Deformation analysis of microcapsules compressed by two rigid parallel plates

Alginate-poly(l)lysine-alginate microcapsules with a diameter of 200–300 μm were produced and subjected to compression experiments using two rigid parallel plates. The deformed shape was observed, and the relationship between the applied force and the displacement of the plate was measured. A practical analysis method is proposed for the prediction of mechanical properties of microcapsules, namely, the changes in force, transmural pressure, and deformed shape due to the change in the displacement of the plate. The analysis is based on a microcapsule model comprising an axi-symmetric elastic membrane with a constant capsule volume during deformation. Young’s modulus of the membrane, which is used in the analysis, was determined by applying the Hertz contact theory to the experimental results obtained by using an atomic force microscope. The bending stiffness and permeability of the membrane as well as the frictional force between the membrane and the plate were neglected in the analysis. A non-dimensional relationship between the applied force and the displacement of the plate was shown. The theoretically predicted compression force was smaller than the experimentally measured force in the small displacement region, whereas both forces were in good agreement in the large displacement region. The effects of change in Poisson’s ratio, which varied from 0 to 0.5, on the force, transmural pressure, and deformed shape were shown. Under the same displacement conditions, it was observed that the calculated deformed shape was almost coincident with the shape observed in the experiment.     

Mechanical and failure properties of single attached cells under compression

Eukaryotic cells are continuously subjected to mechanical forces under normal physiological conditions. These forces and associated cellular deformations induce a variety of biological processes. The degree of deformation depends on the mechanical properties of the cell. As most cells are anchorage dependent for normal functioning, it is important to study the mechanical properties of cells in their attached configuration. The goal of the present study was to obtain the mechanical and failure properties of attached cells. Individual, attached C2C12 mouse myoblasts were subjected to unconfined compression experiments using a recently developed loading device. The device allows global compression of the cell until cell rupture and simultaneously measures the associated forces. Cell bursting was characterized by a typical reduction in the force, referred to as the bursting force. Mean bursting forces were calculated as 8.7+/-2.5 microN at an axial strain of 72+/-4%. Visualization of the cell using confocal microscopy revealed that cell bursting was preceded by the formation of bulges at the cell membrane, which eventually led to rupturing of the cell membrane. Finite element calculations were performed to simulate the obtained force-deformation curves. A finite element mesh was built for each cell to account for its specific geometrical features. Using an axisymmetric approximation of the cell geometry, and a Neo-Hookean constitutive model, excellent agreement between predicted and measured force-deformation curves was obtained, yielding an average Young's modulus of 1.14+/-0.32 kPa.     

Detachment of agglutinin-bonded red blood cells. I. Forces to rupture molecular-point attachments.

A simple micromechanical method has been developed to measure the rupture strength of a molecular-point attachment (focal bond) between two macroscopically smooth membrane capsules. In the procedure, one capsule is prepared with a low density coverage of adhesion molecules, formed as a stiff sphere, and held at fixed position by a micropipette. The second capsule without adhesion molecules is pressurized into a spherical shape with low suction by another pipette. This capsule is maneuvered to initiate point contact at the pole opposite the stiff capsule which leads to formation of a few (or even one) molecular attachments. Then, the deformable capsule is slowly withdrawn by displacement of the pipette. Analysis shows that the end-to-end extension of the capsule provides a direct measure of the force at the point contact and, therefore, the rupture strength when detachment occurs. The range for point forces accessible to this technique depends on the elastic moduli of the membrane, membrane tension, and the size of the capsule. For biological and synthetic vesicle membranes, the range of force lies between 10(-7)-10(-5) dyn (10(-12)-10(-10) N) which is 100-fold less than presently measurable by Atomic Force Microscopy! Here, the approach was used to study the forces required to rupture microscopic attachments between red blood cells formed by a monoclonal antibody to red cell membrane glycophorin, anti-A serum, and a lectin from the snail-helix pomatia. Failure of the attachments appeared to be a stochastic function of the magnitude and duration of the detachment force. We have correlated the statistical behavior observed for rupture with a random process model for failure of small numbers of molecular attachments. The surprising outcome of the measurements and analysis was that the forces deduced for short-time failure of 1-2 molecular attachments were nearly the same for all of the agglutinin, i.e., 1-2 x 10(-6) dyn. Hence, microfluorometric tests were carried out to determine if labeled agglutinins and/or labeled surface molecules were transferred between surfaces after separation of large areas of adhesive contact. The results showed that the attachments failed because receptors were extracted from the membrane.     

