Table 1.
Physical properties of pure detergents.
Figure 1.
Two-component core-shell models used to represent the hydrophobic micelle core and hydrophilic head group shell.
Schematic of the core-shell models having core axial dimensions of a and b with a uniform shell thickness of t for a (A) sphere (a = b), (B) prolate ellipsoid (a>b), and (C) oblate ellipsoid (a<b). The alkyl chain core is typically less electron dense (0.27–0.29 e/Å3) than the solvent (0.33–0.34 e/Å3) and the detergent head group shell (0.49–0.52 e/Å3). These differences in scattering power, along with size and shape of the micelle determine the form factors of the SAXS profile (see Methods S1 for additional descriptions of SAXS theory and core-shell ellipsoid micelle models). Panel (D) shows a comparison of the expected form factors resulting from each of the three different model geometries: prolate ellipsoid in green (a/b = 2); oblate ellipsoid in blue (b/a = 2); and sphere in red (a/b = 1). Core and shell volumes, and electron densities (ρ1 = 0.28, ρ2 = 0.50, ρs = 0.337) were kept constant; sphere, a = b = 20.0 Å, t = 5.0 Å; prolate ellipsoid, a = 31.7 Å, b = 15.9 Å, t = 4.8 Å; oblate ellipsoid, a = 12.6 Å, b = 25.2 Å, t = 4.8 Å.
Figure 2.
Scattering data, Guinier analysis, and core-shell ellipsoid fit for FC14, OM, DG, and LMPG.
(A) SAXS profiles (I(q)) for each detergent at total detergent concentrations of FC14: 58 (red), 78 (purple), 97 (green), 147 (brown), and 199 (cyan) mM; OM: 36 (yellow), 56 (red), 75 (purple), 95 (green), 146 (brown), and 195 (cyan) mM; DG: 12.5 (blue), 25 (yellow), and 50 (red) mM; and LMPG: 16 (blue), 36 (yellow), 54 (red), 75 (purple), 94 (green), 144 (brown), and 193 (cyan) mM. (B) Guinier plot (ln(I) as a function of q2) of the low angle data (same color scheme as part A) and Guinier fits (black lines). For DG, the Guinier region deviated from linearity at low q (denoted by *) as described in the results, and prevented accurate extrapolation to zero-scattering angle. Thus, aggregation numbers for DG could not be determined from the I(0) method, and the plot (panel D, see below) is not presented. An increase in scattering signal with increasing concentration is generally observed, except for LMPG at high concentration and low q (denoted with **) where interparticle effects described in the results become more apparent at higher concentrations. (C) Two-component ellipsoid fit (black solid line) and scattering intensity recorded at low detergent concentration (same color scheme as part A). The residuals of the fit are shown in the upper inset. Fit parameters are presented in Table 2. (D) Apparent aggregation numbers Nexpt (squares, same color scheme as in part A) obtained from the extrapolated forward scattering intensity and eq 7 described in Methods S1. The point at 0 mM (black) corresponds to the estimate obtained by linearly extrapolating the measured profiles for [c–cmc] ≤100 mM to zero micelle concentration (i.e. cmc). Errors are obtained from repeat fits using measurements from three molecular weight standards. Additional descriptions of micelle measurements and calculations can be found in Methods S1.
Table 2.
Geometrical parameters of detergent micelles.
Figure 3.
Radii of gyration obtained from Guinier fits and the ellipsoid models correlate.
Radii of gyration (Rg’s) for varied alkyl chain lengths of phosphocholine (▴), glucoside (•), maltoside (▪), and lysophosphatidyl glycerol (▾) detergent head groups were determined from Guinier analysis of the low angle scattering data and calculated from the model geometry (Methods S1). A correlation plot illustrates the agreement between the Rg determined from the Guinier analysis of the scattering data (Rgexpt) with the Rg calculated from the model geometry (Rgmodel) for each detergent. The dashed line represents a perfect correlation between the two approaches.
Figure 4.
Dependence of aggregation number on alkyl chain length.
(A) The relationship between aggregation numbers determined from hydrophobic core volume (Nmodel) and Guinier analysis (Nexpt) is shown using same shapes for phosphocholine (▴), maltoside (▪), and lysophosphatidyl glycerol (▾) head groups with a dashed line illustrating Nmodel = Nexpt. (B) Aggregation numbers for each alkyl chain series using the same symbols as in (A), as well as glucoside (•), (N-alkylamino)-1-deoxylactitol [30] (□), and sucrose ester [31] (◊) head groups, are plotted against the number of carbons comprising the alkyl chain. Solid lines (and dashed line for sucrose esters and lactitols) are linear fits to each data series, calculated from the hydrophobic core volume (Nmodel). Equations and quality of fit are as follows: (▴), N = 14.5 nc –94, R2 = 0.986; (•), N = 15.0 nc –42, R2 = 0.964; (▪), N = 20.5 nc –97, R2 = 0.998; (□), N = 13.5 nc –75, R2 = 0.999; (◊), N = 14.5 nc –79, R2 = 0.944. Lysophosphatidyl glycerols fits are not reported since there are only two data points in the series.
Figure 5.
Dependence of dominant distance between head groups across the micelle on alkyl chain length.
The dominant distances between head groups across the micelle are shown for phosphocholine (▴), glucoside (•), maltoside (▪), and lysophosphatidyl glycerol (▾) detergents. (A) The correlation is shown between the dominant distance determined from the position of the second peak in the experimental SAXS profiles (Lexpt) and the corresponding distance estimated from the model fit (Lmodel). The dashed line represents a perfect correlation between the two approaches. (B) The distance determined from the best model fit for each detergent (Lmodel) is plotted as a function of the number of carbons in the detergent’s alkyl chain (nc). The dotted line represents the distance of two alkyl chains having a fully extended hydrocarbon chain according to Tanford’s formula for alkyl chain length.