Inward and outward membrane tubes pulled from giant vesicles

Membrane nanotubes are extruded from giant unilamellar lipid vesicles using a controlled hydrodynamic flow and membrane-attached beads manipulated via optical tweezers. Within a single experiment, the technique can be used to assess various important mechanical and rheological characteristics of the membrane such as the bending rigidity, tension and intermonolayer slip. The application of small flow velocities leads to the extrusion of tubes with sufficiently large diameters conveniently measurable under an optical microscope. For the first time, we show that by suitably controlling the medium flow, inward tubes inside the vesicles can be formed. This approach offers great potential for studying tubulation mechanisms in membrane systems, exhibiting positive as well as negative spontaneous curvatures and should offer a more realistic model for biomembranes because the vesicle membrane tension can adapt freely.

Biomembranes are very flexible and can easily bend to adopt the shapes of thin elongated cylinders, known as membrane tubes or tethers. Such structures commonly occur in cells [1] and are involved in a large number of important cellular functions such as cell migration [2], intercellular trafficking [3], intracellular trafficking [4] and signalling [5]. Because biological membranes are fairly complex systems, model membrane systems have been explored to understand the mechanisms driving cellular processes. Among them, giant unilamellar lipid vesicles (GUVs) [6,7] have become very popular because they can be used to visualize the membrane directly under an optical microscope. Membrane tubes have been pulled out of GUVs employing a wide range of approaches based on the use of hydrodynamic flows [8][9][10][11], gravity [12], micromanipulation [8,13,14], magnetic or optical tweezers [15][16][17]. Tube pulling experiments provide a convenient method to study membrane elastic properties and to understand how the bilayer structure and composition can influence membrane behaviour. Tube formation is now conventionally applied for studying membrane curvature sorting and sensing of proteins, see e.g. [18]. Apart from mimicking several biological phenomena, tube extraction in GUVs also finds applications in the fabrication of tube-based networks for nanofluidic devices and in artificial cell design [19].
Among the different techniques used for pulling tubes from lipid membranes, the more widely used approach involves the use of a pipette to aspirate the vesicle, from which a tube is pulled out. In this case, the membrane tension is preset and kept constant by the suction pressure of the aspirating micropipette. However, in cells, the membrane tension may vary and adjust according to the membrane reshaping process and even modulate this very process [20,21]. Furthermore, since the technique essentially requires aspirating the vesicle using a pipette and therefore presetting the membrane tension, it cannot be used to study the response of the membrane to changes in its tension. The need to hold the vesicle via aspiration by itself imposes a minimal tension, below which experiments cannot be performed, limiting the accessible tension range. One approach, for which the membrane tension can vary during the tube formation, is provided by the use of hydrodynamic flows to pull membrane tubes. Tube extrusion has been achieved by using hydrodynamic forces from sedimenting vesicles [11] or from vesicles with an attachment point on either a glass substrate [8] or a micro-rod [9]. However, these experimental scenarios are inherently restrictive compared to an approach combining hydrodynamic flows and magnetic or optical traps as used here. This latter approach allows us to reach the full potential of estimating various elastic properties of the lipid vesicles.
It is also pertinent to note that up to now, all tube pulling experiments report the extrusion of only outward tubes from the vesicle membrane. This approach is suitable for investigating the effect of molecules, which generate positive spontaneous curvature (i.e. outward bending) in the membrane when added to the vesicle exterior. For molecules inducing inward membrane bending, i.e. negative spontaneous curvature, such as I-BAR proteins, which have been shown to induce internal vesicle tubulation [22], pulling inward tubes in giant vesicles would be advantageous.
