Fission of Lipid-Vesicles by Membrane Phase Transitions in Thermal Convection

Unilamellar lipid vesicles can serve as model for protocells. We present a vesicle fission mechanism in a thermal gradient under flow in a convection chamber, where vesicles cycle cold and hot regions periodically. Crucial to obtain fission of the vesicles in this scenario is a temperature-induced membrane phase transition that vesicles experience multiple times. We model the temperature gradient of the chamber with a capillary to study single vesicles on their way through the temperature gradient in an external field of shear forces. Starting in the gel-like phase the spherical vesicles are heated above their main melting temperature resulting in a dumbbell-deformation. Further downstream a temperature drop below the transition temperature induces splitting of the vesicles without further physical or chemical intervention. This mechanism also holds for less cooperative systems, as shown here for a lipid alloy with a broad transition temperature width of 8 K. We find a critical tether length that can be understood from the transition width and the locally applied temperature gradient. This combination of a temperature-induced membrane phase transition and realistic flow scenarios as given e.g. in a white smoker enable a fission mechanism that can contribute to the understanding of more advanced protocell cycles.

Before life on earth emerged, only small molecules existed. The development of complex structures or already simple reactions were unlikely and energetically unfavorable simply due to the assumed very dilute settings of early earth 1,2 . Physical non-equilibrium settings can have a profound influence here: sub-sea hydrothermal microenvironments 3 like pores in submerged volcanic rock provide temperature cycling systems and allow for strong accumulation, as the cooperation of convective flow and thermophoresis can enlarge molecule-and particle-concentrations by several orders of magnitude 4 .
An important concept in early earth's cell evolution is compartmentalization. Following Blain, Szostak 5 and Nourian, Danelon 6 a compartment such as a lipid membrane provides a selective barrier between the inner proto-cell content and the surrounding environment. Schrum et al. describe a pathway for lipid membrane vesicles made from fatty acids known as prebiotically plausible membrane building blocks 7 to more sophisticated phospholipids. They then raise the question how such structurally simple protocells could accomplish essential membrane functions know from modern cells.
In a model cell cycle for vesicles the two phases, formation and inclusion of diluted substances, are well understood 5 . The division-phase has been the subject of several studies 5,6,8,9 . This division is necessary to redistribute enclosed material or reaction products formed in the protocell. While modern cell division is a complicated mechanism mediated by many complex proteins, an early earth protocell must have had a simple fission mechanism. A basic cell division-like fission could have been driven by the environment and membrane properties only, without any active contribution by the protocell itself. The temperature-dependent hydrophobic effect drives the self-assembly of vesicles from dissolved lipids above a critical concentration and e.g. for dipalmitoylphosphatidylcholine (DPPC) based membranes also causes complex reshaping of the vesicle membrane during several phase transitions 10,11 . Temperature induced morphological transitions of DPPC vesicles have been shown by Leirer et al. in absence of additional shear flow. The vesicles showed a pear-shaped morphological transition of previously spherical DPPC vesicles by the DPPC L β' -L α membrane phase transition 12 by quick temperature changes in a static setup. Rapid cooling can fission those vesicles, but the resulting new vesicles differ strongly in size compared to the mother vesicle. They do not result in two or more similarly sized vesicles resembling modern cell division. Moreover, such a temperature setup does not resemble scenarios possible on early earth, as closed fluid compartments with rapid temperature change over some seconds without flow do barely exist in nature.
