Measuring flow-mediated protein drift across stationary supported lipid bilayers

Abstract

Fluid flow near biological membranes influences cell functions such as development, motility, and environmental sensing. Flow can laterally transport extracellular membrane proteins located at the cell-fluid interface. To determine whether this transport contributes to flow signaling in cells, quantitative knowledge of the forces acting on membrane proteins is required. Here, we demonstrate a method for measuring flow-mediated lateral transport of lipid-anchored proteins. We rupture giant unilamellar vesicles to form discrete patches of supported membrane inside rectangular microchannels and then allow proteins to bind to the upper surface of the membrane. While applying flow, we observe the formation of protein concentration gradients that span the membrane patch. By observing how these gradients dynamically respond to changes in applied shear stress, we determine the flow mobility of the lipid-anchored protein. We use simplified model membranes and proteins to demonstrate our method’s sensitivity and reproducibility. Our intention was to design a quantitative, reliable method and analysis for protein mobility that we will use to compare flow transport for a variety of proteins, lipid anchors, and membranes in model systems and on living cells.

Significance

We developed a method for measuring how easily proteins on the outer surface of cells can be moved by fluid flow. Passive transport of membrane proteins could potentially be used by cells to detect flow in their surrounding environment, but this has not been extensively studied. We use fluorescence microscopy to record the dynamics of micron-scale, optically visible concentration gradients formed by membrane-linked proteins on cell-sized model membrane patches. Using image analysis, we measure the forces required to move membrane proteins.

Introduction

Fluid flow is a ubiquitous feature of cellular environments. Flow can occur inside or outside of cells: external flow can arise from ciliary action, circulation of blood or other fluids, or cell motility, and internal flows result from cytoplasmic streaming or contraction of protein networks. These flows can be physiologically important. For example, cytoplasmic flows generate cell-wide cytoplasmic mixing in plant cells (1) and facilitate signal protein transport to establish cell polarity in drosophila oocytes (2).

External flows carry information that is important for cell growth and survival. Therefore, many cell types sense and respond to flow. Flow responses regulate a variety of cellular and physiological functions, including blood pressure, bone density, and development (3,4,5). Unsurprisingly, many of the pathways that have been identified for sensing external flows occur at the cell plasma membrane. Mechanosensitive ion channels, primary cilia, and integrin signaling all contribute to flow sensing in endothelial cells on both long and short time scales (6).

Patterns generated by lateral transport of membrane proteins are required for cell functions such as determining cell polarity or choosing the location of cell division (2,7). Flows of the cytoplasm or membrane lipids, coupled with protein oligomerization and membrane localization, create areas in cells where proteins are selectively enriched. For example, localized exocytosis results in a slow but persistent "fountain" membrane flow in fission yeast cells (8). Membrane proteins that diffuse slowly enough are depleted from the exocytosis zone by this flow, and this is responsible for the spatial distribution of a native membrane protein that regulates the cell’s rod shape. These results suggest that slow membrane flow makes a significant contribution to cell patterning in yeast cells. Cycling of Min proteins between their cytoplasmic and membrane-bound forms can itself generate lateral transport in the form of density waves that propagate along the membrane, determining the location of E. coli cell division (9). Once established, Min density waves can sort and redistribute other membrane proteins by diffusiophoresis (10). The direction and morphology of these traveling density waves can be modulated by flow in the surrounding solution (11,12).

Here, we discuss a third mode of lateral protein transport, relevant to lipid-anchored proteins: flow can apply drag to the aqueous protein, causing it to move relative to the surrounding membrane. In this mode, the protein acts like a molecular sail, catching the flow and dragging its lipid anchor downstream (Fig. 1 A–B). Extracellular lipid-anchored proteins are present on the surface of many different types of cells. Eukaryotic cells frequently use glycosylphosphatidylinositol (GPI) anchors to link proteins to their plasma membranes. GPI-anchored proteins play a variety of roles: for example, they help parasitic trypanosomes evade their hosts’ immune systems (13), enable fungal cells to build their cell walls (14), and form part of the glycoprotein coating that mammalian endothelial cells use to sense and respond to blood flow (3). Gurdap et al. showed recently that the soluble domain of such proteins influences lipid domain partitioning and lateral mobility of their lipid anchors. In their experiments, increasing the size of the soluble protein linked to an individual lipid reduced its partitioning into liquid-ordered domains in giant unilamellar vesicles (GUVs) and plasma membrane vesicles (15).

Figure 1.

