1–stearoyl–2–oleoyl–sn–glycero–3–phosphocholine (SOPC), 1,2–distearoyl–sn–glycero–3–phospho ethanolamine–N–[amino (polyethylene glycol)–2000] (DSPE—PEG 2000), head-labeled 1,2–dioleoyl–sn–glycero–3–phosphoethanolamine–N–[7–nitro–2–1,3–benzoxadiazol–4–yl] (NBD–PE), chain-labeled 1-oleoyl-2-6-[(7-nitro-2-1,3-benzoxadiazol-4-yl)amino]hexanoyl-sn-glycero-3-phosphocholine (NBD-PC) and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine rhodamine B sulfonyl) (RhodamineB) were purchased from Avanti Polar Lipids (Alabaster, AL) and used without further purification. Dextrose (Glucose), BioXtra, ≥ 99.5% (GC) was purchased from Sigma Aldrich, France. The DNA-tethers were short custom-made single-stranded DNA-oligomers from Eurogentech, Belgium. The received lyophilized DNA was dissolved in PBS so as to make 100 μM stock solution and stored at -20C. Prior to use, a working solution of 1 μM was prepared in PBS. For ss-DNA experiments, appropriate amounts of this solution was introduced into the observation chamber containing the SLB immersed in PBS (480 μl), if necessary after further intermediate dilution. For ds-DNA experiments, the ss-DNA strand was first mixed with the complementary backbone strand in approximately 5% excess. The mixture was heated to 60 degC and held at that temperature for about 5 min before allowing the whole to cool down to room temperature. This solution was then introduced into the observation chamber as described above. 20 μL of the GUV solution was introduced into the chamber and the whole was allowed to equilibrate at room temperature for 2 hours before observation.

SLBs were prepared with a film balance (Nima, Coventry, UK) applying the Langmuir-Blodgett Langmuir-Schäfer technique [42]. The subphase was ultrapure water. SLBs consisted of pure SOPC in the proximal layer. The distal layer facing the buffer was formed by SOPC with 2 mol% DSPE-PEG 2000 and 1 mol% NBD-PC (or NBD-PE or RhodamineB). Transfer pressure was set to 20 mN/m. SLBs were constantly kept under water and used directly after preparation. GUVs were prepared using the well established electro-swelling method. Briefly, 10 μL of the lipid mixture (98 mol% SOPC and 2 mol% DSPE-PEG2000) dissolved in chloroform was spread on indium tin oxide coated glass slides (Sigma Aldrich, France). In order to ensure complete evaporation of chloroform the slides were desiccated under vacuum overnight. Two lipid-coated glass slides were mounted in a Teflon chamber filled with 230 mOsmL⁻¹ glucose solution, at a distance of 1 mm. An alternating voltage of 2 V at 10 Hz was applied for 2 h s which resulted in GUVs with an average diameter of around 20–30 μm. For experiments, vesicles were immersed in PBS buffer of 270 mOsmL⁻¹. The difference in osmolarity between the inside and outside solutions resulted in vesicles exhibiting the necessary excess area to build up a contact zone with the substrate. All osmolarities were measured before each experiment with an osmometer (Osmomat 030, Gonotec GmbH, Berlin, Germany). 20–40 μL of the vesicle solution was added into the experimental chamber filled with PBS buffer (volume 1 ml). Vesicles were allowed to sediment and achieve a steady adhesion state before the first measurement. The waiting time on an average was 30 min. Observation chambers were filled completely with PBS and covered with a glass slide to avoid osmolarity changes due to evaporation. For height determination using RICM, the refractive indices of the vesicle solution and the outer buffer were measured for each experiment with an Abbé Refractometer (Kruss, Germany).

For quantification of DNA absorption, images were acquired using a confocal microscope (Leica Microsystems, Germany) fitted with a ×63 oil immersion objective. For all other experiments, images were acquired using an inverted microscope, Zeiss Axiovert 200, equipped with a EM-CCD camera (Andor, Ireland), a filter cube with crossed polarizers and a ×63 Antiflex Plan-Neofluar oil objective (Carl Zeiss, Göttingen,Germany) having a numerical aperture of 1.25. In addition the objective had a built in lambda quarter plate. For reflection interference contrast microscopy (RICM), the green illumination was selected from the light emitted by a metal halogenide lamp (X-Cite, Exfo, Quebec, Canada) using an interference filter (546 ± 12 nm). The numerical aperture of illumination was set to approximately 0.5. Image sequences consisted of 50 consecutive frames with an individual exposure time of 100 ms for each observation set. The adhesion state of GUVs was probed using RICM. Map of membrane-substrate distances from the measured interference patterns were constructed [34]. Briefly, the entire image (the vesicle as well as the background) was first corrected for anomalies arising from an inhomogeneous illumination. Next, the average background intensity (I _bg ) in the image was measured and the entire image was normalized with respect to I _bg . Finally, the normalized intensities were used to find the corresponding height by inverting the intensity height relation [34]. For all quantitative evaluation, images were analyzed using self-written routines in IgorPro (Wavemetrix, Portland, OR).

