Mechanically Enhancing Planar Lipid Bilayers with a Minimal Actin

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Mechanically Enhancing Planar Lipid Bilayers with a Minimal Actin Cortex Daniel Lee Burden, Daniel Kim, Wayland Cheng, Emily Chandler Lawler, Daniel R. Dreyer, and Lisa K Burden Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b01847 • Publication Date (Web): 27 Aug 2018 Downloaded from http://pubs.acs.org on September 4, 2018

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Figure 1. (A) The F-actin network is chemically linked to the bilayer via a biotin-streptavidin-biotin bridge. (B) Schematic of the bilayer chamber used for simultaneous pressure control and measurement, membrane capacitance, channel conductance, and optical microscopy. (C) F-actin filaments can grow over 10 µm in length. Confocal image of a thin layer of fluorescently labeled filaments. (D) Bright-field image of a typical Teflon aperture. (Inset) Confocal fluorescent image of a MAC-derivatized lipid bilayer. F-actin filaments can be seen extending inwardly from the aperture rim. 175x110mm (300 x 300 DPI)


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Figure 2. (A) Single-step pressure test of bilayer membranes formed over the same aperture. At t=0, the trans bilayer pressure was raised to 200 Pa and the resulting membrane expansion was recorded. Typical time courses for the expansion of an uncoated bilayer (pink), a bilayer with one side attached to an F-actin network (light blue), and a bilayer with both sides attached (dark blue) to an F-actin network are displayed. (B) Multi-step pressure response of a typical uncoated bilayer. (C,D) Muti-step pressure response of a typical bilayer with one (C) and two (D) sides connected to an F-actin network (red: measured pressure; black: capacitance change, green: unitless overlay of actuator position. 271x760mm (200 x 200 DPI)


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Figure 3. (A) Comparison of the capacitance change and percent area increase upon trans-bilayer pressure application for an uncoated bilayer (black) and a two-sided F-actin coated bilayer (red). Replicate trials of each membrane type are shown with solid squares, open circles, and open triangles, respectively. Fits to each composite data set denote general trends. (B) Comparison of the average initial elastic moduli (Eo) for uncoated (black), one-sided (blue) and two-sided F-actin coated bilayers. F-actin coating on two sides conveys a modulus increase of ~250x when compared to uncoated bilayers. Data sets represent average moduli from 7, 6, and 3 trials (with standard deviations of 1.4x106, 9.4x106, and 3.0x108) for uncoated, one-sided, and two-sided membranes, respectively. 256x388mm (300 x 300 DPI)


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Figure 4. Ion channel insertions in a bilayer that has been coated with F-actin on both sides. Stepwise changes demonstrate that F-actin network anchored to the bilayer with a streptavidin/biotin linkage does not prohibit nominal nanopore activity. 270x206mm (300 x 300 DPI)


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Mechanically Enhancing Planar Lipid Bilayers with a Minimal Actin Cortex †

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Daniel L. Burden,* Daniel Kim, Wayland Cheng, Emily Chandler Lawler, † †† Daniel R. Dreyer, Lisa M. Keranen Burden

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Wheaton College Chemistry Department Wheaton College Biology Department * Corresponding author: [email protected] ††


