A Test of the Theory of the Steady-State Properties of an Ion Exchange Membrane with Mobile Sites and Dissociated Counterions

An experimental model system, formally equivalent to a liquid ion exchange membrane having completely dissociated sites and counterions, has been devised in order to test the steady-state properties recently deduced theoretically for such a membrane by Conti and Eisenman, (1966). In this system we have obtained quantitative experimental confirmation of the following theoretical expectations. (a) The current-voltage relationship is nonlinear and exhibits finite limiting currents with strong applied fields. (b) The mobile sites rearrange within the “membrane” under applied electric field to give a linear concentration profile and a logarithmic electric potential profile in the steady state. We have also extended the theory to consider the instantaneous conductance in the steady state. Theory and experiment indicate that in a mobile site membrane the instantaneous conductance in the steady state is not given by the chord conductance of the steady-state current-voltage relationship, in contrast to the situation in a fixed site membrane. This finding suggests a way of testing whether ions permeate across an unknown membrane by a fixed site or a dissociated mobile site mechanism.     

Viscoelastic relaxation in the membrane of the auditory outer hair cell.

The outer hair cell (OHC) in the mammalian ear has a unique membrane potential-dependent motility, which is considered to be important for frequency discrimination (tuning). The OHC motile mechanism is located at the cell membrane and is strongly influenced by its passive mechanical properties. To study the viscoelastic properties of OHCs, we exposed cells to a hypoosmotic solution for varying durations and then punctured them, to immediately release the osmotic stress. Using video records of the cells, we determined both the imposed strain and the strain after puncturing, when stress was reset to zero. The strain data were described by a simple rheological model consisting of two springs and a dashpot, and the fit to this model gave a time constant of 40 +/- 19 s for the relaxation (reduction) of tension during prolonged strain. For time scales much shorter or longer than this, we would expect essentially elastic behavior. This relaxation process affects the membrane tension of the cell, and because it has been shown that membrane tension has a modulatory role in the OHC's motility, this relaxation process could be part of an adaptation mechanism, with which the motility system of the OHC can adjust to changing conditions and maintain optimum membrane tension.     

Properties of membrane stationary states

Summary The flux of permeant species through a membrane is examined using discrete state stochastic models for the transport process within the membrane. While a membrane flux is maintained due to a concentration gradient between bathing solutions, the distribution of species within the membrane evolves to a time invariant configuration which can differ significantly from the equilibrium configuration. Some special properties of these stationary states are examined using linear, microcanonical models for the membrane transport process. Analysis of these models reveals properties which are masked by the phenomenological analysis of irreversible thermodynamics. For example, the models can be used to study the nature of multi-state relaxation within the membrane by observation of the time dependence of the net membrane flux when the membrane is perturbed from its stationary state distribution. Under some conditions, multi-state models will produce relaxation similar to that observed for single-state processes. The symmetry within the membrane is a critical factor for monitoring relaxation processes within the membrane. Because of the stationary nature of the membrane configuration, statistical thermodynamic variables can be defined for the membrane configuration. The total system is not in equilibrium since the baths must still be described by dissipation functions. In the stationary state, the configurational entropy of the membrane is lowered relative to equilibrium and is shown to depend quadratically on the time independent parameter (j/p) wherej is the membrane flux andp is a characteristic transition probability for intra-membrane transitions. The basic membrane system serves as a quantitative example of the entropy reduction possible in a stationary state system. An allosteric transition mediated by the stationary state configuration is examined as a means of utilizing this negentropy production.     

Separate Determination of the Electrical Properties of the Tonoplast and the Plasmalemma of the Giant-Celled Alga Valonia utricularis: Vacuolar Perfusion of Turgescent Cells with Nystatin and Other Agents