To understand how such soluble tethers may support contact formation, we adapt an existing statistical mechanical model in which the enthalpy of binding is balanced by total entropy of the system [30, 43]. We model the GUV and the SLB as two equivalent lattices with N lattice sites, of which N _cz < N are in a contact-zone, where tethers can mediate the formation of intimate contact - which will be called adhesion domain. We consider a fixed contact zone, and then the contact zone is relaxed in the second step through the calculation of the spreading pressure. The local bending elasticity of the membrane, as well as the inter-membrane distance, is locally integrated into the parameters of the model [24], but the energy of global shape-change is considered small compared to the free energy stored in the ensemble of linkers [30, 44]. As in the experimental system, the tethers in the contact-zone can be in one of the two states: 1) trans-state, occupying both a single GUV-lattice site and a single SLB-lattice site; or 2) in the cis-state, occupying ϵ GUV-lattice sites or ϵ SLB-lattice sites. The ‘shape factor’ ϵ accounts for the expected difference in the projected area of the cis- and the trans. Clearly, therefore, ϵ ≥ 1, or in other words, the projected area of the cis-state on the membrane-plane is assumed to be ϵ times larger than that of the trans state. The exact value of ϵ depends on the microstructure of the tethers: the size of the cholesterol-occupied membrane patch is not relevant. For example, if the tether is a highly flexible polymeric chain, its geometric size may be estimated by its radius of gyration, which is expected to be larger than the cholesterol-occupied membrane patch and may not be significantly affected by the transition from the cis to the trans-state, resulting in ϵ ∼ 1. On the other hand, if the tether is composed of interconnected rigid rods, as is the case of ds-DNA tethers, the cis to trans transition may significantly decrease its projected area making ϵ ≫ 1. Tethers adsorbed outside the contact zone are assumed to be in the cis-state (see footnote 2 and Figure 1A).

To keep track of tether numbers in each state, we introduce the following variables; N G U V in C and N G U V out C , denoting the number of cis-tethers inside and outside the vesicle contact zone, N S L B in C and N S L B out C , corresponding to the number of cis-tethers inside and outside the contact zone on the SLB, and N ^T representing the number of trans-tethers. The bulk solution surrounding the GUV-SLB system is modeled as an infinite reservoir, characterized by temperature T and chemical potential μ(c), related to the concentration c of tethers in the bulk solution. Assuming tethers in both configurations exchange between the membranes and the reservoir, we model the GUV-SLB system in the grand canonical ensemble, with its state function being the grand potential Ω, given by Ω = U − σ − μ c N T + N V in C + N S L B in C + N S L B out C + N V out C . (2)

Here U is the total binding entalphy of all tethers and σ is their entropy of mixing, expressed in terms of k _B T (k _B being the Boltzmann constant). The last set of terms, proportional to μ(c), are associated with the free energy change for bringing the tether from the bulk onto the designated part of the GUV or SLB surface. Negative μ corresponds to energy cost for absorbing bulk tethers onto the GUV-SLB system, which is decreased by increasing the bulk concentration of tethers (and leading to less negative μ).

The enthalpy of the system is given by U = − E b λ N T + N V in C + N S L B in C + N S L B out C + N V out C , (3) where E _b and λE _b are respectively the cis- and trans- adsorption energies, with λ being a dimensionless number. In the current system E _b = 12k _B T (see footnote 2). It is anticipated that λ < 1, making the cis binding more likely than the adhesive trans state. The reason is the small but finite free energy cost of transitioning from the cis- to the trans-state, due to the relative restriction of the internal configurational space of tethers in the trans-state, as compared to the cis-state. Thus, transition from cis- to trans- actually costs free energy and makes the tether-binding fundamentally different from the typical ligand-receptor pairing [40, 43].

