Interactions of voltage-sensing dyes with membranes. II. Spectrophotometric and electrical correlates of cyanine-dye adsorption to membranes.

The adsorption to bilayer membranes of the thiadicarbocyanine dyes, diSCn(5), has been studied as a function of the membrane's surface-charge density, the aqueous ionic strength, and the length (n) of the hydrocarbon side chain of the dye. "Probe" measurements in planar bilayers, microelectrophoresis of liposomes, and measurement of changes in dye absorbance and fluorescence in liposomes were used to study dye adsorption to membranes. These measurements indicated that the membrane:water partition coefficient for the dye monomer increases with the length of the hydrocarbon side chain. However, the formation of large aggregates in the aqueous phase also increases with increasing chain length and ionic strength so that the actual dye adsorbing to the membrane goes through a maximum at high but not at low ionic strengths. More dye adsorbs to negatively charged than neutral membranes. Membrane-bound dye spectra were easily resolved in negatively charged liposomes where it was observed that these dyes could exist as monomers, dimers, and large aggregates. For diSC1(5) a spectral peak was observed at low but not high ionic strengths (i.e. the conditions in which this dye appears to form voltage-gated channels) corresponding to small aggregates which appeared to adsorb to the membrane. Finally, the adsorption of these dyes to membranes results in more positive electrostatic potentials composed primarily of dye-induced "boundary" potentials and somewhat less of "double-layer" potentials.     

Potential and K+ activity in skinned muscle fibers. Evidence against a simple Donnan equilibrium

It has been suggested that potentials measured with conventional microelectrodes in chemically or mechanically skinned muscle fibers arise from a Donnan equilibrium due to myofilament fixed charges. This hypothesis was tested in mechanically skinned frog (Rana pipiens) semitendinosus fibers by measuring the distribution potential (Ed) between fiber and bath with 3 M KCl-filled microelectrodes and the K+ activity gradient (aik/aok) with K+ ion-selective microelectrodes (KISE). If skinned fibers are a Donnan system, Ed should become more positive as pH is decreased, altering the fixed charge on the myofilaments. Consistent with this expectation, Ed was -4.4, -0.6, and +4.8 mV in ATP-containing solutions and -6.5, -2.2, and +8.4 mV in ATP-free solutions at pH 7, 6, and 5, respectively. Donnan equilibrium also requires that all mobile ionic species be in electrochemical equilibrium. In ATP-containing solutions, this was true for K+ at pH 7. At pH 5, however, KISE indicated that K+ was not in equilibrium; average Ed was 5.9 mV positive to the K+ equilibrium potential, and aik/aok was 1.04, while the Donnan prediction was 0.83. In contrast, KISE measurements in ATP-free solutions indicated that K+ was in equilibrium at all pH studied. Skinned fibers in ATP-containing media are not equilibrium systems because ATPase reactions occur. Under our conditions, frog myofibrils hydrolyze 0.4 and 0.08 mumol ATP/min X mg myofibrillar protein at pH 7 and 5, respectively. It is suggested that in the presence of ATP, Ed is a superposition of Donnan and diffusion potentials, the latter arising from differences in the mobilities of anionic substrate and products that diffuse through the charged myofilament lattice.(ABSTRACT TRUNCATED AT 250 WORDS)     

Donnan membrane equilibrium,sedimentation equilibrium,and coil expansion of DNA in salt solutions

This is a review of applications of the McMillan-Mayer-Hill virial theory and the ionic double-layer theory to dilute colloidal solutions, in particular, solutions of DNA. Interactions of highly charged colloidal rods are developed in terms of the second virial coefficients between two rods, and between one rod and one small co-ion. The relevant cluster integrals are evaluated with interaction potentials based on the Poisson-Boltzmann equation. The treatment is extended to the intrachain repulsion responsible for the statistical swelling of coiled DNA (excluded volume effect). The theory is compared with three sets of experimental data: The salt distribution in Donnan membrane equilibria of DNA-salt solutions, sedimentation equilibria of short DNA fragments at different ionic strengths, and the intrinsic viscosity of T7 DNA in NaCl solutions. In all cases the theory agrees well with the experiments. The agreement is not convincing for the sedimentation equilibrium at low ionic strength, because here the experimental DNA concentration is too high for the truncated dilute solution expansion of the DNA-salt repulsion.     

