interactions.
The attractive S(Q,c) of both iron saturated Lf samples can be modeled by adding a Debye-Hückel type short-range interaction to hard spheres, similar to a screened Coulomb potential: U(r) = γβ − 1 e kx x − 1 for x > 1 (outside the sphere) with x = r/2RHS, β−1 = kBT, k = κ2RHS. The structure factor for this system was derived by Hayter and Penfold in a mean spherical approximation  and has four parameters: radius RHS, screening length κ−1, interaction range γ and volume fraction Φ. This number of parameters makes necessary to fix one of them in order to determine the others by a fitting procedure. We fix RHS to 25 Å, a value close to the results of the pure hard-sphere model, and obtain a screening length κ−1 of 21.4 Å (pD = 5) resp. 19.6 Å (pD = 7) and a contact potential U(2RHS) = γe-k of −0.88 kBT (pD = 5) resp. −0.72 kBT (pD = 7). These values may be biased through the choice of RHS, but they give an impression of the interaction strength and range. Short range attraction with weak long range coulomb repulsion allows formation of equilibrium clusters of several monomers as was shown by Stradner et al. . This is a likely explanation for the small, meta-stable aggregates that can be found in the form factor.
The pD value and the iron binding state of Lf can be excluded as a possible reason for the occurrence of the attractive interaction. However, an influence of free Fe3+-ions in solution is a likely explanation: If Fe3+-ions dock on the surface of the protein, the strong charge is capable to change the local surface-charge of the protein . Strongly charged surface areas lead to a behavior similar to patchy colloids. This might induce an attractive component in the interaction [34–36], which may be dominant in our case. Similar attractive interactions were found by Zhang et al.  for bovine serum albumin (BSA) in the presence of Y3+-ions. The iron saturated, freeze-dried lactoferrin contains probably excess ferric salts from the saturation process. The iron chelator EDTA in the buffer solution of the iron free samples can bind the iron ions and remove this effect, which is consistent with the occurrence of attractive and repulsive behavior. To a lesser degree this holds also for the partially saturated sample.
Dynamics: thermal shape fluctuations
Neutron Spinecho spectroscopy (NSE) is a quasielastic neutron scattering technique that measures temporal and spatial correlations between different scattering particles and from internal motions in the particles resulting in the normalized intermediate scattering function I(Q,t)/I(Q,0) (see Methods). The observed protein dynamics in solution comprises several processes on different length- and timescales. There is the self-diffusion of the single protein molecule, which includes translation and rotation. At low Q the resolvable length scale is bigger than the protein, the protein looks point-like and only translational diffusion is observed. With increasing Q the probed length scale decreases and allows resolving finer details. When the spatial resolution is high enough to resolve the shape of the protein and its deviations from spherical symmetry, rotational diffusion becomes observable. Large-scale internal dynamics like domain motions are typically visible on a similar length scale as rotation. These three processes (translation, rotation, internal dynamics) can occur on different timescales. At even shorter length- and timescales, dynamics of smaller parts of the protein down to atomic groups can be observed. At finite concentrations, the interactions between the protein molecules have to be taken into account. There are direct correlations, such as excluded volume or Coulomb interactions, and indirect i.e. solvent-mediated ones.
To determine the contribution of internal dynamics to the NSE signal, the other above-mentioned components must be known (see Methods). The single particle diffusion D0 for a rigid protein can be calculated from the protein structure by using the HYDROPRO software [38–40] for given temperature and solvent viscosity and is also verified by dynamic light scattering (DLS). The viscosities of the used pure buffer solutions and protein solutions are measured with a rolling ball viscometer (Lovis 2000, Anton Paar) and determine the hydrodynamic function. The measured structure factor is used to account for direct interactions.
