Tension Independence of Lipid Diffusion and Membrane Viscosity

Publication Date (Web): October 6, 2017 ... Remarkably, the two-dimensional analogue of this relationship, the dependence of molecular mobility on ten...
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Tension Independence of Lipid Diffusion and Membrane Viscosity Vincent L Thoms, Tristan T. Hormel, Matthew A. Reyer, and Raghuveer Parthasarathy Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02917 • Publication Date (Web): 06 Oct 2017 Downloaded from http://pubs.acs.org on October 12, 2017

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Title:

Tension Independence of Lipid Diffusion and Membrane Viscosity Authors: Vincent L. Thoms*, Tristan T. Hormel*, Matthew A. Reyer, and Raghuveer Parthasarathy^ * Equal contributors to this work ^ to whom correspondence should be addressed: [email protected]

Affiliation: Department of Physics and Materials Science Institute The University of Oregon Eugene, OR 97403-1274

Abstract The diffusion of biomolecules at lipid membranes is governed by the viscosity of the underlying two-dimensionally fluid lipid bilayer. For common three-dimensional fluids, viscosity can be modulated by hydrostatic pressure, and pressure-viscosity data have been measured for decades. Remarkably, the two-dimensional analogue of this relationship, the dependence of molecular mobility on tension, has to the best of our knowledge never been measured for lipid bilayers, limiting our understanding of cellular mechanotransduction as well as the fundamental fluid mechanics of membranes. Here we report both molecular-scale and mesoscopic measures of fluidity in giant lipid vesicles as a function of mechanical tension applied using micropipette aspiration. Both molecular-scale data, from fluorescence recovery after photobleaching, and micron-scale data, from tracking the diffusion of phase-separated domains, show a surprisingly weak dependence of viscosity on tension, in contrast to predictions of recent molecular dynamics simulations, highlighting fundamental gaps in our understanding of membrane fluidity.

Introduction Viscosity is an essential property of fluids, characterizing their response to shear stresses, and, via the Stokes-Einstein-Sutherland relationship, the diffusivity of embedded objects. The pressure dependence of the viscosity of three-dimensional fluids has long been the subject of both theoretical and experimental study1,2. Though controversies remain3, it is well established that in general, liquid viscosity increases with pressure for simple Newtonian fluids, with a form well fit by free volume models in which the available molecular space decreases with increasing pressure4,5. The liquid nature of cellular membranes and their underlying lipid bilayers has been appreciated for decades6,7, and has been increasingly well-characterized and shown to fit models of two-dimensional Newtonian fluids8–10. Moreover, the temperature dependence of lipid diffusion has often been interpreted in the context of free-area models7,11,12.

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Remarkably, however, despite decades of studies of membrane biophysics there have been no experiments of which we are aware that directly measure the tension-dependence of lipid bilayer viscosity, the two-dimensional analogue of pressure-viscosity relationships, perhaps due to the challenges of applying controlled tensions to model membranes. Tension-mobility relationships have, however, recently been examined computationally. In molecular dynamics (MD) simulations, lipid diffusion coefficients increase by roughly 50-100% over tensions spanning 0 to 20 mN/m, i.e. by measurable amounts over experimentally accessible ranges13,14. These predictions have not been experimentally tested. Furthermore, it is unclear whether such changes in lipid mobility would translate into changes in viscosity at length scales much larger than the lipid molecules themselves, that is, over length scales described by two-dimensional hydrodynamic models15,16. In addition to its fundamental importance to our understanding of membrane fluid mechanics, links between mechanical tension and molecular-scale diffusion could be important in a variety of biological contexts. Mechanical tension is known to impact cellular membrane function in vivo, for example coupling to molecular conformation and thereby regulating signal transduction via mechanosensitive proteins17,18. Protein-independent connections between tension and in-plane viscosity would reveal general mechanisms by which cells could integrate physical signals into biological responses. We therefore performed experiments subjecting giant unilamellar vesicles (GUVs), spherical shells of lipid bilayer tens of microns in diameter, to a range of tensions (τ) applied using micropipette aspiration (Fig. 1). Dating to pioneering work by Evans and colleagues over thirty years ago19,20, the technique of micropipette aspiration has been used to examine membrane mechanical properties in both reconstituted vesicles (e.g. Refs. 21–23) and live cells (e.g. Refs. 24,25). To examine molecular-scale mobility, we performed fluorescence recovery after photobleaching (FRAP) on fluorescent probes in compositionally homogenous GUVs, focusing a laser onto an aspirated vesicle to photobleach a small area and subsequently monitoring the recovery of the spot as it equilibrates via molecular diffusion. To measure large-scale membrane viscosity, we monitored the Brownian dynamics of phase-separated liquid-ordered and liquid-disordered domains in GUVs composed of saturated-chain lipids, unsaturated-chain lipids, and cholesterol, a well characterized model system26,27. As has been detailed in prior work8–10, fluorescence microscopy and image analysis can yield the radii of these domains and their diffusion coefficients, the relationships among which are in accord with two-dimensional hydrodynamic models that can be used to calculate the underlying bilayer viscosity15,16. We performed each of these assays at tensions of up to a maximally accessible value of τ ≈ 20 mN/m, consistent with the rupture strength of lipid membranes28.

