Mathematical modeling of measuring the hydraulic conductivity of roots by the relaxation method

The continuum model of radial mass transfer in plant roots developed previously has been used for processing the nonstationary experiments on determining the root hydraulic conductivity. In contrast to compartmental models, our model allows describing the shape of the relaxation curve, in particular, separating segments with different relaxation times. It is shown that to correctly determine the hydraulic conductivity, the method of data processing should be modified. A method for estimating the extracellular to intracellular conductivity ratio is proposed.     

Magnetic field of a single muscle fiber. First measurements and a core conductor model.

We present the first measurements of the magnetic field from a single muscle fiber of the frog gastrocnemius, obtained by using a toroidal pickup coil coupled to a room-temperature, low-noise amplifier. The axial currents associated with the magnetic fields of single fibers were biphasic and had peak-to-peak amplitudes ranging between 50 and 100 nA, depending primarily on the fiber radius. With an intracellular microelectrode, we measured the action potential of the same fiber, which allowed us to determine that the intracellular conductivity of the muscle fiber in the core conductor approximation was 0.20 +/- 0.09 S/m. Similarly, we found that the effective membrane capacitance was 0.030 +/- 0.011 F/m2. These results were not significantly affected by the anisotropic conductivity of the muscle bundle. We demonstrate how our magnetic technique can be used to determine the transmembrane action potential without penetrating the membrane with a microelectrode, thereby offering a reliable, stable, and atraumatic method for studying contracting muscle fibers.     

Action of calcium ions on channels of inward and outward currents in the molluscan neuron membrane

Changes in the characteristics of activity of sodium, calcium, and potassium channels in the surface membrane during variation of the calcium ion concentration in the extracellular and intracellular medium were investigated by the voltage clamp method during intracellular dialysis of isolated neurons of the mollusksLimnea stagnalis andHelix pomatia. Besides their direct role in passage of the current through the membrane, calcium ions were shown to have two actions, differing in their mechanism, on the functional properties of this membrane. The first was caused by the electrostatic action of calcium ions on the outer surface of the membrane and was manifested as a shift of the potential-dependent characteristics of the ion transport channels along the potential axis; the second is determined by closer interaction of calcium ions with the specific structures of the channels. During the action of calcium-chelating agents EGTA and EDTA on the inner side of the membrane the conductivity of the potassium channels is substantially reduced. With an increase in the intracellular free calcium concentration the conductivity is partially restored. The action of EGTA and EDTA on the outer side of the membrane causes a substantial decrease in the ion selectivity of the calcium channels and changes the kinetics of the portal mechanism. These changes are easily abolished by rinsing off the chelating agents or by returning calcium ions to the external medium. A specific blocking action of an increase in the intracellular free calcium concentration on conductivity of the calcium channels was found.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 9, No. 1, pp. 69–77, January–February, 1977.     

Determination of intracellular conductivity from electrical breakdown measurements

The intracellular resistivity (conductivity) of cells can be easily calculated with high accuracy from electrical membrane breakdown measurements. The method is based on the determination of the size distribution of a cell suspension as a function of the electrical field strength in the orifice of a particle volume analyser (Coulter counter). The underestimation of the size distribution observed beyond the critical external field strength leading to membrane breakdown represents a direct access to the intracellular resistivity as shown by the theoretical analysis of the data. The potential and the accuracy of the method is demonstrated for red blood cells and for ghost cells prepared by electrical haemolysis. The average value of 180 omega X cm for the intracellular resistivity of intact red blood cells is consistent with the literature.     

A sensitivity study of conductivity values in the passive bidomain equation

There is a complex interplay between the four conductivity values used in the bidomain equation and the resulting electric potential distribution in cardiac tissue arising from subendocardial ischaemia. Based on the three commonly used experimentally derived conductivity data sets, a non-dimensional formulation of the passive bidomain equation is derived, which gives rise naturally to several dimensionless conductivity ratios. The data sets are then used to define a parameter space of these ratios, which is studied by considering the correlation coefficients between different epicardial potential distributions.From this study, it is shown that the ratio of the intracellular longitudinal conductivity to the intracellular transverse conductivity is the key parameter in explaining the differences between the epicardial potential distributions observed with these three data sets.     