Total positional entropy is calculated by counting the possible configurations of tethers on the GUV and the SLB, giving: σ = ln N cz N T N cz − N T / ϵ N V in C N cz − N T / ϵ N S L B in C N − N cz / ϵ N V out C N − N cz / ϵ N S L B out C . (4)

Here we take into account the entropy of trans tethers (first term), and cis-tethers inside the contact zone on the vesicle (second term) and the SLB (third term), together with the entropy of cis-tethers on the vesicle (fourth) and the SLB (firth term) outside the contact zone. Here again, the shape-factor ϵ marks an importance difference compared to ligand-receptor binding [40, 43].

Equilibrium densities of cis-states and trans-states are calculated by minimizing eq. 2 with respect to the tether numbers on the SLB and the GUV in and out of the contact zone, under the constraint of the constant chemical potential ∂ Ω ∂ N T = 0 , ∂ Ω ∂ N V in C = 0 , ∂ Ω ∂ N S L B in C = 0 , ∂ Ω ∂ N V out C = 0 , ∂ Ω ∂ N S L B out C = 0 . (5)

Solving the coupled Eq. 5 at equilibrium gives N T = N cz e x p λ E b + μ exp λ E b + μ + 1 + exp E b + μ 2 / ϵ , (6) N V in C = N S L B in C = N cz ϵ exp E b + μ 1 + exp E b + μ + exp λ E b + μ 1 + exp E b + μ 1 − 2 / ϵ , (7) N V out C = N S L B out C = N − N cz ϵ exp E b + μ 1 + exp E b + μ . (8)

N S L B out C is the concentration of tethers on the SLB outside the contact zone, and corresponds to the surface density experimentally measurable by Langmuir absorption isotherm. N ^T /N _cz is the density of trans bonds that create contact between the two membranes and is henceforth called trans-density. It is the equivalent to the density of ligand-receptor bonds in a classical adhesion system. We explore N ^T /N _cz as a function of the chemical potential μ for different shape and energy factors ϵ and λ (Figures 3A,B), to give insight into the mechanisms of contact formation.

We start with the case of identical adsorption affinities of cis- and trans-states (λ = 1), and we explore the role of the shape parameter ϵ (Figure 3A). If ϵ = 1 (cis- and trans-states have the same footprint on the membrane), N ^T /N _cz adopts a bell-shaped curve with a maximum at μ = − E _b . This implies that for high bulk concentrations (μ close to zero), the system strongly prefers cis-state over trans, inhibiting adhesion. Although such behavior is seemingly different from receptor-ligand bonding, where higher concentrations of tethers are expected to strengthen the adhesion, it is not unexpected since the enthalpy density per cis-tether is double that of a trans-tether - the two cholesterols of the cis-tether are inserted into the half of the membrane area of the trans-tether. The bell shaped curve is maintained until ϵ = 2, at which point the trans and the cis-tether contribute equally to the total free energy (λ = 1). Consequently, there are the same number of cis and trans tethers in the μ = 0 limit. In the regime ϵ > 2, the increasing tether concentration results in the monotonous increase of adhesion-promoting trans-tethers and therefore strengthening of adhesion. If the cost for making the trans bond increases (decreasing λ) the trans density rapidly decreases for all μ (Figure 3B). However, binding can still be achieved by increasing ϵ.

This leads to the striking conclusion that the difference in the projected areas between states alone can drive contact formation due to collective entropic considerations. Even more strikingly, this remains true even if the adsorption affinity of the non-adhesive cis-state is larger than that of the adhesion-promoting trans-state, or, in other words, the cis state is on the single-molecule level energetically more favourable. It is important to note that the shape-factor ϵ enters through entropic considerations in eq. 4. Its effect on contact-formation increases with bulk tether density because only in the crowded regime, where cis and trans states compete for adsorption area, do their projected area sizes become important. This can also clearly be seen in Figure 3, where the low tether concentration regime does not depend on ϵ. Adhesion is therefore driven purely by collective effects and not by individual tethers. This indeed may be particularly relevant to the DNA- tethers where λ is indeed expected to be somewhat smaller than one.

Finally, we inspect the tendency of the contact-zone growth by visualizing the change in the system’s energy Ω with the change of the contact zone size N _cz - captured by the so-called spreading pressure ∂Ω/∂N _cz (Figure 3C). The observed negative spreading pressure corresponds to the tendency of the contact zone to spread. A higher tendency for contact-zone spreading is highly correlated with a higher density of trans bonds (compare Figures 3B,C). We therefore expect trans-mediated adhesion to drive the spreading of the contact zone. However, unlike in the ligand-receptor binding, spreading tendency does not depend on the current size of the contact zone. The consequences of this size insensitivity would be very different response to forcefully induced de-adhesion.