Zhu, Budin, and Szostak show the growth and division of proto-cell membranes under mild flow 9,13 . Vesicle growth is driven by uptake of micelles by small unilamellar vesicles, the resulting aggregates are tube-shaped due to the large surface-to-volume ratio of the integrated micelles. The low permeability of the fatty acid bilayer inhibits the influx of water and therefore their reshaping to spheres. Already a mild fluid flow induces shear forces by which these aggregates are ruptured. The tube-like structures shown by Zhu et al. are fragile and too easily divided to be suitable for the robust transport and enclosure of molecules such as DNA. Alternatively, the surface-to-volume imbalance can be achieved by lipid production in the vesicle 14 . Deshpande et. al use the osmotic pressure to increase the surface-to-volume ratio and then use an obstacle in a microfluidic channel to mechanically divide DOPC-vesicles. They note, that the success of vesicle-splitting mainly depends on the surface-to-volume ratio of the mother vesicle and a too small ratio leads to complete rupture of the vesicle 15 .
The concept of a primitive cell cycle with division of cell-sized lipid vesicles is modelled in several studies 16 : in all cases the concept introduces an imbalance of vesicle surface and volume 15,[17][18][19] , as shown above, or shear forces and thermodynamic instability as shown by Szostak et al. In combination with a spontaneous growth mechanism, this "[…] could lead to a primitive cell cycle controlled entirely by the biophysical properties of the membrane and environmental forces" 17,20 .
When modern cells like Bacillus subtilis are treated by antibiotics they lose their cell wall. In turn, their division mechanism (Z-ring) does not work anymore. In order to proliferate, these cells now grow and undergo a shape transformation to pearl or dumbbell-like shapes and split into multiple cells 21 . This observation shows the ability for an alternative self-driven division mechanism in nowadays cells that is comparable to the division of lipid vesicles 22 .
Here, we describe a simple process of splitting Giant Unilamellar lipid Vesicles (GUV) in homogeneously sized daughter vesicles. In our system this process is driven by environmental conditions of flow induced shear forces in a spatial temperature gradient. The vesicles have a stable membrane with low permeability before and after the fission process and hardly lose any membrane area during fission. In contrast to other mechanisms, here no additional chemical or biological effect or mechanism is necessary.

Results and Discussion
In temperature-driven convection chambers we first discovered distinctly deformed DPPC vesicles. The chambers are built to mimic hydrothermal microenvironments 3 and sustain flow through the applied temperature gradient. In nature comparable chambers are located in rocks that are heated from the inside (by lava or hot gases) and cooled from the outside (ocean). Figure 1 illustrates such a rock as well as possible capillary or chamber geometries (closed and open channels). Keil et al. show, that the geometry of a chamber can vary without altering the convection or accumulation effect significantly 4 . Figure 2 shows deformed vesicles in the convective flow. The initially spherically shaped vesicles now show non-spherical forms. Some time after the gradient is applied, those shapes disappear. Screening the vesicles in the chamber before and after temperature cycling results in a distinct difference in size distribution. Figure 3a,b show a schematic illustration of the convection chamber and the parabolic flow profile.
The convection driven flow chamber is constructed following the standard procedure shown in the methods section. Vesicles in the chamber travel in the double parabolic flow profile and experience position-dependent velocity and shear-forces. Figure 3c shows the simulated path of two vesicles in the convective flow. The absolute temperature difference was chosen smaller for the second case with elevated temperatures, as the viscosity of water is lower and, therefore, flow speed increases. In d) we show the vesicle volume distribution. When vesicles do not cross the phase transition temperature of their membrane lipids, the size distribution is shifted towards slightly larger volumes, suggesting smaller vesicles loosely adhering to larger ones. In the second case, vesicles shuttle through the chamber and across the phase transition temperature multiple times. Here, the size distribution is shifted to smaller vesicles, suggesting vesicle fission (see Fig. 3d).
In literature, there are several cases of vesicle fission described: vesicles can divide when shear forces are applied 13 or when they are heated in a stationary case 12 . In our case we do only see the shift in size distribution towards smaller vesicle sizes when the transition temperature is exceeded. Combining these reported findings and the statistically significant shift to smaller vesicle sizes suggest the hypothesis of vesicle fission in the convection chamber. While this setup allows to study several thousand vesicles at the same time, tracking of single vesicles is difficult. To check whether indeed vesicle fission happens, we build a capillary setup mimicking the form of the flow profile and the temperature gradient of the convection chamber, however in a linear one-way version. Combined with lower vesicle density and higher magnification we study single vesicles on their way through the temperature profile.