Experimental Giant Unilamellar Vesicles. Giant Unilamellar Vesicles (GUVs) were made by electroformation29 in 0.1 M sucrose. In all experiments, 1 mol% Texas Red DHPE (Texas Red 1,2-dihexadecanoyl-snglycero-3-phosphoethanolamine) was used as a fluorescent probe. This fluorophore-lipid conjugate has been used in hundreds of published studies, and has been well characterized both experimentally and computationally. For experiments involving Fluorescence Recovery After Photobleaching (FRAP), GUVs were composed of DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) and Texas Red DHPE at a molar ratio of 99:1 DOPC:Texas Red DHPE. The gel-to-liquid crystalline phase transition temperature of DOPC is 253 K; the membranes are therefore fluid at the experimental temperature of 296 ± 1 K. For experiments involving phase-separated domains, GUVs were composed of DPPC (1,2-dipalmitoyl-snglycero-3-phospocholine), DOPC (1,2-dioleoyl-sn-glycero-3phosphocholine), cholesterol and Texas Red DHPE at a molar ratio of 40:20:39:1

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DPPC:DOPC:Cholesterol:Texas Red DHPE, a composition that separates into a liquid-ordered majority phase at room temperature26,27,30–32. Texas Red DHPE selectively partitions into the liquiddisordered phase. Fluorescence Microscopy. Vesicles were placed in 0.1 M sucrose, such that the interior and exterior density and osmolarity were equal, and imaged using a Nikon TE2000 inverted fluorescence microscope. Images were recorded at room temperature (296 ± 1 K) using a Hamamatsu ORCA CCD camera. Micropipette Aspiration. Micropipettes were pulled using a Sutter Instruments P-2000 micropipette puller and polished using a World Precision Instruments DMF1000 microforge. Prior to use, micropipettes were incubated with 0.1 M bovine serum albumin (BSA) to limit vesicle adhesion and rupture. We applied suction to vesicles using hydrostatic pressure, connecting the pipette to a water reservoir mounted on a vertical track. Tension was applied by first zeroing the gravity well reservoir so that no fluid flow through the micropipette was evident, and then lowering the reservoir to increase the applied hydrostatic pressure difference across the vesicle, P. The magnitude of the tension applied to aspirated GUVs was determined from images of the Rp Rv “equatorial” plane of a vesicle (Figure 1A) via the well established relation τ = P , where 2(Rv − R p ) Rv and Rp are the radii of the GUV and the micropipette, respectively19. Fluorescence Recovery After Photobleaching (FRAP). Light from a 50mW 473 nm diode pumped solid state laser (Ultralasers, MBL-III-473-50), focused to an approximately 1 micron spot, was applied for 1 second to locally bleach Texas Red DHPE in aspirated vesicles. FRAP Analysis. Analysis of fluorescence recovery to quantify the lipid diffusion coefficient (D) was performed by comparison of fluorescence images with numerical simulations of Fickian diffusion to determine the best-fit D for each image series, similar to the method described in Ref. 33. In brief: ∂C consider two images I1 and I2 separated by a time ∆t. Using Fick’s law D ∇ 2C = , where ∂t fluorescence intensity is proportional to fluorophore concentration, C, we simulate the timeevolution of the pixel intensities of the first image over some discrete number of timesteps j, generating a calculated image E(I1, j). The j that minimizes the squared deviation of the evolved 2 ∆x 2 image to the measured second image, i.e. ∑ ( E(I1, j) − I 2 ) , gives D from D = j , where ∆x is 2∆t the pixel size. Notably, unlike FRAP analysis methods that fit analytic solutions of the recovery profiles of ideally spatially or temporally localized bleached spots, our approach makes no assumptions about the spot structure, uses the measured initial image as a starting point, and incorporates the effects of noise. In more detail: The Laplacian of the fluorescence intensity is evaluated as a convolution discretely at each pixel, in a neighborhood extending to third-nearest-neighbors. To account for noise, a Gaussian random variable of the same standard deviation, σ, as in an unbleached region of the original measured image is added to each time-evolved image. This procedure is performed independently for each image pair (I1, I2), (I1, I3), ..., (I1, IN), where N is the total number of images 2