(A) Our GUV-derived supported membrane patches (red) are decorated with lipid-anchored proteins (green). When flow is applied, proteins are pushed toward the downstream edge of the stationary lipid patch. (B) Shear flow applies a force $F_w$ to the protruding aqueous protein, and the lipid anchor applies an opposing drag force $F_m$. (C) We include biotinylated lipids (bio-DOPE) in the membrane and then allow Oregon green-labeled neutravidin to bind the biotinylated lipids in the upper leaflet of the supported membrane. A fluorescent lipid, TXRed-DPPE, is included to indicate the location of the lipid patch. To see this figure in color, go online.

The plasma membranes of mammalian cells contain lipids that form a fluid membrane at normal growth temperatures, as indicated by fast diffusion of individual lipids and membrane proteins (16,17). A recent review by Cohen and Shi discusses an apparent paradox in membrane transport: a relatively small fraction of immobile obstacles can effectively prevent collective lipid flow in two-dimensional membranes without appreciably lowering single molecule diffusion constants (18). Consistent with this, recent experimental work shows that in many cell types, coupling to the underlying cytoskeleton prevents rapid flow of membrane lipids (19,20). For this reason, the membrane and cytoskeleton together should be viewed as a composite structure with complex responses to shear and strain.

Diffusion of transmembrane proteins is often confined within submicron regions on the membrane defined by the actin cytoskeleton (21,22). External flow can move microsphere-tagged transmembrane receptor proteins, but they return elastically to their original positions after flow stops (23). By contrast, proteins anchored only to a lipid in the extracellular leaflet of the plasma membrane are not confined within actin mesh domains, so they are free to diffuse across the length of the cell. However, the cytoskeleton also influences the motion of proteins that do not directly interact with it. For instance, recent work showed that the temperature dependence of diffusion of extracellular GPI-anchored proteins follows the dynamics of the actin cytoskeleton via coupling between outer-leaflet GPI and inner-leaflet phosphoserines (24,25).

Several experiments demonstrate that flow can transport extracellular lipid-anchored proteins. In trypanosomes, GPI-anchored coat proteins bind immunoglobulins, and the swimming motion of the organism acts to concentrate bound proteins at the cell posterior (13). Some components of the glycocalyx, or surface coating of glycoproteins that covers endothelial cells, also form transient concentration gradients in response to exterior flow (26,27). However, it is difficult to determine from only a few examples how common advective transport of lipid-anchored proteins may be in physiology. Quantitative estimates of the drag forces applied to lipid-anchored proteins by flow and by the membrane-cytoskeleton complex would help specify the cell types, protein types, and tissues in which this is likely to occur. Minimal model membrane systems are well suited for making these measurements.

Lateral flow transport can be observed in model systems of supported bilayers containing lipid-anchored proteins. Fluid-phase lipid membranes supported on glass resemble cell plasma membranes in that individual lipid diffusion constants remain high (28,29), but collective lipid flow is generally prevented by proximity to the substrate (as inferred from the immobility of coexisting micron-scale liquid domains) (30,31,32). A dramatic exception to this rule occurs when supported bilayers are subjected to high shear stress (15–20 Pa): the upper leaflet begins to slide over the stationary lower leaflet, producing a tank-treading motion at the leading edge where the upper leaflet rolls over to form a new lower leaflet (33). In these experiments, shear flow propels protruding proteins even faster than the sliding motion of the upper-leaflet lipids (34,35). This allows accumulation of membrane-bound proteins and fluorescent lipids at the membrane edge or along membrane domain boundaries. Multiple parameters controlling protein transport were identified in these tank-treading experiments: the hydrodynamic drag force $F_w$ acting to move the proteins, and distinct frictional drag forces acting between the substrate and the membrane, between the membrane leaflets, and between the lipid anchor and the surrounding membrane itself that oppose motion in the flow direction (35,36).

Lateral transport of specific supported bilayer components has also been accomplished by membrane electrophoresis (37,38,39). When an electric field is applied parallel to the membrane, charged lipids or proteins experience a lateral force that adds a constant drift velocity to their diffusive motion. Eventually, the drift and diffusive motion of the charged molecules result in a steady-state concentration gradient that spans the membrane. Interestingly, Lozano et al. showed that when fields are applied to ternary lipid mixtures, concentration gradients of charged lipid species generate corresponding gradients of uncharged lipids as well (38), meaning that the electric field reorganizes the entire membrane. Here, we accomplish similar selective transport of lipids with proteins attached by substituting hydrodynamic drag force for an electric field.

We have developed a geometrically and compositionally simplified model system to analyze the motion of lipid-anchored proteins. We create circular supported membrane patches with diameters between 10 and 100 μm by bursting GUVs inside rectangular microfluidic channels (Fig. 2 A–C). A small percentage of the membrane patch lipids have biotin conjugated to their polar headgroups. After membrane patches form, we inject neutravidin labeled with Oregon green, which binds to the biotinylated lipids in the upper leaflet of the membrane patch (Fig. 1 C). We then observe that the bound neutravidin moves across the membrane in response to flow, and the lipid patch itself remains stationary (Fig. 2 D–F).

