Kinetics of erythrocyte swelling and membrane hole formation in hypotonic media.

Red blood cell (RBC) swelling and membrane hole formation in hypotonic external media were studied by measuring the time-dependent capacitance, C, and the conductance, G, in the beginning of the beta-dispersion range. At high and moderate osmolarities of the external solution the capacitance reaches a steady-state whereas at low osmolarities it reveals a biphasic kinetics. Examination of RBC suspensions exposed to different concentrations of HgCl(2) demonstrates that water transport through mercury-sensitive water channel controls RBC swelling. Unlike the capacitance, an increase in the conductance to a stationary level is observed after a certain delay. A comparison of G(t) curves recorded for the suspensions of the intact cells and those treated with cytochalasin B or glutaraldehyde demonstrates the significant effect of the membrane viscoelasticity on the pore formation. It is shown that the stretched membrane of completely swollen RBC retains its integrity for a certain time, termed as the membrane lifetime, t(memb). Therefore, the resistivity of RBCs to a certain osmotic shock may be quantified by the distribution function of RBC(t(memb)).     

The Influence of H+ on the Membrane Potential and Ion Fluxes of Nitella

The resting membrane potential of the Nitella cell is relatively insensitive to [K]_o, but behaves like a hydrogen electrode. K⁺ and Cl^- effluxes from the cell were measured continuously, while the membrane potential was changed either by means of a negative feedback circuit or by external pH changes. The experiments indicate that P_K and P_Cl are independent of pH but are a function of membrane potential. Slope ion conductances, G_K, G_Cl, and G_Na were calculated from efflux measurements, and their sum was found to be negligible compared to membrane conductance. The possibility that a boundary potential change might be responsible for the membrane potential change was considered but was ruled out by the fact that the peak of the action potential remained at a constant level regardless of pH changes in the external solution. The conductance for H⁺ was estimated by measuring the membrane current change during an external pH change while the membrane potential was clamped at K⁺ equilibrium potential. In the range of external pH 5 to 6, H⁺ chord conductance was substantially equal to the membrane conductance. However, the [H]_i measured by various methods was not such as would be predicted from the [H]_o and the membrane potential using the Nernst equation. In artificial pond water containing DNP, the resting membrane potential decreased; this suggested that some energy-consuming mechanism maintains the membrane potential at the resting level. It is probable that there is a H⁺ extrusion mechanism in the Nitella cell, because the potential difference between the resting potential and the H⁺ equilibrium potential is always maintained notwithstanding a continuous H⁺ inward current which should result from the potential difference.     

Effect of adherence,cell morphology,and lipopolysaccharide on potassium conductance and passive membrane properties of murine macrophage J774.1 cells

Summary The effects of adherence, cell morphology, and lipopolysaccharide on electrical membrane properties and on the expression of the inwardly rectifying K conductance in J774.1 cells were investigated. Whole-cell inwardly rectifying K currents (K _i), membrane capacitance (C _m), and membrane potential (V _m) were measured using the patch-clamp technique. SpecificK _i conductance (G _K i, whole-cell Ki conductance corrected for leak and normalized to membrane capacitance) was measured as a function of time after adherence, and was found to increase almost twofold one day after plating. Membrane potential (V _m) also increased from –42±4 mV (n=32) to –58±2 mV (n=47) over the same time period.G _K i andV _m were correlated with each other;G _L (leak conductance normalized to membrane capacitance) andV _m were not. The magnitudes ofG _K i andV _m 15 min to 2 hr after adherence were unaffected by the presence of 100 m cycloheximide, but the increase inG _K iandV _m that normally occurred between 2 and 8 hr after adherence was abolished by cycloheximide treatment. Membrane properties were analyzed as a function of cell morphology, by dividing cells into three categories ranging from small round cells to large, extremely spread cells. The capacitance of spread cells increased more than twofold within one day after adherence, which indicates that spread cells inserted new membrane. Spread cells had more negative resting membrane potentials than round cells, butG _K i andG _L were not significantly different. Lipopolysaccharide-(LPS; 1 or 10 g/ml) treated cells showed increasedC _m compared to control cells plated for comparable times. In contrast to the effect of adherence, LPS-treated cells exhibited a significantly lowerG _K i than control cells, indicating that the additional membrane did not have as high a density of functionalG _K i channels. We conclude that both adherence and LPS treatment increase the total surface membrane area of J774 cells and change the density of Ki channels. In addition, this study demonstrates that membrane area and density of Ki channels can vary independently of one another.     