In the giant-celled marine algae Valonia utricularis the turgor-sensing mechanism of the plasmalemma and the role of the tonoplast in turgor regulation is unknown because of the lack of solid data about the individual electrical properties of the plasmalemma and the vacuolar membrane. For this reason, a vacuolar perfusion technique was developed that allowed controlled manipulation of the vacuolar sap under turgescent conditions (up to about 0.3 MPa). Charge-pulse relaxation studies on vacuolarly perfused cells at different turgor pressure values showed that the area-specific resistance of the total membrane barrier (tonoplast and plasmalemma) exhibited a similar dependence on turgor pressure as reported in the literature for nonperfused cells: the resistance assumed a minimum value at the physiological turgor pressure of about 0.1 MPa. The agreement of the data suggested that the perfusion process did not alter the transport properties of the membrane barrier. Addition of 16 μm of the H⁺-carrier FCCP (carbonylcyanide p-trifluoromethoxyphenyhydrazone) to the perfusion solution resulted in a drop of the total membrane potential from +4 mV to −22 mV and in an increase of the area-specific membrane resistance from 6.8 × 10⁻² to 40.6 × 10⁻²Ωm². The time constants of the two exponentials of the charge pulse relaxation spectrum increased significantly. These results are inconsistent with the assumption of a high-conductance state of the tonoplast (R. Lainson and C.P. Field, J. Membrane Biol. 29:81–94, 1976). Depending on the site of addition, the pore-forming antibiotics nystatin and amphotericin B affected either the time constant of the fast or of the slow relaxation (provided that the composition of the perfusion solution and the artificial sea water were replaced by a cytoplasma-analogous medium). When 50 μm of the antibiotics were added externally, the fast relaxation process disappeared. Contrastingly, the slow relaxation process disappeared upon vacuolar addition. The antibiotics cannot penetrate biomembranes rapidly, and therefore, the findings suggested that the fast and slow relaxations originated exclusively from the electrical properties of the plasmalemma and the tonoplast respectively. This interpretation implies that the area-specific resistance of the tonoplast is significantly larger than that of the plasmalemma (consistent with the FCCP data) and that the area-specific capacitance of the tonoplast is unusually high (6.21 × 10⁻² Fm⁻² compared to 0.77 × 10⁻² Fm⁻² of the plasmalemma). Thus, we have to assume that the vacuolar membrane of V. utricularis is highly folded (by a factor of about 9 in relation to the geometric area) and/or contains a fairly high concentration of mobile charges of an unknown electrogenic ion carrier system. Received: 22 October 1996/Revised: 16 January 1997     

Population genetics of modifiers of meiotic drive. I. The solution of a special case and some general implications

This is a study of the formal population genetics of a two locus model where the alleles at one locus are subject to meiotic drive and zygotic selection and the only effect of the other locus is the modification of drive intensity. A complete analytic solution is obtained for a biologically reasonable special case. It is then argued, partially with the aid of computer analysis, that with moderate relaxation of assumptions of the special case, the conclusions derived from that case still hold. These conclusions are that if there is linkage a stable two locus polymorphism can result. There is permanent linkage disequilibrium with the loosing allele at the drive locus in coupling with the suppressor allele at the modifier locus, and the driven allele coupled with the modifier allele which enhances drive. It is suggested that this result explains how the SD system in Drosophila maintains its integrity in natural populations.     

Quantitation of lipid phases in phospholipid vesicles by the generalized polarization of Laurdan fluorescence.

The sensitivity of Laurdan (6-dodecanoyl-2-dimethylaminonaphthalene) excitation and emission spectra to the physical state of the membrane arises from dipolar relaxation processes in the membrane region surrounding the Laurdan molecule. Experiments performed using phospholipid vesicles composed of phospholipids with different polar head groups show that this part of the molecule is not responsible for the observed effects. Also, pH titration in the range from pH 4 to 10 shows that the spectral variations are independent of the charge of the polar head. A two-state model of dipolar relaxation is used to qualitatively explain the behavior of Laurdan. It is concluded that the presence of water molecules in the phospholipid matrix are responsible for the spectral properties of Laurdan in the gel phase. In the liquid crystalline phase there is a relaxation process that we attribute to water molecules that can reorientate during the few nanoseconds of the excited state lifetime. The quantitation of lipid phases is obtained using generalized polarization which, after proper choice of excitation and emission wavelengths, satisfies a simple addition rule.     

Viscoelastic properties of gerbil tympanic membrane at very low frequencies

The tympanic membrane transfers sound waves in the ear canal to mechanical vibrations in the middle ear and cochlea. Good estimates of the mechanical properties of the tympanic membrane are important to obtain realistic models. Up till now, only limited resources about tympanic membrane viscoelastic properties are available in the literature. This study aimed to quantify the viscoelastic properties of gerbil tympanic membrane. Step indentations were applied with a custom indenter on four fresh, intact tympanic membranes and the resulting force relaxation was measured. The reduced relaxation functions were then fitted with two viscoelastic model representations: a 5-parameter Maxwell model and a model with a continuous relaxation spectrum. The average relaxation function is described by an initial rapid decrease of 6.5% with characteristic time 0.77 s, followed by a long term decrease with characteristic time 46 s that gradually tends stable till a total relaxation of 15%. The relaxation curves in the time domain were transformed to complex moduli in the frequency domain. It was found that these transformations yield information on strain-rate dependence only from quasi-static to the very lowest acoustic frequencies. Finally, relaxation and hysteresis were simulated in a finite element model with viscoelastic material properties.     

