Light scattering corrections to linear dichroism spectroscopy for liposomes in shear flow using calcein fluorescence and modified Rayleigh-Gans-Debye-Mie scattering
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Abstract
The interpretation of data from absorbance spectroscopy experiments of liposomes in flow systems is often complicated by the fact that there is currently no easy way to account for scattering artefacts. This has proved particularly problematic for linear dichroism (LD) spectroscopy, which may be used to determine binding modes of small molecules, peptides and proteins to liposomes if we can extract the absorbance signal from the combined absorbance/scattering experiment. Equations for a modified Rayleigh-Gans-Debye (RGD) approximation to the turbidity (scattering) LD spectrum are available in the literature though have not been implemented. This review summarises the literature and shows how it can be implemented. The implementation proceeds by first determining volume loss that occurs when a spherical liposome is subjected to flow. Calcein fluorescence can be used for this purpose since at high concentrations (> 60 mM) it has low intensity fluorescence with maxima at 525 and 563 nm whereas at low concentrations (<1 mM) the fluorescence intensity is enhanced and the band shifts to 536 nm. The scattering calculation process yields the average axis ratios of the distorted liposome ellipsoids and extent of orientation of the liposomes in flow. The scattering calculations require methods to estimate liposome integrity, volume loss, and orientation when subjected to shear stresses under flow.
Keywords
Scattering linear dichroism liposomes Rayleigh-Gans-Debye Mie Scattering calceinIntroduction
Linear dichroism
Liposome preparation
Many methods that are variations on a theme have been established to produce liposomes of fairly uniform size (Allen and Cleland 1980b; Ardhammar et al. 1998; Maheux et al. 2016; Rajendra et al. 2006). One approach is to dissolve the lipids (and any probes that are desired to be incorportated into the lipid bilayer) in chloroform, then spread them out in a thin film on the inside of a round-bottomed flask by removing the chloroform using a rotary evaporator and a desiccator under vacuum. When the buffer of choice (e.g. sodium phosphate 10 mM, pH 7.4) is added to a final concentration of ~ 20 mg/mL lipid and the flask sonicated, the result is a wide range of sizes of spherical lipid bilayer particles (liposomes) with buffer inside. Two or three freeze-thaw cycles, using dry ice and ethanol to achieve a flash-freeze at approximately − 78 °C, followed by a room temperature thaw creates a suspension of large liposomes which can be reduced to a fairly uniform size by extrusion (typically 11 or 13 times) through a polycarbonate membrane with the desired pore size (typically 100 nm). Dynamic light scattering (using a nano-series Zetasizer, Malvern, UK) usually indicates a narrow distribtuion about 100 nm (or slightly larger) after extrusion (Damianoglou et al. 2010).
Diphenylhexatriene (DPH) (Wemyss et al. 2018) (1% w/w) works quite well as an integral probe added to the lipids at the start of the liposome preparation. It is sometime also desireable to fill liposomes with a different solution than is outside the liposome. Unless liposomes are particularly leaky (see below), this can be achieved by adding the desired molecule to the resuspension buffer and running the extruded liposome solution down a sepharose column 4B column (size 2.5 cm × 5 cm, Sigma-Aldrich) and collecting the second coloured band to be eluted off the column in a mobile phase of EDTA (0.1 mM), TES (10 mM), and NaCl (100 mM).
If the liposomes remained spherical when subjected to shear flow, they will not have an LD signal. So, the observation of an LD signal shear flow is switched on means the liposomes are distorted. Key parameter for understanding what happens to liposomes in flow is therefore their structural integrity and the volume change when flow is switched on and off. How much volume leaks out of the liposomes gives us information about both aspects. Calcein is a fluorophore that has low intensity fluorescence at high concentration (> 60 mM, see below) whereas at low concentrations (< 1 mM) the intensity is significant. This means that vesicles filled with calcein will have only very low fluorescence, but, if the calcein leaks out, the fluorescence switches on and its wavelength maximum and intensity can be used to measure how much has leaked. Vesicles can be prepared containing 50 mM calcein by adding calcein to the resuspension buffer. After extrusion to the required size, external calcein can be removed by size-exclusion chromatography to exclude free dye.
Liposome LD
Nordén et al.(Ardhammar et al. 2002) reduced with the scattering problem for liposome LD by matching the refractive indices of the lipid vesicles and the surrounding medium via the addition of sucrose, thus lowering the relative refractive indices of the liposomes and their environment. This allowed them to measure an accurate true absorbance LD spectrum of membrane-oriented tryptophan down to ~ 220 nm (much of which was previously obscured by scattering). Unfortunately the refractive index-matching approach does not solve the scattering interference problem at lower wavelengths where sucrose absorbs. Using microvolume Couette flow cells (outer rotating quartz capillary ~ 250 μm from a stationary 3 mm quartz rod, Dioptica Scientific Ltd., Rugby, UK) (Marrington et al. 2005; Marrington et al. 2004) where the sample holder is a curved quartz capillary/quartz rod reduces scattering by acting as an additional focusing lens helps reduce the scattered light that does not reach the detector. However, it does not remove it completely.