VALENCY RULE AND ALLEGED HOFMEISTER SERIES IN THE COLLOIDAL BEHAVIOR OF PROTEINS : I. THE ACTION OF ACIDS.

1. The action of a number of acids on four properties of gelatin (membrane potentials, osmotic pressure, swelling, and viscosity) was studied. The acids used can be divided into three groups; first, monobasic acids (HCl, HBr, HI, HNO₃, acetic, propionic, and lactic acids); second, strong dibasic acids (H₂SO₄ and sulfosalicylic acid) which dissociate as dibasic acids in the range of pH between 4.7 and 2.5; and third, weak dibasic and tribasic acids (succinic, tartaric, citric) which dissociate as monobasic acids at pH 3.0 or below and dissociate increasingly as dibasic acids, according to their strength, with pH increasing above 3.0. 2. If the influence of these acids on the four above mentioned properties of gelatin is plotted as ordinates over the pH of the gelatin solution or gelatin gel as abscissæ, it is found that all the acids have the same effect where the anion is monovalent; this is true for the seven monobasic acids at all pH and for the weak dibasic and tribasic acids at pH below 3.0. The two strong dibasic acids (the anion of which is divalent in the whole range of pH of these experiments) have a much smaller effect than the acids with monovalent anion. The weak dibasic and tribasic acids act, at pH above 3.0, like acids the anion of which is chiefly monovalent but which contain also divalent anions increasing with pH and with the strength of the acid. 3. These experiments prove that only the valency but not the other properties of the anion of an acid influences the four properties of gelatin mentioned, thus absolutely contradicting the Hofmeister anion series in this case which were due to the failure of the earlier experimenters to measure properly the pH of their protein solutions or gels and to compare the effects of acids at the same pH of the protein solution or protein gel after equilibrium was established. 4. It is shown that the validity of the valency rule and the non-validity of the Hofmeister anion series for the four properties of proteins mentioned are consequences of the fact that the influence of acids on the membrane potentials, osmotic pressure, swelling, and viscosity of gelatin is due to the Donnan equilibrium between protein solutions or gels and the surrounding aqueous solution. This equilibrium depends only on the valency but not on any other property of the anion of an acid. 5. That the valency rule is determined by the Donnan equilibrium is strikingly illustrated by the ratio of the membrane potentials for divalent and monovalent anions of acids. Loeb has shown that the Donnan equilibrium demands that this ratio should be 0.66 and the actual measurements agree with this postulate of the theory within the limits of accuracy of the measurements. 6. The valency rule can be expected to hold for only such properties of proteins as depend upon the Donnan equilibrium. Properties of proteins not depending on the Donnan equilibrium may be affected not only by the valency but also by the chemical nature of the anion of an acid.     

Water and electrolyte content of the myofilament phase in the chemically skinned barnacle fiber

Muscle fibers from the giant barnacle, Balanus nubilus, were placed inside the lumen of a porous glass capillary and equilibrated for 48 h in an electrolyte solution containing 2% Tween. The glass capillary prevented the chemically "skinned" fiber from swelling with a water content beyond 80%. Isotope exchange studies using 22Na, 42K, and 36Cl indicated the existence of an intermediate rate constant and compartment which varied with pH. This intermediate rate was attributed to counter-ions and co-ions in the myofilament phase. Analysis of the electrolyte composition of the fiber at pH 8 predicts that the myofilaments contain about 0.3 of the fiber water, and that a -15 mV Donnan potential exists at the myofilament surface. An open-tipped (1- micrometer) microelectrode in the skinned fiber measured a potential (similar in magnitude to the Donnan potential), which decreased and reversed sign as the pH was lowered. The measured cation contents of the fiber between pH 5 and 8 were found to be similar to the cation contents predicted from the measured Donnan potentials. The net negative charge of the myofilaments at pH 7.5 and at ionic strength 0.56 is estimated to be 41 eq per 10(5) g of dry weight.     