Figure 2.

(A and B) Rectangular microfluidic channels 300 $\mu m$ in width and 100 $\mu m$ in height were plasma-bonded to a glass coverslip. (C) Fluorescent membrane patches (red) overlaid with a bright-field image showing the edges of the microfluidic channel. (D–F) A single membrane patch labeled with both TXRed-DPPE (red, top row) and with fluorescent neutravidin (green, bottom row) shown before flow (left), during flow (middle), and 21 min after flow stopped (right). In all images, flow direction was from right to left. To see this figure in color, go online.

The experiments we describe below differ from existing determinations of protein transport by flow because in our experiments, we determine membrane-anchored protein velocity relative to a stationary lipid membrane. We achieve this in two ways: first, by using discrete membrane patches formed from bursting individual GUVs (rather than continuous supported bilayers formed by small vesicle fusion). In supported membrane patches, interactions with the substrate at the boundary prevents sliding of the upper leaflet, even under shear stress large enough to generate sliding in continuous supported bilayers (40). Second, we apply much smaller shear force than was applied in previous work. We applied shear stresses between 0.5 and 5 Pa; these are similar to or lower than those experienced at the walls of large blood vessels in animals (2–4 Pa) (41). These lower flows generate small forces (on the order of femtonewtons) applied to individual proteins.

We find that although our measurement of protein transport is very precise in theory, significant variation in the measured quantities arises from the experimental methods; as with many GUV-based experimental methods, accuracy requires averaging over a sufficient number of observations. We show that this method is suitable for systematic investigations of the forces and frictional coefficients relevant to flow transport of membrane lipids. Our ultimate goal is to generate quantitative predictions about protein transport in physiologically relevant contexts.

Materials and methods

Chemicals

We purchased lipids, including 1,2-diphytanoyl-sn-glycero-3-phosphocholine (DiphyPC), 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-cap biotinyl (bio-DOPE), and 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-biotinyl (bio-DPPE) from Avanti Polar Lipids (Alabaster, AL). Texas red 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine (TXRed-DPPE) and neutravidin conjugated to Oregon green (neutravidin) were obtained from Fisher Scientific (Waltham, MA). All lipids were stored in chloroform at −20°C until use. Sylgard 184 was purchased from Dow Corning (Midland, MI). All other chemicals were procured from Millipore Sigma (Burlington, MA). Lipid structures are illustrated in Fig. S1 in the supporting material.

Experimental procedures

GUVs were produced by electroformation at ${65}^{\circ }$C as described previously (42) in a 200 mM sucrose solution to aid vesicle sedimentation. We made lipid mixtures containing either 97.2 mol% DiphyPC, 2.0 mol% bio-DOPE, and 0.8 mol% TXRed-DPPE or 57.7 mol% DPPC, 40.0 mol% cholesterol, 0.5 mol% bio-DPPE, and 0.8 mol% TXRed-DPPE. Standard flow buffer (100 mM NaCl, 10 mM Tris, and 1 mM etheylenediaminetetraacetic acid (EDTA) at pH 8) and high-viscosity flow buffer (100 mM NaCl, 10 mM Tris, 1 mM EDTA, and 0.59 M sucrose at pH 8) were made on the day of the experiment. All solutions were made using deionized water with conductivity greater than 18 m$\mathrm{\Omega }$ (Millipore Sigma).

Glass coverslips (Corning, Corning, NY) were prepared as described previously (43). Briefly, coverslips were sonicated in a saturated solution of potassium hydroxide in ethanol for 2 min, rinsed with copious amounts of DI water, and dried with a stream of nitrogen before storage. Just before adding the microchannel, coverslips were etched in air plasma for 10 min. Rectangular polydimethylsiloxane (PDMS) microchannels approximately 300 μm wide and 100 μm tall were made from Sylgard 184 that was poured onto a master mold and cured overnight at ${65}^{\circ }$C. Each microchannel was permanently plasma-bonded to a glass coverslip immediately before loading vesicles and was used only once.

GUVs were diluted into a solution of 200 mM glucose and 5 mM calcium chloride and then injected into a microfluidic channel. Vesicles were allowed to sediment and rupture for 2–5 min, resulting in a field of roughly circular membrane patches (Fig. 2 C). After a sufficient number of bilayer patches were formed within a microfluidic channel, a solution of 10 μg/mL neutravidin in standard flow buffer was injected. A period of 30 min was allowed for the protein to bind to the membrane patches; then excess protein was flushed from the channel with flow buffer at a low flow rate (0.008 mL/min, equivalent to a maximum of 0.37 Pa) for 5 min using a syringe pump (Harvard Apparatus, Holliston, MA).

