Compressibility and porosity modulate the mechanical properties of giant gas vesicles
Edited by David Weitz, Harvard University, Cambridge, MA; received July 5, 2022; accepted December 18, 2022
Significance
Gas vesicles are produced in bacteria to achieve cellular buoyancy. These air-filled protein structures were the inspiration for developing a similar system to serve as contrast agents for ultrasound imaging. To characterize their mechanical properties, we study here the micropipette aspiration of giant gas vesicles formed by coating microbubbles with surface-active proteins adsorbed on their surface. We observe a variety of behaviors, such as large or remanent deformations. We extend current theoretical models of vesicle suction to compressible gas-filled systems and introduce the measurement of bubble permeability with this technique. We highlight the possibility of using engineered bubbles for echogenic applications and therapeutic techniques.
Abstract
Gas vesicles used as contrast agents for noninvasive ultrasound imaging must be formulated to be stable, and their mechanical properties must be assessed. We report here the formation of perfluoro-n-butane microbubbles coated with surface-active proteins that are produced by filamentous fungi (hydrophobin HFBI from Trichoderma reesei). Using pendant drop and pipette aspiration techniques, we show that these giant gas vesicles behave like glassy polymersomes, and we discover novel gas extraction regimes. We develop a model to analyze the micropipette aspiration of these compressible gas vesicles and compare them to incompressible liquid-filled vesicles. We introduce a sealing parameter to characterize the leakage of gas under aspiration through the pores of the protein coating. Utilizing this model, we can determine the elastic dilatation modulus, surface viscosity, and porosity of the membrane. These results demonstrate the engineering potential of protein-coated bubbles for echogenic and therapeutic applications and extend the use of the pipette aspiration technique to compressible and porous systems.
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Gas vesicles (GV) that are produced in bacteria to achieve cellular buoyancy have opened new avenues in medicine, both for medical imaging and tumor treatment. They are air-filled protein nanostructures, hundreds of nanometers in size, which have been genetically encoded in cells and bacteria to serve as contrast agents for ultrasound imaging and as cell-killing agents by inertia-induced cavitation (1). If small unilamellar vesicles are used for drug delivery, all experiments to investigate the physics of membranes have been performed using giant unilamellar vesicles. Similarly, we study here the mechanical properties of giant gas vesicles (GGV) of sizes ranging from 10 to about 100 microns, formed by coating microbubbles with surface-active proteins adsorbed on their surface.
Ultrasound imaging is a well-established diagnostic method, and its use has grown rapidly over the past few decades due to several advantages, such as its safety, portability, real-time imaging capability, and cost efficiency (2). It has become the second most commonly used method after X-ray imaging (3). Ultrasound imaging is based on the exposure of a body to high-frequency sound waves, which are reflected at different interfaces. By calculating the propagating time and amplitude of the reflected wave (echo), an image can be constructed (4). As a mechanical wave, the echo of the ultrasound wave mainly depends on the physical properties of the medium and interfaces. To create a clear image using ultrasound, there should be clear differences in the mechanical properties between the investigated body parts. This could be achieved by using ultrasound enhanced contrast agents (UECA), which are substances with predesigned mechanical properties, mainly micro and nano-GV (5, 6).
Currently, GV play a fundamental role in therapeutic techniques and diagnosis. They can be used as drug or oxygen cargo in therapy and as contrast agents in ultrasound reflection imaging (7, 8). The main challenge in the UECA development is finding the balance between the half-life of the GV and their echogenicity, which is the ability of a substance to reflect or transmit ultrasound waves to the surrounding medium (9). This balance depends on the nature of the gas core and interfacial properties of the shell. Due to their unique physical and chemical properties, perfluorocarbons (PFCs) are confidently used in medical applications for diagnostics as well as therapy. PFCs are among the most inert and stable chemicals. Therefore, perfluoro-n-butane gas (C4F10) is one of the most commonly used gases for injectable ultrasound contrast agents (10). Getting insight into the shell properties is of fundamental importance for developing new contrast-enhanced agents. As cargos in therapy or as contrast agents in diagnostic, GV need to be injected intravenously. In this case, they must be robust, as it leads to a significant increase in the pressure of the gas inside, the pressure being the sum of Laplace pressure and blood pressure. The stability of GV is related to the physical properties of their shell, the nature (e.g., molecular size and polarity) of the gas core, and the viscosity of the ambient liquid (11). On the other hand, the echogenicity of GV is highly related to the mechanical properties of the shell. For instance, bubbles stabilized with phospholipids reflect ultrasound waves better than bubbles stabilized with polymers (5, 12), yet are more fragile than protein-coated bubbles. The lysis tension ranges between 2 and 15 mN m−1 for liposomes (13), whereas in our case GV are subjected to tensions up to 55 mN m−1 without rupture.
Hydrophobins are a group of highly surface-active proteins produced by filamentous fungi. They have a common structural feature, which is a characteristic sequence of eight cysteine residues in conserved order in their primary structure (14). These cysteine residues create four disulfide bridges (S-S bond) that bind hydrophobin protein leading to a globular shape. In addition, a hydrophobin molecule can be pictured as a natural Janus nanoparticle due to its non-centrosymmetric amphiphilic structure (15). Hydrophobins are grouped into two classes: Class I and II (16). Even though both classes share the main features such as surface activity and surface adhesion, the main functional difference between them is their solubility. The aggregates of class I hydrophobins are highly insoluble in buffer solution, while class II hydrophobins aggregates dissolve more easily (17). In addition, Linder et al. have reported that there are also differences related to the interfacial structures of class II hydrophobins (18, 19) HFBI and HFBII, which are small-sized proteins (7.5 and 7.2 kDa, respectively), produced by Trichoderma reesei fungi (20). Even though they are produced by the same fungi and share almost the same amphiphilic structure, HFBI and HFBII have different interfacial properties. The clearest difference between these two hydrophobins is that even if both create a viscoelastic layer at gas–liquid interfaces, HFBI layers are more glassy (21). This difference in interfacial behavior is supposed to be related to the hierarchical structure of the hydrophobin film (22). Then, coating microbubbles with HFBI could lead to GV with high stability and mechanical properties.
