Passive mechanical behavior of human neutrophils: effect of cytochalasin B.

Actin is a ubiquitous protein in eukaryotic cells. It plays a major role in cell motility and in the maintenance and control of cell shape. In this article, we intend to address the contribution of actin to the passive mechanical properties of human neutrophils. As a framework for assessing this contribution, the neutrophil is modeled as a simple viscous fluid drop with a constant cortical ("surface") tension. The reagent cytochalasin B (CTB) was used to disrupt the F-actin structure, and the neutrophil cortical tension and cytoplasmic viscosity were evaluated by single-cell micropipette aspiration. The cortical tension was calculated by simple force balance, and the viscosity was calculated according to a numerical analysis of the cell entry into the micropipette. CTB reduced the cell cortical tension in a dose-dependent fashion: by 19% at a concentration of 3 microM and by 49% at 30 microM. CTB also reduced the cytoplasmic viscosity by approximately -25% at a concentration of 3 microM and by approximately 65% at a concentration of 30 microM when compared at the same aspiration pressures. All three groups of neutrophils, normal cells, and cells treated with either 3 or 30 microM CTB, exhibited non-Newtonian behavior, in that the apparent viscosity decreased with increasing shear rate. The dependence of the cytoplasmic viscosity on deformation rate can be described empirically by mu = mu c(gamma m/gamma c)-b, where mu is cytoplasmic viscosity, gamma m is mean shear rate, mu c is the characteristic viscosity at the characteristic shear rate gamma c, and b is a material coefficient.(ABSTRACT TRUNCATED AT 250 WORDS)     

Passive mechanical behavior of human neutrophils: power-law fluid.

The mechanical behavior of the neutrophil plays an important role in both the microcirculation and the immune system. Several laboratories in the past have developed mechanical models to describe different aspects of neutrophil deformability. In this study, the passive mechanical properties of normal human neutrophils have been further characterized. The cellular mechanical properties were assessed by single cell micropipette aspiration at fixed aspiration pressures. A numerical simulation was developed to interpret the experiments in terms of cell mechanical properties based on the Newtonian liquid drop model (Yeung and Evans, Biophys. J., 56: 139-149, 1989). The cytoplasmic viscosity was determined as a function of the ratio of the initial cell size to the pipette radius, the cortical tension, aspiration pressure, and the whole cell aspiration time. The cortical tension of passive neutrophils was measured to be about 2.7 x 10(-5) N/m. The apparent viscosity of neutrophil cytoplasm was found to depend on aspiration pressure, and ranged from approximately 500 Pa.s at an aspiration pressure of 98 Pa (1.0 cm H2O) to approximately 50 Pa.s at 882 Pa (9.0 cm H2O) when tested with a 4.0-micron pipette. These data provide the first documentation that the neutrophil cytoplasm exhibits non-Newtonian behavior. To further characterize the non-Newtonian behavior of human neutrophils, a mean shear rate gamma m was estimated based on the numerical simulation. The apparent cytoplasmic viscosity appears to decrease as the mean shear rate increases. The dependence of cytoplasmic viscosity on the mean shear rate can be approximated as a power-law relationship described by mu = mu c(gamma m/gamma c)-b, where mu is the cytoplasmic viscosity, gamma m is the mean shear rate, mu c is the characteristic viscosity at characteristic shear rate gamma c, and b is a material coefficient. When gamma c was set to 1 s-1, the material coefficients for passive neutrophils were determined to be mu c = 130 +/- 23 Pa.s and b = 0.52 +/- 0.09 for normal neutrophils. The power-law approximation has a remarkable ability to reconcile discrepancies among published values of the cytoplasmic viscosity measured using different techniques, even though these values differ by nearly two orders of magnitude. Thus, the power-law fluid model is a promising candidate for describing the passive mechanical behavior of human neutrophils in large deformation. It can also account for some discrepancies between cellular behavior in single-cell micromechanical experiments and predictions based on the assumption that the cytoplasm is a simple Newtonian fluid.     

