Using light scattering to assess how phospholipid–protein interactions affect complex I functionality in liposomes

Complex I is an essential membrane protein in respiration, oxidising NADH and reducing ubiquinone to contribute to the proton-motive force that powers ATP synthesis. Liposomes provide an attractive platform to investigate complex I in a phospholipid membrane with the native hydrophobic ubiquinone substrate and proton transport across the membrane, but without convoluting contributions from other proteins present in the native mitochondrial inner membrane. Here, we use dynamic and electrophoretic light scattering techniques (DLS and ELS) to show how physical parameters, in particular the zeta potential (ζ-potential), correlate strongly with the biochemical functionality of complex I-containing proteoliposomes. We find that cardiolipin plays a crucial role in the reconstitution and functioning of complex I and that, as a highly charged lipid, it acts as a sensitive reporter on the biochemical competence of proteoliposomes in ELS measurements. We show that the change in ζ-potential between liposomes and proteoliposomes correlates linearly with protein retention and catalytic oxidoreduction activity of complex I. These correlations are dependent on the presence of cardiolipin, but are otherwise independent of the liposome lipid composition. Moreover, changes in the ζ-potential are sensitive to the proton motive force established upon proton pumping by complex I, thereby constituting a complementary technique to established biochemical assays. ELS measurements may thus serve as a more widely useful tool to investigate membrane proteins in lipid systems, especially those that contain charged lipids.


Lipid compositions in liposomes and PLs
For all experiments using a simplified lipid mixture or adjusting the cardiolipin content, the final amounts for each component are summarised in Table S2.

Introduction to Multi-Angle Dynamic Light Scattering (MADLS)
Multi-angle dynamic light scattering (MADLS) provides an angular-independent vesicle size distribution with improved resolution relative to standard DLS techniques measuring at a single angle. 2 As populations may appear weakly scattering at one detection angle, but more apparent at a different one, the combination of all measured size distributions improves insight into all vesicle sizes present in the sample.
The Zetasizer Ultra performs an automated series of single-angle measurements: backscatter (173°), side scatter (90°) and forward scatter (15°). MADLS derives a single number of vesicles for all detection angles by analysing multiple autocorrelations which are treated as parallel observation s.
The goal is to find the size distribution that is the best fit for all data sets. The additional time investment to perform MADLS (~5 min for three replicates) instead of single-angle light scattering (~2 min for three replicates) is minimal.
Single-angle DLS measurements are analysed by applying a least square minimization algorithm on the recorded autocorrelation function to determine the best fit and the related vesicle distribution.
The specific algorithm (here: "General purpose") influences the constraints that may be placed on the solution (e.g. smoothness or non-negativity). The transformation from result to measurement can be described by the following scattering matrix The autocorrelation coefficient ( ) is measured at each lag time τ, whereas the number of vesicles (d) is intrinsically weighted by the intensity of the scattered light of each component. Each element in the scattering matrix, ( , ) can be calculated as a function of lag time and vesicle size distribution according to Eq. 2 where the field autocorrelation function 1 ( ) is further defined by the scattering vector q and the translational diffusion coefficient t . The latter corresponds to the vesicle size (hydrodynamic diameter dH) via the Stokes equation.
MADLS extends the single-angle method by transforming equation 1 into a system containing multiple linear equations where 1 , 2 , and 3 denote the three applied scattering angles. One crucial aspect when combining data from several angles is to preserve the weighting inherent in the vesicle size distribution. Therefore, the scattering matrix for each measurement angle is weighted by the expected scattered intensity. The scattered intensity (specifically differential scattering cross-section) is calculated using Mie theory 3 and requires knowledge of the material and dispersant optical properties (refractive index and absorption).
In deriving the solution, the least squares minimisation algorithm aims to reduce the magnitude of the residual (the difference between the measured autocorrelation function and the prediction).

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Each angular contribution to the residual is weighted separately to account for the result uncertainty expected for that detection angle.

Calculating the number of vesicles using MADLS
The size distribution produced by MADLS applies an array of discrete size classes logarithmically spaced across the measurable size range to represent the distribution of sizes within the sample. Each vesicle contributes to the result by an amount proportional to the intensity of light that it scatters; the respective scattered intensity is, therefore, a function of the vesicle diameter d. As such, the native DLS-derived vesicle size distribution is termed an intensity-weighted size distribution x(d).
The intensity-weighted size distribution is related to the absolute number of vesicle distribution, ρ(d), i.e. the number of vesicles per unit volume per size class, according to equation 4 4 : where d sca dΩ (d) describes the size-dependent differential scattering cross-section of the vesicles, i.e.
the fraction of photons scattered into a unit solid angle, Ipar is the derived photon count rate due to the vesicle scattering, Itol is the derived photon count rate scattered by the reference liquid toluene.
Rtol is the Rayleigh ratio (differential cross-section per unit volume) of toluene. The differential scattering cross-section is calculated applying Mie theory 3 , therefore knowledge about the material and dispersant refractive index are needed.
The left-hand side of the equation can be interpreted as total light scattered by each vesicle size class. The right-hand side, the detected photon count rate, is normalised by the instrument detection efficiency defined via the detected count rate per unit volume for a toluene reference sample. The required information and measurements to derive the number of vesicles via the ZS Xplorer software are listed below: • Backscatter-equivalent intensity-weighted size distribution using MADLS for a given sample