The experiments indeed show vesicle fission as seen in Fig. 4. Figure 4b shows the experimental setup with two copper blocks and a Peltier element for heating and cooling. Figure 4a shows four states of vesicle deformation, that are reproduced in every fission event we monitored (N fission = 55 out of N total = 97). The first state is the static equilibrium. Here, the membrane is in the gel-like phase as the temperature is below the phase transition temperature. The surface area is in equilibrium with the enclosed volume -an outer force acting on the vesicle would lead to a strain in the membrane acting against that deformation. In the second state deformation the vesicle is in the hot part of the capillary and the temperature exceeds the main phase transition temperature of the lipid-membrane. As a result, the membrane expands suddenly while the vesicle volume remains approximatively constant. Additionally, the deformability increases as the bending modulus of the membrane decreases by a factor of about ten 23,24 . The exterior force caused by the parabolic fluid  flow profile is now able to deform the vesicle. Due to the rectangular shape of the capillary the deformation in the z-direction is several times stronger than in the y-direction. The formerly rotationally symmetric (with regard to the x-axis) vesicle is not symmetric in this step and rather flat in the z-direction compared to the y-direction and elongated especially in the x-direction. In the third state domaining new lowest energy states of the vesicle shapes develop: volume containing sections are separated by tether sections of negligible volume. Volume containing sections are typically close to a spherical shape and basically encapsulate the entire vesicle volume (see Fig. 4c-e) with parts of the membrane area. The tube-shaped tether sections accommodate the remaining surface area and connect two neighboring volume sections. These vesicle shapes are stable under given conditions as no disruption has been observed and all vesicles adopt to a comparable shape in all performed experiments (for example see SI-Video). The COMSOL simulation of the flow profile in the chamber overlaid by a particle tracker shows the temperature profile in a stream line over time. For elevated temperatures, the streamline crosses the phase transition temperature of DPPC membranes. To achieve similar mean flow velocities, ΔT of the temperature gradient is reduced to compensate for the lower viscosity of water at higher temperatures. While at lower temperatures the vesicles simply shuttle in the convective flow, at higher temperatures the vesicles experience two phase transitions for each cycle (simulation and particle tracker from Keil 4 ). (d) The vesicle size distribution in the convection chamber before and after cycling. When the applied temperature range does not include the phase transition temperature (silicon: 13 °C, sapphire: 40 °C, see SI) a small shift in the size distribution towards slightly larger vesicles is visible. This can be understood by vesicles sticking together. For higher temperatures (silicon: 34 °C, sapphire: 50 °C) the size distribution is significantly shifted to smaller sizes. (2019) 9:18808 | https://doi.org/10.1038/s41598-019-55110-0 www.nature.com/scientificreports www.nature.com/scientificreports/ In the fourth state fission the rapid cooling of medium and vesicle membrane below the phase transition temperature of the lipid membrane induces the phase transition from the fluid unordered phase to the gel-like membrane phase. The bilayer surface area shrinks back to its pre-phase transition state. At this state for slow temperature changes and low shear flow velocities the vesicle reshapes back to its spherical starting configuration. However, when a distinct threshold of shear flow velocity and temporal temperature gradient is reached, the tethers break apart. Breaking tethers open energetically unfavorable pores in the membranes of the volume domains. The vesicles close these pores by releasing inner volume into the surrounding medium, as e.g. shown earlier for endocytosis-like nanoparticle uptake 25,26 . By such shrinking to a smaller size and thus decreasing the surface-to-volume ratio, these new smaller vesicles are in a mechanical equilibrium state again. The resulting split-up vesicles are about equal in size in all our experiments (for example Fig. 4).