Membrane viscoelasticity.

In this paper, we develop a theory for viscoelastic behavior of large membrane deformations and apply the analysis to the relaxation of projections produced by small micropipette aspiration of red cell discocytes. We show that this relaxation is dominated by the membrane viscosity and that the cytoplasmic and extracellular fluid flow have negligible influence on the relaxation time and can be neglected. From preliminary data, we estimate the total membrane "viscosity" when the membrane material behaves in an elastic solid manner. The total membrane viscosity is calculated to be 10(-3) dyn-s/cm, which is a surface viscosity that is about three orders of magnitude greater than the surface viscosity of lipid membrane components (as determined by "fluidity" measurements). It is apparent that the lipid bilayer contributes little to the fluid dynamic behavior of the whole plasma membrane and that a structural matrix dominates the viscous dissipation. However, we show that viscous flow in the membrane is not responsible for the temporal dependence of the isotropic membrane tension required to produce lysis and that the previous estimates of Rand, Katchalsky, et al., for "viscosity" are six to eight orders of magnitude too large.     

Cortical shell-liquid core model for passive flow of liquid-like spherical cells into micropipets.

Many nonadherent cells exist as spheres in suspension and when sucked into pipets, deform continuously like liquids within the fixed surface area limitation of a plasma membrane envelope. After release, these cells eventually recover their spherical form. Consequently, pipet aspiration test provides a useful method to assay the apparent viscosity of such cells. For this purpose, we have analyzed the inertialess flow of a liquid-like model cell into a tube at constant suction pressure. The cell is modeled as a uniform liquid core encapsulated by a distinct cortical shell. The method of analysis employs a variational approach that minimizes errors in boundary conditions defined by the equations of motion for the cortical shell where the trial functions are exact solutions for the flow field inside the liquid core. For the particular case of an anisotropic liquid cortex with persistent tension, we have determined universal predictions for flow rate scaled by the ratio of excess pressure (above the threshold established by the cortical tension) and core viscosity which is the reciprocal of the dynamic resistance to entry. The results depend on pipet to cell size ratio and a parameter that characterizes the ratio of viscous flow resistance in the cortex to that inside the cytoplasmic core. The rate of entry increases markedly as the pipet size approaches the outer segment diameter of the cell. Viscous dissipation in the cortex strongly influences the entry flow resistance for small tube sizes but has little effect for large tubes. This indicates that with sufficient experimental resolution, measurement of cell entry flow with different-size pipets could establish both the cortex to cell dissipation ratio as well as the apparent viscosity of the cytoplasmic core.     

Axisymmetric Drop Shape Analysis for Estimating the Surface Tension of Cell Aggregates by Centrifugation

Biological tissues behave in certain respects like liquids. Consequently, the surface tension concept can be used to explain aspects of the in vitro and in vivo behavior of multicellular aggregates. Unfortunately, conventional methods of surface tension measurement cannot be readily applied to small cell aggregates. This difficulty can be overcome by an experimentally straightforward method consisting of centrifugation followed by axisymmetric drop shape analysis (ADSA). Since the aggregates typically show roughness, standard ADSA cannot be applied and we introduce a novel numerical method called ADSA-IP (ADSA for imperfect profile) for this purpose. To examine the new methodology, embryonic tissues from the gastrula of the frog, Xenopus laevis, deformed in the centrifuge are used. It is confirmed that surface tension measurements are independent of centrifugal force and aggregate size. Surface tension is measured for ectodermal cells in four sample batches, and varies between 1.1 and 7.7 mJ/m². Surface tension is also measured for aggregates of cells expressing cytoplasmically truncated EP/C-cadherin, and is approximately half as large. In parallel, such aggregates show a reduction in convergent extension-driven elongation after activin treatment, reflecting diminished intercellular cohesion.     

Viscosity of passive human neutrophils undergoing small deformations.

