Poisson's Ratio and Young's Modulus of Lipid Bilayers in Different Phases

Flower-shaped 2D crystals grown in curved fluid vesicle membranes

The morphologies of two-dimensional (2D) crystals, nucleated, grown, and integrated within 2D elastic fluids, for instance in giant vesicle membranes, are dictated by an interplay of mechanics, permeability, and thermal contraction. Mitigation of solid strain drives the formation of crystals with vanishing Gaussian curvature (i.e., developable domain shapes) and, correspondingly, enhanced Gaussian curvature in the surrounding 2D fluid. However, upon cooling to grow the crystals, large vesicles sustain greater inflation and tension because their small area-to-volume ratio slows water permeation. As a result, more elaborate shapes, for instance, flowers with bendable but inextensible petals, form on large vesicles despite their more gradual curvature, while small vesicles harbor compact planar crystals. This size dependence runs counter to the known cumulative growth of strain energy of 2D colloidal crystals on rigid spherical templates. This interplay of intra-membrane mechanics and processing points to the scalable production of flexible molecular crystals of controllable complex shape.

Gold nanoparticle adsorption alters the cell stiffness and cell wall bio-chemical landscape of Candida albicans fungal cells

HYPOTHESIS

Nanomaterials have been extensively investigated for a wide range of biomedical applications, including as antimicrobial agents, drug delivery vehicles, and diagnostic devices. The commonality between these biomedical applications is the necessity for the nanoparticle to interact with or pass through the cellular wall and membrane. Cell-nanomaterial interactions/uptake can occur in various ways, including adhering to the cell wall, forming aggregates on the surface, becoming absorbed within the cell wall itself, or transversing into the cell cytoplasm. These interactions are common to mammalian cells, bacteria, and yeast cells. This variety of interactions can cause changes to the integrity of the cell wall and the cell overall, but the precise mechanisms underpinning such interactions remain poorly understood. Here, we investigate the interaction between commonly investigated gold nanoparticles (AuNPs) and the cell wall/membrane of a model fungal cell to explore the general effects of interaction and uptake.

EXPERIMENTS

The interactions between 100 nm citrate-capped AuNPs and the cell wall of Candida albicans fungal cells were studied using a range of advanced microscopy techniques, including atomic force microscopy, confocal laser scanning microscopy, scanning electron microscopy, transmission electron microscopy, and synchrotron-FTIR micro-spectroscopy.

FINDINGS

In most cases, particles adhered on the cell surface, although instances of particles being up-taken into the cell cytoplasm and localised within the cell wall and membrane were also observed. There was a measurable increase in the stiffness of the fungal cell after AuNPs were introduced. Analysis of the synchrotron-FTIR data showed significant changes in spectral features associated with phospholipids and proteins after exposure to AuNPs.

Viscosity-Sensitive Membrane Dyes as Tools To Estimate the Crystalline Structure of Lipid Bilayers

Lipid membranes are crucial for cellular integrity and regulation, and tight control of their structural and mechanical properties is vital to ensure that they function properly. Fluorescent probes sensitive to the membrane's microenvironment are useful for investigating lipid membrane properties; however, there is currently a lack of quantitative correlation between the exact parameters of lipid organization and a readout from these dyes. Here, we investigate this relationship for "molecular rotors", or microviscosity sensors, by simultaneously measuring their fluorescence lifetime to determine the membrane viscosity, while using X-ray diffraction to determine the membrane's structural properties. Our results reveal a phase-dependent correlation between the membrane's structural parameters and mechanical properties measured by a BODIPY-based molecular rotor, giving excellent predictive power for the structural descriptors of the lipid bilayer. We also demonstrate that differences in membrane thickness between different lipid phases are not a prerequisite for the formation of lipid microdomains and that this requirement can be disrupted by the presence of line-active molecules. Our results underpin the use of membrane-sensitive dyes as reporters of the structure of lipid membranes.

A Review of Continuum Mechanics for Mechanical Deformation of Lipid Membranes

Mechanical deformation of lipid membranes plays important roles in various cellular tasks. Curvature deformation and lateral stretching are two major energy contributions to the mechanical deformation of lipid membranes. In this paper, continuum theories for these two major membrane deformation events were reviewed. Theories based on curvature elasticity and lateral surface tension were introduced. Numerical methods as well as biological applications of the theories were discussed.

