Osmotic Pressure Enables High-Yield Assembly of Giant Vesicles in Solutions of Physiological Ionic Strengths

Giant unilamellar vesicles (GUVs) are micrometer-scale minimal cellular mimics that are useful for bottom-up synthetic biology and drug delivery. Unlike assembly in low-salt solutions, assembly of GUVs in solutions with ionic concentrations of 100–150 mM Na/KCl (salty solutions) is challenging. Chemical compounds deposited on the substrate or incorporated into the lipid mixture could assist in the assembly of GUVs. Here, we investigate quantitatively the effects of temperature and chemical identity of six polymeric compounds and one small molecule compound on the molar yields of GUVs composed of three different lipid mixtures using high-resolution confocal microscopy and large data set image analysis. All the polymers moderately increased the yields of GUVs either at 22 or 37 °C, whereas the small molecule compound was ineffective. Low-gelling temperature agarose is the singular compound that consistently produces yields of GUVs of greater than 10%. We propose a free energy model of budding to explain the effects of polymers in assisting the assembly of GUVs. The osmotic pressure exerted on the membranes by the dissolved polymer balances the increased adhesion between the membranes, thus reducing the free energy for bud formation. Data obtained by modulating the ionic strength and ion valency of the solution shows that the evolution of the yield of GUVs supports our model’s prediction. In addition, polymer-specific interactions with the substrate and the lipid mixture affects yields. The uncovered mechanistic insights provide a quantitative experimental and theoretical framework to guide future studies. Additionally, this work shows a facile means for obtaining GUVs in solutions of physiological ionic strengths.

To demonstrate, we calculate the maximum possible concentration of polymeric molecules in the solution containing the harvested GUVs (assuming all the polymer molecules dissolve) using Equation S1. We assume all solutions have the density of water 1 g/mL.

S1
In Note that in actuality, the polymers that we use are only partially soluble, thus the concentration of dissolved polymeric molecules is expected to be much lower than this maximum value.
The imaging chamber that we used has a height of 1000 μm. The vesicles are initially present in all locations in the chamber since they are well-mixed. To test for differences, after 3 hours, we image the solution at the imaging plane (5 μm above the coverslip) and the bulk at 100 μm and 900 μm above the imaging plane for GUVs composed of DOPC harvested from bare glass without any assisting compounds and when LGT agarose is used as the assisting compound. In both cases, we observe a large number of GUVs in the imaging plane and no GUVs in the locations in the bulk (Fig. S1). Our results confirm that the low concentration of polymeric molecules, ≪ 0.016 wt %, in the solution in the imaging chamber does not have any measurable effect on the sedimentation behavior of GUVs.
Calculation of molar yield from the literature. Reference 1 reports that the total number of GUVs with diameters between 10 µm and 80 µm in a 20 µL aliquot from a harvested volume of 500 µL is 63 ± 14. The molar yield is defined as the mols of lipids in GUV membranes divided by the mols of lipids used to assemble the GUVs 2 . The mols of lipid initially used in Reference 1 was 1 10 -9 mols 1 . We estimate the maximum possible mols of lipids in the harvested vesicles reported in Reference 1 using Equation S2.