The Coalescent Process in Models with Selection and Recombination

The statistical properties of the process describing the genealogical history of a random sample of genes at a selectively neutral locus which is linked to a locus at which natural selection operates are investigated. It is found that the equations describing this process are simple modifications of the equations describing the process assuming that the two loci are completely linked. Thus, the statistical properties of the genealogical process for a random sample at a neutral locus linked to a locus with selection follow from the results obtained for the selected locus. Sequence data from the alcohol dehydrogenase (Adh) region of Drosophila melanogaster are examined and compared to predictions based on the theory. It is found that the spatial distribution of nucleotide differences between Fast and Slow alleles of Adh is very similar to the spatial distribution predicted if balancing selection operates to maintain the allozyme variation at the Adh locus. The spatial distribution of nucleotide differences between different Slow alleles of Adh do not match the predictions of this simple model very well.     

Evidence for the presence of mobile charges in the cell membrane of Valonia utricularis.

Charge-pulse relaxation studies were performed on cells of the giant marine alga Valonia utricularis with microelectrodes inserted into the vacuole. If the cell was charged by short pulses of 200 ns duration, the decay of the initial membrane voltage could be described by two relaxation processes at normal pH (8.2). The fast exponential relaxation had a time constant of approximately 100 microseconds whereas the the time constant of the slow relaxation ranged between 2 and 15 ms. The ratio of the two amplitudes varied between 10 and 20 and was found to be independent of the initial voltage, up to 400 mV. In contrast to the time constants, the amplitude ratio was a function of the duration of the charge pulse. As the pulse length was increased to 10 ms, the fast relaxation disappeared. A change in pH of the natural sea water from 8.2 to 4 resulted in the disappearance of both exponential processes and the appearance of one single exponential with a 1-ms time constant over the whole pulse-length range. The analysis of the data in terms of a two-membrane model leads to unusual values and a pH-dependence of the specific capacitances (0.6 and 6 microF cm-2) of the two membranes, which can be treated as two serial circuits of a capacitor and a resistor in parallel. The charge-pulse and the current-clamp data are consistent with the assumption that the cell membrane of V. utricularis contains mobile charges with a total surface concentration of approximately 4 pmol cm-2. These charges cross the membrane barrier with a translocation rate constant around 500 s-1 and become neutralized at low pH. From our experimental results it cannot be completely excluded that the tonoplast has also a high specific resistance. But in this case it has to be assumed that the tonoplast and plasmalemma have very similar electrical properties and contain both mobile charges, so that the two membranes appear as a single membrane. Experiments on artificial lipid bilayer membranes in the presence of the lipophilic ion dipicrylamine, support our mobile charge concept for the cell membrane of V. utricularis.     

Frequency dispersions of human skin dielectrics.

The electrical properties of many biological materials are known to exhibit frequency dispersions. In the human skin, the impedance measured at various frequencies closely describes a circular locus of the Cole-Cole type in the complex impedance plane. In this report, the formative mechanisms responsible for the anomalous circular-arc behavior of skin impedance were investigated, using data from impedance measurements taken after successive strippings of the skin. The data were analyzed with respect to changes in the parameters of the equivalent Cole-Cole model after each stripping. For an exponential resistivity profile (Tregear, 1966, Physical Functions of Skin; Yamamoto and Yamamoto, 1976, Med. Biol. Eng., 14:151--158), the profile of the dielectric constant was shown to be uniform across the epidermis. Based on these results, a structural model has been formulated in terms of the relaxation theory of Maxwell and Wagner for inhomogeneous dielectric materials. The impedance locus obtained from the model approximates a circular are with phase constant alpha = 0.82, which compares favorably with experimental data. At higher frequencies a constant-phase, frequency-dependent component having the same phase constant alpha is also demonstrated. It is suggested that an approximately rectangular distribution of the relaxation time over the epidermal dielectric sheath is adequate to account for the anomalous frequency characteristics of human skin impedance.     

Fast kinetic studies on the allosteric interactions between acetylcholine receptor and local anesthetic binding sites.