An electro-diffusion model for computing membrane potentials and ionic concentrations in branching dendrites,spines and axons

The Nernst-Planck equation for electrodiffusion was applied to axons, dendrites and spines. For thick processes (1 m) the results of computer simulation agreed accurately with the cable model for passive conduction and for propagating action potentials. For thin processes (0.1 m) and spines, however, the cable model may fail during transient events such as synaptic potentials. First, ionic concentrations can rapidly change in small compartments, altering ionic equilibrium potentials and the driving forces for movement of ions across the membrane. Second, longitudinal diffusion may dominate over electrical forces when ionic concentration gradients become large. We compare predictions of the cable model and the electro-diffusion model for excitatory postsynaptic potentials on spines and show that there are significant discrepancies for large conductance changes. The electro-diffusion model also predicts that inhibition on small structures such as spines and thin processes is ineffective. We suggest a modified cable model that gives better agreement with the electro-diffusion model.     

The Donnan Equilibrium: A Theoretical Study of the Effects of Interionic Forces

We investigate the conditions under which nonideality in solution influences the Donnan equilibrium. Of the various parameters that characterize this equilibrium, the osmotic pressure established across the Donnan membrane is found to be particularly sensitive to intermolecular interactions between the diffusible and nondiffusible ionic species. Under physiologically appropriate conditions, we find that it is almost never valid to use Debye-Hückel theory to calculate ionic activities: it is important to take proper account of ion size. When the diffusible species is a 1-1 electrolyte, this can be done using the mean spherical approximation (MSA) for a mixture of ions of different diameters. For 2-2, or higher-valent, electrolytes one should also include the effects of the second ionic virial coefficient, which the MSA omits.     

Donnan potentials from striated muscle liquid crystals. Sarcomere length dependence.

Donnan potentials from A-bands and I-bands were measured as a function of sarcomere length in skinned long-tonic muscle fibers of the crayfish. These measurements were made using standard electrophysiological technique. Simultaneously, the relative cross-sectional area of the fibers was determined. Lattice plane spacings and hence unit-cell volumes were determined by low-angle x-ray diffraction. At a sarcomere length at which the myosin filaments and actin filaments nominally do not overlap, measurements of potential, relative cross-sectional area, and unit-cell volume were used in conjunction with Donnan equilibrium theory to calculate the effective linear charge densities along the myosin filament (6.6 X 10(4) e-/mu) and actin filament (6.8 X 10(3) e-/mu). Using these linear charge densities, unit-cell volumes and Donnan equilibrium theory, an algorithm was developed to predict A-band and I-band potentials at any sarcomere length. Over the range of sarcomere lengths investigated, the predicted values coincide with the experimental data. The ability of the model to predict the data demonstrates the applicability of Donnan equilibrium theory to measurements of electrochemical potential from liquid-crystalline systems.     

Note on the Donnan equilibrium

The solution for the spatial distribution of ions in a Donnan equilibrium has been given by J. H. Bartlett and R. A. Kromhout (1952). The present note gives an explicit solution for the case in which the length of the region containing the membrane is large; in biological situations this requires only that the length considered should be greater than a few hundred Ångstrom units. The Donnan equilibrium may be considered to be a special case of a situation in which forces other than electrical act upon the ions; in particular, it represents the case in which only one ion is acted upon and the energy difference on the two sides of the membrane is infinite. An expression is given for the difference in energy of theith in terms of the electrical potential and of the ion concentrations. As an illustration, the results are applied to nerve membrane potentials.     

