Size Matters: Rethinking Hertz Model Interpretation for Cell Mechanics Using AFM.

Cell mechanics are a biophysical indicator of cell state, such as cancer metastasis, leukocyte activation, and cell cycle progression. Atomic force microscopy (AFM) is a widely used technique to measure cell mechanics, where the Young modulus of a cell is usually derived from the Hertz contact model. However, the Hertz model assumes that the cell is an elastic, isotropic, and homogeneous material and that the indentation is small compared to the cell size. These assumptions neglect the effects of the cytoskeleton, cell size and shape, and cell environment on cell deformation. In this study, we investigated the influence of cell size on the estimated Young's modulus using liposomes as cell models. Liposomes were prepared with different sizes and filled with phosphate buffered saline (PBS) or hyaluronic acid (HA) to mimic the cytoplasm. AFM was used to obtain the force indentation curves and fit them to the Hertz model. We found that the larger the liposome, the lower the estimated Young's modulus for both PBS-filled and HA-filled liposomes. This suggests that the Young modulus obtained from the Hertz model is not only a property of the cell material but also depends on the cell dimensions. Therefore, when comparing or interpreting cell mechanics using the Hertz model, it is essential to account for cell size.

Solitons in the Heimburg-Jackson model of sound propagation in lipid bilayers are enabled by dispersion of a stiff membrane.

Experiments show that elastic constants of lipid bilayers vary greatly during the liquid-to-gel phase transition. This fact forms the cornerstone of the Heimburg-Jackson model of soliton propagation along membranes of axons, in which the action potential is accompanied by a traveling phase transition. However, the dispersion term, which is crucial for the existence of solitons, is added to the Heimburg-Jackson model ad hoc and set to fit experimental observations. In the present paper, we aim to consolidate this view with continuous membrane mechanics. Using literature data, we show that the compression modulus of a DPPC membrane is smaller by approximately an order of magnitude during phase transition. With a series expansion of the compression modulus, we write the action of a membrane and solve the corresponding wave equation analytically using an Exp-function method. We confirm that membrane solitons with speeds around 200 m/s are possible with amplitudes inversely proportional to their speed. We conclude that dispersion necessary for existence of solitons is directly related to a membrane's bending properties, offering a possible explanation for h. Our findings are in general agreement with existing literature and give insight into a general mechanism of wave propagation in membranes close to transition.

A Monte Carlo study of giant vesicle morphologies in nonequilibrium environments.

It is known that giant vesicles undergo dynamic morphological changes when exposed to a detergent. The solubilization process may take multiple pathways. In this work, we identify lipid vesicle shape dynamics before the solubilization of 1,2-dioleoyl-sn-glycero-3-phosphocholine giant vesicles with Triton X-100 (TR) detergent. The violent lipid vesicle dynamics was observed with laser confocal scanning microscopy and was qualitatively explained via a numerical simulation. A three-dimensional Monte Carlo scheme was constructed that emulated the nonequilibrium conditions at the beginning stages of solubilization, accounting for a gradual addition of TR detergent molecules into the lipid bilayers. We suggest that the main driving factor for morphology change in lipid vesicles is the associative tendency of the TR molecules, which induces spontaneous curvature of the detergent inclusions, an intrinsic consequence of their molecular shape. The majority of the observed lipid vesicle shapes in the experiments were found to correspond very well to the numerically calculated shapes in the phase space of possible solutions. The results give an insight into the early stages of lipid vesicle solubilization by amphiphilic molecules, which is nonequilibrium in nature and very difficult to study.

On the Role of Curved Membrane Nanodomains, and Passive and Active Skeleton Forces in the Determination of Cell Shape and Membrane Budding.

Biological membranes are composed of isotropic and anisotropic curved nanodomains. Anisotropic membrane components, such as Bin/Amphiphysin/Rvs (BAR) superfamily protein domains, could trigger/facilitate the growth of membrane tubular protrusions, while isotropic curved nanodomains may induce undulated (necklace-like) membrane protrusions. We review the role of isotropic and anisotropic membrane nanodomains in stability of tubular and undulated membrane structures generated or stabilized by cyto- or membrane-skeleton. We also describe the theory of spontaneous self-assembly of isotropic curved membrane nanodomains and derive the critical concentration above which the spontaneous necklace-like membrane protrusion growth is favorable. We show that the actin cytoskeleton growth inside the vesicle or cell can change its equilibrium shape, induce higher degree of segregation of membrane nanodomains or even alter the average orientation angle of anisotropic nanodomains such as BAR domains. These effects may indicate whether the actin cytoskeleton role is only to stabilize membrane protrusions or to generate them by stretching the vesicle membrane. Furthermore, we demonstrate that by taking into account the in-plane orientational ordering of anisotropic membrane nanodomains, direct interactions between them and the extrinsic (deviatoric) curvature elasticity, it is possible to explain the experimentally observed stability of oblate (discocyte) shapes of red blood cells in a broad interval of cell reduced volume. Finally, we present results of numerical calculations and Monte-Carlo simulations which indicate that the active forces of membrane skeleton and cytoskeleton applied to plasma membrane may considerably influence cell shape and membrane budding.