Cell Membrane Oscillations under Radiofrequency Electromagnetic Modulation

Cell responses to external radiofrequencies (RF) are a fundamental problem of much scientific research, clinical applications, and even daily lives surrounded by wireless communication hardware. In this work, we report an unexpected observation that the cell membrane can oscillate at the nanometer scale in phase with the external RF radiation from kHz to GHz. By analyzing the oscillation modes, we reveal the mechanism behind the membrane oscillation resonance, membrane blebbing, the resulting cell death, and the selectivity of plasma-based cancer treatment based on the difference in the membrane's natural frequencies among cell lines. Therefore, a selectivity of treatment can be achieved by aiming at the natural frequency of the target cell line to focus the membrane damage on the cancer cells and avoid normal tissues nearby. This gives a promising cancer therapy that is especially effective in the mixing lesion of the cancer cells and normal cells such as glioblastoma where surgical removal is not applicable. Along with these new phenomena, this work provides a general understanding of the cell coupling with RF radiation from the externally stimulated membrane behavior to the cell apoptosis and necrosis.

Changes in Mechanical Properties of Vesicles by Mucin in Aqueous Solution

The mechanical properties of vesicles were investigated as they were prepared, according to the ratio of mucin to dipalmitoylphosphatidylcholine (DPPC), using an atomic force microscope (AFM). After the confirmation of the vesicle adsorption on a mica surface, an AFM-tip deflection, caused by the interaction between the tip and the vesicle, was measured. The deflection showed that the tip broke through into the vesicle twice. Each break meant a tip-penetration into the upper and lower portion of the vesicle. Only the first penetration allowed the Hertzian model available to estimate the vesicle mechanical moduli. Two moduli reduced as the ratio of mucin to DPPC increased to 0.5, but the moduli were little changed above the 0.5 ratio. These results seem to be a platform for the effect of the mucin on the plasma-membrane anchoring and cellular signaling.

Viscoelastic damage evaluation of the axon

In this manuscript, we have studied the microstructure of the axonal cytoskeleton and adopted a bottom-up approach to evaluate the mechanical responses of axons. The cytoskeleton of the axon includes the microtubules (MT), Tau proteins (Tau), neurofilaments (NF), and microfilaments (MF). Although most of the rigidity of the axons is due to the MT, the viscoelastic response of axons comes from the Tau. Early studies have shown that NF and MF do not provide significant elasticity to the overall response of axons. Therefore, the most critical aspect of the mechanical response of axons is the microstructural topology of how MT and Tau are connected and construct the cross-linked network. Using a scanning electron microscope (SEM), the cross-sectional view of the axons revealed that the MTs are organized in a hexagonal array and cross-linked by Tau. Therefore, we have developed a hexagonal Representative Volume Element (RVE) of the axonal microstructure with MT and Tau as fibers. The matrix of the RVE is modeled by considering a combined effect of NF and MF. A parametric study is done by varying fiber geometric and mechanical properties. The Young’s modulus and spacing of MT are varied between 1.5 and 1.9 GPa and 20–38 nm, respectively. Tau is modeled as a 3-parameter General Maxwell viscoelastic material. The failure strains for MT and Tau are taken to be 50 and 40%, respectively. A total of 4 RVEs are prepared for finite element analysis, and six loading cases are inspected to quantify the three-dimensional (3D) viscoelastic relaxation response. The volume-averaged stress and strain are then used to fit the relaxation Prony series. Next, we imposed varying strain rates (between 10/sec to 50/sec) on the RVE and analyzed the axonal failure process. We have observed that the 40% failure strain of Tau is achieved in all strain rates before the MT reaches its failure strain of 50%. The corresponding axonal failure strain and stress vary between 6 and 11% and 5–19.8 MPa, respectively. This study can be used to model macroscale axonal aggregate typical of the white matter region of the brain tissue.