GCEMC Simulations of “Swiss Cheese” Ion Exchange Membranes in Dilute Solutions of Primitive Model 1:1 Electrolytes with Different Sizes of Ions or 2:1 Electrolytes with Different Bjerrum Parameters

Abstract

Monte Carlo simulations using a Markov process corresponding to a (generalized) Grand Canonical Ensemble have been performed for a number of spherical micropores in equilibrium with dilute external bulk solutions of primitive model electrolytes. Dilute solutions of 1:1 electrolytes with a Bjerrum parameter B = 1.546 with cations three times larger than the anions have been simulated. Also, dilute solutions of 2:1 electrolytes with ions of equal size and reduced Bjerrum parameters B_r = 1.546 and 3 have been simulated. The pores are primitive pores with hard walls and the same dielectric permittivity in the wall and in the pore solution. They range from a pore radius = 5 times the mean ionic diameter to 35 times this diameter, and they carry a fixed charge equal to + 5,0 and ?5 elementary charges. The fixed charge is modelled as smoothly distributed on the pore-wall interface. In addition to the electric potential of the interfacial charge and the electric potential of the spherical double layer, a potential Δ between the pore solution and the bulk solution may be deliberately added. For single pores we may take Δ = 0, but then the pore is generally not electroneutral. In a “Swiss cheese” membrane with a lot of (equally sized) pores, the membrane phase has to approach electroneutrality for growing size of the phase. This is approximated by means of a membrane generated potential Δ in each pore (from the electrostatic interactions with the other pores). The potential A so chosen to obtain electroneutrality is the GCEMC Donnan potential. These non-ideal Donnan potentials are compared to the ideal values (with activity coefficients equal to zero). From the mean occupation numbers of cations and anions in the pores, the average pore values of the mean ionic and the single ionic activity coefficients of the ions are calculated. These are very dependent on pore sizes and on the potential in the pore. The excess energy and the electrostatic Helmholtz free energy of the ions in the pores are also simulated directly. The electrostatic entropy is found as the difference.     

Error analysis in equilibrium dialysis: evaluation of adsorption phenomena

Various sources of error in equilibrium dialysis may lead to inaccurate results of binding experiments: (i) the finite time of dialysis; (ii) the Donnan effects; (iii) the adsorption of ligand to the membrane; and (iv) release of contaminating material from dialysis casings. These errors were analyzed for a polynucleotide-oligopeptide model system with particular regard to adsorption phenomena and the underlying mechanisms. Adsorption data were treated according to Freundlich and Langmuir isotherms. The latter turned out to be more appropriate for the consideration of adsorption phenomena with respect to a minimum error propagation. Furthermore, it was shown that the degree of adsorption varies with ionic strength and temperature and could be interpreted in terms of polyelectrolyte theory. The kinetics of both adsorption and of the ligand distribution between the polymer and buffer compartments follow first order at the beginning of dialysis which is in line with a simple diffusion process. After 13-15 h data deviate from first order kinetics indicating an alteration in the transport mechanism. The effects of errors on binding parameters were determined and a detailed protocol for correction is presented allowing one to obtain binding data from equilibrium dialysis experiments with the required degree of accuracy. The fundamental principles and results for the system under investigation generally apply to all protein-ligand systems.     

The relationship between the poisson-boltzmann model and the condensation hypothesis: an analysis based on the low salt form of the Donnan coefficient

Two common models for the interaction of counterions with cylindrical polyions are considered in the context of the Donnan membrane equilibrium. General analytic expressions are obtained from the Poisson-Boltzmann equation for the Donnan coefficient in terms of the potential at the surface of the polyion or the local concentration of unbound ions at the surface. Analysis based on these expressions shows that if, and only if, the polyion charge density exceeds a certain critical value a large local concentration of ions will persist near the polyion surface at low ionic strengths. We therefore conclude that this principal hypothesis of the condensation model is consistent with the characteristics of the Poisson-Boltzmann potential at the surface of the polyion.     