The internal dynamics A(Q)e-Γt in equ. 3 (see Methods) is able to model one additional internal relaxation process with characteristic time 1/Γ and magnitude A(Q) . This model is fitted to all Q values of the experimental intermediate scattering function of one sample simultaneously, with the only free parameters 1/Γ and A(Q). As a check if all features of the experimental data are represented in this model after the least square fitting procedure, we perform the same analysis of initial and long time effective diffusion on the same time scales. This is plotted in Fig. 6 and shows good agreement with the experiment verifying the partial relaxation of rotational diffusion in midrange Q. (see Additional file 1 S4 for pD7)
Input parameters DT, DR and HT for the fitted model, and obtained time scale 1/Γ of internal dynamics
pD = 5
pD = 5
pD = 7
55.6 ± 13
50.9 ± 8.5
33.6 ± 5.1
The expected A(Q) for C-domain closure can be calculated from the difference in the configurations used as displacement vector and is shown in Fig. 7b with a dominant contribution at larger Q. Even partial closing of both binding clefts would significantly influence the observed A(Q) and generate a clear difference between iron free and iron saturated Lf, which is not observed.
To grasp the nature of the observed internal dynamics, we use elastic normal modes to describe thermal fluctuations of the protein structure and calculate the expected amplitude A(Q) (see Methods). Normal modes were obtained by an all-atom normal mode analysis with the Amber99 force field and are sorted in ascending order of their eigen frequencies. The slowest, softest modes come first. We assume thermal displacements from the equilibrium structure and over-damped relaxation due to solvent friction and protein internal friction.
Examining the contribution of the first non-trivial mode 6, we notice that the resulting A(Q) does not match the experimental A(Q) at all (see Fig. 7b). The calculated A(Q) of mode 6 with amplitude corresponding to the later modes 7–11 shows a steeper increase that starts at higher Q compared to the experiment. Mode 6 together with the higher order modes would thus lead to a strong overshot at larger Q in A(Q) suggesting a suppression of this mode leading to a minor negligible contribution of mode 6. A likely explanation for the suppression of mode 6 is a steric hindrance of the torsional motion represented by mode 6, which blocks larger displacements not taken into account by normal mode analysis at the energetic minimum. If we assume that mode 6 is strongly suppressed and we start the summation of modes at number 7, the resulting A(Q) is already very similar to the experiment with only 3–4 modes combined. It can be seen that the shoulder around 0.1 Å−1 evolves by adding normal mode 9. Adding more modes does not change the shape of A(Q) significantly, because the amplitudes for higher order modes become too small irrespective of their pattern. These modes describe more local deformations instead of large-scale domain motions of the lower modes.
The experiments confirm the closed-closed and closed-open structures for Fe(III)2-Lf and Fe(III)1-Lf respectively in solution. The overall shape, i.e. the position of the two lobes relative to each other, is basically the same as in the respective structure models based on x-ray crystallography. Apo-Lf showed to be consistent with a new homology model with both clefts open.
The structure factors of the protein solutions reveal that lactoferrin can show repulsive interaction (due to the excluded-volume as hard spheres without significant contributions from surface charges) or attractive interaction. Attractive interactions may be induced by binding of Fe3+-ions and local charge inversion at the surface building attractive patches .
A look at the internal dynamics shows that its magnitude A(Q) is independent of the investigated solvent conditions with repulsive or attractive interactions and independent of the iron binding state of lactoferrin. Solely the characteristic time scale depends on the pD-value of the solvent: as the pD mainly changes the charge distribution on the protein surface, an influence of the surface charge on the observed dynamics between the two lobes is suggested.
Modeling the motional pattern of the internal dynamics shows that not only the magnitude A(Q), but also the actual displacement pattern is independent from the examined conditions, including the suppression of the torsional mode 6 due to steric hindrance. The relevant normal modes show that the dominant motions are relative displacements of the two lobes that stretch and twist the protein. It is a remarkable result, that the conformational change related to the cleft opening has very little influence on the large-scale interdomain motion.
Regarding the closing mechanism for the binding of an iron ion, it was hypothesized that equilibrium fluctuations of the cleft between the two domains of a lobe bring the binding sites closer together [11, 16]. If thermal fluctuations on any timescale would notably include closing of the binding clefts, this would change the measured form factor significantly. Already the SANS results let the dynamical closing within thermal fluctuations appear unlikely or being connected with a larger energy difference between open and closed state (>2kT). Thermal fluctuations of the cleft around an open equilibrium configuration with relevant amplitudes are not observed within the NSE timescale as well. Therefore the conclusion is that both states seem to have a larger energy difference than assumed by Baker and Gerstein, which suppresses thermal fluctuations of relevant amplitude.