(

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captured. For each pair, χ k 2 ( j) = ∑ ( E(I1 , j) − I 2 ) / 2σ 2 is minimal at some j, corresponding to

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∆x 2 some D via D = j . Moreover, pk = exp − χ k 2 provides a probability distribution for the 2∆t likelihood of that D. These probability distributions can be multiplied for the different image pairs, and the D that maximizes the joint probability ∏ pk (D) gives the best estimate of the diffusion coefficient. We assessed the performance of this analysis approach using simulated images of 2D diffusion. In these, the fluorescence intensity profile is determined by the analytic solution to the diffusion of a Gaussian spot, to which we incorporate pixelation and noise, mimicking experimental images. Notably, the simulations use the same pixel sizes, and frame rates as the experimental data, as well as typical bleached spot sizes, noise values, image sizes, and fluorescence intensities. Comparison of diffusion coefficient values output from analysis of the simulated images with the values input to the simulation allows evaluation of the analysis method. As shown in Supplemental Figure 1, agreement between the true and estimated diffusion coefficient values, for experimentally relevant parameters, was within 20%. Moreover, the disagreement was clearly systematic; as expected, evaluation of D from numerical integration of Fick’s laws over a finite image size is less accurate for larger D, as the spatial extent of diffusion more rapidly reaches the image boundaries. This systematic error is well fit by a quadratic function; correcting for this gives residuals of less than 3% over the entire range of D values of interest, and a mean error over 1-10 µm2/s of 1.4%. We apply this quadratic correction to all the measured D values. (Omitting the correction does not change any of our conclusions.)

(

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Domain Tracking. We identified domains in phase separated GUVs using intensity based thresholding, localized these objects by fitting their intensity profiles to two-dimensional Gaussian functions using maximum likelihood estimation, and determined domain size using a bilateral filter, all as in Ref. 10. We assess the localization error associated with this procedure to be no more than 70 nm using two independent techniques: statistical analysis as given in Ref. 34, and by simulating images at experimental signal-to-noise ratios. Because domains grow over the course of an experiment, uncertainties in domain radius can exceed 10%. However, our derived viscosity measurements depend weakly on this parameter. Finally, since the images we acquire are 2D projections of a spherical vesicle surface, we geometrically mapped trajectories back to the GUV surface before calculating the displacements used to estimate trajectory statistics, such as diffusion coefficients. Viscosity calculation. We estimated membrane viscosity (η) using measurements of phase separated domain diffusion, performing one-point microrheology as in Ref. 10. In brief: we fit the set of measured diffusion coefficients D and domain radii a to the hydrodynamic model of membrane fluidity due to Hughes, Pailthorpe, and White16 (HPW), an extension of the earlier SaffmanDelbrück model15 to arbitrary inclusion radii and membrane viscosity, which gives a computationally tractable expression D(η,a). We fit η by minimizing a reduced χ2 test statistic.

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Figure 1. Micropipette aspiration and Fluorescence Recovery after photobleaching. (a) Fluorescence image of a giant unilamellar vesicle, focused on the equatorial plane, under suction from a micropipette at the right of the image. Symbols indicate the vesicle and pipette radius. (b-e) A series of fluorescence images, each separated by 0.11 seconds and focused near the pole of the vesicle, immediately after photobleaching by a laser spot. Recovery of the bleached spot (arrow) is evident. Scale bars: 20 microns.

