Cations Regulate Membrane Attachment and Functionality of DNA Nanostructures

The interplay between nucleic acids and lipids underpins several key processes in molecular biology, synthetic biotechnology, vaccine technology, and nanomedicine. These interactions are often electrostatic in nature, and much of their rich phenomenology remains unexplored in view of the chemical diversity of lipids, the heterogeneity of their phases, and the broad range of relevant solvent conditions. Here we unravel the electrostatic interactions between zwitterionic lipid membranes and DNA nanostructures in the presence of physiologically relevant cations, with the purpose of identifying new routes to program DNA–lipid complexation and membrane-active nanodevices. We demonstrate that this interplay is influenced by both the phase of the lipid membranes and the valency of the ions and observe divalent cation bridging between nucleic acids and gel-phase bilayers. Furthermore, even in the presence of hydrophobic modifications on the DNA, we find that cations are still required to enable DNA adhesion to liquid-phase membranes. We show that the latter mechanism can be exploited to control the degree of attachment of cholesterol-modified DNA nanostructures by modifying their overall hydrophobicity and charge. Besides their biological relevance, the interaction mechanisms we explored hold great practical potential in the design of biomimetic nanodevices, as we show by constructing an ion-regulated DNA-based synthetic enzyme.


S1 DNA nanostructure assembly
All the reagents used in this work were acquired from Sigma Aldrich, unless stated otherwise. Each singlestranded DNA oligo was analysed using the NUPACK suite 1 , in order to prevent formation of secondary structures, and to ensure sufficient yield of folding. Oligonucleotides were obtained from Integrated DNA Technologies, Inc. All the strands were dissolved to a final concentration of 100 µM: unmodified ones in IDTE buffer (10 mM Tris, 0.1 mM EDTA (Ethylenediaminetetraacetic acid), pH 8.0) and labelled ones in Milli-Q purified water. Strands were then stored at 4°C, except for dye-modified ones, which were stored in -20 °C.
In order to fold the designed structures, the strands were mixed to a final concentration of 1 µM in TE buffer (10 mM Tris, 1 mM EDTA, pH 8.0), with cholesterol-modified strands heated beforehand to 70 °C for 10 min. In the case of UV-vis measurements and PAGE analysis, the structures were folded in a buffer with magnesium concentration stated for each experiment. DNA duplexes were left for half an hour at room temperature before proceeding with experiments. Folded structures were all stored at 4°C. The structures used in this work were: -36 bp-long duplex: D1' + D1'', Cy3-labelled -48 bp-long duplex: (D1 + D1') + (D2+D2'), Cy3-labelled, with 0/1/2 cholesterol modifications The sequences and details of modifications are listed in Table 1, as well as illustrated in Supplementary Fig. 1.

S2 Vesicle preparation
GUVs used in the assay were prepared with electroformation, as reported previously 2 . POPC (1-palmitoyl-2oleoyl-glycero-3-phosphocholine) or DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine) with an addition of NBD-PC lipids (1-palmitoyl-2-{6-[(7-nitro-2-1,3-benzoxadiazol-4-yl)amino]hexanoyl}-sn-glycero-3phosphocholine), all acquired from Avanti® Polar Lipids, were used in a ratio of 200:1, with the final concentration of 5 mg/ml in chloroform. 600 µl of 1 M sorbitol in 200 mM sucrose was used as a buffer. The osmolality of the buffer was around 1200 mOsm, with all the dilution buffers used in the experiments adjusted accordingly. Since for cell plasma the osmolality ranges between 275 -325 mOsm 3 , therefore we do not claim a biological osmolality. All the buffers were adjusted to pH 7.5 (using sodium hydroxide and hydrochloride solutions) -the value within the acidity range observed in natural systems 4 . In the case of electroformation of GUVs containing lipids with high-melting temperatures (i.e. DPPC), the process was performed at 60°C to ensure bilayer fluidity.
LUVs used for the zeta (ξ) potential measurements were prepared with extrusion, using a commercially available extruder (Avanti® Polar Lipids, Avanti Mini Extruder), following producer's protocol. Whatman ® Filter Supports and Whatman ® Nuclepore Track-Etched Membranes (200 nm) were obtained from Sigma Aldrich. The DPPC layer was hydrated in 200 mM sucrose, and the extrusion was performed at 60°C to ensure bilayer fluidity.

