On the measurement of shear elastic moduli and viscosities of erythrocyte plasma membranes by transient deformation in high frequency electric fields.

We present a new method to measure the shear elastic moduli and viscosities of erythrocyte membranes which is based on the fixation and transient deformation of cells in a high-frequency electric field. A frequency domain of constant force (arising by Maxwell Wagner polarization) is selected to minimize dissipative effects. The electric force is thus calculated by electrostatic principles by considering the cell as a conducting body in a dielectric fluid and neglecting membrane polarization effects. The elongation A of the cells perpendicular to their rotational axis exhibits a linear regime (A proportional to Maxwell tension or to square of the electric field E2) at small, and a nonlinear regime (A proportional to square root of Maxwell tension or to the electric field E) at large extensions with a cross-over at A approximately 0.5 micron. The nonlinearity leads to amplitude-dependent response times and to differences of the viscoelastic response and relaxation functions. The cells exhibit pronounced yet completely reversible tip formations at large extensions. Absolute values of the shear elastic modulus, mu, and membrane viscosity, eta, are determined by assuming that field-induced stretching of the biconcave cell may be approximately described in terms of a sphere to ellipsoid deformation. The (nonlinear) elongation-vs.-force relationship calculated by the elastic theory of shells agress well with the experimentally observed curves and the values of mu = 6.1 x 10(-6) N/m and eta = 3.4 x 10(-7) Ns/m are in good agreement with the micropipette results of Evans and co-workers. The effect of physical, biochemical, and disease-induced structural changes on the viscoelastic parameters is studied. The variability of mu and eta of a cell population of a healthy donor is +/- 45%, which is mainly due to differences in the cell age. The average mu value of cells of different healthy donors scatters by +/- 18%. Osmotic deflation of the cells leads to a fivefold increase of mu and 10-fold increase of eta at 500 mosm. The shear modulus mu increases with temperature showing that the cytoskeleton does not behave as a network of entropy elastic springs. Elliptic cells of patients suffering from elliptocytosis of the Leach phenotype exhibit a threefold larger value of mu than normal discocytes of control donors. Cross-linking of the spectrin by the divalent S-H agents diamide (1 mM, 15 min incubation) leads to an eightfold increase of mu whereas eta is essentially constant. The effect of diamide is reversed after treatment with S-S bond splitting agents.     

The measurement of shear modulus and membrane surface viscosity of RBC membrane with Ektacytometry: a new technique

A new technique is proposed to estimate the shear modulus (mu) and membrane surface viscosity (eta(m)) of red blood cell (RBC). Theoretical formulae for finding these two parameters are first derived based on the force balance on a RBC in a flow field of low viscosity. Different types of Ektacytometry are then used to measure relevant quantities. The obtained values (mu=6.1 x 10(-6)N/m, eta(m)=8.8 x10 (-7)Ns/m for normal RBC) are consistent with those previously found by micropipette technique and in AC electric field. The present technique is, however, much easier to operate and more advantageous in reflecting the average properties of a large quantity of RBCs, and it is much cheaper to be applied in clinical practice than any other method of measuring the two parameters. The sensitivity of the technique is demonstrated by testing RBCs treated with glutaraldehyde of different concentrations. This technique was demonstrated by the flow chamber.     

Bioelectrorheological model of the cell. 5. Electrodestruction of cellular membrane in alternating electric field.

Recently proposed analysis of the extensil stress developed in a cellular membrane subjected to an alternating electric field (Pawłowski, P., and M. Fikus, 1993. Bioelectrorheological model of the cell. 4. Analysis of the extensil deformation of the membrane in an alternating field. Biophys. J. 65:535-540) was applied in calculations of extensil stress threshold values, sigma eo[d], producing experimentally observed electrodestruction of cells within the frequency range of 7 x 10(1) - 3 x 10(5) Hz. It was shown that the susceptibility (s[d] = 1/sigma eo[d]), of the membrane to this process varies with field frequency and depends on the type of cells. Electrodestruction is facilitated in the 10(5)-Hz field. A rheological hypothesis explaining the experimentally observed dependence of membrane stability on electric field frequency was proposed and successfully tested for two other phenomena: electroporation and electrofusion.     

Elastic and viscous properties of resting frog skeletal muscle.

