A Method for High‐Throughput Measurements of Viscosity in Sub‐micrometer‐Sized Membrane Systems†

Abstract To unravel the underlying principles of membrane adaptation in small systems like bacterial cells, robust approaches to characterize membrane fluidity are needed. Currently available relevant methods require advanced instrumentation and are not suitable for high‐throughput settings needed to elucidate the biochemical pathways involved in adaptation. We developed a fast, robust, and financially accessible quantitative method to measure the microviscosity of lipid membranes in bulk suspension using a commercially available plate reader. Our approach, which is suitable for high‐throughput screening, is based on the simultaneous measurements of absorbance and fluorescence emission of a viscosity‐sensitive fluorescent dye, 9‐(2,2‐dicyanovinyl)julolidine (DCVJ), incorporated into a lipid membrane. We validated our method using artificial membranes with various lipid compositions over a range of temperatures and observed values that were in good agreement with previously published results. Using our approach, we were able to detect a lipid phase transition in the ruminant pathogen Mycoplasma mycoides.


Introduction
Viscosity is ac rucial physicalp roperty of living membranes that is tightly regulated though homeostatica daptation to environmental and physiological challenges. [1][2][3][4][5][6][7] Measuring viscosity is important for investigating the mechanismsi nvolvedi n membrane adaptation and to constrain the range of membrane properties that can support life. In particular,s tudying relativelys imple bacterial model organismsc an provide insight into fundamentalp rinciples underlying membrane homeostasis and adaptivity.P resently,h owever,t here are no highthroughput or broadly accessible methods to measurev iscosity in bacterial cells or submicron scale synthetic membrane systems.
Currently existingm ethodsfor measuring membrane viscosity are relativelyl ow-throughput or require specialized instrumentation not available to many laboratories. Fluorescence correlation spectroscopy (FCS) can provide estimates of diffusivity of am olecular probe. [8,9] FCS, however,r equires ar elatively specialized microscopy setup, and measuring diffusion in sub-micrometer scale membrane systemsc an be particularly challenging. Similarly,f luorescencer ecovery after photobleaching is not feasible on small vesicles because of spatial resolution limitations. [10] Another common method to estimate membrane viscosity is based on emission anisotropy of fluorescent probes. [11] In this case, however,t he interpretationo fr esults is not always straightforward. [12] Recently,t here have been a number of promising studies measuring viscosity using the fluorescencel ifetimeo fv iscosity-sensitivef luorescent probes. While this approach could be applied to submicron membrane systems, the technology is fairly expensive, and high-throughput instrumentation is currently not commerciallya vailable.
In this study,w edeveloped am ethod to estimate membrane viscosity by measuringt he relative brightness of av iscosity-sensitive fluorescence dye using as imple plate reader capable of simultaneously measuring absorbance and fluorescence emission. Our method is based on the empirical finding of Fçrster and Hoffmann that certain fluorescence probesu ndergoing twisted intramolecularc harge transfer (TICT) show a power-law dependence of their brightness (fluorescence quantum yield, f)o nt he viscosity h of bulk solvents: f / h p . [13] This relationh olds in cases where the non-radiatived ecay rate is controlled by the viscosity of the medium, as long as the nonradiatived ecay rate is much higher than the radiative decay rate. In that case one can use this effect to monitor the microviscosity via either fluorescenceq uantum yield or by the excited-state lifetime. [14][15][16][17][18] Among others, 9-(2,2-dicyanovinyl)julolidine (DCVJ) is aw ell characterized TICT probe (Figure 1) with the fluorescencee mission in the visible range of the light spectrum. [19] It was shown that DCVJ can be used to estimate the viscosity of lipid membranesusing the relative quantum yield approach. [16] Moreover, the dye is commerciallya vailablea tav ery accessible price To unravel the underlying principles of membrane adaptation in small systems like bacterial cells, robust approaches to characterizemembrane fluidity are needed. Currently available relevant methods requirea dvanced instrumentation and are not suitable forh igh-throughput settings neededt oe lucidate the biochemical pathways involved in adaptation. We developed a fast, robust, and financially accessibleq uantitative methodt o measuret he microviscosity of lipid membranes in bulk suspension using ac ommerciallya vailable plate reader. Our approach, which is suitable for high-throughput screening, is based on the simultaneousm easurements of absorbance and fluorescence emission of av iscosity-sensitivef luorescent dye, 9-(2,2dicyanovinyl)julolidine (DCVJ), incorporated into al ipid membrane.W ev alidated our method using artificial membranes with various lipid compositions over ar ange of temperatures and observed values that were in good agreement with previously published results.U sing our approach, we were able to detect al ipid phase transition in the ruminant pathogen Mycoplasma mycoides.
