Selected interactions of ubiquinone with the membrane environment. Ubiquinone is represented in sticks and the lipid bilayer is represented in lines and balls with phosphate P in ochre and choline N in blue. Water molecules and atoms of lipid that interact with UQ1 and UQ1H2 are depicted in balls and sticks, and hydrogen bonds are indicated in black dashed line. Carbon atoms are colored cyan, H in white and O in red. Panels A and B show bidentate water – ubiquinone oxygen hydrogen bonds. Hydrogen bonds of ubiquinol hydrogen with water are show in panel C and with POPC phosphate is shown in panel D. 

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... fi cient reported for UQ0 was obtained in a water – octanol mixture [65]. For the other ubiquinones, partition coef fi cients were obtained in bovine heart submitochondrial particles with a mixed lipid composition [66], or in sonicated asolectin vesicles mainly composed by phosphatidylcholine [67]. Thus, part of the diver- gence between experimental and simulated values may be attributed to differences in the model composition. The highest differences from experiment in the binding free energy calculations are observed for UQ1 and UQ1H2 in Table 1. For the quinone, the calculated Δ G ∘ b suggests an af fi nity of 6 – 12 kJ mol − 1 lower than the experimental values. For the quinol, an af fi nity of 8 kJ mol − 1 higher than experiment is found. These differences may be due to unbalanced interactions of the quinone (or quinol) head with the lipid polar group. Values calculated for UQ0 and UQ2 are almost equivalent to the experimental measurements. No experimental value for UQ6 partition coef fi cient is available, but the binding free energy for biological ubiquinones was estimated to be more negative than − 60 kJ mol − 1 [66]. As noted above, we do not expect to have a quanti- tative value for UQ6 binding free energy. Thus, given the statistical uncertainty in the simulations, the composition differences between the simulated models and experimental setups, and the variations of measured values, we conclude that our force- fi eld yields PMFs and derived free energy quantities in good agreement with experimental observations. The agreement of Δ G ∘ b calculated for UQ1 and UQ2 between US and BEMD methods also suggests a good accuracy for the calculated PMFs. These two methods estimate free energies using different assumptions and the simulations were carried out independently in different bilayer preparations (LS for US and SS for BEMD). The in fl uence of the bilayer size on the binding free energy calculated here from the BEMD simulation should be negligible. For instance, Δ G ∘ b = − 10 ± 3 kJ mol − 1 for UQ1 insertion in the MS bilayer is equivalent to the value calculated for the SS bilayer (Table 1). On the other hand, the force- fi eld description changes the calculated biding free energy considerably. For the insertion of UQ1 in the LS membrane using US and the force- fi eld proposed by Kaszuba et al. [28], the calculated Δ G ∘ b = 1 ± 1 kJ mol − 1 is 18 kJ mol − 1 higher than the experimental value. Such high hydrophilicity of the Kaszuba et al. potential can be attributed to the incorrect high polarity of the isoprenoid tail observed with their charge parametrization (Table S4). This artifact will be more pronounced for ubiquinones with longer isoprenoid tails as the total dipole for the longer tails will be a vector sum of the contributions of each isoprenoid unit. Convergence of the calculated PMFs can be accessed from the derived free energies of binding obtained over different equilibration (US) or total simulation (BEMD) times as shown in the insets of Figs. 4 and 5. For the US simulations, the calculated Δ G ∘ b shows variations smaller than ~3 kJ mol − 1 after 15 ns of equilibration time in each window. For the BEMD simulations, Δ G ∘ b shows variations smaller than ~ 6 kJ mol − 1 after 80 ns of total simulation time. Both variations are comparable to the uncertainties estimated from the PMFs. Higher precision would require much longer simulation times [61]. However, we do not judge a higher precision necessary as the variations of reference partition coef fi cients measured for same ubiquinone in different experimental preparations are similar to the present calculated statistical uncertainties (~3 kJ mol − 1 ). Besides essential sampling over the bilayer insertion coordinate ( z axis), we identify that enhanced sampling over the coordination numbers between water or lipid molecules and the ubiquinone head and tail ( N g 1 – g 2 in Eq. (1)) are the most important ones in order to describe the slow relaxation of the solvation substitution process in the membrane interface. Thus, convergence of calculated PMFs in BEMD simulations can be signi fi cantly accelerated for ubiquinones with longer isoprenoid tails by enhanced sampling of the coordination between water and tail. Enhanced sampling of ubiquinone orientation and internal degrees of freedom are less important. For instance, a BEMD simulation with enhanced sampling of methoxide bonds (C2 – O2 and C3 – O3) resulted in a Δ G ∘ b = 1 ± 1 kJ mol − 1 for UQ0 which is equivalent to the binding free energy calculated for UQ0 without such enhancement (Table 1). Rotations through these methoxide bonds as well as in