Simultaneous measurement of surface and bilayer tension in a microfluidic chip

Navid Khangholi; Ralf Seemann; Jean-Baptiste Fleury

doi:10.1063/1.5137810

Biomicrofluidics. 2020 Mar; 14(2): 024117.

Published online 2020 Apr 27. doi: 10.1063/1.5137810

PMCID: PMC7188485

PMID: 32549923

Simultaneous measurement of surface and bilayer tension in a microfluidic chip

Navid Khangholi, Ralf Seemann, and Jean-Baptiste Fleury^a)

Author information Article notes Copyright and License information PMC Disclaimer

Abstract

Freestanding lipid bilayers are one of the most used model systems to mimic biological cell membranes. To form an unsupported bilayer, we employ two aqueous fingers in a microfluidic chip surrounded by an oily phase that contains lipids. Upon pushing two aqueous fingers forward, their interface becomes decorated with a lipid monolayer and eventually zip to form a bilayer when the monolayers have nanoscopic contact with each other. Using this straightforward approach, the quick and easy bilayer formation is facilitated by oil draining into the microfluidic device material consisting of polydimethylsiloxane. However, the oil drainage limits the lifetime of a bilayer to about 1 h. We demonstrate that this drainage can be managed, resulting in superior bilayer stability and an increased lifetime of several hours when using a pressure-controlled system. Applying different pressures to the aqueous fingers in the microfluidic chip, the formed bilayer can even be bent to a desired curvature. Extracting the contact angle and the resulting curvature of the bilayer region, for a given applied pressure difference, both the bilayer tension and the surface tension of each lipid monolayer can be derived from a single experiment using the Young Laplace pressure equation.

I. INTRODUCTION

A cell membrane is a barrier to the external environment that is commonly mimicked in model systems by a simple phospholipid bilayer. Artificial lipid bilayers are simplified models that have been used as platforms to understand biological processes occurring at the cell membrane.^1,2 They are also used for biotechnological purposes such as DNA-chip fast sequencing,³ drug delivery,^4,5 or artificial photosynthesis.^6,7

There are two major platforms to explore the properties of lipid bilayers, which are either lipid vesicles or planar bilayers. Lipid vesicles are basically bilayers in a spherical shape, which are commonly used in biological and biochemical purposes because of their ease of synthesis and handling.⁸ Instead, a planar lipid bilayer consisting of two separated lipid monolayers stabilized by a solvent is referred to as a Black Lipid Membrane (BLM). BLMs can be formed either on a supported solid substrate^9–11or can be unsupported.^12–14 Advantages of the BLM methods over the lipid vesicle method are the possibility of electrophysiological measurements and the exchange of chemical reagents without the need of tedious vesicle handling and manipulation.^15–17 Moreover, a major issue for using supported lipid bilayers (SLBs) for biomembrane modeling is decoupling of the membrane from the substrate. Therefore, in this work, we would like to emphasize on studying the properties and features of an unsupported lipid bilayer.

One of the recent approaches with this technique, the droplet interface bilayer (DIB), has been specifically developed to produce a solvent-free lipid bilayer having a rich lipid composition. This method also enables a rapid membrane characterization, drug screening, and ion channel recordings, whereas the possibility of having a continuous flow surrounding the bilayer in the DIB technique is somehow limited.^18–22 Thus, many miniaturized apparatus have been developed, such as microfluidic devices, to overcome the drawbacks of all the previous techniques.^19,23–25 Moreover, the formation of lipid bilayers in microfluidic devices presents the advantage of changing the buffer around the bilayer^26,27 while enabling good optical and electrophysiological access without using an undesired solvent (typically oil), which is essential for various biotechnological purposes.²⁸ However, it is well-understood that in microfluidic devices made of PDMS (polydimethylsiloxane), the oil is absorbed by the PDMS with time, due to the drainage of the oil. This supports the formation of the bilayer and also affects its lifetime, which is essentially destroyed when too much of the oil is drained.^26,27 Nevertheless, despite the large body of research in the literature on the freestanding bilayer in microfluidics, the stability and lifetime of the freestanding bilayers are, in general, barely discussed.^29,30

In this article, it is shown how the oil that is draining into the PDMS can be restored and subsequently how the lifetime of the bilayer can be improved substantially, which enables new classes of experiments to explore bilayer properties. Taking advantage of the improved lifetime, we presented a new approach to measuring the bilayer tension of symmetric and asymmetric lipid bilayers in a microfluidic device.