Determination of intracellular conductivity from electrical breakdown measurements

The intracellular resistivity (conductivity) of cells can be easily calculated with high accuracy from electrical membrane breakdown measurements. The method is based on the determination of the size distribution of a cell suspension as a function of the electrical field strength in the orifice of a particle volume analyser (Coulter counter). The underestimation of the size distribution observed beyond the critical external field strength leading to membrane breakdown represents a direct access to the intracellular resistivity as shown by the theoretical analysis of the data. The potential and the accuracy of the method is demonstrated for red blood cells and for ghost cells prepared by electrical haemolysis. The average value of 180 Ω - cm for the intracellular resistivity of intact red blood cells is consistent with the literature.     

高温胁迫对菊花电阻抗图谱参数的影响

以菊花(Chrysanthemum morifolium)‘神马’扦插苗茎段和叶片为材料,测定其高温胁迫(25~50℃)下电阻抗图谱参数的变化,通过膜透性(相对电导率)与电阻抗图谱参数间的相关性,来证明电阻抗图谱法研究菊花耐热性的有效性。结果表明:随着温度升高,茎叶的胞外电阻、胞内电阻、弛豫时间呈现先增加,后急剧下降的趋势,而弛豫时间分布系数变化趋势为不规则下降。茎叶相对电导率是随着温度的升高先增加后降低再急剧增加。经过菊花茎叶电阻抗图谱参数拟合菊花的耐热性与相对电导率表示的耐热性温度极为接近。相关分析表明,高温胁迫下菊花茎叶相对电导率与胞外电阻(茎p<0.01,叶p<0.05)、弛豫时间(p<0.05)之间有显著的相关。由此可见,胞外电阻和弛豫时间是测定菊花耐热性的适合参数。     

Temperature dependence of the dielectric properties of blood

The aim of the work was to investigate the temperature effect in physiological range on the dielectric properties of a fish (Cyprinus carpio) blood. By applying an empirical non-damaging method and statistical analysis of the dielectric data, it is observed that a heating of carp blood induces an almost linear value variation of the electrical conductivity and permittivity of the intracellular matter of carp red blood cells. The dielectric data, however, reveal anomalous behaviour for conductivity and permittivity of the interior of carp erythrocytes at 23 degrees C and 23 degrees, 37 degrees C, respectively and for both volume fraction and dielectric loss factor tg delta at 30 degrees, 35 degrees, 37 degrees C. For the presented dielectric parameters the temperature coefficient and the Arrhenius activation energy were estimated. Moreover, this work led to conclusion that the changes of the volume fraction of carp erythrocytes induce corresponding variations of the maximum of the dielectric loss factor tg delta determined for a whole blood.     

Derivation of the Macroscopic Intracellular Conductivity of Deformed Myocardium on the Basis of Microstructure Analysis

Biophysics - A model of changes in the intracellular conductivity of the myocardium due to its deformation was developed. Macroconductivities were derived using the microstructure-based model...     

A mathematical model for calculating the vector magnetic field of a single muscle fiber.

A mathematical model is described for calculating the volume-conducted magnetic field from active muscle fibers in an anisotropic bundle. With earlier models, the azimuthal magnetic field of a nerve bundle was calculated and the results were compared with the fields measured by toroidal pickup coils. The present model is capable of evaluating all three of the magnetic field components and is thus applicable for analyzing SQUID magnetometer recordings of fields from a muscle bundle. The component of the magnetic field parallel to the fiber axis is more than an order of magnitude smaller than either of the other two components. The amplitude of the magnetic signal is strongly dependent upon the anisotropy of the muscle bundle, the intracellular conductivity, the radius of the muscle fiber, the radius of the muscle bundle, and the location of the fiber in the muscle bundle. The peak-to-peak amplitude of the single-muscle-fiber action field increases linearly with increasing intracellular conductivity, as the square of the radius of the muscle fiber, and exponentially with the distance between the location of the fiber and the center of the bundle.     