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ABSTRACT All cells in all domains of life possess a cytoskeleton that provides mechanical resistance to deformation and general stability to the plasma membrane. Here, we utilize a two-dimensional scaffolding created by actin filaments to convey mechanical support upon relatively fragile planar bilayer membranes (Black Lipid Membranes, BLMs). Robust biomembranes play a critical role in the development of protein nanopore sensor applications and might also prove helpful in ion channel research. Our investigation utilizes a minimal actin cortex (MAC) that is formed by anchoring actin filaments to lipid membranes via a biotin-streptavidin-biotin bridge. We characterize the joined structure using various modes of optical microscopy, electrophysiology, and applied mechanical stress (including measurements of elastic modulus). Our findings show the resulting structure includes a thin supporting layer of actin. Electrical studies indicate that the integrity of the MAC-bilayer composite remains unchanged over the limits of our tests (i.e., hours to days). The actin filament structure can remain intact for months. Minimalistic layering of the actin support network produces an increase in the apparent elastic modulus of the MAC-derivatized bilayer by >100x, compared to unmodified BLMs. Furthermore, the resistance to applied stress improves with the number of actin layers, which can be cross-linked to arbitrary thicknesses, in principle. The web-like support structure retains the lateral fluidity of the BLM, maintains the high electrical resistance typical of traditional BLMs, enables relatively uninhibited molecular access to the lipid surface from bulk solution, and permits nanopore self-assembly and insertion in the bilayer. These interfacial features are highly desirable for ion channel and nanopore sensing applications.


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INTRODUCTION Over the past two decades, nanopore sensing applications have expanded rapidly.1–9 Typically, these assays involve the creation of a single aqueous-filled pore of ~100 nm lumen diameter in an electrically impermeable barrier. Upon application of an electric potential, analytes are detected as they pass from one side of the pore to the other. A myriad of ions, small molecules, polymers, and nanoparticles can now be distinguished using biological nanopores, as well as pores milled in solid-state materials such as silicon nitride or graphene.10,11 More recently, assays have arisen that successfully extend the use of biological nanopores into complex chemical matrices, such as cell lysates and blood plasma.12–17 Together these factors underscore the potential of nanopore sensing technologies, including commercial ventures aimed at a variety of markets that range from DNA sequencing to clinical microbiology. Although the number and type of analyte species that can be revealed with nanopores continues to grow, devices featuring protein nanopores have been limited, in part, by the membrane structures that incorporate the pore.18–20 The earliest ion-channel characterization platforms employed unsupported lipid films, often designated as black lipid membranes (BLMs), freely suspended across relatively large apertures (~102 µm diam.).21 These lipid bilayers are ideal for protein nanopores owing to their fluidity, thickness (~5 nm), organized layering of hydrophobic and hydrophilic regions in the membrane, and highly resistive electrical properties (e.g., Gohm seals). They also enable direct aqueous access to embedded nanopores from either side of the membrane. In essence, BLMs provide a simplistic approximation of a cell membrane, which is the native environment for ion channels. However, the mechanical fragility and relatively short lifetimes of free-standing BLMs creates time-consuming barriers to investigation of pore-forming proteins. Various strategies have been developed to enhance the stability and mechanical properties of BLMs. These include reducing the aperture size,22,23 limiting the surface energy of the aperture substrates,24 forming bilayers on hydrated polymer cushions,25 tethering the bilayer to solid surfaces,26 trapping the bilayer between two hydrogel layers,27 photopolymerizing reactive amphiphiles in the lipid membrane,28 cross-linking lipid molecules within the bilayer,29 and the creation of bilayer structures using water droplets immersed in oil (known as droplet interface bilayers, or DIBs).30 Each approach has meritorious features; but limitations remain. For example, bilayers formed over a solid-supported polymer cushion provide greater tolerance to mechanical perturbation. But these structures have not yet been reported to give the electrical resistance needed for single-channel analysis.3 Similar challenges arise for lipid bilayers that are tethered to solid supports via covalent links to a solid surface.3 Bilayers formed using photopolymerizable components possess enhanced mechanical rigidity. However, results indicate that the lipid fluidity can be reduced, that phase domains can interfere with bilayer stability,29 and that the conductivity of inserted pores can be altered.28 The hydrogel sandwich approach conveys notable durability and longevity; however, the thickness of the support structure reduces diffusive transport to the lipid membrane surface by ~70%.28 In an independent scientific effort, recent papers have appeared that explore the concept of minimal actin cortices (MACs).31–39 This growing body of work aims to better understand the


