A sufficiently large force acting on a single point of the fluid membrane of a flaccid phospholipid vesicle is known to cause the formation of a narrow bilayer tube (tether). We analyze this phenomenon by means of general mathematical methods allowing us to determine the shapes of strongly deformed vesicles including their stability. Starting from a free vesicle with an axisymmetric, prolate equilibrium shape, we consider an axial load that pulls (or pushes) the poles of the vesicle apart. Arranging the resulting shapes of strained vesicles in dependence of the axial deformation and of the area difference of monolayers, phase diagrams of stable shapes are presented comprising prolate shapes with or without equatorial mirror symmetry. For realistic values of membrane parameters, we study the force-extension relation of strained vesicles, and we demonstrate in detail how the initially elongated shape of an axially stretched vesicle transforms into a shape involving a membrane tether. This tethering transition may be continuous or discontinuous. If the free vesicle is mirror symmetric, the mirror symmetry is broken as the tether forms. The stability analysis of tethered shapes reveals that, for the considered vesicles, the stable shape is always asymmetric (polar), i.e., it involves only a single tether on one side of the main vesicle body. Although a bilayer tube formed from a closed vesicle is not an ideal cylinder, we show that, for most practical purposes, it is safe to assume a cylindrical geometry of tethers. This analysis is supplemented by the documentation of a prototype experiment supporting our theoretical predictions. It shows that the currently accepted model for the description of lipid-bilayer elasticity (generalized bilayer couple model) properly accounts for the tethering phenomenon.

A theoretical analysis is presented of the formation of membrane tethers from micropipette-aspirated phospholipid vesicles. In particular, it is taken into account that the phospholipid membrane is composed of two layers which are in contact but unconnected. The elastic energy of the bilayer is taken to be the sum of contributions from area expansivity, relative expansivity of the two monolayers, and bending. The vesicle is aspirated into a pipette and a constant point force is applied at the opposite side in the direction away from the pipette. The shape of the vesicle in approximated as a cylindrical projection into the pipette with a hemispherical cap, a spherical section, and a cylindrical tether with a hemispherical cap. The dimensions of the different regions of the vesicle are obtained by minimizing its elastic energy subject to the condition that the volume of the vesicle is fixed. The range of values for the parameters of the system is determined at which the existence of a tether is possible. Stability analysis is performed showing which of these configurations are stable. The importance of the relative expansion and compression of the constituent monolayers is established by recognizing that local bending energy by itself does not stabilize the vesicle geometry, and that in the limit as the relative expansivity modulus becomes infinitely large, a tether cannot be formed. Predictions are made for the functional relationships among experimentally observable quantities. In a companion report, the results of this analysis are applied to experimental measurements of tether formation, and used to calculate values for the membrane material coefficients.

A red blood cell (RBC) performs its function of adequately carrying respiratory gases in blood by its volume being $60% of that of a sphere with the same membrane area. For this purpose, human and most other vertebrate RBCs regulate their content of potassium (K þ ) and sodium (Na þ ) ions. The focus considered here is on K þ efflux through calcium-ion (Ca 2þ )-activated Gá rdos channels. These channels open under conditions that allow Ca 2þ to enter RBCs through Piezo1 mechanosensitive cation-permeable channels. It is postulated that the fraction of open Piezo1 channels depends on the RBC shape as a result of the curvature-dependent Piezo1-bilayer membrane interaction. The consequences of this postulate are studied by introducing a simple model of RBC osmotic behavior supplemented by the dependence of RBC membrane K þ permeability on the reduced volume (i.e., the ratio of cell volume to its maximal possible volume) of RBC discoid shapes. It is assumed that because of its intrinsic curvature and strong interaction with the surrounding membrane, Piezo1 tends to concentrate in the dimple regions of these shapes, and the fraction of open Piezo1 channels depends on the membrane curvature in that region. It is shown that the properties of the described model can provide the basis for the formation of the negative feedback loop that interrelates cell volume and its content of potassium ions. The model predicts the relation, valid for each cell in an RBC population, between RBC volume and membrane area, thus explaining the large value of the measured membrane area versus the volume correlation coefficient. The mechanism proposed here for RBC volume regulation is in accord with the loss of this correlation in RBCs of Piezo1 knockout mice.

Recently, there has been an increasing interest in the chemistry and biological potential of mosses, since a large number of biologically active compounds have been found within these species. This study aimed at examining the chemical composition and immunomodulatory potential (antioxidant, antidiabetic, anti-neuroinflammatory/antineurodegenerative, and antitumor activities) of moss Hypnum cupressiforme Hedw. extracts. Corresponding extracts have been obtained applying Soxhlet extractor. The chemical characterization was performed using spectrophotometric assays and liquid chromatography–mass spectrometry (LC-MS). The extracts were analyzed for antioxidant activity and for inhibitory activities on α-glucosidase, α-amylase, acetylcholinesterase, and tyrosinase. Additionally, extracts were tested against four cell lines—MRC-5, BV2, HCT-116, and MDA-MB-231—for antitumor and anti-inflammatory activities. Chemical analysis of extracts revealed the presence of flavonoids, phenolic acids, and triterpenoids. Major compounds identified by LC-MS in H. cupressiforme were kaempferol and five phenolic acids: p-hydroxybenzoic, protocatechuic, p-coumaric, gallic, and caffeic acid. According to biochemical assays the investigated extracts exhibited significant immunomodulatory potential. Significant antiproliferative potential against MDA-MB-231 cells has been observed together with the promising anti-neuroinflammatory application. The obtained data suggest that moss H. cupressiforme is a valuable natural source of biologically active compounds with potential application in the pharmaceutical industry.

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