Membrane tension regulates water transport in yeast

Evidence that membrane surface tension regulates water fluxes in intact cells of a Saccharomyces cerevisiae strain overexpressing aquaporin AQY1 was obtained by assessing the osmotic water transport parameters in cells equilibrated in different osmolarities. The osmotic water permeability coefficients (P_f) obtained for yeast cells overexpressing AQY1 incubated in low osmolarity buffers were similar to those obtained for a double mutant aqy1aqy2 and approximately three times lower (with higher activation energy, E_a) than values obtained for cells incubated in higher osmolarities (with lower E_a). Moreover, the initial inner volumes attained a maximum value for cells equilibrated in lower osmolarities (below 0.75 M) suggesting a pre-swollen state with the membrane under tension, independent of aquaporin expression. In this situation, the impairment of water channel activity suggested by lower P_f and higher E_a could probably be the first available volume regulatory tool that, in cooperation with other osmosensitive solute transporters, aims to maintain cell volume. The results presented point to the regulation of yeast water channels by membrane tension, as previously described in other cell systems.     

Synaptic Electrogenesis in Eel Electroplaques

Whether evoked by neural or by chemical stimulation, the synaptic membrane of eel electroplaques contributes a depolarizing electrogenesis that is due to an increased conductance for Na and K. The reversal potential (E_S) is the same for the two modes of synaptic activation. It is inside-positive by about 30–60 mv, or about midway between the emf's of the ionic batteries for Na (E_Na) and K(E_K). The total conductance contributed by synaptic activity (G_S) varied over a fivefold range, but the individual ionic branches, G_SSNa, and G_SSK, change nearly equally so that the ratio G_SSNa:G_SSK is near unity. G_SSK increases independently of the presence or absence of Na in the bathing medium, and independently of the presence or absence of the electrically excitable G_K channels. When activated, the synaptic membrane appears to be slightly permeable to Ca and Mg. When the membrane is depolarized into inside positivity the conductance of the synaptic components decreases and approaches zero for large inside-positive values. Thus, the synaptic components become electrically excitable when the potential across the membrane becomes inside-positive, responding as do the nonsynaptic components, with depolarizing inactivation.     

Allocation to leaf area and sapwood area affects water relations of co-occurring savanna and forest trees

Water availability is a principal factor limiting the distribution of closed-canopy forest in the seasonal tropics, suggesting that forest tree species may not be well adapted to cope with seasonal drought. We studied 11 congeneric species pairs, each containing one forest and one savanna species, to test the hypothesis that forest trees have a lower capacity to maintain seasonal homeostasis in water relations relative to savanna species. To quantify this, we measured sap flow, leaf water potential (Ψ_L), stomatal conductance (g _s), wood density, and Huber value (sapwood area:leaf area) of the 22 study species. We found significant differences in the water relations of these two species types. Leaf area specific hydraulic conductance of the soil/root/leaf pathway (G _t) was greater for savanna species than forest species. The lower G _t of forest trees resulted in significantly lower Ψ_L and g _s in the late dry season relative to savanna trees. The differences in G _t can be explained by differences in biomass allocation of savanna and forest trees. Savanna species had higher Huber values relative to forest species, conferring greater transport capacity on a leaf area basis. Forest trees have a lower capacity to maintain homeostasis in Ψ_L due to greater allocation to leaf area relative to savanna species. Despite significant differences in water relations, relationships between traits such as wood density and minimum Ψ_L were indistinguishable for the two species groups, indicating that forest and savanna share a common axis of water-use strategies involving multiple traits.     