Diffusion of charged ions in mucus gel: effect of net charge

The interposition of a neutral starch gel greatly retarded bulk ionic movement by free flow. A mucus (charged) gel preparation of identical concentration and thickness further retarded ionic diffusion. The findings suggest that the charges in the mucus matrix may exert an ionic exclusion effect (Donnan Exclusion), thus retarding other ionic diffusion. We speculate that a mucus layer may physiologically behave as an ion exchange gel column and modify the traffic of charged ions through it.     

APPLICATION OF THE DIFFUSION HYPOTHESIS TO MEMBRANE POTENTIALS

A system consisting of two aqueous solutions, containing equal concentrations of lactic acid, but different concentrations of Na lactate, separated by a layer of amyl alcohol has been described. This system exhibits electrical properties ranging (as the concentration of NaL is increased) from those characteristic of a simple Donnan equilibrium to those characteristic of simple diffusion. The fact that the Donnan P.D. can be treated as a special case of a diffusion potential has been emphasized. The experiments call attention to the effect of the thermodynamic properties of the membrane, and it is suggested that such properties as conductivities, ionic mobilities, and distribution coefficients in membranes of any sort should be investigated. The experiments afford an interesting example of "phase reversal."     

A mathematical model of blood-interstitial acid-base balance: application to dilution acidosis and acid-base status

We developed mathematical models that predict equilibrium distribution of water and electrolytes (proteins and simple ions), metabolites, and other species between plasma and erythrocyte fluids (blood) and interstitial fluid. The models use physicochemical principles of electroneutrality in a fluid compartment and osmotic equilibrium between compartments and transmembrane Donnan relationships for mobile species. Across the erythrocyte membrane, the significant mobile species Cl? is assumed to reach electrochemical equilibrium, whereas Na(+) and K(+) distributions are away from equilibrium because of the Na(+)/K(+) pump, but movement from this steady state is restricted because of their effective short-term impermeability. Across the capillary membrane separating plasma and interstitial fluid, Na(+), K(+), Ca2(+), Mg2(+), Cl?, and H(+) are mobile and establish Donnan equilibrium distribution ratios. In each compartment, attainment of equilibrium by carbonates, phosphates, proteins, and metabolites is determined by their reactions with H(+). These relationships produce the recognized exchange of Cl(-) and bicarbonate across the erythrocyte membrane. The blood submodel was validated by its close predictions of in vitro experimental data, blood pH, pH-dependent ratio of H(+), Cl?, and HCO?? concentrations in erythrocytes to that in plasma, and blood hematocrit. The blood-interstitial model was validated against available in vivo laboratory data from humans with respiratory acid-base disorders. Model predictions were used to gain understanding of the important acid-base disorder caused by addition of saline solutions. Blood model results were used as a basis for estimating errors in base excess predictions in blood by the traditional approach of Siggaard-Andersen (acid-base status) and more recent approaches by others using measured blood pH and Pco? values. Blood-interstitial model predictions were also used as a basis for assessing prediction errors of extracellular acid-base status values, such as by the standard base excess approach. Hence, these new models can give considerable insight into the physicochemical mechanisms producing acid-base disorders and aid in their diagnoses.     

pH gradient across the lysosomal membrane generated by selective cation permeability and Donnan equilibrium.

The pH within isolated Triton WR 1339-filled rat liver lysosomes was determined by measuring the distribution of [14C]methylamine between the intra- and extralysosomal space. The intralysosomal pH was found to be approximately one pH unit lower than that of the surrounding medium. Increasing the extralysosomal cation concentration lowered the pH gradient by a cation exchange indicating the presence of a Donnan equilibrium. The lysosomal membrane was found to be significantly more permeable to protons than to other cations. The relative mobility of cations through the lysosomal membrane is H+ greater than Cs+ greater than Rb+ greater than K greater than Na+ greater than Li+ greater than Mg2+, Ca2+. The presented data suggest that the acidity within isolated Triton WR 1339-filled lysosomes is maintained by: (1) a Donnan equilibrium resulting from the intralysosomal accumulation of nondiffusible anions and (2) a selective permeability of the lysosomal membrane to cations.     