Within each microfluidic channel, 10–20 of the most symmetrical patches were chosen and imaged using a spinning disk confocal microscope (Intelligent Imaging Innovations, Denver, CO) equipped with a motorized translation stage. Using a 40x objective and an sCMOS camera (Photometrics, Tuscon, AZ), timelapse images of the TXRed-DPPE and neutravidin signal from each patch were recorded while flow was applied for 17–21 min, with frames acquired every 35 or 60 s depending on the number of patches identified. Recordings were taken at four to five different flow rates yielding shear stresses at the lower channel surface between 0.7 and 5 Pa. Another timelapse recording was made for 20–30 min after the flow was turned off. Flow rate in the channel reached steady state within about 1–2 min after changing syringe pump settings, as indicated by pressure measurements at the channel inlet and by visual observation. All measurements were conducted at lab room temperature, which was approximately 27°C–28°C.

Image analysis

Images were analyzed using custom MATLAB code. Although we used an autofocus system during time-lapse imaging, gradual shifts in the coverslip position could cause the field of membrane patches to be unevenly illuminated if the coverslip was not exactly perpendicular to the objective. This would create the appearance of an intensity gradient. Small shifts in the position of the coverslip occurred whenever flow was turned on and off due to expansion and retraction of the PDMS channel and changes in the position of the connected tubing. Since TXRed-DPPE fluorescence did not change under flow, we corrected for small shifts in coverslip position by normalizing the neutravidin signal by the TXRed-DPPE signal at each time point.

Measuring diffusion by gradient relaxation method

We used the relaxation dynamics of the flow-generated neutravidin concentration gradients to determine the diffusion constant, following a recently published method (44). For each patch, we first chose a rectangular region spanning the approximate center of the patch for analysis (Fig. 3 A). We then vertically averaged the fluorescence signal at each pixel inside the rectangle, obtaining the fluorescence intensity as a function of position (Fig. 3 E). We assumed that fluorescence intensity was proportional to the surface concentration of neutravidin, so the averaged fluorescence intensity yields a relative concentration profile $c\left(x\right)$ spanning the patch. We then Fourier transformed the concentration profile for each time point. The amplitude of the first mode $a\left(t\right)$ is expected to decay with time according to

$$a\left(t\right)=e^{\frac{-Dt{\pi }^2}{L^2}}\text{,}$$ (Equation 1)

where L is the diameter of the patch (44). We fit the time decay of $a\left(t\right)$ for each patch to Eq. 1 to obtain a patch-specific collective diffusion constant D (Fig. 3 F). We refer to this method of determining the diffusion coefficient as the "gradient relaxation method."

Figure 3.

Gradient relaxation method for determining neutravidin diffusion constant. (A–D) show neutravidin fluorescence at four time points after flow stopped. The yellow box in (A) encloses the region that was vertically averaged to produce the intensity profiles plotted in (E). The average fluorescence intensity was subtracted from each profile for ease of comparison. (F) The amplitude of the first Fourier mode of the intensity profile, a(t), decays over time. Fitting the time decay to Eq. 1 (red line) yields the collective diffusion constant. To see this figure in color, go online.

Flow analysis

When flow was turned on, the neutravidin concentration profile evolved over several minutes from a flat to an exponential steady state (Fig. 4 A–D). At steady state, protein diffusion and advection are balanced, and the position-dependent concentration $c\left(x\right)$ along the direction of flow has the exponential form:

$$c\left(x\right)=e^{\frac{v}{D}x}\text{,}$$ (Equation 2)

where v is the protein drift velocity, and D is the protein diffusion coefficient. This expression is valid in the limit where the protein is sufficiently dilute that crowding is not significant. Note that here we obtained negative values for the exponential coefficient $\frac{v}{D}$, because we applied flow in the direction from right to left (Fig. 4 E and F). Similar steady-state concentration gradients of charged molecules have been previously observed in membrane electrophoresis experiments (37). We generally observed good agreement between our steady-state concentration profiles and single-exponential fits. To ensure that we only included data where this was the case, we calculated the $R^2$ value for each fit and rejected any with a value smaller than 0.85. We also rejected data that appeared to have a nonexponential shape, even if $R^2$ was greater than 0.85 (for details, see Fig. S2). To recover drift velocity for the protein, we multiplied the exponential coefficient for an individual patch by the diffusion constant obtained by the gradient relaxation method. We used regression through the origin to fit the velocity versus shear stress data (though allowing a nonzero intercept always resulted in the intercept falling within a standard deviation of zero).

Figure 4.