This mechanism represents a reproducible, controlled way to divide lipid vesicles with a structural membrane phase transition in microfluidic pore setups. Moreover, no processes other than a non-uniformal flow profile and a local temperature gradient are necessary for the division process. Most of the vesicle volume is preserved and still enclosed in the unilamellar bilayer vesicle. In control experiments under the same conditions DPPC was replaced by 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), a lipid lacking a phase transition in the respective temperature range. Here, not a single fission event was observed despite high deformability of the www.nature.com/scientificreports www.nature.com/scientificreports/ fluid membrane. Following Mercier et al. 16 the unbalanced surface-to-volume ratio is key to vesicle division. The main phase transition of DPPC and the resulting increase in surface area provides this imbalance, while DOPC is lacking this property, explaining the lack of fission events described above. For deformed DPPC vesicles the fast phase transition back from fluid to gel-like state enables the vesicle division.
Furthermore, we assume the vesicles in the fluid phase to be equilibrated to the environmental conditions (temperature and shear force), when the front section of a tethered vesicle enters the steep temperature gradient as shown in Fig. 4. The immediate phase transition of the membrane with its accompanied decrease in area leads to a drastic increase in membrane tension. In turn, the increased tension leads to Marangoni flow of lipids from the tether and the rear vesicle section towards the front vesicle section 27 . This is accompanied by a flow of surrounding water, being dragged by the flowing lipid to the front vesicle section. This hinders volume flow towards the back vesicle section what becomes less important with increasing tether radius 27 .
Detailing the fission mechanism, we first investigate the energy necessary for a fission event.
Energy required for fission. As the fission event requires the formation of two pores for the rupture of the tether (one in the volume section and one on the tether), we estimate an upper limit for the energy E pore necessary for pore formation. We assume a pore radius of r = 25 nm and membrane tension σ ≈ 0. Following Taupin et al. 28,29 γ π σ π = ⋅ ⋅ − ⋅ ⋅ . This results in ≈ − E 10 J pore 18 . However, for some finite membrane tension of about 1 mPa, E pore can take a maximal value of ≈ − E 10 J pore 19 for r = 7 nm and becomes even negative for pore radii larger than r = 14 nm.
Energy supplied by a phase transition of the front vesicle. We can estimate the energy contributions of this transition following the approach of Heimburg 11 as follows: The contribution to the Gibbs Free Energy density due to area changes g A is where K A is the area compression modulus and ΔA the deviation from the equilibrium (here the gel-like phase) area A 0 . Moreover, with the area compressibility κ T A . In our experiment prior to the steep temperature gradient from hot to cold the vesicle is in an equilibrium shape as a result of temperature and shear forces. For the following energy estimation, we illustrate the front vesicle of our dumbbell shaped vesicle as a spherical vesicle in Fig. 5.
Starting from point 1 in the graph of area compression modulus as function of temperature, the vesicle quickly passes the transition temperature towards a lower temperature below the main transition (point 2). The vesicle keeps its geometry due to the incompressibility of water and only a minor chance to release volume from the interior during the short moment when the vesicle reaches the main transition temperature. Thus, at point 2 the vesicle still has the area of a fluid phase vesicle but is in the gel phase at around 35 °C. This is equivalent to a stretching of a gel phase vesicle (dashed line) to the size of a fluid phase vesicle (solid line). Thus, accepting the approximate volume conservation (see also Fig. 6), the energy difference between the points 1 and 2 is equal to a membrane expansion of about 25% using the K ( Where, ΔG _ A mol and A fluid are the change in Gibbs Free Energy and area per molecule respectively. This energy can be compared with the energy necessary for the formation of a pore with radius r.
Thus, the Gibbs Free Energy ΔG _ A ves for a typical vesicle with radius = R 10 µm is "E pore ". This energy easily suffices for arbitrarily large pores, even for vesicles that do not experience shear stress with membrane tension σ = .