Development of dielectrophoresis separator with an insulating porous membrane using DC‐Offset AC Electric Fields

Our previous studies revealed that the dielectrophoresis method is effective for separating cells having different dielectric properties. The purpose of this study was to evaluate the separation characteristics of two kinds of cells by direct current (DC) voltage offset/alternating current (AC) voltage using an insulating porous membrane dielectrophoretic separator. The separation device gives dielectrophoretic (DEP) force and electrophoretic (EP) force to dispersed particles by applying the DC‐offset AC voltage. This device separates cells of different DEP properties by adopting a structure in which only the parallel plate electrodes and the insulating porous membrane are disposed in the flow path through which the cell‐suspension flows. The difference in the retention ratios of electrically homogeneous 4.5 μm or 20.0 μm diameter standard particles was a maximum of 82 points. Furthermore, the influences of the AC voltage or offset voltage on the retention ratios of mouse hybridoma 3‐2H3 cells and horse red blood cells (HRBC) were investigated. The difference in the retention ratio of the two kinds of cells was a maximum of 56 points. The separation efficiency of this device is expected to be improved by changing the device shape, number of pores, and pore placement. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:1292–1300, 2016     

Mechanics of the Formation,Interaction, and Evolution of Membrane Tubular Structures

Membrane nanotubes, also known as membrane tethers, play important functional roles in many cellular processes, such as trafficking and signaling. Although considerable progresses have been made in understanding the physics regulating the mechanical behaviors of individual membrane nanotubes, relatively little is known about the formation of multiple membrane nanotubes due to the rapid occurring process involving strong cooperative effects and complex configurational transitions. By exerting a pair of external extraction upon two separate membrane regions, here, we combine molecular dynamics simulations and theoretical analysis to investigate how the membrane nanotube formation and pulling behaviors are regulated by the separation between the pulling forces and how the membrane protrusions interact with each other. As the force separation increases, different membrane configurations are observed, including an individual tubular protrusion, a relatively less deformed protrusion with two nanotubes on its top forming a V shape, a Y-shaped configuration through nanotube coalescence via a zipper-like mechanism, and two weakly interacting tubular protrusions. The energy profile as a function of the separation is determined. Moreover, the directional flow of lipid molecules accompanying the membrane shape transition is analyzed. Our results provide new, to our knowledge, insights at a molecular level into the interaction between membrane protrusions and help in understanding the formation and evolution of intra- and intercellular membrane tubular networks involved in numerous cell activities.     

Lateral organization of membranes and cell shapes.

The relations among membrane structure, mechanical properties, and cell shape have been investigated. The fluid mosaic membrane models used contains several components that move freely in the membrane plane. These components interact with each other and determine properties of the membrane such as curvature and elasticity. A free energy equation is postulated for such a multicomponent membrane and the condition of free energy minimum is used to obtain differential equations relating the distribution of membrane components and the local membrane curvature. The force that moves membrane components along the membrane in a variable curvature field is calculated. A change in the intramembrane interactions can bring about phase separation or particle clustering. This, in turn, may strongly affect the local curvature. The numerical solution of the set of equations for the two dimensional case allows determination of the cell shape and the component distribution along the membrane. The model has been applied to describe certain erythrocytes shape transformations.     

A structural constitutive model for the human lens capsule

Published data on the mechanical performance of the human lens capsule when tested under uniaxial and biaxial conditions are reviewed. It is concluded that two simple phenomenological constitutive models (namely a linear elastic model and a Fung-type hyperelastic model) are unable to provide satisfactory representations of the mechanical behaviour of the capsule for both of these loading conditions. The possibility of resolving these difficulties using a structural constitutive model for the capsule, of a form that is inspired by the network of collagen IV filaments that exist within the lens capsule, is explored. The model is implemented within a rectangular periodic cell. Prescribed stretches are imposed on the periodic cell and the network is allowed to deform in a non-affine manner. The performance of the constitutive model correlates well with previously published test data. One possible application of the model is in the development of a multi-scale analysis of the mechanics of the human lens capsule.     