At issue is the type of constitutive equation that can be used to describe all possible types of deformation of the neutrophil. Here a neutrophil undergoing small deformations is studied by aspirating it into a glass pipet with a diameter that is only slightly smaller than the diameter of the spherically shaped cell. After being held in the pipet for at least seven seconds, the cell is rapidly expelled and allowed to recover its undeformed, spherical shape. The recovery takes approximately 15 s. An analysis of the recovery process that treats the cell as a simple Newtonian liquid drop with a constant cortical (surface) tension gives a value of 3.3 x 10(-5) cm/s for the ratio of the cortical tension to cytoplasmic viscosity. This value is about twice as large as a previously published value obtained with the same model from studies of large deformations of neutrophils. This discrepancy indicates that the cytoplasmic viscosity decreases as the amount of deformation decreases. An extrapolated value for the cytoplasmic viscosity at zero deformation is approximately 600 poise when a value for the cortical tension of 0.024 dyn/cm is assumed. Clearly the neutrophil does not behave like a simple Newtonian liquid drop in that small deformations are inherently different from large deformations. More complex models consisting either of two or more fluids or multiple shells must be developed. The complex structure inside the neutrophil is shown in scanning electron micrographs of osmotically burst cells and cells whose membrane has been dissolved away.     

Instability development in heated human erthrocytes.

Heated human erythrocytes gradually lose their form-maintaining structure as the temperature is increased to 50 degrees C and can behave in some respects as a viscous fluid. We have developed a technique for heating and stressing these cells that is novel, simple and quantitatively precise. We have applied this technique to heated human erythrocytes and have measured instability development in cells. We have employed instability growth theory to calculate a value for an effective surface tension which, in contrast to other methods of membrane surface tension measurement sought to minimize the effects of membrane supporting structural elements. The value obtained for the surface tension of the heated erythrocyte membrane was 0.9 . 10(-6) N/m with a range of variation from 0.4 . 10(-6)N/m to 1.4 . 10(-6) N/m. The methods described may be useful for determining fundamental physical parameters such as internal viscosity and interfacial tension in other systems.     

A statistical framework for multiparameter analysis at the single-cell level

Phenotypic characterization of individual cells provides crucial insights into intercellular heterogeneity and enables access to information that is unavailable from ensemble averaged, bulk cell analyses. Single-cell studies have attracted significant interest in recent years and spurred the development of a variety of commercially available and research-grade technologies. To quantify cell-to-cell variability of cell populations, we have developed an experimental platform for real-time measurements of oxygen consumption (OC) kinetics at the single-cell level. Unique challenges inherent to these single-cell measurements arise, and no existing data analysis methodology is available to address them. Here we present a data processing and analysis method that addresses challenges encountered with this unique type of data in order to extract biologically relevant information. We applied the method to analyze OC profiles obtained with single cells of two different cell lines derived from metaplastic and dysplastic human Barrett's esophageal epithelium. In terms of method development, three main challenges were considered for this heterogeneous dynamic system: (i) high levels of noise, (ii) the lack of a priori knowledge of single-cell dynamics, and (iii) the role of intercellular variability within and across cell types. Several strategies and solutions to address each of these three challenges are presented. The features such as slopes, intercepts, breakpoint or change-point were extracted for every OC profile and compared across individual cells and cell types. The results demonstrated that the extracted features facilitated exposition of subtle differences between individual cells and their responses to cell-cell interactions. With minor modifications, this method can be used to process and analyze data from other acquisition and experimental modalities at the single-cell level, providing a valuable statistical framework for single-cell analysis.     

Epithelia as bubble rafts: A new method for analysis of cell shape and intercellular adhesion in embryonic and other epithelia

Cell-cell interactions may often be characterized by a work of adhesion or equivalent surface tension between cells. This intercellular surface tension may vary from one part of an epithelium to another. Such gradients in surface tension may be important driving factors in morphogenesis. A computational method for the measurement of parameters of cell shape involved in surface tension has been developed. It permits detailed observational analysis of cell-cell interface curvature. The information thus obtained is utilized in an algorithm for estimating gradients of surface tension in epithelia. The use of these methods should permit cell biologists and embryologists to decide whether or not developing cells behave like bubbles, and if so, to what extent their adhesive forces contribute to various aspects of embryogenesis.     