S3 Confocal microscopy imaging
Confocal microscopy images were acquired on an Olympus FluoView filter-based FV1200F-IX83 laser scanning microscope using a 60x oil immersion objective (UPLSAPO60XO/1.35). NBD excitation was performed using a 25 mW 473 nm laser diode at 1% laser power, with emission collected between 490 and 525 nm. Cy3 excitation was performed using a 1.5 mW 543 nm HeNe laser at 3% laser power, with emission collected between 560 and 590 nm. FIJI was used to analyse the images 5 . In the experiments listed below 20 µl of electroformed liposomes were incubated for 1 h with 50 µl of DNA structures diluted in an osmotically balanced glucosebased buffer, also containing 25 mM HEPES (4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid). The difference in sugar densities caused sucrose-filled vesicles to sediment to the bottom of the incubation chamber.
The experiment inducing attachment/detachment of nanostructures to the membrane (described in Fig. 4 of the main text) was performed with a 48 bp-long 2C (2 x cholesterol) duplex. Initially, no Mg 2+ was present in the chamber; it was subsequently added after recording a number of frames, to a final concentration of 4 mM, without disrupting acquisition. Upon observing DNA attachment, EDTA was added to the chamber to a final concentration of 10 mM. The next Mg 2+ addition increased its concentration to 20 mM. All of the added substances were diluted in osmotically balanced glucose buffer. Images were recorded every 10 s, with a sampling speed of 2.0 µs/pixel, and FIJI 5 was used to measure changing intensity of the DNA vesicle coating.
In order to avoid GUV disruption or drift, the Mg/EDTA solutions are gently added to the surface of the chamber, without active mixing. Therefore, the changes in the attachment are only detected after the ions/chelating agents have diffused to the observed part of the chamber. As the diffusion rate for Mg 2+ at room temperature (≈ 25 °C) is reported to be in a range of [100, 1000] µm 2 /s 6 , we do expect a delay on a minute scale in the diffusion on millimeters distances. FRAP measurements were performed to confirm the presence of gel and liquid phases in the experiments, the results are collected in Supplementary Fig. 6. Using the FRAP function of the microscope's software (tornado mode), a spot of Ø4.4 μm was bleached and the fluorescence recovery observed. 10 frames were collected pre-bleaching. Bleaching was performed over 0.5 s with 99% laser power and the fluorescence recovery was recorded for 100 frames.
Collected recovery curves were fitted using exponential function (1).
where fluorescence intensity in time , fitting parameter, final intensity after recovery, -recovery time constant was then used to calculate recovery half-time as in (2) where radius of bleached area. 7 For the experiments presented on Fig. 3, series of representative images from across the sample were collected for 2C, 1C and ss1C (D1 in Tab. S1) structures, incubated in magnesium concentration varying from 0 to 4 mM. The intensities of vesicles were measured, and an average value (Gaussian fit to histograms) for every condition was obtained and presented in Table S2, as well as on the plot in Fig. 3b. The error bars represent Gaussian RMS width. Data points were fitted to a Hill function (4): where fluorescence intensity, maximum intensity observed, [ ] ion concentration, Hill coefficient, ion concentration associated with 50% of maximum attachment ( = 0.5) The dissociation constants were then calculated using equation (5)

= (5)
The parameters obtained for each studied structure are collated in Table S3. We have opted for the Hill function in order to describe empirically ion-nucleic acid interactions, as done previously 8 10 . However, it must be noted that the equation was employed here to allow an illustrative comparison of studied constructs, rather than as a mathematical model of the underlying process. Therefore, the calculated parameters do not necessarily carry the meaning most frequently ascribed to them.
In the case of temperature ramps presented in Fig. 1, borosilicate glass capillaries (CM Scientific, with internal section of 2 mm × 0.2 mm) were cleaned by sonication cycles of 15 min (Hellmanax III [purchased from HellmaAnalytics] at 2%/Isopropanol/milli-Q water). Once dried, they were passivated by filling them with a solution of bovine serum albumin (BSA) 0.1% and incubated at 60°C for one hour. They were subsequently cleaned with water to remove excess of BSA, and filled with vesicle samples. The sides were sealed using a two component epoxy-resin hardener onto a clean glass cover slip. The coverslip was fixed to a custom-built copper plate connected to a Peltier element using aluminium tape and coupled to a thermocouple for temperature control. Micrographs of these systems were acquired using a Leica TCS SP5 confocal microscope equipped with an HC PL APO CORR CS 40× / 0.85 dry objective. NBD (excitation maximum 490 nm; emission maximum 525 nm) and Cy3 (excitation maximum 550; emission maximum 570 nm) fluorophores were tracked using an Ar-ion (488 nm) laser and a He-Ne (543 nm) laser lines, respectively. Data points were collected every 5 °C between 20 and 40 °C, and every 1 °C between 40 and 50 °C. The sample was equilibrated for a minute upon each temperature change. To assess the kinetics of the DNA desorption upon phase transition, the same experimental system was used to instantaneously cross the Tm of DPPC (increase from 35 °C to 50 °C), while imaging.