[a] Dr. G making it ap erfect candidate for application in large-scale screening assays.
To estimate membrane viscosity,w ec ompared the relative brightnesso fD CVJi ncorporated into liposomes with the brightness of DCVJ measured in solvents of known viscosities.T ot his end, we developed an experimental protocol that overcomes the limitations of the analytical noise of the plate readera nd artifacts related to the sample structure and construction of the multi-well plate. To validate our method, we measured the relative brightness of DCVJ in liposomes composed of several well-characterized lipid species and lipid mixtures at the physiological range of temperatures. We showedt hat the viscosity activation energies obtained using our method agree within experimental error with those reported in the literature.U sing our approach, we report values for membrane viscosity in liposomes made of several different lipid species and provide a first estimate of the membrane viscosity of the ruminant pathogen Mycoplasmam ycoides. The methodw er eport provides an affordablea nd fast means to measure the viscosity of membranes and couldb eu sed in screening settings where, for example, al arge number of bacterials trains or mutants could be studied.

Establishing ap late readerassay for measuring variations in membrane viscosity
We aimed at establishing am ethod that would allow accurate measurements of the membrane viscosity in lipid vesicles. To this end, we made use of the power-law dependence of the fluorescenceq uantum yield of DCVJ on the viscosity of its microenvironment. As the measurement of the quantum yield is problematic in our experimental setting, we replace it by the fluorescenceb rightnessd enoted here as R and defineda st he ratio of integrated fluorescencee mission and absorbance of the probe in the sample (for details, see the Experimental Section). To calibrateo ur method, we carried out measurements of R for DCVJ in several mediac overing aw ide range of viscosities expected for lipid membranes. To this end, we used two neat viscous solvents, glycerol and ethylene glycol, whose viscosity strongly dependso nt he temperature, and measured R in these solvents over ar ange of temperatures relevant foro ur membrane experiments. Additionally, R was measured in a series of glycerol/methanol mixtures at the room temperature. The resultso ft he temperature-independent and temperaturedependentm easurements agree with each other very well (Figure 2), which shows that the fluorescence brightnesso f DCVJ can be used to report the viscosity of its microenvironment, irrespectiveo ft he temperature. As expected, R shows a power-law dependence on the viscosity with the exponent p = 0.53 AE 0.01 falling into range of values (0.51-0.59) reported previously. [15] This power-law correspondence allows us to con-vert the measured brightness of the DCVJ fluorescencei nto the viscosity of its microenvironment (for details, see the Experimental Section). It is important to emphasize that the fluorescenceq uantum yield-and hence fluorescenceb rightness R-of am olecular rotor reflects the rotational mobility of the dicyanovinyl moiety of the molecule. As ar esult, the method reports the viscosity of the microenvironment of the probe in the membrane, which will be referredt oi nw hat follows as microviscosity.A tt he same time, the methods based on translationald iffusion of relatively large membrane inclusions like proteins,c olloidalp articles, or membrane domains, give information on the surfacev iscosity of the lipid bilayer, [20][21][22] which, with the use of the bilayer thickness, can be converted into an estimate of the bulk viscosity of the membrane material. In contrast, methodsb ased on measuring translational diffusion of fluorescent lipid analogues or fluorescently labeled lipids, which are too small to warrant the hydrodynamics-based descriptiono ft heir motion,d on ot allow one to obtain valid estimates of membrane viscosity.