Baseline mechanical characterization of J774 macrophages

Macrophage cell lines like J774 cells are ideal model systems for establishing the biophysical foundations of autonomous deformation and motility of immune cells. To aid comparative studies on these and other types of motile cells, we report measurements of the cortical tension and cytoplasmic viscosity of J774 macrophages using micropipette aspiration. Passive J774 cells cultured in suspension exhibited a cortical resting tension of ∼0.14 mN/m and a viscosity (at room temperature) of 0.93 kPa·s. Both values are about one order of magnitude higher than the respective values obtained for human neutrophils, lending support to the hypothesis that a tight balance between cortical tension and cytoplasmic viscosity is a physical prerequisite for eukaryotic cell motility. The relatively large stiffness of passive J774 cells contrasts with their capacity for a more than fivefold increase in apparent surface area during active deformation in phagocytosis. Scanning electron micrographs show how microscopic membrane wrinkles are smoothed out and recruited into the apparent surface area during phagocytosis of large targets.     

Is cell sorting caused by differences in the work of intercellular adhesion? A critique of the steinberg hypothesis

The differential adhesion hypothesis, developed by Malcolm Steinberg, proposes that the histotypic sorting out behavior of aggregated cells is mechanistically equivalent to certain aspects of liquid surface tension, specifically the spontaneous separation of immiscible liquids of differing surface tension. According to Steinberg's hypothesis, the adhesive forces between aggregated cells play essentially the same role in cell sorting as are played by intermolecular attractive forces in liquid surface tension.In this paper I discuss a number of crucial distinctions between intermolecular attraction (in liquids) and intercellular adhesion (in aggregates). First, liquid drops are closed systems thermodynamically whereas aggregates of living cells can generate an indeterminate amount of metabolic energy capable of altering cell positions and adhesions. Secondly, intercellular adhesions are more than just close range attractions since cells can be held together by forces in addition to those which originally pulled them together. Third, the breakage of intercellular adhesions need not be simply the reverse, thermodynamically, of the formation of those adhesions. And fourthly, because intercellular adhesion is generally concentrated at relatively small foci such as desmosomes, a maximization of intercellular adhesion does not necessarily require a maximization of intercellular contact area, or vice versa.In addition, several alternative hypotheses are proposed, each of which is theoretically capable of explaining cell sorting and the other surface tension-like aspects of cell aggregate behavior which Steinberg has sought to explain as consequences of differential adhesion. In particular, a differential surface contraction hypothesis is proposed, according to which cell sorting and related phenomena are the results of cell surface contractions induced to occur over those portions of the cell surface which are exposed to the surrounding culture medium. Because of the evidence that various invagination type movements of embryonic epithelia are caused by cell surface contractions, it is suggested that differential surface contraction is the most likely explanation of histotypic cell sorting. A number of experiments are suggested by which these various hypotheses might be tested.     

Measurement of Aggregate Cohesion by Tissue Surface Tensiometry

Rigorous measurement of intercellular binding energy can only be made using methods grounded in thermodynamic principles in systems at equilibrium. We have developed tissue surface tensiometry (TST) specifically to measure the surface free energy of interaction between cells. The biophysical concepts underlying TST have been previously described in detail^1,2. The method is based on the observation that mutually cohesive cells, if maintained in shaking culture, will spontaneously assemble into clusters. Over time, these clusters will round up to form spheres. This rounding-up behavior mimics the behavior characteristic of liquid systems. Intercellular binding energy is measured by compressing spherical aggregates between parallel plates in a custom-designed tissue surface tensiometer. The same mathematical equation used to measure the surface tension of a liquid droplet is used to measure surface tension of 3D tissue-like spherical aggregates. The cellular equivalent of liquid surface tension is intercellular binding energy, or more generally, tissue cohesivity. Previous studies from our laboratory have shown that tissue surface tension (1) predicts how two groups of embryonic cells will interact with one another^1-5, (2) can strongly influence the ability of tissues to interact with biomaterials⁶, (3) can be altered not only through direct manipulation of cadherin-based intercellular cohesion⁷, but also by manipulation of key ECM molecules such as FN^8-11 and 4) correlates with invasive potential of lung cancer¹², fibrosarcoma¹³, brain tumor¹⁴ and prostate tumor cell lines¹⁵. In this article we will describe the apparatus, detail the steps required to generate spheroids, to load the spheroids into the tensiometer chamber, to initiate aggregate compression, and to analyze and validate the tissue surface tension measurements generated.Download video file.^{(79M, mov)}     