During the last few decades, one of the most utilized methods for measuring interfacial mechanics is surface dilatational rheology based on axisymmetric drop shape analysis (ADSA) (23–25). There are various advantages that make ADSA a cornerstone technique in many laboratories doing interfacial research. In comparison with other methods, such as Langmuir trough and Wilhelmy plate, ADSA is easy to handle, needs a relatively small sample (that makes it very popular especially if the sample is expensive), and can be done in challenging experimental conditions such as high pressure and temperature. The theory and the applications of the ADSA method are explained in a number of review articles (26–28). This technique has been used previously to approximate the surface tension of HFBI films at the air/water interface. Also, the viscoelastic properties of HFBI and HFBII films and HFBII macroscopic liquid droplets have been reported using surface shear rheology (17) and ADSA (29), respectively. Still, a challenge is to find a way to measure the properties of glassy membrane-like HFBI layer stabilizing microbubble. In this study, the mechanical properties of HFBI hydrophobin layer assembled at the gas–liquid (C4F10-water) bubble interface are measured using micropipette technique as an alternative to the traditional surface dilatational rheology technique, which failed to measure the storage and loss modulus due to the glassy nature of the layer.
The pipette aspiration technique has been developed to characterize mechanical properties of GUV (13), in particular the membrane tension, the dilatation elastic modulus, and the membrane viscosity. Its use has been extended to a wide variety of soft matter objects from living systems such as single cells (30–32) or cellular aggregates (33), to artificial systems such as liposomes (13, 34–36), emulsions (37–41), or polymersomes (42, 43). The new features of the GGV studied here include that their interior is compressible and that their membrane is slightly permeable to gas, which requires the development of a new model. We started from a preexisting model used for the analysis of incompressible capsules, which is then expanded to the case of compressible porous capsules. As a result, the aspiration of GGV with a micropipette allowed us to determine not only their elastic modulus and their surface viscosity, but also their porosity. Micropipette aspiration has previously been used to measure the water porosity of liposomes (44, 45). A liposome initially in an observation chamber at low osmolarity is aspirated in a micropipette and then transferred in another one with a higher osmolarity. The tongue length of the liposome in the micropipette is monitored. Because of the osmolarity change, the reduction of the volume of the vesicle gives rise to an excess area, which is incorporated in the tube, and the length of the aspirated tongue increases. For GV, the leaking out is induced by the Laplace pressure acting on the sucked bubble.
Model of Aspiration of GGV: Role of Compressibility and Porosity
The mechanical parameters of the bubbles can be deduced from the micropipette aspiration method developed by Evans (35). A pressure difference ΔP is imposed between a liquid medium and a pipette, and the capsule penetrates the pipette forming a tongue of length L. We describe the statics and the dynamics of suction for four cases: 1) incompressible, 2) compressible, 3) porous GV (Fig. 1 A–C), and 4) ultra-rigid GV (Fig. 1 D–F).
Fig. 1.
Incompressible Vesicles
Let us first describe the classical case of an incompressible vesicle. When a suction pressure is applied, the very narrow micropipette allows us to amplify the variation of the surface, while the vesicle size is almost constant. As the penetration length L increases, the surface area A of the vesicle increases, as well as its membrane tension σ from the initial tension at rest to a plateau value .
The increase in tension is related to the increase in capsule area .
[1]
where is the dilatation modulus.
The surface of the tongue leads to
[2]
The driving force on the hatched region (Fig. 1A) is the sum of capillary and pressure forces
[3]
where is the pipette radius, is the pressure inside the capsule, and is the external pressure. can be written as
[4]
where is the threshold aspiration pressure before the deformation of the protein network. Notice that this expression is valid only if L is larger than the pipette radius because the curvature radius of the liquid/GV meniscus involved in the Laplace law used to derive Eq. 4 is Rp.
At equilibrium, = 0 leads to the Laplace relationship relating to , which can be written as
[5]
Equilibrium state of the tongue L = Le
Leading to
[6]
Dynamics of Penetration
When L < Le, the driving force is positive and is balanced by the friction force (46)
[7]
where is the surface viscosity of the membrane of thickness e.
leads to the dynamical equation for L(t)
[8]
This equation involves a characteristic time τM
[9]
if ≪ R and the solution L(t) is given by
[10]
where is the initial deformation at time t0.
Compressible GV
For a liquid droplet, the volume is conserved. For a gas bubble, the internal pressure of the gas increases as σ increases and the volume of the compressed gas decreases. For the internal gas, is constant, with N the number of gas molecules and k the Boltzmann constant.
Before the GV’s suction, and . As the GV is sucked, , the membrane tension σ increases, and . This ideal gas law leads to . Assuming , we get
[11]
The compression of the gas leads to a decrease of the capsule area A, which is now given by
Since Eq. 1 now leads to
[12]
At equilibrium, is given by the Laplace law and . Inserting in Eq. 13 leads to
[14]
with .
