three favorable factors: (i) they are rare (typically ~0.1% of DAPol in mass; see Gohon et al. 2006 and
Chap. 4, ibid.); (ii) they do not bind BR (note the absence of low-angle deflection when DAPol is
contrast-matched; inverted triangles); and (iii) due to their large R g , their contribution falls rapidly at
high Q, so that they do not scatter significantly in nor beyond the Guinier region used for determining
the mass and R g of the complexes, where the signal from BR/DAPol complexes and small DAPol
particles is predominant.
At ~85% D 2 O (inverted triangles), where DAPol is contrast-matched (Gohon et al. 2006),
Guinier plots are essentially linear, consistent with the limited polydispersity of BR/DAPol complexes
already observed by SEC (§ 9.3.2) and AUC (§ 9.3.7). The curvature of the curve due to the presence
of ~20% dimers and ~5% trimers (see below) is barely detectable.
Figure 9.19C, D shows the normalized forward intensities (Panel C) and radii of gyration (Panel
D), respectively, derived from the extrapolated value at zero angle and from the slope of the Guinier
plots. In Panel C, the value of Æ (N A I(0)/c BR )½ is plotted as a function of the percentage of D 2 O in the
solvent. This term includes the contributions of both BR/DAPol complexes and small free DAPol
particles. The contribution of the latter is small (~15% of I(0) in H 2 O), but, close to the contrastmatching point of the complexes, it prevents perfect matching, so that I(0) never falls exactly to zero.
The composition of the BR/lipid/DAPol complexes determines their contrast-matching point (experimental interpolated value, 61 Æ 2% D 2 O), whereas the presence of multimers affects slightly the slope
of the Guinier plot, from which the R g of the complexes is derived, and the value of I(0), used to
calculate their mass (cf. Panel B). Predicted I(0) values were calculated for various models and
compared to experimental ones. The BR/DAPol sample was assumed to contain a major species,
comprised of one molecule of BR, purple membrane lipids in the same ratio as in the membrane, and
1.8 or 2.2 g DAPol per g of BR (models 1 and 2, respectively), along with an adjustable number of
multimers thereof. Scattering by free DAPol particles (~0.38 gÁL
À1 , based on sedimentation velocity
data) was taken to be identical to that of pure DAPol solutions (Gohon et al. 2006). The calculated
contribution of the different components is shown (thin dashed lines). A good fit of the forward
intensities is obtained, for this sample, for 75% monomers, 20% dimers, and 5% trimers (w/w), which
is consistent with sedimentation velocity results.
SANS data also contain information about the relative arrangement of the protein and APol in
the BR/DAPol complexes. In Panel D, a so-called Stuhrmann plot is shown, in which the square of the
radius of gyration of BR/DAPol particles, R g
2 , is plotted vs. the inverse of the contrast, ρ N – ρ 0 ,
between the complex and the solvent. The plot is linear, which indicates that BR and the DAPol moiety
of the complexes have the same center of mass (Stuhrmann 1970). The positive slope of the plot
indicates that, as expected, the component of highest scattering density (DAPol) lies farther from the
center of mass of the particle than BR. The point where the plot crosses (ρ N – ρ 0 )
À1
¼ 0 (infinite
contrast) yields R g
, the radius of gyration that the complex would exhibit were it chemically
homogeneous, a very useful constraint for model building.
From the ensemble of chemical analysis, AUC and SANS data, a crude model of the complex
was built (Fig. 9.20). It includes one BR monomer with the crystallographic structure of BR and nine
protein-bound purple membrane lipids (Belrhali et al. 1999), to which 2 g DAPol per g BR has been
added as a 1.7 nm thick belt surrounding the TM surface. The R g for monomeric BR calculated from
the PDB file is 1.8 nm; the R g
(R g at infinite contrast) calculated for the model is 2.6 nm. As expected,
given the slight heterogeneity of the samples (see above), experimental values are somewhat larger,
namely R g % 2.3 nm at the match point of DAPol (signal due to BR and lipids) and R g
% 3.0 nm
(Fig. 9.19D). The R g at the match point of BR (where scattering is due to DAPol and lipids) is 3.2 nm,
which is, logically, larger than that measured for pure DAPol particles (2.4 nm) (Gohon et al. 2006).