Applications of field-flow fractionation in proteomics: presence and future

Field-flow fractionation (FFF) represents a group of elution separation methods where external force fields act perpendicularly on analytes in a carrier liquid flows with nonuniform velocity profiles. It is an elution separation method that enables to separate analytes in relatively short times and collect fractions for further characterization or for investigation of their properties. Other advantages of FFF are small consumption of samples and gentle experimental conditions. These make FFF uniquely qualified for separation and purification of biological samples. The most promising are applications of different variants of flow FFF utilizing a cross flow through membrane channel walls to separate proteins. The separation is based on differences in protein diffusion coefficients, which allows calculating the size of macromolecules. Other FFF techniques (e.g., electrical, isoelectric, and sedimentation FFF) were also used for separation of biomolecules. FFF appears to be not only promising rapid technique for protein separation but it offers some other advantages in sample preparation, especially, focusing (hyperlayer) FFF techniques that enable preparation of homogeneous fractions of cells. Selected applications of FFF to protein analysis are described and future trends in application of FFF to proteomics are discussed.     

Experimental evaluation of a newly developed 90 degree angle plate (MC angle plate) for intertrochanteric derotation osteotomy]

A newly developed 90 degrees angled blade plate that permits high interfragmentary compression with a potential sliding way of 9 mm, is described. In the majority of intertrochanteric osteotomies, and especially when applying "functional pre-bending", the use of an external compression device is not necessary with this plate. The plate consists of 2 modules which permit a temporary thickening of the plate up to 10 mm, and the principle of dynamic compression can be performed with a 45 degree screw hole for the sliding way of 9 mm. The results of testing showed that a compression force of up to 1200 N was possible. The resulting interfragmentary compression could not be increased even with the aid of an external compression device or by idealized experimental conditions. Whenever dynamic compression is necessary for fixation, the modular compression principle described here can be used with any other plate system.     

Dynamic unconfined compression of articular cartilage under a cyclic compressive load

To study the effect of dynamic mechanical force on cartilage metabolism, many investigators have applied a cyclic compressive load to cartilage disc explants in vitro. The most frequently used in vitro testing protocol has been the cyclic unconfined compression of articular cartilage in a bath of culture medium. Cyclic compression has been achieved by applying either a prescribed cyclic displacement or a prescribed cyclic force on a loading platen placed on the top surface of a cylindrical cartilage disc. It was found that the separation of the loading platen from the tissue surface was likely when a prescribed cyclic displacement was applied at a high frequency.The purpose of the present study was to simulate mathematically the dynamic behavior of a cylindrical cartilage disc subjected to cyclic unconfined compression under a dynamic force boundary condition protocol, and to provide a parametric analysis of mechanical deformations within the extracellular matrix. The frequency-dependent dynamic characteristics of dilatation, hydrostatic pressure and interstitial fluid velocity were analyzed over a wide range of loading frequencies without the separation of the loading platen. The result predicted that a cyclic compressive force created an oscillating positive-negative hydrostatic pressure together with a forced circulation of interstitial fluid within the tissue matrix. It was also found that the load partitioning mechanism between the solid and fluid phases was a function of loading frequency. At a relatively high loading frequency, a localized dynamic zone was developed near the peripheral free surface of the cartilage disc, where a large dynamic pressure gradient exists, causing vigorous interstitial fluid flow.     

The effect of lipid demixing on the electrostatic interaction of planar membranes across a salt solution

We study the effect of lipid demixing on the electrostatic interaction of two oppositely-charged membranes in solution, modeled here as an incompressible two-dimensional fluid mixture of neutral and charged mobile lipids. We calculate, within linear and nonlinear Poisson-Boltzmann theory, the membrane separation at which the net electrostatic force between the membranes vanishes, for a variety of different system parameters. According to Parsegian and Gingell, contact between oppositely-charged surfaces in an electrolyte is possible only if the two surfaces have exactly the same charge density (sigma(1) = -sigma(2)). If this condition is not fulfilled, the surfaces can repel each other, even though they are oppositely charged. In our model of a membrane, the lipidic charge distribution on the membrane surface is not homogeneous and frozen, but the lipids are allowed to freely move within the plane of the membrane. We show that lipid demixing allows contact between membranes even if there is a certain charge mismatch, /sigma(1)/ not equal /sigma(2)/, and that in certain limiting cases, contact is always possible, regardless of the value of sigma(1)/sigma(2) (if sigma(1)/sigma(2) < 0). We furthermore find that of the two interacting membranes, only one membrane shows a major rearrangement of lipids, whereas the other remains in exactly the same state it has in isolation and that, at zero-disjoining pressure, the electrostatic mean-field potential between the membranes follows a Gouy-Chapman potential from the more strongly charged membrane up to the point of the other, more weakly charged membrane.     