Quantitative Models of Lipid Transfer and Membrane Contact Formation

Lipid transfer proteins (LTPs) transfer lipids between different organelles, and thus play key roles in lipid homeostasis and organelle dynamics. The lipid transfer often occurs at the membrane contact sites (MCS) where two membranes are held within 10-30 nm. While most LTPs act as a shuttle to transfer lipids, recent experiments reveal a new category of eukaryotic LTPs that may serve as a bridge to transport lipids in bulk at MCSs. However, the molecular mechanisms underlying lipid transfer and MCS formation are not well understood. Here, we first review two recent studies of extended synaptotagmin (E-Syt)-mediated membrane binding and lipid transfer using novel approaches. Then we describe mathematical models to quantify the kinetics of lipid transfer by shuttle LTPs based on a lipid exchange mechanism. We find that simple lipid mixing among membranes of similar composition and/or lipid partitioning among membranes of distinct composition can explain lipid transfer against a concentration gradient widely observed for LTPs. We predict that selective transport of lipids, but not membrane proteins, by bridge LTPs leads to osmotic membrane tension by analogy to the osmotic pressure across a semipermeable membrane. A gradient of such tension and the conventional membrane tension may drive bulk lipid flow through bridge LTPs at a speed consistent with the fast membrane expansion observed in vivo. Finally, we discuss the implications of membrane tension and lipid transfer in organelle biogenesis. Overall, the quantitative models may help clarify the mechanisms of LTP-mediated MCS formation and lipid transfer.

Modelling the Effect of Geometry and Loading on Mechanical Response of SARS-CoV-2

In recent times, coronavirus (SARS-CoV-2) becomes a pandemic disease across the globe. This virus affects the severe acute respiratory system that causes a type of pneumonia, which results in an outbreak in Wuhan, China, and then in whole global countries. The virus possesses a complex structure and varied in composition along with its geometrical shape and size. Contributions of the lipid and protein components of a virus to the influenza viral envelope’s mechanical properties are still unknown. In this work, the virus is modeled like the SARS-CoV-2 and surrounded with spikes made up of S glycoproteins, and numerical analysis was made to predict its mechanical behavior while resting on the substrate. The static and viscoelastic response of the virus was carried out in a finite element (FE) commercial software Ansys. The impact of changing viral envelope thickness on SARS-CoV-2 and bald virus stiffness was investigated. The viscoelastic analysis shows the increase in the deformation and stress with an increase in the pressure. The static analysis predicts the lower stiffness for SARS-CoV-2 compared to bald virion and increases with the increase in the envelop thickness. This study is useful for analyzing the effect of geometry and mechanical properties on the mechanical response of SARS-CoV-2.

Modeling cell membrane electrodeformation by alternating electric fields

With the aim of characterizing and gaining insight into the frequency response of cells suspended in a fluid medium and deformed with a controlled alternating electric field, a continuum-based analysis is presented for modeling electrodeformation (ED) via Maxwell stress tensor (MST) calculation. Our purpose here is to apply this approach to explain the fact that the electric field anisotropy and electrical conductivity ratio Λ of the cytoplasm and the extracellular medium significantly impact the MST exerted on the cytoplasm-membrane interface. One important finding is that the modulation of electrical cues and MST force by the frequency of the applied electric field provides an extremely rich tool kit for manipulating cells. We show the extreme sensitivity of proximity-induced capacitive coupling arising concomitantly when the magnitude of the MST increases as the distance between cells is decreased and the spatial anisotropy becomes important. Moreover, our model highlights the strongly localized character of the electrostatic field effect emanating from neighboring cells and suggests the possibility of exploiting cell distribution as a powerful tool to engineer the functional performance of cell assemblies by controlling ED and capacitive coupling. We furthermore show that frequency has a significant impact on the attenuation-amplification transition of MST, suggesting that shape anisotropy has a much weaker influence on ED of the cell membrane compared to the anisotropy induced by the orientation angle itself.