quinol hydroxide bonds (H1 – O1 and H4 – O4) are observed over the simulation time of the US and BEMD simulations (Fig. S5). It should be noted that rotations over C6 – C7 bonds were not observed during the accumulation time of the US windows, but were observed on the longer free MD simulations (see Section 3.3 and the discussion of Fig. 8). However, increasing the sampling of this C6 – C7 bond as done in the BEMD simulations does not lead to signi fi cant differences in the calculated PMF and derived quantities. Ubiquinone insertion induced a structural perturbation in the bilayer when the ubiquinone polar head group is located near the membrane midplane (ubiquinone head COM with z b 0.6 nm) as shown in Fig. 6. This protrusion has a “ funnel ” -like shape and corresponds to both lipid head groups and water molecules dragged towards the membrane center. The number of contacts with water also reports the signi fi cant hydration of the ubiquinone head when partitioned inside the membrane (Fig. S3). The opposite effect when ubiquinone desorbs from the bilayer was not observed [61], suggesting that the solvation substitution in the bilayer interface is more favorable than membrane deformation. Results presented over the remaining of this and the next sections (Figs. 7 – 12) were obtained from unconstrained MDs started from the last frame of the 60 ns US window with lowest free energy value in the respective PMF. This should correspond to the equilibrium con fi guration of ubiquinone embedded in the bilayer. Isoprenoid tails should be well equilibrated as restrictions in US were included only in the ubiquinone head. The last 180 ns for UQ1 – UQ2 and the last 360 ns for UQ6 and UQ10 of the unconstrained MD trajectories are used for analysis. Considerable effort has been made towards describing ubiquinone localization in lipid bilayers. The two main proposals in the literature suggest that ubiquinone head lies in the bilayer midplane, oriented parallel to membrane plane [6 – 10] or that the head group is localized near the water – bilayer interface close to the glycerol average position [12 – 15]. Our results strongly support the second model as the minima observed in all PMFs calculated here corresponds to z ≈ 1.6 nm. The z insertion coordinate is equivalent to the distance between the membrane midplane and the COM of the ubiquinone head. Thus, contrary to previous suggestions [16], the localization of the ubiquinone head does not change signi fi cantly with the length of the isoprenoid tail. It is remarkable that the average positions of ubiquinone ring in cytochrome bc 1 (complex III) for both the Q o and Q i redox sites are observed around the same z -axis values (±1.6 nm) [68,69]. The entrance of the narrow ubiquinone chamber in NADH:ubiquinone reductase (complex I) is also located near the membrane interface at an approximately similar z -axis value [70]. Thus, the equilibrium location of ubiquinones in a bilayer matches the position of protein binding sites in respiratory complexes, probably facilitating the binding mechanism and increasing the rate of protein binding and unbinding. The sharp monotonic distribution of the distance between the last isoprenoid carbon (CT) and the COM of the ubiquinone head shown in Fig. 7A for UQ1 and UQ2 suggests a reduced internal fl exibility for the tails of ubiquinones with few isoprenoid units. The UQ6 tail, however, has high internal conformational fl exibility and a broad distribution centered at 2 nm. A similar broad distribution is observed for the UQ10 terminal isoprenoid carbon (data not shown). The UQ6 tail distribution is altered when ubiquinone is moved inside the membrane (Fig. S4) suggesting that a tail rearrangement is observed during the ubiquinone fl ip- fl op pathway. Fig. 7B shows the localization of CT regarding membrane normal. The isoprenoid tail is mostly extended and in contact with lipid acyl chains up to about the sixth isoprenoid unit. Given the polar head localization discussed above, ubiquinones span the membrane similar to a POPC molecule. For UQ6 and longer ubiquinones, the tail length is longer than the POPC acyl chain. CT interdigitates over the two bilayer lea fl ets and it is preferentially localized in the lea fl et opposed to its head. For UQ10, the four terminal isoprenoid units have increasingly higher fl exibility. In fact, the terminal CT in UQ10 equally samples the whole apolar region of both membrane lea fl ets (Fig. S4). This is contrary to previous suggestions that the isoprenoid tail would fold over itself [22,19] and suggests that no aggregation or clustering of ubiquinones inside the lipid bilayer should be observed in the concentration range studied here (~2% per mol) [66]. It should be noted that the distribution of z -axis position of the terminal carbon in POPC (both chains, data not shown) is about an order of magnitude less broad than observed here for ubiquinone CT. The higher fl exibility in the ubiquinone tail might be related to its higher diffusion rates (Section 3.4) [19] and may also facilitate binding into the narrow NADH:ubiquinone reductase ubiquinone chamber. The equilibrium ubiquinone head orientation is indicated in Fig. 7C. For all ubiquinones studied (UQ1 up to UQ10), the quinone head is oriented normal to the membrane, forming ...