Liposome shapes in flow
Before reviewing scattering equations derived in the literature of relevance to this problem and illustrating how they can be applied, we need to understand the shapes that liposomes adopt in flow. The fact that liposomes orient in flow means they are not spherical. Marmottant et al. undertook an analytical study of small vesicle deformation for arbitrary flow fields (Marmottant et al. 2008) following the usual assumption that liposomes distort into some kind of ovoid shape in flow. Using phase contrast microscopy of giant (> μm diameter) vesicles Mader et al. (2006) visualised the shape of shear distorted liposomes as ellipses of about 2–3:1 axial ratio and considered their tank-treading and tumbling motion based on the theoretical work of Keller and Skalak (1982). We have used the simpler model of a cylinder with hemispherical caps to model liposomes in previous work (Rodger et al. 2002). For all distortions from spherical, liposome surface area or internal volume or both must change when a solution of liposomes is made to flow. So step 1 for LD analysis is to determine what volume leaks out of liposomes when they are subject to flow distortion.
Calcein fluorescence calibration
At concentrations, above 50 mM, the fluorescence is very weak and the solutions are very dark. In the context of liposome leakage, the wavelength dependence of calcein fluorescence has the advantage over the usually used intensity measurements of directly enabling a quick estimate of liposome integrity. As the chromatography step of producing calcein filled liposomes in a calcein-free solution produced samples with different total amounts of calcein, referencing the calibration to the total calcein present in an experiment is essential. This can be done by rupturing remaining vesicles at the end of a leakage experiment (usually about 30 min) using detergent (e.g., 0.1% w/v Triton X-100) to give the maximum possible fluorescence signal.
Effect of flow on liposome integrity
Liposome volume loss in Couette flow
There are various ways to configure fluorescence experiments, but as a complement to microvolume Couette flow LD experiments, we found that 180° detection with a high quality 480-nm cut-off filter (e.g. Hoya Y-50 long-pass filter (Hoya, Santa Clara, CA, USA) in the transmission path after the sample enables only calcein fluorescence to be detected (Fig. 5) (Wemyss et al. 2018), whereas a second photo-detector at 90° (with no filter) detected both fluorescent and scattered incident light analogous.
It is apparent that most of the stationary liposome samples of Fig. 6 leak to some degree and all samples leak more under flow. Pure POPC, soybean PC and BLTE retained most of their integrity whilst stationary and exhibited only a small volume losses under steady shear flow. DMPC (a very common model membrane system used in biophysical experiments) by way of contrast leaked most of its contents within 500 s when stationary, and much more quickly in flow. To ascertain the volume loss explicitly caused by the distortion of the vesicles under flow what needs to be considered is not simply the volume loss under flow (~ 3.6% for POPC), but rather the additional loss (1.4% for POPC) induced in flow compared with non-flow leakage. The volume loss data can be used to estimate sizes of ellipsoids upon making some assumptions about whether surface area changes or not upon initiation of flow.
Geometry of liposomes in shear flow
Values of orientation parameter, S, and volume, V, calculated according to reference (McLachlan et al. 2013b) for ovoids of length, L, and radius, r, with the same surface area as a sphere of radius 50 nm and volume 524,000 nm^{3}. This makes an upper bound for volume change induced by shear flow and a lower bound for S
r/nm | L/nm | Axis ratio | V/nm^{3} | Fraction V loss | S |
---|---|---|---|---|---|
49 | 104 | 1.06 | 5.23 × 10^{5} | 0.001 | 0.018 |
45 | 121 | 1.34 | 5.12 × 10^{5} | 0.02 | 0.020 |
42 | 134 | 1.60 | 4.96 × 10^{5} | 0.05 | 0.024 |
38 | 154 | 2.03 | 4.67 × 10^{5} | 0.11 | 0.030 |
35 | 171 | 2.45 | 4.39 × 10^{5} | 0.16 | 0.038 |
32 | 191 | 2.98 | 4.09 × 10^{5} | 0.22 | 0.050 |
26 | 240 | 4.62 | 3.40 × 10^{5} | 0.35 | 0.090 |
20 | 316 | 7.90 | 2.65 × 10^{5} | 0.49 | 0.17 |
15 | 423 | 14.1 | 2.00 × 10^{5} | 0.62 | 0.29 |
10 | 636 | 31.8 | 1.33 × 10^{5} | 0.75 | 0.44 |
5. | 1270 | 127 | 6.67 × 10^{5} | 0.87 | 0.67 |
Lipid | Fraction volume loss | Surface area/nm^{3} | r/nm | L/nm | Axis ratio | S |
---|---|---|---|---|---|---|
BTLE | 0.004 | 31,410 | 48 | 108 | 1.12 | 0.018 |
Soy-PC | 0.006 | 31,410 | 47 | 110 | 1.16 | 0.018 |
POPC | 0.014 | 31,410 | 46 | 117 | 1.27 | 0.020 |
POPC/POPS/chol | 0.017 | 31,410 | 45 | 118 | 1.29 | 0.020 |
BTLE | 0.004 | 33,710 | 44 | 138 | 1.58 | 0.028 |
Soy-PC | 0.006 | 33,710 | 43 | 144 | 1.70 | 0.030 |
POPC | 0.014 | 33,710 | 39 | 160 | 2.04 | 0.037 |
POPC/POPS/chol | 0.017 | 33,710 | 38 | 168 | 2.22 | 0.040 |
Options for correcting for scattering contributions to flow LD spectra of liposomes
Although Eq. (6) has been previously used with apparent success (Beevers et al. 2010; Mikati et al. 1987), a wide variation of values for g are required even for similar spectra, in addition to potential for heavily over-correcting at low wavelengths (< 230 nm).