The mechanical properties of the resting, whole semitendinosus muscle of the frog have been characterized as functions of both muscle length and temperature. Measurements were made of pseudorandom white noise (PRWN) displacements (less than 10 A/half-sarcomere) applied to the muscle and the force responses to these movements. Signal correlation techniques were then used to obtain the dynamic modulus function for the muscle in the frequency range 2.44-320 Hz. This function was represented by a series combination of a Voigt element and a time delay element for tension propagation along the muscle. A dynamic elastic modulus (E), coefficient of damping (B), and tension transmission velocity (V) were measured for resting muscle on the basis of this model. For each of these parameters, a marked variation with sarcomere length (s) was found. The mean values for E and B at LO (s=2.25 mum) were 1.84+/-0.24 X 10(5) N/m2 and 2.33+/-0.25 X 10(2) Ns/m2, respectively. Further, B demonstrated a negative temperature dependence, Q10=0.78 (P less than 0.05), in the range s=2.6-3.0 mum, while E was not significantly temperature dependent. The length-dependent variations of E and B are interpreted as deriving from both passive muscle elements and attached crossbridges. Velocity was calculated at a single displacing frequency for every experiment; the mean value at LO and all temperatures was v=11.7+/-0.6 m/s. Velocity was also calculated as a function of frequency within several experiments: the results indicate considerable variation of v with frequency.     

Bioelectrorheological model of the cell. 1. Analysis of stresses and deformations

An electrorheological model of a cell in alternating electric field is proposed. The model relates changes in the spherical cell's shape to the field conditions, electric parameters of cytoplasm, cell membrane and external medium, and to the rheological parameters of the membrane. Stresses were determined using Maxwell's stress tensor for isotropic media. Shear stresses in the cell membrane were analyzed. Predictions of the model for variations of shear stress in cellular membranes subjected to an external periodic electric field are presented and related to the conditions prevailing in electrobiological research.     

A theoretically estimated optimal cooling rate for the cryopreservation of sperm cells from a live-bearing fish, the green swordtail Xiphophorus helleri

Sperm cryopreservation of live-bearing fishes, such as those of the genus Xiphophorus is only beginning to be studied, although these fishes are valuable models for biomedical research and are commercially raised as ornamental fish for use in aquariums. To explore optimization of techniques for sperm cryopreservation of these fishes, this study measured the volumetric shrinkage response during freezing of sperm cells of Xiphophorus helleri by use of a shape-independent differential scanning calorimeter (DSC) technique. Volumetric shrinkage during freezing of X. helleri sperm cell suspensions was obtained in the presence of extracellular ice at a cooling rate of 20 degrees C/min in three different media: (1) Hanks' balanced salt solution (HBSS) without cryoprotective agents (CPAs); (2) HBSS with 14% (v/v) glycerol; and (3) HBSS with 10% (v/v) dimethyl sulfoxide (DMSO). The sperm cell was modeled as a cylinder of 33.3 microm in length and 0.59 microm in diameter with an osmotically inactive cell volume (V(b)) of 0.6V(o), where V(o) is the isotonic or initial cell volume. By fitting a model of water transport to the experimentally determined volumetric shrinkage data, the best-fit membrane permeability parameters (reference membrane permeability to water, L(pg) or L(pg)[cpa] and the activation energy, E(Lp) or E(Lp)[cpa]) of the Xiphophorus helleri sperm cell membrane were determined. The best-fit membrane permeability parameters at 20 degrees C/min in the absence of CPAs were: L(pg)=0.776 x 10(-15)m3/Ns (0.0046 microm/min atm), and E(Lp)=50.1 kJ/mol (11.97 kcal/mol) (R2=0.997). The corresponding parameters in the presence of 14% glycerol were L(pg)[cpa]=1.063 x 10(-15)m3/Ns (0.0063 microm/min atm), and E(Lp)[cpa]=83.81 kJ/mol (20.04 kcal/mol) (R2=0.997). The parameters in the presence of 10% DMSO were L(pg)[cpa]=1.4 x 10(-15)m3/Ns (0.0083 microm/min atm), and E(Lp)[cpa]=90.96 kJ/mol (21.75 kcal/mol) (R2=0.996). Parameters obtained in this study suggested that the optimal rate of cooling for X. helleri sperm cells in the presence of CPAs ranged from 20 to 35 degrees C/min and were in close agreement with recently published, empirically determined optimal cooling rates.     