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nature of the actin cell cortex through bottom-up in vitro experiments that couple actin filaments to a lipid membrane.31,38,35 For ease of study, the lipid bilayers are commonly formed on solid surfaces and later coupled to polymerized actin filaments. Actin filament coatings have also been applied to giant unilamellar vesicles (GUVs)34,37 and lipid monolayers.31 Much of the work to date has emphasized the role of myosin and the structural changes induced in the lipid bilayer by the generation of lateral contractile force.36,38–40 This study merges a MAC with a planar BLM to investigate interface properties relevant to ion channel research and nanopore sensing applications. Like the hydrogel sandwich approach, we begin by forming a BLM that possesses the electrical characteristics necessary for singlechannel recording. Then, in a second step, pre-formed filamentous actin is chemically joined to the bilayer. Links to the lipid bilayer are formed using a biotin-streptavidin-biotin complex, which creates a connection to the strong hydrophobic forces that hold the bilayer leaflets together. In living cells, the formation and destruction of actin filaments (F-actin) is a continuously dynamic process driven by a host of molecular interactions.41,42 Once stable filaments are formed, they can be anchored to the lipid bilayer by spectrin.43 The unique interlocking structure of actin monomers forms a filamentous web that can propel shape changes in the plasma membrane. Yet, the actin network can maintain a thickness that approximates a thin twodimensional sheet. A non-dynamic MAC with similar structural features preserves a combination of important lipid bilayer properties that are needed for ion channel and nanopore research. These include lateral lipid fluidity, direct diffusional access to the lipid bilayer from solution (from two sides), and a very high electrical resistance that enables single-channel detection sensitivity. Previous bilayer enhancement strategies do not preserve all these desirable characteristics. Our measurements explore the mechanical enhancements and electrical properties of MACderivatized BLMs when a phalloidin-stabilized F-actin support structure is chemically linked to the lipid bilayer. After formation of the scaffolding, we assess changes by applying transmembrane pressure and determining the area expansion and elastic modulus of the composite structure. We also characterize the structure electrically and with optical microscopy. Lastly, we demonstrate that the support network permits direct diffusional access to the lipid bilayer and that alpha-hemolysin (αHL) nanopores inserted into the supported bilayer retain their normal kinetic and electrical characteristics. EXPERIMENTAL Lipids. Diphytanoyl 1,2,-diacyl-sn-glycero-3-[phospho-L-serine] (DiPhyPC) and N-Biotinyl-PE 16:0 were purchased from Avanti Polar Lipids (Alabaster, AL). All lipid materials were dissolved in either hexadecane (Aldrich, Milwaukee, WI) or pentane (VWR, Bridgeport, NJ). A 5:1 mole ratio of DiPhyPC:N-Biotinyl-PE was used to create lipid bilayers. Filamentous Actin. Rabbit skeletal muscle actin monomers [Cytoskeleton Inc., >99% purity] were polymerized into filamentous form (F-actin) from monomers using varying ratios of globular actin (G-actin) [AR05], biotinylated actin [AB07], and rhodamine-phalloidin [PHDR1]. Phalloidin is a seven amino acid peptide toxin from the mushroom Amanita phalloides that binds to the


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helical structure of F-actin and was dissolved in methanol from lyophilized powder. Actin monomers (5:1 mole ratio, G-actin:biotin actin) were reconstituted in a buffer of 0.2 mM CaCl2 and 5 mM Tris-HCl, pH 8.0 and placed on ice for one hour. Cooling reduces the number of nucleating centers so that maximal fluorescent intensity changes can be measured upon polymerization. Polymerization was then initiated by the addition of KCl, MgCl2, and Adenosine Triphosphate (ATP). A 10-fold molar excess of phalloidin was also added to the mixture to promote filament elongation and reduce the critical concentration required for filament elongation. The final F-actin growth media contained 2 µM actin (5:1 G-actin/biotin actin), 20 µM phalloidin, 1 M KCl, 10 mM Tris-HCl (pH 7.5-8.0), 2 mM MgCl2, 1 mM ATP, 0.1 mM CaCl2 and 95% of the protein present in the sample. The yield of αHL was ~1 mg from 50 ml of cell culture. Optical Imaging. Creation of F-actin filaments was verified by imaging via confocal fluorescence microscopy on glass slides using 514-nm laser excitation and 565-580 nm emission band. Figure 1B illustrates the bilayer chamber used in both confocal and wide-field imaging experiments. The optical train consists of a confocal microscope that was modified from previous work45 to enable simultaneous electrical and optical recordings. The microscope