Here, we show that membrane tubes extruded under hydrodynamic flows with the help of optical tweezers can be used to obtain various important mechanical and rheological characteristics of the membrane within a single experiment. Our approach starts with the formation of outward tubes. A vesicle was brought into contact with an optically trapped bead and thereafter dragged away from the bead by a controlled hydrodynamic flow. No preset tension on the vesicles needed to be applied and the vesicles were predominantly being acted upon by very small tensions corresponding to the entropic regime. Thus, under slow flow velocities, this method offers formation of tubes with sufficiently large diameters (above the optical resolution limit) which could be directly measured. At higher flow velocities, thinner tubes could be formed. By suitably accounting for the hydrodynamic drag on the vesicle and studying the statics and dynamics of the tube pulling forces, we could assess several important material properties of the lipid membrane within a single experiment. We could also use the approach to manipulate a bead towards the vesicle interior. Once attached to the membrane, we could employ the trapped bead to pull inward tubes into the vesicle. This technique offers significant potential for studying processes promoting negative curvature in lipid membranes.
For vanishing spontaneous curvature, the tube pulling force can be written as [23], where L(t) is the length of the tube changing with time t anḋ L(t) is the rate of change. The first term in this equation, the static pulling force f s (t), is given by where (t) is the membrane tension and κ is the bending stiffness. The second term in equation (1) involves the friction between the two leaflets where b is the intermonolayer slip coefficient, h is the thickness of the hydrophobic bilayer, and R v and R c are the radii of the vesicle and the cylindrical tube, respectively. In equation (1), we have omitted the contribution of the restoring force opposing the asymmetry between the two membrane leaflets, arising from the unequal changes in their areas. This term is on the order of κ Neglecting the small changes in vesicle tension due to hydrodynamic friction [8], for a flaccid vesicle with initial tension 0 , the increasing tension during tube formation can be given as [24], is the area of the cylindrical tube and A 0 = 4πR 2 v is the surface area of the vesicle. When using hydrodynamic flow to extract a tube, the tube extrusion force increases with increasing length (as the vesicle is displaced). When the increased tension of the membrane counteracts the vesicle displacement with the flowing fluid, the vesicle becomes stationary. The maximum tension m reached at this point with flow velocity U , can thus be obtained from Since R c (t) = √ κ/2 (t), the corresponding tube radius at the maximum tension is Inserting the expression for m in equation (3), for the maximum tube length at the stationary state we have At this point, when the medium flow is stopped the vesicle retracts towards the trapped bead and the tube shrinks in length. Note that during tube pulling and release, the vesicle size was not observed to change within the measurement error. The hydrodynamic drag acting on the retracting vesicle, −6πηR vL (t), balances the mechanical force of the tube following Here the interleaflet friction acts to slow down the retraction process. Inserting from equation (3) and neglecting the variation in R c with time [24], the time evolution of a shrinking membrane tube can be described as For extrusion of membrane tubes oriented inward, we made use of hydrodynamic force to press the vesicle onto the bead and bring it to the vesicle interior. Once inside the vesicle, the trapped bead could be used to extrude tubes in a similar manner as used for pulling tubes outside the vesicle.
The experimental set-up [25] was built around a motorized inverted microscope (Axiovert 200 M, Zeiss) and comprises of single beam optical tweezers formed by focusing a 1064 nm, cw laser beam from a Nd : YAG laser (Spectra Physics, USA) through a 100×, NA 1.25 objective lens (Acroplan, Zeiss). The optical tweezers were used to trap streptavidincoated polystyrene beads (Polyscience Inc) of 2 ± 0.045 µm diameter and the trapping force was calibrated by applying varying viscous drag on the trapped sphere by movement of the motorized microscope stage (LStep13, Märzhäuser) and measuring the position of the trapped bead using the centroid tracking algorithm [26]. The precision of position sensing using the centroid tracking technique could be estimated to be ∼4 and ∼6 nm along the x and y directions, respectively. All measurements were performed at a height of ∼25 µm from the bottom glass boundary of the sample chamber. The stiffness of the tweezers was found to be ∼70.2 pN µm −1 W −1 . Typical laser powers used were ∼0.5 W at the sample.
