large contaminants seen by DLS, and its amplitude is consistent with their small mass fraction (see
below).
Stuhrmann plots, which examine the variations of R g
2 vs. the inverse of the contrast between the
particles and the solution – the latter being modulated by adjusting the D 2 O/H 2 O ratio in the buffer –
yield information about the organization of the various moieties inside the particles (Stuhrmann 1970).
The plots for DAPol solutions are consistent with the hydrophobic alkyl chains occupying the core of
the particles and the hydrophilic backbone the surface, as expected, whereas those for HAPol solutions
are too noisy to be conclusive (Gohon 2001; Gohon et al. 2006).
Taken together, this ensemble of data is consistent with A8-35 particles being roughly spherical,
having a mass of ~40 kDa, a radius of gyration R g % 2.4 nm, and a Stokes radius R S % 3.15 nm
(Table 4.3). A particle of 40 kDa comprises 75–80 octyl chains, which is similar to the number of
detergent alkyl chains in most micelles (Chap. 2), as well as to the number of alkyl chains that form
hydrophobic clusters in sparingly modified polyacrylates (Petit-Agnely and Iliopoulos 1999; PetitAgnely et al. 2000). The existence, within A8-35 particles, of a hydrophobic core whose size is similar
to that in detergent micelles is expected on thermodynamic reasons, consistent with the Stuhrmann
plots derived from SANS measurements on DAPol particles (Gohon et al. 2006), and strongly
supported by MD calculations (Perlmutter et al. 2011; see next section).
Taking the number-average mass of A8-35 molecules, hM n i, to be ~4.3 kDa, the average particle
is therefore comprised of ~9 mol. Given the broad mass distribution of the molecules, some particles
will actually comprise only a few large ones and some 20 or more small ones. Comparison of the dry
mass and volume of the particles suggests that they are highly hydrated, comprising ~1.2 g water per g
of APol (Table 4.3). As will be further discussed below (§ 4.3.1.2.5), the size and shape of the particles
do not appear to change as a function of concentration, in keeping with FRET data (Giusti et al. 2012),
which also suggest that the size of the assemblies does not change much (Fig. 4.10). Table 4.3,
reproduced from Gohon et al. 2006, sums up the main properties of A8-35 particles and the way each
piece of information has been acquired.
It is interesting to note that neither the variable length of the chains nor the random distribution of
octyl side groups in A8-35 hampers the formation of well-defined particles, even though those are not
perfectly monodisperse. Particle polydispersity is more likely due to individual differences between
molecules in the batch rather than to metastability or a broad equilibrium distribution of energetically
nearly equivalent sizes around an optimal one, based on the following two arguments: (i) fractions
selected by SEC from a batch that migrates as a broad peak will yield a narrow one upon being
fractionated again (Gohon et al. 2006), suggestive of differences of composition between big and small
particles, and (ii) exchange of molecules between small A8-35 particles is likely to be fast on the time
d
Scattering length density in H 2 O, from Gohon et al. (2004)
e Molecular mass calculated from the forward intensity at zero angle according to Jacrot and Zaccai (1981)
f
Molecular mass calculated using data collected at 5
C and 12,000 rpm and the whole sedimentation
profile
g
Sedimentation coefficient of the major population of small particles, representing the indicated mass
fraction
h
Operational parameter φ
0 (apparent specific volume), from Gohon et al. (2004)
i
Molecular mass calculated from s 20,w , φ
0 , and R S from SEC and SANS using the Svedberg equation
j
Consensus number-average mass, hM n i, averaged from SANS and sedimentation velocity AUC estimates
k
Partial specific volume, from Gohon et al. (2004)
l
Radius of a sphere of dry APol with the consensus mass
m
Maximal amount of associated water, estimated from R S /R min
4.3 Self-Association Behavior of Amphipols in Aqueous Solutions
181
below).
Stuhrmann plots, which examine the variations of R g
2 vs. the inverse of the contrast between the
particles and the solution – the latter being modulated by adjusting the D 2 O/H 2 O ratio in the buffer –
yield information about the organization of the various moieties inside the particles (Stuhrmann 1970).
The plots for DAPol solutions are consistent with the hydrophobic alkyl chains occupying the core of
the particles and the hydrophilic backbone the surface, as expected, whereas those for HAPol solutions
are too noisy to be conclusive (Gohon 2001; Gohon et al. 2006).
Taken together, this ensemble of data is consistent with A8-35 particles being roughly spherical,
having a mass of ~40 kDa, a radius of gyration R g % 2.4 nm, and a Stokes radius R S % 3.15 nm
(Table 4.3). A particle of 40 kDa comprises 75–80 octyl chains, which is similar to the number of
detergent alkyl chains in most micelles (Chap. 2), as well as to the number of alkyl chains that form
hydrophobic clusters in sparingly modified polyacrylates (Petit-Agnely and Iliopoulos 1999; PetitAgnely et al. 2000). The existence, within A8-35 particles, of a hydrophobic core whose size is similar
to that in detergent micelles is expected on thermodynamic reasons, consistent with the Stuhrmann
plots derived from SANS measurements on DAPol particles (Gohon et al. 2006), and strongly
supported by MD calculations (Perlmutter et al. 2011; see next section).
Taking the number-average mass of A8-35 molecules, hM n i, to be ~4.3 kDa, the average particle
is therefore comprised of ~9 mol. Given the broad mass distribution of the molecules, some particles
will actually comprise only a few large ones and some 20 or more small ones. Comparison of the dry
mass and volume of the particles suggests that they are highly hydrated, comprising ~1.2 g water per g
of APol (Table 4.3). As will be further discussed below (§ 4.3.1.2.5), the size and shape of the particles
do not appear to change as a function of concentration, in keeping with FRET data (Giusti et al. 2012),
which also suggest that the size of the assemblies does not change much (Fig. 4.10). Table 4.3,
reproduced from Gohon et al. 2006, sums up the main properties of A8-35 particles and the way each
piece of information has been acquired.
It is interesting to note that neither the variable length of the chains nor the random distribution of
octyl side groups in A8-35 hampers the formation of well-defined particles, even though those are not
perfectly monodisperse. Particle polydispersity is more likely due to individual differences between
molecules in the batch rather than to metastability or a broad equilibrium distribution of energetically
nearly equivalent sizes around an optimal one, based on the following two arguments: (i) fractions
selected by SEC from a batch that migrates as a broad peak will yield a narrow one upon being
fractionated again (Gohon et al. 2006), suggestive of differences of composition between big and small
particles, and (ii) exchange of molecules between small A8-35 particles is likely to be fast on the time
d
Scattering length density in H 2 O, from Gohon et al. (2004)
e Molecular mass calculated from the forward intensity at zero angle according to Jacrot and Zaccai (1981)
f
Molecular mass calculated using data collected at 5
C and 12,000 rpm and the whole sedimentation
profile
g
Sedimentation coefficient of the major population of small particles, representing the indicated mass
fraction
h
Operational parameter φ
0 (apparent specific volume), from Gohon et al. (2004)
i
Molecular mass calculated from s 20,w , φ
0 , and R S from SEC and SANS using the Svedberg equation
j
Consensus number-average mass, hM n i, averaged from SANS and sedimentation velocity AUC estimates
k
Partial specific volume, from Gohon et al. (2004)
l
Radius of a sphere of dry APol with the consensus mass
m
Maximal amount of associated water, estimated from R S /R min
4.3 Self-Association Behavior of Amphipols in Aqueous Solutions
181