Modeling electroporation in a single cell. I. Effects Of field strength and rest potential.

This study develops a model for a single cell electroporated by an external electric field and uses it to investigate the effects of shock strength and rest potential on the transmembrane potential V(m) and pore density N around the cell. As compared to the induced potential predicted by resistive-capacitive theory, the model of electroporation predicts a smaller magnitude of V(m) throughout the cell. Both V(m) and N are symmetric about the equator with the same value at both poles of the cell. Larger shocks do not increase the maximum magnitude of V(m) because more pores form to shunt the excess stimulus current across the membrane. In addition, the value of the rest potential does not affect V(m) around the cell because the electroporation current is several orders of magnitude larger than the ionic current that supports the rest potential. Once the field is removed, the shock-induced V(m) discharges within 2 micros, but the pores persist in the membrane for several seconds. Complete resealing to preshock conditions requires approximately 20 s. These results agree qualitatively and quantitatively with the experimental data reported by Kinosita and coworkers for unfertilized sea urchin eggs exposed to large electric fields.     

Experimental and biphasic FEM determinations of the material properties and hydraulic permeability of the meniscus in tension

Tensile tests and biphasic finite element modeling were used to determine a set of transversely isotropic properties for the meniscus, including the hydraulic permeability coefficients and solid matrix properties. Stress-relaxation tests were conducted on planar samples of canine meniscus samples of different orientations, and the solid matrix properties were determined from equilibrium data. A 3-D linear biphasic and tranversely isotropic finite element model was developed to model the stress-relaxation behavior of the samples in tension, and optimization was used to determine the permeability coefficients, k1 and k2, governing fluid flow parallel and perpendicular to the collagen fibers, respectively. The collagen fibrillar orientation was observed to have an effect on the Young's moduli (E1=67.8 MPa, E2=11.1 MPa) and Poisson's ratios (v12=2.13, v21 =1.50, v23=1.02). However, a significant effect of anisotropy on permeability was not detected (k1 =0.09x10(-16) m4/Ns, k2=0.10x10(-16) m4/Ns). The low permeability values determined in this study provide insight into the extent of fluid pressurization in the meniscus and will impact modeling predictions of load support in the meniscus.     

Red cell extensional recovery and the determination of membrane viscosity.

A theory of membrane viscoelasticity developed by Evans and Hochmuth in 1976 is used to analyze the time-dependent recovery of an elongated cell. Before release, the elongated cell is the static equilibrium where external forces are balanced by membrane elastic force resultants. Upon release, the cell recovers its initial shape with a time-dependent exponential behavior characteristic of the viscoelastic solid model. It is shown that the model describes the time-dependent recovery process very well for a time constant in the range of 0.1-0.13 s. The time constant is the ratio membrane surface viscosity eta:membrane surface elasticity mu. Measurements for the shear modulus mu of 0.006 dyne/cm give a value for the surface viscosity of red cell membrane as a viscoelastic solid material of eta = mu tc = (6-8) X 10(-4) poise . cm.     

Subzero water permeability parameters of mouse spermatozoa in the presence of extracellular ice and cryoprotective agents.

