Box 5.3 (continued)
effect and consider that the associated surfactant mixture has the same composition whether
adsorbed to the protein or free as protein-free particles. Finally, a last assumption is that the
concentration of detergent monomers is given by the CMC multiplied by the volume fraction of
the detergent in the belts and particles. This approximation rests on the double assumption that
(i) the rate of collision of the monomers with the surface of the particles or belts, and the probability
that the collision will lead to the monomer being incorporated, is about the same whatever the
composition of the belt or particle, and (ii) that the residence time of a monomer in a particle or belt
does not depend on the latter’s composition. The first hypothesis is probably reasonable for an
uncharged detergent like C 12 E 8 . The second one seems reasonable as well, given that it is the free
energy cost of extracting the hydrophobic chain of the detergent and exposing it to water that
determines the residence time (see e.g. Frindi et al. 1992a, b) and that this value is not going to
change significantly with the composition of the mixture. It could change, however, if the mixture is
not ideal and detergent polar heads, for instance, interact more or less favorably with the APol than
they do between themselves.
The concentration of C 12 E 8 monomers in an A8-35/C 12 E 8 aqueous mixture, [Det] mono , is
equal to [Det] tot – [Det] mic , where [Det] tot is the total concentration of detergent in the sample and
[Det] mic that of the aggregated detergent present in the mixed micelles and protein-bound belts.
Given the assumptions discussed above, [Det] mic is given by the following quadratic equation:
a Á Det
½ mic
2 þ b Á Det
½ mic þ c ¼ 0
with:
a ¼
v det ,
b ¼ CMCÁ v det – [Det] tot Á v det + [A8-35] tot Á v A8-35 ,
c ¼ À [Det] tot Á[A8-35] tot Á v A8-35 .
v A8-35 ¼ 0.809 LÁg
À1 (Gohon et al. 2004) and
v det ¼ 0.973 LÁg
À1 (le Maire et al. 2000) are
respectively the specific volumes of A8-35 and C 12 E 8 and [A8-35] tot the total concentration of APol
in the sample. The composition of the protein-bound belt and mixed particles under the experimental conditions of Fig. 5.31 as calculated according to this equation are given in the legend to the
figure and have been used to draw its Panel C.
The diminished activity of SERCA1a when its environment is enriched in APols is accompanied
by biochemical stabilization. As shown in Fig. 5.33, the ATPase inactivates within minutes if it is
deprived of Ca
2+ in the presence of detergent (blue curve). Upon transfer into an environment
comprising, in mass, about 3 g of A8-35 per g of C 12 E 8 , the rate of inactivation is considerably
slowed, with the time for half-inactivation reaching ~1 h (green curve). An intermediate situation is
observed when the surfactant belt contains about equal masses of APol and detergent (purple curve)
(Champeil et al. 2000). As shown in Fig. 5.31C, the first condition corresponds, in the presence of ATP
and Ca
2+ , to full activity, the second one to an activity reduced to ~10% of that in pure detergent, and
the third one to ~20% activity.
