Frequency domain analysis of membrane capacitance of cultured cells (HeLa and myeloma) using the micropipette technique.

The membrane capacitance and conductance of cultured cells (HeLa and mouse myeloma) are investigated using the micropipette method. Mean values of the membrane capacities were found to be 1.9 microF/cm2 for HeLa cells and 1.0 microF/cm2 for myeloma cells. These values are in agreement with those obtained using the suspension method. Whereas the suspension method is unable to provide the information on membrane conductance, the micropipette method is able to measure even an extremely small membrane conductance if leakage current is negligibly small. The membrane conductances were found, using this technique, to be approximately 90-100 microS/cm2 for both HeLa and myeloma cells. One of the purposes of this study is to establish the frequency profile of membrane capacitance. It was found, however, that membrane capacitances of these cells are independent of frequency between 1 Hz and 1 KHz within the resolution of this technique.     

Frequency domain impedance measurements of erythrocytes. Constant phase angle impedance characteristics and a phase transition.

We report measurements of the electrical impedance of human erythrocytes in the frequency range from 1 Hz to 10 MHz, and for temperatures from 4 to 40 degrees C. In order to achieve high sensitivity in this frequency range, we embedded the cells in the pores of a filter, which constrains the current to pass through the cells in the pores. Based on the geometry of the cells embedded in the filter a circuit model is proposed for the cell-filter saline system. A constant phase angle (CPA) element, i.e., an impedance of the form Z = A/(j omega)alpha, where A is a constant, j = square root of -1, omega is angular frequency, and 0 less than alpha less than 1 has been used to describe the ac response of the interface between the cell surface and the electrolyte solution, i.e., the electrical double layer. The CPA and other elements of the circuit model are determined by a complex nonlinear least squares (CNLS) fit, which simultaneously fits the real and imaginary parts of the experimental data to the circuit model. The specific membrane capacitance is determined to be 0.901 +/- 0.036 microF/cm2, and the specific cytoplasm conductivity to be 0.413 +/- 0.031 S/m at 26 degrees C. The temperature dependence of the cytoplasm conductivity, membrane capacitance, and CPA element has been obtained. The membrane capacitance increases markedly at approximately 37 degrees C, which suggests a phase transition in the cell membrane.     

Differences in membrane properties between unfertilised and fertilised single rabbit oocytes demonstrated by electro-rotation. Comparison with cells from early embryos

The apparent membrane capacity of tubular rabbit oocytes increases from 1.7-2.0 microF/cm2 before fertilisation to 3.7-4.0 microF/cm2 after fertilisation. The membrane conductivity measured on single cells was also increased by fertilisation from less than 1 mS/cm2 to 14 mS/cm2. Cells obtained from 2-, 4- or 8-cell embryos exhibited intermediate values of membrane capacity (2.3-2.8 microF/cm2) and conductivity (5-22 mS/cm2). The values quoted are those effective between 1 and 10 kHz, the frequency of the rotating field used. The large apparent capacities are probably due to the presence of structures such as microvilli which cause the actual membrane area to exceed the smooth sphere area. It must be assumed that these structures change in form or number on fertilisation, and that they persist in embryos, at least up to the 8-cell stage. No difference was apparent between cells fertilised in vitro or in vivo. Comparison of the above zona-free data with measurements on zona-complete oocytes indicate how fertilised and unfertilised rabbit eggs may be distinguished from one another, even in the presence of the zona pellucida.     

Current noise parameters derived from voltage noise and impedance in embryonic heart cell aggregates.

We have recorded membrane impedance and voltage noise in the pacemaker range of potentials (-70 to -59 mV) from spheroidal aggregates of 7-d embryonic chick ventricle cells made quiescent by exposure to tetrodotoxin in medium containing 4.5 mM K+. The input capacitance is proportional to aggregate volume and therefore to total membrane area. The specific membrane capacitance is 1.24 microF/cm2. The input resistance at constant potential is inversely proportional to aggregate volume and therefore to total membrane area. The specific membrane resistance in 18 k omega . cm2 at -70 mV and increases to 81 k omega . cm2 at -59 mV. The RC time constant is 22 ms at -70 mV and increases to 146 ms at -59 mV. The aggregate transmembrane small-signal impedance can be represented by a parallel RC circuit itself in parallel with an inductive branch consisting of a resistor (rL) and an inductor (L) in series. The time constant of the inductive branch (L/rL) is 340 ms, and is only weakly dependent on potential. Correlation functions of aggregate voltage noise and the impedance data were modeled by a population of channels with simple open-close kinetics. The time constant of a channel (tau s) derived from the noise analysis is 300 ms. The low frequency limit of the pacemaker current noise (SI[0]), derived from the voltage noise and impedance, increases from 10(-20) A2/Hz . cm2 at -67 mV to 10(-19) A2/Hz . cm2 at -61 mV.     