The compression of the bubble reduces its area, leading to a more elongated tongue. The increase of Le due to the gas compression is . This will be an important correction if is large, which is the case of HFBI coating layers where the Laplace pressure of the bubble is comparable to the atmospheric pressure Pe. The dynamics of penetration of the compressible GV L(t) is still given by Eq. 10, with
[15]
Aspiration of a Porous Vesicle
As shown in Fig. 1B, the length of the tongue does not reach a plateau value but instead increases with time. It shows that the vesicle is permeable. In the case of a porous vesicle, the increase of the Laplace pressure leads to a leak-out of the internal gas. The flux J through the n pores (47) is
[16]
where ηL is the viscosity of the ambient medium and is the radius of the pores.
If we want to determine the porosity PM of the GV, we can write the flow J in terms of the porosity as follows
where , with v0 the volume of a gas molecule.
This leak-out leads to a decrease of the internal volume
[17]
While the leak-out leads to a decrease of the vesicle area , the suction of the tongue leads to an increase . The total change of the area of the vesicle per unit time is thus given by
[18]
When the stationary regime is reached , σ tends to and tends to a constant . The length L(t) of the tongue increases at constant velocity. and are related by
[19]
given by Eq. 18 for .
We now calculate the dynamics of suction. The insertion of in the derivation of Δσ given by Eq. 12 leads to
[20]
with derived from the force balance . That leads to
[21]
Considering , Eq. 21 becomes
which can be written as
[22]
where , by setting , where is the viscous membrane flow relaxation time, and , where is the leak-out flow relaxation time.
At short time, and Eq. 22 leads to
with and
[23]
where , the sealing parameter, is defined by the ratio
[24]
by setting . We can also express Q in terms of the porosity PM using
[25]
The sealing parameter Q controls two regimes:
A) In the limit of a low porosity membrane Q ≫ 1 () and the relaxation time , we have a weak leak-out and . The velocity of extrusion given by Eq. 19 is
[26]
B) In the limit of a highly porous membrane, (), we have a strong leak-out and This is a new regime, which could be obtained if the mesh size of the coating network is loose or for Pickering bubbles, when microparticles coat the interface.
In that case, , and
[27]
which can be written in term of porosity as
[29]
Aspiration of Liquid Porous Compressible GV
We summarize here the results of the previous parts of the model to describe the aspiration length L(t) assuming that the vesicles are in a liquid state, i.e. for glassy vesicles.
A) The aspiration length tends to a plateau value if the porosity of the polymer coating is extremely low, corresponding to Q → ∞
This length L(t) tends to Le exponentially (Eq. 10).
B) For intermediate values of Q, , the dynamics L(t) can be written as
[30]
where is given by Eq. 26.
Aspiration of Ultra-Rigid GV: Gas Extraction Regime
Glassy regimes are observed for bubbles below a radius . Both and the rigidity of the coating depend on the incubation time. These GV are characterized by a yield stress σy. If , the coating cannot expand and σ remains equal to the initial tension σ0. We show here that a tongue of gas can form if , where is the surface tension of the medium equal to 64.5 mN m−1 for a glycerol solution (50% w/w in distilled water) and 72 mN m−1 for pure water. We study the regime illustrated in Fig. 1 D–F.
In this case, σ is constant (σ = σ0) and the driving force on the tongue is given by
As soon as , a tongue of gas is formed and expands. The gas pressure decreases and may lead to a deflation of the capsule. The tongue ultimately stops when all the gas is sucked in the pipette. We have 18 kPa for Rp = 7 μm and γ = 64.5 mN m−1.
The dynamics of the tongue is extremely fast. fM is balanced by the friction force , due to the viscous flow inside the pipette induced by the expansion of the tongue of gas, where Lt is the length of the micropipette and the medium viscosity. It leads to
[31]
Considering Rp = 7 μm, ηL = 6.5 10−3 Pa s, Lt = 1 cm, and 2 kPa, it leads to an aspiration velocity = 200 μm s−1. This value is in agreement with the experimental data, where the very fast aspiration of the tongue can be seen in the plot in Fig. 1F.
Results and Discussion
Formation of GV.
The GV are produced by mechanical agitation. 15 min after their formation, a single white phase is observed. Afterward, they migrate according to their size and we observe the formation of a very diffuse layer on the top containing the larger GV, while the rest of the sample, less diffusive and opaque, contains the smaller ones (SI Appendix, Fig. S1).
Structure of GV.
Due to its amphiphilic nature (Fig. 2A) and its high affinity to self-assemble at hydrophobic–hydrophilic interfaces, HFBI creates an amphiphilic shell around C4F10 bubbles, resulting in spherical GV of nanometer to micrometer size (SI Appendix, Fig. S1). The structure of these GV studied by Cryotransmission Electron Microscopy (cryo-TEM) (Fig. 2B) shows that for all sizes encountered (up to 1 µm), the membrane thickness is 2.7 ± 0.4 nm (n = 8, Fig. 2C). As this value is comparable to the size of an HFBI protein (21), we can deduce that the bubbles are covered by a protein monolayer. We are not able to measure larger GV by cryo-TEM, but we assume that their membrane thickness also corresponds to a protein monolayer.
Fig. 2.
The Atomic Force Microscopy (AFM) image of the HFBI layer at the air/water interface (Fig. 2D) shows a crystalline arrangement of HFBI molecules with a regular roughly hexagonal pattern of holes. These nanosized holes represent the structural porosity of the shell. The large dark areas in the image are empty and most probably are sample preparation defects. The layer structure in this image matches the structure reported in the literature (21, 22). Even though the molecular size and polarity of C4F10 and air differ, we assume that the HFBI layer structure could be the same because both gases are hydrophobic.