Equilibrium mechanics of monolayered epithelium

In order to fully understand the epithelial mechanics it is essential to integrate different levels of epithelial organization. In this work, we propose a theoretical approach for connecting the macroscopic mechanical properties of a monolayered epithelium to the mechanical properties at the cellular level. The analysis is based on the established mechanical models—at the macroscopic scale the epithelium is described within the mechanics of thin layers, while the cellular level is modeled in terms of the cellular surface (cortical) tension and the intercellular adhesion. The macroscopic elastic energy of the epithelium is linked to the energy of an average epithelial cell. The epithelial equilibrium state is determined by energy minimization and the macroscopic elastic moduli are calculated from deformations around the equilibrium. The results indicate that the epithelial equilibrium state is defined by the ratio between the adhesion strength and the cellular surface tension. The lower and the upper bounds for this ratio are estimated. If the ratio is small, the epithelium is cuboidal, if it is large, the epithelium becomes columnar. Importantly, it is found that the cellular cortical tension and the intercellular adhesion alone cannot produce the flattened squamous epithelium. Any difference in the surface tension between the apical and basal cellular sides bends the epithelium towards the side with the larger surface tension. Interestingly, the analysis shows that the epithelial area expansivity modulus and the shear modulus depend only on the cellular surface tension and not on the intercellular adhesion. The results are presented in a general analytical form, and are thus applicable to a variety of monolayered epithelia, without relying on the specifics of numerical finite-element methods. In addition, by using the standard theoretical tools for multi-laminar systems, the results can be applied to epithelia consisting of layers with different mechanical properties.     

Transverse mechanical properties of cell walls of single living plant cells probed by laser-generated acoustic waves

Probing the mechanical properties of plant cell wall is crucial to understand tissue dynamics. However, the exact symmetry of the mechanical properties of this anisotropic fiber-reinforced composite remains uncertain. For this reason, biologically relevant measurements of the stiffness coefficients on individual living cells are a challenge. For this purpose, we have developed the single-cell optoacoustic nanoprobe (SCOPE) technique, which uses laser-generated acoustic waves to probe the stiffness, thickness and viscosity of live single-cell subcompartments. This all-optical technique offers a sub-micrometer lateral resolution, nanometer in-depth resolution, and allows the non-contact measurement of the mechanical properties of live turgid tissues without any assumption of mechanical symmetry. SCOPE experiments reveal that single-cell wall transverse stiffness in the direction perpendicular to the epidermis layer of onion cells is close to that of cellulose. This observation demonstrates that cellulose microfibrils are the main load-bearing structure in this direction, and suggests strong bonding of microfibrils by hemicelluloses. Altogether our measurement of the viscosity at high frequencies suggests that the rheology of the wall is dominated by glass-like dynamics. From a comparison with literature, we attribute this behavior to the influence of the pectin matrix. SCOPE’s ability to unravel cell rheology and cell anisotropy defines a new class of experiments to enlighten cell nano-mechanics.     

Sampling efficiency of a single-cell capillary electrophoresis system.