Dielectric properties of yeast cells as determined by electrorotation.

Electrorotational spectra of yeast cells, Saccharomyces cerevisiae strain R XII, were measured over a frequency range of nearly 7 decades. The physical properties of distinct cell parts were simultaneously determined for individual cells by comparison with an electrical two-shell model: The conductivity of the cytoplasm, cell wall and cytoplasmic membrane of living cells were found to be 5.5 mS/cm, 0.1 to more than 0.5 mS/cm and less than 0.25 nS/cm to 4.5 microS/cm, respectively. The conductivity of the cytoplasmic membrane was dependent on the conductivity of the medium. Membrane behaviour is interpreted as an opening of membrane channels when the environment becomes more physiological. The specific membrane capacitance was determined to be 1.1 microF/cm2 and the thickness of the cell wall was calculated as 0.11 micron. Heat treated cells showed an increased membrane conductivity of more than 0.1 microS/cm (at 25 microS/cm medium conductivity) and a drop in cytoplasmic conductivity to between 0.1 and 0.8 mS/cm, depending on the length of time the cells were suspended in low conductivity water (25 microS/cm), indicating a perforation of the membrane. A slightly decreased spinning speed scaling factor for dead cells suggests a modification to the cellular surface, while the principal structure of the cell wall appears to be uneffected. It can be demonstrated by these observations, that cellular electrorotation permits the simultaneous investigation of the different cellular compartments of individual cells in vivo under various environmental conditions.     

Passive electrical properties of the membrane and cytoplasm of cultured rat basophil leukemia cells. I. Dielectric behavior of cell suspensions in 0.01-500 MHz and its simulation with a single-shell model

Frequency dependence of relative permittivity (dielectric constant) and conductivity, or the 'dielectric dispersion', of cultured cells (RBL-1 line) in suspension was measured using a fast impedance analyzer system capable of scanning 92 frequency points over a 10 kHz-500 MHz range within 80 s. Examination of the resulting dispersion curves of an improved reliability revealed that the dispersions consisted of at least two separate components. The low-frequency component (dispersion 1) had a permittivity increment (delta epsilon) of 10(3)-10(4) and a characteristic frequency (fc) at several hundred kHz; for the high-frequency component (dispersion 2), delta epsilon was smaller by a factor of 10(2) and fc = 10-30 MHz. Increments delta epsilon for both components increased with the volume fraction of cell suspension, while fc did not change appreciably as long as the conductivity of suspending medium was fixed. By fitting a model for shelled spheres (the 'single-shell' model) to the data of dispersion 1, the dielectric capacity of the plasma membrane phase (Cm) was estimated to be approx. 1.4 microF/cm2 for the cells in an isotonic medium. However, simulation by this particular shell model failed to reproduce the entire dispersion profile leaving a sizable discrepancy between theory and experiment especially at frequencies above 1 MHz where dispersion 2 took place. This discrepancy could not be filled up even by taking into consideration either the effect of cell size distribution actually determined or that of possible heterogeneity in the intracellular conductivity. The present data strongly indicate the need for a more penetrating model that effectively accounts for the behavior of dispersion 2.     

Capacitance and resistance of the bilayer lipid membrane formed of phosphatidylcholine and cholesterol

Capacity and electric resistance of lipid membranes composed of lecithin and cholesterol were determined. The components were chosen for the study because they were present in biological membranes. Capacitance of the lecithin and cholesterol membranes amounts to 0.38 and 0.61 microF/cm(2), and resistance to 1.44(10(4)and 2.12(10(6)Omega cm(2), respectively. A 1:1 complex appears as a result of lecithin-cholesterol membrane formation. Parameters of the membrane formed of the lecithin-cholesterol complex were determined: surface concentration (Gamma(3)), capacitance (C(3)), and conductance (R;(3)(-1), as well as the stability constant (K) of the complex. The mean values of those magnitudes are as follows: 4.265(10(-6)mol/m(2), 0.54 microF/cm(2), 1.381(10(-6)Omega(-1)cm(-2)and 3.748(10(7), respectively.     