II. EXPERIMENTAL SECTION

A. Lipid preparation

DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine), DPhPC (1,2-diphytanoyl-sn-glycero-3-phosphocholine), and Monoolein (1-Oleoyl-rac-glycerol) were used as test lipids. DOPC is one of the most common lipids in the human cell membrane. DPhPC is a less biological relevant lipid, but known to produce a very stable bilayer. DOPC and DPhPC lipids were purchased from Avanti Polar Lipids, and Monoolein was purchased from Sigma Aldrich. The surface tensions of lipid decorated interfaces between aqueous buffer solution and squalene (Table I) were determined using the standard pendant drop technique using a commercial device (OCA20, Data Physics). To prepare the oil lipid solution, 5 mg/ml of the lipids were dissolved in 1 ml of pure squalene oil at $45^{°} C$ during continuous stirring for 3 h.

TABLE I.

Surface tension of the lipid monolayer σ obtained from (a) the radius of the curvature of the free interfaces with respect to pressure difference using the Young–Laplace equation (1) and (b) from the pendant droplet measurement. The bilayer tension Γ obtained from (c) the radius of the curvature of the bilayer using Eq. (2) and (d) obtained using Eq. (3).

	Lipid monolayer	DOPC (mN/m)	DPhPC (mN/m)	Monoolein (mN/m)
(a)	σ using Eq. (1)	8.2 ± 0.2	5.8 ± 0.2	2.5 ± 0.1
(b)	σ using pendant drop	7.3 ± 1.7	6.1 ± 1.6	1.9 ± 0.3
(c)	Γ using Eq. (2)	12.6 ± 0.7	10.3 ± 0.6	4.8 ± 0.4
(d)	Γ using Eq. (3)	12.4 ± 3	9.8 ± 2.6	4.2 ± 1.8

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B. Device fabrication and setup operation

The microfluidic geometry consisted of two channels side by side forming an $X$ geometry, as can be seen in Fig. 1. The channels have a rectangular cross section of $300 μ m$ width and $100 μ m$ height. The two microchannels meet at an intersection with an extension of $150 μ m$ . Microfluidic devices with this geometry were fabricated using standard soft lithography protocols.³¹ The device was molded into Sylgard 184 (Dow Corning, USA) from a SU-8 photoresist structure on a silicon wafer. After removing the mold, the surface of the Sylgard 184 devices was exposed to nitrogen plasma (Diener electronic GmbH, Germany) and the device was sealed with a plasma-treated glass cover slide. The glass cover slide was also coated with a very thin layer of PDMS (approximately $100 μ m$ ). The sealed device was rendered hydrophobic again by heating it to $135^{°} C$ overnight.

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FIG. 1.

Schematic of the microfluidic setup including the hydrostatic pressure control and the microfluidic mold structure. The inlets of the microfluidic device are connected to two syringes that are fixed on a motorized stage, and the outlets are connected to two reservoirs at a fixed height position.

The microfluidic device was connected to a hydrostatic pressure system that is presented in Fig. 1. The two inlets were connected to two 50 ml syringes via 50-cm-long Teflon tubes. The two outlets were connected to other reservoir vials with a fixed position. To guarantee a constant pressure at the outlets, the vials are open to the ambient air and are sufficiently large so that the liquid level does not rise remarkably during an experiment. The flows in the channels were controlled by adjusting the height of the inlet reservoirs, which were fixed on a motorized positioning stage with a resolution of $10 μ m$ giving a pressure resolution of approximately $0.1 Pa$ . Depending on height of the inlet reservoirs, positive or negative pressures could be applied to the channels causing the liquid finger to move forward or backward (Fig. 1). The approximate pressure to induce $0.001 μ l / s$ flow is about 0.5 Pa.