S4 DLS and zeta potential
The measurements were performed on a Zetasizer Nano ZSP (Malvern Panalytical) with an excitation wavelength of 633 nm and a scattering angle fixed at 173°. For assessing hydrodynamic radius, 100 µl of 10× diluted vesicles were measured. The ξ-potential measurements were performed in a DTS1070 cell, with Lognormal distribution curves were fitted to the obtained histograms of LUVs size, following function (6).
where 0 offset, center, log standard deviation, area.

S5 Assessment of DNA constructs' temperature stability using UV-Vis absorption spectroscopy
The effect of magnesium concentration on the stability of unmodified 48 bp DNA constructs (0C) was assessed using a UV-vis spectrophotometer (Cary 300 Bio, Agilent); thermal studies were performed in order to obtain melting curves of the structures. 100 μl of 1 μM DNA sample folded in the stated concentration of MgCl2 were heated from 10 to 90°C, with a heating rate of 1°C/min. Absorbance spectra were collected at 260 nm, and the melting temperature was obtained from the median of the two linear regions (upper and lower). The data, and their analysis, were processed using Origin software for all measurements taken. Similarly, the melting profiles for the unmodified 36 bp duplex were acquired in quartz cuvettes filled with 1.1 mL of sample, capped with 400 μl of mineral oil and sealed to prevent evaporation. Absorbance measurements were collected over two contiguous temperature ramps: first cooling (90 to 10°C) and then heating (10 to 90°C) at a rate of 0.2°C/min. The melting profile of 36 bp dsDNA is shown in Supplementary Fig. 9, while the melting profiles of 48 bp DNA construct in a range of Mg 2+ concentration can be found in Supplementary Fig. 15.

S6 Native polyacrylamide gel electrophoresis (PAGE)
Polyacrylamide gel electrophoresis was used to confirm the proper folding of DNA designs. The gels were prepared at a concentration of 10% polyacrylamide, 0.5× TBE (Tris, borate, EDTA) and with 11 mM MgCl2, unless stated otherwise. Addition of 0.01 vol% ammonium persulfate (APS) (10%) and 6.7 × 10 -4 % N,N,N',N' Tetramethylethylenediamine (TEMED) were used to initialise polymerisation, which proceeded for an hour. Subsequently, 2 µl of a DNA sample was mixed with 0.4 µl of 6× loading dye (15% Ficoll R400, 0.9 % Orange G diluted in Mili-Q water), and then 2 µl of sample were loaded into the well. GeneRuler Low Range ladder (Thermo Fisher Scientific Inc.) was used as a reference. The gel was run in a Mini-PROTEAN R Tetra Cell (Bio-Rad), in 0.5x TBE with 11 mM MgCl2 (unless stated otherwise) at 100 mV for 90 min. Afterwards, the gel was immersed for 10 min in GelRed (Biotium), in order to stain the DNA. Imaging was performed on a GelDoc-It TM (UVP), and FIJI was used to analyse gel images.
The DNA samples were folded in TE buffer with different concentrations of magnesium: 0, 0.2, 0.5, 1, 2, 4 mM. Further experiments were performed with 11, 4, 1 or no magnesium in either the buffer or the gel itself, and run with DNA folded in respective Mg 2+ solutions. After running all four gels in the same settings (100 mV for 60 min), the position of bands was compared (Supplementary Discussion 4) to show the effect of charge screening on DNA.

