1 A minimalist model lipid system mimicking the biophysical properties of Escherichia coli’s inner membrane Nicolo Tormena1, Teuta Pilizota*,2,3, Kislon Voitchovsky*,1 1. Physics Department, Durham University, South Road, Durham DH1 3LE, UK 2. School of Biological Sciences and Centre for Engineering Biology, The University of Edinburgh, Alexander Crum Brown Road, Edinburgh, EH9 3FF, UK 3. Department of Physics, University of Cambridge, JJ Thompson Avenue, CB3 0HE, Cambridge, UK *Correspondance: tp579@cam.ac.uk, kislon.voitchovsky@durham.ac.uk Abstract Biological membranes are essential for the development and survival of organisms. They can be highly complex, usually comprising a variety of lipids, proteins, and other biomolecules organised around a lipid bilayer structure. This complexity makes studying specific features of biological membranes difficult, with many research studies relying on simplified models such as artificial vesicles or supported lipid bilayers. Here, we search for a minimal, lipid-only model system of the Escherichia coli inner membrane. We aim to retain the main lipidomic components in their native ratio while mimicking the membrane's thermal and mechanical properties. Based on previous studies, we identify 18 potential model systems reflecting key aspects of the known lipidomic composition and progressively narrow down our selection based on the systems’ phase transition temperature and mechanical properties. We identify 3 ternary model systems able to form stable bilayers that can be made of the commercially available synthetic lipids 16:0-18:1 phosphatidylethanolamine (POPE), 16:0-18:1 phosphatidylglycerol (POPG), and 16:0-18:1 Cardiolipin (CL). We anticipate our results to be of interest for future studies making use of E. coli models, for example, investigating membrane proteins’ function or macromolecule-membrane interactions. mailto:tp579@cam.ac.uk mailto:kislon.voitchovsky@durham.ac.uk 2 Introduction All types of organisms, from prokaryotic to eukaryotic, separate their internal environment from the exterior using biological membranes that consist of a self-assembled and self-synthesized double layer of phospholipids with a hydrophobic matrix in which a large number of proteins and sugars are bound or embedded 1. The function of biological membranes is multifold, first acting as a physical barrier, but also serving as a unique environment for many biological processes 2–5. The prokaryotic cell envelope consists not only of the cell membrane(s) but also of a cell wall, a structural layer made of a peptidoglycan matrix 6. In Gram-positive bacteria, the cell envelope is composed of one plasma membrane and a thick external peptidoglycan layer, while Gram-negative bacteria are characterized by a thinner cell wall that separates two phospholipid membranes called inner and outer membranes, respectively 7. Because of its fast growth rate, genetic simplicity and ease of culturing, Gram-negative Escherichia coli is one of the most common and well-studied model organisms, and as such of great importance for biotechnology and human health 8–14. E. coli's inner and outer membranes present a plethora of specific proteins and the inner membrane acts as a capacitor for ions, allowing the generation of electrochemical gradients that contribute to powering the cell 2. Both membranes share a broadly similar phospholipid composition, with slight variations in phosphate headgroup and acyl chain distribution15–20. The outer membrane also contains lipopolysaccharides (LPS), which are absent in the inner membrane and contribute to its defensive and permeability functions. The composition and biophysical properties of the membranes are known to adapt to the environment15–17 and have been demonstrated to have compositional asymmetry between the two lipid leaflets21,22. These features add to the challenge of developing a suitable model E. coli membrane system, with various studies often taking different approaches 23–32. For example, some studies omit cardiolipin, a key component of E. coli membrane23,24, while others use a wide range of phospholipid headgroups with different alkyl chain lengths25–30, with or without cardiolipin. Furthermore, the biophysical properties of the model membranes are rarely investigated despite being crucial for the structural stabilization, active functionality, and localization of membrane proteins31,32. Given the complexity of E. coli membranes and their dependence on the environment, even the best model systems are unlikely to capture all of the native membrane’s properties, but broadly replicating the native lipidomic ratios and biophysical properties would already provide a valuable basis for a wide range of studies33,34. This is the aim of the present study. Our strategy relies on previous lipidomic studies15–20,35,36 to identify binary and ternary lipid combinations that recapitulate the main aspects of E. coli’s inner membrane lipidic composition and stoichiometry at standard growth temperature (37 °C). We then narrow down possible models by comparatively testing their thermal and mechanical properties against the