First, we tested the fluorescencer esponse of DCVJ to temperaturei nm embranes comprised of DOPC which is an unsaturated phospholipid with am elting temperature below À20 8C. Thus, under our experimental conditions it is in the fluid state far from the lipid meltingp hase transition. The DOPC viscosity estimated from the DCVJ fluorescenceb rightness for the temperature range used in our experiment could be very well described by the Arrheniusl aw ( Figure 3) with the activation energy of 54 AE 9kJmol À1 ,w hich agreesw ith previous findings based on measurements of the fluorescence lifetime of am olecular rotor ( Table 1). The previously reported absolutev alues of the viscosity are in the range from 13 to 74 mPa sa nd are of the same order of magnitude as reported by Kung and Reed for the DPPC membrane in the liquid phase. [23] While it is clear that methods reporting microviscosity are relative, it is still valuablet oe stimate the scale of discrepancy between the relevant methods. When comparedw ith membrane studies involvingt he laterald iffusion of membrane inclusionsf ulfilling the requirementso ft he hydrodynamic   [20][21][22] our resultsa re roughlya factor of 3l ower (128 mPa sa t2 48Cv s. 41 AE10 mPa sa t2 58C in our case). On the other hand, Wu et al., [18] using an approach based on the microviscosity dependenceo ft he fluorescence lifetime of am olecular rotor,r eported 228 mPa sf or DOPC membrane at 25 8C. Hence, it is clear that discrepancies of af actor of 2t o6are common for such measurements and show the specificity of the approach rather than itsd rawbacks.

Influence of cholesterol on viscosityo fp hospholipid membranes
Living organismsu se cholesterol toc ontrol and adapt their membranes to constantly changing environmental conditions. Therefore, ar obusta ssay to estimate the influence of cholesterol on membrane properties is crucial.T ot est the sensitivity of our methodt oc holesterol content,w em easured the viscosity of DOPC membrane supplemented with 40 mol %ofcholesterol. (Figure 4). Cholesterol introduced as ubstantial increase in the viscosity at all temperatures ( Figure 4). The estimated activation energy for viscosity is 63 AE 8kJmol À1 ,r oughly 17 % higher than that for the pure DOPC membrane. Our value is thus close to that of Petrova nd Schwille who analyzed results of Cicuta et al. [22,24] for the liquid disordered (Ld) phase of DOPC/DPPC/cholesterol ternary mixture, for which the activation energy was estimated to be 77 kJ mol À1 .Asimilar increase in the activation energy (18 %) upon addition of the same amount of cholesterol was found by Filippov et al. using an NMR-based approach; [25] here, however,iti si mportant to point out that the activation energies were reported not for membrane viscosity,but rather for the diffusion coefficient of ad euterated lipid in the membrane, which could potentially explain the difference in the results. Based on fluorescencel ifetime measurements of am olecular rotor,W ue tal. studied the lipid mixture, and, whilet he activation energy of the viscosity was not reported, [18] they found ar elatively moderate increase (16 %) in the absolute viscosity.I nc ontrast, we observed an 85 %i ncrease in the membrane viscosity upon addition of cholesterol for the same temperature. As imilart rend in viscosity was observed in experiments involving translational diffusion of membrane inclusions that fulfil the requirements of the hydrodynamic model: based on the published results on the surfacem embrane viscosity obtained there, we calculated the bulk membrane viscosity forD OPC (140 mPa s, 24 8C) and cholesterol-enriched Ld phase of DOPC/cholesterol( 270 mPa s, 25 8C) assuming the membrane thickness to be 3.7 nm. [22,26,27]    The viscosity difference between pure lipid and cholesteroldoped bilayer comprises 70 %a nd is reasonably close to our results. Therefore, we argue that the sensitivity of our approach to cholesterol is similart ot hat of studies based on translational diffusiono fm embrane inclusionsa nd thus the approachc orrectly reflects the viscous properties of the membrane material.

Sensitivity to variation in phospholipidacyl chain saturation and length
Besides cholesterol, the physical properties of biological membranesc an be regulated by the length and saturation of phospholipid acyl chains. We therefore evaluated the effect of the acyl chain composition on membrane microviscosity as sensed by DCVJ fluorescence. We first addressed the variation in saturationu sing lipid vesicles comprised of DLPC (2 C18:2), DOPC (2 C18:1), and SOPC (C18:0,C 18:1). Thea verage membrane viscosity for all compositions is similar within the experimental errors showing that within the analytical error of the method we cannot successfully resolve such subtle differences in viscosity ( Figure 5).
The estimated activation energies of the viscosity for DLPC, DOPC, andS OPC (52 AE 13, 54 AE 9, and 68 AE 8kJmol À1 ,r espectively) show the expected trend DLPC < DOPC < SOPC, althought he differences between the activation energies of DLPC and DOPC viscosities are not significant. On the other hand, SOPC shows ar elativelyh igh activation energy of 68 AE 8kJmol À1 which is close to the value of the DOPC/cholesterol 6:4mixture.