S7 Dithionite quenching of NBD-lipids
The NBD quenching assay described in Fig. 4 was performed with the Olympus FluoView imaging setup described above. Here, the concentration of DNA was 0.11 µM, with no magnesium present in the chamber. Immediately preceding the assay, sodium dithionite was diluted in 1 M Tris (pH 10) to a concentration of 15 mM. This solution was further diluted in osmotically balanced glucose solution, from which 30 µl were added to the chamber. The final concentrations of DNA and dithionite were 0.08 µM and 4.5 mM, respectively. Images were recorded every 10 s, with a sampling speed of 2.0 µs/pixel. After the initial intensity decrease, magnesium chloride, diluted (50 mM) in the osmotically balanced glucose solution, was added to the sample to a final concentration = 4 mM. The imaging continued without interruption. As a control, the same experiment was performed with the 1C structure, which showed similar attachment upon magnesium addition, but no lipid flipping activity occurred (see Supplementary Fig. 19).

S8 Differential Scanning Calorimetry of DPPC vesicles
Differential Scanning Calorimetry (DSC) was performed on DPPC lipid vesicles using standard aluminum DSC pans in a PerkinElmer DSC 4000 instrument. Samples were heated from 20°C to 60°C at 1°C/min, equilibrated at 60°C for two minutes, and then cooled down to 20°C at the same rate. Throughout the ramp, heat flow (mW) was recorded for vesicles in both the presence and absence of dsDNA and Mg 2+ ions (see Supplementary Fig. 4).

S9 Molecular Dynamics Methods
General simulation protocols. All MD simulations were performed using program NAMD2 11 , a 2 fs integration time step, 2-2-6 multiple time stepping, periodic boundary conditions, and particle mesh Ewald (PME) method over a 1-Å resolution grid to calculate the long-range electrostatic interaction 12 . The Nose-Hoover Langevin piston 13 and Langevin thermostat were used to maintain the constant pressure and temperature in the system. An 8-10-12 Å cutoff scheme was used to calculate van der Waals and short-range electrostatic forces. SETTLE algorithm 14 was applied to keep water molecules rigid whereas RATTLE algorithm 15 constrained all other covalent bonds involving hydrogen atoms. CHARMM36 force field parameters described the bonded and nonbonded interactions among the atoms of DNA 16 , lipid 17 , water and ions 18 . Magnesium ions were modeled as magnesium hexahydrates (Mg[H2O]6 2+ ) 19 . Corrections to non-bonded interactions were applied to improve description of ion-DNA 19 , ion-ion, and DNA-lipid interactions 20 . The coordinates of the system were saved every 20 ps. The visualisation, analysis, and post-processing the simulation trajectories were performed using VMD 21 and CPPTRAJ 22 .
Initial models of fluid and gel phase membranes. The initial configuration of the 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine (DPPE) lipid bilayer membrane containing 64 lipids in each leaflet was generated from the CHARMM-GUI membrane builder 23 . A pre-equilibrated patch of 1,2-diphytanoyl-sn-glycero-3-phosphoethanolamine (DPhPE) containing 64 lipids in each leaflet was obtained from a previous study 2 . Both membranes were solvated with TIP3P water molecules 24 . Magnesium hexahydrade and chloride ions were placed randomly in the solvent at 300 mM concentration. Fully assembled DPPE and DPhPE membrane systems contained 30,410 and 48,288 atoms, respectively. Each system was first subject to energy minimisation using the conjugate gradient method, which removed steric clashes between the solute and the solvent. The systems were then equilibrated without any restraints for several hundreds of nanosecond in a constant number of atoms (N), pressure (P = 1 bar) and temperature (T = 300 K) ensemble. Anisotropic pressure coupling was used to maintain the constant ratio of the system's dimension within the membrane, allowing the system's dimension normal to the membrane to adjust independently of the other dimensions. Following that, Mg[H2O]6 2+ ions located approximately 30 Å away from the center of the membrane were removed, producing two systems of approximately 100 mM MgCl2 concentration. Each system was then in equilibration for additional 0.5 µs. ion with respect to the center of the membrane using a force constant of 2.5 kcal/mol/ Å 2 . The first 5 ns of the simulation was excluded, and WHAM was used to compute the PMF profile from the later part of the simulation trajectories.