Eq. (6) is reminiscent of Rayleigh scattering which is the elastic scattering of light by particles much smaller than the wavelength of the radiation. With Rayleigh scattering, g = 4. However, our liposomes are comparable in size to the wavelength of the light we use to study them and empirically, we find g < 4. As outlined below, Gans and Debye modified Rayleigh scattering giving the Rayleigh-Gans-Debye (RGD) approximation (Meeten 1981; Mikati et al. 1987; van de Hulst 1981). It has been used theoretically to model light scattering in a much more sophisticated manner than Rayleigh scattering or Eq. (6). However, as noted by Nordén et al. (Ardhammar et al. 2002) these classical scattering theories assumes that particles are isotropically oriented and solid, but liposomes in flow are anisotropic and hollow. The literature contains what is needed to proceed further for LD experiments, though it has yet to be applied to remove τ_{LD} to give A_{LD} from an experiment with significant scattering occurring.
Axiss systems
Rayleigh-Gans-Debye theory applied to LD
In the literature, Eq. (14) is commonly found without any explanation of the terms. If the goal is to calculate the scattering for oriented rods or ellipsoids, a level of understanding is required (Mikati et al. 1987; Craig and Thirunamachandran 1984; Long 2002; van de Hulst 1981). k accounts for the S_{i} amplitude wavelength dependence; α is the isotropic polarizability of the particle; R is described variously as the interference function, form function, or form vector, which accounts for particle orientation and geometry. Since RGD scattering treats every volume element as an independent scatterer, all the waves scattered in a particular direction (β, ε) interfere because of their different origins in space. R(β, ε) therefore represents a phase factor to correct for these interference effects, relating the phases of all the scattered waves to a common origin.
Polarisability, α
R form function for solid ovoids and rod-like particles
The form vectors, R(β, ε), depend on the particle shape, size, axis ratio and orientation. The RGD form factor with a wavelength relationship of k^{4} is attractively simple. However, it was found not to work for tubulin microtubules (Nordh et al. 1986) (Marrington et al. 2006) and actin microfilaments (Rodger et al. 2006) experimental data and our attemtps to make it work for liposomes also failed. Dupuy and Montagu compared RGD and Mie theory (which has a k^{2} dependence, k = 2π/λ) for liposomes of size 170–300 nm, and found Mie theory together with a constant term described the behaviour better. The expressions used in (Meeten 1981; van de Hulst 1981) for two cases: solid ovoids, with long and short semi-axis lengths of a and b, respectively, and rod-like particles of length l, and diameter d have approximately the same k dependence.
K_{O} and the corresponding arguments in Eq. (24) denote the phase shift of the particle (ovoid and rod, respectively) in relation to the particle position and polar/azimuthal angles (β, ε).
Incident intensity–distance relationship and accounting for hollow spheres
A key parameter for calculating the scattering is the instrument parameter I_{0}/r^{2}. Previous workers have failed to explain exactly how this parameter can be determined and by taking ratios of e.g. LD and absorbance avoided the issue. Determination of I_{0} for a particular emitter although complex is possible, however, hard to do accurately in part because of the difficulty in a classical LD experimental setup of determining a value for r. An alternative is to parametrise I_{0}/r^{2} via the fitting of a scattering curve to a spectrum with known liposome deformation and orientation.