For a Figure360 author presentation of this figure, see https://doi.org/10.1016/j.bpj.2023.03.042

(A–D) Neutravidin fluorescence from a membrane patch at four different time points after 0.95 Pa of shear stress was applied. We obtained concentration profiles $c\left(x\right)$ from the averaged fluorescence intensity inside the rectangle in (A). $c\left(x,t\right)$ is plotted in (E) for each of the time points shown in (A–D). Each intensity profile was fit to Eq. 2 to obtain the coefficient of the exponential fit, $v/D$ (F). In this patch, the concentration gradient reached a steady state about 700 s after the start of flow. To see this figure in color, go online.

Calculating shear stress

Membrane patches near the edges of the microfluidic channel experience less shear stress than those in the center of the channel. To account for this, we determined the distance between the center of each membrane patch and the channel edges, and we calculated the average surface shear stress at each patch center. Calculation of shear stress at the coverslip surface was done as in previous work (34), using the expression:

$$\tau =\eta \ast \frac{6Q}{h^2\left(w-0.630h\right)}\left[1-\frac{8}{{\pi }^2}\sum _{n_{odd}}^{39}\frac{1}{n^2}\frac{\mathit{cosh}\left(\frac{n\pi y}{h}\right)}{\mathit{cosh}\left(\frac{n\pi w}{2h}\right)}\right]\text{,}$$ (Equation 3)

where η is the viscosity of the flow buffer, Q is the flow rate, w and h are the width and height respectively of the microfluidic channel, and y is the distance of the bilayer patch from the center of the microfluidic channel. We measured the cross-sectional dimensions of a representative set of PDMS microchannels in 12 locations and found that the average channel width was $289\pm 10.8$ $\mu m$ and average height was $88\pm 5.4$ $\mu m$. We used the expression above to estimate the uncertainty in our calculated shear stress (Fig. S3). We assumed that the shear stress at the membrane surface was identical to the shear stress at the coverslip, since the height difference of a few nanometers is much smaller than the other experimental uncertainties.

We measured the viscosity of the flow buffers at typical lab temperature of ${27}^{\circ }$C directly using an Ubbeholde viscometer (Thermo Fisher Scientific, Waltham, MA). We found our standard buffer viscosity was 0.87 mPa s, and high sucrose buffer viscosity was 1.44 mPa s. We estimated protein surface concentration retroactively following a method published previously (45) (described in the supporting material).

Results

We began by measuring the mobility of neutravidin bound to membrane patches made from DiphyPC containing 2.0 mol% biotinylated DOPC. Using the gradient relaxation method, we found that the average diffusion coefficient was $0.39\pm 0.12$ $\mu m^2/s$ (Fig. 5 A). This value and variation are consistent with previous measurements of diffusivity of fluorescent streptavidin bound to biotinylated lipids in supported bilayers (46).

Figure 5.

(A) Diffusion coefficient of neutravidin in 64 DiphyPC membrane patches versus membrane patch radius, found via gradient relaxation. (B) Exponential fit coefficients $v/D$ for the same membrane patches are plotted versus the calculated shear stress at the coverslip. (C) Drift velocity for neutravidin in five different DiphyPC patches (varying colors/symbols) increased linearly with shear stress. (D) Drift velocity for neutravidin in all 64 DiphyPC membrane patches, with average mobility = 15.1 $\pm$ 3.9 nm/s Pa. Shaded regions are two standard deviations wide.To see this figure in color, go online.

In each individual patch, neutravidin drift velocity increased linearly with surface shear stress (Fig. 5 C), as expected for low surface concentrations. To ensure that we captured the possible variation between different patches, glass surfaces, and GUV preparations, we measured drift velocity in 64 individual membrane patches, deposited in eight different microchannels (Fig. 5 D). We observed that the average velocity increased from about 15 nm/s at the lowest shear stress, to 35 nm/s at the highest. In order to compare our results with previous work, we define the "flow mobility" $M_{L_d}$, the drift velocity per shear force applied by the flow. For neutravidin in DiphyPC membranes, this is the slope of the line in Fig. 5 D, which has the value $M_{L_d}$ = 15.1 $\pm 3.9$ nm/(s Pa).

We also investigated whether the variation in diffusion constant that we observe between different membrane patches was due to uncertainty in the method or to variation in the physical properties of the membrane patches. By subjecting the same membrane patches to repeated flow and relaxation cycles, we observed that there was smaller variation in the measured diffusion constants obtained for a single patch than between different patches (Fig. 6 A). This indicates that lipid mobility was not identical in different membrane patches, even within the same lipid preparation and the same microfluidic channel. This heterogeneity may arise from variation in the glass surface or from differences in the lipid packing or membrane tension present in the membrane patches. GUV-derived patches form via multiple rupture pathways (47), which may generate variation in their mechanical properties. Because of this observation, we considered the measured diffusion constant to be specific to an individual membrane patch, and thus we calculated drift velocity using the exponential coefficient and diffusion constant values that were measured in each patch.

