Keywords

12.1 Historical Overview

The application of small-angle neutron scattering (SANS) for the structural study of (weakly scattering) biological systems such as solubilized membrane proteins became technically feasible with the advent of high-flux neutron sources in the 1960s and 1970s. Earliest work, carried out at the Institut Laue-Langevin (Grenoble, France) and at the High Flux Beam Reactor (Brookhaven, USA) includes studies on several membrane protein systems purified directly from biological tissues: human serum low-density lipoprotein (Stuhrmann et al. 1975), bovine and frog rhodopsin (Osborne et al. 1978; Yeager 1976), the acetylcholine receptor from Torpedo californica (Wise et al. 1979) and porcine pancreatic colipase (Charles et al. 1980). Most of this early work was able to provide important model-free parameters of the protein-detergent complexes such as radii of gyration R G of both the complex and the individual partners, their stoichiometry, and molecular masses. The qualitative relative arrangements (in particular the distances) between protein and detergent moieties were obtained by a Stuhrmann analysis (Stuhrmann 1973), i.e. by interpreting the change of the measured R G at different contrast conditions (H2O:D2O ratio in the solvent), occasionally combined with deuterated detergent to enhance contrast. In some cases, simple geometrical bodies were proposed for the protein and detergent moieties (Wise et al. 1979; Charles et al. 1980). Even though the functional interpretations of these pioneering results were limited in the absence of atomic-resolution structures, they allowed to probe and validate (or discard) basic working models of the membrane proteins studied. A more exhaustive overview on early SANS results from membrane protein systems can be found elsewhere (Timmins and Zaccai 1988).

In the second half of the 1980s the routine use of recombinant protein expression (Atkinson and Small 1986) made a wider range of membrane protein systems accessible to SANS, in particular in combination with an increasing commercial availability of deuterated detergent molecules. Concomitantly, more sophisticated modelling approaches using a number of beads to represent protein shapes were being developed (Perkins and Weiss 1983). The investigation of atomic-resolution membrane protein models became available in the 1990s with the first structures being deposited in the protein data bank (PDB) and the development of computer programs to back-calculate SANS curves efficiently from them (Svergun et al. 1998). At the same time, ab initio shape analysis was being developed (Svergun 1999; Chacon et al. 1998) and since the turn of the millennium, an increasingly versatile toolbox of computer programs for the interpretation of SANS data, including rigid body modeling and the comparison to cryo-EM data has become available (Zaccai et al. 2016; Chaudhuri 2015; Petoukhov et al. 2012). In parallel, ever more sophisticated labeling schemes (e.g. partial deuteration) became available for detergent/lipid molecules (Hiruma-Shimizu et al. 2016; Haertlein et al. 2016; Maric et al. 2015) to fine-tune contrast matching approaches.

12.2 Neutron Scattering Theory and Experimental Considerations

The general theory of small-angle scattering (SAS) as well as the specific theory and experimental setup for general SANS experiment have been introduced in previous sections of this book or in recent reviews and I will summarize here only briefly specific points related to membrane protein systems (Clifton et al. 2013).

The SANS signal measured from a solution of arbitrarily oriented particles i (after solvent subtraction) corresponds to a one-dimensional intensity I versus the modulus of the wave vector q and can be expressed as follows:

$$ I(q)=\sum \limits_i{N}_i\left\langle {\left|\int \Delta {\rho}_i\kern0.1em {e}^{i\overrightarrow{q}\cdot \overrightarrow{r}}{dV}_i\right|}^2\right\rangle, \kern1em q=\frac{4\pi }{\lambda}\sin \theta $$
(12.1)

Where λ is the neutron wavelength and 2θ the scattering angle. N i is the number of particles of a distinct species i. For solubilized membrane proteins these species correspond in practice to protein-detergent/lipid complexes (PDC), protein-free detergent/lipid aggregates (such as micelles, vesicles etc.) and single, free detergent and/or lipid molecules (Fig. 12.1). Δρ i is the neutron scattering length density (SLD) contrast of specific particles with respect to the solvent. It varies in general for neutrons between protein and detergent/lipid head- and tail-groups (Timmins and Zaccai 1988; Jacrot 1976) (Fig. 12.2) and therefore has to be integrated over the whole particle volume V i . The broken brackets correspond to a rotational average over all possible particle orientations.