A finite element model of an osteoblast to quantify the transduction of exogenous forces to cellular components

Encouraged by recent advances of biophysical and biochemical assays we introduce a 3D finite element model of an osteoblast, seeking an analogue between exogenous forces and intracellularly activated sensory mechanisms. The cell was reverse engineered and the dimensions of the internal cellular structures were based on literature data. The model was verified and validated against atomic force microscopy experiments and four loading scenarios were considered. The stress distributions developing on the main cellular components were calculated along with their corresponding strain values. The nucleus and mitochondria exhibited similar loading trends, with the mitochondria being stressed by an order of magnitude higher than the nucleus (e.g. 1.4 vs. 0.16 MPa). Equivalent stiffness was determined to increase by almost 50%, from the apex to the cell's periphery, as was the cell's elasticity, which was lowest when the load was exerted directly above the nucleus. The assessment of how extrinsic loads are propagated to a cell's internal structures is inherently a problem of high complexity. The findings presented in this study can provide important insight into biophysical and biochemical responses elicited in cells through mechanical stimulus. This was evident in both the nuclear and mitochondrial loading and would stipulate the important contribution of even more accurate models in the interpretation of cellular events. One Sentence Summary: The results of this numerical biomechanical study demonstrated that even minor extrinsic loads irrespective of the application site, are transduced by a fraction of the cytoskeleton to its internal structure (primarily to its mitochondria and secondary to the cell's nucleus), indicating mechanical stimulus as the dominant pathway to cell expression.

Interaction of LL-37 human cathelicidin peptide with a model microbial-like lipid membrane

The only representative of cathelicidin peptides in humans is LL-37, a multifunctional antimicrobial peptide (AMP) that is a part of the innate immune response. Details of the LL-37 direct activity against pathogens are not well understood at the molecular level. Here, we present research on the mechanism of interaction between LL-37 and a model multicomponent bilayer lipid membrane (BLM), mimicking microbial cell membrane. Electrochemical impedance spectroscopy (EIS), high-resolution atomic force microscopy (AFM) imaging, and polarization-modulation infrared reflection-absorption spectroscopy (PM-IRRAS) were applied to study the peptide influence on a model microbial-like membrane. We show that LL-37 causes changes in the phospholipid molecules conformation and orientation, leading to membrane disintegration, significantly affecting the membrane electrical parameters, such as capacitance and resistance. High-resolution AFM imaging shows topographical and mechanical effects of such disintegration, while PM-IRRAS data indicates that introduction of LL-37 causes changes in the phospholipid acyl chains from all-trans to gauche conformations. Moreover, the presence of LL-37 significantly alters the value of the phospholipid tilt angle. Altogether, our results suggest a "carpet" membrane dissolution followed by a detergent-like membrane disruption mechanism upon LL-37 activity. This research gives a novel insight into the understanding of LL-37 influence on multicomponent model membranes and a promising contribution to the development of LL-37-derived therapeutic agents against drug-resistant bacteria.

Determination of the Mechanical Properties of Model Lipid Bilayers Using Atomic Force Microscopy Indentation

By conducting a systematic study of model lipid membranes using the atomic force microscopy (AFM) indentation, we demonstrate the importance of an experimental protocol on the determination of their mechanical parameters. We refine the experimental approach by analyzing the influence of the contact mechanics models used to process the data, substrate preparation, and indenter geometry. We show that both bending rigidity and area compressibility can be determined from a single AFM indentation measurement.

Mechanical properties of lipid bilayers: a note on the Poisson ratio

We investigate the Poisson ratio ν of fluid lipid bilayers, i.e., the question how area strains compare to the changes in membrane thickness (or, equivalently, volume) that accompany them. We first examine existing experimental results on the area- and volume compressibility of lipid membranes. Analyzing them within the framework of linear elasticity theory for homogeneous thin fluid sheets leads us to conclude that lipid membrane deformations are to a very good approximation volume-preserving, with a Poisson ratio that is likely about 3% smaller than the common soft matter limit . These results are fully consistent with atomistic simulations of a DOPC membrane at varying amount of applied lateral stress, for which we instead deduce ν by directly comparing area- and volume strains. To assess the problematic assumption of transverse homogeneity, we also define a depth-resolved Poisson ratio ν(z) and determine it through a refined analysis of the same set of simulations. We find that throughout the membrane's thickness, ν(z) is close to the value derived assuming homogeneity, with only minor variations of borderline statistical significance.