PMF of single
Spontaneous binding of dsDNA to lipid membrane. A 21 base pair fragment of dsDNA was built using the NAB module 28 of AMBERTOOLs. The DNA fragment was made effectively infinite along its helical axis by linking the strands to themselves across the periodic boundary (along the y-axis) of the systems. A 10 x 7.1 nm 2 rectangular patch of either DPPE or DPhPE membrane was carved out from the equilibrated systems, matching the systems' dimension along the y-axis to that of the DNA. The DNA model was combined with that of each membrane, placing the DNA 5 nm away (along the z-axis) from the center of the membrane. The number density, n, of ions adsorbed to a membrane patch of area can be computed using the Langmuir isotherm model (8)  , of Mg 2+ . In our simulation setup, these Mg[H2O]6 2+ ions were uniformly distributed among the lipid head groups in each leaflet of the membrane with their z-coordinate set to the minimum of the respective Mg[H2O]6 2+ PMF. These DNA-membrane systems were then solvated with water; sodium and chloride ions were added to neutralize the total charge of the system. The fully assembled systems measured 10 x 7.1 x 14 nm 3 contains 96,329 (DPPE) and 91,542 (DPhPE) atoms. After a brief energy minimisation, the systems were equilibrated without any restraints for 1 µs a constant pressure (P = 1 bar) and temperature (T = 300 K); all system's dimensions were allowed to adjust independently to maintain the target pressure.
PMF of dsDNA. Starting from the microscopic configurations reached after approximately 0.2 µs free equilibration of the respective dsDNA/lipid membrane systems, 41 copies of each system were created using the frames from an 80-ns SMD simulation where the dsDNA's center of mass was moved from 20 to 60 Å along the z-axis. In contrast to the free-equilibration simulations, a separate colvars module (distance Z, spring constant 10 kcal/mol/Å 2 ) was used to ensure the z-coordinates of the MGHH 2+ ions remained at the minima (± 1 Å) of the respective single ion Mg 2+ PMF; the ions were free to move parallel to the plane of the membrane (x-y plane). Two additional systems containing no MgCl2 but 150 mM NaCl were built for each membrane type. Replica exchange umbrella sampling simulations were performed using the 1 Å sampling window for the DNA's center of mass z-coordinate which was maintained in each window using a harmonic potential with the spring constant of 2.5 kcal/mol/ Å 2 . Each replica was run for approximately 190 ns. The PMFs were reconstructed using WHAM 27 . To compute the PMF profile corresponding to 4mM bulk concentration of MgCl2, we removed all monovalent and divalent ions from the system, except 21 Mg[H2O]6 2+ ions which were required for neutralizing the charge of the DNA backbone. Additionally, we kept 3 and 1 Mg[H2O]6 2+ ions on the each leaflet of the DPPE and DPhPE membrane, respectively, in accordance with numbers prescribed by the Langmuir isotherm model for 4 mM bulk concentration. The initial configurations of the system in 41 sampling windows (varying in the center of mass z coordinate of the DNA with respect to the center of the membrane along z-axis from 20 to 60 Å) were obtained from the respective 20 mM replica systems. Each sampling window was simulated for 130 ns, WHAM was used to subtract the effect of the harmonic potential and obtain the PMF profile. The first 5 ns of the simulation trajectories were excluded from the WHAM analysis.