Fig. 12.1
figure 1

Schematic representation of compounds in a solubilized membrane protein sample. This schematic and strongly simplified overview shows a selection of individual particles in a sample of DDM (n-Dodecyl β-D-maltoside)-solubilized membrane proteins: free detergent molecules, free micelles, and the protein-detergent/lipid complex (PDC). The designations of geometric parameters (radii, thicknesses) in this figure correspond to the ones used in the following sections. Different shades of grey symbolize different contrasts Δρ (Table 12.1)

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Fig. 12.2
figure 2

Neutron scattering length densities (SLD) ρ of proteins and DDM detergent. The values are calculated from literature (Jacrot 1976; Breyton et al. 2013a). The contrast Δρ (Eq. 12.1) at a given H2O:D2O ratio of each compound/moiety is defined as the difference between its own SLD and the one of the solvent (mixture of ordinary and heavy water). The orange circle indicates the contrast match point (CMP, i.e. Δρ = 0) of an entire DDM molecule (head- plus tail-group) at ~22% D2O. h-protein is a natural, hydrogenated protein, d-protein is a perdeuterated protein (all hydrogens replaced by deuterium). In general, all hydrogenated proteins have similar SLDs as the one depicted here while the SLDs for different detergents can deviate significantly from those of DDM (Breyton et al. 2013a)

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Figure 12.2 represents the basics of contrast variation, that is the possibility by SANS to minimize the signal of either detergents/lipids or protein by measuring at an appropriate H2O:D2O ratio and to focus on structural information from specific parts of a complex membrane protein system. Reasonable signal/noise on the most performant present-day SANS instruments can be obtained from membrane protein solutions in the (protein) concentration range 1–10 mg/mL for protein molecular masses in the range from ~20 kDa to several 100 kDa and for 100–200 μL sample volumes with exposure times varying between a few minutes and several hours, depending on contrast and instrumental setup.

As in the case of water-soluble proteins, mastery of the biochemistry and sample preparation prior to the experiment is of paramount importance for the interpretation of the experimental SANS curves in terms of structural parameters (Jacques and Trewhella 2010). For solubilized membrane proteins in particular, the monodispersity of the PDC and the detergent/lipid aggregates should be checked by preliminary complementary techniques including analytical ultracentrifugation (AUC) and size-exclusion chromatography (SEC) (Le Roy et al. 2015; le Maire et al. 2000). Ideally, the buffer subtracted from the sample containing the protein should match the latter in concentration of individual detergent/lipid molecules as well as free detergent/lipid aggregates (e.g. micelles) in order to eliminate their contribution to the SANS signal completely. If feasible, the buffer from the last purification (gel filtration) step should be used without further concentration if the detergent/lipid aggregate sizes and shapes depend on concentration.

Three major criteria should be respected when considering the choice of a detergent/lipid system for solubilizing membrane proteins for SANS experiments: (1) the detergent/lipid system should solubilize the membrane protein in a stable, monodisperse complex and in a functionally relevant state, (2) the contrast between protein and detergent/lipid (Fig. 12.2) should be chosen as high as possible and (3) protein-free detergent/lipid aggregates should be kept at a minimal concentration and as monodisperse as possible, i.e. in practice large aggregates such as vesicles, rod-like structures etc. should be avoided in order not to dominate the protein signal (see also following section). Point (3) requires a good knowledge of the detergent/lipid phase diagram and in particular the critical micellar concentration (CMC) (le Maire et al. 2000; Helenius and Simons 1975).

12.3 Influence of Membrane Protein Sample Heterogeneity on the SANS Signal: A Simple Geometrical Case Study

The extraction and interpretation of structural information by small angle neutron scattering according to Eq. 12.1 requires that the membrane proteins be solubilized in the presence of detergent and/or lipids. The required experimental conditions give rise to a composite system of (at least) three chemically different components with specific and distinct scattering length densities (SLDs): protein, detergent/lipids and (aqueous) solvent. In many cases, several distinct particulate species are formed (we exclude non-particulate systems such as lamellar phases, interconnected networks etc. (Qian and Heller 2015; Harroun et al. 2005; Seddon et al. 2004) and their respective scattering contributions need to be described separately: free (single) detergent/lipid molecules, protein-free detergent/lipid aggregates (micelles, vesicles etc.) and protein-detergent/lipid complexes (PDC) (Fig. 12.1). The general equation of the measured intensity (Eq. 12.1) can thus be rewritten as follows:

$$ {\displaystyle \begin{array}{l}I(q)\kern1.00em \\ {}\begin{array}{l}\kern1.00em \\ {}\propto {N}_{PDC}\ \left\langle {\left|{M}_{prot}{A}_{prot}(q)+{M}_{lipid\_ bound}\ {A}_{lipid\_ bound}\ (q)\right|}^2\right\rangle \kern1.00em \end{array}\\ {}\kern2em +{N}_{aggregates}\ \left\langle {\left|{M}_{lipid\_ aggregates}\ {A}_{lipid\_ aggregates}\ (q)\right|}^2\right\rangle \kern3.00em \\ {}+{N}_{free}\ \left\langle {\left|{M}_{lipid\_ free}\ {A}_{lipid\_ free}\ (q)\right|}^2\right\rangle \kern1.00em \end{array}} $$
(12.2)

N PDC , N aggregates and N free designate the number of particles of the respective species in solution. A prot , A lipid_bound , A lipid_aggregates and A lipid_free correspond, respectively, to the scattering amplitudes (form factors) of the protein, the lipids/detergents bound to it, the lipids/detergents associated in protein-free aggregates (micelles, vesicles etc.) and the free, single lipid/detergent molecules (for the sake of simplicity we use the index “lipid” in Eq. 12.2 for both lipid and detergent molecules). M i are the scattering masses of the respective parts of the systems and are given by∫Δρ i  dV i .

The significance and impact of Eq. 12.2 on the interpretation of SANS data is illustrated by a simplified model system consisting of a (hypothetical) spherical membrane protein covered entirely by a monolayer of detergent in addition to free, spherical micelles (Fig. 12.1). For the explicit calculations (see details in the Appendix), we assumed a hydrogenated protein and DDM (n-Dodecyl-β-D-maltopyranoside) detergent molecules at both 0 and 22% D2O, the latter contrast corresponding to the overall contrast match point (CMP) of DDM detergent molecules (Fig. 12.2). The contrasts of the individual components are listed in Table 12.1 and in all cases random orientations of all individual components are assumed.

Table 12.1 SLD differences (i.e. contrast) Δρ of individual components shown in Figs. 12.1, 12.2, and 12.3
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At 0% D2O (DDM not matched) the presence of bound detergent modifies both the intensity and the form factor of the protein (Fig. 12.3a, blue line vs continuous red line) and increases its apparent size (increase of I(q = 0) intensity by a factor of 2.5 and radius of gyration R G by 24% from 31.4 to 38.8 Å). The relative contribution to the signal of free micelles (green line) with respect to the PDC complex (red line) is about 8% in intensity (at a stoichiometry 10:1) at small angles and reduces the R G of the PDC by 3% (to 37.7 Å). More importantly, their presence modifies the scattering curve from the complex significantly at intermediate q-ranges (0.07…0.25 Å−1) (red continuous vs broken lines). Therefore, SANS curves of PDC complexes (in the absence or presence of additional free micelles) for non-matched detergent/lipids cannot, in general, be interpreted in terms of molecular mass or shape of the embedded proteins alone.

Fig. 12.3
figure 3

Theoretical SANS curves of simple, composite membrane protein systems at 0% (a) and 22% (b) D2O. SANS curves calculated for free protein, free DDM micelle, isolated PDC complex and mixtures of PDC and micelles at two different stoichiometric ratios. The curves were calculated with Eq. 12.2 and the equations presented in the Appendix, by using neutron scattering length densities from literature (Jacrot 1976; Breyton et al. 2013a), listed in Table 12.1, and represent faithfully the relative intensities. The geometrical shapes of the micelle and PDC were assumed to be spherical as in Fig. 12.1, with the additional assumption that a detergent monolayer covers the protein completely (black lines, Fig. 12.1). The numerical values of the different parameters (protein radius, micelle core and shell radii and detergent head and tail lengths) are detailed in Table 12.1. The SANS curve of an individual DDM molecule was calculated with CRYSON (Svergun et al. 1998) using its atomic structure from the PDB (ligand ID entry “LMT”)