Preincubation of receptor-rich membrane fragments from Torpedo marmorata with tertiary amine local anesthetics and several toxins such as histrionicotoxin, crotoxin and cerulotoxin, modifies the amplitude and time course of the relaxation processes monitored upon rapid mixing of the membrane fragments with the fluorescent agonist, Dns-C6-Cho. In particular, the amplitude of the rapid relaxation process, which is proportional to the fraction of acetylcholine receptor sites in a high-affinity state, increases; accordingly, the rate constant of the 'slow' and 'intermediate' relaxation processes also increases up to ten times (except with histrionicotoxin) whereas in a higher range of local anesthetic concentrations the rate constant of the 'rapid' relaxation process decreases. The data are accounted for by a two-state model of the acetylcholine regulator, assuming distinct binding sites for cholinergic agonists and local anesthetics and allosteric interactions between these two classes of sites; local anesthetics stabilize the regulator in a high-affinity state for agonists even in the absence of agonist, and modify the rate constants for th interconversions between the low-affinity and high-affinity states. The model accounts for the 'slow' fluorescence increase monitored upon addition of local anesthetics to a suspension of receptor-rich membranes supplemented with trace amounts of Dns-C6-Cho. The effect of local anesthetics on the apparent rate constant of the 'rapid' relaxation process can be accounted for on the basis of an additional low-affinity binding of local anesthetics to the acetylcholine receptor site. Finally the increase of the apparent rate constant of the 'intermediate' relaxation process can be simply accounted for by assuming the existence of a third state, corresponding to the 'active' state, to which local anesthetics bind and block ionic transport.     

Theoretical evaluation of the distributed power dissipation in biological cells exposed to electric fields

The paper deals with the power dissipation caused by exposure of biological cells to electric fields of various frequencies. With DC and sub-MHz AC frequencies, power dissipation in the cell membrane is of the same order of magnitude as in the external medium. At MHz and GHz frequencies, dielectric relaxation leads to dielectric power dissipation gradually increasing with frequency, and total power dissipation within the membrane rises significantly. Since such local increase can lead to considerable biochemical and biophysical changes within the membrane, especially at higher frequencies, the bulk treatment does not provide a complete picture of effects of an exposure. In this paper, we theoretically analyze the distribution of power dissipation as a function of field frequency. We first discuss conductive power dissipation generated by DC exposures. Then, we focus on AC fields; starting with the established first-order model, which includes only conductive power dissipation and is valid at sub-MHz frequencies, we enhance it in two steps. We first introduce the capacitive properties of the cytoplasm and the external medium to obtain a second-order model, which still includes only conductive power dissipation. Then we enhance this model further by accounting for dielectric relaxation effects, thereby introducing dielectric power dissipation. The calculations show that due to the latter component, in the MHz range the power dissipation within the membrane significantly exceeds the value in the external medium, while in the lower GHz range this effect is even more pronounced. This implies that even in exposures that do not cause a significant temperature rise at the macroscopic, whole-system level, the locally increased power dissipation in cell membranes could lead to various effects at the microscopic, single-cell level.     

The steady-state properties of an ion exchange membrane with mobile sites

A study of the properties of the steady states of a system composed of two solutions separated by an ion exchange membrane having mobile sites is presented. It is assumed that the membrane is impermeable to coions; the solutions contain no more than two species of counterions, both of the same valence; and no flow of bulk solution occurs. Assuming that all ions are completely dissociated, behave ideally, and have constant mobilities throughout the membrane, explicit expressions are derived for the steady states of the electric current, individual fluxes, and concentration profiles as functions of the compositions of the solutions and of the difference of electric potential between them. The derived expressions are compared with those for an ion exchange membrane having fixed sites; and it is found that the expressions of certain quantities, such as the difference of electric potential between the two solutions for zero current or the ratio of the fluxes of the counterions as functions of the external parameters of the system, are the same for both types of membranes. On the other hand, differences in the behavior of the two types of membranes are found from other expressions-for example, the current-voltage relationship. In the mobile site ion exchanger the current asymptotically approaches finite limiting values for high positive and negative voltages while in the fixed site ion exchanger it is the conductance which approaches finite limiting values.     

Long and short distance movements of β(2)-adrenoceptor in cell membrane assessed by photoconvertible fluorescent protein dendra2-β(2)-adrenoceptor fusion