Simultaneous Measurements of Cytoplasmic K Concentration and the Plasma Membrane Electrical Parameters in Single Membrane Samples of Chara corallina

The electrophysiological properties of cytoplasm-rich fragments (single membrane samples) prepared from internodal cells of Chara corallina were explored in conjunction with K⁺-sensitive microelectrode and current-voltage (I-V) measurements. This system eliminated the problem of the inaccessible cytoplasmic layer, while preserving many of the electrical characteristics of the intact cells. In 0.1 millimolar external K concentration (K_o⁺), the resting conductance (membrane conductance G_m, 0.85 ± 0.25 Siemens per square meter (±standard error)) of the single membrane samples, was dominated by the proton pump, as suggested by the response of the near-linear I-V characteristic to changes in external pH. Initial cytoplasmic K⁺ activities (a_K+), judged most reliable, gave values of 117 ± 67 millimolar; stable a_K+ values were 77 ± 31 millimolar. Equilibrium potentials for K⁺ (Nernst equilibrium potential) (E_K) calculated, using either of these data sets, were near the mean membrane potential (V_m). On a cell-to-cell basis, however, E_K was generally negative of the V_m, despite an electrogenic contribution from the Chara proton pump. When K_o⁺ was increased to 1.0 millimolar or above, G_m rose (by 8- to 10-fold in 10 millimolar K_o⁺), the steady state I-V characteristics showed a region of negative slope conductance, and V_m followed E_K. These results confirm previous studies which implicated a K_o⁺-induced and voltage-dependent permeability to K⁺ at the Chara plasma membrane. They provide an explanation for transitions between apparent K_o⁺-insensitive and K_o⁺-sensitive (`K⁺ electrode') behavior displayed by the membrane potential, as recorded in many algae and higher plant cells.     

Control of transpiration in three coffee cultivars: the role of hydraulic and crown architecture

Water use and hydraulic architecture were studied in the coffee (Coffea arabica) cultivars San Ramon, Yellow Caturra and Typica growing in the field under similar environmental conditions. The cultivars differed in growth habit, crown architecture, basal sapwood area and total leaf surface area. Transpiration per unit leaf area (E), stomatal conductance (g _s), crown conductance (g _c), total hydraulic conductance of the soil/leaf pathway (G _t) and the stomatal decoupling coefficient, omega (Ω) (Jarvis and McNaughton 1986) were assessed over a range of soil moisture and during partial defoliation treatments. The relationship between sap flow and sapwood area was linear and appeared to be similar for the three cultivars. Variation in g _c, E, and G _t of intact plants and leaf area-specific hydraulic conductivity (k _l) of excised lateral branches was negatively correlated with variation in the ratio of leaf area to sapwood area. Transpiration, g _c, and g _s were positively correlated with G _t. Transpiration and G _t varied with total leaf area and were greatest at intermediate values (10 m²) of leaf area. Omega was greatest in Yellow Caturra, the cultivar with the greatest leaf area and a dense crown, and was smallest in Typica, the cultivar with an open crown. Differences in omega were attributable primarily to differences in leaf boundary layer conductance among the cultivars. Plants of each cultivar that were 40% defoliated maintained sap flows comparable to pretreatment plants, but expected compensatory increases in g _s were not consistently observed. Despite their contrasting crown morphologies and hydraulic architecture, the three cultivars shared common relationships between water use and hydraulic architectural traits. Received: 17 February 1999 / Accepted: 28 July 1999     

Red blood cell membrane water permeability increases with length of ex vivo storage