Dielectric properties of yeast cells

Summary Dielectric measurements were made on suspensions of intact yeast cells over a frequency range of 10 kHz to 100 MHz. The suspensions showed typical dielectric dispersions, which are considered to be caused by the presence of cytoplasmic membranes with sufficiently low conductivity. Since the conductivity of the cell wall was found to be of nearly the same value as that of the suspending medium, composed of KCl solutions in a range from 10 to 80mm, the cell wall may be ignored in establishing an electrical model of the cells suspended in such media. An analysis of the dielectric data was carried out by use of Pauly and Schwan's theory. The membrane capacitance was estimated to be 1.1±0.1 F/cm², which is compared with values reported so far for most biological membranes. The conductivity of the cell interior was almost unchanged with varying KCl concentrations and showed low values owing to the presence of less conducting particles, presumably intracellular organelles. The relatively low dielectric constant of about 50 obtained for the cell interior, in comparison with values of aqueous solutions, may be attributed also to the presence of intracellular organelles and proteins.     

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.     

A membrane model describing the effect of temperature on the water conductivity of erythrocyte membranes at subzero temperatures

Thermodynamic models show that the loss of intracellular water from human erythrocytes during freezing depends heavily upon the water conductivity of the erythrocyte membrane. These calculations, which are based on the simple extrapolation of ambient conductivity data to subzero temperatures, show that more than 95% of cell water is transferable during freezing, whereas experiments show that at least 20% of cell water is retained. A study of the effects of different published values for the membrane water conductivity on cell water retained during freezing shows that this discrepancy may be a consequence of the simple extrapolation procedure.For a homogeneous membrane system, absolute reaction rate theory was used to develop a surface-limited permeation model that includes the resistance to the flow of water not only through the interior region of the membrane but also across possible rate-limiting barriers at the solution-membrane interfaces. The model shows that it is unlikely that a single ratelimiting process dominates water transport in the red cell as it is being cooled from ambient to subzero temperatures. The effective membrane conductivity at subzero temperatures could possibly be much lower than a simple extrapolation of existing data would predict. With the aid of this model analytical predictions of intracellular water during freezing are more consistent with experimental observations.     

Interaction of melittin with ion channels of excitable membranes

The effect of the neurotoxin melittin on the activation of ion channels of excitable membrane, the plasmalemma of Characeae algae cells, isolated membrane patches of neurons of mollusc L. stagnalis and Vero cells was studied by the method of intracellular perfusion and the patch-clamp technique in inside-out configuration. It was shown that melittin disturbs the conductivity of plasmalemma and modifieds Ca(2+)-channels of plant membrane. The leakage current that appears by the action of melittin can be restored by substituting calmodulin for melittin. Melittin modifies K(+)-channels of animal cell membrane by disrupting the phospholipid matrix and forms conductive structures in the membrane by interacting with channel proteins, which is evidenced by the appearance of additional ion channels.     

Evaluation of centrifugal methods for measuring xylem cavitation in conifers, diffuse- and ring-porous angiosperms

A centrifugal method is used to measure 'vulnerability curves' which show the loss of hydraulic conductivity in xylem by cavitation. Until recently, conductivity was measured between bouts of centrifugation using a gravity-induced head. Now, conductivity can be measured during centrifugation. This 'spin' method is faster than the 'gravity' technique, but correspondence between the two has not been evaluated. The two methods were compared on the same stem segments for two conifer, four diffuse-porous, and four ring-porous species. Only 17 of 60 conductivity measurements differed, with differences in the order of 10%. When different, the spin method gave higher conductivities at the beginning of the curve and lower at the end. Pressure at 50% loss of conductivity, and mean cavitation pressure, were the same in 14 of 20 comparisons. When different, the spin method averaged 0.32 MPa less negative. Ring-porous species showed a precipitous initial drop in conductivity by both techniques. This striking pattern was confirmed by the air-injection method and native embolism measurements. Close correspondence inspires confidence in both methods, each of which has unique advantages. The observation that ring-porous species operate at only a fraction of their potential conductivity at midday demands further study.     

Multifrequency permittivity measurements enable on‐line monitoring of changes in intracellular conductivity due to nutrient limitations during batch cultivations of CHO cells