Supplementary Discussion 1. Effects of biologically-relevant cations on DNA-lipid bridging
The presence of high concentration of monovalent cations in cellular fluids has significant implications for the bridging phenomenon observed between gel-phase membranes and non-cholesterolized DNA duplexes, mediated by divalent cations. Since the efficiency of cation-mediated bridging has been shown to depend on monovalent/divalent ion ratio 30 , we hypothesized that the observed degree of attachment would vary in different cation mixtures, thus providing another route to fine-tune NA-lipid interactions. In order to exemplify this concept, we have chosen to work with compositions that mimic that of the intercellular media 31 , where we introduce 100 mM Na + as the monovalent "base" of the solution, and later add different divalent cations at various concentrations (Supplementary Figure D1.1).
As expected, no DNA attachment is observed in the absence of divalent cations. Adding 1 mM Mg 2+ results in a faint DNA coating, significantly less pronounced than that observed with 1 mM Mg 2+ in the absence of sodium. This observation confirms that the competition between divalent and monovalent ions weakens bridging, and can be potentially used to modulate DNA-membrane adhesion. At higher, but still biologically-relevant concentrations, magnesium can outcompete sodium, as demonstrated by the strong DNA attachment observed with 20 mM Mg 2+ . We have then carried out analogous experiments exploring the competition of sodium with calcium, instead of magnesium. Fluctuations in Ca 2+ concentration bear a particular biological relevance owing to the pivotal role that intercellular calcium waves play in coordinating cellular responses 32 . We have observed that, when present at the same concentrations tested for Mg 2+ , Ca 2+ induces a much stronger bridging action, consistently with previous observations of lower sensitivity to the competing effect of monovalent cations 33 . The results presented in Supplementary Fig. D1.1 highlight how the mechanisms for ion-mediated DNA-lipid interactions are sensitive not only to ion concentration, but also to ion identity and the composition of ionic mixtures. For instance, our findings suggest that in certain ion mixtures an increase in calcium content could induce DNA attachment, while a similar change in magnesium concentration will not generate a strong response. It is thus possible to envisage updates in the design of DNA nanostructures specifically aimed at enhancing ion-selectivity, opening up a whole new range of possible targeting mechanisms and responses, e.g. sensitive to ion-mediated signalling and enzymatic action 34 . Additionally, the nanodevices could be made sensitive to deregulated ion transport, which is often a hallmark of a damaged cellular functioning, with altered Ca 2+ signalling in cancer cells being one particularly illustrative example 35 .
Despite the zwitterionic nature of the PC head group, we observe a negative ξ-potential (-12.2 ± 0.2 mV) for the LUVs in solution with no added salt. The net surface charge is thought to emerge from the orientation of the PC head group, in which the positively charged choline moiety arranges itself towards the bilayer core, leaving the anionic phosphate more exposed to the solvent 36,37 . The negative surface charge explains the lack of DNA attachment in the absence of cations 38 . After the addition of magnesium ions, the surface charge is screened (ξ-potential = -0.5 ± 0.1 mV), suggesting cation adsorption to the surface, which may in turn lead to DNA adsorption through bridging. Once the system is heated up, causing the vesicles to transition to the liquid phase, the ξ-potential drops back to -9.0 ± 1.0 mV, indicating magnesium desorption. The reversible attachment of DNA can also be observed via ξ-potential measurements: the ξ-potential of DNA-coated vesicles reaches -2.7 ± 0.2 mV, and drops to -7.1 ± 0.7 mV after heating the samples above the transition temperature of the membranes.
Measurements performed on liquid-phase POPC vesicles in the absence of salts, however, result in a value of ξ-potential similar to the one recorded for gel-phase DPPC, suggesting that factors other than surface charge regulate adsorption of cations onto PC bilayers, and thus DNA adhesion.

Supplementary Discussion 3. Effects of biologically-relevant cations on DNA-lipid screening
We have performed additional studies to compare the ability of all four major biologically-relevant cations, monovalent potassium (K + ) and sodium (Na + ), and divalent magnesium (Mg 2+ ) and calcium (Ca 2+ ), to modulate the attractive interaction between ss1C constructs and POPC bilayers through screening. Comparing the two divalent ions (Supplementary Fig. D3.1a), we have established that Ca 2+ has higher screening efficiency than Mg 2+ , in agreement with the previously observed higher affinity of calcium for DNA 33 . Similarly, sodium has higher screening efficiency than potassium, again consistently with the greater affinity of Na + for nucleic acids 39 41 . The difference is possibly also influenced by the greater tendency of K + to form clusters with Cl -, hence reducing the number of potassium cations available for DNA binding 39 . Interestingly, comparing the behavior of cation species of the same valency shows that their different affinities agree with their order in the Hofmeister series (by ion-hydration: Na + > K + , Ca 2+ > Mg 2+ ) 42 , which classifies ions with respect to their effects on proteins. Such agreement can hint on the involved molecular phenomena, and also suggests another point in which the similarity between DNA and proteins can be exploited for mimicking membrane structures.
Importantly, the concentrations of the two monovalent cations differ between biological environments, with potassium dominating in intra-cellular and sodium in inter-cellular fluids ( Supplementary Fig. D3.1b). Therefore, the observed differences in screening efficiency, leading to different levels of DNA-lipid interactions, can be potentially exploited for in vivo nanotechnological applications, and bear potential relevance for biological phenomena.
The histograms in Supplementary Fig. D3.1c present the fluorescence intensity measured from a cholesterolmodified DNA construct (ss1C) for concentrations of monovalent cations approximately representing those encountered in key cellular compartments (5, 10 and 100 mM). In this respect, mitochondria and nuclei are of particulate interest, as the former exhibit lower 43,44 , and the latter higher 31,45 cation concentration compared to the cytoplasm. These differences could be directly exploited in further studies to construct DNA probes that target specific organelle membranes. Note, however, that experiments shown here are performed on model, singlecomponent bilayers, so further investigations would be required to address the potential effects arising for the complex chemistry of biological membranes.