Water transport across the red blood cell (RBC) membrane is an essential cell function that needs to be preserved during ex vivo storage. Progressive biochemical depletion during storage can result in significant conformational and compositional changes to the membrane. Characterizing the changes to RBC water permeability can help in evaluating the quality of stored blood products and aid in the development of improved methods for the cryopreservation of red blood cells. This study aimed to characterize the water permeability (L_p), osmotically inactive fraction (b), and Arrhenius activation energy (E_a) at defined storage time-points throughout storage and to correlate the observed results with other in vitro RBC quality parameters. RBCs were collected from age- and sex-matched blood donors. A stopped flow spectrophotometer was used to determine L_p and b by monitoring changes in hemoglobin autofluorescence when RBCs were exposed to anisotonic solutions. Experimental values of L_p were characterized at three different temperatures (4, 20 and 37 °C) to determine the E_a. Results showed that L_p, b, and E_a of stored RBCs significantly increase by day 21 of storage. Degradation of the RBC membrane with length of storage was seen as an increase in hemolysis and supernatant potassium, and a decrease in deformability, mean corpuscular hemoglobin concentration and supernatant sodium. RBC osmotic characteristics were shown to change with storage and correlate with changes in RBC membrane quality metrics. Monitoring water parameters is a predictor of membrane damage and loss of membrane integrity in ex vivo stored RBCs.     

Conductometric study of shear-dependent processes in red cell suspensions. II. Transient cross-stream hematocrit distribution

A novel experimental approach based on electrical properties of red blood cell (RBC) suspensions was applied to study the effects of the size and morphology of RBC aggregates on the transient cross-stream hematocrit distribution in suspensions flowing through a square cross-section flow channel. The information about the effective size of RBC aggregates and their morphology is extracted from the capacitance (C) and conductance (G) recorded during RBC aggregation, whereas a slower process of particle migration is manifested by delayed long-term changes in the conductance. Migration-induced changes in the conductance measured at low shear rates (< or =3.1 s(-1)) for suspensions of RBCs in a strongly aggregating medium reveal an increase to a maximum followed by a decrease to the stationary level. The ascending branch of G(t) curves reflects the aggregate migration in the direction of decreasing shear rate. A further RBC aggregation in the region of lower shear stresses leads to the formation of RBC networks and results in the transformation of the rheological behavior of suspensions from the thinning to the thickening. It is suggested that the descending branches of the G(t) curves recorded at low shear rates reflect an adjustment of the Hct distribution to a new state caused by a partial dispersion of RBC networks. For suspensions of non-aggregating RBCs it is found that depending on whether the shear rate is higher or lower compared with the prior value, individual RBCs migrate either toward the centerline of the flow or in the opposite direction.     

Properties of the large ion-permeable pores formed from protein F of Pseudomonas aeruginosa in lipid bilayer membranes

The incorporation of porin protein F from the outer membrane of Pseudomonas aeruginosa into artificial lipid bilayers results in an increase of the membrane conductance by many orders of magnitude. The membrane conductance is caused by the formation of large ion-permeable channels with a single-channel conductance in the order of 5 nS for 1 M alkali chlorides. The conductance has an ohmic current vs. voltage relationship. Further information on the structure of the pore formed by protein F was obtained by determining the single-channel conductance for various species differing in charge and size, and from zero-current potential measurements. The channel was found to be permeable for large organic ions (Tris⁺, N(C₂H₅)₄⁺, Hepes^?) and a channel diameter of 2.2 nm could be estimated from the conductance data (pore length of 7.5 nm). At neutral pH the pore is about two times more permeable for cations than for anions, possibly caused by negative charges in the pore. The consistent observation of large water filled pores formed by porin protein F in model membrane systems is discussed in the light of the known low permeability of the Ps. aeruginosa outer membrane towards antibiotics. It is suggested that this results from a relatively low proportion of open functional porin protein F pores in vivo.     

