Electrokinetic and electrostatic properties of bilayers containing gangliosides GM1, GD1a, or GT1. Comparison with a nonlinear theory.

We formed vesicles from mixtures of egg phosphatidylcholine (PC) and the gangliosides GM1, GD1a, or GT1 to model the electrokinetic properties of biological membranes. The electrophoretic mobilities of the vesicles are similar in NaCl, CsCl, and TMACl solutions, suggesting that monovalent cations do not bind significantly to these gangliosides. If we assume the sialic acid groups on the gangliosides are located some distance from the surface of the vesicle and the sugar moieties exert hydrodynamic drag, we can describe the mobility data in 1, 10, and 100 mM monovalent salt solutions with a combination of the Navier-Stokes and nonlinear Poisson-Boltzmann equations. The values we assume for the thickness of the ganglioside head group and the location of the charge affect the theoretical predictions markedly, but the Stokes radius of each sugar and the location of the hydrodynamic shear plane do not. We obtain a reasonable fit to the mobility data by assuming that all ganglioside head groups project 2.5 nm from the bilayer and all fixed charges are in a plane 1 nm from the bilayer surface. We tested the latter assumption by estimating the surface potentials of PC/ganglioside bilayers using four techniques: we made 31P nuclear magnetic resonance, fluorescence, electron spin resonance, and conductance measurements. The results are qualitatively consistent with our assumption.     

Dimethonium,a divalent cation that exerts only a screening effect on the electrostatic potential adjacent to negatively charged phospholipid bilayer membranes

Calcium and other alkaline earth cations change the electrostatic potential adjacent to negatively charged bilayer membranes both by accumulating in the aqueous diffuse double layer adjacent to the membrane and by adsorbing to the phospholipids. The effects of these cations on the electrostatic potential are described adequately by the Gouy-Chapman-Stern theory. We report the results of experiments with ethane-bis-trimethylammonium, a cation that has been termed "dimethonium" or "ethamethonium" in analogy with hexamethonium (hexane-1,6-bis-trimethylammonium) and decamethonium (decane-1,10-bis-trimethylammonium). We examined the effect of dimethonium on the zeta potential of multilamellar vesicles formed from the negative lipid phosphatidylserine (PS) and from 5:1 phosphatidylcholine/phosphatidylserine mixtures in solutions containing 0.1, 0.01 and 0.001 M sodium, cesium, or tetramethylammonium chloride. We also examined the effect of dimethonium on the conductance of planar PS bilayer membranes and the 31P NMR signal from sonicated PS vesicles formed in 0.1 M NaCl. We found no evidence that dimethonium adsorbs specifically to bilayer membranes. All the results, except for those obtained with vesicles of low charge density formed in a solution with a high salt concentration, are consistent with the predictions of the Gouy-Chapman theory. We conclude that dimethonium, which does not have the pharmacological effects of hexamethonium and decamethonium, is a useful divalent cation for physiologists interested in investigating electrostatic potentials adjacent to biological membranes.     

The adsorption of divalent cations to phosphatidylglycerol bilayer membranes

The ability of the Stern equation to describe the adsorption of divalent cations to phosphatidylglycerol membranes was tested by combining ³¹P-NMR and electrophoretic mobility measurements. In 0.1 M sodium chloride both the ³¹P-NMR and the zeta potential data are well described by the Stern equation. ³¹P-NMR and ¹³C-NMR results indicate that cobalt forms inner-sphere complexes only with the phosphate group of phosphatidylglycerol molecules and that a substantial fraction of the adsorbed cobalt ions form outer-sphere complexes. Evidence is presented that suggests the alkaline earth cations also bind to phospholipids mainly by forming outer sphere complexes. Electrophoretic mobility measurements were performed with several different divalent cations. In all cases the zeta potentials in 0.1 M sodium chloride were well described by the Stern equation. The intrinsic 1 : 1 association constants (M^?1) for the phosphatidylglycerol complexes decreased in the sequence: Mn²⁺, 11.5; Ca²⁺, 8.5; Ni²⁺, 7.5; Co²⁺, 6.5; Mg²⁺, 6.0; Ba²⁺, 5.5 and Sr²⁺, 5.0.     

Adsorption of divalent cations to bilayer membranes containing phosphatidylserine

The Stern equation, a combination of the Langmuir adsorption isotherm, the Boltzmann relation, and the Grahame equation from the theory of the diffuse double layer, provides a simple theoretical framework for describing the adsorption of charged molecules to surfaces. The ability of this equation to describe the adsorption of divalent cations to membranes containing brain phosphatidylserine (PS) was tested in the following manner. Charge reversal measurements were first made to determine the intrinsic 1:1 association constants of the divalent cations with the anionic PS molecules: when the net charge of a PS vesicle is zero one-half of the available sites are occupied by divalent cations. The intrinsic association constant, therefore, is equal to the reciprocal of the divalent cation concentration at which the mobility of a PS vesicle reverses sign. The Stern equation with this association constant is capable of accurately describing both the zeta potential data obtained with PS vesicles at other concentrations of the divalent cations and the data obtained with with vesicles formed from mixtures of PS and zwitterionic phospholipids. Independent measurements of the number of ions adsorbed to sonicated PS vesicles were made with a calcium-sensitive electrode. The results agreed with the zeta potential results obtained with multilamellar vesicles. When membranes are formed at 20 degrees C in 0.1 M NaCl, the intrinsic 1:1 association constants of Ni, Co, Mn, Ba, Sr, Ca, and Mg with PS are 40, 28, 25, 20, 14, 12, and 8 M-1, respectively.     