To produce a symmetric bilayer, the microfluidic chip is initially filled with squalene containing dissolved lipids. To form a bilayer, two buffer fingers containing 100 mM NaCl are injected into the channels applying the same pressure difference between inlets and outlets. Upon injection of the buffer solutions, their water–oil interfaces get decorated with lipids, until they gently meet at the intersection [cf. Fig. 2(a) (left) (Multimedia view)]. When the two lipid decorated water–oil interfaces come sufficiently close to each other, the lipids start to rearrange at their interface and form a bilayer, which can be observed by optical microscopy as seen in Fig. 2(a) (right) (Multimedia view).

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FIG. 2.

(a) Top view of the intersection in the microfluidic device, where two phospholipid monolayers are gently brought into contact with each other (left) and form a lipid bilayer by zipping after a few seconds (right). (b) Electrophysiological measurements during the formation of the lipid bilayer. To record the red data, a constant pressure difference $Δ P = P_{o u t l e t s} - P_{i n l e t s} \approx 25 mPa$ was applied to both aqueous fingers, resulting in a slow continuous forward movement of the aqueous finger and a continuously increasing bilayer length. To record the black data, the same initial pressure was applied, but reduced to zero within about 10 min after bilayer formation, resulting in a constant bilayer length, i.e., a constant capacitance signal. In order to increase the lifetime of the bilayer up to approximately $6 h$ , the drainage of the oil should be restored in the oil reservoir by applying slightly negative pressure difference. Multimedia view: https://doi.org/10.1063/1.5137810.1; https://doi.org/10.1063/1.5137810.2 Download video file.^{(578K, mp4)} Download video file.^{(5.3M, mp4)}

To produce an asymmetric bilayer, different lipids are sonicated in the buffer solution leading to vesicles with a diameter of approximately 40 nm. In this case, initially, pure oil is flushed into the microfluidic chip, and two buffer fingers containing different vesicles are injected into the channels and meet at the intersection to form an asymmetric bilayer.²⁸

The electrical properties of a bilayer can be analyzed by electrophysical measurements using a patch-clamp amplifier, EPC 10 USB (Heka Electronics). For that purpose Ag/AgCl electrodes were prepared by inserting a 5-cm-long silver wire in a borosilicate glass pipet containing a 100 mM NaCl electrolyte solution and applying 5 V for 30 min. The prepared electrodes were inserted into the circular inlet areas of the microfluidic device. The capacitance of the bilayer is measured using the lock-in function provided by the patch-clamp amplifier, while applying an 10 mV sinusoidal wave with a frequency of 10 kHz as an excitation signal.

III. RESULTS AND DISCUSSION

Figure 2(b) shows two capacitance measurements, which were recorded during the formation of the bilayer. At the beginning of the experiments, a pressure difference $Δ P$ was applied to both liquid fingers in order to bring them into contact at the intersection and to form a bilayer. This pressure difference $Δ P$ is defined as the difference of the applied pressure to the inlets and outlets $Δ P = P_{o u t l e t s} - P_{i n l e t s}$ . In order to keep the bilayer flat, an equal pressure difference is applied to the upper and bottom channels, $Δ P_{u p} = Δ P_{d o w n}$ . From an electrical point of view, a lipid bilayer can be considered as a capacitor and the formation of a lipid bilayer leads to a jump in the capacitance signal, which confirms that the two involved lipid monolayers become closer during the so-called zipping step. In Fig. 2(b), the first jump in both capacitance signals is related to the zipping of the bilayer, i.e., the bilayer formation. As for the red signal, the applied pressure remained constant $(Δ P > 0)$ , and, therefore, both aqueous fingers continue to move forward at slow speed. During the shown time period, slightly more than 1 h the bilayer extended to the edge of the structure and finally ruptured, which can be seen by the increasing and then suddenly ending capacitance signal [cf. red curve in Fig. 2(b)]. For the black capacitance signal, the pressure applied to both aqueous fingers ( $Δ P_{u p} = Δ P_{D o w n}$ ) was slowly reduced to zero $(Δ P = 0)$ , within about 10 min after the zipping. This eventually stopped the forward movement of the aqueous fingers and resulted in a steady value for the capacitance measurement and a superior bilayer stability of typically 6 h.