Surface Tension of GV.
A non-polar gas bubble (C4F10) is initiated on the tip of a hooked needle inside a solution consisting of 0.01 mg mL−1 of HFBI (Fig. 3). The surface tension versus time plot shows the three phases of the self-assembly process. First, the HFBI molecules diffuse to the bubble surface. Second, the molecules adsorb at the interface, and lastly, the surface reaches the saturation state, whose surface tension value represents the static surface tension of the HFBI solution at the gas surface. The value is about = 55 mN m−1, which is significantly lower than the surface tension of pure water (72 mN m−1). It means that we have a layer of HFBI adsorbed at the interface. Also, the figure shows that at the end of the surface tension curve, there is some increase in the surface tension value. This phenomenon does not indicate a true increase but is rather due to a misfitting of the Laplace equation, as the software was not able to calculate the correct value of the surface tension. The best interpretation of this case is that a quite rigid HFBI layer is formed, which does not obey the liquid properties required by the Laplace equation. Furthermore, when sinusoidal volume changes were applied on the same GV, the software failed to measure the mechanical properties of the layer. As shown in SI Appendix, Fig. S3, the volume curve does not fit the surface tension curve and has some values that are not correct. Therefore, finding an alternative method to measure the mechanical properties of the protein layer represents a fundamental priority to complete this study and any similar future works related to self-assembled rigid layers.
Fig. 3.
For comparison, surface tensions ranging from 30 mN m−1 to 50 mN m−1 were found performing equilibrium surface tensiometry experiments for similar HFBI concentrations (17) and shape analysis of deflated capsules (29). Also, the determination of the surface tension for high concentrations has to be taken with caution due to the formation of the glassy film of HFBI (17). The difficulty in determining the surface tension of HFBI layers is confirmed by Szilvay et al. (21) who failed to determine it using the ADSA method due to the unexpected deformation of the drops. Details about the ADSA method can be found in SI Appendix, Fig. S4.
Micropipette Aspiration of GV.
To study the elastic and viscous properties of the GV, we use the micropipette aspiration technique. The details of all the main parameters determined and calculated for the experiments performed in distilled water are given in SI Appendix, Table S1.
As we will see, it is necessary to apply high pressures to aspirate these GV. It is then cumbersome to use a classical pipette setup in which the pressure is controlled by modifying the height between the observation chamber and the water reservoir. Instead, we use here a piezoelectric pressure controller allowing to easily exceed 10 kPa, otherwise requiring classically a displacement of the water tank higher than 1 m.
GV range in size from the nanoscale to the micrometer scale. Since we are limited by the minimum radius of the micropipettes that can be prepared, we consider GV with R ≥ 15 μm when their dynamics of aspiration is studied, and R ≥ 10 μm when only the observation of their behavior is needed (i.e., without parameter determination). We apply a pressure ΔP between 12 and 20 kPa, which is extremely large , meaning that the gas compression will be an important factor.
We aspirate a GV for about 10 to 60 s so that the length of the tongue in the pipette is at least 3 times the pipette radius (Fig. 4 A–D). The parameters are chosen individually for each GV to apply sufficient pressure to aspirate the vesicles and sufficient time so that we observe both the initial elastic deformation followed by a steady flow in the pipette. As the GV is aspirated, its shape becomes less and less spherical. At that point, we stop the applied pressure and observe two types of behavior: either a liquid-like behavior where the tongue retracts completely, and the bubble recovers completely with spherical shape as before the aspiration (Movie S1) or a glassy behavior (Movie S2) where the tongue does not relax and retains the sleeve shape, while the vesicle keeps a pear-like shape (Fig. 4E and Movie S3). The tongue remains permanent after expulsion from the pipette (Movie S4). The phase diagram liquid versus glassy as a function of the size and aging times of GV is shown in SI Appendix, Fig. S6. The liquid-like behavior is observed for “young” and large GV, whereas the solid-like behavior for small and mature GV.
Fig. 4.
Movie S1.
Bright-field observation of a gas vesicle in a liquid regime aspirated in a micropipette (ΔP = 13 kPa).
Movie S2.
Bright-field observation of a gas vesicle in a glassy regime aspirated in a micropipette (ΔP = 18 kPa).
Movie S3.
Bright-field observation of a solid-like gas vesicle aspirated in a micropipette (ΔP = 13 kPa).
Movie S4.
Observation of a gas vesicle during the first 10 min following its deformation by a micropipette, highlighting a solid-like behavior.
We also successively aspirated the GV, changing the position of the micropipette on the surface of the same vesicles between several consecutive aspirations. For liquid-like GV that showed no deformation during the first aspiration (Movie S1), there was still no change after several successive aspirations. On the other hand, for the more rigid GV that were moderately deformed after the first aspiration, the deformation is increasingly pronounced. Finally, for glassy GV with a strong remanent deformation after the first aspiration, we observe the aspiration of a new tongue accompanied simultaneously by the retraction of the first one (Fig. 4 E–H and Movie S5). This feature has also been observed for glassy lipid vesicles and glassy polymersomes, which flow above a threshold pressure named the yield stress (42). The remanent deformation disappears when we apply a pressure higher than the yield stress, which ranges from 8.1 to 13.1 kPa, n = 8, with a mean value 10.5 kPa.
Movie S5.
Aspiration of an already deformed gas vesicle on the other side, leading to the decrease of the length of the free tongue and revealing a gel-like behavior.