An apparent anticorrelation between activity and stability was also observed when comparing
the protective and inhibitory effects of various types of APols on SERCA1a (Picard et al. 2006). Four
APols were tested, namely A8-35, PMAL-C12, PMALA-C12, and a SAPol. In addition to the
inhibition of ATPase activity (Fig. 28A) and the stability over time upon calcium removal
(Fig. 28C), the slowing down by APols of the rate of Ca
2+ release from TM binding site I was also
examined (Fig. 5.34B). This process requires opening of the bundle of TM helices to create a way out
for the ion (Toyoshima and Nomura 2002; Toyoshima and Inesi 2004; Obara et al. 2005; see Chap. 1,
§ 1.6.3). As a rule, little or no difference is observed, at a given APol concentration, between the effects
of A8-35, PMAL-C12, and PMALA-C12. SAPol, on the contrary, was found to be both less inhibitory
5.6 Membrane Protein Dynamics and the Effects of Amphipols on Stability and Function
299
effect and consider that the associated surfactant mixture has the same composition whether
adsorbed to the protein or free as protein-free particles. Finally, a last assumption is that the
concentration of detergent monomers is given by the CMC multiplied by the volume fraction of
the detergent in the belts and particles. This approximation rests on the double assumption that
(i) the rate of collision of the monomers with the surface of the particles or belts, and the probability
that the collision will lead to the monomer being incorporated, is about the same whatever the
composition of the belt or particle, and (ii) that the residence time of a monomer in a particle or belt
does not depend on the latter’s composition. The first hypothesis is probably reasonable for an
uncharged detergent like C 12 E 8 . The second one seems reasonable as well, given that it is the free
energy cost of extracting the hydrophobic chain of the detergent and exposing it to water that
determines the residence time (see e.g. Frindi et al. 1992a, b) and that this value is not going to
change significantly with the composition of the mixture. It could change, however, if the mixture is
not ideal and detergent polar heads, for instance, interact more or less favorably with the APol than
they do between themselves.
The concentration of C 12 E 8 monomers in an A8-35/C 12 E 8 aqueous mixture, [Det] mono , is
equal to [Det] tot – [Det] mic , where [Det] tot is the total concentration of detergent in the sample and
[Det] mic that of the aggregated detergent present in the mixed micelles and protein-bound belts.
Given the assumptions discussed above, [Det] mic is given by the following quadratic equation:
a Á Det
½ mic
2 þ b Á Det
½ mic þ c ¼ 0
with:
a ¼
v det ,
b ¼ CMCÁ v det – [Det] tot Á v det + [A8-35] tot Á v A8-35 ,
c ¼ À [Det] tot Á[A8-35] tot Á v A8-35 .
v A8-35 ¼ 0.809 LÁg
À1 (Gohon et al. 2004) and
v det ¼ 0.973 LÁg
À1 (le Maire et al. 2000) are
respectively the specific volumes of A8-35 and C 12 E 8 and [A8-35] tot the total concentration of APol
in the sample. The composition of the protein-bound belt and mixed particles under the experimental conditions of Fig. 5.31 as calculated according to this equation are given in the legend to the
figure and have been used to draw its Panel C.
The diminished activity of SERCA1a when its environment is enriched in APols is accompanied
by biochemical stabilization. As shown in Fig. 5.33, the ATPase inactivates within minutes if it is
deprived of Ca
2+ in the presence of detergent (blue curve). Upon transfer into an environment
comprising, in mass, about 3 g of A8-35 per g of C 12 E 8 , the rate of inactivation is considerably
slowed, with the time for half-inactivation reaching ~1 h (green curve). An intermediate situation is
observed when the surfactant belt contains about equal masses of APol and detergent (purple curve)
(Champeil et al. 2000). As shown in Fig. 5.31C, the first condition corresponds, in the presence of ATP
and Ca
2+ , to full activity, the second one to an activity reduced to ~10% of that in pure detergent, and
the third one to ~20% activity.
An apparent anticorrelation between activity and stability was also observed when comparing
the protective and inhibitory effects of various types of APols on SERCA1a (Picard et al. 2006). Four
APols were tested, namely A8-35, PMAL-C12, PMALA-C12, and a SAPol. In addition to the
inhibition of ATPase activity (Fig. 28A) and the stability over time upon calcium removal
(Fig. 28C), the slowing down by APols of the rate of Ca
2+ release from TM binding site I was also
examined (Fig. 5.34B). This process requires opening of the bundle of TM helices to create a way out
for the ion (Toyoshima and Nomura 2002; Toyoshima and Inesi 2004; Obara et al. 2005; see Chap. 1,
§ 1.6.3). As a rule, little or no difference is observed, at a given APol concentration, between the effects
of A8-35, PMAL-C12, and PMALA-C12. SAPol, on the contrary, was found to be both less inhibitory
5.6 Membrane Protein Dynamics and the Effects of Amphipols on Stability and Function
299