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9 Solution Studies of Membrane Protein/Amphipol Complexes
Chap. 4, ibid.); (ii) they do not bind BR (note the absence of low-angle deflection when DAPol is
contrast-matched; inverted triangles); and (iii) due to their large R g , their contribution falls rapidly at
high Q, so that they do not scatter significantly in nor beyond the Guinier region used for determining
the mass and R g of the complexes, where the signal from BR/DAPol complexes and small DAPol
particles is predominant.
At ~85% D 2 O (inverted triangles), where DAPol is contrast-matched (Gohon et al. 2006),
Guinier plots are essentially linear, consistent with the limited polydispersity of BR/DAPol complexes
already observed by SEC (§ 9.3.2) and AUC (§ 9.3.7). The curvature of the curve due to the presence
of ~20% dimers and ~5% trimers (see below) is barely detectable.
Figure 9.19C, D shows the normalized forward intensities (Panel C) and radii of gyration (Panel
D), respectively, derived from the extrapolated value at zero angle and from the slope of the Guinier
plots. In Panel C, the value of Æ (N A I(0)/c BR )½ is plotted as a function of the percentage of D 2 O in the
solvent. This term includes the contributions of both BR/DAPol complexes and small free DAPol
particles. The contribution of the latter is small (~15% of I(0) in H 2 O), but, close to the contrastmatching point of the complexes, it prevents perfect matching, so that I(0) never falls exactly to zero.
The composition of the BR/lipid/DAPol complexes determines their contrast-matching point (experimental interpolated value, 61 Æ 2% D 2 O), whereas the presence of multimers affects slightly the slope
of the Guinier plot, from which the R g of the complexes is derived, and the value of I(0), used to
calculate their mass (cf. Panel B). Predicted I(0) values were calculated for various models and
compared to experimental ones. The BR/DAPol sample was assumed to contain a major species,
comprised of one molecule of BR, purple membrane lipids in the same ratio as in the membrane, and
1.8 or 2.2 g DAPol per g of BR (models 1 and 2, respectively), along with an adjustable number of
multimers thereof. Scattering by free DAPol particles (~0.38 gÁL
À1 , based on sedimentation velocity
data) was taken to be identical to that of pure DAPol solutions (Gohon et al. 2006). The calculated
contribution of the different components is shown (thin dashed lines). A good fit of the forward
intensities is obtained, for this sample, for 75% monomers, 20% dimers, and 5% trimers (w/w), which
is consistent with sedimentation velocity results.
SANS data also contain information about the relative arrangement of the protein and APol in
the BR/DAPol complexes. In Panel D, a so-called Stuhrmann plot is shown, in which the square of the
radius of gyration of BR/DAPol particles, R g
2 , is plotted vs. the inverse of the contrast, ρ N – ρ 0 ,
between the complex and the solvent. The plot is linear, which indicates that BR and the DAPol moiety
of the complexes have the same center of mass (Stuhrmann 1970). The positive slope of the plot
indicates that, as expected, the component of highest scattering density (DAPol) lies farther from the
center of mass of the particle than BR. The point where the plot crosses (ρ N – ρ 0 )
À1
¼ 0 (infinite
contrast) yields R g
, the radius of gyration that the complex would exhibit were it chemically
homogeneous, a very useful constraint for model building.
From the ensemble of chemical analysis, AUC and SANS data, a crude model of the complex
was built (Fig. 9.20). It includes one BR monomer with the crystallographic structure of BR and nine
protein-bound purple membrane lipids (Belrhali et al. 1999), to which 2 g DAPol per g BR has been
added as a 1.7 nm thick belt surrounding the TM surface. The R g for monomeric BR calculated from
the PDB file is 1.8 nm; the R g
(R g at infinite contrast) calculated for the model is 2.6 nm. As expected,
given the slight heterogeneity of the samples (see above), experimental values are somewhat larger,
namely R g % 2.3 nm at the match point of DAPol (signal due to BR and lipids) and R g
% 3.0 nm
(Fig. 9.19D). The R g at the match point of BR (where scattering is due to DAPol and lipids) is 3.2 nm,
which is, logically, larger than that measured for pure DAPol particles (2.4 nm) (Gohon et al. 2006).
434
9 Solution Studies of Membrane Protein/Amphipol Complexes