Supplementary Discussion 4. Charge screening studied with PAGE
One may argue that the observed dependency of the fluorescent intensity of membrane-adsorbed DNA on cation concentration might be influenced by artefacts associated with the decreased stability of the DNA duplexes at low ionic strength. Indeed, for both the duplex nanostructures (1C and 2C), the cholesterol(s) and the fluorophores are covalently linked to separate single-stranded components ( Supplementary Fig. 1), thus if the nanostructures were to disassemble at low ionic strength one could still have non-fluorescent cholesterolmodified DNA localising on the membranes, and the hydrophilic fluorescent strands remaining in solution.
We ruled out this artefact by performing PAGE analysis, showing that at the studied magnesium concentrations the majority of DNA strands are indeed assembled into duplexes (Supplementary Fig. D4.1). Representative intensity profiles recorded from two different gels at 0 and 4 mM Mg 2+ are shown in Figure 3c, for the case of 2C motifs. In the absence of salt, a small proportion of the constructs did not assemble properly (grey triangle), however most of the strands -85% -formed the designed 48-bp duplex (turquoise triangle), as indicated by the size reference. Expectedly, single-stranded components were not observed in samples prepared at 4 mM Mg 2+ . The difference in migration distance recorded in the two different gels, and explored further in Supplementary Fig. D4.2, is ascribed to the effect that shielding the negatively-charged phosphate has on the rate of migration 46 Fig. 1. (a) Melting profiles (absorbance at 260 nm) collected for the 36 bp duplex used in the temperature-controlled experiments. Measurements of the sample containing 1 and 0.1 µM DNA were conducted in the presence of 1 mM MgCl2, and in both cases the melting transition is found above the temperature range relevant for the experiments summarized in Fig. 1c: [20,50] °C (highlighted in orange). The data were normalized to the initial value of each set. (b) Melting profiles obtained for the same structure via NUPACK 1 analysis, showing that with increasing DNA concentration the melting temperature also increases. Given the adhesive effect driven by Mg 2+ -mediated bridging, we expect the concentration of DNA to be higher at the membrane interface than in the solution (0.1 µM), which further supports ruling out temperature instability as a possible source of artefacts impacting our results. Figure 10. Co-localization of DNA nanostructures and NBD-PC in de-mixed 15% cholesterol/DPPC vesicles. Representative micrographs, alongside average intensity values of the two phases (liquid ordered and gel) stated in arbitrary units, illustrate the lateral partitioning of NBD-PC lipids. The colocalization of the fluorescent signals from the DNA and NBD suggests that they both tag the gel-phased domains of the membrane. Scale bar represents 5 µm.  Fig. 3b in the main text. The three DNA constructs bear Cy3 as fluorophore, depicted as a circle in orange. Figure 19. Lipid-flipping activity is only induced by membrane-spanning DNA nanostructures. Representative fluorescence trace of NBD-labelled lipids (blue) upon addition of dithionite, alongside the trace of Cy3-labelled (1C) DNA construct (black), coating the vesicle after addition of magnesium (arrow). Note that, unlike its analogue 2C, the 1C nanostructure does not insert into membranes, and thus does not create a toroidal pore. Therefore, after DNA attachment, significant bleaching of NBD is not observed. This assay serves as a control for the Mg 2+ -triggered flipping activity experiment (Figure 4d Table 3. Average fluorescence intensity from the DNA coating of vesicles incubated in varying magnesium concentrations for the structures tested in Fig. 3 and shown in Supplementary Fig. 1. The values were normalised to the peak value for 2C intensities in 4 mM magnesium.