Figure 6.

(A) Diffusion coefficient of neutravidin in 12 different DiphyPC patches distributed throughout the same microfluidic channel, determined using three subsequent cycles of flow and gradient relaxation. Black triangles indicate the diffusion coefficient measured after the first flow cycle, dark blue the second, and cyan the third. The average diffusion constant (circles) and an error bar two standard deviations wide are shown for each individual patch. (B) Exponential fit coefficients $v/D$ for the same membrane patches, determined using the same three identical flow cycles in which shear stress of approximately 1.1 Pa was applied. To see this figure in color, go online.

Close examination of Fig. 6 A shows that in most cases, the measured diffusion constant decreased slightly on subsequent measurements. We also observed a decrease in the magnitude of the velocity/diffusion constant ratio (Fig. 6 B) measured during each subsequent flow cycle. Together, these measurements indicate that lipid mobility gradually decreased over the course of the 3-h experiment. One possible explanation for this decrease is that individual neutravidin molecules encountered and bound to additional biotinylated lipids over time, increasing membrane drag and lowering their mobility. Another possibility is that the membrane composition changed over time, possibly due to lipid oxidation and subsequent desorption of the products (48). It is also possible that the repeated cycles of shear stress caused changes to lipid density in the patch, occurring due to the repeated expansion and partial retraction of the patch area (49). Although the decrease in these quantities over the course of 3 h and multiple flow cycles was smaller than the intrinsic variation between different membrane patches in the same sample, we conclude that in order to obtain consistent results, it is important to make observations as quickly as possible after forming supported lipid bilayers.

We next prepared membrane patches made from a 3:2 ratio of DPPC:cholesterol and included biotinylated DPPE (instead of bio-DOPE) to anchor the neutravidin to the bilayers. We expected that the combination of higher membrane viscosity and saturated biotinylated anchors would have the effect of increasing membrane drag $F_m$ that resists flow transport. We first confirmed that the membranes were fluid at lab temperature by observation of fluctuations in GUVs and by fluorescence recovery after photobleaching on supported membrane patches. Fig. 7 A shows our determination of diffusion constant for neutravidin in 42 different membrane patches by gradient relaxation. As expected, we found that D was 0.12 $\pm$ 0.04 $\mu m^2/s$ (Fig. 7 A)—approximately one-third of the value in DiphyPC patches. The observed exponential fit coefficients were also significantly smaller compared with those for neutravidin in DiphyPC (Fig. 7 B). In fact, we had to apply larger flow rates to the membranes in order to observe concentration gradients. Drift velocities again increased linearly with shear stress and ranged from 1 to 4 nm/s. As anticipated, the flow mobility for this membrane composition, $M_{L_o}=1.12\pm 0.48$ nm/(s Pa), was lower than that found for DiphyPC membranes (Fig. 7 C and D).

Figure 7.

(A) Diffusion constant for neutravidin measured by gradient relaxation in 42 different DPPC-cholesterol patches, compared with those measured in DiphyPC patches. (B) Exponential fit coefficients measured in DPPC-cholesterol patches (blue triangles) were smaller than those measured in DiphyPC patches (black circles). (C) Drift velocity of neutravidin in all 42 DPPC-cholesterol (blue triangles) was significantly lower than in DiphyPC patches (black circles). (D) Average mobility in DPPC-cholesterol membranes was significantly smaller (1.12 $\pm$ 0.48 nm/(s Pa)) than in DiphyPC patches. Shaded areas and error bars are two standard deviations wide. To see this figure in color, go online.

Finally, we wanted to modify the applied hydrodynamic force while leaving membrane drag unchanged. We increased the viscosity of the flow buffer 1.7 times by adding 0.59 M sucrose and then repeated our mobility measurement of neutravidin in DiphyPC patches. We reasoned that this change would increase the force applied to the proteins, compared with the force applied by standard buffer at the same flow rate. Since solution viscosity is used to calculate the shear stress at the coverslip, we expected to observe no change in the mobility. In high-viscosity buffer, we observed a small but statistically significant reduction in the average diffusion constant for neutravidin in membrane patches (Figs. 8 A and S4; D = $0.33\pm 0.09$ $\mu m^2/s$, different from the no-sucrose value with p < 0.05). This small decrease is consistent with previous observations that a similar sucrose concentration lowers the lateral mobility of phospholipids in GUVs (50). In addition, it indicates that lipid-anchored neutravidin diffusion is dominated by membrane drag, since a larger decrease would be expected for diffusion of neutravidin alone (the three-dimensional diffusion constant in 0.59 M sucrose should be approximately 59% of the value in water). Fig. 8 B shows that the exponential coefficients for the intensity gradients were similar to those observed in standard buffer. In this case, although the same flow rates were applied to the membrane patches, the applied shear stress was larger than that applied with the standard buffer. The calculated flow mobility $M_s=10.7\pm 3.5$ nm/s Pa was lower in the high-viscosity buffer than in standard buffer (Fig. 8 C and D). However, within our experimental uncertainty, this mobility decrease can be entirely explained by the decrease in the observed diffusion constant.