Electrical Impedance Analysis in Plant Tissues3

Based on the electrical model for plant tissue proposed by Hayden,Moyse, Calder, Crawford, and Fensom (1969), a method is describedfor calculating symplasmic resistance and cell membrane capacitancefrom impedances measured over a range of alternating current(AC) frequencies. The method of calculation has been appliedto ten different plant organs using frequencies from 20 Hz to300 KHz. In contrast with previous assumptions, it was foundthat both the symplasmic resistance and the membrane capacitancewere not constant but decreased with increasing frequency, giventhe constraints of the Hayden model. In cucumber fruit tissue,the symplasmic resistance was 20 000 ohms at 3 KHz but only1200 ohms at 200 KHz; the capacitance was 2.4 nF at 3 KHz butonly 0.8 nF at 200 KHz. The changes were similar in other materials,such as carrot root and cabbage leaf. It is concluded that theHayden model does not represent plant tissues accurately. Itis suggested that a better representation would be obtainedby including a capacitor in the component of the circuit whichrepresents the symplasm, in order to make allowance for membranesof organelles, particularly the vacuole. Key words: Electrical impedance, electrical modelling, membrane capacitance     

AC impedance of the perineurium of the frog sciatic nerve

The AC impedance of the isolated perineurium of the frog sciatic nerve was examined at frequencies from 2 Hz to 100 kHz. A Nyquist plot of the imaginary and real components of the impedance demonstrated more than 1 capacitative element, and a DC resistance of 478 +/- 34 (SEM, n = 27) omega cm2. Transperineurial potential in the absence of externally applied current was 0.0 +/- 0.5 mV. The impedance data were fitted by nonlinear least squares to an equation representing the generalized impedance of four equivalent circuits each with two resistive and two capacitative elements. Only two of these circuits were consistent with perineurial morphology, however. In both, the perineurial cells were represented by a resistive and capacitative element in parallel, where capacitance was less than 0.1 microF/cm2. The extracellular matrix and intercellular junctions of the perineurium were represented as single resistive and capacitative elements in parallel or in series, where capacitance exceeded 2 microF/cm2. Immersion of the perineurium in low conductance Ringer's solution increased DC resistive elements as compared with their values in isotonic Ringer's solution, whereas treatment for 10 min with a hypertonic Ringer's solution (containing an additional 1.0 or 2.0 mol NaCl/liter of solution) reduced DC resistive elements, consistent with changes in perineurial permeability. The results indicate that (a) perineurial impedance contains two time constants and can be analyzed in terms of contributions from cellular and extracellular elements, and (b) transperineurial DC resistance, which is intermediate between DC resistance for leaky and nonleaky epithelia, represents intercellular resistance and can be experimentally modified by hypertonicity.     

Electrorotation of single yeast cells at frequencies between 100 Hz and 1.6 GHz.

The determination of complete electrorotation spectra of living cells has been made possible by the development of a quadrature generator and an electrode assembly that span the frequency range between 100 Hz and 1.6 GHz. Multiple spectra of single cells of the yeast Saccharomyces cerevisiae have been measured at different medium conductivities ranging from 0.7 to 550 microS cm-1. A spherical four-shell model was applied that simulated the experimental data well and disclosed the four-layer structure of the cell envelope attributed to the plasma membrane, the periplasmic space, and a thick inner and a thin outer wall region. Below 10 kHz an additional rotation effect was found, which changed its direction depending on the ionic strength of the medium. This is supposed to be connected with properties of the cell surface and its close vicinity. From the four-shell simulation the following physical properties of cell compartments could be derived: specific capacitance of plasma membrane (0.76 microF cm-2), periplasmic space (0.5 microF cm-2), and outer wall region (0.1 microF cm-2). The conductivity of cytoplasm, plasma membrane, and inner wall region were found to vary with medium ionic strength from 9 to 12 mS cm-1, 5.8 nS cm-1 to approximately 50 nS cm-1, and 6 microS cm-1 to 240 microS cm-1, respectively.     