These behaviors differ greatly from what we would have obtained with uncoated bubbles. They would have been completely aspirated as soon as ΔP is larger than a critical pressure (Movie S6), related to the surface tension γ of the liquid, which is constant. In the presence of the hydrophobin coating of the bubbles, γ is replaced by the membrane tension σ, which increases when the vesicle is sucked into the pipette.
Movie S6.
Bright-field observation of a non-coated air microbubble aspirated in a micropipette (ΔP = 18 kPa).
To interpret the role of bubble size in the liquid-like or glassy behavior of GV, we postulate that this transition is a result of the larger vesicles needing more time to reach the saturated state of the adsorbed layer. If we assume that the proteins are deposited by diffusion, at a time t the proteins in a volume will cover the surface area of the bubble, where D is the diffusion coefficient of the proteins. This simple argument shows that the equilibrium coating time te, given by is proportional to and is shorter for smaller vesicles. In the phase diagram representing liquid versus glassy behavior for GV of different radii versus time, we should be able to fit the coexistence curve using the following equation
[32]
where c is the initial protein concentration and cS is the protein density of the shell at saturation.
To test this model, we study versus c for different initial protein concentrations (0.2, 0.067, and 0.02 mg mL−1). We set t = 0 the time when the bubbles are prepared, and we first consider c = 0.2 mg mL−1 (Fig. 5). During the first 3 h after their formation, all GV, regardless of their size (within the low size limit that can be aspirated with the micropipettes), show no deformation after aspiration. Between 3 and 7 h, the smallest aspirated vesicles show persistent deformation, and then the GV that remain deformed are increasingly larger, with a radius of up to 20 μm. At longer times, persistent deformation of much larger GV is observed, for example with radii up to 100 μm after 3 d (SI Appendix, Fig. S5). Approximating a value of cS = , where a0 is the surface area per protein of order 9 nm2, cS = 1017 molecules per m2, the fit of Eq. 30 leads to ms−¾. We can deduce a diffusion coefficient D ~ 10−14 m2 s−1. By performing similar experiments with lower initial protein concentrations, the transition is still observed but is shifted toward long times and for smaller GV as c decreases (SI Appendix, Fig. S6). For c = 0.067 and 0.02 mg mL−1, we find, respectively, = 1.1 10−8 and 9.5 10−9, which is in agreement with the scaling relationship for versus c.
Fig. 5.
Using the model developed in the theoretical part, we can analyze the data to determine the mechanical properties of the GV. We plot the aspiration length of the tongue inside the pipette over time. Upon application of suction pressure ΔP, we observe a rapid increase in length during the first few seconds corresponding to the regime described by Eq. 10 that is followed by a penetration at constant velocity due to the permeability of the porous membrane, leading to the leakage of gas molecules. The data can be fitted with Eq. 30 , with Li the initial tongue length, Le the final tongue length expected in the absence of gas leakage, t0 the time at which the pressure was applied, the characteristic relaxation time of the compressible GV (Eq. 15), and the aspiration velocity in the pipette.
We also observed on many occasions that GV prepared with an initial protein concentration of 0.067 mg mL−1 presented a fragmentation of their tongue in the pipette during their aspiration (SI Appendix, Fig. S7). That phenomenon is called budding. It has been mentioned for GUVs and polymer-coated bubbles and is known to be caused by the minimization of the bending energy (48, 49).
Role of Compressibility.
With the fit L(t), we can obtain the value of Le, which leads to a derivation of the dilatation modulus . According to Eq. 14, Le is given by the classical model for incompressible capsules with an effective dilatation modulus . We find average values of 0.18 N m−1 (from 0.01 to 0.91 N m−1, n = 22) and 0.32 N m−1 (from 0.14 to 1.38 N m−1, n = 18) for liquid-like and glassy bubbles, respectively.
From , according to Eq. 14, we can derive the elastic modulus , that is larger than , with average values of 0.24 N m−1 (from 0.01 to 1.87 N m−1, n = 22, Fig. 6A) and 0.40 N m−1 (from 0.16 to 1.92 N m−1, n = 18, Fig. 6A). With these values of , we can estimate the increase Δ of the tongue due to the compressibility from Eq. 14. for liquid GV and 0.16 for glassy GV, which shows that the compressibility should be considered. This is due to the high rigidity of the coating, giving rise to a large membrane tension compressing the bubble.
Fig. 6.
The values of are high, but it makes sense giving the high pressures of at least 12 kPa needed to aspirate the GV. We can notice that a few articles reporting elastic properties of similar systems are comparable to ours. First, millimetric bubbles coated with HFBII were found to have an area compression modulus evolving between 0.16 and 2 N m−1 using wrinkle analysis of a pendant capsule (analysis based on the formation of wrinkles on the surface of the protein membrane as the capsule is deflated) (29). Second, the surface expansion modulus of polymer-coated air bubbles has been reported using the classical model for incompressible systems (49). Depending on the polymer used, values from 0.075 to 0.65 N m−1 have been reported which are also quite similar to those presented in our work. Finally, HFBI monolayers at air/water interface have been studied using the surface shear rheology, and a surface shear elasticity G’ equal to 0.7 N m−1 has been determined (17).
With and the characteristic time τM found using the fit, we determine an average surface viscosity ηs of 3.2 mN s m−1 for liquid-like bubbles (from 0.06 to 8.7 mN s m−1, n = 22, Fig. 6B) and 8.9 mN s m−1 for glassy bubbles (from 0.4 to 24.9 mN s m−1, n = 18, Fig. 6B) using the equation . Since we determined the thickness of the hydrophobin membrane, we can approximate a bulk rigidity and a bulk viscosity. Considering the membrane thickness e = 2.7 ± 0.4 nm (n = 8) determined by cryo-TEM, we obtain rigidities E = /e ~ 8.9 107 Pa and 1.5 108 Pa, as well as bulk viscosities η = ηs / e ~ 1.2 106 Pa s and 3.3 106 Pa s for liquid-like and glassy GV, respectively. By comparison, we have (glassy) = 1.7 (liquid) and ηs (glassy) = 2.8 ηs (liquid). These results indicate significantly higher mechanical properties of glassy GV compared to the liquid-like one, which can be explained if we consider that glassy GV have a denser protein network than their liquid-like counterpart. This is in agreement with the higher coating density of glassy GV.