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was configured in an upright geometry and used water-immersion optics to interrogate composite membranes formed on a horizontal bilayer sample chamber, and also to estimate the length of the F-actin filaments spread on a microscope slide. Confocal images (10 x 10 um) were acquired using mechanical scanning and 100-nm step resolution. Widefield images were acquired using an intensified CCD camera (ICCD) with 0.5-1 µm resolution in both the brightfield and fluorescence modes (see SI for further details). Microscope Slide Preparation. Slides were prepared by cleaning with detergent, isopropanol, and water and incubating for 30 mins with a small droplet of streptavidin at 1 mg/mL. After a wash with buffer, the F-actin growth solution was applied and allowed to bind to the streptavidincoated surface. Following a gentle rinse with buffer, slides were imaged with a confocal microscope. Lipid Membrane Formation. Unsupported lipid bilayers were formed on a small Teflon aperture with a modified version of the Mueller-Rudin technique.46 A horizontal bilayer chamber, similar to that described elsewhere,45,47 was placed under an upright microscope for imaging with a low magnification microscope objective (Figure 1B). A constriction was formed between an upper and lower solution-filled chamber (1 M KCl, 5 mM HEPES, pH 7.5) by forcing a steel needle tip through a Teflon plug (~5 mm thick) until the sharpened end punctured the surface. After needle extraction, the remaining conduit left a taper with an inside diameter that changed from 20-100 µm over a distance of 1-2 mm and an approximately circular opening at the plug’s surface. The most commonly used plugs possessed end-of-conduit openings (i.e., apertures) with diameters ranging from 30-50 µm. Bilayers were prepared by first allowing a lipid in pentane solution to dry on the aperture surface. The upper and lower chambers were then filled with aqueous buffer solution containing 1 M KCl. Any solid lipid material remaining in the Teflon conduit was expelled using gentle pressure applied to the bottom chamber. A small amount of lipid dissolved in hexadecane was then applied to the aperture using a single filament from a camel hair brush. Lastly, lipid bilayers were created by stroking lipid in hexadecane across the aperture using a small bubble formed at the end of a pipette tip. See SI for more details. F-actin was chemically linked to the bilayer using streptavidin. Following bilayer formation, a small aliquot of streptavidin was applied over the lipid surface via pipette. After ~5 min incubation period for streptavidin to bind with biotinylated lipids, the chamber was rinsed (~3-5 volume exchanges) with KCl buffer. F-actin polymer filaments containing 20% mole ratio biotinylated monomers were then applied using a truncated pipette tip and incubated for 5 mins before executing another chamber rinse. The same rinsing procedure was used to create monolayers of F-actin on streptavidin-coated glass microscope slides for filament length and filament density estimates. Electrical Recordings. Electrical potentials were applied across the aperture using a DC-10 MHz waveform generator (Hewlett Packard 33120A, Palo Alto, CA) and Ag/AgCl electrodes (In Vivo Metric, Ukiah, CA) which were placed above and below the Teflon plug. Potentials were referenced to the top chamber, which was set to ground. The ionic current was amplified by a factor of 106-109 using a custom-built current-to-voltage converter and low-pass filtered using an 8-pole Bessel active filter (Frequency Devices 9002, Haverhill, MA). Data were digitized at 10 Hz using a 12-bit analog-to-digital converter (PCI-MIO-16E-1, National Instruments, Austin, TX) and were analyzed with software written in LabVIEW. The bilayer chamber and the microscope were isolated from sound and light, as well as external electrical fields, by an enclosed Faraday cage.