Capillary electrophoresis (CE) combined with a laser-induced fluorescence (LIF) detection scheme is a powerful approach for single-cell analysis. For measurements requiring a high temporal resolution, CE-LIF is often combined with cell lysis systems based on pulsed lasers. Although extremely rapid, laser lysis has raised some concerns about the efficiency at which the cell contents are sampled. We have assembled a single-cell CE-LIF mounted on the stage of a microscope. This system was coupled with a nanosecond pulsed laser for cell lysis. We have analyzed green fluorescent protein (GFP) expressed in single mammalian cells and developed a novel approach to estimate the cell sampling efficiency (SE) based on the use of fluorescent calibration microspheres and flow cytometry. A significant advantage of this method is that it does not require any knowledge or assumption regarding the cell volume. We have evaluated the SE for different laser pulse energies (from 2 to 9 microJ) and two different pulse focal positions in the xy plane (0-10 microm from the center of the cell). We found the maximum SE at the lowest energy (2 microJ), with the pulse focused directly on the cell. We have demonstrated the utility of a novel method to measure the SE of a single-cell CE system. The measurements presented in this study indicate that rapid cell lysis with nanosecond lasers requires careful optimization of pulse parameters for maximum sampling of the cell contents.     

Low viscosity in the aqueous domain of cell cytoplasm measured by picosecond polarization microfluorimetry

Information about the rheological characteristics of the aqueous cytoplasm can be provided by analysis of the rotational motion of small polar molecules introduced into the cell. To determine fluid-phase cytoplasmic viscosity in intact cells, a polarization microscope was constructed for measurement of picosecond anisotropy decay of fluorescent probes in the cell cytoplasm. We found that the rotational correlation time (tc) of the probes, 2,7-bis-(2-carboxyethyl)-5-(and-6-)carboxyfluorescein (BCECF), 6-carboxyfluorescein, and 8-hydroxypyrene-1,3,6-trisulfonic acid (HPTS) provided a direct measure of fluid-phase cytoplasmic viscosity that was independent of probe binding. In quiescent Swiss 3T3 fibroblasts, tc values were 20-40% longer than those in water, indicating that the fluid-phase cytoplasm is only 1.2-1.4 times as viscous as water. The activation energy of fluid-phase cytoplasmic viscosity was 4 kcal/mol, which is similar to that of water. Fluid-phase cytoplasmic viscosity was altered by less than 10% upon addition of sucrose to decrease cell volume, cytochalasin B to disrupt cell cytoskeleton, and vasopressin to activate phospholipase C. Nucleoplasmic and peripheral cytoplasmic viscosities were not different. Our results establish a novel method to measure fluid-phase cytoplasmic viscosity, and indicate that fluid-phase cytoplasmic viscosity in fibroblasts is similar to that of free water.     

INSISTC: Incorporating network structure information for single-cell type classification

Uncovering gene regulatory mechanisms in individual cells can provide insight into cell heterogeneity and function. Recent accumulated Single-Cell RNA-Seq data have made it possible to analyze gene regulation at single-cell resolution. Understanding cell-type-specific gene regulation can assist in more accurate cell type and state identification. Computational approaches utilizing such relationships are under development. Methods pioneering in integrating gene regulatory mechanism discovery with cell-type classification encounter challenges such as determine gene regulatory relationships and incorporate gene regulatory network structure. To fill this gap, we developed INSISTC, a computational method to incorporate gene regulatory network structure information for single-cell type classification. INSISTC is capable of identifying cell-type-specific gene regulatory mechanisms while performing single-cell type classification. INSISTC demonstrated its accuracy in cell type classification and its potential for providing insight into molecular mechanisms specific to individual cells. In comparison with the alternative methods, INSISTC demonstrated its complementary performance for gene regulation interpretation.     

Apparent viscosity and cortical tension of blood granulocytes determined by micropipet aspiration.