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... as shown in Fig. 6. This protrusion has a “ funnel ” -like shape and corresponds to both lipid head groups and water molecules dragged towards the membrane center. The number of contacts with water also reports the signi fi cant hydration of the ubiquinone head when partitioned inside the membrane (Fig. S3). The opposite effect when ubiquinone desorbs from the bilayer was not observed [61], suggesting that the solvation substitution in the bilayer interface is more favorable than membrane deformation. Results presented over the remaining of this and the next sections (Figs. 7 – 12) were obtained from unconstrained MDs started from the last frame of the 60 ns US window with lowest free energy value in the respective PMF. This should correspond to the equilibrium con fi guration of ubiquinone embedded in the bilayer. Isoprenoid tails should be well equilibrated as restrictions in US were included only in the ubiquinone head. The last 180 ns for UQ1 – UQ2 and the last 360 ns for UQ6 and UQ10 of the unconstrained MD trajectories are used for analysis. Considerable effort has been made towards describing ubiquinone localization in lipid bilayers. The two main proposals in the literature suggest that ubiquinone head lies in the bilayer midplane, oriented parallel to membrane plane [6 – 10] or that the head group is localized near the water – bilayer interface close to the glycerol average position [12 – 15]. Our results strongly support the second model as the minima observed in all PMFs calculated here corresponds to z ≈ 1.6 nm. The z insertion coordinate is equivalent to the distance between the membrane midplane and the COM of the ubiquinone head. Thus, contrary to previous suggestions [16], the localization of the ubiquinone head does not change signi fi cantly with the length of the isoprenoid tail. It is remarkable that the average positions of ubiquinone ring in cytochrome bc 1 (complex III) for both the Q o and Q i redox sites are observed around the same z -axis values (±1.6 nm) [68,69]. The entrance of the narrow ubiquinone chamber in NADH:ubiquinone reductase (complex I) is also located near the membrane interface at an approximately similar z -axis value [70]. Thus, the equilibrium location of ubiquinones in a bilayer matches the position of protein binding sites in respiratory complexes, probably facilitating the binding mechanism and increasing the rate of protein binding and unbinding. The sharp monotonic distribution of the distance between the last isoprenoid carbon (CT) and the COM of the ubiquinone head shown in Fig. 7A for UQ1 and UQ2 suggests a reduced internal fl exibility for the tails of ubiquinones with few isoprenoid units. The UQ6 tail, however, has high internal conformational fl exibility and a broad distribution centered at 2 nm. A similar broad distribution is observed for the UQ10 terminal isoprenoid carbon (data not shown). The UQ6 tail distribution is altered when ubiquinone is moved inside the membrane (Fig. S4) suggesting that a tail rearrangement is observed during the ubiquinone fl ip- fl op pathway. Fig. 7B shows the localization of CT regarding membrane normal. The isoprenoid tail is mostly extended and in contact with lipid acyl chains up to about the sixth isoprenoid unit. Given the polar head localization discussed above, ubiquinones span the membrane similar to a POPC molecule. For UQ6 and longer ubiquinones, the tail length is longer than the POPC acyl chain. CT interdigitates over the two bilayer lea fl ets and it is preferentially localized in the lea fl et opposed to its head. For UQ10, the four terminal isoprenoid units have increasingly higher fl exibility. In fact, the terminal CT in UQ10 equally samples the whole apolar region of both membrane lea fl ets (Fig. S4). This is contrary to previous suggestions that the isoprenoid tail would fold over itself [22,19] and suggests that no aggregation or clustering of ubiquinones inside the lipid bilayer should be observed in the concentration range studied here (~2% per mol) [66]. It should be noted that the distribution of z -axis position of the terminal carbon in POPC (both chains, data not shown) is about an order of magnitude less broad than observed here for ubiquinone CT. The higher fl exibility in the ubiquinone tail might be related to its higher diffusion rates (Section 3.4) [19] and may also facilitate binding into the narrow NADH:ubiquinone reductase ubiquinone chamber. The equilibrium ubiquinone head orientation is indicated in Fig. 7C. For all ubiquinones studied (UQ1 up to UQ10), the quinone head is oriented normal to the membrane, forming an angle of ~ 90° with the midplane. The angle distribution is rather sharp, with fl uctuations smaller than 30° in the time scale of the unconstrained MD simulations. Atoms C5 and C6 of the ubiquinone ring point to the center of the bilayer and atoms C1 – C4 point towards the solution phase as expected from the more hydrophilic groups attached to the last centers (Fig. 8). Thus, the ubiquinone orientation when bound to the membrane does not change with increased isoprenoid tail length. When the quinone head is inserted into the low-packing bilayer center ( z ~ 0 nm) as well as when it is free in solution ( z N 4.0 nm) during the US simulations the whole orientation space is sampled and ubiquinone head tumbles almost freely (Fig. S4). Since ubiquinones have been suggested to order lipid membranes [9], we have computed carbon – hydrogen order parameters S CD for sn − 1 and sn − 2 chains of POPC for simulations of ubiquinone-free bilayers and for bilayers containing ubiquinones of different isoprenoid chain length. While average S CD order parameters show small shifts for ubiquinone containing bilayers, there was a signi fi cant change in order parameters of POPC molecules approximately in the fi rst ubiquinone lipid shell (within 0.7 – 0.8 nm) as shown in Fig. 9. Acyl chain order- ing upon ubiquinone addition observed in fl uorescence anisotropy measurements [9] was more pronounced for short tail homologs. This is again in agreement with our simulation results. Ubiquinone and ubiquinol oxygens were highly hydrated when partitioned into the membrane as shown in Fig. 10. This is due to the interfacial localization of the quinone head and to the bilayer protrusion (Fig. 6). Ubiquinone oxygens, both ketonic and methoxyl (Figs. 10A and S6A) have a fi rst solvation layer formed by water and lipid choline groups. Glycerols have also signi fi cant contribution to the fi rst interaction layer, while phosphate groups were farther away. This is again in agreement with previous suggestions from experimental studies [12 – 15]. Ubiquinol showed a very similar interaction pattern for methoxyl oxygens (Fig. S6B), while hydroxyl oxygens show a perturbed pattern in comparison to the quinone oxygens (Fig. 10B). These hydroxyl oxygens have sharper interactions with the water solvent and with the lipid phosphate group because of the donation of hydrogen bonds. H1 and H4 establish bonds with lipid phosphate groups (Fig. 8D) and water molecules (Fig. 8C) for half of the simulation time. In approximately the other half of the simulation, intramolecular bonds are formed between H1 (H4) and O2 (O3). When located inside the bilayer, the intramolecular hydrogen bonds are prevailing. However, it should be noted that all these hydrogen bonds break and form quickly with an average life time of 1 ns. The intramolecular hydrogen bonds in UQ1H2 can also be analyzed from the respective C1 – O1 (or C4 – O4) bond torsions (Fig. 11). The energy minimum of the force- fi eld calculated in vacuum found at ~ 0° is normally populated in solution as it corresponds to the intramolecular hydrogen bond H1 – O2 and H4 – O3. The second energy minimum at ± 180° is not populated in solution or in the membrane, as water or any H-bond acceptor (such as the lipid phosphate, Fig. 8) is hindered by HM5 or H7 and no hydrogen bond can be established for this con fi guration. The intermolecular acceptors bind to UQ1H2 hydrogens when this torsion is ±60°, resulting in a broad distribution for C1 – O1 (or C4 – O4) bond torsions in the [ − 90°,90°] range. Rotamers of the methoxide groups with angles of ±70° for torsion of bonds C2 – O2 and C3 – O3 are more populated in condensed phase than expected from their force- fi eld energy pro fi les (Fig. 11B). As described above, O2 and O3 are available as H-bond acceptors preferentially for these dihedral angles (Fig. 8A and B) [29]. The region around 0° is less populated as these con fi gurations partially block hydrogen bonding to O1/O4. In the bilayer interior, where no H-bond donors are available, bond torsion distributions are closer to what is