native membrane, using a combination of differential scanning calorimetry (DSC), atomic force microscopy (AFM), and optical microscopy. The main transition temperature (Tm) is used to quantify the systems’ thermal characteristics, noting that Tm also offers good indications of how the membrane behaves mechanically: at Tm the thermal 3 energy overcomes the internal energy of the membrane which is dominated by the average inter-lipid interaction energy. The internal energy influences both molecular order and dynamics within the membrane37, and hence the propagation of any imposed mechanical stress. We directly access the mechanical properties of the membranes by measuring elastic modulus 𝑌𝑌, and from it, we estimate the stretching modulus 𝐾𝐾𝑎𝑎, equivalent to first Lamé coefficient. This is justified by the fact that the Helmholtz free energy of the E. coli ‘s inner membrane consists of the stretching and turgor pressure energies38, with the bending energy being generally negligible38 and the fact that fluid membranes cannot support in-plane shear39. Practically, we narrow down 18 possible combinations of the three main lipids present in E. coli and identify three mixtures that form stable and reproducible E. coli model membrane systems with the desired biophysical characteristics. Materials and methods All chemicals and lipids were obtained from commercial sources and used without further purification. Lipids All the lipids were purchased from Avanti Polar Lipids (Alabaster, AL). The following lipids were purchased and dissolved in chloroform: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE), 1-palmitoyl-2- oleoyl-sn-glycero-3-phospho-(1’-rac-glycerol) (POPG), and 1’,3’-bis[1-palmitoyl-2-oleoyl-sn-glycero-3- phospho]-glycerol (CL). 1,2-dipalmitoyl-sn-glycero-3-phospho-(1’-rac-glycerol) (DPPG) was obtained in powder form. The native E. coli membranes (37 °C growth) were obtained as E. coli Extract Polar (comprising only the polar lipids component) and E. coli Total Extract (full lipid extract) already dissolved in a chloroform- methanol solution. These membranes were obtained from E. coli B (ATCC 11303) grown in Kornberg Minimal media at 37 °C, as described by Avanti. We note that most studies on E. coli membrane lipidomic composition as well as the majority of modern-day microbiology studies rely on K-12 strain isolates. These two commonly used E. coli strains present highly similar genomes, which mainly diverge in their proteomic profiles 40,41, but no alterations have been detected in their lipidomic profile nor on the key proteins involved in phospholipid synthesis, confirming the highly conserved composition of E. coli membrane within different strains. Chemicals Salts (all >99% purity) were purchased from Sigma-Aldrich (Dorset, UK) and dissolved/diluted in ultrapure water (at 18MOhm obtained with Merck-Millipore, Watford, UK). MOPS buffer-based solution was prepared with specific ion concentrations as follows: 50 mM NaCl, 9.5 mM NH4Cl, 0.5 mM MgCl2, 0.3 mM K2SO4, and 1μM CaCl2-2H2O. The pH was adjusted to 6.5 prior to mixing with lipids. 4 Large multilamellar vesicles preparation Lipids dissolved in chloroform were mixed following the appropriate molar ratios into a 4 mL glass vial, pre- dried under a gentle nitrogen flow, and fully dried overnight in a vacuum chamber. Large multi-lamellar vesicles were obtained by freeze-thawing 42,43. Briefly, the lipid film was rehydrated in 2 mL of MOPS buffer- based solution to obtain a lipid concentration of 10 mg/mL and then briefly heated while sonicating in the sonication bath. Subsequently, the vial was frozen (left in the freezer for 15 min). This heating-freezing process was repeated for 6 consecutive cycles to successfully form large multilamellar vesicles (LMVs), which was confirmed by the lower turbidity of the solution and optical microscopy imaging. Unilamellar vesicles preparation Lipids were mixed and dried following the same protocol for the LMVs preparation. The lipid film was subsequently rehydrated in 1mL of MOPS buffer-based solution, obtaining a lipid concentration of 1mg/mL. The vial was gently bath sonicated for 15 min at a temperature 5-10 °C higher than the highest Tm of the lipid species in the mixture until the solution looked milky, indicating the formation of multilamellar vesicles. For small unilamellar vesicles (SUVs), the solution was extruded 31 times using a Mini-Extruder kit (Avanti Polar Lipids) with 1 Whatman 100 nm filter (GE Healthcare Life Sciences, Little Chalfont, UK). Supported lipid bilayers preparation The SUVs solution was diluted 5 times to reach a 0.2 mg/mL concentration. 