Electric Double Layer and Orientational Ordering of Water Dipoles in Narrow Channels within a Modified Langevin Poisson-Boltzmann Model.

The electric double layer (EDL) is an important phenomenon that arises in systems where a charged surface comes into contact with an electrolyte solution. In this work we describe the generalization of classic Poisson-Boltzmann (PB) theory for point-like ions by taking into account orientational ordering of water molecules. The modified Langevin Poisson-Boltzmann (LPB) model of EDL is derived by minimizing the corresponding Helmholtz free energy functional, which includes also orientational entropy contribution of water dipoles. The formation of EDL is important in many artificial and biological systems bound by a cylindrical geometry. We therefore numerically solve the modified LPB equation in cylindrical coordinates, determining the spatial dependencies of electric potential, relative permittivity and average orientations of water dipoles within charged tubes of different radii. Results show that for tubes of a large radius, macroscopic (net) volume charge density of coions and counterions is zero at the geometrical axis. This is attributed to effective electrolyte charge screening in the vicinity of the inner charged surface of the tube. For tubes of small radii, the screening region extends into the whole inner space of the tube, leading to non-zero net volume charge density and non-zero orientational ordering of water dipoles near the axis.

Theoretical study of vesicle shapes driven by coupling curved proteins and active cytoskeletal forces.

Eukaryote cells have a flexible shape, which dynamically changes according to the function performed by the cell. One mechanism for deforming the cell membrane into the desired shape is through the expression of curved membrane proteins. Furthermore, these curved membrane proteins are often associated with the recruitment of the cytoskeleton, which then applies active forces that deform the membrane. This coupling between curvature and activity was previously explored theoretically in the linear limit of small deformations, and low dimensionality. Here we explore the unrestricted shapes of vesicles that contain active curved membrane proteins, in three-dimensions, using Monte-Carlo numerical simulations. The activity of the proteins is in the form of protrusive forces that push the membrane outwards, as may arise from the cytoskeleton of the cell due to actin or microtubule polymerization occurring near the membrane. For proteins that have an isotropic convex shape, the additional protrusive force enhances their tendency to aggregate and form membrane protrusions (buds). In addition, we find another transition from deformed spheres with necklace type aggregates, to flat pancake-shaped vesicles, where the curved proteins line the outer rim. This second transition is driven by the active forces, coupled to the spontaneous curvature, and the resulting configurations may shed light on the formation of sheet-like protrusions and lamellipodia of adhered and motile cells.

Investigation of nano- and microdomains formed by ceramide 1 phosphate in lipid bilayers.

Biological membranes are renowned for their intricate complexity, with the formation of membrane domains being pivotal to the successful execution of numerous cellular processes. However, due to their nanoscale characteristics, these domains are often understudied, as the experimental techniques required for quantitative investigation present significant challenges. In this study we employ spot-variation z-scan fluorescence correlation spectroscopy (svzFCS) tailored for artificial lipid vesicles of varying composition and combine this approach with high-resolution imaging. This method has been harnessed to examine the lipid-segregation behavior of distinct types of ceramide-1-phosphate (C1P), a crucial class of signaling molecules, within these membranes. Moreover, we provide a quantitative portrayal of the lipid membranes studied and the domains induced by C1P at both nano and microscales. Given the lack of definitive conclusions from the experimental data obtained, it was supplemented with comprehensive in silico studies-including the analysis of diffusion coefficient via molecular dynamics and domain populations via Monte Carlo simulations. This approach enhanced our insight into the dynamic behavior of these molecules within model lipid membranes, confirming that nano- and microdomains can co-exist in lipid vesicles.

Surfactin molecules with a cone-like structure promote the formation of membrane domains with negative spontaneous curvature and induce membrane invaginations.

Surfactin uniquely influences lipid bilayer structure by initially inducing membrane invaginations before solubilization. In this study, we exposed DOPC giant vesicles to various surfactin concentrations at different temperatures and observed surfactin-induced membrane invaginations by using differential interference contrast and confocal laser fluorescence microscopy. These invaginations were stable at room temperature but not at higher temperatures. Surfactin molecules induce membrane nanodomains with negative spontaneous curvature and membrane invaginations despite their intrinsic conical shape and intrinsic positive curvature. Considering the experimentally observed capacity of surfactin to fluidize lipid acyl chains and induce partial dehydration of lipid headgroups, we propose that the resulting surfactin-lipid complexes exhibit a net negative spontaneous curvature. We further conducted 3D numerical Monte Carlo (MC) simulations to investigate the behaviour of vesicles containing negative curvature nanodomains within their membrane at varying temperatures. MC simulations demonstrated strong agreement with experimental results, revealing that invaginations are preferentially formed at low temperatures, while being less pronounced at elevated temperatures. Our findings go beyond the expectations of the Israelachvili molecular shape and packing concepts analysis. These concepts do not take into account the influence of specific interactions between neighboring molecules on the inherent shapes of molecules and their arrangement within curved membrane nanodomains. Our work contributes to a more comprehensive understanding of the complex factors governing vesicle morphology and membrane organization and provides insight into the role of detergent-lipid interactions in modulating vesicle morphology.