To quantify tether-mediated membrane contact formation, we let GUVs interact with DNA-tether decorated SLBs. GUVs are introduced into a chamber containing an SLB already incubated with DNA-tethers. Due to the high adsorption affinity, tethers incorporate into the SLB as well as GUV membrane, probably both in cis (“U”) configuration (see footnote 2). GUV sedimentation is followed by formation of close contacts with the SLB visible as dark patches in RICM. The GUVs usually form an expanding contact zone, where the two membranes are closely apposed. In this zone, referred to as the adhesion domain, the two membranes are held together by DNA-tethers in trans (“I”) configurations (Figure 2C). In the absence of tethers, no formation of adhesion domains and no widening of the contact zone is observed. If tethers are present, in all cases we obtain a circular adhesion zone, leading us to infer that the adhesion proceeded through the formation of a radially growing adhesion patch [24]. This patch is formed by the transitioning of adsorbed cis tethers to the trans configuration through the re-insertion of one of the cholesterols into the apposing membrane. Alternatively, tethers can be adsorbed in trans configuration directly from the bulk solution. Both processes lead to adhesion (Figure 1A) and result in identical end-states that are indistinguishable in an equilibrium analysis.

Visual inspection of RICM images reveals that in the same sample, some vesicles simply hover close to the SLB (non-adhered), some adhere exhibiting many fringes (weak), some adhere with just a few fringes visible (intermediate) and few have no fringes at all (complete adhesion). Figure 4A illustrates the different adhesion states that are encountered. The defined visual categories can be attributed objectively by defining an “adhesion parameter” f, which is given by the ratio of the diameter of the adhesion patch and the diameter of the GUV. f for each category is: No Adhesion 0 < f < 0.15, Weak 0.15 < f < 0.5, Intermediate 0.5 < f < 0.75, Complete 0.75 < f < 1.

Though we attributed names to the adhesion states based on morphology, only the so-called weak adhesion state can be quantified using the Bruinsma construction which uses the Young-Dupre law, with an ad-hoc line tension that takes into account the elastic cost of extra bending due to the adhesion induced deformation [45, 46], to infer adhesion energy density. We calculated the free energy in this state and find that all vesicles, irrespective of tether type and concentration, identified to be in the weak adhesion state have an adhesion energy ranging from about 0.002 to 0.1 μJ/m² (with mean at 0.02, averaged over 65 GUVs over different conditions), and the final membrane tension of about 0.02–0.9 mN/m (with mean at 0.2, averaged over the same 65 GUVs). Importantly, for this given ‘f’ range, all the vesicles exhibit adhesion energy in the same range independently of the tether type, concentration or GUV size - implying that the classification according to f is consistent.

We characterize the extent of contact formation by counting the number of GUVs in each of these adhesion states (Figure 4B). Increasing the bulk concentration consistently increases the average contact zone size, independently of the tether type. Within the different tether types, ds-DNA clearly emerges as a more efficient binder than ss-DNA as seen at low concentrations.

It should be noted that while the distribution of different adhesion states (f) may arise from the inevitable tension polydispersity, the shifts in this distribution at population level, with varying experimental conditions, arises due to variations in adhesion energy, which can be expressed as a spreading pressure [24, 25, 31]. The polydispersity in spreading behaviour is much more pronounced in this system than in previously studied ligand-receptor mediated GUV/SLB adhesion, even though the GUVs are identically prepared and hence expected to have the same tension distribution.

Another difference compared to the traditionally studied ligand-receptor system is that there, addition of binders, in the form of competing soluble ligands, induces un-binding of the GUV [25]. Here addition of binders in solution results in their recruitment to the membrane which leads to higher adhesion. While such a mechanism could be devised for ligand-receptor system, that would be atypical.