Figure 8.

(A) Diffusion constants measured by gradient relaxation in DiphyPC membrane patches, using standard flow buffer (black circles) and buffer containing sucrose to increase its viscosity (magenta squares). (B) Exponential fit coefficients measured in high-viscosity buffer (magenta squares) were similar to those measured in standard buffer (black circles). (C) Drift velocity per applied force in high-viscosity buffer (magenta squares) was slightly lower than that measured in standard buffer (black circles). (D) We observed a small reduction in mobility when high-viscosity buffer was used to apply shear flow. Shaded regions and error bars are two standard deviations wide. To see this figure in color, go online.

Discussion

In our experiments, fluid shear stress is low and membrane lipids are, on average, stationary. These two factors differ from previous measurements of flow-induced lipid-anchored transport (35,36), in which higher shear stress caused the lipid membrane to tank-tread during measurements. This simplifies our analysis, since the separate frictional drag coefficients discussed by Hu et al. (e.g., friction between the membrane leaflets, and between the lower leaflet and the substrate (35)) all collapse into an effective total membrane drag that we call $F_m$. When protein velocity is small, we expect that membrane frictional drag is linearly proportional to the protein’s velocity and that the protein reaches a "terminal velocity" that depends on the ratio of force exerted by the flow $F_w$ and this drag force $F_m$.

The flow mobility $M_{Ld}$ we measured for neutravidin in DiphyPC membranes is significantly lower than those determined previously for streptavidin in tank-treading membranes, 190 $\pm 40$ nm/(s Pa) and 90 $\pm 30$ nm/(s Pa) (35). Jönsson et al. also found significantly higher values for flow mobility of streptavidin bound to bio-DPPE in POPC membranes, between 84 and 122 nm/(s Pa) (depending on protein surface concentration) (51). In contrast, we measured flow mobilities between 1 and 15 nm/(s Pa).

The fact that our experiments were performed in stationary membranes, unlike both of the previous experiments, may explain this difference. In previous work, protein movement was measured relative to an upper leaflet that was actively sliding over the lower leaflet. Blosser et al. previously observed that continuous supported membranes do not tank-tread below a threshold value of shear stress, indicating static interleaflet friction that prevents movement at lower shear (32). We conjecture that in our experiments, additional static friction between the two leaflets was present, and that this increased total membrane resistance to protein movement in our experiments.

Our preparation used DiphyPC instead of DOPC, and in DiphyPC membranes, we used bio-DOPE as the anchor lipid rather than bio-DPPE. Both of these changes might alter the frictional drag between the anchor and the surrounding lipids. Since we included a larger concentration of biotinylated lipids in our membranes than Jönsson et al., our experiments may have yielded larger numbers of anchor lipids bound to each neutravidin, which would also increase membrane drag. Each neutravidin tetramer can bind up to four biotinylated lipids. However, biotin binding sites are oriented in pairs on opposite faces of the protein, so it is likely that on flat supported bilayers, the maximum number of bound lipids is two (52). The model developed in Hu et al. predicted that mobility would drop by more than half when streptavidin was bound to two biotinylated lipids instead of one, and they observed two populations of streptavidin with different mobilities consistent with this prediction. However, their lower mobility estimate (90 $\pm 30$ nm/(s Pa)) is still much larger than any value we obtained (35). In other experiments, only one mobility was observed for an entire population of streptavidin (34). We did not determine the number of biotinylated lipids bound to each protein in our experiments, but our observation of single-exponential concentration functions suggests that each membrane patch contained a mostly homogeneous population, especially considering the large mobility difference expected for proteins bound to different numbers of lipids. However, it is possible that some of the variation in flow mobility between different experiments that we observed could be explained by variation in the number of lipids bound to neutravidin. Future experiments will use a series of monomeric membrane-binding proteins of varying sizes to eliminate this uncertainty.

Substantial uncertainty exists regarding the expected mobility of lipids in the plasma membranes of living cells. Shi and Cohen defined a collective mobility coefficient to describe how easily membrane lipids flow in response to tension gradients, using the ratio of the Darcy permeability to the membrane viscosity (18). For two-dimensional membranes, lipid flow depends strongly on the area fraction of immobile obstacles, whereas individual lipid diffusion constants are relatively insensitive to it. Their calculations of permeability from experimentally determined parameters yielded estimated collective membrane mobility coefficients that span several orders of magnitude (from <0.4 to 7300 nm/(s Pa)). The collective mobility coefficient described by Shi and Cohen is distinct from the flow mobility we measure for lipid-anchored proteins, which are able to diffuse around obstacles. If collective lipid mobility were measured in our membrane patches, we would expect it to be extremely small since membrane patch lipids do not move in the flow direction.