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Capacitance Recordings. A time course of capacitance readings was used to signal successful bilayer formation. Capacitance measurements also provide a means to monitor the bilayer response to transmembrane pressure, as the area of the membrane changes in response to stress. A triangle wave (400 Hz, 100 mV peak-peak) applied across the aperture opening generated a corresponding output square wave after membrane formation. The amplitude of this signal was converted into a calibrated capacitance value, which was continuously logged at 1 Hz (see SI for further background information). Typical capacitance readings for properly formed planar bilayers on our apertures ranged from 15-30 pF, depending upon the aperture size. Given the area of the aperture as determined by image analysis, a specific capacitance of ~0.7 µF/cm2 was determined. Others have reported similar specific capacitance values (0.4-1 µF/cm2) for functional lipid bilayers.48,49 Current Recordings. A -120 mV applied DC electrical potential enabled measurement of open αHL channels in the membrane. Protein monomers of αHL were pipetted to the top solution chamber in close proximity to the aperture. After addition, an ~20 s incubation period was permitted to allow protein migration, channel assembly, and pore opening. Current measurements were acquired using a 500 Hz low-pass filter and were logged at 10 Hz. Pressure Control and Measurement. One portal of a differential pressure transducer (Honeywell, 164PC01D37) was connected via buffer-filled Tygon tubing to the bottom chamber of the bilayer apparatus. Output voltage from the transducer is directly proportional to pressure from 0-10 inches H2O (0-2490 Pa) @ 20C. The second portal of the pressure transducer was left open to ambient atmospheric conditions. The bottom of the bilayer chamber was connected to a second segment of tubing filled with buffer. This tubing arm formed a 90 degree vertical elbow several inches away from the chamber and extended upward several more inches, well above the liquid level contained in the top bilayer chamber. The bottom portion of this arm consisted of compressible ¼-in i.d. Tygon tubing that contained a relatively large volume of buffer. A smaller diameter tubing (1 mm i.d.) extended above the elbow by several inches, with the end of the tube left open to the atmosphere. The ratio of large and small diameter tubing volumes was designed so that fluid displacement in the large diameter tube would cause the fluid level in the narrow tube to rise upward, thereby increasing the pressure in the bottom chamber and the connected portal of the pressure transducer. By positioning the flexible large-diameter tube against a fixed barrier, the height of the water level above the top chamber in the small-diameter tube could be controlled via compression from a stepper-motor-controlled actuator. Raising the level of solution in the tube above the equilibrium level for the top chamber increased the transmembrane solution pressure, applying a controlled and reversible force to the lipid bilayer spanning the aperture. Calibration of the pressure control and measurement system was performed using a sealed Teflon plug (i.e., no aperture or bilayer) against the measured vertical displacement of water above the equilibrium level. The system demonstrated a linear response with negligible hysteresis, as long as all air bubbles were flushed from the system. Changes in pressure could be measured below ∆2 Pa. RESULTS AND DISCUSSION Linked F-actin Surface Coverage. After the formation of a bilayer, we add components for the support network in a stepwise manner. Each step is followed by a rinse of approximately 3-5