expected from the force- fi eld pro fi le (Fig. S5A). Distributions of non-polar bond torsions are not changed from the corresponding torsion potentials, as shown in Fig. 11C and D for the C6 – C7 and C9 – C11 bonds in the isoprenoid tail. It should be noted that transitions over the high energy barriers around bond C6 – C7 were observed during the unconstrained MD simulation time scale (200 ns). The dynamics of ubiquinone embedded in the bilayer was investi- gated by the self part of van Hove correlation function, G s ( r , Δ t ) [71, 72]. This function gives the probability for a particle to show position displacements ( r ) in Δ t time intervals. The van Hove distributions for POPC at 0.01 ns and longer times are gaussian-shaped as shown in Fig. 12. This is expected for a simple diffusion mechanism and is in agreement with a fast characteristic relaxation time ( b 10 ps) for lipids in liquid crystalline phase [73,74]. In this regime, the mean square dis- placement has a linear dependence with respect to time ( x 2 ( t ) ∝ t ). The same behavior is observed for ubiquinone and ubiquinol, but relaxation times are shorter and higher displacements are observed in the same timescale. In contrast to what is observed for the pure POPC ...

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... tail distribution is altered when ubiquinone is moved inside the membrane (Fig. S4) suggesting that a tail rearrangement is observed during the ubiquinone fl ip- fl op pathway. Fig. 7B shows the localization of CT regarding membrane normal. The isoprenoid tail is mostly extended and in contact with lipid acyl chains up to about the sixth isoprenoid unit. Given the polar head localization discussed above, ubiquinones span the membrane similar to a POPC molecule. For UQ6 and longer ubiquinones, the tail length is longer than the POPC acyl chain. CT interdigitates over the two bilayer lea fl ets and it is preferentially localized in the lea fl et opposed to its head. For UQ10, the four terminal isoprenoid units have increasingly higher fl exibility. In fact, the terminal CT in UQ10 equally samples the whole apolar region of both membrane lea fl ets (Fig. S4). This is contrary to previous suggestions that the isoprenoid tail would fold over itself [22,19] and suggests that no aggregation or clustering of ubiquinones inside the lipid bilayer should be observed in the concentration range studied here (~2% per mol) [66]. It should be noted that the distribution of z -axis position of the terminal carbon in POPC (both chains, data not shown) is about an order of magnitude less broad than observed here for ubiquinone CT. The higher fl exibility in the ubiquinone tail might be related to its higher diffusion rates (Section 3.4) [19] and may also facilitate binding into the narrow NADH:ubiquinone reductase ubiquinone chamber. The equilibrium ubiquinone head orientation is indicated in Fig. 7C. For all ubiquinones studied (UQ1 up to UQ10), the quinone head is oriented normal to the membrane, forming an angle of ~ 90° with the midplane. The angle distribution is rather sharp, with fl uctuations smaller than 30° in the time scale of the unconstrained MD simulations. Atoms C5 and C6 of the ubiquinone ring point to the center of the bilayer and atoms C1 – C4 point towards the solution phase as expected from the more hydrophilic groups attached to the last centers (Fig. 8). Thus, the ubiquinone orientation when bound to the membrane does not change with increased isoprenoid tail length. When the quinone head is inserted into the low-packing bilayer center ( z ~ 0 nm) as well as when it is free in solution ( z N 4.0 nm) during the US simulations the whole orientation space is sampled and ubiquinone head tumbles almost freely (Fig. S4). Since ubiquinones have been suggested to order lipid membranes [9], we have computed carbon – hydrogen order parameters S CD for sn − 1 and sn − 2 chains of POPC for simulations of ubiquinone-free bilayers and for bilayers containing ubiquinones of different isoprenoid chain length. While average S CD order parameters show small shifts for ubiquinone containing bilayers, there was a signi fi cant change in order parameters of POPC molecules approximately in the fi rst ubiquinone lipid shell (within 0.7 – 0.8 nm) as shown in Fig. 9. Acyl chain order- ing upon ubiquinone addition observed in fl uorescence anisotropy