Single cell analytics for nanobiology

Single cell analytics allows quantitative investigation of single biological cells from a structural, functional and proteomics point of view and opens possibilities to a novel unamplified cell analysis inherently insensitive to ensemble-averaging, cell-cycle or cell-population effects. We report on three different experimental methods and their application to cellular systems with single molecule sensitivity at the single cell level. Firstly, atomic force microscopy (AFM) can be used to elucidate the surface structure of living bacteria down to the nanometer scale where identification of irregular surface areas and 2D-arrays of regular protein s-layers is possible. Secondly, single cell manipulation and probing experiments with optical tweezers (OT) force spectroscopy allows quantitative identification of individual recognition events of membrane bound receptors. And thirdly, a novel, single cell analysis for protein fingerprinting in structured microfluidic device format will allow a future (label-free) on-chip electrophoretical protein separation of single cells without preamplification.     

Confocal arthroscopy-based patient-specific constitutive models of cartilaginous tissues - II: prediction of reaction force history of meniscal cartilage specimens

The theoretical framework developed in a companion paper (Part I) is used to derive estimates of mechanical response of two meniscal cartilage specimens. The previously developed framework consisted of a constitutive model capable of incorporating confocal image-derived tissue microstructural data. In the present paper (Part II) fibre and matrix constitutive parameters are first estimated from mechanical testing of a batch of specimens similar to, but independent from those under consideration. Image analysis techniques which allow estimation of tissue microstructural parameters form confocal images are presented. The constitutive model and image-derived structural parameters are then used to predict the reaction force history of the two meniscal specimens subjected to partially confined compression. The predictions are made on the basis of the specimens' individual structural condition as assessed by confocal microscopy and involve no tuning of material parameters. Although the model does not reproduce all features of the experimental curves, as an unfitted estimate of mechanical response the prediction is quite accurate. In light of the obtained results it is judged that more general non-invasive estimation of tissue mechanical properties is possible using the developed framework.     

Mechanical properties of desiccated ragweed pollen grains determined by micromanipulation and theoretical modelling

The mechanical properties of desiccated ragweed pollen grains were determined using a micromanipulation technique and a theoretical model. Single pollen grains with a diameter of approximately 20 microm were compressed and held, compressed and released, and compressed to rupture at different speeds between two parallel surfaces. Simultaneously, the force being imposed on the pollen grains was measured. It has been found that the rupture force of pollen grains increased linearly with their displacement at rupture on average, but was independent of their diameter. The mean rupture force was 1.20 +/- 0.03 mN, and mean deformation (the ratio between the displacement and diameter) at rupture was 22 +/- 0.6%. Single pollen grains were modeled as a capsule with a core full of air and a non permeable wall. A constitutive equation based on Hookean law was used to determine the mechanical property parameters Eh (product of the Young's modulus and wall thickness), and the mean value of Eh of desiccated pollen gains was estimated to be 1653 +/- 36 N/m.     

Gelation conditions and transport properties of hollow calcium alginate capsules

The diameter, membrane thickness, and compression intensity of hollow Ca-alginate capsules were measured at different gelation conditions, such as the reactant concentration, dropping velocity, and gelation time. The optimum operation conditions for preparing capsules were determined at 100 g/L CaCl(2), 10 g/L sodium alginate (Na-alginate), a dropping velocity of 150 droplets/min, and a gelation time of 10 min. Diffusion of some saccharide and amino acid from bulk solution into capsules was investigated, and the diffusion coefficients were calculated by the developed mathematical model. All the tested substances can diffuse easily into the capsules. The combined diffusion coefficients of the capsule D(m) are 92-99% as large as their diffusion coefficients in pure water, while the diffusion coefficients in the capsule membrane D(1) are 60-95% as large as those. By employing polyethylene glycol (PEG) and bovine serum albumin (fraction V) (BSA(V)), the molecular weight cut-off of the capsule was determined. For linear macromolecules, hollow Ca-alginate capsules have a molecular weight cut-off of 4000. No diffusion of BSA(V) into the capsules was observed.     

Millipore Filtration of Conjugating Bacterial Cells, with Epoxy Embedding for Electron Microscopy

Broth cultures of Escherichia coli, strains Hfr G6 and F^- 464 grown separately, were mixed (2 ml of each) and the mixture filtered through a 0.45 μ pore size, 25 mm diameter, MF-Millipore membrane. The membrane was placed, cell side up, on a nutrient agar plate and incubated 15 min at 37 C. Processing in the customary manner to include fixation, staining and epoxy embedding for electron microscopy followed. The technique provides greater concentration of cells, allows less opportunity for separation of conjugating cells and is less time consuming than procedures involving concentration by centrifugation and enclosure in agar as prerequisities to resin embedding.     

