monomer. We describe here (i) how best to express the amount of APol bound per MP, (ii) how to
estimate a priori the amount of APol a given MP is likely to bind, and (iii) three protocols for
measuring it using FAPols.
5.9.2.1 Why Is It Preferable to Express the Amount of APols Bound per MP in Mass
Rather Than as a Number of Molecules?
APols being highly polydisperse polymers, the size of individual molecule varies considerably, and
their MW can be estimated only on average (see Chap. 4, Box 4.1). The number-average mass of
A8-35 molecules is ~4.3 kDa, but they are widely polydisperse (see Chap. 4, § 4.2.1). Nevertheless,
despite the variable mass of individual APol chains, the particles they form in solution migrate upon
SEC with a size distribution almost as narrow as that of globular proteins. SANS and AUC analyses
indicate that they feature a well-defined Stokes radius (R S % 3.15 nm) and mass (~40 kDa) (Gohon
et al. 2006) (Chap. 4, Table 4.3). The average mass of individual molecules being only a rough
estimate, the amount of APol bound per MP is more meaningfully expressed in mass ratio rather than
as a molar stoichiometry. Similarly, in the case of functionalized APols, to preserve accuracy and
reliability, the number of fluorophores or tags is better expressed as their number per 40 kDa APol
particle, which can be used as a mass reference, rather than as their number per APol chain, which
has no great significance and is inaccurate.
5.9.2.2 How to Estimate A Priori the Likely Amount of APols Bound per MP Based
on Structural Data?
In the case of α-helical MPs, the most thoroughly studied MP/APol complexes are those of BR with
A8-35. In the complexes, the protein/APol mass ratio is ~1:2, i.e. ~54 kDa of A8-35 per monomer of
BR (27 kDa) (Gohon et al. 2008). Lipids (~9 kDa) are also present in the complexes. In the case of
β-barrel MPs, the best characterized complexes, in terms of composition, are those of tOmpA with
A8-35. The mass ratio that has been estimated is ~1:1.3, i.e. ~25 kDa of A8-35 per monomer of tOmpA
(19 kDa) (Zoonens et al. 2007). This value should be considered as a minimal value, however, because
the conditions under which the measurements were done (see below) led to some aggregation and,
very likely, to the loss of some APol. MD calculations suggest an upper value of ~45 kDa A8-35 per
tOmpA monomer (Perlmutter et al. 2014) (see § 5.3.3). The truth lies probably between these two
estimates.
Based on these values, and assuming that the volume of the A8-35 belt surrounding a MP is
roughly proportional to the perimeter of the TM domain to be covered, it is possible to estimate the
amount of APols interacting with any other MP. The only information needed is the dimensions of the
hydrophobic domain of the protein of interest, modeled as a cylinder filled up by the TM helices or
delimited by the TM β-strands, whose perimeter increases roughly as the square root of the number of
helices (α-helical bundles) or linearly with the number of β-strands. For instance, the TM domain of
BR is a bundle of seven α-helices. If the MP of interest has a similar TM topology, like a GPCR, it can
be expected to bind approximately the same amount of A8-35, i.e. ~54 kDa (BR/A8-35 complexes
comprise ~9 kDa of bound lipids (Gohon et al. 2008), which increases slightly the TM perimeter, but
the effect on APol binding is likely to be minor). On the other hand, if the MP contains twice more
helices than BR and features a more or less homothetic shape, the volume of its TM domain doubles,
while the TM surface increases by ~40%, and one can expect in the ballpark of ~75 kDa of bound
A8-35. It is fair to say, however, that too few accurate measurements are available to date (Table 5.5)
to gather how reliable such an approach is, the plot of whatever few binding data are available vs. the
square root of the number of TM helices showing a considerable scatter (Fig. 5.13). The only other
relatively precise estimate of bound A8-35 has been obtained with the cytochrome bc 1 dimer, which
5.9 Protocols
315
estimate a priori the amount of APol a given MP is likely to bind, and (iii) three protocols for
measuring it using FAPols.
5.9.2.1 Why Is It Preferable to Express the Amount of APols Bound per MP in Mass
Rather Than as a Number of Molecules?
APols being highly polydisperse polymers, the size of individual molecule varies considerably, and
their MW can be estimated only on average (see Chap. 4, Box 4.1). The number-average mass of
A8-35 molecules is ~4.3 kDa, but they are widely polydisperse (see Chap. 4, § 4.2.1). Nevertheless,
despite the variable mass of individual APol chains, the particles they form in solution migrate upon
SEC with a size distribution almost as narrow as that of globular proteins. SANS and AUC analyses
indicate that they feature a well-defined Stokes radius (R S % 3.15 nm) and mass (~40 kDa) (Gohon
et al. 2006) (Chap. 4, Table 4.3). The average mass of individual molecules being only a rough
estimate, the amount of APol bound per MP is more meaningfully expressed in mass ratio rather than
as a molar stoichiometry. Similarly, in the case of functionalized APols, to preserve accuracy and
reliability, the number of fluorophores or tags is better expressed as their number per 40 kDa APol
particle, which can be used as a mass reference, rather than as their number per APol chain, which
has no great significance and is inaccurate.
5.9.2.2 How to Estimate A Priori the Likely Amount of APols Bound per MP Based
on Structural Data?
In the case of α-helical MPs, the most thoroughly studied MP/APol complexes are those of BR with
A8-35. In the complexes, the protein/APol mass ratio is ~1:2, i.e. ~54 kDa of A8-35 per monomer of
BR (27 kDa) (Gohon et al. 2008). Lipids (~9 kDa) are also present in the complexes. In the case of
β-barrel MPs, the best characterized complexes, in terms of composition, are those of tOmpA with
A8-35. The mass ratio that has been estimated is ~1:1.3, i.e. ~25 kDa of A8-35 per monomer of tOmpA
(19 kDa) (Zoonens et al. 2007). This value should be considered as a minimal value, however, because
the conditions under which the measurements were done (see below) led to some aggregation and,
very likely, to the loss of some APol. MD calculations suggest an upper value of ~45 kDa A8-35 per
tOmpA monomer (Perlmutter et al. 2014) (see § 5.3.3). The truth lies probably between these two
estimates.
Based on these values, and assuming that the volume of the A8-35 belt surrounding a MP is
roughly proportional to the perimeter of the TM domain to be covered, it is possible to estimate the
amount of APols interacting with any other MP. The only information needed is the dimensions of the
hydrophobic domain of the protein of interest, modeled as a cylinder filled up by the TM helices or
delimited by the TM β-strands, whose perimeter increases roughly as the square root of the number of
helices (α-helical bundles) or linearly with the number of β-strands. For instance, the TM domain of
BR is a bundle of seven α-helices. If the MP of interest has a similar TM topology, like a GPCR, it can
be expected to bind approximately the same amount of A8-35, i.e. ~54 kDa (BR/A8-35 complexes
comprise ~9 kDa of bound lipids (Gohon et al. 2008), which increases slightly the TM perimeter, but
the effect on APol binding is likely to be minor). On the other hand, if the MP contains twice more
helices than BR and features a more or less homothetic shape, the volume of its TM domain doubles,
while the TM surface increases by ~40%, and one can expect in the ballpark of ~75 kDa of bound
A8-35. It is fair to say, however, that too few accurate measurements are available to date (Table 5.5)
to gather how reliable such an approach is, the plot of whatever few binding data are available vs. the
square root of the number of TM helices showing a considerable scatter (Fig. 5.13). The only other
relatively precise estimate of bound A8-35 has been obtained with the cytochrome bc 1 dimer, which
5.9 Protocols
315