measurements [9] was more pronounced for short tail homologs. This is again in agreement with our simulation results. Ubiquinone and ubiquinol oxygens were highly hydrated when partitioned into the membrane as shown in Fig. 10. This is due to the interfacial localization of the quinone head and to the bilayer protrusion (Fig. 6). Ubiquinone oxygens, both ketonic and methoxyl (Figs. 10A and S6A) have a fi rst solvation layer formed by water and lipid choline groups. Glycerols have also signi fi cant contribution to the fi rst interaction layer, while phosphate groups were farther away. This is again in agreement with previous suggestions from experimental studies [12 – 15]. Ubiquinol showed a very similar interaction pattern for methoxyl oxygens (Fig. S6B), while hydroxyl oxygens show a perturbed pattern in comparison to the quinone oxygens (Fig. 10B). These hydroxyl oxygens have sharper interactions with the water solvent and with the lipid phosphate group because of the donation of hydrogen bonds. H1 and H4 establish bonds with lipid phosphate groups (Fig. 8D) and water molecules (Fig. 8C) for half of the simulation time. In approximately the other half of the simulation, intramolecular bonds are formed between H1 (H4) and O2 (O3). When located inside the bilayer, the intramolecular hydrogen bonds are prevailing. However, it should be noted that all these hydrogen bonds break and form quickly with an average life time of 1 ns. The intramolecular hydrogen bonds in UQ1H2 can also be analyzed from the respective C1 – O1 (or C4 – O4) bond torsions (Fig. 11). The energy minimum of the force- fi eld calculated in vacuum found at ~ 0° is normally populated in solution as it corresponds to the intramolecular hydrogen bond H1 – O2 and H4 – O3. The second energy minimum at ± 180° is not populated in solution or in the membrane, as water or any H-bond acceptor (such as the lipid phosphate, Fig. 8) is hindered by HM5 or H7 and no hydrogen bond can be established for this con fi guration. The intermolecular acceptors bind to UQ1H2 hydrogens when this torsion is ±60°, resulting in a broad distribution for C1 – O1 (or C4 – O4) bond torsions in the [ − 90°,90°] range. Rotamers of the methoxide groups with angles of ±70° for torsion of bonds C2 – O2 and C3 – O3 are more populated in condensed phase than expected from their force- fi eld energy pro fi les (Fig. 11B). As described above, O2 and O3 are available as H-bond acceptors preferentially for these dihedral angles (Fig. 8A and B) [29]. The region around 0° is less populated as these con fi gurations partially block hydrogen bonding to O1/O4. In the bilayer interior, where no H-bond donors are available, bond torsion distributions are closer to what is expected from the force- fi eld pro fi le (Fig. S5A). Distributions of non-polar bond torsions are not changed from the corresponding torsion potentials, as shown in Fig. 11C and D for the C6 – C7 and C9 – C11 bonds in the isoprenoid tail. It should be noted that transitions over the high energy barriers around bond C6 – C7 were observed during the unconstrained MD simulation time scale (200 ns). The dynamics of ubiquinone embedded in the bilayer was investi- gated by the self part of van Hove correlation function, G s ( r , Δ t ) [71, 72]. This function gives the probability for a particle to show position displacements ( r ) in Δ t time intervals. The van Hove distributions for POPC at 0.01 ns and longer times are gaussian-shaped as shown in Fig. 12. This is expected for a simple diffusion mechanism and is in agreement with a fast characteristic relaxation time ( b 10 ps) for lipids in liquid crystalline phase [73,74]. In this regime, the mean square dis- placement has a linear dependence with respect to time ( x 2 ( t ) ∝ t ). The same behavior is observed for ubiquinone and ubiquinol, but relaxation times are shorter and higher displacements are observed in the same timescale. In contrast to what is observed for the pure POPC lipid, linearity of squared-displacement x 2 ( t ) with time is lost for ubiquinones at times longer than 25 ns, already observed from the non-gaussian shape of the t = 10 ns curve for UQ6 (Fig. 12B). It may be attributed to a slow relaxation process of the lipid polar group and water solvating ubiquinone at the bilayer interface. Table 2 shows lateral diffusion coef fi cients D calculated from the Einstein ...