Dynamical nonlinear memory capacitance in biomimetic membranes

Two-terminal memory elements, or memelements, capable of co-locating signal processing and memory via history-dependent reconfigurability at the nanoscale are vital for next-generation computing materials striving to match the brain's efficiency and flexible cognitive capabilities. While memory resistors, or memristors, have been widely reported, other types of memelements remain underexplored or undiscovered. Here we report the first example of a volatile, voltage-controlled memcapacitor in which capacitive memory arises from reversible and hysteretic geometrical changes in a lipid bilayer that mimics the composition and structure of biomembranes. We demonstrate that the nonlinear dynamics and memory are governed by two implicitly-coupled, voltage-dependent state variables-membrane radius and thickness. Further, our system is capable of tuneable signal processing and learning via synapse-like, short-term capacitive plasticity. These findings will accelerate the development of low-energy, biomolecular neuromorphic memelements, which, in turn, could also serve as models to study capacitive memory and signal processing in neuronal membranes.

Quantitative atomic force microscopy provides new insight into matrix vesicle mineralization

Matrix vesicles (MVs) are a class of extracellular vesicles that initiate mineralization in cartilage, bone, and other vertebrate tissues by accumulating calcium ions (Ca²⁺) and inorganic phosphate (P_i) within their lumen and forming a nucleation core (NC). After further sequestration of Ca²⁺ and P_i, the NC transforms into crystalline complexes. Direct evidence of the existence of the NC and its maturation have been provided solely by analyses of dried samples. We isolated MVs from chicken embryo cartilage and used atomic force microscopy peak force quantitative nanomechanical property mapping (AFM-PFQNM) to measure the nanomechanical and morphological properties of individual MVs under both mineralizing (+Ca²⁺) and non-mineralizing (-Ca²⁺) fluid conditions. The elastic modulus of MVs significantly increased by 4-fold after incubation in mineralization buffer. From AFM mapping data, we inferred the morphological changes of MVs as mineralization progresses: prior to mineralization, a punctate feature, the NC, is present within MVs and this feature grows and stiffens during mineralization until it occupies most of the MV lumen. Dynamic light scattering showed a significant increase in hydrodynamic diameter and no change in the zeta potential of hydrated MVs after incubation with Ca²⁺. This validates that crystalline complexes, which are strongly negative relative to MVs, were forming within the lumen of MVs. These data were substantiated by transmission electron microscopy energy dispersive X-ray and Fourier transform infrared spectroscopic analyses of dried MVs, which provide evidence that the complexes increased in size, crystallinity, and Ca/P ratio within MVs during the mineralization process.

Pore Forming Properties of Alamethicin in Negatively Charged Floating Bilayer Lipid Membranes Supported on Gold Electrodes

Electrochemical impedance spectroscopy (EIS), atomic force microscopy (AFM), and photon polarization modulation infrared reflection absorption spectroscopy (PM-IRRAS) were employed to investigate the formation of alamethicin pores in negatively charged bilayers composed of a mixture of 1,2-dimyristoyl- sn-glycero-3-phosphocholine (DMPC) and egg-PG floating at gold (111) electrode surfaces modified by self-assembled monolayers of 1-thio-β-d-glucose (β-Tg). The EIS data showed that the presence of alamethicin decreases the membrane resistivity by about 1 order of magnitude. PM-IRRAS measurements provided information about the tilt angles of peptide helical axis with respect to the bilayer normal. The small tilt angles obtained for the peptide helical axis prove that the alamethicin molecules were inserted into the DMPC/egg-PG membranes. The tilt angles decreased when negative potentials were applied, which correlates with the observed decrease in membrane resistivity, indicating that ion pore formation is assisted by the transmembrane potential. Molecular resolution AFM images provided visual evidence that alamethicin molecules aggregate forming hexagonal porous 2D lattices with periodicities of 2.0 ± 0.2 nm. The pore formation by alamethicin in the negatively charged membrane was compared with the interaction of this peptide with a bilayer formed by zwitterionic lipids. The comparison of these results showed that alamethicin preferentially forms ion translocating pores in negatively charged phospholipid membranes.