Development of a new rapid measurement technique for fish embryo membrane permeability studies using impedance spectroscopy

Information on fish embryo membrane permeability is vital in their cryopreservation. Whilst conventional volumetric measurement based assessment methods have been widely used in fish embryo membrane permeability studies, they are lengthy and reduce the capacity for multi-embryo measurement during an experimental run. A new rapid 'real-time' measurement technique is required to determine membrane permeability during cryoprotectant treatment. In this study, zebrafish (Danio rerio) embryo membrane permeability to cryoprotectants was investigated using impedance spectroscopy. An embryo holding cell, capable of holding up to 10 zebrafish embryos was built incorporating the original system electrods for measuring the impedance spectra. The holding cell was tested with deionised water and a series of KCl solutions with known conductance values to confirm the performance of the modified system. Untreated intact embryos were then tested to optimise the loading capacity and sensitivity of the system. To study the impedance changes of zebrafish embryos during cryoprotectant exposure, three, six or nine embryos at 50% epiboly stage were loaded into the holding cell in egg water, which was then removed and replaced by 0.5, 1.0, 2.0 or 3M methanol or dimethyl sulfoxide (DMSO). The impedance changes of the loaded embryos in different cryoprotectant solutions were monitored over 30 min at 22 degrees C, immediately following embryo exposure to cryoprotectants, at the frequency range of 10-10(6)Hz. The impedance changes of the embryos in egg water were used as controls. Results from this study showed that the optimum embryo loading level was six embryos per cell for each experimental run. The optimum frequency was identified at 10(3.14) or 1,380 Hz which provided good sensitivity and reproducibility. Significant impedance changes were detected after embryos were exposed to different concentrations of cryoprotectants. The results agreed well with those obtained from conventional volumetric based studies.     

Resistance and capacity in the thallus of Marchantia polymorpha

Calculations of the resistance r and capacity c of cell membrances and the resistancer ₁ of cell interiors of a community of cells in Marchantia polymorpha L. thalli are presented. These parameters of a multicellular system were determined by the adaptation of methods employed for the calculation of the resistance and capacity of single cells. The obtained results indicate that such a procedure is justified. A generally accepted resistance-capacity model of the cell was used as a basis for the determination of r, c, and r₁ (representing membrane resistance, membrane capacity, and resistance of cell interior, respectively). The calculations were based on measurements of impedance and phase shift within the frequency range of 5 Hz-1000 Hz. Stainless steel plates were employed as the measuring electrodes; polarization resistance and capacity were determined by separate measurements. The calculations confirmed the assumption that the parameters r, c, and r₁ were constant within the investigated frequency range.
The calculations of resistance and capacity for 25 plants were constant within the investigated frequency range. The calculations of resistance and capacity for 25 plants were carried out by four different methods and they yielded results of the order of : r = 0.45 kΩ± 0.15 kΩ, r₁= 1.0 kΩ± 0.45 kΩ, c = 11 μF ± 3.5 μF. Circular diagrams of impedance also confirmed the validity of the accepted model within the frequency range of 25–300 Hz.     

ELECTRIC IMPEDANCE OF NITELLA DURING ACTIVITY

The changes in the alternating current impedance which occur during activity of cells of the fresh water plant Nitella have been measured with the current flow normal to the cell axis, at eight frequencies from 0.05 to 20 kilocycles per second, and with simultaneous records of the action potential under the impedance electrodes. At each frequency the resting cell was balanced in a Wheatstone bridge with a cathode ray oscillograph, and after electrical stimulation at one end of the cell, the changes in the complex impedance were determined from the bridge unbalance recorded by motion pictures of the oscillograph figure. An extension of the previous technique of interpretation of the transverse impedance shows that the normal membrane capacity of 0.9 µf./cm.² decreases about 15 per cent without change of phase angle, while the membrane resistance decreases from 10⁵ ohm cm.² to about 500 ohm cm.² during the passage of the excitation wave. This membrane change occurs during the latter part of the rising phase of the action potential, and it is shown that the membrane electromotive force remains unchanged until nearly the same time. The part of the action potential preceding these membrane changes is probably a passive fall of potential ahead of a partial short circuit.     

Contribution of electrogenic ion transport to impedance of the algae Valonia utricularis and artificial membranes.