If electrostatic interactions due to charges are ruled out too, then the activation of dynamics due to iron binding prior to domain closing seems to be possible. The CO3 2− anion binds in front of the N-terminus of helix 5, which belongs to the domain that moves to close the hinge (residue 91–250, see Additional file 1: Figure S6), before the complex with the iron ion is formed . The residues Tyr92 and His253 contribute to the iron binding and are both located close to the hinge (residue 90–91 and 250–251) . Tyr92 is able to bind to the iron prior to cleft closure, as it is located in the closing domain. We can only speculate that binding of Tyr92 to iron or a similar mechanism may destabilize one strand of the hinge (or both due to hydrogen bonds) and enable large cleft closure movements by reducing the energy difference between open and closed conformation and thus softening the hinge region. This would allow His253 binding for stabilization of the closed cleft. For a short time, until the cleft is stabilized again in the closed conformation, thermal domain motions would be possible, which would not show up in our measurements or structural measurements by X-ray or SANS, but would enable a dynamic cleft closure.
The molecular mass of human lactoferrin is reported in a range of 75–80 kDa [43, 44], in this work an average value of 77 kDa is used (as in ). This value is very close to the calculated mass from the crystal structure of 76.1 kDa. Lactoferrin from human milk was purchased from Sigma-Aldrich, Munich, Germany as lyophilized powder. The protein comes in two different variants: iron saturated (product code L3770) and with no specified iron content (product code L0520). In combination with different buffer conditions, this allows to prepare samples with different iron binding states: Iron-saturated lactoferrin was prepared by dissolving the L3770 powder in a D2O-buffer (100 mM 2-(N-morpholino)ethanesulfonic acid (MES), 150 mM NaCl) at pD = 5 and pD = 7. Partially saturated lactoferrin was prepared from L3770, iron-free lactoferrin from L0520, both in an iron-depleting D2O-buffer (100 mM MES, 180 mM NaCl, 200 mM NaH2PO4, 40 mM ethylenediaminetetraacetic acid (EDTA) ) at pD = 5. The iron saturation of the protein was measured with light absorption spectroscopy at λ = 465 nm with A1% = 0.58 at an optical path length of 1 mm corresponding to 100 % saturation at a concentration of 1 % weight/volume , resulting in 87 %, 30 % and 5 %. The samples were ultra-centrifuged at 150000 g for 2 h to remove larger aggregates. With Dynamic Light Scattering (DLS) measurements the removal of aggregates was verified. The samples were then diluted to the desired concentrations of 2.5, 5, 10 and 50 mg/ml for SANS and NSE measurements. The concentrations were measured with light absorption spectroscopy at λ = 280 nm with an extinction coefficient of e280 = 8.85 104 M−1cm−1 . All experiments mentioned in this work were performed at a temperature of 7 °C to slow down formation of stable aggregates. The release of iron from L3770 (in buffer with EDTA) and iron uptake from iron-free L0520 (in 0.1 M sodium citrate containing FeCl3 and NaHCO3) showing the expected decrease respectively increase of the 465 nm Fe[III] peak was tested by UV–vis spectroscopy.
Small angle neutron scattering
Small Angle Neutron Scattering (SANS) is a technique to study the microscopic structural properties of the sample. The SANS measurements were performed at the instruments KWS1 and KWS2  at the MLZ in Garching, Germany. With a neutron wavelength of λ = 4.5 Å and two detector distances of 1.5 m resp. 2 m and 8 m, a Q-range of about 0.01-0.45 resp. 0.33 Å−1 was covered. The wavelength distribution width FWHM was 20 % for KWS2, 10 % for KWS1.