Optimization of techniques for cryopreservation of mammalian sperm is limited by a lack of knowledge regarding water permeability characteristics during freezing in the presence of extracellular ice and cryoprotective agents (CPAs). Cryomicroscopy cannot be used to measure dehydration during freezing in mammalian sperm because they are highly nonspherical and their small dimensions are at the limits of light microscopic resolution. Using a new shape-independent differential scanning calorimeter (DSC) technique, volumetric shrinkage during freezing of ICR mouse epididymal sperm cell suspensions was obtained at cooling rates of 5 and 20 degrees C/min in the presence of extracellular ice and CPAs. Using previously published data, the mouse sperm cell was modeled as a cylinder (122-microm long, radius 0.46 microm) with an osmotically inactive cell volume (V(b)) of 0.61V(o), where V(o) is the isotonic cell volume. By fitting a model of water transport to the experimentally obtained volumetric shrinkage data, the best-fit membrane permeability parameters (L(pg) and E(Lp)) were determined. The "combined best-fit" membrane permeability parameters at 5 and 20 degrees C/min for mouse sperm cells in solution are as follows: in D-PBS: L(pg) = 1.7 x 10(-15) m(3)/Ns (0.01 microm/min-atm) and E(Lp) = 94.1 kJ/mole (22.5 kcal/mole) (R(2) = 0.94); in "low" CPA media (consisting of 1% glycerol, 6% raffinose, and 15% egg yolk in D-PBS): L(pg)[cpa] = 1.7 x 10(-15) m(3)/Ns (0.01 microm/min-atm) and E(Lp)[cpa] = 122.2 kJ/mole (29.2 kcal/mole) (R(2) = 0.98); and in "high" CPA media (consisting of 4% glycerol, 16% raffinose, and 15% egg yolk in D-PBS): L(pg)[cpa] = 0.68 x 10(-15) m(3)/Ns (0.004 microm/min-atm) and E(Lp)[cpa] = 63.6 kJ/mole (15.2 kcal/mole) (R(2) = 0.99). These parameters are significantly different than previously published parameters for mammalian sperm obtained at suprazero temperatures and at subzero temperatures in the absence of extracellular ice. The parameters obtained in this study also suggest that damaging intracellular ice formation (IIF) could occur in mouse sperm cells at cooling rates as low as 25-45 degrees C/min, depending on the concentrations of the CPAs. This may help to explain the discrepancy between the empirically determined optimal cryopreservation cooling rates, 10-40 degrees C/min, and the numerically predicted optimal cooling rates, greater than 5000 degrees C/min, obtained using suprazero mouse sperm permeability parameters that do not account for the presence of extracellular ice. As an independent test of this prediction, the percentages of viable and motile sperm cells were obtained after freezing at two different cooling rates ("slow" or 5 degrees C/min; "fast," or 20 degrees C/min) in both the low and high CPA media. The greatest sperm motility and viability was found with the low CPA media under fast (20 degrees C/min) cooling conditions.     

Influence of ammonium chloride feeding time and light intensity on the cultivation of Spirulina (Arthrospira) platensis

This study dealt with the influence of both the feeding time and light intensity on the fed-batch culture of the cyanobacterium Spirulina (Arthrospira) platensis using ammonium chloride as a nitrogen source. For this purpose, a 2(2) plus star central composite experimental design combined with response surface methodology was employed, and the maximum cell concentration (X(m)), the cell productivity (P(X)), and the yield of biomass on nitrogen (Y(X/N)) were selected as the response variables. The optimum values of X(m) (1,833 mg L(-1)) and Y(X/N) (5.9 g g(-1)) estimated by the model at light intensity of 13 klux and feeding time of 17.2 days were very close to those obtained experimentally under these conditions (X(m) = 1,771 +/- 41 mg L(-1); Y(X/N) = 5.7 +/- 0.17 g g(-1)). The cell productivity was a decreasing function of the ammonium chloride feeding time and a quadratic function of the light intensity. The protein and lipid contents of dry biomass collected at the end of cultivations were shown to decrease with increasing light intensity.     

Study of mechanisms of electric field-induced DNA transfection. II. Transfection by low-amplitude, low-frequency alternating electric fields.

Electroporation for DNA transfection generally uses short intense electric pulses (direct current of kilovolts per centimeter, microseconds to milliseconds), or intense dc shifted radio-frequency oscillating fields. These methods, while remarkably effective, often cause death of certain cell populations. Previously it was shown that a completely reversible, high ionic permeation state of membranes could be induced by a low-frequency alternating electric field (ac) with a strength one-tenth, or less, of the critical breakdown voltage of the cell membrane (Teissie, J., and T. Y. Tsong. 1981. J. Physiol. (Paris). 77:1043-1053). We report the transfection of E. coli (JM105) by plasmid PUC18 DNA, which carries an ampicillin-resistance gene, using low-amplitude, low-frequency ac fields. E. coli transformants confer the ampicillin resistance and the efficiency of the transfection can be conveniently assayed by counting colonies in a selection medium containing ampicillin. For the range of ac fields employed (peak-to-peak amplitude 50-200 V/cm, frequency 0.1 Hz-1 MHz, duration 1-100 s), 100% of the E. coli survived the electric field treatment. Transfection efficiencies varied with field strength and frequency, and as high as 1 x 10(5)/micrograms DNA was obtained with a 200 V/cm square wave, 1 Hz ac field, 30 s exposure time, when the DNA/cell ratio was 50-75. Control samples gave a background transfection of much less than 10/micrograms DNA. With a square wave ac field, the transfection efficiency showed a frequency window: the optimal frequency was 1 Hz with a 200 V/cm field, and was approximately 0.1 Hz with a 50 V/cm field.(ABSTRACT TRUNCATED AT 250 WORDS)     

Red blood cell orientation in orbit C = 0.