For chain length variation, we studied membranes composed of phospholipids whose 18-or 16-carbonl ong acyl chains contained one double bond:S OPC (18:0, 18:1) and POPC (16:0, 18:1). We find that variations in acyl chain structure do not result in statistically significant changes in either the viscosity values ( Figure 6) nor in the viscosity activation energies (53 AE 10 and 68 AE 8kJmol À1 for POPC and SOPC, respectively).
Ta ken together,o ur results demonstrate that the microviscositieso fl ipid membranesa sr eported by DCVJ fluorescence, do not show ap ronounced dependence on either the length or saturation of acyl chains.

Localization of DCVJ in lipid bilayer
The assay presented in this work reports the viscosity of an immediate surroundingo ft he fluorescent probe. Therefore, the results obtained using this approachs hould reflect the particular localization of the dye in the membrane. Al ot can be learneda lready from the position of the fluorescence emission peak of DCVJ in the membrane. It has been previously shown that the positiono ft he emission peak of DCVJ is correlated with the solventp olarity. [15] The emission peak of DCVJ in lipid membranes is very close to that of its fluorescencei nn eat glycerol, suggesting that DCVJ is located in the vicinity of the glycerolb ackboneo fp hospholipids rather than around the terminal methyl moiety of acyl chains. Further,h igh sensitivity of DCVJ to the cholesterol content of the lipid membrane indicates its preferentiall ocalization in the proximity of membrane cholesterol, which typically resides next to the glycerol backbone in the direction of the acyl chains. [28] Moreover,this localization of the dye is stable as we did not detect noticeable changes in emission spectra of DCVJf or different membrane compositions and temperatures (datanot shown).
Ta ken together,t he experimental evidence suggests that DCVJ is stably localized close to the cholesterol pocket of the lipid membrane.

Measuring viscosity in biologically relevant membranes
To test the applicability of our approacht ob iological membranes, we measured the temperature dependence of the viscosity of membranesp urified from M. mycoides,o ne of the simplest living organisms (Figure 7). [29] It has been previously shown that at temperatures above the growth conditions the lipid membrane of microorganisms is in Ld state, [30,31] At temperatures lower than the growth temperature, the membranes of microorganisms are known to undergo ap hase transition to  as tate characterized by ac onsiderably higher viscosity, [1][2][3][4][5][6][7] including am icroorganism closely related to M. mycoides. [32] Therefore, one should expect this effect to take place also for membranes of M. mycoides. It would be instrumental, therefore, to compare measurements on the M. mycoides membranesw ith two reference lipid mixtures that can model the expected behavior of the bacterial membrane above and below the growth temperature.
To model the behavior of the membrane at the growth temperaturea nd above, we used the POPC/cholesterol 1:1l ipid mixture, which constitutes vast majority of the native membrane of Mycoplasma. [33] This mixture is known to be in the Ld state within the range of temperatures of our study. [25] In contrast, al ipid mixture consisting of DPPC/cholesterol 1:1t hat has been shown to be in am ore viscous liquid-ordered (Lo) state within the temperature range of our experiments was used as ar eference for the more viscousm embrane state that should be expected for the bacterial membrane below the growth temperature. [34] Comparison of the results for viscosity of M. mycoides membranesw ith those for the artificial lipid mixtures shows that indeed, at temperatures of 37 and 42 8Cw hich are equal or above the growth conditions, bacterial membranes have a very similar viscositya nd its temperature dependence to that of the Ld state artificial lipid mixture. At the same time, for the temperatures of 18 and 25 8Cw hich are below the growth temperature, the viscosity of the bacterial membrane approaches the values of the lipid mixture in the Lo phase. Remarkably,t he activation energy at the lower end of the temperaturer ange is approximately the same as for the Ld phase. At the same time, as ubstantial increase in the viscosity activation energy is expected if at ransition to the gel phase takes place. [23] This observation suggests that indeed, in agreement with our expectations,t he lipid membrane of M. mycoides exists in the fluid (liquid-disordered) state at and above the growth temperature, and transforms into am ore viscous (liquid-ordered)p hase characterized by ah igher lipid order at temperatures about 10 degrees below the growth temperature. It also agrees well with the resultso fL inden et al. showing that cell membranes isolatedf rom Escherichia coli exhibit liquid-liquid phase separation upon cooling below the cell growth temperature. [31] According to the concept of homeoviscous adaptation put forward by Sinensky in 1974 the temperature of the phase transition from the fluid phase characteristic of the functional membrane to the more viscousp hase-coexistence state should follow the growth temperature of bacteria. [1] This hasi ndeed been previously shown for al arge number of microorganisms. [1][2][3][4][5][6][7] Our measurements for membranes of M. mycoides growna tt wo different temperatures, 30 and3 78Ci ndeeds uggest that the expected trend might take place:t he transition from the low-viscosity fluid state to the high viscosity phaseseparated state is shifted in accordancew ith the growth temperature. Here, however,w eh ave to point out that the effect is within the experimental error of the methoda nd further experiments are needed to confirmthe trend.