Apical Cl− Channels in A6 Cells

Short-circuit current (I _sc ), transepithelial conductance (G _t ), electrical capacitance (C _T ) and the fluctuation in I _sc were analyzed in polarized epithelial cells from the distal nephron of Xenopus laevis (A6 cell line). Tissues were incubated with Na⁺- and Cl⁻-free solutions on the apical surface. Basolateral perfusate was NaCl-Ringer. Agents that increase cellular cAMP evoked increases in G _t , C _T , I _sc and generated a Lorentzian I _sc -noise. The responses could be related to active, electrogenic secretion of Cl⁻. Arginine-vasotocin and oxytocin caused a typical peak-plateau response pattern. Stimulation with a membrane-permeant nonhydrolyzable cAMP analogue or forskolin showed stable increases in G _t with only moderate peaking of I _sc . Phosphodiesterase inhibitors also stimulated Cl⁻ secretion with peaking responses in G _t and I _sc . All stimulants elicited a spontaneous Lorentzian noise, originating from the activated apical Cl⁻ channel, with almost identical corner frequency (40–50 Hz). Repetitive challenge with the hormones led to a refractory behavior of all parameters. Activation of the cAMP route could overcome this refractoriness. All agents caused C _T , a measure of apical membrane area, to increase in a manner roughly synchronous with G _t . These results suggest that activation of the cAMP-messenger route may, at least partly, involve exocytosis of a vesicular Cl⁻ channel pool. Apical flufenamate depressed Cl⁻ current and conductance and apparently generated blocker-noise. However, blocking kinetics extracted from noise experiments could not be reconciled with those obtained from current inhibition, suggesting the drug does not act as simple open-channel inhibitor. Received: 20 May 1998/Revised: 8 September 1998     

Membrane permeabilization and cell damage by ultrashort electric field shocks

Mammalian cells exposed to electric field pulses of nanosecond duration (nsPEF; 60-ns, 12 kV/cm) experienced a profound and long-lasting increase in passive electrical conductance (G_m) of the cell membrane, probably caused by opening of stable conductance pores (CPs). The CPs were permeable to Cl⁻ and alkali metal cations, but not to larger molecules such as propidium iodide (PI). CPs gradually resealed; the process took minutes and could be observed even in dialyzed cells and in ATP- and glucose-free solutions. Cells subjected to long nsPEF trains (up to 200 pulses) underwent severe and immediate necrotic transformation (cell swelling, blebbing, cytoplasm granulation), but remained impermeable to PI for at least 30-60 min after the exposure. Both G_m increase after short nsPEF trains and necrotic changes after long nsPEF trains were cell type-dependent: they were much weaker in HeLa than in GH3 cells. La³⁺ and Gd³⁺ ions significantly inhibited the nsPEF-induced G_m increase (probably by blocking the CPs), and effectively protected intensely exposed cells from developing necrosis. We conclude that plasma membrane permeabilization is the principal cause of necrotic transformation in nsPEF-exposed cells and probably contributes to other known nsPEF bioeffects.     

Studies of electric capacitance of membranes

Summary The electric capacitance and conductance of a model membrane composed of a hydrophobic filter paper and a synthetic lipid analogue, i.e., dioleylphosphate, immersed in an electrolyte solution were observed with various frequencies ranging from 20 to 3×10⁶ Hz. With successive increase of salt concentration in the external solution, the capacitance and conductance of the membrane increased discontinuously at a certain critical value of the external salt concentration. This variation of the capacitance and conductance of the membrane with the salt concentration was found to be reversible, and the critical value of salt concentration was independent of the adsorbed quantity of the lipid, and of the pore size of the filter paper as far as the adsorbed quantity of the dioleylphosphate was large.A theoretical analysis based on the membrane model for the filter paper-phospholipid system proposed in Part I of this series revealed that the dioleylphosphate impregnated in the filter paper changed its conformation from oil droplets or globular micelles to a number of bilayer membranes when the salt concentration reached the critical value for a given pair of electrolyte species and the membrane. The conformational change of the lipid analogue in the filter paper is discussed in connection with the ability of formation and stability of a black bilayer membrane of the dioleylphosphate.     