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chamber volumes (9-15 mL). Presumably, the available biotin binding sites are nearly filled by the streptavidin addition. Polymerized F-actin is then added and given several minutes to bind before the second rinse commences. Confocal fluorescence microscopy reveals that this layering procedure typically results in a thin deposit of actin (Figure 1C and 1D), as individual filaments can be readily distinguished stretching over the surface. Widefield fluorescence images also support the presence of interspersed filaments connected to lipid headgroups in a single layer (see SI). In this context, we use the term single layer to describe an open mesh connected to the lipid bilayer primarily through direct linkage with streptavidin. Overlapping actin filaments, or filaments that bridge each other to reconnect with the lipid bilayer exist, but the lipid bilayer provides the main anchoring location. Filaments that bind to each other through streptavidin cross-links (i.e., filament-streptavidin-filament binding), with little or no connection to the lipid bilayer are a feature of multiple layers, by this definition. Since we only add streptavidin to the bilayer once and rinse excess material from the chamber prior to the addition of actin, we reason that the primary point of filament connection lies with the lipid bilayer and that filamentto-filament cross-linking is rare. Thus, we use the term single layer, even though much of the bilayer surface area is not covered by actin. A typical actin mesh applied to glass is shown in Figure 1C, revealing an approximate distribution of polymer filament lengths that range from 3-15 µm. Mesh spacing likely differs from experiment to experiment depending on the effectiveness of the manual application from the pipette; however, we regularly observed inter-filament openings of 5-50 µm2 (as estimated by empirical observation). Figure 1D shows a bright-field image of an aperture in Teflon. The inset to 1D was collected from the rim of the aperture via a confocal scan after a bilayer was suspended and derivatized with both streptavidin and F-actin. The Teflon and hexadecane annulus ring appear to fluoresce at a level that competes with the intensity of single F-actin filaments. Filaments can be seen covering the area around the aperture rim and the solvent annulus ring. It is possible that a favorable nonspecific interaction between Teflon and actin (both above and below the lipid bilayer) assists in anchoring the filaments. Filaments can also be seen extending inwardly across the lipid bilayer (see additional images in the SI). To assess the thickness of the filamentous netting applied to a BLM, a z stack of images was collected. Filaments disappeared in scans collected 2.0 µm away from the surface, which is the approximate axial resolution of the confocal system (see SI). A linear axial scan of a MAC derivatized bilayer using 100-nm axial step increments produces an intensity vs. position peak that is effectively identical to the confocal instrument response (see SI). These data indicate that the support structure forms a thin, primarily two-dimensional network with a thickness that is less than the axial resolution of confocal optical microscopy.


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Figure 1. (A) The F-actin network is chemically linked to the bilayer via a biotinstreptavidin-biotin bridge. (B) Schematic of the bilayer chamber used for simultaneous pressure control and measurement, membrane capacitance, channel conductance, and optical microscopy. (C) Factin filaments can grow over 10 µm in length. Confocal image of a thin layer of fluorescently labeled filaments. (D) Brightfield image of a typical Teflon aperture. (Inset) Confocal fluorescent image of a MAC-derivatized lipid bilayer. F-actin filaments can be seen extending inwardly from the aperture rim.

Temporal Response to Applied Pressure. Figure 2 displays results from several experiments where trans-aperture pressure is applied. Membrane expansion is monitored over time via capacitance and video recording. Typically, we continue experiments until the membrane begins to expand uncontrollably, or it ruptures. Rupture events can be visualized via video microscopy as a small burst of fluid is released upon membrane breakage (see video S1 in the SI). We performed two styles of experiments: single-step pressure tests and multi-step pressure tests. Single-step tests employ relatively high, but constant, applied pressure. Multi-step tests apply pressure in small step-wise increments, which enables a more controlled membrane area expansion and calculation of the in-plane elastic modulus. We also investigated bilayers with an F-actin mesh connected to one or both sides of the membrane. For one-sided measurements, F-actin was pipetted from the top bilayer chamber, followed by a chamber rinse to sweep away excess material. For two-sided experiments, breakage was induced via the application of high voltage after the first addition of streptavidin and F-actin. A second aliquot of streptavidin and F-actin was then delivered near the open aperture, followed by a short incubation to allow material to settle within the aperture opening. The lipid bilayer was reformed by manipulating a bubble from a pipette tip across the aperture. Membrane capacitance measurements confirmed the bilayer was of appropriate thickness (~5 nm) before continuing with the experiment (see video S2). As can be seen in Figure 2A, uncoated lipid bilayers expand to breakage rapidly upon the addition of 200 Pa of pressure. Composite membranes with one actin coated side respond with a much slower expansion, but still typically expand to breakage within seconds to minutes. However, composite membranes modified with filamentous actin on both sides of the aperture yield a flat capacitance response over time, indicative of the improved mechanical resilience conveyed by the supporting mesh. Our observations suggest that it is possible for all three membrane types to remain intact for several hours in the absence of applied stress. A few MAC-derived bilayers were left overnight (24+ hours, without continuous data logging) and were found to be electrically intact the following day (i.e., unchanged capacitance and resistivity). The membranes broke upon application of a 1V “zapping” potential, as do lipid bilayers without