Conclusion
In this work, we showedt hat using an experimental arrangement based on as tandardp late reader capable of simultaneously measuring weaka bsorbance and relative changes of weak fluorescences ignals one can obtain reliable estimates of the lipid membrane viscosity in sub-micrometer-sized liposomesu sing aT ICT dye DCVJ. In addition to absolute values of viscosity,w ewere able to reproducibly measure viscosity activation energies for membranesc omposed of severald ifferent lipid species and their mixtures. We also show that thesemeasurements are compatible with bacterial membranes, and could detectl iquid-liquidp hase transition in minimal membrane modelo rganism M. mycoides. Application of am ulti-well plate readerw ould allow one to employ the method in highthroughput bacterialmembrane phenotype screening.

Experimental Section
Chemicals and materials: 1,2-dioleoyl-sn-glycero-3-phosphocholine (dioleoylphosphatidylcholine;D OPC), 1-stearoyl-2-oleoyl-snglycero-3-phosphocholine (SOPC), 1-palmitoyl-2-oleoyl-glycero-3phosphocholine (POPC), 1,2-dilinoleoyl-sn-glycero-3-phosphocholine (DLPC), and cholesterol were all purchased from Avanti Polar Lipids (Alabaster,A L, USA) and used without further purification. 9-   nitrogen. Subsequently,t he lipid films were kept in vacuum overnight to remove traces of the organic solvent. To form vesicles, the vials containing the lipid films were filled with 10 mm HEPES buffer with 150 mm NaCl at pH 7a nd incubated at least 20 8C above the lipid melting temperature for 30 min. Samples were then subjected to 10 cycles of freezing and thawing procedure which was followed by extrusion through ap olycarbonate filter with 100 nm pores (10 ). By this means, suspensions of lipid vesicles with the total lipid concentration of 1mm were formed. Directly before measurements, the vesicle suspensions were diluted to 0.2 mm lipid concentration and DCVJ from as tock solution in DMSO (400 mm)w as added to the final concentration of 50 nm resulting in the 400:1 lipid-to-dye ratio. Samples were then incubated for 30 min at 45 8Ca nd 500 rpm using ThermoMixer (Eppendorf, Wesseling/Berzdorf, Germany). The labelling protocol was tested in ac ontrol experiment in which DCVJ was added to lipid solution in chloroform before the formation of the lipid film. The viscosity values we obtained using our method for these samples were identical with those produced using the protocol described above. After incubation, the samples where pipetted into the 96well plate in the amount of 200 mLp er well.
Preparation of bacterial membranes: M. mycoides GM12 were grown on SP4 medium at 30 and 37 8Ca nd supplemented with fetal bovine serum as al ipid source. Cells were harvested at midexponential phase and washed twice in buffer (HEPES 25 mm,N aCl 200 mm,g lucose 1%,p H7). Washed cells were lysed on an Emulsiflex-B15 (Avestin, Ottawa, Canada) by passaging three times at 4bar pressure. The cell lysate was centrifuged at 4000 g for 10 min to remove non-lysed cells. The lysate was then loaded onto as ucrose step gradient (10, 30, 50 % w/v)a nd spun overnight at 4 8C on aB eckman Ti45 rotor at 250 000 g. Am embrane fraction was collected at the 30 %/50 %i nterface. To remove excess sucrose, the membrane fraction was resuspended in 1.5 mL buffer and pelleted at 70 000 g for 1h.T he cell membrane fraction was then resuspended in buffer and stored at À80 8Cu ntil analysis.