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At 22% D2O (CMP of DDM), free micelles scatter very weakly at low angles (q < 0.05 Å−1) with respect to the solubilized proteins and their contribution to I(0) and the R G can be neglected, even in tenfold molar excess with respect to the PDC complexes (Fig. 12.3b, green and red broken lines). At intermediate q-values (0.07…0.25 Å−1) the situation is similar to the one at 0% D2O with a modification of the signal from the isolated PDC complex (red lines). The situation is more complex for protein-bound detergent: even though matched on average at 22% D2O and therefore not modifying the I(0) intensity and the apparent molecular mass of the protein, the form factor of the PDC complex is not the same as the one of the isolated protein alone (blue vs continuous red line) but increases the R G by 14% from 31.4 to 35.7 Å. This effect is due to the specific spatial arrangement and contrast of detergent moieties with respect to the protein: tail-groups are closer to the protein and have negative contrast while head-groups are further away from the protein and have positive contrast (Table 12.1). While their respective contributions to the scattered intensity (Eq. 12.1) cancels in the forward scattering direction I(q = 0), they do not annihilate for q > 0.

While instructive regarding the sensitivity of SANS signal from complex, solubilized membrane protein systems regarding internal SLD heterogeneity and sizes of different particles, the analytical analysis presented here is heavily oversimplified with respect to several aspects: assumption of a spherical protein, covered homogeneously and completely by a double layer representing a head- and tail-group of detergent/lipid molecules, and a monodisperse and spherical population of micelles, composed of neatly separated homogeneous layers. More accurate descriptions of realistic systems would include non-spherical proteins, covered only partly by detergent/lipids and ellipsoidal micellar structures (Lipfert et al. 2007) as well as polydispersity in micellar size (Manet et al. 2011). These modifications would qualitatively lead to more smeared minima of the idealized calculated curves here but would not change the overall conclusions. Unfortunately, form factors of geometrical bodies that deviate even slightly from the spherical shape (e.g. ellipsoids, cylinders etc.) can no longer be written explicitly but are represented by mathematical integrals that need to be solved numerically (Pedersen 2002). Finally, it should be noted that the conclusions drawn here on micellar detergent/lipid aggregates as “contaminants” of the SANS signal of solubilized membrane proteins are even more pronounced when larger aggregates such as vesicles, liposomes or rods are present (Rubinson et al. 2013; Qian and Heller 2011; Breyton et al. 2009; Hunt et al. 1997).

12.4 Strategies to Minimize/Homogenize the Detergent/Lipid SANS Signal and Shape Analysis

The previous section illustrates that the internal (SLD) heterogeneity of detergent/lipid molecules and their presence both in the protein-detergent/lipid complex and in the form of free micelles has a strong impact on the interpretation of membrane protein structures by SANS experiments. While it is in general reliable to extract molecular masses of membrane proteins from the I(0) intensity at the detergent/lipid contrast match point (Fig. 12.3b, I(0) intensities of blue and red curves) and therefore determine their oligomeric state (Compton et al. 2011), other elementary structural parameters such as the radius of gyration (R G) cannot be interpreted as due to the protein alone. Moreover, ab initio shape analysis using single phases such as DAMMIN (Svergun 1999) will yield erroneous envelopes, encompassing both bound detergent/lipid molecules as well as a weighted contributions of micellar features from intermediate q-ranges (Fig. 12.3, deviations between red broken lines from red continuous lines). Several strategies have therefore been applied in literature to focus on the signal of the embedded membrane protein and to minimize the signal due to protein-bound detergent/lipid and/or free detergent/lipid aggregates:

  1. 1.

    Reinforcing contrast by deuteration: the relative contribution of internal SLD fluctuations of free detergent/lipid aggregates can be minimized by either increasing the signal of the protein by its deuteration in the presence of hydrogenated detergents/lipids or by working with deuterated lipids/detergents and hydrogenated proteins at elevated D2O percentages in the solvent (Compton et al. 2011; Gabel et al. 2014). In the former approach, the contrast of the deuterated protein (d-protein, Fig. 12.2) is much larger than the SLD fluctuations between head/tail of the detergent/lipid molecules which can be neglected in favorable cases, in particular for small differences between head/tail SLDs (Breyton et al. 2013a), by choosing detergent/lipids with low aggregation numbers close to their CMC (le Maire et al. 2000) or when only a few detergent/lipid molecules are attached to a protein complex of very large size (Efremov et al. 2015). Deuteration of lipids has the advantage of homogenizing the internal SLD variation for certain detergents/lipids (Timmins and Zaccai 1988; Breyton et al. 2013a) and, in addition, allows to work at high D2O concentrations which minimizes incoherent neutron scattering background (Gabel et al. 2002) and therefore improves signal/noise.