For comparison, our average values of ηs are similar to that of giant liquid crystal polymersomes using the micropipette aspiration technique where 4.0 and 7.9 mN s m−1 have been found (50). Also, Cox et al. reported surface shear viscosities G’’ = 0.2 N m−1 (for 7.5 10−2 mg mL−1 and ω = 1 Hz) and 0.04 N m−1 (for 0.75 mg mL−1 and ω = 1 Hz) that are 1 order higher than our values (17).
Permeation of GV.
Measuring the aspiration velocity , the micropipette aspiration technique allows us to determine the permeation of gas across hydrophobin membranes. This method is convenient because it can be determined along with and ηs and does not require additional experiments.
As demonstrated previously, the permeation parameter can be determined using Eq. 26 assuming Q >1, where is the volume of a gas molecule inside the bubble. If we approximate the C4F10 volume to 35 nm3 (ρ = 11.21 kg m−3 and Mw = 238.028 g mol−1), we obtain average permeabilities of 1.5 10−7 m s−1 for liquid-like GV (from 5.5 10−9 to 1.9 10−6 m s−1, n = 18, Fig. 6D) and 1.3 10−8 m s−1 for glassy GV (from 1.6 10−9 to 4.5 10−8 m s−1, n = 18, Fig. 6D). It shows that liquid GV are more permeable than glassy GV as expected by our model on the dynamics of protein adsorption. In comparison with the literature, our average values are three to four orders of magnitude lower to that obtained for vesicles with aquaporin pores (6.6 10−5 ± 1.5 10−5 m s−1) (51). It is also equivalent to the porosity of (liquid-filled) polymersomes where the porosity varies mainly between 10−9 and 10−6 m s−1 depending on the systems studied (50, 52, 53). Considering that polymersomes are usually made of several layers of charged polyelectrolyte while in our case the membrane is made of a single layer of protein, it means that our protein membrane has a pretty good impermeability, which is very interesting considering the echogenic applications we are aiming at. The sealing parameter can be determined using Eq. 13. We obtain average values of 23.1 for liquid-like GV (from 2.6 to 67.1, n = 18, Fig. 6C) and 58.7 for glassy GV (from 5.9 to 249, n = 18, Fig. 6C). These values, significantly higher than 1, confirm that we are working with a weakly permeable system and that we used the good formula to determine PM and then Q. By comparison, we find PM (glassy) = 0.09 PM (liquid) and Q (glassy) = 2.5 Q (liquid). It tends to indicate that glassy GV are less permeable than the liquid-like ones, which again makes sense if we consider that glassy GV have an increased density at the interface compared to the liquid-like ones.
To check the model of permeation, we vary the medium viscosity and aspirate GV either in distilled water or a glycerol solution (50% w/w in distilled water). We measure the viscosity of distilled water and the glycerol solution, and we obtain values of ηwater = 0.92 mPa s and ηglycerol = 6.5 mPa s (SI Appendix) leading to 7.1 ηwater= ηglycerol. We determine the permeability from the velocity of extrusion given by Eq. 26. The average value of PM is 2.9 10−9 m s−1 (from 1.6 10−9 to 5.2 10−9 m s−1, n = 9) and is significantly lower than the median value obtained in distilled water.
Since , we expect to obtain values of PM that about 7 times higher in water than in the glycerol solution. We found PM (water, liquid) = 52 PM (glycerol) and PM (water, glassy) = 5 PM (glycerol). This decrease of the permeability in glycerol confirms our model and is strongest than expected, which may be explained by a modification of the protein coating in glycerol.
Materials and Methods
Materials.
HFBI hydrophobin protein is produced and purified as described in Linder et al. (21) C4F10 98% (CAS 355-25-9) was purchased from ABCR (Karlsruhe, Germany). Water was purified using a Milli-Q system (Millipore) with resistivity around 18.2 MΩ cm.
Formation of Bubbles.
The bubbles used in this study were created by a mechanical agitation method. The desired amount of HFBI (0.02, 0.067, or 0.2 mg) was solubilized in 1 mL of phosphate buffer saline (1×) placed inside a 2.5 mL glass vial. The vial was sealed using an aluminum cap and a septum, and the air inside was replaced with C4F10 using a 50 mL Hamilton syringe. The vial was placed in a VialMix shaker (Lantheus) and agitated for 45 s, forming a white-colored suspension consisting of micro- and nanobubbles (SI Appendix, Fig. S1).
Cryo-TEM.
A 5 μL droplet of nanosized bubble dispersion was deposited onto a plasma-treated lacey carbon-coated copper grid (Electron Microscopy Sciences). The droplet was blotted with filter paper, plunged into liquid ethane (–170 °C) using an automatic plunge freezer (EM GP2, Leica), and stored in liquid nitrogen. The samples were inspected using a JEM-3200FSC (JEOL) microscope with an accelerating voltage of 300 kV, and images were acquired using Digital Micrograph software (Gatan, version 1.83.842).
AFM.