Measurement protocol: All spectroscopic measurements were carried out using aS PARK 20M plate reader (Tecan, Grçdig, Austria) equipped with at hermostat capable of maintaining the temperature of the sample in the range of 18-42 8Cw ith the accuracy of AE 1 8C. The temperature-dependent measurements were carried out at five sample temperatures:4 2, 37, 30, 25, and 18 8Cs tarting with 42 8Ca nd subsequently cooling down the sample in steps. Upon reaching as pecified temperature, the sample was first incubated for 5min at 150 rpm using internal sample holder to ensure thermal equilibrium, after which absorption and fluorescence spectra were measured. To reduce evaporation of the samples, the multi-well plate was covered with al id that was automatically taken off for absorbance measurements and replaced after their completion. At each temperature step, absorption spectra were recorded for each of the wells, after which fluorescence emission spectra from the same wells were collected. Absorbance was measured within the spectral range of 350-550 nm in 2nms teps with the spectral slit width set to 3.5 nm. Fluorescence emission was measured in the "bottom reading mode" of the setup in the epiconfiguration using a5 0/50 mirror.F luorescence excitation and emission wavelengths were selected using the monochromators with the spectral slit widths set to 7.5 nm. Fluorescence was excited at 440 nm using ax enon flash lamp, and the emission spectra were measured in the range of 460-650 nm in 2nms teps.
Data analysis: Raw data from the plate reader were automatically saved for subsequent processing. For further analysis data were imported into RStudio using home-written script in Rl anguage. [36] The ratiometric method described in the present paper requires accurate measurements of the absorption and fluorescence emission of the fluorescent label bound to liposomes. Working at low concentrations typical for the experiments reported here requires that special care should be taken during the analysis of the measured absorbance and fluorescence emission data. Because of the low total concentration of the dye in the volume of the sample (liposome suspension), prior to analysis, the recorded raw spectroscopic data need to be corrected for artefacts to extract the pure absorption and fluorescence spectra.
Absorption spectra: Absorption spectra of DCVJ-labeled liposomes ( Figure 8) consist of the absorbance spectrum of the dye sitting on top of the smooth background sloping down toward longer wavelengths that originates from light scattering by the vesicles in suspension. In our measurement geometry which is based on the use of am ulti-well plate, the light beam propagates in the vertical direction and passes through the free liquid-air interface. As ar esult, the absorption spectrum was found to be additionally affected by the presence of the meniscus. To account for the above-mentioned artefacts, we perform absorbance correction as follows. First, the absorption spectrum of ab lank sample containing the same amount of pure buffer was subtracted from the raw absorption spectrum of the sample. This step compensates for the meniscus effect. After this step, the resulting spectrum represents the DCVJ absorption spectrum sitting on top of the smooth background due to light scattering by liposomes. The absorption spectrum of the DCVJ dye represents aw ell-defined bell-shaped curve, which allowed us to separate the absorption and scattering contributions. To do this, the absorption spectrum was recorded within the spectral range wider than the absorption spectrum of DCVJ, and the outermost portions of the measured absorption which is known to be ap roper phenomenological model to describe the effect of light scattering by liposomes. [37] The scattering background, determined by the fitting routine separately for each well, was then subtracted from the corresponding absorption spectra. By this means, we were able to compensate not only for the above-mentioned phenomena, but also for small absorption offsets caused by the instrument electronics and stray light.
Fluorescence spectra: Raw fluorescence spectra of our samples ( Figure 9A)a re composed of the DCVJ fluorescence emission spectrum, peak of the Raman scattering of water,a nd background fluorescence of the 96-well plate. Surprisingly,t he background fluorescence of the plate was found to depend on the temperature and showing ap rogressive increase at its longer wavelength tail upon heating. Furthermore, this effect was systematically stronger at lower rows of the multi-well plate, but reproducible within each of the rows. To remove the artefacts from the fluorescence spectra, one well in each row was filled with the pure buffer solution and was used for measuring the blank spectrum. The blank fluorescence emission spectrum ( Figure 9C)w as subtracted from the sample spectra ( Figure 9B)t oremove the effect of the Raman scattering and background fluorescence of the multi-well plate itself.
Knowing that the DCVJ fluorescence emission spectrum in our case goes down to zero at around 640 nm, the constant offset was removed by subtracting the mean signal in the spectral range of 640-650 nm from the spectrum thus resulting in the "clean" fluorescence spectrum of DCVJ in membranes ( Figure 9D).
The method is very robust and provides highly reproducible measurement of artefact-free fluorescence spectra under these challenging experimental conditions.
Estimation of membrane viscosity and its Arrhenius activation energy: The method we describe here is based on the dependence of the fluorescence quantum yield of the DCVJ dye on the microviscosity of its immediate environment. [16] As the experimental determination of the absolute fluorescence quantum yield is very challenging, especially under our experimental conditions, we resort instead to the use of ap roxy quantity defined as ar atio of the fluorescence emission intensity and absorbance of membranebound DCVJ.