Monovalent cation-induced fusion of acidic phospholipid vesicles

Fusion of small unilamellar vesicles (SUV) consisting of dimyristoylphosphatidylcholine (DMPC), dimyristoylphosphatidylglycerol (DMPG) and phosphatidylglycerol (PG) from egg yolk, dipalmitoylphosphatidylserine (DPPS) and phosphatidylserine (PS) from bovine brain was studied as a function of monovalent cation concentration. Fusion was detected by measuring the changes in the excimer to monomer fluorescence intensity ratio (IE/M) of pyrene-labeled phospholipid analogues upon fusion of the pyrene-labeled and unlabeled vesicles. No fusion was observed from vesicles consisting of DMPC, PS from bovine brain or PG from egg yolk upon addition of NaCl (up to 1 M). However, considerable fusion was evident for vesicles consisting of DMPG or DPPS upon addition of monovalent cations (300 mM to 1 M). Fusion kinetics were fast reaching a plateau after 5 min of addition of cations. The order of efficiency of different monovalent cations to induce the fusion of DMPG vesicles as judged by the changes of the IE/M ratio was Li+ greater than Na+ greater than K+ greater than Cs+. DSC-scan of sonicated DMPG vesicles showed, in the absence of salt, a phase transition at 19.2 degrees C with enthalpy of 1.1 kcal.mol-1. After incubation in the presence of 600 mM NaCl the DSC scan showed a narrow phase transition at 24.1 degrees C with enthalpy of 6.9 kcal.mol-1 and a pronounced pretransition, both supporting that the fusion of the vesicles had occurred in the presence of NaCl. The results indicate that sonicated vesicles consisting of acidic phospholipids with fully saturated fatty acids fuse in the presence of monovalent cations, whereas those containing unsaturated fatty acids do not.     

Calculations of the electrostatic potential adjacent to model phospholipid bilayers.

We used the nonlinear Poisson-Boltzmann equation to calculate electrostatic potentials in the aqueous phase adjacent to model phospholipid bilayers containing mixtures of zwitterionic lipids (phosphatidylcholine) and acidic lipids (phosphatidylserine or phosphatidylglycerol). The aqueous phase (relative permittivity, epsilon r = 80) contains 0.1 M monovalent salt. When the bilayers contain < 11% acidic lipid, the -25 mV equipotential surfaces are discrete domes centered over the negatively charged lipids and are approximately twice the value calculated using Debye-Hückel theory. When the bilayers contain > 25% acidic lipid, the -25 mV equipotential profiles are essentially flat and agree well with the values calculated using Gouy-Chapman theory. When the bilayers contain 100% acidic lipid, all of the equipotential surfaces are flat and agree with Gouy-Chapman predictions (including the -100 mV surface, which is located only 1 A from the outermost atoms). Even our model bilayers are not simple systems: the charge on each lipid is distributed over several atoms, these partial charges are non-coplanar, there is a 2 A ion-exclusion region (epsilon r = 80) adjacent to the polar headgroups, and the molecular surface is rough. We investigated the effect of these four factors using smooth (or bumpy) epsilon r = 2 slabs with embedded point charges: these factors had only minor effects on the potential in the aqueous phase.     

Modeling the electrophoresis of rigid polyions: application to lysozyme.

An algorithm is developed to determine the electrophoretic mobility of a rigid polyion modeled as a low dielectric volume element of arbitrary shape containing an arbitrary charge distribution. The solvent is modeled as a high dielectric continuum with salt distributed according to the linearized Poisson Boltzmann equation. Account is also taken of a Stern layer that separates the molecular surface and the surface of hydrodynamic shear, or Stern surface. Relaxation of the ion atmosphere because of the presence of the external field is ignored. The electrostatic and hydrodynamic problems are both solved by boundary element methods. The procedure is first applied to spherical polyions containing monopolar, dipolar, and quadrupolar charge distributions, and calculated mobilities are found to be in excellent agreement with the theory of Yoon and Kim. It is then applied to lysozyme by using models that account for the detailed shape and charge distribution of the enzyme. For reasonable choices of the molecular and Stern surfaces, calculated and experimental mobilities are found to be in fair agreement with each other. However, if a pH independent Stern layer (or, equivalently, translational diffusion constant, Dt) is assumed, the calculated mobilities exhibit a stronger pH dependence than is observed experimentally. A small increase in Dt with increasing pH could correct this discrepancy.     

Ion-binding to phospholipids. Interaction of calcium with phosphatidylserine.