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a MAC coating. However, under applied pressure, only composite membranes coated on both sides remain stable for multiple hours before the recordings are intentionally terminated.

Figure 2. (A) Single-step pressure test of bilayer membranes formed over the same aperture. At t=0, the trans bilayer pressure was raised to 200 Pa and the resulting membrane expansion was recorded. Typical time courses for the expansion of an uncoated bilayer (pink), a bilayer with one side attached to an F-actin network (light blue), and a bilayer with both sides attached (dark blue) to an F-actin network are displayed. (B) Multi-step pressure response of a typical uncoated bilayer. (C,D) Muti-step pressure response of a typical bilayer with one (C) and two (D) sides connected to an F-actin network (red: measured pressure; black: capacitance change, green: unitless overlay of actuator position.

Figures 2B-2D show multi-step pressure tests for an uncoated bilayer and a bilayer coated on one side only. A computer-controlled actuator (green) regulates the trans-aperture pressure increase in small steps, which is registered by the pressure transducer (red). The actuator position, overlaid as a unitless quantity, shows clear correspondence between pressure application and the detected pressure increase. Commonly, a slight measured pressure loss follows a step increment, presumably due to membrane bulging or movement that permits a


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volume increase in the bottom chamber. Capacitance recordings begin with a value that is characteristic of a flat bilayer spanning the entire area of the aperture. This value increases in response to applied pressure, as the membrane bows upward and the area of the membrane expands. The storage of lipid molecules in the torus of a BLM most likely assists expansion because additional solvated material can be physically drawn into the bilayer as the area increases. Figures 2B-2D show the change in capacitance (black) which is proportional to the change in membrane surface area. Frequently, we observe membranes expanding to an equilibrium position in stepwise synchrony with applied pressure, particularly at the beginning of an experiment, when the area expansion is small. All multi-step experiments continue until the rate of membrane expansion transitions into a region of large or continuous growth. In Figures 2B-2D, these “run-away” thresholds appear at ~130 s, ~260 s, and ~675 s, respectively (or at pressures of ~60, ~90 and ~150 Pa). The pressure at which this transition occurs varies from trial to trial by as much as ~30%, as an apparent random consequence of the size of the solvent torus, the size of the aperture, or the density of actin filaments spread over the bilayer. However, application of the linked F-actin network to one, or both, sides of the bilayer consistently stiffens the membrane, allowing it to tolerate significantly higher pressures than the underivatized counterparts. Theory of in-plane expansion modulus. To compare mechanical properties of bilayers under applied stress, we adopt a basic model of elastic bodies which assumes isotropic homogeneity of the membrane and allows calculation of the modulus of elasticity from readily observable parameters. Here, we modify the theory summarized by Hianik50 for our experimental configuration. The area extension in a planar membrane presumes equal stress (σ) in the X and Y directions. The Young’s elastic modulus can be defined as

ǁ =

σ + σ ∆ / = 2σ∆ /

Eqn 1

where σ and σ are applied stresses in the X and Y directions and ∆ / is the change in the bilayer area ∆ relative to the undistorted area . Here, ∆ / = ∆/ , since capacitance is a direct measure of bilayer area. The technique of measuring the modulus assumes membranes with spherical surfaces that bulge as a consequence of an applied hydrostatic pressure gradient (). For a spherical membrane51

= ℎ2/ thus,

=

ǁ ℎ∆/ ℎǁ ∆ / =

Eqn 2

Eqn 3

where ℎ represents the membrane thickness and is the radius of curvature that characterizes out-of-plane deformation.