Two modes of behavior of single human red cells in a shear field have been described. It is known that in low viscosity media and at shear rates less than 20 s-1, the cells rotate with a periodically varying angular velocity, in accord with the theory of Jeffery (1922) for oblate spheroids. In media of viscosity greater than approximately 5 mPa s and sufficiently high shear rates, the cells align themselves at a constant angle to the direction of flow with the membrane undergoing tank-tread motion. Also, in low viscosity media, as the shear rate is increased, more and more cells lie in the plane of shear, undergoing spin with their axes of symmetry aligned with the vorticity axis of the shear field in an orbit "C = 0" (Goldsmith and Marlow, 1972). We have explored this latter phenomenon using two experimental methods. First, the erythrocytes were observed in the rheoscope and their diameters measured. Forward light scattering patterns were correlated with the red cell orientation mode. Light flux variations after flow onset or stop were measured, and the characteristic times of erythrocyte orientation and disorientation were assessed. The characteristic time of erythrocyte orientation in Orbit C = 0 is proportional to the inverse of the shear rate. The corresponding coefficient of proportionality depends on the suspending medium viscosity eta o. The disorientation time tau D, after flow has been stopped, is such that the ratio tau D/eta o is independent of the initial applied shear stress. However, tau D is much shorter than one would expect if pure Brownian motion were involved. The proportion of erythrocytes in orbit C = 0 was also measured. It was found that this proportion is a function of both the shear rate and eta o. At low values of eta o, the proportion increases with increasing shear rate and then reaches a plateau. For higher values of eta o (5 to 10 mPa s), the proportion of RBC in orbit C = 0 is a decreasing function of the shear stress. A critical transition between orbit C = 0 and parallel alignment was observed at high values of eta o, when the shear stress is on the order of 1 N/m2. Finally, the effect of altering membrane viscoelastic properties (by heat or diamide treatment) was tested. The proportion of oriented cells is a steep decreasing function of red cell rigidity.     

Dielectric behavior of polyelectrolytes. VI. Dynamic response of cylindrical biopolymers to electric fields

The time dependence of the orientation of a cylindrical biopolymer and the configuration of its counterion complement in the presence of an external electric field is found by solving a model forced diffusion equation. The solution is a high temperature expansion in the external field strength and is used to predict the nature of the dielectric relaxation and the dynamic Kerr effect for such systems. Specific application is made to the dynamic Kerr effect of a DNA oligomer for which experimental data appear in the literature. The analysis yields a value for the surface diffusion coefficient of a sodium ion on DNA at 20 degrees C of 3.8 x 10(-10) m2 s-1.     

Viscosity and molecular weight of hyaluronic acids.

The intrinsic viscosity ([eta]) and the molecular weight (M) by sedimentation equilibrium were determined for hyaluronic acids of low (M=104--7.2X10(4)) and high (M=3.1X10(5)--1.5X10(6)) molecular weights. Double logarithmic plot of [eta] against M gave different lines for the two groups. The relationship between [eta] and M was [eta]=3.0X10(6)XM1,20 for the former and [eta]=5.7X10(-4)XM0.46 for the latter group. The molecular weight at the point of intersection of the two lines was about 1.5X10(5). The rheological behavior of the hyaluronic acids below M=2.1X10(4), for which the value of reduced viscosity was independent of concentration, was different from that of the hyaluronic acids above M=5.1X10(4), for which the value of reduced viscosity increased with concentration.     