To obtain lipid viscosity estimates, we first calculated the ratio R = F/A of the quantities representing the fluorescence intensity (F) and absorbance (A)o fmembrane-bound DCVJ.
The quantity A was evaluated by integrating the artefact-free absorption spectrum over an interval of wavelengths that was centered on the fluorescence excitation wavelength and had aw idth corresponding to the spectral slit width in the fluorescence measurements. The quantity F was evaluated by integrating the artefact-free fluorescence emission spectrum over the whole spectral range of fluorescence measurements.
Results from three independent replicates (5 analytical replicates each) were grouped together,a nd the mean values of fluorescence intensity hFi and absorbance hAi,a nd their standard deviations s F and s A were calculated. Subsequently,f luorescence-to-absorbance ratio hRi = hFi/hAi was calculated, and the corresponding standard error was estimated using the error propagation as follows [Eq. (2)]: Similar to what has been previously reported, [15,16] the dependence of the fluorescence-to-absorbance ratio R of DCVJ on the viscosity of the medium was found to follow the power law R = Bh p ( Figure 2).
The value of the exponent p = 0.53 AE 0.01 was determined by fitting the power law to the dependence of R on h using aw eighted nonlinear least squares routine and was found to be in excellent agreement with the previous findings. [15] The value of the constant prefactor B depends on the particular instrument and measurement settings (which were kept constant in our measurements), and is therefore not reported here. Reverting this relationship allows one to obtain an estimate of the microviscosity of the DCVJ environment based on the measured value of the fluorescence-toabsorption ratio R. The uncertainties in the estimates of the microviscosity were calculated using the error propagation as follows [Eq. (3)]: To obtain the Arrhenius activation energies of the viscosity,t he temperature dependences of the estimated viscosities of the samples were analyzed using the Arrhenius law [Eq. (4)] in which E a is the activation energy, T is the absolute temperature, N A is the Avogadro number, k B is the Boltzmann constant, and C is the numerical prefactor (irrelevant for our study). The analysis was based on aw eighted nonlinear least squares routine that took into account the uncertainties in the viscosity values and provided the best estimate of the fitting parameters along with the estimates of their uncertainties.
Partitioning of DCVJ in lipid membrane: The present method is based on the assumption that only the dye molecules which partition into the lipid membrane contribute to the measured ratio R.
Because DCVJ does not fluoresce in the aqueous environment but still is capable of absorbing light, the presence of non-membranebound dye molecules in the sample would lead to underestimation of R. Based on the chemical structure of the dye, its strong affinity toward the non-polar lipid environment should be expected, but still requires an experimental verification. Conveniently,o ur setup allows us to monitor both the dye and lipid vesicle content in the sample via absorption measurements (see above). Namely,t he smooth background due to scattering of light by liposomes is proportional to their concentration, whereas the DCVJ absorption peak "sitting" on top of that background is proportional to the dye content in the sample. If the dye predominantly partitions in the lipid membrane, then removal of liposomes from the sample should result in the proportional decrease in the liposome scattering contribution and the DCVJ absorption peak. To test whether this is indeed the case, we carried out as eries of consecutive ultracentrifugation steps. At each step, the sample was subjected to ultracentrifugation at 186 000 g for 45 min, after which the supernatant depleted in the content of lipid vesicles was carefully collected, and was used partly for absorbance measurements and partly for the next ultracentrifugation step. We carried out three consecutive ultracentrifugation steps, and found that after each step both the liposome scattering contribution and DCVJ absorbance dropped in ac orrelated manner.A sa na dditional step, we subjected our samples to ultrafiltration (Amicon Ultra 10 K, Merck KGaA, Darmstadt, Germany) which was expected to remove the liposomes from the sample, but not affect the presence of the small dye molecules potentially dissolved in the buffer solution.
The samples subjected to ultrafiltration showed absorption spectra indistinguishable from the base line, indicating the absence of both the liposomes and DCVJ in the sample. Al inear fit of the data set comprised of the measurements on as ample prepared in a standard manner,t hree samples produced from the original sample by consecutive ultracentrifugation steps, and as ample produced from the original sample by ultrafiltration, shows an inter-cept statistically indistinguishable from zero ( Figure 10). These results fully justify the assumption that the presence of free, nonmembrane-bound, DCVJ dye in our samples can be neglected.