Decrease in Cellular Nanovesicles Concentration in Blood of Athletes More Than 15 Hours After Marathon.

INTRODUCTION: Cellular nanovesicles (CNVs), that are shed from cells, have been recognized as promising indicators of health status. We analyzed the effect of long-distance running on concentration of CNVs, along with some standard blood parameters, in 27 athletes two days before and >15 hours after physical effort. METHODS: CNVs were isolated by repetitive centrifugation and washing of samples, and assessed by flow cytometry. Cholinesterase (ChE) and glutathione S-transferase (GST) activity were measured spectrophotometrically. Interleukin 6 (IL-6) and tumor necrosis factor-α (TNF-α) concentrations were measured using enzyme-linked immunosorbent assay (ELISA). C-reactive protein (CRP) was measured with immunoturbidimetric determination and lipidogram parameters were measured by enzymatic colorimetric assay. Flow cytometry was used for blood cell count and mean platelet volume (MPV) measurement. RESULTS: More than 15 hours after physical effort a decrease was found in CNVs' concentration in isolates from blood (46%; p<0.05), in ChE activity in whole blood (47%; p<0.001), in plasma (34%; p<0.01), and in erythrocyte suspension (54%; p<0.001), as well as in GST activity in erythrocyte suspension (16%; p<0.01) and in IL-6 concentration in plasma (63%; p<0.05). We found no change in GST activity in plasma and in TNF-α concentration in plasma. Correlations (>0.8; p<0.001) between CNVs' concentration and ChE activity, and GST activity, respectively, in erythrocyte suspension were found. CONCLUSION: We found that >15 hours post-physical effort, CNVs' concentration was below the initial value, concomitant with other measured parameters: ChE and GST activity as well as IL-6 concentration, indicating a favorable effect of physical effort on health status. CNVs' concentration and ChE activity in isolates from peripheral blood proved to have potential as indicators of the response of the human body to inflammation after physical effort. Physical activity should be considered as an important factor in preparation of subjects for blood sampling in procedures focusing on CNV-containing diagnostic and therapeutic compounds.

Magneto-mechanical actuation of barium-hexaferrite nanoplatelets for the disruption of phospholipid membranes.

HYPOTHESIS: The magneto-mechanical actuation (MMA) of magnetic nanoparticles with a low-frequency alternating magnetic field (AMF) can be used to destroy cancer cells. So far, MMA was tested on different cells using different nanoparticles and different field characteristics, which makes comparisons and any generalizations about the results of MMA difficult. In this paper we propose the use of giant unilamellar vesicles (GUVs) as a simple model system to study the effect of MMA on a closed lipid bilayer membrane, i.e., a basic building block of any cell. EXPERIMENTS: The GUVs were exposed to barium-hexaferrite nanoplatelets (NPLs, ~50 nm wide and 3 nm thick) with unique magnetic properties dominated by a permanent magnetic moment that is perpendicular to the platelet, at different concentrations (1-50 µg/mL) and pH values (4.2-7.4) of the aqueous suspension. The GUVs were observed with an optical microscope while being exposed to a uniaxial AMF (3-100 Hz, 2.2-10.6 mT). FINDINGS: When the NPLs were electrostatically attached to the GUV membranes, the MMA induced cyclic fluctuations of the GUVs' shape corresponding to the AMF frequency at the low NPL concentration (1 µm/mL), whereas the GUVs were bursting at the higher concentration (10 µg/mL). Theoretical considerations suggested that the bursting of the GUVs is a consequence of the local action of an assembly of several NPLs, rather than a collective effect of all the absorbed NPLs.

Inception Mechanisms of Tunneling Nanotubes.

Tunneling nanotubes (TNTs) are thin membranous tubes that interconnect cells, representing a novel route of cell-to-cell communication and spreading of pathogens. TNTs form between many cell types, yet their inception mechanisms remain elusive. We review in this study general concepts related to the formation and stability of membranous tubular structures with a focus on a deviatoric elasticity model of membrane nanodomains. We review experimental evidence that tubular structures initiate from local membrane bending facilitated by laterally distributed proteins or anisotropic membrane nanodomains. We further discuss the numerical results of several theoretical and simulation models of nanodomain segregation suggesting the mechanisms of TNT inception and stability. We discuss the coupling of nanodomain segregation with the action of protruding cytoskeletal forces, which are mostly provided in eukaryotic cells by the polymerization of f-actin, and review recent inception mechanisms of TNTs in relation to motor proteins.