Peridynamic Modeling of Ruptures in Biomembranes

We simulate the formation of spontaneous ruptures in supported phospholipid double bilayer membranes, using peridynamic modeling. Experiments performed on spreading double bilayers typically show two distinct kinds of ruptures, floral and fractal, which form spontaneously in the distal (upper) bilayer at late stages of double bilayer formation on high energy substrates. It is, however, currently unresolved which factors govern the occurrence of either rupture type. Variations in the distance between the two bilayers, and the occurrence of interconnections (“pinning sites”) are suspected of contributing to the process. Our new simulations indicate that the pinned regions which form, presumably due to Ca²⁺ ions serving as bridging agent between the distal and the proximal bilayer, act as nucleation sites for the ruptures. Moreover, assuming that the pinning sites cause a non-zero shear modulus, our simulations also show that they change the rupture mode from floral to fractal. At zero shear modulus the pores appear to be circular, subsequently evolving into floral pores. With increasing shear modulus the pore edges start to branch, favoring fractal morphologies. We conclude that the pinning sites may indirectly determine the rupture morphology by contributing to shear stress in the distal membrane.

Magnetoliposomes as Potential Carriers of Doxorubicin to Tumours

Studies on magnetoliposomes (MLUV) as potential carriers for magnetic-field-dependent drug delivery are presented. The systems were formed with hydrophobic superparamagnetic iron oxide nanoparticles (SPIONs) confined within the bilayer of the liposomes. The nanomechanical properties of bilayer lipid membranes were evaluated and related to the amount of incorporated SPIONs. It was found that the presence of SPIONs in the lipid membrane leads to overall stiffening and increases morphological inhomogeneity, facilitating rupture of the MLUV membrane in a low-frequency alternating magnetic field (AMF). To verify the findings, doxorubicin release from MLUVs in the presence and absence of an AMF was measured. Under experimental conditions, drug release proceeds through MLUV rupture induced by mechanical vibration of SPIONs rather than through localized heating in the vicinity of the SPIONs.

Magnetic domain wall tweezers: a new tool for mechanobiology studies on individual target cells

In vitro tests are of fundamental importance for investigating cell mechanisms in response to mechanical stimuli or the impact of the genotype on cell mechanical properties. In particular, the application of controlled forces to activate specific bio-pathways and investigate their effects, mimicking the role of the cellular environment, is becoming a prominent approach in the emerging field of mechanobiology. Here, we present an on-chip device based on magnetic domain wall manipulators, which allows the application of finely controlled and localized forces on target living cells. In particular, we demonstrate the application of a magnetic force in the order of hundreds of pN on the membrane of HeLa cells cultured on-chip, via manipulation of 1 μm superparamagnetic beads. Such a mechanical stimulus produces a sizable local indentation of the cellular membrane of about 2 μm. Upon evaluation of the beads' position within the magnetic field originated by the domain wall, the force applied during the experiments is accurately quantified via micromagnetic simulations. The obtained value is in good agreement with that calculated by the application of an elastic model to the cellular membrane.

The effect of the physical properties of the substrate on the kinetics of cell adhesion and crawling studied by an axisymmetric diffusion-energy balance coupled model

In this paper an analytical approach to study the effect of the substrate physical properties on the kinetics of adhesion and motility behavior of cells is presented. Cell adhesion is mediated by the binding of cell wall receptors and substrate's complementary ligands, and tight adhesion is accomplished by the recruitment of the cell wall binders to the adhesion zone. The binders' movement is modeled as their axisymmetric diffusion in the fluid-like cell membrane. In order to preserve the thermodynamic consistency, the energy balance for the cell-substrate interaction is imposed on the diffusion equation. Solving the axisymmetric diffusion-energy balance coupled equations, it turns out that the physical properties of the substrate (substrate's ligand spacing and stiffness) have considerable effects on the cell adhesion and motility kinetics. For a rigid substrate with uniform distribution of immobile ligands, the maximum ligand spacing which does not interrupt adhesion growth is found to be about 57 nm. It is also found that as a consequence of the reduction in the energy dissipation in the isolated adhesion system, cell adhesion is facilitated by increasing substrate's stiffness. Moreover, the directional movement of cells on a substrate with gradients in mechanical compliance is explored with an extension of the adhesion formulation. It is shown that cells tend to move from soft to stiff regions of the substrate, but their movement is decelerated as the stiffness of the substrate increases. These findings based on the proposed theoretical model are in excellent agreement with the previous experimental observations.