Temporary network formation of hyaluronate under a physiological condition. 1. Molecular-weight dependence

The dynamic shear moduli at various frequencies and stress growth after the sudden start of steady shear were measured for 1% HA (hyaluronic acid) solutions with different molecular weights. From the results of the zero shear viscosity, eta 0, the steady shear compliance, J 0e, and delta eta defined as delta eta = eta 0 - eta a (infinity), where eta a (infinity) is the apparent viscosity at the steady state, it was shown that the molecular mechanism of flow of 1% HA solutions was classified into four regions with respect to molecular weight: (I) the viscosity-average molecular weight Mv less than 35 X 10(4), HA chains are dispersed molecularly in solution; (II) 35 X 10(4) less than Mv less than 100 X 10(4), the polymer chains form a weak entanglement network observed only through eta 0; (III) 100 X 10(4) less than Mv less than 160 X 10(4), the network is strengthened with increasing molecular weight and becomes detectable through both eta 0 and J 0e and also through the overshoot phenomenon; and (IV) 160 X 10(4) less than Mv, the network is "saturated" or "completed" dynamically. This is the conjecture presented for the first time by the present work.     

Electrical stimulation of hybridoma cells producing monoclonal antibody to cAMP

Electrical stimulation was applied to hybridoma cells in order to activate metabolic activities and increase the monoclonal antibody production. Hybridoma cells that produce monoclonal antibody to adenosine 3':5'-cyclic monophosphate were placed on a transparent glass electrode immersed in medium and subjected to electric pulses (pulse shape, alternating rectangular; field strength, 4 X 10(3) V X m-1; frequency, 5 kHz; pulse mode, 0.5 min application and 4.5 min pause). After 48 h of incubation, the concentration of lactic acid in the medium reached 8.4 mM, approx. 30% higher than that obtained without electric stimulation. Similarly, cell growth rate was promoted by the electric stimulation, reaching a maximum stimulation after 40 h. When the hybridoma was cultured for 48 h with electrical stimulation, the antibody concentration in the medium reached 22.3 microgram X ml-1, approx. 10% higher than the control, with a concomitant 16% increase in cell concentration. Longer periods of electric pulse application, however, caused an inhibitory effect on the hybridoma growth. The most probable cause of the inhibition are reactive oxygen species such as superoxide and hydrogen peroxide, which are inevitably generated by electrolysis. The presence of superoxide dismutase (EC 1.15.1.1) reduced the inhibitory effects. In conclusion, metabolic activities including monoclonal antibody production were activated by the electrical stimulation.     

Continuous cultivation of the diatom Nitzschia laevis for eicosapentaenoic acid production: physiological study and process optimization

The continuous cultures of the diatom Nitzschia laevis were performed at different dilution rates (D) and feed glucose concentrations (S(0)) to investigate cellular physiological responses and its production potential of eicosapentaenoic acid (EPA). Steady-state cell dry weight, residual glucose concentration, cell growth yield, specific glucose consumption rate, and fatty acid profiles were investigated within the range of D from 0.1 to 1.0 day(-1) (S(0) fixed at 20 g/L) and the range of S(0) from 5 to 35 g/L (D fixed at 0.3 day(-1)), respectively. The highest EPA productivity of 73 mg L(-1) day(-1) was obtained at D = 0.5 day(-1) and S(0) = 20 g/L. However, when the continuous culture achieved high productivities of EPA at certain dilution rates and feed glucose concentrations, glucose in the feed could not be consumed completely. Accordingly, the continuous culture was evaluated in terms of both EPA productivity (P) and glucose assimilation efficiency (E). The parameter eta, defined as the product of P and E, was used as an overall performance index. Since eta is a function of the two independent variables D and S(0), we employed a central composite design to optimize D and S(0) for the highest eta value. Based on the experimental results of the design, a second-order polynomial equation was established to represent the relationship between eta and D and S(0). The optimal values of D and S(0) were subsequently determined as 0.481 day(-1) and 15.56 g/L, respectively by the empirical model. The verification experiment confirmed the validity of the model. Under the optimal conditions, eta value reached 46.5 mg L(-1) day(-1), suggesting a considerably high efficiency of the continuous culture of N. laevis in terms of EPA production and glucose utilization.     

Thermal excitations of a bilipid membrane.

Propagating modes of vibration of a bilipid membrane have been detected with light beating spectroscopy. The dependence of omega on q is consistent with a model of a fluid film of surface tension sigma = 2.5 +/- 0.5 dyn cm-1 surrounded by a medium with rho = 1 g cm-3 and eta = 1.01 X 10(-2) P.