0 This estimation shows that all vesicles in our experiments could fission, if the pore formation energy would be the single decisive parameter. However, only a subset of vesicles experiences a fission in the capillary setup. Therefore, we investigate the influence of geometrical parameters like tether length, radius and flow velocity on the fission behavior.
First, we estimate the shear stress σ using a mean shear rate for each vesicle depending on its particular position within the parabolic flow profile in the channel. In the experiments presented here the shear stress typically is σ γ η = ≈ ⋅ 1 shear 1 s mPa s = 1 mPa. Fig. 6c shows boxplots of the estimated shear force f as a product of σ and the total area of each vesicle for all vesicles categorized as fission and no fission. The median overall shear force f for vesicles that do fission during the experiment and those that reshape without fission are = . pN, respectively. Vesicles that fission do on average experience an 1.8-fold higher shear stress. Second, we measure the mean tether radius from the fluorescence micrographs. Figure 6d shows boxplots of the tether radii for all vesicles categorized as fission and no fission. The median apparent tether radii ρ for vesicles that are divided during the experiment and those that reshape without fission are ρ = . µm, respectively. This is in line with the argumentation on Marangoni flow as discussed above, especially concerning the dependence of flow resistance from the radius ρ 4 . The mean difference of 15 % in radius results in a flow resistance difference by a factor of two. www.nature.com/scientificreports www.nature.com/scientificreports/ Third, we measured the tether lengths from the fluorescence micrographs immediately before the vesicles pass the steep temperature gradient from the hot to the cold region. Figure 7e shows boxplots of the tether length for all vesicles categorized as fission and no fission. The median tether length l for vesicles are µm. Therefore, we see a strong correlation of tether length and fission events. Long tethers are prone to fission.
Defining the mean value of l fission and l _ no fission as the transition tether length l trans we can compare l trans with the width of the phase transition: the setup provides a steep temperature gradient of 0.07 K/µm at the phase transition region. Thus, the transition tether length l trans corresponds to a temperature difference of Δ = T 10 K. This ΔT is about 2.3 times the FWHM of the phase transition temperature width of the used lipid mixture, see Fig. 7a. Even more convincing, 10 K is almost exactly the width of the complete phase transition width. www.nature.com/scientificreports www.nature.com/scientificreports/ Summing this discussion up, we conclude that shear forces acting on the vesicles result in a shape change with the formation of a tether of distinct length and radius. The tether radius and length determine the relaxation dynamics of membrane tension after the phase transition of the front vesicle section. In combination with the temperature gradient in the capillary these parameters then determine the Gibbs Free Energy change, that finally leads to the fission event. Or in even simpler words: the shear force decides about the fission indirectly while the phase transition delivers the energy for the fission.
As DOPC-membranes do not have a phase transition in this temperature range, DOPC-vesicles do not change their shape irreversibly and no fission event can be detected. This also holds for vesicles from cholesterol-DPPC mixtures (≥30% cholesterol, see SI). Thus, the capillary setup experiments proof our hypothesis concluded from the shift in size distribution in the convection driven chamber: a robust vesicles fission takes place under the influence of shear flow and a temperature gradient reaching across a phase transition temperature of the membrane. Important for protocells, especially for early earth scenarios, is the conservation of its building blocks. In a dilute ocean shell material as well as encapsulated material were scarce 1,2,30 . In Fig. 6 the mean volume and surface of the vesicles before and after passing the capillary are shown. Due to the setup geometry only the 2D-projections in the x-y-plane are analyzed. Vesicles are assumed to be rotationally symmetric. Measurements of vesicles in the capillary setup are classified in three categories: no fission, partial fission and complete fission. Here, partial fission summarizes all irreversible shape deformations including incomplete separation of tether and daughter vesicles.