100 μL of the SUVs solution was deposited on a disk of Grade 1 freshly cleaved Muscovite mica (SPI Supplies, West Chester, PA, USA). The disk, already mounted on the AFM stage, was left incubating for 20 min at 50 °C, covered with a Petri dish. The sample was then gently rinsed with MOPS-buffer to remove any unfused lipid SUVs. The temperature was then cooled down to 40 °C and equilibrated for 15 min, as a starting point for the measurement. The salt concentration in the MOPS buffer is sufficient to ensure the formation of a spread and uniform supported lipid bilayers (SLB) system over the flat mica surface. Differential Scanning Calorimetry (DSC) To observe the lipids main melting transition and extract the associated melting temperature values, DSC measurements were performed on a DSC 2500 (TA Instruments, Delaware, USA). Preliminary DSC heating tests were performed to identify ideal lipids concentration and DSC scan parameters, and to ensure satisfactory signal to noise ratio and reproducibility of the data (Figure S1): with DSC, faster scan rates tend to provide a better signal to noise ratio, but potentially lower temperature resolution. DSC test runs on binary lipid mixture were performed with increasing lipid concentration (from 1 mg/mL up to 10 mg/mL) and heating scan rate (from 2 °C/min up to 10 °C/min) while maintaining the temperature scanning range of -10 °C – 60 5 °C (Figure S1 A, S1 B). Since the scan rate can shift the experimental melting point, DSC cooling experiments were performed with the same increasing scan rates (from 2 °C/min up to 10 °C/min) and temperature range (Figure S1 C, S1 D). This enables us to infer the melting point of our reference mixture at 0 °C/min scan rate (thermodynamic equilibrium) and therefore quantify the effect of the scan rate on the experimental melting point (Figure S1 E). The dependence of the measured transition temperature on the scan rate is not trivial, with previous studies 44,45 reporting the following nonlinear behaviour: 𝑇𝑇𝑚𝑚,𝛽𝛽 = 𝑇𝑇𝑚𝑚 + 𝐵𝐵𝛽𝛽𝑧𝑧 (1) Where 𝑇𝑇𝑚𝑚,𝛽𝛽 is the measured melting temperature at each scan rate, 𝑇𝑇𝑚𝑚 is the equilibrium or ‘true’ melting temperature, 𝛽𝛽 is the scan rate, and 𝐵𝐵 and 𝑧𝑧 are fitting parameters. Experiments run at different scan rates enabled us to determine 𝐵𝐵 and 𝑧𝑧 to subsequently correct all the measured transition temperatures (see fits in Figure S1 E). All other experiments were performed as follows: 10 μL of LMVs solutions at 10 mg/mL were loaded into the calorimeter and a heating rate of 5 °C/min was used in a temperature range of -10 °C – 60 °C. Samples were equilibrated for 5 min at the starting temperature (-10 °C) before starting the measurement. Three independent samples of each mixture were analysed separately to ensure reliable statistical analysis. Optical brightfield microscopy Images of LMVs were taken using an Eclipse E200 (Nikon) microscope with 10× and 40× phase contrast objectives. Vesicles were imaged in a tunnel slide prepared as previously reported 3,46. Briefly, two parallel strips of double-sided sticky tape were positioned onto a microscope slide and covered with a 22 mm × 40 mm cover glass, which was then pressed against the tape to form a tunnel. Approximately 10 µl of vesicles in solution was added to the tunnel for imaging. Pixel size was calibrated using a coverslip presenting a 10 x 10 square grid with 0.1 mm spacing (Graticules Optics). Atomic Force Microscopy Imaging was conducted using a commercial Cypher ES AFM (Oxford Instruments, Santa Barbara, CA, USA), equipped with temperature control. SNL-10 cantilevers (Bruker Scientific Instruments, Billerica, MA, USA) with a nominal spring constant of 0.35 N/m were used. The tip has a pyramidal shape with a tip radius. of less than 12 nm at its apex. The AFM imaging was performed in amplitude modulation, fully immersing the sample and cantilever/tip in the liquid. The cantilever was acoustically oscillated at a frequency close to its resonance in liquid (~10 kHz), with the images acquired while the oscillating tip raster scans the surface while keeping the oscillation amplitude constant. Force spectroscopy mapping was conducted in contact mode (no acoustic excitation). A schematic illustration of the measurement principle is shown in Figure S2. A force map was created from 1024 force curves (32 x 32) over a 25 µm2 area. Calibration of the cantilever’s spring constant was performed by first determining its 6 inverse optical lever sensitivity from a force-distance curve acquired on a stiff surface (bare mica). The spring constant of each cantilever was subsequently determined from their thermal spectrum 47. This allowed for accurate derivation of the 𝑌𝑌 and membrane rupture force 𝐹𝐹𝑟𝑟 . For the analysis, we use the following relationship between the force 𝐹𝐹𝑠𝑠𝑠𝑠ℎ𝑒𝑒𝑟𝑟𝑒𝑒 applied by the tip (assumed locally spherical), the indentation depth 𝛿𝛿 of the tip into the membrane, 𝑅𝑅 the radius of curvature of the tip, and the membrane thickness ℎ 48: 𝐹𝐹𝑠𝑠𝑠𝑠ℎ𝑒𝑒𝑟𝑟𝑒𝑒 = 16 9 𝑌𝑌�𝑅𝑅𝛿𝛿3 �1 + 1.133√𝛿𝛿𝑅𝑅 ℎ + 1.497𝛿𝛿𝑅𝑅 ℎ2 + 1.469𝛿𝛿𝑅𝑅√𝛿𝛿𝑅𝑅 ℎ3 + 0.755(𝛿𝛿2𝑅𝑅2) ℎ4 � (2) where δ ≤ 𝑅𝑅. This formula was derived assuming a thin membrane on a much stiffer substrate, and that the Poisson ratio, which couples in-plane and out-of-plan strain is exactly ν = 0.5. In other words, the membrane is assumed incompressible with its volume conserved under compression. This assumption is common for bio-systems 49 and usually a good approximation, but it is not necessarily exact 50,51. In practice, the indentation of the membrane is carried out with an AFM tip, and ensuring a linear indentation regime 52 to derive 