The AFM measurements were carried out using a Dimension Icon AFM (Bruker AXS, France; formerly Veeco) with ScanAsyst-air cantilevers (sharp silicon nitride tips with a nominal radius of 2 nm for PeakForce Tapping in air). The scan size was set to 100 nm × 100 nm with a resolution of 256 pix × 256 pix, and the scanning was performed with a scan rate of 1 kHz. ScanAsyst Auto control was set to “individual” for the sample with PeakForce Amplitude of 170 nm. The spring constant and peak force frequency were 0.4 N m−1 and 2 kHz for all samples. Individual scans for each sample were taken at multiple locations on the surface.
Sample Preparation for AFM.
A 100 mL droplet of HFBI solution (0.2 mg mL−1) was placed on a parafilm substrate for about 1 h to get a flattened area on the top of the droplet and confirm that we had a monolayer at the interface. After that, a highly ordered pyrolytic graphite substrate was brought into contact with the top of the droplet. The substrate with the hydrophobin monolayer was gently washed with 200 mL of Milli-Q water. The sample was placed on the AFM stage, and we waited for about 30 min to ensure that the sample was dry. Finally, the sample was imaged. SI Appendix, Fig. S2 shows the sample preparation procedure.
Surface Tension and Surface Dilatational Rheology.
Measurements of the surface tension and mechanical properties of the HFBI adsorbed layer were carried out using an optical tensiometer (Theta tensiometer, Biolin Scientific, Finland), and the obtained data were analyzed using the instrument software (OneAttension). A hooked needle filled with C4F10 using a Hamilton syringe was immersed in a solution of HFBI (0.01 mg mL−1). Then, a 10 μL gas bubble was created on the needle tip, and the bubble was monitored for about 3 h until the surface tension curvature reached a steady state. At that point, the static surface tension was measured by applying a sinusoidal volume disruption using an integrated pulsated droplet module (PD-200, Biolin Scientific, Finland). The change in bubble volume was monitored for 40 s (SI Appendix, Table S2).
Density and Viscosity Measurements.
Density measurements of distilled water (as a reference) and a glycerol solution (50% w/w in distilled water) were performed in triplicate using a handheld density meter (Mettler Toledo, DensitoPro model) (SI Appendix, Table S3).
The viscosity of these solutions was then measured using a homemade setup consisting of a piezoelectric pressure controller (OB1 Mk3, Elveflow) connected to a balance via a reservoir. The reservoir was filled with the solution to be characterized and connected to the balance via a tubing inside a glass vial placed on the balance. The flow rate Q of the liquid was deduced by observing the increase in mass of the vial after a 30 s increase in pressure in the reservoir and using the density of the solution. Pressures of 125 Pa were applied for distilled water and 500 Pa for the glycerol solution using Elveflow pressure controller (software ESI v3.06.05). Measurements were performed at room temperature (T = 23 ± 1 °C) and were repeated 15 times for each solution. The flow rate was then used to determine the viscosity of the solution using the Hagen–Poiseuille equation
where ΔP is the applied pressure, r is the radius of the tubing, and L is the length of the tubing (SI Appendix, Table S4).
Pipette Aspiration Setup and Microscopy.
Micropipettes were prepared by pulling borosilicate capillaries (WPI, 1 mm/0.5 mm outer/inner diameter) using a puller (PN-31, Narishige). Afterward, the micropipettes were sized to a few micrometers in diameter and bent using a microforge (MF-900, Narishige) to introduce the pipette horizontally in the observation chamber. The pipette was connected through tubing to a water tank attached to the piezoelectric pressure controller mentioned previously and then filled with water. The observation chamber was made of two glass coverslips separated with a few layers of parafilm and was filled with the solution containing the bubbles. The micropipette was brought into contact with a GGV (HFBI-coated microbubble) and a negative pressure was applied, resulting in the suction of the microbubble with the formation of a tongue of length L(t). The experiments were performed at room temperature (T = 23 ± 1 °C), and aspirated microbubbles were visualized with an inverted microscope (Nikon Eclipse Ti). Bright-field images were recorded with a sCMOS camera (Zyla-4.2-CL10, Andor) at a time interval between 0.2 and 1 s and operated using μManager (2.0 beta) open-source microscopy software (SI Appendix, Table S1 and S5).
Conclusion
The mechanical properties and stability of GV are crucial as they play a fundamental role in therapeutic and diagnostic techniques as contrast agents for ultrasound imaging. In addition, they can be used as a drug and oxygen cargo for therapy. It has also been shown that they can serve as agents for cell destruction and tissue disruption through ultrasound-induced inertial cavitation (54). This property is enabled by GV produced by bacteria, which are protein nanostructures filled with gas to achieve cellular buoyancy. They have given rise to bacterial therapies since the genes that encode GV can be expressed in mammalian cells. The GGV studied here are not protein nanostructures but microstructures, which allows to study their mechanical properties. It will also be interesting to form GV with proteins from bacteria.
We have demonstrated that the hydrophobin-coated bubbles formed here have improved mechanical properties, which will enable them to be used for echogenic applications. Their stability is ensured by the adsorption of proteins at the liquid–gas interface. This surface film can be in the liquid or solid state depending on the amount of hydrophobin adsorbed at the interface. In the first case, the surface tension can be measured by the hanging drop technique by analyzing its shape. Alternatively, the response of the surface tension σ (V, ω) to a periodic modulation of the volume of the bubble can be measured. This allows to highlight the viscoelastic properties of the surface film from the phase shift between the volume change and the response of the protein film tension.