The cell membrane of Valonia utricularis contains an electrogenic carrier system for chloride (Wang et al., Biophys J. 59:235-248 (1991)). The electrical impedance of V. utricularis was measured in the frequency range between 1 Hz and 50 kHz. The analysis of the impedance spectra from V. utricularis and its comparison with equivalent circuit models showed that the transport system created a characteristic contribution to the impedance in the frequency range between 10 Hz and 5 kHz. The fit of the impedance spectra with the formalism derived from the theory of carrier-mediated transport allowed the determination of the kinetic parameters of chloride transport through the cell membrane of V. utricularis, and its passive electrical properties. Simultaneous measurements of the kinetic parameters with the charge pulse method demonstrated the equivalence of both experimental approaches with respect to the evaluation of the translocation rate constants of the free and the charged carriers and the total density of carriers within the membrane. Moreover, the impedance spectra of the protonophor-mediated proton transport by FCCP (carbonylcyanide p-trifluoromethoxyphenyl-hydrazone) were measured in model membranes. The carrier system made a substantial contribution to the impedance of the artificial membranes. The analysis of the spectra in terms of a simple carrier system (Benz and McLaughlin, 1983, Biophys. J. 41:381-398) allowed the evaluation of the kinetic and equilibrium parameters of the FCCP-mediated proton transport. The possible application of the measurement of impedance spectra for the study of biological transport systems is discussed.     

Highly robust lipid membranes on crystalline S-layer supports investigated by electrochemical impedance spectroscopy

In the present work, S-layer supported lipid membranes formed by a modified Langmuir-Blodgett technique were investigated by electrochemical impedance spectroscopy (EIS). Basically two intermediate hydrophilic supports for phospholipid- (DPhyPC) and bipolar tetraetherlipid- (MPL from Thermoplasma acidophilum) membranes have been applied: first, the S-layer protein SbpA isolated from Bacillus sphaericus CCM 2177 recrystallized onto a gold electrode; and second, as a reference support, an S-layer ultrafiltration membrane (SUM), which consists of a microfiltration membrane (MFM) with deposited S-layer carrying cell wall fragments. The electrochemical properties and the stability of DPhyPC and MPL membranes were found to depend on the used support. The specific capacitances were 0.53 and 0.69 microF/cm(2) for DPhyPC bilayers and 0.75 and 0.77 microF/cm(2) for MPL monolayers resting on SbpA and SUM, respectively. Membrane resistances of up to 80 mega Ohm cm(2) were observed for DPhyPC bilayers on SbpA. In addition, membranes supported by SbpA exhibited a remarkable long-term robustness of up to 2 days. The membrane functionality could be demonstrated by reconstitution of membrane-active peptides such as valinomycin and alamethicin. The present results recommend S-layer-supported lipid membranes as promising structures for membrane protein-based biosensor technology.     

PGE(2) activation of apical membrane Cl(-) channels in A6 epithelia: impedance analysis.

Measurements of transepithelial electrical impedance of continuously short-circuited A6 epithelia were made at audio frequencies (0.244 Hz to 10.45 kHz) to investigate the time course and extent to which prostaglandin E(2) (PGE(2)) modulates Cl(-) transport and apical membrane capacitance in this cell-cultured model epithelium. Apical and basolateral membrane resistances were determined by nonlinear curve-fitting of the impedance vectors at relatively low frequencies (<50 Hz) to equations (P?unescu, T. G., and S. I. Helman. 2001. Biophys. J. 81:838--851) where depressed Nyquist impedance semicircles were characteristic of the membrane impedances under control Na(+)-transporting and amiloride-inhibited conditions. In all tissues (control, amiloride-blocked, and amiloride-blocked and furosemide-pretreated), PGE(2) caused relatively small (< approximately 3 microA/cm(2)) and rapid (<60 s) maximal increase of chloride current due to activation of a rather large increase of apical membrane conductance that preceded significant activation of Na(+) transport through amiloride-sensitive epithelial Na(+) channels (ENaCs). Apical membrane capacitance was frequency-dependent with a Cole-Cole dielectric dispersion whose relaxation frequency was near 150 Hz. Analysis of the time-dependent changes of the complex frequency-dependent equivalent capacitance of the cells at frequencies >1.5 kHz revealed that the mean 9.8% increase of capacitance caused by PGE(2) was not correlated in time with activation of chloride conductance, but rather correlated with activation of apical membrane Na(+) transport.     

Non-invasive determination of bacterial single cell properties by electrorotation

So far, electrorotation and its application to the determination of single cell properties have been limited to eukaryotes. Here an experimental system is described that allows the recording of electrorotation spectra of single bacterial cells. The small physical dimensions of the developed measuring chamber combined with a single frame video analysis made it possible to monitor the rotation of objects as small as bacteria by microscopical observation despite Brownian rotation and cellular movement. Thus physical properties of distinct organelles of E. coli could be simultaneously determined in vivo at frequencies between 1 kHz and 1 GHz. Experimental data were evaluated following a three-shell model of the cell. Electrical conductivities of cytoplasm and outer membrane were determined to 4.4 mS/cm and 25 microS/cm, respectively, that of the periplasmic space was found to increase with the square root of the medium ionic strength. Specific capacitances of inner and outer membrane amounted to 1.4 microF/cm2 and 0.26 microF/cm2, respectively, the thickness of the periplasm to about 50 nm. Heat treatment of the cells lead to a reduction of cytoplasmic conductivity to 0.9 mS/cm, probably caused by an efflux of ions through the permeabilized inner membrane.     