Giant vesicles were grown at room temperature using the electroformation technique [27] in a solution of sucrose (100 mOsm) from 1-palmitoyl-2-oleoyl-sn-glycero-3phosphatidylcholine (POPC) doped with 0.1 mol% biotinyl cap phosphatidylethanolamine (PE). All lipids were purchased from Avanti Polar Lipids. The biotinylated lipid serves to make vesicles adhere to the streptavidin-coated beads, which subsequently act as handles to pull the tubes. For better observations under the microscope and to facilitate streptavidin-biotin bonding, the vesicles were suspended in an isotonic medium of 40 mM glucose and 30 mM sodium chloride. All measurements were performed at ∼23 • C. Images were captured by an electron-multiplying chargecoupled device (EMCCD) camera (ImagEM, Hamamatsu Corp) at 30 frames per second. ImageJ was used for size and co-ordinate analysis of the vesicles using edge detection techniques [28].
When a flaccid vesicle was brought into contact with a trapped bead and subsequently dragged away by a hydrodynamic flow, a membrane tube could be seen to form at very low speeds of separation of a few µm s −1 . Interestingly, the tubes thus formed have diameters of a few hundred nm, conveniently measurable under optical microscope. This is unlike typically thin tubes with diameters of a few tens of nm formed from aspirated vesicle set under tension. Figure 1(a) shows a membrane tube pulled under a hydrodynamic flow U ∼ = 10 µm s −1 . At that speed, the static tube length was 3.2 µm. For measuring the tube diameter we plotted the grey level distribution in the transverse section of the tube averaged over seven locations along its length ( figure 1(b)). The data were fitted to a Gaussian [29], which gives the tube diameter for the vesicle shown as 2R cm ∼ = 0.63 µm. Therefore, from equation (6), we could estimate the bending rigidity κ = (1.01±0.09)×10 −19 J or κ = 26±2k B T . The error represents the standard deviation over ten experiments. Measurements over five other vesicles yield κ = (1.14 ± 0.18) × 10 −19 J or κ = 28 ± 4k B T . These results are in good agreement with previous reports for POPC [30]. For the vesicle in figure 1, knowing κ we can also estimate the maximum membrane tension, m ∼ = 5.1×10 −7 N m −1 using equation (4) and taking η = 1.015 cP for the viscosity of 40 mM glucose solution [31]. The initial tension of the vesicle (before the tube was pulled) using equation (3) When the vesicle was subjected to changing hydrodynamic velocities, stationary membrane tubes of varying length could be formed ( figure 2(a)). In figure 2(b), we have shown the measured lengths of tubes at varying flow velocities for a single vesicle (the same vesicle as in figure 1). The data represent the mean values of ten measurements at each flow speed. The measured values were fitted using equation (6) with κ and 0 as fitting parameters (solid curve in figure 2(b)). It can be seen that the experimental data agree well with the predictions from equation (6). The best fit was obtained for κ = 1.21 × 10 −19 J and 0 = 1.48 × 10 −8 N m −1 , values in good agreement with the estimate made from directly measuring the tube radius (figure 1). Similar measurements were carried out over five other vesicles yielding for the bending rigidity κ ∼ = (1.22 ± 0.25) × 10 −19 J or (29 ± 6)k B T .
From the theoretical curves in figure 2(b) and equation (6), it is evident that the formation of the membrane tube can be initiated at flow velocities as low as ∼3 µm s −1 , requiring a pulling force of only ∼0.5 pN. This value is about two orders of magnitude lower than the typical threshold needed when working with vesicles aspirated in a micropipette. This can be of significant advantage when studying membrane tubulation mechanisms. The use of such low forces expands For the staining, the membrane was labeled with 0.1 mol% DiIC18. (c) Retraction of a membrane tube after being extracted using flow velocity U = 50 µm s −1 . Errors represent standard deviations over ten measurements. The solid curve is a fit following equation (8), see text for details. the concentration range for curvature generating molecules towards much lower concentrations.