Cell Swelling Activates the K+ Conductance and Inhibits the Cl? Conductance of the Basolateral Membrane of Cells from a Leaky Epithelium

Necturus gallbladder epithelial cells bathed in 10 mM HCO₃/1% CO₂ display sizable basolateral membrane conductances for Cl⁻ (G_Cl ^b) and K ⁺ (G_K ^b). Lowering the osmolality of the apical bathing solution hyperpolarized both apical and basolateral membranes and increased the K ⁺/Cl⁻ selectivity of the basolateral membrane. Hyperosmotic solutions had the opposite effects. Intracellular free-calcium concentration ([Ca²⁺]_i) increased transiently during hyposmotic swelling (peak at ∼30 s, return to baseline within ∼90 s), but chelation of cell Ca²⁺ did not prevent the membrane hyperpolarization elicited by the hyposmotic solution. Cable analysis experiments showed that the electrical resistance of the basolateral membrane decreased during hyposmotic swelling and increased during hyperosmotic shrinkage, whereas the apical membrane resistance was unchanged in hyposmotic solution and decreased in hyperosmotic solution. We assessed changes in cell volume in the epithelium by measuring changes in the intracellular concentration of an impermeant cation (tetramethylammonium), and in isolated polarized cells measuring changes in intracellular calcein fluorescence, and observed that these epithelial cells do not undergo measurable volume regulation over 10–12 min after osmotic swelling. Depolarization of the basolateral membrane voltage (V_cs) produced a significant increase in the change in V_cs elicited by lowering basolateral solution [Cl⁻], whereas hyperpolarization of V_cs had the opposite effect. These results suggest that: (a) Hyposmotic swelling increases G_K ^b and decreases G _Cl ^b. These two effects appear to be linked, i.e., the increase in G _K ^b produces membrane hyperpolarization, which in turn reduces G _Cl ^b. ( b) Hyperosmotic shrinkage has the opposite effects on G_K ^b and G _Cl ^b. ( c) Cell swelling causes a transient increase in [Ca²⁺]_i, but this response may not be necessary for the increase in G_K ^b during cell swelling.     

Electrical characteristics of the apical and basal-lateral membranes in the turtle bladder epithelial cell layer

(1) The active transport of Na⁺ across the turtle bladder epithelial cell layer consists of a passive entry step through a Na⁺-selective path in the apical membrane and an active extrusion step through Na⁺ pump-containing path in the basal-lateral membrane together with some back-leakage through the paracellular spaces and tight junctions between the epithelial cells. This hypothesis has now been verified qualitatively and to some extent, quantitatively by the use of an intracellularly-located microelectrode in conjunction with a conventional assembly of extracellularly-located macroelectrodes mainly in short-circuited bladders bathed by Na⁺-rich Ringer media. Under these conditions, the intracellular potential (V_sc) averaged 38.4 mV with the cell electronegative; the fractional resistance of the apical membrane ($\text{?R}{}_{\mathrm{<mtext>a</mtext>}}$) averaged 0.55; while the concomitant transepithelial parameters, short circuiting current (I_sc) and electrical conductance (G_t), average 68.6 μA/cm² and 0.98 mS/cm², respectively. (2) The relation between these parameters and the transepithelial flow of Na⁺ (orI_sc) is evoked by blocking Na⁺ entry into the cell (by the mucosal addition of amiloride or removal of mucosal Na⁺). Amiloride-induced blockade of the Na⁺ entry step results in a rapid hyperpolarization of the cell interior during which V_sc = —79.1 mV and $\text{?R}{}_{\mathrm{<mtext>a</mtext>}}\text{= 0.92}$. I_sc and G_t (equivalent to the shunt conductance under these conditions) averaged 5 μA/cm² and 0.35 mS/cm², respectively. The entire process is reversible on re-admission of Na⁺ entry into the cell. (3) A slow depolarization of the cell interior in the period of blocked transapical Na⁺ entry is opposite to that expected from an electroneutral Na⁺-K⁺ exchanging pump; but instead is the predictable response of an electrogenic Na⁺ pump in parallel with a passive K⁺-selective conductance in the basal-lateral membrane. (4) The electrogenicity concept is substantiated after pretreatment of the bladder with serosal ouabain, which changes the response of V_sc to amiloride (from the aforementioned biphasic response) to a step-function response, attributable mainly to the development of a slowly dissipating K⁺ diffusion potential across the basallateral membrane. (5) Under open-circuit conditions, the electronegativity of cell to mucosa (V_a) is a linear inverse function of the electropositivity of serosa to mucosa (V_t). For V_t ? 100 mV, V_a is positive; and for V_t between ?30 and 90 mV, V_a is negative.     