To understand the improved stability of the bilayer when reducing the applied pressure, we first have to understand what typically leads to the bilayer rupture. Initially, when two aqueous fingers are injected into the channels, they displace the oil in such a way that some of the oil wets the walls of the channels. It is well-known that liquids can penetrate through PDMS even if not noticeably swelling it,²⁸ and certainly our used oil (squalene) is drained into the PDMS chip. When the remaining oil on the wall of the channels is drained into the PDMS chip and not replenished, the bilayer ruptures after a long time. In general, the drainage time is a function of the oil viscosity. The more viscous the oil is, the longer the oil drainage takes. The oil drainage is visible by a reduced extension of the “oil reservoirs” to the left and right of the bilayer and a parallel extension of the bilayer [cf. Fig. 2(a) (right) (Multimedia view)]. However, to replenish the drained oil on the wall of the channels’ oil reservoir [see Fig. 2(a) (right) (Multimedia view)], we need a source of oil enabling a flow through the wall of the channels. This source is the remaining oil surrounding the lipid bilayer. By applying a slightly negative pressure to the liquid finger, the remaining oil in the microfluidic channel can even restore the oil in the oil reservoir [see Fig. 2(a) (right) (Multimedia view)]. This effect would also allow us to change the bilayer area by applying positive and negative pressure difference [see Fig. 2(a) (right) (Multimedia view)]. Properly adjusting the applied pressure $(Δ P)$ between inlet and outlet thus facilitates maintaining a bilayer with a superior lifetime of approximately $6 h$ (Multimedia view). The images collected for recording the bilayer lifetime of 6 h were 969 images with 22 Hz to frame per second (FPS). However, the lifetime is also limited in this case due to the mechanical fluctuation or flow fluctuation.

Taking advantage of the optimized control of the bilayer formation and increased lifetime, a new class of experiments is feasible. In the following, we will show how surface and bilayer tensions of symmetric and asymmetric bilayers can be simultaneously obtained, from a single experiment using this type of pressure control.

A. Simultaneous surface tension and bilayer tension measurements

When the pressure difference $Δ P^{'}$ between the upper channel and the lower channel is zero $Δ P^{'} = Δ P_{U p} - Δ P_{D o w n} = 0$ , a bilayer remains flat, provided that the bilayer is symmetric, i.e., both leaflets consist of the same type of lipids. In case $Δ P^{'} \neq 0$ , the pressure difference between the two fingers leads to a curvature of a symmetric bilayer. In other words, a bilayer bends away from the side where the pressure is larger. Of course, such a bent bilayer can be brought back to its flat shape, once the pressure difference between both sides become equal again.

Figure 3(a) shows image series of a bilayer at different pressure differences $| Δ P^{'} | = | Δ P_{U p} - Δ P_{D o w n} |$ that was applied between the upper and the lower aqueous finger for about 40 s each and given about 10 s time in between to relax [see Fig. 3 (Multimedia view)]. The corresponding capacitance measurements are shown in Fig. 3(b) and confirm that by bending the bilayer, the length of the bilayer (respectively, the bilayer area) increases, resulting in the increase of capacitance. It must be mentioned that the overall increase of the capacitance (respectively, the bilayer area) from $t \approx 100 s$ to $t \approx 600$ s is due to the drainage of the oil into the PDMS as not enough relaxation time was given in between the various applied pressure steps.

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FIG. 3.