Considerations for semi-rigid particles
Although in this work, we calculate S directly following McLachlan et al. (2013b), for completeness and for use in further work where the rigid rod approximation may be inapplicable, the equations for S in the three axis systems used in this work are given below. Mikati et al.(1987) also make use of such equations. In spectroscopic applications, S is usually calculated in terms of the angles with respect to the flow direction. So, in addition to the angles defined in Figures A1 and A2, we define Θ to be the angle between z and Z and Φ to be the angle between the projection of z onto the XY plane and Y. We also follow Mikati et al.(1987) and define hydrodynamic angles where θ_{p} is the angle between Y and y and ϕ_{p} is the angle between the XZ projection of z and X.
Application of Eq. (7) to remove scattering contributions to measured LD spectra
Vesicle scattering correction input parameters (http://www.liposomes.org/search/label/Number%20of%20lipid%20molecules%20per%20liposome; Kucerka et al. 2011; Kučerka et al. 2011) for the code written to implement Eq. (7) in MatLab.(MATLAB and statistics toolbox release 2014b, 2014)
Input parameter | Value |
---|---|
Lipids per vesicle | 8.17 × 10^{4} |
Lipid membrane thickness/nm | 4 |
Capillary volume/μl | 83.25 × 10^{−6} |
Capillary outer diameter/mm | 2.9 |
Capillary inner diameter/mm | 2.4 |
Shear rate/s^{−1} | 1.8 × 10^{3} |
Medium refractive index | 1.33 |
Vesicle refractive index | 1.42 |
Incident light wavelength range/nm | As in experiment |
Distance from detector/cm | 3 |
Detector radius/cm | 1.5 |
I_{0}/r^{2} | 1.05 × 10^{−12} |
Rod-shaped (rather than ovoid) fits were also attempted for the same liposome data, however, although similar fits could be obtained at higher vesicle concentrations, rod-fitting did not work well at low concentrations and was therefore rejected in favour of purely ovoid scattering.
Conclusions
In this work, we have reviewed literature scattering theory for flow LD spectroscopy and illustrated an implementation of the Rayleigh-Gans-Debye scattering theory. We have relied on the expansion of RGD theory undertaken by van de Hulst (1981), Meeten (1981), and Mikati et al.(1987). We used the rigid rod Peterlin-Stuart probability distribution calculation of the orientation parameter, S, to calculate the turbidity linear dichroism of liposomes. The combination enables the absorption linear dichroism even in the presence of significant scattering to be determined. Values for the degree of deformation and volume loss in the LD experiment is a by-product of the spectral correction process. Thus we only need to do the calcein fluorescence assay for the calibrating liposome sample. In this work, we selected a stable set of liposome deformation data to act as a standard from which to calculate instrument parameters τ_{LD} for any lipid system collected in that instrument configuration. Thus, for the first time, we showed that literature theory can be applied to extract the true absorbance LD spectra of light scattering samples, rather than only ratios.
Although the focus in this review has been almost exclusively on flow LD spectroscopy, any optical spectroscopy technique which is less complicated can be addressed with the same approach. The differential intensity term would in general be replaced by an isotropic incident intensity term and we would not need to worry about flow-induced particle volume changes during the experiment.
According to Rayleigh theory, the relationship that a particle has with the wavelength of the incident light has a k^{4} dependence. However, it has been previously shown that this power relationship does not fit experiment for liposomes. Instead the relationship that is demonstrated is far closer to that of classical Mie theory, with a k^{2} dependence. Since our particles are approaching the limits of the size restriction outlined by RGD theory, and just barely under the minimum for Mie theory, it is not unreasonable to see elements of both in effect. The main differences in the approximations for each approach are the particle shape factors, since Mie is primarily restricted to spherical particles whereas RGD allows for asymmetrical particles, and a constant term. The parametrisation approach taken here allows us to take into account unknown constants (e.g. stray light, inhomogeneity, hollow particles)) into the I_{0}/r^{2} term. Therefore, what we have illustrated is a quasi RGD-Mie theory instead of strictly classical RGD.
A calcein fluorescence intensity assay to measure volume loss from liposomes when stationary and when deformed under shear flow was also illustrated. Calcein fluorescence not only enhances significantly with dilution as is well established but also shifts from 525/563 nm to 536 nm. 1/λ_{max} can be used to determine calcein concentration below ~ 45 mM with fluorescence depending approximately linearly on concentration between 45 and 10 mM. Leakage depends upon the type of lipid and the duration of flow, with the shorter chain DMPC exhibiting the highest degree of leakage even when stationary, questioning the usefulness of the extensive DMPC liposome work in the literature for kinetics and comparison studies.
Notes
Funding Information
Financial support from the Engineering and Physical Sciences Research Council grant EP/F500378/1 for the MOAC Doctoral Training Centre is gratefully acknowledged.
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