𝑌𝑌. Both 𝑌𝑌 and 𝐹𝐹𝑟𝑟 were obtained using a same tip for all the measurements to ensure direct comparability between the results, regardless of any possible systematic offset. The emphasis is hence not placed on the absolute stiffness values 53,54 but rather the relative differences between samples, with phases yielding the expected bimodal distribution. All the force maps over all the different samples were acquired with the same AFM cantilever/tip. The cantilever was cleaned with isopropanol and ultrapure water and calibrated before starting a new measurement to check its conditions. Moreover, to ensure the reliability of the results, AFM images were taken before and after the measurement, comparing the membrane’s topographical features. Data analysis DCS results were analysed with the TRIOS Software, provided by the instrument’s manufacturer. The software was used to correct thermogram baselines and then obtain Tm at the highest point of the calorimetric peak. DLS data was analysed using the Zetasizer Family Software v.8.01, provided by the instrument’s manufacturer. The size and of the vesicles and the associated uncertainty (standard deviation) was obtained by fitting the experimental size histogram with a Gaussian distribution. AFM images and topographical information (section profiles) were obtained using Gwyddion 55, an open-source modular software for scanning probe microscopy data visualization and analysis. Optical microscopy images were analysed using the open-source image processing package ImageJ/FIJI 56. Force spectroscopy data from indentation measurements were analysed using bespoke routines programmed in Igor Pro (Wavemetrics, Lake Oswego, OR, US) and Python 57. 7 Results and Discussion PE, PG and CL are the main lipid species in E. coli’s membrane The composition of E. coli ‘s inner membrane obtained from previous lipidomic and mass spectroscopy assays is summarised in Table 1. Where available, melting temperatures obtained from previous calorimetric studies15,17,58 are also shown. To control the thermal and mechanical properties of the model system, we need to consider: (i) the lipid polar head distribution which controls lipid-lipid interactions and charge distribution along the surface, (ii) the acyl chain length which controls membrane thickness, fluidity and membrane packing, and (iii) acyl chain saturation degree since it regulates lipid packing within the bilayer. Tm values are typically 7 °C to 16 °C lower than the growth temperature in a specific medium because E. coli membranes are fluid, dynamic, and able to rearrange composition through epigenetic reprogramming. Polar head distribution Lipid chain length Lipid species Concentration (%) Chain length Concentration (%) PE 7516,18, 70-7835, ~8036, 81.720, 6259 12C 016, PG 1916, 2018, 11-1835, ~1536, 6.520, 1459 14C 416,1-335, 3-558, 4.720 CL 7-1235, ~536, 2459 16C 74.716,63-7335, 43-7458, 67.120 17C 7-2235, 7-2958, 4.420 18C 16.316, 8-2135, 1958,23.320 Chain saturation degree E. coli membrane melting temperature Saturation degree Concentration (%) Growth T (°C) Tm (°C) Saturated 48.516, 46-38.960,47-5635, 39.420 17 1015,1017 Unsaturated 46.916, 32.4-3.760, 44- 5335, 64-5258, 60.620 27 1515 Cyclized 0.7-32.560 37 28.515,21.317, 25<58 Table 1. Summary of the E. coli inner membrane’s composition and properties, when grown at the standard growth temperature of 37 °C (upper part) and variation of E. coli membrane melting temperature based on growth temperature (lower part). The data compiles results obtained from published literature. Here we focus on mimicking the inner membrane of E. coli grown at physiological temperature (37 °C). The Tm of the model membrane should therefore be lower than 30 °C while maintaining the lipid polar headgroup ratios, chain length, and the overall degree of saturation as close as possible to that of the native membrane. From Table 1, the reported compositional ratios of E. coli inner membrane vary by up to 20% 16,18,35,36,59, but all studies suggest that the main lipid species are phosphatidylethanolamines (PEs, 60-80% molar ratio) 8 followed by phosphatidylglycerols (PGs, 15-30% molar ratio) and other minor lipids. Within these minor species, the most abundant is cardiolipin (CL, ~5 %), which, due to its unusual structure (see Figure S3), plays a crucial role in the membrane’s physiological behaviour, including mechanotransduction 61–63. We, therefore, include CL in our candidate model membranes. Apart from CL, most lipids in E. coli's inner membrane show long carbon chains (>16C), with an even distribution between saturated and unsaturated lipid chains. Cyclized lipid chains are also found in relatively high concentrations in the inner membrane 60, and are known to significantly reduce the lipid packing density 25. Mass spectroscopy results show that the three most common lipid chains are C16:0, C18:1, and the cyclized C17:1 (cyC17:1) 64. The cyclized lipids have been reported to influence membrane fluidity thanks to their cyclic motifs 65. However, because cyclized lipids are rare in other organisms and not commercially available, and keeping with our goal