Determining the lipid concentration in liposomes and PLs via light scattering
Based on the approach introduced by Di Prima et.al. 5 , the essential parameters that need to be fixed for the two performed extrusions are: • Weighted total mass of lipid components employed for preparation of the starting film (M0) • Recovered volumes after the first and second extrusion cycle (V1, V2) • Total volume inserted into extruder (V T ), i.e. the sum of the starting volume and the volume of solvent which is added for second extrusion. Note that VT will not correspond to the sum V1 + V2, since the dead volume ΔV remains trapped.
By measuring the volume obtained after the second extrusion, we could determine the dead volume of the setup.
To calculate the actual weight concentration in our samples, the light scattering intensity on appropriate dilutions of the two extruded solutions (I and II) is measured. The static light scattering intensity measured at a specific detection angle = w θ Eq. 5 is linked to the weight averaged molecular mass (Mw), the weight concentration (c) and the so-called form factor ( θ ). The constant k depends on the experimental setup and sample parameters. Equation 5 is valid for diluted conditions, where particle interactions are absent. Moreover, the form factor can be approximated to 1 if the dimension of the studied particles is smaller than 1/10 of the laser wavelength used.
For the extruded samples I and II, the light scattering is measured with diluted samples (dilution factors d1 and d2) and can be expressed as: Eq. 6.1 Eq. 6.2 For the two samples, the parameters k, M w and θ are the same. Since the form factor depends on the vesicle size distribution, MADLS measurements are used to compare the distribution between I and II to ensure this approach is applicable for the prepared samples.
The two equations 6.1 and 6.2 can be combined into: which contains two unknown variables with 1 and 2 . However, based on the extrusion experiment, we can describe how the lipid mass is conserved by 0 = 1 1 + 2 ( T − 1 ), Eq. 8 applying the correlation of 2 + = T − 1 . In the calculations, it is assumed that the concentration in volume 2 and corresponds to 2 (since the amount of spare lipids trapped in the extruder is negligible). Equations 7 and 8 can be combined to give: , the concentrations of interest can be calculated using: Eq. 10

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The method presented is applicable to vesicles of various dimensions and the signal can be collected at any detection angle for the two samples. In case of the Zetasizer Ultra, data measured at back and side scattering were used for the lipid concentration calculations.
For our PLs samples, the same calculation was applied, but instead of comparing the two extruded samples, extrusion I was correlated with the PL data.

Principle
Calculation of the ζ-potential involves the measurement of electrophoretic mobility µe as well as knowledge of solvent viscosity, ionic strength, and vesicle size. Under an applied electrical field, charged vesicles move due to their ζ-potential, which cannot be measured directly and is deduced from µe. 6 The electrophoretic mobility (equation 11) itself is defined as: with v as the velocity of the charged vesicles and E as electric field strength. By electrophoretic light scattering (here Phase Analysis Light Scattering; PALS), the speed of the mobile vesicles is determined through the frequency shift between the light scattered by the sample and the original laser (Doppler shift). 7 The ζ-potential is calculated with the measured electrophoretic mobility µe using Henry's equation: Eq. 12 where ε0 = vacuum permittivity, εr = relative permittivity, F(κa) = Henry's function and η = viscosity. Henry's function itself depends on the thickness of the electrical double layer κ −1 and the vesicle radius a, which we here replace with the mean value of the measured hydrodynamic radii RH for each vesicle system. To determine the actual ζ-potential values, we used the relative permittivity and viscosity of pure water directly from the ZS Xplorer database included with the analysis software. The thickness of the electrical double layer κ −1 , also known as the Debye length, can be calculated as follows: ( ) = 16 + 18 + 3( ) 2 16 + 18 + 2( ) 2 .

Eq. 14
The values determined for the ionic strength and Henry's function for each vesicle system are used to translate the measured electrophoretic mobility into the desired ζ-potential.

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The overall workflow to determine the ζ-potential is summarised in Scheme S1.
Scheme S1 -Relationships between the concepts and parameters involved with electrophoretic mobility measurements and ζ-potential estimates. Scheme adapted from Lowry et al. 9

Calculation
The ζ-potentials determined from the measured electrophoretic mobilities are summarised in Table S4, for liposomes and proteoliposomes with the lipid composition of DOPC:DOPE:CL 8:1:1.
The thickness of the electric double layer (κ − ) is the same for most of the performed measurements due to the constant measurement conditions for pH, ionic strength and ionic components inside the dispersant. Hence, only the change in vesicle radius (a) affects Henry's function. In most cases, the size of our vesicle systems is very similar, therefore the variations in F(κa) are minor. The main contribution to the changes in the presented ζ-potential values therefore derives from the different electrophoretic mobilities of the measured vesicle species.