Passive electrical properties of the membrane and cytoplasm of cultured rat basophil leukemia cells. II. Effects of osmotic perturbation

The effects of osmotic perturbation on the dielectric behavior of cultured rat basophilic leukemia (RBL-1) cells were examined. Cells exposed to osmolalities (pi) of 145-650 mosmolal showed dielectric dispersions of the following characteristics: Permittivity increment delta epsilon(= epsilon l - epsilon h where epsilon l and epsilon h refer to the low- and high-frequency limit values) for a fixed volume concentration increased with pi; gross permittivity behavior was apparently of a typical Cole-Cole type; however, frequency dependence of conductivity was undulant and could be simulated by a superposition of two separate Cole-Cole type dispersions; separation of these subdispersions along the frequency axis was an increasing function of pi, and so was conductivity increment in the high-frequency region. As examined by light microscopy, the cells were spherical in spite of imposed anisotonic stresses and behaved as osmometers at 200-410 mosmolal. When normalized by dividing by number (not volume) concentration, delta epsilon remained relatively constant irrespective of pi. Apparent membrane capacities (Cm), analyzed by applying a single-shell model, increased systematically from a hypotonic value of approx. 1 microF/cm2 up to 5 microF/cm2 at 650 mosmolal. This increase was interpreted as due to increased cellular 'surface/volume' ratios that were confirmed by scanning electron microscopy. Cole-Cole's beta parameter, which culminated around 0.9 for isotonic cells and declined to approx. 0.8 for anisotonic cells, did not parallel the broadening of cell volume distribution but appeared to reflect changes in the intracellular conductivity caused by the anisotonic challenge. The results indicate that the dispersion method can probe changes in surface morphology as well as subcellular organelles' constitution of living cells.     

Impedance analysis of MDCK cells measured by electric cell-substrate impedance sensing.

Transepithelial impedance of Madin-Darby canine kidney cell layers is measured by a new instrumental method, referred to as electric cell-substrate impedance sensing. In this method, cells are cultured on small evaporated gold electrodes, and the impedance is measured in the frequency range 20-50,000 Hz by a small probing current. A model for impedance analysis of epithelial cells measured by this method is developed. The model considers three different pathways for the current flowing from the electrode through the cell layer: (1) in through the basal and out through the apical membrane, (2) in through the lateral and out through the apical membrane, and (3) between the cells through the paracellular space. By comparing model calculation with experimental impedance data, several morphological and cellular parameters can be determined: (1) the resistivity of the cell layer, (2) the average distance between the basal cell surface and substratum, and (3) the capacitance of apical, basal, and lateral cell membranes. This model is used to analyze impedance changes on removal of Ca2+ from confluent Mardin-Darby canine kidney cell layers. The method shows that reduction of Ca2+ concentration causes junction resistance between cells to drop and the distance between the basal cell surface and substratum to increase.     

Minimum energy analysis of membrane deformation applied to pipet aspiration and surface adhesion of red blood cells.

An experimental procedure is demonstrated which can be used to determine the interfacial free energy density for red cell membrane adhesion and membrane elastic properties. The experiment involves micropipet aspiration of a flaccid red blood cell and manipulation of the cell proximal to a surface where adhesion occurs. A minimum free energy method is developed to model the equilibrium contour of unsupported membrane regions and to evaluate the partial derivatives of the total free energy, which correspond to the micropipet suction force and the interfacial free energy density of adhesion. It is shown that the bending elasticity of the red cell membrane does not contribute significantly to the pressure required to aspirate a flaccid red cell. Based on experimental evidence, the upper bound for the bending or curvature elastic modulus of the red cell membranes is 10-12 ergs (dyn-cm). Analysis of the adhesion experiment shows that interfacial free energy densities for red cell adhesion can be measured from a lower limit of 10-4 ergs/cm2 to an upper limit established by the membrane tension for lysis of 5-10 ergs/cm2.