The data reduction to one dimension and merging of the detector distances was done with the instrument-software QtiKWS. The background scattering of the buffer solution was measured separately, scaled with the volume fraction of the buffer and subtracted from the sample signal. The Q-independent incoherent scattering of the protein was calculated from the amino acid sequence, scaled with the protein concentration (e.g. Iinc(c = 10 mg/ml) = 0.00202 cm−1) and subtracted as well (taking into account H/D-exchange between protein and buffer solution [48, 49]). Smearing of the data is taken into account according to Pedersen et al. .
The scattering intensity I(Q) of N identical particles is proportional to I(Q) ~ NF(Q)S(Q,c), with the orientational averaged, concentration-independent form factor F(Q) = <Σ i,j b i b j exp(iQ(r i -r j ))>, containing information about the shape of the protein and the concentration-dependent structure factor S(Q,c), which represents direct interactions between the proteins in solution. Q is the scattering vector, bi is the coherent neutron scattering length of atom i at position ri. For proteins in solution the contrast and H/D exchange have to be considered according to Jacrot . A concentration series allows to extrapolate to c = 0 for each Q-value from the concentration-normalized scattering intensity I(Q)/c to obtain the form factor F(Q) (with S(Q,c = 0) = 1) and to extract the structure factor S(Q,c) successively .
The form factor for a protein in solution has an additional contribution from the hydration layer around the protein with a larger density than bulk water . The density of the hydration layer depends on the selected protein and the solvent composition. By a combination of SANS and SAXS the density in the hydration layer can be determined. The main influence for SANS in D2O due to the hydration layer is a decrease of the radius of gyration Rg and a change in slope at larger Q (e.g. for hLf a reduction of 1 Å for 10 % increase in layer density and the slope flattens significantly). The good reproduction of the hLf form factor without hydration layer in the range 0.07 Å−1–0.15 Å−1 shows that the change in density for the here examined protein is negligible.
A common issue when dealing with proteins in solution is the formation of aggregates. If the aggregates are sufficiently larger than the single protein molecule, they can be easily detected by dynamic light scattering (DLS) and removed with e.g. centrifugation or filtration. If attractive protein-protein interactions are existent, aggregates will emerge again. However, if the aggregates are similar in size to the protein (Raggregate/Rprotein < 5), they may not be distinguishable any more by DLS and cannot be removed easily. Such a mixture can potentially lead to wrong results in the protein size determination (radius of gyration Rg) or calculated radial distribution functions as P(r) from SANS data and a false conclusion regarding the conformation.
Our approach is to compare the experimental data with the calculated F(Q) from atomistic protein structures. This provides the opportunity to fathom the reason behind an apparent change in the radius of gyration. Differentiation between conformational changes that alters the protein size and a mixture of single protein molecules and aggregates, both leading to increase in measured radius of gyration Rg, is possible. A configurational change e.g. by deformation along a dominant normal mode, which leads to an elongated shape with increased Rg, will presumably alter the detailed structure visible in F(Q) at larger Q, too. The comparison with the experiment is the criterion to rule out specific deformations. To achieve a protein structure model describing the experimental F(Q) in terms of size (low Q regime) and detailed structure (high Q regime) at the same time, we apply a multi-parameter least square fitting routine. On the one hand, we allow deformations of the protein by e.g. normal modes. On the other hand we enclose additional aggregates and include these in our description by assuming an additional contribution from a Guinier form factor Fagg(Q) ~ exp(−Q2Ragg 2/3) for the aggregates. In general the Guinier approximation is valid for QRg < 31/2. To justify the Guinier approximation also for larger Q we compared the scattering of 9 and 10mer metastable clusters and found that the Guinier approximation describes the metastable clusters up to Q = 0.05 Å−1 (see Additional file 1: Figure S1).
Neutron spin echo spectroscopy
Neutron Spin Echo Spectroscopy (NSE) is a high-resolving quasielastic neutron scattering method to measure the spatial and temporal correlations of scatterers. One obtains directly the normalized intermediate scattering function I(Q,t)/I(Q,0) as the spatial Fourier transform of the Van Hove function G(r,t) . NSE measures coherent and incoherent contribution where the coherent contribution dominates in the SANS regime at low Q. All NSE experiments were performed at the instrument IN15  at the ILL, Grenoble, France. Neutrons with wavelengths of λ = 8, 10, 12 and 16 Å were used, giving an accessible Fourier-time range of up to 200 ns. Only the highest concentration of c = 50 mg/ml of each sample condition was measured. The background contribution of the buffer solution was measured independently and the data for the protein sample was corrected accordingly . Full measurements are shown in the Additional file 1: Figure S3a-c.