S2
Here is the number of GUVs, taken as 77, is the diameter of the GUVs, taken to be 80 µm, is the headgroup area of the lipid which for DOPC is 72.4 10 -4 µm 2 , 6.023 10 23 is Avogadro's number, is the harvested volume which is 500 µL, and is the aliquot volume that was quantified which is 20 µL. Choosing the largest diameter of GUV reported and the upper range of GUVs counted in the experiment ensures that we are calculating the maximum possible mols of lipids harvested as GUVs from Reference 1.
Dividing the mols of lipid in the harvested vesicles with the mols of lipids initially used gives a maximum molar yield of 6.0 10 -4 % for Reference 1. Notably, the diameters of GUVs quantified in Reference 1 were limited to 10 µm ≤ < 100 µm 1 . When we similarly limit our range, we find that the yield of GUVs from the fructose-doped technique that we performed is 3.9 S4 10 -2 %. This result is ~ 2 orders of magnitude greater than that calculated from Reference 1.
The second term on the RHS of Equation S4 introduces a constraint for a section of the membrane to transition into a spherical bud at a constant area. If there is a lipid source, the membrane can transition without requiring breaks by recruiting lipids from the source 3 . In the absence of a lipid source, the membrane must form breaks, with an edge energy , to allow the lipids to reconfigure to form a spherical bud. In the main manuscript, for simplicity, we assume that the membrane has a source and does not break during budding, thus 0. We assume that the effects of the salt and polymers on the edge energy, , and the bending rigidity, , to be negligible. The change in energy in the low-salt condition, Δ and salty condition, Δ is given by Equations S5 and S6.
In these equations, is the adhesion energy in the low salt solution, is the adhesion energy in the salty solution, Δ is the osmotic pressure difference, assumed to be constant, and is the change in volume.
The change in volume from a disk-shaped bilayer on the surface with radius and interlamellar spacing height, to a spherical bud of radius is given by Equation S7a Δ S7a We used for the transition between a disk to a spherical bud at a constant surface area to express Equation S3a in terms of .
For an ideal small molecule osmolyte at low concentrations, Δ is related to the concentration of the osmolyte, by Equation S7b.

Δ S7b
In this equation, is the ideal gas constant, and is the temperature.
We obtain Equations S7c and S7d which satisfies the condition that there be no change in energy between assembly of GUVs in the low salt solution and the salty solution.
We substitute Equation S7a and S7b into equation S7d to get Equation S8. Equation S8 relates the concentration of the polymer in the interlamellar space that is needed to balance the increase in the adhesion energy in the salty solution compared to the low salt solution.

S8
We take 1 10 J m for DOPC membranes in low-salt solutions and 1 10 J m for DOPC membranes in salty solutions 3 . We use 4 nm and 1 μm for a GUV bud 1 μm in diameter. We get 0.2407 0.24 mM. The use of the ideal expression for osmotic pressure in the dilute limit does not change our conclusion that low amounts dissolved polymer is sufficient to exert an osmotic pressure that balances the adhesion energy in high salt solutions. For macromolecular polymers at moderate concentrations, the osmotic pressure is often expressed as Δ , where is the second virial coefficient and is the molecular weight of the polymer 4 . The magnitude of the osmotic pressure, Δ , is thus expected to be higher for polymers compared to small molecule solutes for the same dissolved concentration, . A lower amount of dissolved polymer than predicted by Equation S8 will be sufficient to balance the increased adhesion between membranes in salty solutions.

S8
Electrostatic interaction between membranes. The adhesion of membranes is affected by the presence of ions in solutions [5][6][7] . Ions promote adhesion by screening repulsive electrostatic interactions. The effectiveness of screening can be estimated using the Debye screening length 3 .
Smaller screening lengths reflect a shorter range in which electrostatic repulsion is felt, thus allowing attractive van der Waals interaction to dominate 3 . We use Equation S9 3 to calculate the Debye screening length, .

∑ S9
Here is Avogadro's number, is the elementary charge, is the concentration of ionic species , is the charge of ionic species , is the permittivity of free space, is the dielectric constant, is the Boltzmann constant, and is the absolute temperature.
We report the ionic composition of the buffers used for the experiments in Figure 9 in Table   S10. We report the ionic species and the calculated Debye screening lengths in Table S11. Note that the solutions consisting of 100 mM sucrose and 140 mM KCl + 5 mM CaCl2 are unbuffered.
Our measurements showed that they have a pH of 5.5. This value of pH is consistent with the formation of carbonic acid when ultrapure water is in equilibrium with atmospheric carbon

PVA
LGT 3.86E-08 *** The difference in yield between PVA and LGT is significant.

MGT
LGT 3.85E-08 *** The difference in yield between MGT and LGT is significant.

PVA
LGT 1.15E-07 *** The difference in yield between PVA and LGT is significant.

MGT
LGT 4.53E-08 *** The difference in yield between MGT and LGT is significant.  table and table of

Group p-value Significance Comments
LGT LGT HGT 0.00110 ** The difference of yield between LGT and HGT is significant

HGT
LGT 8.819E-14 *** The difference of yield between HGT and LGT is significant.

PVA
LGT 4.041E-12 *** The difference of yield between PVA and LGT is significant.