Results We performed FRAP experiments on micropipette-aspirated GUVs composed of the simple phospholipid DOPC doped with 1 mol% Texas Red DHPE, as described in Experimental Methods. As expected, the vesicles were optically homogenous, and laser-photobleached spots a few micrometers in diameter recovered on timescales of tenths of seconds (Figure 1). FRAP-derived lipid diffusion coefficients (D) for 86 vesicles, each examined at a single value of applied tension, are plotted in Figure 2A. Each data point is an average of roughly four FRAP measurements per vesicle. The average standard deviation of measurements of D from the same vesicle was 15% of its mean. As described in Experimental Methods, the estimated precision of each FRAP measurement is roughly 3%. Within uncertainties, the data show no discernable dependence of D on applied tension over the range τ = 1.4 to 17 mN/m. A linear fit of D versus τ gives a slope of -7.8 ± 45.3 µm2 m/Ns, consistent with zero. Degradation of lipid stocks or subtle differences in vesicle preparation methods may lead to sample-to-sample variability in lipid mobility. We therefore, for all data presented, conducted measurements over a range of applied tensions within a single day. The data of Figure 2A are subdivided by day into four sets in Figure 2B. The mean D values are different, spanning a range of roughly 2 µm2/s, indicating variability between preparations. Three of the four datasets show slopes of D versus τ whose 68% confidence interval includes zero; one dataset has a positive slope. The average slope of D versus τ for the four datasets is 55 ± 63 µm2 m/Ns, indicating little or no effect of tension on molecular diffusion coefficients.

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Figure 2. (a) FRAP-derived diffusion coefficients as a function of applied tension, from measurements of 85 vesicles. A linear fit to all the data points shows no appreciable nonzero slope. Binned data points are shown for clarity. Also plotted are D vs. τ from two recent molecular dynamics simulations of lipid membrane mobility. (b) The same data as in (a), separated into sets corresponding to the same vesicle preparation measured on the same day. Lines indicate linear fits to each dataset, and closed symbols are binned data points, shown for clarity. The large orange circles and thick line correspond to all the data, as plotted in (a). We also plot in Figure 2A diffusion coefficient values derived from molecular dynamics simulations of DOPC membranes (blue diamonds, from Ref. 14), which show a rise in D with tension. In addition, we plot D(τ) from MD simulations of a saturated phospholipid with the same headgroup, dipalmitoylphosphatidylcholine
(DPPC) (green squares, from Ref. 13), which again shows an increase of D with τ, though with opposite concavity as the other simulation. While both our data and these simulations were conducted at fixed temperatures, above the gel-to-liquid crystalline transition temperature of the particular lipid, there are some differences in conditions that bear mentioning. There is a large disparity in timescales between our experimental data (seconds) and the MD simulations (picoseconds), but because diffusion on longer time scales is the cumulative result of shorter time scale processes, a comparison is still meaningful. Additionally, it is clear that the data from Ref. 14, which show only a modest increase in diffusivity with tension, are more similar to our experimental observations than those from Ref. 13; quantitatively, the Reddy et al. values14 give a slope of 237 ± 63 µm2 m/Ns, or 199 ± 65 µm2 m/Ns if the lowest point is neglected, and the Muddana et al. data13 give 884 ± 195 µm2 m/Ns. One possible explanation is that our study and that of Ref. 14 involved primarily unsaturated lipids (DOPC), and in contrast to Ref. 13, which considered saturated lipids. Nonetheless, it is clear that both of the MD simulations show an increasing D(τ), in contrast to our experimental data. To determine whether tension influences continuum viscosity and collective mobility at length scales larger than that of single lipids, we examined phase-separated domains in GUVs formed from ternary mixtures of the saturated-chain lipid DPPC, the unsaturated-chain lipid DOPC, and cholesterol, doped with 1 mol% of Texas-Red conjugated DHPE, at a molar ratio of 40:20:39:1 DPPC:DOPC:Cholesterol:TR-DHPE, a composition well-known to phase separate at room temperature into coexisting liquid-ordered and liquid-disordered domains. For disk-like objects embedded in a two-dimensionally fluid membrane, the diffusion coefficient is a function of the disk radius (a), the membrane viscosity (η), the viscosity of the surrounding aqueous medium