Similar steady-state exponential concentration profiles were recently used to analyze membrane protein and lipid gradients created by electrophoresis in membrane patches derived from giant plasma membrane vesicles (39). In that work, a strategy opposite to ours was employed: the drift velocity was obtained from changes in the apparent average position of the protein signal, and this velocity was then subsequently used to determine a protein or lipid diffusion constant from the steady-state concentration profile. We calculated drift velocities directly from our initial flow movies for two different membrane compositions and found good agreement between the average drift velocities obtained by the two methods (Fig. S5). Agreement between these two methods also implies that neutravidin diffusion constants did not change significantly when the flow was turned on, despite the shifts in supported membrane area that have are observed in solid-supported bilayers under shear flow (40,49).

Surface concentration of the protein is an important factor in analyzing mobility data. Jönsson et al. showed that membrane-anchored molecules start to shield each other from hydrodynamic flow at high surface coverage and estimated that this effect becomes important when surface coverage exceeds approximately 10% (53). In other experiments, withdrawing flow through a micropipette positioned a few microns away from a supported bilayer was used to accumulate lipid-anchored proteins underneath (51). In these experiments, the maximum surface coverage of streptavidin accumulating underneath the pipette was estimated not to exceed 30%, a limit that is possibly due to charge repulsion between the streptavidin molecules (46). Neutravidin is deglycosylated in order to give it a neutral charge and lower nonspecific binding, so it could be expected to have less self-repulsion than streptavidin.

We included 2.0 mol% of bio-DOPE in our DiphyPC membranes, giving a theoretical maximum neutravidin surface concentration of approximately $2.48·{10}^4$/$\mu m^2$ (calculated using an average lipid area of 0.806 $n{m}^2$ (54)), which would yield a surface area fraction of approximately 60% (assuming protein area is approximately 25 $n{m}^2$ (55) and that each neutravidin is bound to a single bio-DOPE). Although we did not directly measure surface protein concentration during our flow experiments, several observations support the conclusion that the actual neutravidin surface concentration was much smaller than this upper bound: in addition to observing steady-state concentration profiles that were consistent with exponential functions, we observed that in all patches neutravidin fluorescence intensity increased by at least an order of magnitude when the flow was turned on. These increases would have been limited by crowding if protein concentration was already high.

It is possible for the surface concentration of neutravidin on each membrane patch to vary from patch to patch and from experiment to experiment. This can arise from variations in lipid composition between individual electroformed vesicles (see Fig. S6) or variation in biotin binding during incubation with the neutravidin solution. We did not observe any trends in diffusion constant or drift velocity with the patch fluorescence intensity (Fig. S7), which further supports our assumption that our average surface protein concentrations were relatively low.

Our experimental data show that variation in observed protein velocities occurs even when the same membrane lipids and proteins are used in preparation. We determined that mobility varied by approximately 20% even when examining membrane patches within the same microchannel (Fig. S8). Examining multiple patches inside the same channel eliminates possible inconsistency in applying or calculating shear stress, as well as in neutravidin incubation time and concentration. We therefore conclude that variation most likely arises from differences between the membrane patches themselves. It may indicate that the mechanical properties of each supported membrane patch are highly sensitive to the details of the GUV rupture process.

Despite the presence of variation, our results demonstrate that our method is able to distinguish different flow mobilities for the same protein bound to membrane patches with different compositions. We observed that increasing drag on the protein by increasing membrane viscosity caused a decrease in flow mobility. We anticipated that increasing solution viscosity would leave flow mobility unchanged, and we found that this was the case (after allowing for the decrease in protein diffusion constant in the more viscous medium). Our experiments take advantage of the fact that flow passively transports membrane-linked proteins over large distances to form micron-scale, optically visible concentration gradients. We anticipate that similar gradients form on the surface of living cells, and that these could be physiologically relevant. We plan to extend this method to explore flow transport of membrane proteins involved in flow mechanosensing by cells. Our method will also make it possible to compare mobility of the same proteins in living cells and in supported bilayers to determine the mechanical properties of the membrane-cytoskeleton complex.

Author contributions

A.M.R. and A.H.-S. designed the research. A.M.R., S.S., X.I.R.G., E.J.M., L.S., and A.A.A. carried out the experiments. A.M.R. and A.H.-S. wrote code for data analysis; A.M.R., S.S., X.I.R.G., L.S., and A.H.-S. analyzed the data. A.M.R., S.S., and A.H.-S. wrote the article.

Editor: Rumiana Dimova