Modeling diffusion and internal dynamics
with the form factor F(Q) and the positions rj and scattering lengths bj of the atoms of the protein. The 6x6 diffusion tensor D, the translational diffusion D0T and the rotational diffusion D0R, the later two as trace of D can be calculated with the HYDROPRO software from the atomic coordinates [38–40]. The translational diffusion component D0(Q = 0) can be verified within the experimental accuracy by DLS using a concentration series and extrapolation to c = 0. The collective diffusion at finite concentration c is given by D(Q) = D0(Q)H(Q)/S(Q,c) [53–56]. The effect of the direct interactions is measured in SANS as the structure factor S(Q,c). The solvent-mediated interactions are included in the hydrodynamic function H(Q), which can be assumed to be Q-independent for flexible globular proteins  in contrast to rigid globular proteins . From known D0(Q) and S(Q,c), the value of H can be determined by DLS and NSE at low Q, where only translational diffusion is observed.
Thereby, scalar values DT and DR for translational and rotational diffusion are used, as 1/3 of the traces of the respective 3x3 sub-tensors of D from HYDROPRO. The inaccuracy introduced by using two scalars instead of the full tensor can be minimized (<2 %) by rescaling of DR in a way that the initial Deff of [I(Q,t)/I(Q,0)] T,R (for c = 0) matches the calculated D0(Q) with the full tensor. The hydrodynamic factor for translation HT is fitted in the low Q regime as described before. The rotational hydrodynamic factor HR is linked to HT and is assumed to have a weaker effect by a factor of 3, as derived by Degiorgio et al. as 1-HR ≈ (1-HT)/3 for hard sphere colloids . With the terms Sl(Q) of a multipole expansion, including the spherical Bessel functions jl and the spherical harmonics Yl,m, the protein structure is implicitly included in this calculation. Internal dynamics is described by a Q dependent amplitude A(Q) and an exponential relaxation with relaxation time 1/Γ. Resulting fits to experimental data are shown in Additional file 1: Figure S3a-c.
The eigen frequencies ωα have no real physical meaning, since the normal modes are calculated in vacuum. However, they serve as a measure of stiffness of the respective mode and are used to distribute the thermal energy over all modes equally according to the equipartition theorem. To each normal mode α is assigned a displacement amplitude relative to the first non-trivial mode 6: aα = aω6 2/ωα 2 (modes 0–2 describe translation and modes 3–5 relate to rotation along the three space-axes). Higher frequency modes are suppressed stronger and thus the summation can be limited to the low frequency modes. This leaves the common prefactor a as single free parameter.
Calculations are done under usage of protein structures from the Protein Data Bank (PDB) and the molecular modeling toolkit MMTK [60–62]. SANS form factor calculations and structure refinement by normal modes is done in self-made routines taking into account H/D-exchange as described elsewhere  and the contrast of protein scattering with respect to the solvent. Normal modes as motifs for deformation of the unperturbed protein structure were calculated with MMTK using the built-in Amber99 force-field without solvent.
PDB ID: 1lfh, 1b0l, 1dtz
Neutron beam time for this research was allocated by Jülich Center for Neutron Sciences, JCNS1, outstation at MLZ, 85747 Garching, Germany.
Availability of data and materials
The datasets supporting the conclusions of this article are included within the article and its additional files.
CS, RB, BM designed and performed the experiments, analysed the data, discussed results and wrote the paper; RB developed the model and supervised; DR and RM supervised, discussed the results and wrote the paper; BF was the NSE instrument responsible and performed NSE measurements; AR and MSA were instrument responsible for KWS2 and KWS1 respectively and performed SANS measurements. All authors have given approval to the final version of the manuscript.
The authors declare that they have no competing interests.
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