Next, we studied tube retraction. Medium flow velocity of 50 µm s −1 was first applied to form the tube. After the vesicle has attained the stationary state, the medium flow was quickly stopped to allow the tube to retract while still holding the bead with the optical tweezers. This dynamic process now involves the main counter force from hydrodynamic drag friction between the rapidly moving internal and external bilayer leaflets as discussed in the context of equation (1). The changing length of the tube was monitored over the time scale of retraction. Figure 2(c) shows the measured tube lengths at 0.2 s time intervals during retraction. The data shown are the averages over ten measurements. They were fitted following equation (8) with b as a fitting parameter and using the estimated values for κ and 0 from figure 2(b), taking h ∼ = 2.71 nm for the thickness of the hydrophobic bilayer [32]. The solid line shows the best fit obtained with interlayer viscosity b = (3.74 ± 0.28) × 10 9 N s m −3 . Similar measurements carried out over five other vesicles yield values for b as (3.32 ± 0.73) × 10 9 N s m −3 . This value is somewhat higher than that measured on lipids with identical hydrophobic chains such as dimyristoylphosphatidylcholine (DMPC) and dioleoylphosphatidylcholine (DOPC) [33]. The slightly higher value of b which we report here most likely reflects partial interdigitation as predicted in reference [33]. Interdigitation is expected for bilayers made of lipids with different chains, such as POPC used in this work.
In systems exhibiting inward membrane tubulation, namely in vesicles with negative spontaneous curvature [34,35], it is very advantageous if one can pull inward tubes (in the vesicle interior). For this purpose it is required to manipulate the trapped bead across the membrane and take it to the vesicle interior. As shown in figures 3(a)-(d), a trapped bead can be brought into the vesicle interior upon applying fluid flow pressure on the vesicle. To test how the theoretical analysis applies to inward tubes, we used the same vesicle as in figures 1 and 2, for which we had already obtained the initial membrane tension from pulling outward tubes.
After having manipulated the bead inside the vesicle, we could use it to pull inward tubes by dragging the vesicle relative to the trapped bead via controlling the fluid flow. In figures 3(a)-(d), extrusion of an inward tube with a length of approximately 11 µm is shown. The tube is not visible under phase contrast observation, but can be seen in fluorescence, see figure 3(d) (the membrane was stained with DiIC18). Inside the vesicle, the maximum tube length is limited by the vesicle and bead sizes. Applying a flow velocity of U ∼ = 30 µm s −1 we could extrude a tube with maximal length L m ∼ = 16.4 µm. Following equation (6), this gives an estimate for the initial membrane tension 0 ∼ = 1.12 × 10 −8 N m −1 , which is in good agreement with the estimate made from studying outward tubes. When the flow is stopped the tube retracts, dragging the vesicle back onto the trapped bead ( figure 3(c)). In figure 3(e), we show the retraction profile of the inwardly pulled tube. The profile follows the logarithmic pattern well as predicted by equation (8), showing similar dynamics as that followed by the external tubes (compare with figure 2(c)). From the retraction profile we could estimate the interlayer slip coefficient as b = (3.19 ± 0.38) × 10 9 N s m −3 , which is again in excellent agreement with results from pulling outward tubes. The values of b obtained from studying six vesicles is (3.43 ± 0.71) × 10 9 N s m −3 . The vesicle diameters during extrusion and retraction of both inward and outward tubes were found to be unchanged within the measurement error of ±0.2 µm. We have shown here that optically trapped beads can be used to investigate free flaccid vesicles with the aid of a controlled medium flow.
Theoretical results and experimental studies have been presented to show that the method of pulling inward and outward tubes from vesicles manipulated with a hydrodynamic flow can provide means to estimate several important mechanical parameters of the vesicle membrane simultaneously. The technique can be used to form membrane tubes with directly measurable diameters, enabling estimation of elastic coefficients of the membrane within a single experiment. The results here were obtained on neutrally charged vesicles, but since pulling tubes from GUVs containing charged lipids have been shown to proceed analogously (see e.g. [36]), we expect that the method is applicable to charged membranes as well. The application of a very minute force of less than a pN to extrude tubes from flaccid vesicles suggests the important potential of this approach for investigating membrane tubulation processes caused by very low concentrations of curvature-active proteins. Most significantly, for the first time membrane tubes in the interior of a vesicle could be extruded and studied, a technique with potentially promising applications in future studies of bending mechanisms in membranes with negative spontaneous curvature.