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(ηf), and the ambient thermal energy. The relationship between these properties is given by the hydrodynamic model of Hughes, Pailthorpe, and White16 (HPW), and its applicability to phase separated domain motion in lipid bilayers has been well established by past studies8–10. The HPW model itself an extension of a simpler model by Saffman and Delbrück15, valid only in the limit of inclusion radii that are small compared to the characteristic lengthscale η/2ηf. The HPW model does not admit a simple algebraic description, but numerical approximations can be efficiently computed. We measured the radii and diffusion coefficients of liquid-disordered domains in thirty micropipette-aspirated vesicles over a range of applied tensions from 0.02 to 15 mN/m (Figure 3). All of the data are plotted together in Figure 3c, which does not reveal any obvious segregation of points based on applied tension. To probe further, we grouped datasets by tension values and, for each subset, fit D(a) to the HPW model to extract the membrane viscosity, η (Figure 3d). For each range of tensions examined, the viscosity is between 1.8 and 2.0 ×10-9 Pa s m, with no discernible tension dependence (Figure 3e). A linear fit of η versus log(τ/(N/m)) gives a slope of (0.1 ± 4.6) ×10-11 Pa s m, indistinguishable from zero.

Figure 3. (a, b) Fluorescence images of a phase-separated giant unilamellar vesicle, focused on the equatorial plane (a) and near the pole (b). Liquid-disordered, Texas-Red DHPE-rich domains are evident as bright circles. (c) Measured diffusion coefficients (D) and domain radii for all domains in

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all aspirated vesicles examined, color-coded by the tension applied to the vesicle. (d) D versus radius for a subset of the data in (c), from τ = 13.0 to 15.0 mN/m, together with a fit to the HPW twodimensional hydrodynamic model. Solid circles are binned data, shown for clarity. (e) Membrane viscosity versus tension, grouping all of the data into one of three tension bins.

Discussion We have provided, to the best of our knowledge, the first direct measurements of lipid mobility as a function of applied mechanical tension, evaluated at both molecular and mesoscopic length scales. We find an absence of measurable signatures of tension-dependent lipid diffusion coefficients or continuum viscosities, in contrast to general expectations based on analogous responses in threedimensional fluids as well as specific recent predictions from molecular dynamics simulations. One possible interpretation is simply that our measurements are not precise enough. Within vesicles, the precision of our FRAP-derived D values is roughly 15%. Between vesicles, however, there is much greater variation, though we attempted to mitigate sample-to-sample differences by restricting our analysis to days in which a complete range of tension values could be collected from a single preparation of vesicles. Despite the uncertainties of individual datapoints, the population statistics are robust: uncertainty in the overall trend of diffusion with tension is small enough to indicate discordance with conclusions from both published MD simulations. In our experiments, each individual GUV is examined at a single tension value. A better approach would be to perform multiple diffusion coefficient measurements at different tensions applied to the same vesicle. We have repeatedly attempted this, but due to the fragility of GUVs and the difficulty of long-term aspiration of single vesicles, especially at high and changing tension, we have not succeeded. Nonetheless, it is in principle possible, and we hope our work encourages future developments in this direction. We also note that it is conceivable that Texas Red DHPE is an unreliable lipid conjugate, despite its use in hundreds of biophysical studies. Molecular dynamics simulations of fluid DPPC membranes with 4.7 mol% Texas Red DHPE have shown a 35% lower D for the probe than for DPPC molecules35; there is no reason, however, to expect that this would be tension dependent, especially not in such a way as to exactly cancel effects of membrane stretching. Another possible interpretation is that there really is little or no tension dependence to the mobility of two-dimensionally fluid lipid membranes. This contradicts intuition derived from threedimensional liquids, for which free volume models provide a good framework for understanding the pressure dependence of viscosity, and also contradicts quantitative predictions from recent molecular dynamics simulations13,14. Regarding theory, we note that though free-area models have been applied to membrane diffusion in the past11,36,37, this has often been in the context of explaining the temperature-dependence of mobility, which convolves strong thermal activation of molecular hopping with area expansion, rather than examining the latter alone. Regarding numerical simulations, it should be noted that molecular dynamics simulations are necessarily limited by the accuracy of their underlying force models, and that evaluation of mechanical properties from spatially and temporally limited simulations is notoriously challenging. Moreover, the two published simulations13,14, while both predicting an increase of D with tension, disagree in the magnitudes and even the concavity of the expected D(τ) relationship. The relationship between fluidity and compression or tension is a fundamental property of liquids, and has been investigated for three-dimensional fluids for many decades. Its twodimensional analogue is both intrinsically interesting, and also practically important for enabling a quantitative understanding of cellular membrane mechanics. Our data suggest that basic aspects of

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the fluid mechanics of lipid bilayers remain unresolved, and we hope to spur further work along these lines.