A biophysical model for plant cell plate maturation based on the contribution of a spreading force

Plant cytokinesis, a fundamental process of plant life, involves de novo formation of a “cell plate” partitioning the cytoplasm of dividing cells. Cell plate formation is directed by orchestrated delivery, fusion of cytokinetic vesicles, and membrane maturation to form a nascent cell wall by timely deposition of polysaccharides. During cell plate maturation, the fragile membrane network transitions to a fenestrated sheet and finally a young cell wall. Here, we approximated cell plate sub-structures with testable shapes and adopted the Helfrich-free energy model for membranes, including a stabilizing and spreading force, to understand the transition from a vesicular network to a fenestrated sheet and mature cell plate. Regular cell plate development in the model was possible, with suitable bending modulus, for a two-dimensional late stage spreading force of 2–6 pN/nm, an osmotic pressure difference of 2–10 kPa, and spontaneous curvature between 0 and 0.04 nm⁻¹. With these conditions, stable membrane conformation sizes and morphologies emerged in concordance with stages of cell plate development. To reach a mature cell plate, our model required the late-stage onset of a spreading/stabilizing force coupled with a concurrent loss of spontaneous curvature. Absence of a spreading/stabilizing force predicts failure of maturation. The proposed model provides a framework to interrogate different players in late cytokinesis and potentially other membrane networks that undergo such transitions. Callose, is a polysaccharide that accumulates transiently during cell plate maturation. Callose-related observations were consistent with the proposed model’s concept, suggesting that it is one of the factors involved in establishing the spreading force.

The late-stage onset of an “areal” spreading and stabilizing force is essential for regular plant cell plate development and maturation.     

Forces and stresses acting on fusion pore membrane during secretion

To assess the forces and stresses present in fusion pore during secretion the stationary convective flux of lipid through a fusion pore connecting two planar membranes under different tensions was investigated through computer simulations. The physics of the problem is described by Navier-Stokes equations, and the convective flux of lipid was evaluated using finite element method. Each of the membrane monolayer is considered separately as an isotropic, homogeneous and incompressible viscous medium with the same viscosity. The difference in membrane tensions, which is simulated as the pressure difference at two ends of each monolayer, is the driving force of the lipid flow. The two monolayers interact by sliding past each other with inter-monolayer frictional viscosity. Fluid velocity, pressure, shear and normal stresses, viscous and frictional dissipations and forces were calculated to evaluate where the fusion pore will deform, extend (or compress) and dilate. The pressure changes little in the planar sections, whereas in the toroidal section the change is rapid. The magnitude of lipid velocity peaks at the pore neck. The radial lipid velocity is zero at the neck, has two peaks one on each side of the pore neck, and diminishes without going to zero in planar parts of two monolayers. The peaks are of opposite signs due to the change of direction of lipid flow. The axial velocity is confined to the toroidal section, peaks at the neck and is clearly greater in the outer monolayer. As a result of the spatially highly uneven lipid flow the membrane is under a significant stress, shear and normal. The shear stress, which indicates where the membrane will deform without changing the volume, has two peaks placed symmetrically about the neck. The normal stress shows where the membrane may extend or compress. Both, the radial and axial normal stresses are negative (extensive) in the upper toroidal section and positive (compressive) in the lower toroidal section. The pressure difference determines lipid velocity and velocity dependent variables (shear as well as normal axial and radial stresses), but also contributes directly to the force on the membranes and critically influences where and to what extent the membrane will deform, extend or dilate. The viscosity coefficient (due to friction of one element of lipid against neighboring ones), and frictional coefficient (due to friction between two monolayers sliding past each other) further modulate some variables. Lipid velocity rises as pressure difference increases, diminishes as the viscosity coefficient rises but is unaffected by the frictional coefficient. The shear and normal stresses rise as pressure difference increases, but the change of the viscosity coefficients has no effect. Both the viscous dissipation (which has two peaks placed symmetrically about the neck) and much smaller frictional dissipation (which peaks at the pore neck) rise with pressure and diminish if the viscosity coefficient rises, but only the frictional dissipation increases if the frictional coefficient increases. Finally, the radial force causing pore dilatation, and which is significant only in the planar section of the vesicular membrane, is governed almost entirely by the pressure, whereas the viscosity and frictional coefficients have only a marginal effect. Many variables are altered during pore dilatation. The lipid velocity and dissipations (viscous and frictional) rise approximately linearly with pore radius, whereas the lipid mass flow increases supra-linearly owing to the combined effects of the changes in pore radius and greater lipid velocity. Interestingly the radial force on the vesicular membrane increases only marginally.