Average number of R-CI per PL
To determine the average number of R-CI in PLs, the combination of the total protein concentration (cR-CI; NADH:APAD + assay) and number of vesicles is needed. The total protein content is required to calculate the number of R-CI molecules inside the measurement cell (sample volume V = 0.06 mL); dividing this number by the measured number of vesicles yields the average number of enzymes per PL.

Average number of CLs per PL
Based on the measured total lipid concentration and the applied lipid mixture, we can use the number of vesicles from the MADLS to determine the amount of each lipid type in the lipid bilayer.  (Table S5).

Contributions to Δζ and average number of 'associated' CLs to reconstituted R-CI
The calculated change in ζ-potential is affected by interconnected parameters such as protein-lipid interactions, the total number of reconstituted R-CI as well as number of outward-facing hydrophilic domains of the protein. Moreover, at higher protein:lipid ratios, protein-protein interactions can contribute to the measured effective surface charge. By comparing changes in Δζ with the changes for outward-facing R-CI (Table S6), an estimate of the contribution of protein-lipid interactions and the amount of outward-facing R-CI to Δζ can be obtained. Table S6. Calculation of the impact of outward-facing R-CI domains and protein-lipid interactions (especially CL) on the measured change in ζ-potential defined as Δζ = ζ(PLs)-ζ(liposomes). Data sets are taken from Figure 2E and Table 1 (variable lipid compositions with fixed protein:lipid ratio of 1:25).

NR-CI (outward)
Δζ relative to DOPC NR-CI change relative to DOPC Impact of R-CI in % (5)
The comparisons indicate that the change in the effective surface charge from PLs containing only DOPC and DOPE relative to the 'optimised' composition is dominated by the increased amount of outward-facing R-CI (~72% contribution). The 72% estimate from Table S6 can be used to determine how many CL molecules are 'associated' per reconstituted R-CI (Table S7). See main text for a discussion of the meaning of 'associated' CL with R-CI.  Figure 2E/ Table 1.  Figure 2E). **The %-change in row 4 was obtained by reducing the value from row 3 by the percentage values presented in Table S6 (27.9% for data columns 2 and 3, hence 'adjusted Δζ'). Row 5 was obtained by multiplying the values in row 1 with those in row 4 ÷ 100.

Aggregation of AOX and influence on liposomes
Before carrying out ζ-potential measurements, the influence of AOX on liposomes and PL size was investigated. Below an AOX concentration of 1.0 µg/mL (0.67:1 AOX to R-CI mass ratio), no significant changes in the size distributions are visible. At higher values, the size distribution shifts to a larger hydrodynamic diameter, indicating surface association of AOX on the lipid bilayer (see Figure S4). AOX alone at 10 µg/mL in aqueous buffer solution results in one peak at larger diameters, indicating S14 the presence of aggregated AOX (black traces). These aggregates are not present in the liposomes and PL vesicle systems, meaning that all the AOX is assembled on the surface. For the same set of liposomes and PLs, the change in the mean hydrodynamic diameter and ζpotential are shown in Figure S5. . The ζ-potential values for liposomes and PLs without AOX are included as a black and red bar, respectively. The data relate Figure S4. Note that the red data points in B are equivalent to the black data points in Figure 4Ai in the main text, except that they were obtained on a different batch of PLs (showing some variation in the data). S15

Figure S7
is an alternative representation of the data in Figure 4Bi, i.e. the red/blue arrows correspond to the red/blue bars in Figures 4Bi and S7, respectively. Control experiments with piericidin (at 2.5 wt% and 10 wt% CL) show that there are no significant ζ-potential changes in the presence of this R-CI inhibitor (the black/red/blue bars are all zero within error). S17 Figure S8 -Change in ζ-potential between liposomes and PLs containing 2.5-10 wt% CL plotted against (A) protein retention, (B) outward orientation, (C) catalytical activity (as relative value using the 10 wt% CL mixture as reference point) and (D) average amount of outward-facing R-CI. The mean values for the two measured PL sets (with protein:lipid ratio 1:50) are plotted as well as the two data sets individually.

Figure S9
-Change in ζ-potential between liposomes and PLs with (A) an increase in protein:lipid ratio (fixed 10 wt% CL) and (B) increase CL content (fixed 1:50 protein:lipid ratio) against the total average number (black squares) and outward-facing (red circles) amount of reconstituted R-CI per PL. For A, data points correlate with results shown in Figure 2B and Table 1, whereas panel B presents the mean values for two measured PLs sets are shown (see Figure S8 for individual data sets); data points linked to 0 wt% Cl are shown as hollow symbols. The primary data for the 20 wt% CL sample (mean value from two separate PL batches) can be found in Table  S9.

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The primary data set for the presented 20 wt% CL lipid mixture in Figures 5Bi and Bii are summarised in Table S9.