of a simple model system, we focus here on more common non-cyclized lipids. This limitation is mitigated by the inclusion of CL, which has been shown to exert similar fluidity modulation 66,67 as other bacterial-specific lipids such as hopanoids 68. Moreover, CL introduces additional biologically relevant features, including membrane curvature regulation 69 and the formation of protein-interaction motifs 62, representing a crucial element for the E. coli membrane function. Based on our literature review, we devised 18 different lipid mixtures by systematically varying the stoichiometries of the four main lipid types in 5% steps around the reported values for E. coli’s inner membrane grown at 37 °C (Table 2). For simplicity, we use binary and ternary mixtures of POPE, POPG (both lipids with 16:0-18:1 chains), DPPG (16:0 chains) and CL (2 chains 16:0 and 2 chains 18:1), which all theoretically match the structural requirements for native E. coli inner membrane. POPE and CL were selected for their acyl chain compositions, which closely match the natural pattern of the E. coli inner membrane (Table 1), and present two of the most common lipid chains in this bilayer 64. On the other hand, both POPG and DPPG could work as the PG source for the E. coli-like model because they exhibit the most common acyl chains in these bacteria. POPG is often used for its relatively low Tm (-2 °C), thus preventing phase separation in the membrane or the formation of ordered, raft-like domains. In contrast, DPPG has a transition temperature of Tm = 41 °C which is more likely to induce phase separation, but its two saturated acyl chains bring the overall molar ratio of unsaturated chains closer to the native ratio. Since the charged headgroup that characterize the PG family can, in principle, help prevent phase separation of DPPG, we kept both POPG and DPPG in our candidate model system. Mixture name POPE (%) POPG (%) DPPG (%) CL (%) 1-A 80 20 0 0 1-B 80 0 20 0 2-A 75 25 0 0 2-B 75 0 25 0 3-A 70 30 0 0 3-B 70 0 30 0 9 4-A 60 40 0 0 4-B 60 0 40 0 5-A 80 15 0 5 5-B 80 0 15 5 6-A 75 20 0 5 6-B 75 0 20 5 7-A 70 25 0 5 7-B 70 0 25 5 8-A 70 20 0 10 8-B 70 0 20 10 9-A 65 25 0 10 9-B 65 0 25 10 Table 2. Candidate lipid mixtures to be used as model systems for E. coli’s inner membrane, when grown at physiological temperature (37 °C). Each mixture contains two or three types of phospholipids: POPE, POPG, DPPG and CL (16:0-18:1). Mixtures are indicated with a number and a letter, with the number indicating a specific lipid molar ratio and the letter indicating the specific PG lipid used (“A” being POPG and “B” being DPPG). POPG Ternary mixtures successfully mimic E. coli inner membrane transition temperature Having identified candidate model membranes in Table 2, we next determine their melting temperatures. We use lipidic LMVs samples in a MOPS buffer-based solution (see Materials and Methods) and extract Tm for each sample from the DSC transition peak. The composition of MOPS matches the salt concentrations of commonly used E. coli growth media 70–72, but lacking the nutrients. LMVs are routinely used for this type of measurement because they enhance the signal-to-noise ratio (SNR) compared to other types of lipid vesicles 42,73–77. We selected a heating rate of 5 °C/min for optimal SNR and corrected it for kinetic effects 44,45 to infer the ‘true’ (i.e. thermodynamic equilibrium) Tm value (see Materials and Methods and Figure S1 for more details). We also analysed two commercial E. coli membrane extracts that we refer to as E. coli ‘Native’ and E. coli ‘Polar Extract’. E. coli Native is a direct lipid extract from both E. coli membranes, while E. coli Polar Extract has been further purified to remove unknown lipid species. The PE and PG ratios in the Polar align closely with most literature-reported values for the inner membrane. However, a recent study on the PE composition of E. coli reports ~60% PE for the inner membrane, closer to the E. coli ‘Native’ PE composition. We hence keep both extracts as references (Table 1). Unlike for the native extracts, the composition of the synthetic lipid mixtures is precisely controlled, allowing us to isolate the effects of specific lipids and acyl chain structures. This reduction in complexity enables more tractability for studies aiming to ascribe observations to specific molecular effects. In contrast, lipid extracts, while more biologically representative, often contain uncharacterized species and high heterogeneity. 