Conductometric study of shear-dependent processes in red cell suspensions. I. Effect of red blood cell aggregate morphology on blood conductance

The conductance and capacitance of flowing and quiescent red blood cell (RBC) suspensions were measured at a frequency of 0.2 MHz. The results demonstrate that the time-dependent changes in the conductance recorded during the aggregation process differ in nature for suspensions of short linear rouleaux, branched aggregates and RBC networks. It is shown that the conductance of RBC suspensions measured during the aggregation and disaggregation processes follows the morphological transformations of the RBC aggregates. Thus, this method enables characterization of the morphology of RBC aggregates formed in whole blood and in suspensions with physiological hematocrits both under flow conditions and in stasis. These results in combination with previous ones suggest that this technique can be used for studies of dynamic RBC aggregation and probably for diagnostic use.     

THE KINETICS OF OSMOTIC SWELLING IN LIVING CELLS

The rate of swelling of unfertilized sea urchin eggs in hypotonic sea water was investigated. Analysis of curves leads to the following conclusions. 1. The rate of swelling follows the equation, See PDF for Equation where V _eq., V ₀, and V_t stand for volume at equilibrium, at first instant, and at time t, respectively, the other symbols having their usual significance. This equation is found to hold over a wide range of temperatures and osmotic pressures. This relation is the one expected in a diffusion process. 2. The rate of swelling is found to have a high temperature coefficient (Q ₁₀ = 2 to 3, or µ = 13,000 to 19,000). This deviation from the usual effect of temperature on diffusion processes is thought to be associated with changes in cell permeability to water. The possible influence of changes in viscosity is discussed. 3. The lower the osmotic pressure of the solution, the longer it takes for swelling of the cell. Thus at 15° in 80 per cent sea water, the velocity constant has a value of 0.072, in 20 per cent sea water, of 0.006.     

Voltage and Current Clamp Transients with Membrane Dielectric Loss

Transient responses of a space-clamped squid axon membrane to step changes of voltage or current are often approximated by exponential functions of time, corresponding to a series resistance and a membrane capacity of 1.0 μF/cm². Curtis and Cole (1938, J. Gen. Physiol. 21:757) found, however, that the membrane had a constant phase angle impedance z = z₁(jωτ)^-α, with a mean α = 0.85. (α = 1.0 for an ideal capacitor; α < 1.0 may represent dielectric loss.) This result is supported by more recently published experimental data. For comparison with experiments, we have computed functions expressing voltage and current transients with constant phase angle capacitance, a parallel leakage conductance, and a series resistance, at nine values of α from 0.5 to 1.0. A series in powers of t^α provided a good approximation for short times; one in powers of t^-α, for long times; for intermediate times, a rational approximation matching both series for a finite number of terms was used. These computations may help in determining experimental series resistances and parallel leakage conductances from membrane voltage or current clamp data.     

Intracellular Biopotentials During Static Extracellular Stimulation

Two properties of the intracellular potentials and electric fields resulting from static extracellular stimulation are obtained for arbitrarily shaped cells. First, the values of intracellular potential are shown to be bounded by the maximum and minimum values of extracellular potential on the surface of the cell. Second, the volume average of the magnitude of intracellular electric field is shown to have an upper bound given by the ratio of the magnitude of the largest extracellular potential difference on the surface of the cell to a generalized length constant λ = [σ_intraV_cell/(σ_memb A_cell)]^1/2, where V_cell and A_cell are the volume and surface area of the cell, σ_intra is the intracellular conductivity (reciprocal ohms per centimeter), and σ_memb is the membrane conductivity (reciprocal ohms per square centimeter). The use of the upper bound on the volume average of the magnitude of intracellular electric field as an estimate for intracellular isopotentiality is discussed and the use of the generalized length constant for electrically describing arbitrary cells is illustrated for cylindrical- and spheroidal-shaped cells.