Acknowledgements This material is based in part upon work supported by the National Science Foundation under Award Number 1507115. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation The authors thank Tristan Ursell for useful conversations and Edouard Hay and Mae Voeun for assistance with data analysis.

Figure Captions Figure 1. Micropipette aspiration and Fluorescence Recovery after photobleaching. (a) Fluorescence image of a giant unilamellar vesicle, focused on the equatorial plane, under suction from a micropipette at the right of the image. Symbols indicate the vesicle and pipette radius. (b-e) A series of fluorescence images, each separated by 0.11 seconds and focused near the pole of the vesicle, immediately after photobleaching by a laser spot. Recovery of the bleached spot (arrow) is evident. Scale bars: 20 microns. Figure 2. (a) FRAP-derived diffusion coefficients as a function of applied tension, from measurements of 85 vesicles. A linear fit to all the data points shows no appreciable nonzero slope. Binned data points are shown for clarity. Also plotted are D vs. τ from two recent molecular dynamics simulations of lipid membrane mobility. (b) The same data as in (a), separated into sets corresponding to the same vesicle preparation measured on the same day. Lines indicate linear fits to each dataset, and closed symbols are binned data points, shown for clarity. The large orange circles and thick line correspond to all the data, as plotted in (a). Figure 3. (a, b) Fluorescence images of a phase-separated giant unilamellar vesicle, focused on the equatorial plane (a) and near the pole (b). Liquid-disordered, Texas-Red DHPE-rich domains are evident as bright circles. (c) Measured diffusion coefficients (D) and domain radii for all domains in all aspirated vesicles examined, color-coded by the tension applied to the vesicle. (d) D versus radius for a subset of the data in (c), from τ = 13.0 to 15.0 mN/m, together with a fit to the HPW twodimensional hydrodynamic model. Solid circles are binned data, shown for clarity. (e) Membrane viscosity versus tension, grouping all of the data into one of three tension bins.

Supporting Information Supplemental Figure 1. Estimated and true diffusion coefficients from simulated FRAP images. (PDF). This is available free of charge via the Internet at http://pubs.acs.org.

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References (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21)