10 Figure 1 displays the result from the DSC analysis, with our candidate samples graphically summarised in Supplementary Figure S4 A-C. In line with previous lipidomic studies (Table 1), E. coli Native and Polar Extract mixtures exhibit Tm = 22.7 ± 0.3 °C and Tm = 20.7 ± 0.4 °C, respectively. Mixtures containing POPG show a significantly lower melting point than those with DPPG, with an average 8-10 °C gap between equivalent mixtures. These differences reflect the Tm difference between the two pure lipid species and suggest their homogeneous mixing in POPE. The measured Tm values are in agreement with a previous work 78, where Tm of some of our binary mixtures have been previously tested, strengthening our DSC results. Moreover, the presence of a unique main peak in the DSC curves (see Figure S5) and its 20-40 kJ/mol change in enthalpy (see Figure S6) are also consistent with the melting transition of a homogenous lipid membrane 79. All mixtures exhibit a Tm lower than 37 °C – our reference E. coli growth temperature. Ternary mixtures exhibit a more complex transition behaviour, without any obvious trend for Tm. This is expected from previous studies of CL-containing membranes 80–82. Figure 1. Melting temperatures of vesicles composed of the different model lipid mixtures aiming to replicate the behaviour and lipid composition of the E. coli inner membrane grown at 37 °C. The dashed box enclosed the values obtained for the native E. coli inner membrane in reference experiments. For each model systems, the DSC results are given for POPG (red) and DPPG (blue) as a PG source. All the averages and standard deviations are presented in Table S1, where theoretical, measured and corrected values are presented. Comparing the results in Fig. 1 to our reference E. coli Polar and Native Extract mixtures rules out the use of DPPG as a PG source for our model membrane. The best matching candidates are 3 different ternary mixtures: 80% POPE, 15% POPG and 5% CL (composition #5A), 75% POPE, 20% POPG and 5% CL (composition #6A) and POPE 65%, 25% POPG and 10% CL (composition #9A). Two binary mixtures also match E. coli Polar and Native Extract mixtures Tm: 80% POPE and 20% POPG (composition #1A) and 75% POPE and 25% POPG (composition #2A). These mixtures still reflect molecular ratios of the most abundant lipids reported for E. coli and might hence be sufficient for certain studies, provided CL is not critical. Interestingly, if considering the recent report of only ~60% PE content for the inner membrane59, our results suggest a unique candidate for the E. coli model membrane: POPE 65%, 25% POPG, and 10% CL (composition #9-A). 11 Mechanical properties of the candidate and E. coli membranes Before measuring the mechanical properties of the remaining candidate systems, it is necessary to demonstrate that the lipid mixtures can form stable and homogenous unilamellar vesicles, as well as smooth, stable supported lipid bilayers (SLBs). The formation of stable and homogenous SLBs from SUV deposition is not obvious because CL can affect the bilayer fluidity, evolution and membrane packing 83, sometimes inducing molecular rearrangement over time and precluding the formation of stable flat SLBs 66. Additionally, the formation of SLBs with PE and PG has been previously reported as challenging due to the negative charge of the PG headgroups, the conformation of POPE/POPG molecules 84 and the effect of PE lipids on membrane curvature 85. Here, we employed one of our candidate mixtures (MIX 6A) to check the stability of model membrane systems containing PE/PG and CL. Stable and homogenous SUVs were confirmed using optical microscopy (Figure 2A-B), showing rounded vesicles that remained stable for at least 14 days. Similarly, AFM imaging of candidate SLBs (Figure 2C) reveal smooth, stable patches. Here, SLBs were formed on an atomically flat mica surface using extruded 100 nm SUVs (see Materials and Methods). By working at a relatively low SUV concentration, isolated membrane patches could be formed and imaged, confirming the presence of a single, stable lipid bilayer in fluid phase. The patches thickness of 4.7±0.1 nm is in line with the expected thickness for such fluid bilayers 86 (Figure 2D). Increasing the SUV concentration enabled full substrate coverage with a membrane exhibiting only minor defects (see Figure S7). Figure 2. Demonstration of stable membrane formation with the candidate mixture 6A. In bulk solution (A-B), optical microscopy (phase contrast) shows the formation of stable vesicular model membrane systems for the ternary POPE-POPG-CL mixture. Images of spherical lipid vesicles formed with the mixture were taken with 10× (A) and 40× (B) objectives. 1 μm size vesicles have been indicated with red arrows for clarity (B). The vesicles were stable for two weeks after preparation. Stable SLBs could also be formed on a mica substrate in solution (C-D) with patches visible. AFM imaging (C) quantifies the thickness of a typical patch with an associated line profile (D). The scale bars are 50 μm (A – 10× objective), 13 μm (B – 40× objective) and 100 nm (C). 