Local movements of receptors in the plasma membrane have been extensively studied, as it is generally believed that the dynamics of membrane distribution of receptors regulate their functions. However, the properties of large-scale (>5μm) receptor movements in the membrane are relatively obscure. In the present study, we addressed the question as to whether the large-scale movement of receptor in the plasma membrane at the whole cell level can be explained quantitatively by its local diffusive properties. We used HEK 293 cells transfected with human β2-adrenoceptor fused to photoconvertible fluorescent protein dendra2 as a model system; and found that 1) functional integrity of the dendra2-tagged receptor remains apparently intact; 2) in a mesoscopic scale (~4μm), ~90% of the receptors are mobile on average, and receptor influx to, and out-flux from a membrane area can be symmetrically explained by a diffusion-like process with an effective diffusion coefficient of ~0.1μm(2)/s; 3) these mobility parameters are not affected by the activity state of the receptor (assessed by using constitutively active receptor mutants); 4) in the macroscopic scale (4-40μm), although a slowly diffusing fraction of receptors (with D<0.01μm(2)/s) is identifiable in some cases, the movement of the predominant fraction is perfectly explained by the same effective diffusion process observed in the mesoscopic scale, suggesting that the large scale structure of the cell membrane as felt by the receptor is apparently homogeneous in terms of its mesoscopic properties. We also showed that intracellular compartments and plasma membrane are kinetically connected even at steady-state.     

Changes in membrane dynamics associated with myogenic cell fusion

Changes in membrane dynamic properties associated with membrane fusion are studied employing in vitro myoblast fusion as a model system. We utilize a microscopic fluorescence relaxation approach which makes feasible the study of local variations in membrane dynamics within surface subdomains of single intact cells. Studies of the average rotational mobility of the fluorescent probe-1-anilino-naphthalene-8-sulfonate by this technique indicate that myoblast fusion activity is preceded by a generalized increased in membrane fluidity and that areas of cell contact between fusing cells exhibit higher fluidity and polarity, locally, than non-fusion regions.     

Statistical Properties of a DNA Sample under the Finite-Sites Model

Statistical properties of a DNA sample from a random-mating population of constant size are studied under the finite-sites model. It is assumed that there is no migration and no recombination occurs within the locus. A Markov process model is used for nucleotide substitution, allowing for multiple substitutions at a single site. The evolutionary rates among sites are treated as either constant or variable. The general likelihood calculation using numerical integration involves intensive computation and is feasible for three or four sequences only; it may be used for validating approximate algorithms. Methods are developed to approximate the probability distribution of the number of segregating sites in a random sample of n sequences, with either constant or variable substitution rates across sites. Calculations using parameter estimates obtained for human D-loop mitochondrial DNAs show that among-site rate variation has a major effect on the distribution of the number of segregating sites; the distribution under the finite-sites model with variable rates among sites is quite different from that under the infinite-sites model.     

Mobile charges in the cell membranes ofHalicystis parvula

Charge-pulse experiments were performed on cells of the giant marine algaHalicystis parvula. At normal pH (8.2), the voltage decay following a charge-pulse of 500 ns duration fed to the vacuole could be described by summing two exponential relaxations. The amplitudes and time constants of these relaxations were widely separated. The parameters of the two relaxation processes were found to be pH-dependent. Reduction of the external pH value from pH 8.2 to 5 resulted in a complete change of the two relaxation processes within a few minutes. Only one relaxation process could be observed at pH 5, within the time resolution of our instrumentation. The experimental data could not be explained by a two-membrane model with reasonable values for the specific capacitances of tonoplast and plasmalemma. The results of the charge-pulse relaxations were found to be consistent with the assumption that both membranes have very similar electrical properties and that both contain mobile charges with a total surface concentration of about 30 nmol·m^-2 and a translocation-rate constant of about 500·s^-1. The mobile charges became neutralized at pH 5 hhich led to a decrease of the apparent specific capacitance of the algal cells. They are presumably either part of a transport system for cations or connected with the chloride pump ofHalicystis parvula.Abbreviation RC (R)esistance·(C)apacitance     

Mobility of water bound to biological membranes: A proton NMR relaxation study

Water proton nuclear magnetic resonance relaxation measurements have been obtained for aqueous suspensions of red cell membranes. These data support a model in which water molecules are exchanging rapidly between a bound phase with restricted motions and a free phase with dynamic properties similar to liquid water. From this model and these data, estimates are obtained for the relaxation time for bound phase water. Possible relaxation mechanisms for bound phase water are discussed and some support is found for an intermolecular interaction modulated by translational motions characterized by a diffusion constant of 10^?9 cm²/s.     

Polaron stability in oligoacene crystals

The polaron stability in organic molecular crystals is theoretically investigated in the scope of a two-dimensional Holstein–Peierls model that includes lattice relaxation. Particularly, the investigation is focused on designing a model Hamiltonian that can address properly the polaron properties in different model oligoacene crystals. The findings showed that a suitable choice for a set of parameters can play the role of distinguishing the model crystals and, consequently, different properties related to the polaron stability in these systems are observed. Importantly, the usefulness of this model is stressed by investigating the electronic localization of the polaron, which provides a deeper understanding into the properties associated with the polaron stability in oligoacene crystals.