Bridgman, P. W. The Physics of High Pressure; G. Bell and Sons: London, 1931. Stephan, K.; Lucas, K. Viscosity of Dense Fluids; Plenum Publishing: New York, 1979. Schmelzer, J. W. P.; Zanotto, E. D.; Fokin, V. M. Pressure Dependence of Viscosity. The Journal of Chemical Physics 2005, 122 (7), 074511. Doolittle, A. K. Studies in Newtonian Flow. II. The Dependence of the Viscosity of Liquids on Free‐Space. Journal of Applied Physics 1951, 22 (12), 1471–1475. M. H. Cohen; Turnbull, D. Molecular Transport in Liquids and Glasses. The Journal of Chemical Physics 1959, 31 (5), 1164–1169. Singer, S. J.; Nicolson, G. L. The Fluid Mosaic Model of the Structure of Cell Membranes. Science 1972, 175 (23), 720–731. Vaz, W. L. C.; Goodsaid-Zalduondo, F.; Jacobson, K. Lateral Diffusion of Lipids and Proteins in Bilayer Membranes. FEBS Letters 1984, 174 (2), 199–207. Cicuta, P.; Keller, S. L.; Veatch, S. L. Diffusion of Liquid Domains in Lipid Bilayer Membranes. J. Phys. Chem. B 2007, 111 (13), 3328–3331. Petrov, E. P.; Petrosyan, R.; Schwille, P. Translational and Rotational Diffusion of Micrometer-Sized Solid Domains in Lipid Membranes. Soft Matter 2012, 8 (29), 7552–7555. Hormel, T. T.; Reyer, M. A.; Parthasarathy, R. Two-Point Microrheology of Phase-Separated Domains in Lipid Bilayers. Biophysical Journal 2015, 109 (4), 732–736. Almeida, P. F.; Vaz, W. L.; Thompson, T. E. Lateral Diffusion in the Liquid Phases of Dimyristoylphosphatidylcholine/cholesterol Lipid Bilayers: A Free Volume Analysis. Biochemistry 1992, 31 (29), 6739–6747. Galla, H.-J.; Hartmann, W.; Theilen, U.; Sackmann, E. On Two-Dimensional Passive Random Walk in Lipid Bilayers and Fluid Pathways in Biomembranes. J. Membrain Biol. 1979, 48 (3), 215–236. Muddana, H. S.; Gullapalli, R. R.; Manias, E.; Butler, P. J. Atomistic Simulation of Lipid and DiI Dynamics in Membrane Bilayers under Tension. Phys. Chem. Chem. Phys. 2011, 13 (4), 1368–1378. Reddy, A. S.; Warshaviak, D. T.; Chachisvilis, M. Effect of Membrane Tension on the Physical Properties of DOPC Lipid Bilayer Membrane. Biochimica et Biophysica Acta (BBA) Biomembranes 2012, 1818 (9), 2271–2281. Saffman, P. G.; Delbrück, M. Brownian Motion in Biological Membranes. Proc. Natl. Acad. Sci. USA 1975, 72 (8), 3111–3113. Hughes, B. D.; Pailthorpe, B. A.; White L. R. The Translational and Rotational Drag on a Cylinder Moving in a Membrane. J. Fluid. Mech. 1981, 110, 349–372. Hamill, O. P.; Martinac, B. Molecular Basis of Mechanotransduction in Living Cells. Physiol. Rev. 2001, 81 (2), 685–740. Perozo, E.; Cortes, D. M.; Sompornpisut, P.; Kloda, A.; Martinac, B. Open Channel Structure of MscL and the Gating Mechanism of Mechanosensitive Channels. Nature 2002, 418 (6901), 942–948. Kwok, R.; Evans, E. Thermoelasticity of Large Lecithin Bilayer Vesicles. Biophys J 1981, 35 (3), 637–652. Evans, E.; Rawicz, W. Entropy-Driven Tension and Bending Elasticity in Condensed-Fluid Membranes. Phys. Rev. Lett. 1990, 64 (17), 2094–2097. Manneville, J. B.; Bassereau, P.; Ramaswamy, S.; Prost, J. Active Membrane Fluctuations Studied by Micropipet Aspiration. Phys. Rev. E 2001, 64 (2 Pt 1), 021908.