12 Perpendicular compression of the membrane The mechanical properties of the membranes, namely 𝑌𝑌 and 𝐾𝐾𝑎𝑎, are quantified from AFM nano-indentation measurements. For simplicity, we assume the membrane behaves as a homogenous isotropic solid, in line with the single DSC peak. AFM can also distinguish between domains in different phases, ensuring membrane homogeneity on the scale of the measurement. Following this assumption, we use thin plate theory 87,88 to relate Ka and 𝑌𝑌 through the well-known relationship: 𝐾𝐾𝑎𝑎 = 𝑌𝑌ℎ 2(1 −𝜈𝜈) (3) where 𝑌𝑌 is experimentally measured by AFM, ℎ is the membrane thickness and 𝜈𝜈 its Poisson ratio. AFM nano- indentation on SLBs requires correcting the established Hertz indentation model 89 for the finite thickness of the membrane and the hard substrate underneath48,52 (see Eq. (2) in Materials and Methods, and Figure S2 for more details). We probed the Young’s modulus of mixtures 6A and 9A, and compared them with E. coli Polar extract obtained in the same manner. E. coli Native is again given for completeness. The two lipid mixtures reflect model systems with different CL content (5% for 6A and 10% for 9A), known to shape the fluidity of the bilayer and therefore its mechanical properties. The mechanical assays were also performed on two negative controls: the DPPG-based mixture 2B and a pure POPE, with both controls forming stable SLBs. In all cases, we distinguished the fluid pre-transition phase (when cooling) and the more ordered post- transition phase when conducting the measurements (Figure 3). The more ordered domains are 0.5 nm to 0.7 nm taller than the remaining pre-transition domains (see Figure S2A), consistent with the expected membrane thickness variation between the two phases 90,91. The relatively small differences between pre- and post-transition values for the E. coli samples and the MIX 6A and 9A come from the fact that both phases retain some level of molecular mobility (fluidity) albeit different; they represent different degrees of molecular ordering and should hence not be thought of as a fluid and a gel phases. 13 Figure 3. Analysis of the native and candidate model membranes using AFM nanomechanical indentation. (A) Membrane-averaged 𝑌𝑌 values, calculated from the indentation region of the curves (elastic indentation) and assuming a spherical tip (radius 12 nm, from manufacturer). The results confirm the mechanical similarities between the E. coli references and the two ternary POPE-POPG-CL candidate mixtures. (B) When increasing the indentation force, the tip eventually punctures the membrane. The rupture force 𝐹𝐹𝑟𝑟 is an indication of the bilayer strength and cohesion. For each sample, all the force spectroscopy data has been acquired at 2 °C below the Tm. For (A) and (B), the data is present as boxplots distinguishing the post-transition and pre-transition phases. The upper and lower whiskers extend to the furthest data point within 1.5 times the inter-quartile range, hence indicating the variability outside the upper and lower quartiles respectively. The overlayed scatter plot shows the nanomechanical values for each single indentation performed on the membrane. Examples of force maps and measurement principle are illustrated in Figure S2 B-D. We performed so-called force maps 53,92 whereby force-distance curves – the resistance experienced by the tip as it presses on the membrane – are systematically acquired across randomly selected regions of the membrane (see Figure S2C-D). From each curve, we immediately get 𝐹𝐹𝑟𝑟 90 and can calculate 𝑌𝑌. While adhesion forces can also be probed using AFM — particularly from the retraction segment of the force–distance curve — they are not included in our analysis. This is because our measurement involves the tip punching through the bilayer, making retraction features from the inside of the membrane difficult to interpret in terms of interactions between the tip and the surface of the membrane. However, no significant attractive features were observed in the approach curves, suggesting a low magnitude of adhesive interactions (Figure S8). Both E. coli extracts, and our two candidate mixtures show comparable values on the pre-transition phase (𝑌𝑌 ~ 17.5 MPa and 𝐹𝐹𝑟𝑟 ~ 3.0 nN) and the more ordered post-transition phase (𝑌𝑌 ~ 25.8 MPa and 𝐹𝐹𝑟𝑟 ~ 3.4 nN). All the averages and standard deviations are presented in Table S2. This similarity in mechanical properties is meaningful, as confirmed by the significantly different values obtained for the two negative controls (pure POPE and the DPPG-based samples). 14 In-plane stretching/compression of the membrane From the derived 𝑌𝑌 values and taking 𝜈𝜈 = 0.5 (incompressible membrane) and ℎ = 4.7 nm (obtained in Figure 2D) we can calculate 𝐾𝐾𝑎𝑎 using Eq. 3. The results, given in Figure 4, suggests 𝐾𝐾𝑎𝑎 values slightly lower than the average 0.2 N/m obtained through micropipette aspiration from previous reports on native E. coli spheroplast and artificial lipid vesicles 93–97. A separate study on monolayers of mixtures similar to our 1A and 2A reports 𝐾𝐾𝑎𝑎 values around 0.12 N/m 27, in line with our present results. The difference might be explained by AFM indentation measurements predominantly probing the top leaflet of the bilayer – effectively a monolayer. However, other sources of error may also be at play, including our assumption of the membrane behaving as a homogenous isotropic solid. Still, both our out-of-plane and in-plane mechanical estimates support mixtures 6A and 9A as a suitable composition to reproduce the biophysical properties of E. coli’s inner membrane lipids. Figure 4: Comparison of the 𝐾𝐾𝑎𝑎 values derived from the measured Y values through Eq. (3) for each phase of the different candidate membranes. The error bars represent two standard deviations. 