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In general, the surface area of a spherical segment is computed as the zone of a sphere52

= 2√ −

− √ − ! "

Eqn 4

where ! and are radii associated with the upper and lower boundaries of the zone and is the radius of the sphere. When adapted for the case of a circular membrane deformed from its initial planar geometry, → 0 and ! = %, where % is the radius of the supporting aperture. Thus, the out-of-plane radius of curvature of a bulging membrane can be computed as

=

/2 √ − %

Eqn 5

Since the relative change in surface area is proportional to the capacitance change, ∆ ⁄ = − ⁄ = ∆/ = − / , can be found by estimating from optical microscopy and scaling it by the measured relative capacitance change.

= ∆/

Eqn 6

thus,

=

∆/ /2" ' ∆/ − %

Eqn 7

To calculate ǁ using Eqn. 3, we measure the radius of the aperture % and initial area via optical microscopy, measure the relative change in capacitance ∆/ , compute the radius of curvature of the deformed membrane, determine the pressure gradient , and make an approximation that ℎ remains effectively constant (~5 nm) for both coated and uncoated scenarios. Because the modulus changes nonlinearly for large area expansions, we compare coated and uncoated membranes using the limiting condition of small area expansion, ǁ =

lim∆+/+, →- ǁ .

Area Expansion and Modulus Comparison. Figure 3A compares the typical area expansion of uncoated bilayers to those observed for bilayers with a linked support on both sides. The original surface area of the membrane is determined using optical microscopy, where the membrane is presumed flat. As pressure increases, the measured change in relative capacitance ∆/ allows computation of the expanded surface area . As can be seen, from 0-50 Pa applied pressure, the area expansion for coated membranes is far less than the area expansion for supported membranes. Following Eqn 3, a plot of pressure, , vs. ℎ∆/ ⁄ yields the in-plane modulus for the membrane. Assuming ℎ remains constant for both coated and uncoated membranes (e.g., 5 nm), we directly compare moduli for the different membrane types. Because the modulus changes as a function of expansion, the most meaningful region for comparing moduli arises


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Langmuir

from small membrane displacements. Thus, this analysis emphasizes data collected at low applied pressures relative to the data in Figure 3A. The linear fits shown in Figure 3B arise from

the 4 lowest pressure data points in each set. The calculated slopes show an approximate 250fold increase in modulus ǁ for membranes with F-actin applied to both sides, in comparison to their uncoated counterparts. Bilayers coated on one side exhibit an elastic modulus between these two extremes. Figure 3. (A) Comparison of the capacitance change and percent area increase upon trans-bilayer pressure application for an uncoated bilayer (black) and a two-sided F-actin coated bilayer (red). Replicate trials of each membrane type are shown with solid squares, open circles, and open triangles, respectively. Fits to each composite data set denote general trends. (B) Comparison of the average initial elastic moduli (Eo) for uncoated (black), onesided (blue) and two-sided F-actin coated bilayers. F-actin coating on two sides conveys a modulus increase of ~250x when compared to uncoated bilayers. Data sets represent average moduli from 7, 6, and 3 trials (with 6 6 8 standard deviations of 1.4x10 , 9.4x10 , and 3.0x10 ) for uncoated, one-sided, and two-sided membranes, respectively.

Other investigators have performed measurements on free-standing BLMs using the application of a small time-dependent alternating hydrostatic pressure. However, the magnitude of the applied pressure displaced the lipid bilayer from its equilibrium position very little.53,54 Although the instruments for these investigations differed significantly from ours, the moduli obtained at


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Mechanically Enhancing Planar Lipid Bilayers with a Minimal Actin

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