In this system, the existence of stable adhesion, found both in experiments and in theory, is in itself non-trivial. In the well-studied ligand-receptor case, membrane adhesion is driven by the free energy gain due to establishment of an individual bond. In the current system, the cis configuration is, from the perspective of the free energy of a single binder, the preferred state, as compared to the membrane adhesion inducing trans configuration. This energetic preference can be estimated by assuming that the cholesterol insertion is mostly independent of the tether type, while the difference between the free energy of cis and trans configurations occurs due to the restriction of the internal structural degrees of freedom of the tethers upon transitioning from the cis to the trans state, quantified by the entropic cost of transition. The measure of the entropic cost λ can be estimated from the ratio of the expected tether volumes in cis and trans states, and is therefore related to the estimate of ϵ, with larger ϵ corresponding to smaller λ. Assuming Gaussian chains for the ss-DNA tethers (which do not significantly change their accessible conformation space on cis to trans transformation), and treating the ds-DNA tethers as two rods connected by a flexible joints (which do change their conformation space significantly), leads to estimates presented in Figure 3D. As expected, the estimated volume change is more significant for short tethers which are stretched more significantly compared to their long counterparts. This is quantified by larger ϵ and smaller λ for long tethers compared to their shorter counterparts. Furthermore, the entropic cost is larger for the rigid ds-DNA tethers as compared to the flexible ss-DNA tethers, quantified by larger ϵ and smaller λ for ds-DNA tether compared to ss-DNA tether. It is clear from (Figure 3D) that small changes in the choice of the parameters can make substantial changes in the spreading pressure. The range of μ is chosen to be consistent with the experimental range of concentrations, and the theoretical behaviour of the spreading pressure reproduces the experimentally observed monotonous growth of pressure with concentration. Moreover, our model predicts that the ds-short tethers are the most efficient for promoting adhesion, again in accordance with experimental observations. Hence, our model offers an underlying explanation for the experimentally observed trends.

Furthermore, our theory predicts and experiments confirm that titration of additional DNA tethers yields stronger adhesion. The dependence on the concentration of titrated tethers is clearly seen in experiments for all the different tethers where the tendency to adhesion increases with increasing bulk concentration of the tethers and then saturates when all available area is exhausted. This tendency is reflected in the monotonic increase and saturation seen in (Figure 3C) which plots the theoretical spreading pressure ∂Ω/∂N _cz (a measure of the tendency of an adhesion zone to increase in size) as a function of the chemical potential determined by the bulk concentration.

Another observation, namely the large spread in adhesion state for a given experimental condition, can also be understood in the light of the model which clearly shows that since the DNA-tethers freely exchange between the different membranes, individual GUVs do not equilibriate as isolated systems. Instead, the entire system equilibrates collectively. Thus, unlike in ligand-receptor mediated adhesion, the relevant parameter should not be the individual f values but rather the collective total area. Hence, the adhesion state of an individual GUV evolves not only according to their initial membrane tension but also under the influence of their interaction history. Thus, an equilibrium analysis of individual GUVs is not expected to be meaningful. Instead, the focus should be on the population-wide trends.

We also exploit the fact that RICM is almost the unique tool to measure the distance between two interacting membranes. As could be expected, the inter-membrane distance (h) increases with increasing tether length (Figure 5A). However, h is independent of the bulk concentration of tethers, suggesting that a relatively high density of trans tethers is obtained in all cases. This is furthermore confirmed by the values of membrane roughness (defined as the spatial variation in h), which also adopts values independent of the tether concentrations. h depends weakly on the tether stiffness (ss or ds), the gap being wider for ds-tethers. As expected, longer tethers support wider gaps.

These findings are supported by theoretical calculations of the mean membrane height and roughness using the well-studied formalism for receptor-ligand cell adhesion [47]. Here, trans configurations are modeled as elastic springs pinning the membrane. By varying their density, length and stiffness we reproduce the qualitative behaviour observed in experiments (Figure 5B), as long as the rigidity of the tether is not very high. The roughness (represented by error bar) is calculated as the true variation in membrane height averaged over the surface area. The height and the roughness of the membrane both decrease with density and independently of tether type, and both saturate to a constant value when the surface coverage of tethers in trans configurations exceeds a threshold density. However, the density dependent changes in roughness are very weak, and with the experimental resolution of few nanometers, they are not likely to be observed. Interestingly, the membrane height is sensitive to both the rest length of the tether and its stiffness. For a given stiffness, h is of course larger for longer tethers. For a given length, the softer tethers tend to support wider gaps. Note that the gap between the two membranes is set by the bio-mechanical properties of the membranes and the linkers. For tethers that are shorter than the gap-size determined by non-specific interactions that emerge from fixing the membrane properties, softer tethers allow for larger extensions, yielding larger gaps. This effect is not unique for DNA tethers and would work in the same way for ligand-receptor constructs [24]. Comparing this result with experiments, we conclude that a jointed-rod configuration (ds-tethers) may in fact appear softer than a polymer-like configuration (ss-DNA tethers), due to the very flexible joint. Over all, the gap-width can be regulated by adjusting either the length or the overall effective stiffness of the tethers.