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Henriksen, J. R.; Ipsen, J. H. Measurement of Membrane Elasticity by Micro-Pipette Aspiration. The European Physical Journal E 2004, 14 (2), 149–167. Capraro, B. R.; Yoon, Y.; Cho, W.; Baumgart, T. Curvature Sensing by the Epsin N-Terminal Homology Domain Measured on Cylindrical Lipid Membrane Tethers. J. Am. Chem. Soc. 2010, 132 (4), 1200–1201. Hochmuth, F. M.; Shao, J. Y.; Dai, J.; Sheetz, M. P. Deformation and Flow of Membrane into Tethers Extracted from Neuronal Growth Cones. Biophys. J. 1996, 70 (1), 358–369. Brugues, J.; Maugis, B.; Casademunt, J.; Nassoy, P.; Amblard, F.; Sens, P. Dynamical Organization of the Cytoskeletal Cortex Probed by Micropipette Aspiration. Proc Natl Acad Sci U S A 2010, 107 (35), 15415–15420. Veatch, S. L.; Keller, S. L. Separation of Liquid Phases in Giant Vesicles of Ternary Mixtures of Phospholipids and Cholesterol. Biophys. J. 2003, 85 (5), 3074–3083. Stanich, C. A.; Honerkamp-Smith, A. R.; Putzel, G. G.; Warth, C. S.; Lamprecht, A. K.; Mandal, P.; Mann, E.; Hua, T.-A. D.; Keller, S. L. Coarsening Dynamics of Domains in Lipid Membranes. Biophysical Journal 2013, 105 (2), 444–454. Rawicz, W.; Olbrich, K. C.; McIntosh, T.; Needham, D.; Evans, E. Effect of Chain Length and Unsaturation on Elasticity of Lipid Bilayers. Biophys J 2000, 79 (1), 328–339. Veatch, S. L. Electro-Formation and Fluorescence Microscopy of Giant Vesicles with Coexisting Liquid Phases. Methods Mol Biol 2007, 398, 59–72. Veatch, S. L.; Keller, S. L. Miscibility Phase Diagrams of Giant Vesicles Containing Sphingomyelin. Phys. Rev. Lett. 2005, 94 (14), 148101. Collins, M. D.; Keller, S. L. Tuning Lipid Mixtures to Induce or Suppress Domain Formation across Leaflets of Unsupported Asymmetric Bilayers. Proc. Natl. Acad. Sci. USA 2008, 105 (1), 124–128. Honerkamp-Smith, A. R.; Machta, B. B.; Keller, S. L. Experimental Observations of Dynamic Critical Phenomena in a Lipid Membrane. Phys. Rev. Lett. 2012, 108 (26), 265702. Harland, C. W.; Rabuka, D.; Bertozzi, C. R.; Parthasarathy, R. The M. Tuberculosis Virulence Factor Trehalose Dimycolate Imparts Desiccation Resistance to Model Mycobacterial Membranes. Biophys. J. 2008, 94, 4718–4724. Vestergaard, C. L.; Blainey, P. C.; Flyvbjerg, H. Optimal Estimation of Diffusion Coefficients from Single-Particle Trajectories. Phys. Rev. E 2014, 89 (2), 022726. Skaug, M. J.; Longo, M. L.; Faller, R. Computational Studies of Texas Red-1,2Dihexadecanoyl-Sn-Glycero-3-Phosphoethanolamine ; Model Building and Applications. J. Phys. Chem. B 0, 0 (0). Vaz, W. L.; Clegg, R. M.; Hallmann, D. Translational Diffusion of Lipids in Liquid Crystalline Phase Phosphatidylcholine Multibilayers. A Comparison of Experiment with Theory. Biochemistry 1985, 24 (3), 781–786. Falck, E.; Patra, M.; Karttunen, M.; Hyvönen, M. T.; Vattulainen, I. Lessons of Slicing Membranes: Interplay of Packing, Free Area, and Lateral Diffusion in Phospholipid/Cholesterol Bilayers. Biophysical Journal 2004, 87 (2), 1076–1091.

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Figure 1. Micropipette aspiration and Fluorescence Recovery after photobleaching. (a) Fluorescence image of a giant unilamellar vesicle, focused on the equatorial plane, under suction from a micropipette at the right of the image. Symbols indicate the vesicle and pipette radius. (b-e) A series of fluorescence images, each separated by 0.11 seconds and focused near the pole of the vesicle, immediately after photobleaching by a laser spot. Recovery of the bleached spot (arrow) is evident. Scale bars: 20 microns. 79x38mm (300 x 300 DPI)

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Figure 2. (a) FRAP-derived diffusion coefficients as a function of applied tension, from measurements of 85 vesicles. A linear fit to all the data points shows no appreciable nonzero slope. Binned data points are shown for clarity. Also plotted are D vs. τ from two recent molecular dynamics simulations of lipid membrane mobility. (b) The same data as in (a), separated into sets corresponding to the same vesicle preparation measured on the same day. Lines indicate linear fits to each dataset, and closed symbols are binned data points, shown for clarity. The large orange circles and thick line correspond to all the data, as plotted in (a). 82x64mm (300 x 300 DPI)

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Figure 3. (a, b) Fluorescence images of a phase-separated giant unilamellar vesicle, focused on the equatorial plane (a) and near the pole (b). Liquid-disordered, Texas-Red DHPE-rich domains are evident as bright circles. (c) Measured diffusion coefficients (D) and domain radii for all domains in all aspirated vesicles examined, color-coded by the tension applied to the vesicle. (d) D versus radius for a subset of the data in (c), from τ = 13.0 to 15.0 mN/m, together with a fit to the HPW two-dimensional hydrodynamic model. Solid circles are binned data, shown for clarity. (e) Membrane viscosity versus tension, grouping all of the data into one of three tension bins. 82x135mm (300 x 300 DPI)

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