The total vesicle volume decreases only slightly when there is no fission, decreases for about 35% at partial fission and for about 40% for complete fission. An ideal fission event would not lose any surface area. But the resulting daughter spheres of course have a combined volume smaller than the initial volume. For two and three equally sized daughter vesicles this decrease of volume is about 30% and 42%, respectively. Thus, the fissioned vesicles retain roughly as much volume as geometrically possible (analytical estimation shown in SI).
Along the same line, surface area remains constant if the vesicles do not fission. The slight increase in Fig. 6b points towards a systematic error in the calculation of surface and volume from the 2D-projection (e.g. selection error in fluorescent micrograph). For partial and complete fission, the surface area decreases up to 10% and 25%, respectively. Partially this is due to split off tether-sections as shown in Fig. 6c. conclusion The mechanism described here shows a division pathway that combines a steep temperature-gradient and a parabolic flow profile, that reliably divides lipid vesicles. Without the need for additional, chemically induced processes, vesicles with a first order membrane phase transition are prone to fission by this mechanism. In a thermal convection chamber we find a significant reduction of the size distribution for a wide range of vesicle sizes. Tracing single vesicles in a capillary we monitored vesicle shape transformations resulting in fission. From these observations we deduce the underlying mechanism: domaining due to the experienced shear forces causes a separation of vesicle volume by tether-like surface domains which rupture during the phase transition back to the gel-like phase.
It would be highly interesting to extend existing theoretical models from Canham, Helfrich, Evans, Seifert, Miao and Döbereiner [31][32][33][34][35][36][37][38] to vesicles experiencing force fields in a scenario as shown here including the non-linear behavior due to membrane phase transitions. Developing this idea further should also consider the sensitivity of these phase transitions to interaction with the enclosed material 39 like proteins or RNA. The temperature cycling is one of the two driving forces of this simple proto-cell division mechanism. But the combination of DNA in the proto-cell with these temperature oscillations can even melt double stranded DNA into single strands and make them accessible for replication mechanism as proposed by Mansy and Szostak 40 . In combination with the fission mechanism discussed in this paper a full cell cycle with included information distribution might be provided.
In a context of Origin of Life, vesicles could be a step on the way to proto-cells that enclose, replicate, transport, shield, and distribute information, e.g. in the form of nucleic acids. Without the sophisticated division mechanisms of evolved modern cells, a much simpler and reliable mechanism for proto-cell division is necessary to have a complete cell cycle of formation, information-inclusion, division, and growth for lipid vesicles. Also, both capillary and convection chamber are experimental realizations of hydrothermal microenvironments. They combine non-uniform flow profiles with rapid temperature-changes, a setting which is plausible in the context of the Origin of Life and is known to have the ability to accumulate dissolved molecules from strongly diluted solutions and provide a mechanism for the formation of lipid-vesicles, a structure that is widely seen as a proto-cell candidate.
Prebiotically plausible protocells probably had multiple different membrane molecules. Membrane phase transitions would not have been as sharp as shown here. The environment in our experiments is also very controlled. Loosening those parameters would probably lead to a lower fission efficiency or the emergence of new division mechanisms which might show similar characteristics. However, the same physics as for our protocell model with a structurally simple membrane would apply. Taken together, a robust fission mechanism can arise from simple gradients, fluid flow and non-linear mechanical membrane properties, as present at temperature induced membrane phase transitions.

Methods
Vesicle preparation. In this paper, we use Giant Unilamellar lipid Vesicles (GUV) with a diameter of up to image transformation for size distribution. In contrast to the capillary setup where a single vesicle is followed with the motor stage and camera of the microscope, in the chamber setup the entire chamber is scanned. Vesicles are imaged without convective flow, before and after thermo-induced convective cycling. A simple threshold filter creates a binary version of the images with white (0) background and black (1) vesicles. The visualization by accumulated integration has the advantage of not being influenced by a bin size selection as it is the case in standard histograms. The normalization allows to compare the size-distribution of two scans of the same sample before and after temperature cycling.