  2. 2.

    Homogenizing internal contrast of detergents/lipids: while internal SLD fluctuations between head- and tail-groups of detergent/lipid molecules can often be reduced by deuteration (see above), full deuteration unfortunately leads to SLD that can no longer be matched, even when working in 100% D2O (Breyton et al. 2013a). Alternatively, some detergent molecules have small SLD fluctuations in their natural (hydrogenated) state, e.g. fluorinated surfactants (Breyton et al. 2013b). Some of these compounds, however, have a match point close to 40% D2O and therefore require the use of deuterated proteins for structural studies by SANS. Another strategy consists in mixing hydrogenated and deuterated detergents/lipids at appropriate ratios in order to obtain a desired match point (Osborne et al. 1978; Clifton et al. 2012). Finally, more complex systems such as nanodiscs (mixed polypeptide/detergent/lipid particles) have been used recently to solubilize membrane proteins (Kynde et al. 2014; Skar-Gislinge et al. 2010; Bayburt and Sligar 2010; Nakano et al. 2009). In some cases (so-called “stealth nanodiscs”), the systems were designed to be matched out relatively homogeneously at about 100% D2O allowing thus the study of hydrogenated membrane proteins with very good signal/noise (Maric et al. 2014).

The strategies (1) and (2) allow, in a more or less accurate way, to assume that the detergents/lipids can be considered to be homogeneous (in terms of SLD fluctuations between head- and tail-groups) and that the measured SANS signal at their contrast match point is due exclusively to the solubilized membrane proteins themselves. Under these conditions, the same approaches developed for water-soluble proteins have been applied on membrane proteins, in particular single- (Compton et al. 2011, 2014; Breyton et al. 2013b; Le et al. 2014; Sharma et al. 2012; Tang et al. 2010; Nogales et al. 2010; Cardoso et al. 2009; Zimmer et al. 2006; Johs et al. 2006; Bu et al. 2003) and multi-phase (Clifton et al. 2012) ab initio shape reconstructions. In the latter case, both detergents/lipids and protein are represented by two distinct envelopes and it is possible to determine their relative shapes and positions simultaneously by fitting SANS curves at multiple contrasts, e.g. with the program MONSA (Svergun 1999; Petoukhov and Svergun 2006).

12.5 Full-Atomic and Other Sophisticated Modelling Approaches

The previous section assumes that deuteration strategies allow to interpret SANS signals from complex systems (PDC plus free detergent/lipid aggregates) exclusively in terms of the protein structure at the detergent/lipid contrast match point. This is unfortunately not possible in all experimental cases and in general, a non-negligible contribution of bound detergent/lipid as well as free detergent/lipid aggregates to the overall SANS signal needs to be taken into account. Size exclusion chromatography, coupled to SANS (SEC-SANS), which in analogy to SEC-SAXS experiments would allow the separation of the PDC from detergent/lipid aggregates such as micelles (see next section), has been developed recently (Jordan et al. 2016) but has not been applied, to our best knowledge, to membrane protein systems so far.

An accurate approach if SANS signals of detergent/lipid molecules cannot be neglected due to internal heterogeneity or due to perdeuteration, is to model the PDC with several distinct parts, including detergent/lipid molecules. Several studies have applied coarse-grain/dummy-atoms or simple geometric models of detergent/lipids (Kynde et al. 2014; Tang et al. 2010; Cardoso et al. 2009; Gohon et al. 2008) to represent the internal heterogeneity, including between different detergent/lipid moieties such as head- and tail groups. In some cases, full-atom detergent/lipid models have been produced by MD simulations (Gabel et al. 2014; Le et al. 2014). When integrating SANS datasets from different contrasts, these sophisticated approaches allow to distinguish between modestly different protein conformations as well as to fine-tune the shape and topology of the bound detergent/lipid molecules (Fig. 12.4). The combination of MD simulations with SANS (and SAXS) data from membrane protein systems is a very active field at the moment and diverse new approaches are being developed (Perez and Koutsioubas 2015; Chen and Hub 2015). Importantly, care needs to be taken that the programs that back-calculate SANS curves from membrane protein complexes take exchangeable hydrogens from detergent/lipid molecules correctly into account.