(a) Optical micrographs of the symmetric bilayer with various pressure differences $Δ P^{'} = Δ P_{U p} - Δ P_{D o w n}$ applied to the aqueous fingers in the up and down channels. (b) Corresponding capacitance measurements of the bend bilayer; the bilayer area and thus the capacitance increase as the bilayer bends. Multimedia view: https://doi.org/10.1063/1.5137810.3 Download video file.^{(1.1M, mov)}

The applied pressure differences $Δ P^{'}$ can be expressed also by the difference in Laplace pressures of the free interfaces of the upper monolayer $Δ P_{U p} \approx \frac{σ_{U p}}{R_{U p}}$ and the lower monolayer $Δ P_{D o w n} \approx \frac{σ_{D o w n}}{R_{D o w n}}$ ,

Δ P^{'} = Δ P_{U p} - Δ P_{D o w n} \approx \frac{σ_{U p}}{R_{U p}} - \frac{σ_{D o w n}}{R_{D o w n}} .

(1)

In Eq. (1), $σ_{U p}$ and $σ_{D o w n}$ are the surface tensions of the respective oil–water interfaces decorated with a lipid monolayer. In this case, only the principal curvatures in horizontal direction $R_{U p}$ and $R_{D o w n}$ are considered, whereas the principal curvatures in vertical direction (perpendicular to the image plane) are very small and can be safely neglected.

The externally applied pressure difference $Δ P^{'}$ between both liquid fingers is known and the radii of the curvature of the monolayer $R_{U p}$ and $R_{D o w n}$ can be obtained from the microscopic images by fitting circular arcs to the free lipid decorated oil–water interfaces, as indicated in Fig. 4. So, in the symmetric case where the surface tensions of the upper and lower water finger against oil are equal, it is straightforward to obtain $σ = σ_{U p} = σ_{D o w n}$ using the Young–Laplace equation (1).

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FIG. 4.

Micrograph of a symmetric bilayer formed at the intersection of the microfluidic device with a negative pressure difference applied ( $Δ P^{'} = Δ P_{U p} - Δ P_{D o w n} < 0$ ) bending the bilayer upward. The principal radii of the curvature of the free monolayer of the upper ( $R_{U p}$ ) and lower aqueous finger ( $R_{D o w n}$ ) at the “oil triangle” and the radius of the curvature of the bilayer ( $R_{b i l a y e r}$ ) are indicated.

In Fig. 5, those measurements are shown for six different applied pressure conditions, whereas the fitted slope provides the surface tension averaged over these six measurements for the oil–water interface decorated with a certain lipid. Using this protocol, the phospholipids DPhPC, DOPC, and Monoolein were tested separately to obtain their surface tensions and were compared to values obtained by standard surface tension measurements in Table I. The obtained values agree quite well within experimental error, while the experimental accuracy of our presented surface tension measurement is improved by a factor of 5–10 with respect to the standard pendant drop measurement. The errors in our case typically come from the precision of fitting the surface curvature via the software ImageJ and could be further decreased by increasing the image resolution. All the measurements for the surface tension and the bilayer tension have been done for the same badge of phospholipids. However, according to the literature, it could be possible that with different oil compositions, different results may be obtained.^26,27,32

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FIG. 5.

The fitted slope provides the averaged surface tension, which is the pressure difference as a function of the increased curvature of the lipid monolayer on the both sides. The shown data are present for a DPhPC lipid monolayer.

Besides the surface tension $σ$ of the monolayer decorated oil–water interfaces, the bilayer tension $Γ$ of both symmetric and asymmetric bilayers can also be obtained from the same optical images when additionally fitting the radius of the curvature of the bilayer $R_{b i l a y e r}$ (cf. Fig. 4) for a known applied pressure difference $Δ P^{'}$ ,

Δ P^{'} = \frac{Γ}{R_{b i l a y e r}} .