Electrical potentials of plant cell walls in response to the ionic environment

Electrical potentials in cell walls (psi(Wall)) and at plasma membrane surfaces (psi(PM)) are determinants of ion activities in these phases. The psi(PM) plays a demonstrated role in ion uptake and intoxication, but a comprehensive electrostatic theory of plant-ion interactions will require further understanding of psi(Wall). psi(Wall) from potato (Solanum tuberosum) tubers and wheat (Triticum aestivum) roots was monitored in response to ionic changes by placing glass microelectrodes against cell surfaces. Cations reduced the negativity of psi(Wall) with effectiveness in the order Al(3+) > La(3+) > H(+) > Cu(2+) > Ni(2+) > Ca(2+) > Co(2+) > Cd(2+) > Mg(2+) > Zn(2+) > hexamethonium(2+) > Rb(+) > K(+) > Cs(+) > Na(+). This order resembles substantially the order of plant-root intoxicating effectiveness and indicates a role for both ion charge and size. Our measurements were combined with the few published measurements of psi(Wall), and all were considered in terms of a model composed of Donnan theory and ion binding. Measured and model-computed values for psi(Wall) were in close agreement, usually, and we consider psi(Wall) to be at least proportional to the actual Donnan potentials. psi(Wall) and psi(PM) display similar trends in their responses to ionic solutes, but ions appear to bind more strongly to plasma membrane sites than to readily accessible cell wall sites. psi(Wall) is involved in swelling and extension capabilities of the cell wall lattice and thus may play a role in pectin bonding, texture, and intercellular adhesion.     

Effect of bilayer membrane curvature on activity of phosphatidylcholine exchange protein

Effect of bilayer membrane curvature of substrate phosphatidylcholine and inhibitor phosphatidylserine on the activity of phosphatidylcholine exchange protein has been studied by measuring transfer of spin-labeled phosphatidylcholine between vesicles, vesicles and liposomes, and between liposomes. The transfer rate between vesicles was more than 100 times larger than that between vesicles and liposomes. The transfer rate between liposomes was still smaller than that between vesicles and liposomes and nearly the same as that in the absence of exchange protein. The markedly enhanced exchange with vesicles was ascribed to the asymmetric packing of phospholipid molecules in the outer layer of the highly curved bilayer membrane. The inhibitory effect of phosphatidylserine was also greatly dependent on the membrane curvature. The vesicles with diameter of 17 nm showed more than 20 times larger inhibitory activity than those with diameter of 22 nm. The inhibitory effect of liposomes was very small. The size dependence was ascribed to stronger binding of the exchange protein to membranes with higher curvatures. The protein-mediated transfer from vesicles to spiculated erythrocyte ghosts was about four times faster than that to cup-shaped ghosts. This was ascribed to enhanced transfer to the highly curved spiculated membrane sites rather than greater mobility of phosphatidylcholine in the spiculated ghost membrane.     

Estimation of transmembrane potentials from phase equilibria of hydrophobic paramagnetic ions.

Positively charged hydrophobic spin labels have been synthesized which respond to transmembrane potentials in sonicated liposomes. Electron paramagnetic resonance spectroscopy is used to show that the distribution of these probes between aqueous and membrane phases changes as a function of transmembrane potential. When liposomes are made more inside-negative, the fraction of membrane associated probe increases while the fraction of probe in the aqueous phase decreases. The results are in quantitative agreement with a simple equilibrium thermodynamic theory which allows estimation of absolute transmembrane potentials in phospholipid vesicles.