Fig. 12.4
figure 4

Full-atomic model of membrane protein FhaC, including deuterated d-DDM detergent. The structural model displayed was fitted against SANS data in solution at 42 and 90% D2O (contrast match points of protein and d-DDM, respectively) using the program CRYSON (Svergun et al. 1998). Detergent was built by MD simulations. Both SANS data sets were recorded at the instrument D22 at the Institut Laue-Langevin (ILL Grenoble, France) during 20 min at a protein concentration of 13 mg/mL. The figure was created based on data published by Gabel et al. (2014)

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12.6 Comparison with Small-Angle X-Ray Scattering (SAXS)

The SANS sister technique, small-angle X-ray scattering (SAXS) has been used for several decades to characterize solubilized detergents (Bouwstra et al. 1993) and has provided models for the shapes and internal structure of isolated micelles (Oliver et al. 2013; Lipfert et al. 2007; D’Andrea et al. 2011; Gobl et al. 2010) and nanodiscs (Skar-Gislinge and Arleth 2011). SAXS has also been used as a high-throughput tool to probe crystallization phases (Joseph et al. 2011). First applications of SAXS to model solubilized membrane proteins in the presence of lipids/detergent are more recent (O’Neill et al. 2007; Columbus et al. 2006; Watanabe and Inoko 2005; Hong et al. 2004; Haas et al. 2004). While it was possible in some favorable cases to describe protein-detergent complexes by ab initio models using “static” SAXS experiments (Calcutta et al. 2012) the strong scattering contribution from detergent aggregates such as free micelles represents in general an important obstacle to such approaches. Due to their elevated electronic density, most detergent and lipid molecules cannot be easily contrast matched by the solvent and SAXS is therefore limited to a small number of compounds (Lipfert et al. 2007; Bu and Engelman 1999). A major breakthrough in recent years has been the advent of online size-exclusion chromatography (SEC), coupled to SAXS, which allowed to separate protein-detergent complexes from micelles and to apply sophisticated modeling approaches (Perez and Koutsioubas 2015; Dovling Kaspersen et al. 2014; Koutsioubas et al. 2013; Berthaud et al. 2012; Wright et al. 2011). Another promising recent development, so far specific to SAXS, are microfluidic platforms (Kondrashkina et al. 2013; Khvostichenko et al. 2013) that would allow the application of kinetic experiments to membrane protein systems.

12.7 Conclusions and Outlook

The past 10 years have witnessed an increasing number of SANS applications on solubilized membrane systems, as well as a rising level of sophisticated data interpretation (multiphase and full-atomic modelling) and biochemical sample preparation (deuteration strategies and choice of detergent/lipid/nanodisc systems). The ensemble of studies presented here illustrates that SANS is gaining momentum as a complementary structural biology technique to crystallography, cryo-EM and NMR and continues to provide valuable new insights into membrane protein function. Recently, SANS has also been used as a tool to optimize and tune detergent/lipid arrangements to solubilize and to study membrane proteins (Ashkar et al. 2015; O’Malley et al. 2011). It can be expected that over the next 5–10 years exciting new developments in instrumentation, sample environment, biochemistry and data analysis will help to improve the accuracy of SANS data from membrane proteins and the structural questions that can be addressed. Some recent developments that will gain momentum include SEC-SANS, MD simulations (Le et al. 2014; Chen and Hub 2015; Herrera et al. 2014; Perlmutter et al. 2011) and new labeling schemes for detergent/lipid compounds (Hiruma-Shimizu et al. 2016; Haertlein et al. 2016; Maric et al. 2015; Breyton et al. 2013b; Sverzhinsky et al. 2014) as well as new systems to solubilize membrane proteins (Maric et al. 2014; Midtgaard et al. 2014). Finally, newly developed or upgraded SANS instruments at various neutron sources (Dewhurst et al. 2016; Abbas et al. 2015; Jaksch et al. 2014; Heller et al. 2014; Liu et al. 2013) will improve the accessibility and impact of the technique further and open it to a broader scientific community.