Continuous deformation and entry flow of single blood granulocytes into small caliber micropipets at various suction pressures have been studied to determine an apparent viscosity for the cell contents and to estimate the extent that dissipation in a cortical layer adjacent to the cell surface contributes to the total viscous flow resistance. Experiments were carried out with a wide range of pipet sizes (2.0-7.5 microns) and suction pressures (10(2)-10(4) dyn/cm2) to examine the details of the entry flow. The results show that the outer cortex of the cell maintains a small persistent tension of approximately 0.035 dyn/cm. The tension creates a threshold pressure below which the cell will not enter the pipet. The superficial plasma membrane of these cells appears to establish an upper limit to surface dilation which is reached after microscopic "ruffles" and "folds" have been pulled smooth. With aspiration of cells by small pipets (less than 2.7 microns), the limit to surface expansion was derived from the maximal extension of the cell into the pipet; final areas were measured to be 2.1 to 2.2 times the area of the initial spherical shape. For suctions in excess of a threshold, the response to constant pressure was continuous flow in proportion to excess pressure above the threshold with only a small nonlinearity over time until the cell completely entered the pipet (for pipet calibers greater than 2.7 microns). With a theoretical model introduced in a companion paper, (Yeung, A., and E. Evans., 1989, Biophys. J. 56:139-149) the entry flow response versus pipet size and suction pressure was analyzed to estimate the apparent viscosity of the cell interior and the ratio of cortical flow resistance to flow resistance from the cell interior. The apparent viscosity was found to depend strongly on temperature with values on the order of 2 x 10(3) poise at 23 degrees C, lower values of 1 x 10(3) poise at 37 degrees C, but extremely large values in excess of 10(4) poise below 10 degrees C. Because of scatter in cell response, it was not possible to accurately establish the characteristic ratio for flow resistance in the cortex to that inside the cell; however, the data showed that the cortex does not contribute significantly to the total flow resistance.     

Role of the membrane cortex in neutrophil deformation in small pipets.

The simplest model for a neutrophil in its "passive" state views the cell as consisting of a liquid-like cytoplasmic region surrounded by a membrane. The cell surface is in a state of isotropic contraction, which causes the cell to assume a spherical shape. This contraction is characterized by the cortical tension. The cortical tension shows a weak area dilation dependence, and it determines the elastic properties of the cell for small curvature deformations. At high curvature deformations in small pipets (with internal radii less than 1 micron), the measured critical suction pressure for cell flow into the pipet is larger than its estimate from the law of Laplace. A model is proposed where the region consisting of the cytoplasm membrane and the underlying cortex (having a finite thickness) is introduced at the cell surface. The mechanical properties of this region are characterized by the apparent cortical tension (defined as a free contraction energy per unit area) and the apparent bending modulus (introduced as a bending free energy per unit area) of its middle plane. The model predicts that for small curvature deformations (in pipets having radii larger than 1.2 microns) the role of the cortical thickness and the resistance for bending of the membrane-cortex complex is negligible. For high curvature deformations, they lead to elevated suction pressures above the values predicted from the law of Laplace. The existence of elevated suction pressures for pipets with radii from 1 micron down to 0.24 micron is found experimentally. The measured excess suction pressures cannot be explained only by the modified law of Laplace (for a cortex with finite thickness and negligible bending resistance), because it predicts unacceptable high cortical thicknesses (from 0.3 to 0.7 micron). It is concluded that the membrane-cortex complex has an apparent bending modulus from 1 x 10(-18) to 2 x 10(-18) J for a cortex with a thickness from 0.1 micron down to values much smaller than the radius of the smallest pipet (0.24 micron) used in this study.     

Surface tension gradients: feasible model for gliding motility of Myxococcus xanthus.

We propose that surface tension is the driving force for the gliding motility of Myxococcus xanthus. Our model requires that the cell be able to excrete surfactant in a polar and reversible fashion. We present calculations that (i) estimate the surface tension difference across a cell necessary to move the cell at the observed rate, which is less than 10(-5) dyn/cm, an extremely small value; (ii) estimate the rate of surfactant excretion necessary to produce the required surface tension difference, a rate that we conclude to be metabolically reasonable; (iii) predict the behavior of cells moving in close apposition to each other, and show that the model is consistent with observed behavior; and (iv) predict the behavior of cells moving in dense swarms. In an accompanying paper we present experimental evidence to support the surface tension model.