(2)

In Fig. 6(a), the applied pressure difference $Δ P^{'}$ is shown as a function of the corresponding bilayer curvature $R_{b i l a y e r}$ for an asymmetric DOPC/DPhPC bilayer. Fitting the slope provides an averaged value for the bilayer tension, leading to ( $12.4 \pm 0.5$ ) mN/m in this case. The values for the bilayer tension $Γ$ obtained for symmetric DOPC, DPhPC, and Monoolein bilayer using this approach [Eq. (2)] are also given in Table I. These values are in agreement with those calculated from the surface tensions of symmetric leaflets ( $σ_{U p} = σ_{D o w n} = σ$ ) and the corresponding contact angle $θ = θ_{U p} + θ_{D o w n}$ in between them [cf. Fig. 6(b)], using

Γ = 2 \cdot σ \cdot \cos (\frac{θ}{2}) .

(3)

However, even though the results from both approaches are identical with respect to their experimental uncertainty, we find that experimental uncertainty is reduced by a factor of about four when using the approach of a bent bilayer, i.e., Eq. (2).

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FIG. 6.

(a) Applied pressure difference $Δ P$ plotted against the corresponding bilayer curvature $1 / R_{b i l a y e r}$ for an asymmetric DOPC/DPhPC bilayer. The slope yields the bilayer tension $Γ$ . (b) Optical micrograph of an asymmetric DOPC/DPhPC bilayer with indicated bilayer and surface tensions and the corresponding contact angle $θ$ .

In the case of an asymmetric bilayer, we cannot use Eq. (3), and the bilayer tension is given by

Γ = σ_{U p} \cos θ_{U p} + σ_{D o w n} \cos θ_{D o w n},

(4)

whereas $θ_{U p}$ and $θ_{D o w n}$ have to be measured with respect to the tangent to the bilayer at the three-phase contact point [see Fig. 6(b)]. However, measuring the contact angles with respect to the tangent is very hard to do and provides a large error. But based on our experimental finding for the tested combinations of lipids, both angles are very similar, $θ_{U p} \approx θ_{D o w n}$ . Using this experimental finding in Eq. (4), the bilayer tension can be written as $Γ \approx (σ_{U p} + σ_{D o w n}) \cos (\frac{θ}{2})$ . So, knowing $Γ$ from Eq. (2), we can solve the equation for one of the surface tensions $σ_{U p}$ or $σ_{D o w n}$ and insert this in Eq. (1), respectively, to obtain both surface tensions and the bilayer tension from a single microscopy image. This has been done for the previous example of an asymmetric DOPC/DPhPC bilayer and the obtained surface tensions of $σ_{D O P C} = (8.0 \pm 0.8)$ mN/m and $σ_{D P h P C} = (6.3 \pm 0.2)$ mN/m agree within experimental uncertainty and those obtained for the symmetric bilayers, which are listed in Table I.

IV. CONCLUSION

It was demonstrated that the freestanding fluid bilayer could be produced at a desired location in a microfluidic device. This microfluidic approach allows for good optical and electrophysiological accessibility, as well as precise monitoring of ongoing processes; thus, it combines several desired features in order to explore model membranes. In particular, we demonstrated that, by using a pressure-controlled system, the lifetime of a bilayer could be increased massively (to approximately $6$ h) by balancing the oil drainage in a PDMS chip.

Applying controlled pressure differences across such a bilayer combined with the superior lifetime, we showed that this system can be used to measure simultaneously the surface tensions of lipid decorated oil–water interfaces, and the bilayer tension from a single experiment. The experimental error from this approach is clearly reduced with respect to known standard measurements as shown in Table I. Moreover, besides measuring the surface tension and membrane tensions for the symmetric bilayer, we extended this method to measure surface and bilayer tensions of the asymmetric lipid bilayer.

For the presented measurements, we restricted to the case of lipids in a fluid phase. However, we assume that the asymmetric lipid bilayer with a gel/fluid composition may also be formed and analyzed in the future with our method, provided they are sufficiently stable during bending. Additionally, the increased bilayer lifetime combined with the controlled bilayer curvature is opening new possibilities like the investigation of biological processes that require the extended experimental time scales or the protein–lipid interactions as functions of a well-defined bilayer curvature such as mechano-sensitive channels.

ACKNOWLEDGMENTS

All the authors acknowledge funding from the German Science Foundation within the SFB1027, “Physical modeling of non-equilibrium processes in biological systems” (Project B4).

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