Lab and pilot scale batch cultivations of a CHO K1/dhfr^? host cell line were conducted to evaluate on‐line multifrequency permittivity measurements as a process monitoring tool. The β‐dispersion parameters such as the characteristic frequency (f_C) and the permittivity increment (Δε_max) were calculated on‐line from the permittivity spectra. The dual‐frequency permittivity signal correlated well with the off‐line measured biovolume and the viable cell density. A significant drop in permittivity was monitored at the transition from exponential growth to a phase with reduced growth rate. Although not reflected in off‐line biovolume measurements, this decrease coincided with a drop in OUR and was probably caused by the depletion of glutamine and a metabolic shift occurring at the same time. Sudden changes in cell density, cell size, viability, capacitance per membrane area (C_M), and effects caused by medium conductivity (σ_m) could be excluded as reasons for the decrease in permittivity. After analysis of the process data, a drop in f_C as a result of a fall in intracellular conductivity (σ_i) was identified as responsible for the observed changes in the dual‐frequency permittivity signal. It is hypothesized that the β‐dispersion parameter f_C is indicative of changes in nutrient availability that have an impact on intracellular conductivity σ_i. On‐line permittivity measurements consequently not only reflect the biovolume but also the physiological state of mammalian cell cultures. These findings should pave the way for a better understanding of the intracellular state of cells and render permittivity measurements an important tool in process development and control. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Apparatus for measuring the swelling dependent electrical conductivity of charged hydrated soft tissues

This paper describes a new apparatus and method for measuring swelling dependent electrical conductivity of charged hydrated soft tissues. The apparatus was calibrated using a conductivity standard. Swelling dependent specific conductivity of porcine annulus fibrosis (AF) samples was determined. The conductivity values for porcine AF were similar to those for human and bovine articular cartilage found in the literature. Results revealed a significant linear correlation between specific conductivity and water content for porcine AF tissues tested in phosphate buffered saline (PBS).     

Effect of cold acclimation on intracellular ice formation in isolated protoplasts

When cooled at rapid rates to temperatures between −10 and −30°C, the incidence of intracellular ice formation was less in protoplasts enzymically isolated from cold acclimated leaves of rye (Secale cereale L. cv Puma) than that observed in protoplasts isolated from nonacclimated leaves. The extent of supercooling of the intracellular solution at any given temperature increased in both nonacclimated and acclimated protoplasts as the rate of cooling increased. There was no unique relationship between the extent of supercooling and the incidence of intracellular ice formation in either nonacclimated or acclimated protoplasts. In both nonacclimated and acclimated protoplasts, the extent of intracellular supercooling was similar under conditions that resulted in the greatest difference in the incidence of intracellular ice formation—cooling to −15 or −20°C at rates of 10 or 16°C/minute. Further, the hydraulic conductivity determined during freeze-induced dehydration at −5°C was similar for both nonacclimated and acclimated protoplasts. A major distinction between nonacclimated and acclimated protoplasts was the temperature at which nucleation occurred. In nonacclimated protoplasts, nucleation occurred over a relatively narrow temperature range with a median nucleation temperature of −15°C, whereas in acclimated protoplasts, nucleation occurred over a broader temperature range with a median nucleation temperature of −42°C. We conclude that the decreased incidence of intracellular ice formation in acclimated protoplasts is attributable to an increase in the stability of the plasma membrane which precludes nucleation of the supercooled intracellular solution and is not attributable to an increase in hydraulic conductivity of the plasma membrane which purportedly precludes supercooling of the intracellular solution.     

Predictive water loss curves for ram spermatozoa during cryopreservation: comparison with experimental observations.

Calculated curves predicting intracellular water loss during cryopreservation at different cooling rates were calculated from published equations. To compute these curves, basic cell parameters specific to ram spermatozoa were measured, i.e., the total surface area (139 microns2), the hydraulic conductivity (0.222 micron3/micron2.atm-1.min-1), and its temperature dependence (0.045/degree C). Cell surface area was derived from measurements of physical dimensions. Hydraulic conductivity was calculated from measurements of the critical medium hypotonicity on exposure of sperm to various hypotonic solutions and the time taken for membrane rupture in sperm exposed to distilled water (spermolysis time). The temperature dependence of the water permeability was derived from measurements of spermolysis time at various temperatures above zero. Several discrepancies were noted between the resulting calculated curves and experimental observations made on the effects of cooling rate on sperm cell survival. These could be due to errors in the estimates of the basic parameters, or to false assumptions in the basic equations used to compute the curves, e.g., the validity of the Boyle-van't Hoff relationship. Nevertheless, this study represents a first attempt to predict intracellular water loss from ram sperm during cooling and may provide a novel approach for the interpretation of the many empirical studies carried out to investigate optimal conditions for the cryopreservation of sperm.