We show here that the micropipette aspiration technique is the most efficient because it allows the study of GV in both liquid and glassy states. If the film is glassy, it presents a transition to a liquid state if a stress higher than a yield stress is applied to it. It corresponds to a threshold suction pressure above which the GV enters the pipette in a liquid state, forming a sleeve that adapts the shape of the pipette. In all cases, the vesicles penetrate only if is larger than the Laplace threshold . Contrary to the suction of simple bubbles or liquid drops, the GV penetrates only partially because the membrane tension increases with the size of the sleeve, and the penetration stops when . In the glassy case, the tongue penetration is achieved if both conditions (σ larger than the yield stress and the aspiration Laplace pressure threshold) are met. When the aspiration is stopped, the sleeve becomes glassy again and keeps its shape. It can be resorbed by sucking the deformed vesicle beyond the yield stress. We have discovered a new regime where a very long tongue is formed at ultra-fast velocity. It corresponds to the aspiration of gas from the glassy vesicles. In this case, the stress σ acting on the protein shell is smaller than the yield stress and larger than the Laplace pressure to aspirate a bubble of gas. This extraction of gas from solid GV may have applications in ultrasound-induced inertial cavitation.
GGV aspiration was modeled by introducing both gas compressibility and film permeability. We demonstrate that compression leads to an increase in tongue penetration of the order of 12%, which is not negligible due to the high value of the dilatation modulus . In addition, membrane permeability gives rise to new laws relating the membrane tension to the applied pressure.
Thanks to the model, we were able to measure the static and dynamic properties of the interfacial film: its elastic stretch modulus, its viscosity, and its porosity.
We have shown that the membrane tension σ is not always given by the Laplace formula relating the tension to σ and the pipette radius Rp. We defined the sealing parameter Q that separates two regimes of low and high porosity, where the bubble tension almost vanishes in the steady-state regime. It would be interesting to investigate the case of more porous systems, either by varying the mesh size of the surface protein network, or by looking at the case of Pickering bubbles where the pores have sizes comparable to the size of the particles adsorbed at the interface.
Finally, the mechanical properties we were able to measure indicate that the GV developed in this project can be used as a multifunctional platform for both targeting for molecular imaging and for drug delivery after modification of the shell with specific targeting agents.
Data, Materials, and Software Availability
All study data are included in the article and/or SI Appendix.
Acknowledgments
This work was carried out under the Academy of Finland Center of Excellence Program (2022-2029) in Life-Inspired Hybrid Materials (LIBER) (project numbers 346109 and 346112). The authors acknowledge the provision of facilities and technical support by Aalto University at OtaNano Nanomicroscopy Center (Aalto-NMC) and Pascal Hersen for stimulating discussions on gas vesicles.
Author contributions
H.H.A.-T., G.B., A.P., J.V.I.T., J.J., F.B.-W., and R.H.A.R. designed research; H.H.A.-T., G.B., M.J., J.S., and F.B.-W. performed research; H.H.A.-T., G.B., and F.B.-W. analyzed data; and H.H.A.-T., G.B., F.B.-W., and R.H.A.R. wrote the paper.
Competing interest
The authors have patent filings to disclose. H.H.A.-T., G.B., J.V.I.T., and R.H.A.R. are inventors on a patent application relating to this work.
Supporting Information
Appendix 01 (PDF)
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Movie S1.
Bright-field observation of a gas vesicle in a liquid regime aspirated in a micropipette (ΔP = 13 kPa).
- Download
- 7.74 MB
Movie S2.
Bright-field observation of a gas vesicle in a glassy regime aspirated in a micropipette (ΔP = 18 kPa).
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- 3.84 MB
Movie S3.
Bright-field observation of a solid-like gas vesicle aspirated in a micropipette (ΔP = 13 kPa).
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- 12.57 MB
Movie S4.
Observation of a gas vesicle during the first 10 min following its deformation by a micropipette, highlighting a solid-like behavior.
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- 6.70 MB
Movie S5.
Aspiration of an already deformed gas vesicle on the other side, leading to the decrease of the length of the free tongue and revealing a gel-like behavior.
- Download
- 1.43 MB
Movie S6.
Bright-field observation of a non-coated air microbubble aspirated in a micropipette (ΔP = 18 kPa).
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- 3.49 MB
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Copyright © 2023 the Author(s). Published by PNAS. This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).
Data, Materials, and Software Availability
All study data are included in the article and/or SI Appendix.
Submission history
Received: July 5, 2022
Accepted: December 18, 2022
Published online: January 17, 2023
Published in issue: January 24, 2023
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Acknowledgments
This work was carried out under the Academy of Finland Center of Excellence Program (2022-2029) in Life-Inspired Hybrid Materials (LIBER) (project numbers 346109 and 346112). The authors acknowledge the provision of facilities and technical support by Aalto University at OtaNano Nanomicroscopy Center (Aalto-NMC) and Pascal Hersen for stimulating discussions on gas vesicles.
Author contributions
H.H.A.-T., G.B., A.P., J.V.I.T., J.J., F.B.-W., and R.H.A.R. designed research; H.H.A.-T., G.B., M.J., J.S., and F.B.-W. performed research; H.H.A.-T., G.B., and F.B.-W. analyzed data; and H.H.A.-T., G.B., F.B.-W., and R.H.A.R. wrote the paper.
Competing interest
The authors have patent filings to disclose. H.H.A.-T., G.B., J.V.I.T., and R.H.A.R. are inventors on a patent application relating to this work.
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Compressibility and porosity modulate the mechanical properties of giant gas vesicles, Proc. Natl. Acad. Sci. U.S.A.
120 (4) e2211509120,
https://doi.org/10.1073/pnas.2211509120
(2023).
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