𝐾𝐾𝑎𝑎 values reported in a previous study 98 have been shown for comparison (light grey shaded areas), comprising values derived from artificial giant lipid vesicles** and metabolically active E. coli spheroplast***. Overall, the results point to MIX 6A and 9A as suitable model systems that replicate the main aspects of E. coli’s inner membrane lipid composition and mechanical properties based on commercially available lipid mixtures. We find that DPPG is not suitable as a PG source for model E. coli membranes under standard growth conditions, although mixtures involving DPPG do not phase separate despite their high Tm (single peaks in DSC, Figure S5). Instead, our results point to three ternary mixtures of POPE, POPG and CL for model systems. Graphically comparing the composition of our model systems with previously reported E. coli membrane models mixtures 22,25-27,29,73,80,99-107 (Figure S9) shows that most reported models differ 15 substantially from each other, and from our mixtures. Given the lack of any accepted standard models, the ability of our model systems to reproduce some of the main elements of the membranes’ biomechanical properties could be helpful for studies where active molecules or forces are at play, for example, investigations of force transduction within membranes or active response to stimuli achieved through integral proteins such as mechanosensitive channels and PIEZO proteins 108–110. The dynamical shift of Tm as a function of E. coli’s growth environment indicates a clear correlation between the membrane functionality, the activity of embedded macromolecules and the overall physiological transduction of these stimuli across the cell. The model systems developed here could also be used to investigate the passive mechanisms behind lipid bilayer asymmetry, an intrinsic property of biological membranes 21, and its effects on the functional features of native membranes. Recent work highlighted how CL can show leaflet preferentiality depending on vesicles curvature111, suggesting the possibility of developing model membrane system with controlled compositional asymmetry that could be employed to explore this phenomenon in future work. More sophisticated models will be needed to account for the significant local variations in native membranes’ macromolecular content 112, an important element in many experimental 113,114 and computational 115 studies. The consistency between the measurements on the two mechanically different lipid phases and the general agreement with existing literature support our present approach to estimate 𝐾𝐾𝑎𝑎, but the results need to be taken with caution because the lipid bilayer is not an isotropic 3D material, as assumed with the thin plate model. Future studies aimed at determining the bending modulus of our model systems will likely be of interest as well. For example, E. coli produces small spherical structures, termed bacterial vesicles, which help with the exchange of genetic material, molecules and proteins 118–120. Presumably, these vesicles are under less pressure than E. coli, making the bending contribution to Helmholtz free energy relevant. One previous study used a mixture107 similar to our 8A model (with 18:1 chain content set to 41:59, slightly higher than our 50:50) to study colistin, but reported bending moduli of only single-component membranes. Conclusion In this study we identify minimal, lipid-only model systems for the E. coli inner membrane. The models, composed of synthetic lipids 16:0-18:1 phosphatidylethanolamine (POPE), 16:0-18:1 phosphatidylglycerol (POPG), and 16:0-18:1 Cardiolipin (CL), achieve a similar lipid composition and ratio to that found in the native membrane, and can reproduce its elastic moduli and thermomechanical properties. Like for all lipid-only model membranes, our model systems cannot fully reproduce the complexity of the native membranes due to the absence of proteins, complex biomolecules and a plethora of native lipids 105,116,117. Instead, our goal is to establish a simplified yet fully tractable system that captures key compositional and biophysical features of the E. coli inner membrane. We anticipate the models to be particularly useful for studies focusing on 16 mechanical forces in E. coli membranes, for example, to investigate the function and mechano-transduction of membrane proteins or macromolecule-membrane interactions. Conflicts of interest There are no conflicts of interest to declare. Authors contributions KV and TP designed the study. NT performed all the experiments and carried out the analysis of the results with input from KV and TP. All the authors co-wrote the papers and commented on the results. Acknowledgments Funding from the Engineering and Physical Sciences Research Council SOFI2 Doctoral Training Centre through the EPSRC grant EP/L015536/1 is acknowledged. We also thank Denise Li from the Edinburgh Complex Fluid Partnership for help with the calorimetry measurements. Supporting Information The Supporting Information is available free of charge at https://pubs.acs.org/doi/.... 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