The binding of Ca2+ to monolayers and bilayers of phosphatidylserine has been investigated as a function of pH, ionic strength (NaCl concentration) and Ca2+ concentration using surface and colloid chemical techniques. The molar ratio of lipid to bound calcium decreases to 2 as the Ca2+ concentration is increased to about 0.1 mM. At [Ca2+] greater than 0.1 mM a 1:1 complex is formed. The apparent binding constant Ka ranges from about approximately 10(6) - 10(4) l/mol depending on the Ca2+ concentration. After allowing for electrostatic effects and neighbour group interactions, the intrinsic binding constant Ki of the phosphorylserine polar group at pH 7 (I = 0.01 M), where it carries a net negative charge of one, is approximately 10(4) l/mol; consistent values for Ki were obtained using several independent approaches. Ka for Ca2+ binding decreases with increasing NaCl concentration because the monovalent cations compete with Ca2+ for the same binding site. Na+ and K+ are equally effective in displacing 45Ca2+ adsorbed to monolayers of phosphatidylserine, both with respect to the kinetics and the equilibrium of the displacement. Ka for the reaction between phosphatidylserine and monovalent cations is about 10(3)-fold smaller than that of Ca2+. An investigation of the binding of Mn2+ to phosphatidylserine by both surface chemical and nuclear magnetic resonance methods shows that this cation has a similar binding constant to that of Ca2+. The Ca2+-binding capabilities of monolayers containing only carboxyl groups (i.e. arachidic acid) and phosphodiester groups (i.e. dicetyl phosphate) have also been determined; the apparent pK for the - COOH group in monolayers is larger than or equal to 9 and that for the phosphodiester group is less than 4. Since these groups do not retain the same pK values when they are in close proximity in the phosphorylserine group, the relative contributions of the two groups to the binding of Ca2+ to phosphatidylserine is not obvious.     

Effect of pH and monovalent cations on the ionization state of phosphatidylglycerol in monolayers. An experimental (surface potential) and theoretical (Gouy-Chapman) approach

Ionization of the acidic phospholipid phosphatidylglycerol has been studied by measuring the surface potential of monomolecular films of the lipid as a function of the aqueous subphase pH and the concentration of monovalent cations (Li, Na, Cs). It is shown that the experimental data can be interpreted by means of the Gouy-Chapman theory in its simplest formulation, provided an adsorption of cations at the membrane surface is accounted for. This allows us to predict the ionization state of the lipid for given ionic conditions in the subphase. Above pH 4, for subphase ion concentration higher than 10 mM, or for ion concentrations above 0.1 mM at pH 5.6, phosphatidylglycerol is fully deprotonated. Within the limits of our theoretical approach, association constants of the cations to the lipid lie around 0.1-0.6 M-1.     

Cation binding to membranes: Competition between mono-, di- and trivalent cations

The binding of mono-, di- and trivalent cations to negatively charged surfaces is studied within the framework of a modified Gouy-Chapman equation. For any given combination of ions of the above valences, the existence and uniqueness of the solution for the surface potential is shown. The treatment provides the surface potential and charge density. For a system containing only monovalent and divalent ions, analytical solutions are given. When trivalent ions are also present, a procedure based on numerical integration is described. The distance dependence of the electrostatic potential for planar surfaces is given. The calculations provide the amount of cations tightly bound and the amount trapped in the double layer region. The competition between cations for binding to surfaces is elucidated.     

Effects of cations and polyamines on the aggregation and fusion of phosphatidylserine membranes

Effects of various metal cations and polyamines on aggregation and fusion of phosphatidylserine vesicles and their associated physicochemical properties (such as surface tension and vesicle electrophoretic mobility) have been studied. It was found that metal polycations and hydrogen ion caused an increase in the surface tension of a phosphatidylserine monolayer, whereas the polyamines and other monovalent cations did not increase the surface tension of the membrane appreciably. All cations used affected the vesicle mobility roughly in the order of the number of their valencies and linearly with respect to the logarithm of their concentrations of ions; vesicle surface charge densities are reduced by adsorption and screening of the counter ions depending on their valencies and concentrations. The degree of aggregation of lipid vesicles parallels somewhat that of the reduction of vesicle electrophoretic mobilities. However, the degree of membrane fusion induced by these cations parallels that of the increase in surface tension of the membranes induced by these cations.     

Divalent cation binding to phospholipid veiscles. Dependence on temperature and lipid fluidity.

Mn2+ binding to vesicles prepared from several different species of anionic phospholipids was determined as a function of temperature by electron paramagnetic resonance (EPR). The Mn2+ affinities of phosphatidylserine, cardiolipin and egg yolk phosphatidylglycerol all increased monitonically with temperature. Vesicles prepared from hydrogenated and natural (bovine) phosphatidylserine were monitored with respect to hydrocarbon chain fluidity as well as Mn2+ binding. Contrary to expectations based on surface potential considerations, the affinity of phosphatidylserine for divalent cations was apparently not lowered in going from the gel state to the lipid crystalline state of the bilayer. The results are instead consistent with an enhancement in cation affinity with increased lipid fluidity. Dipalmitoyl phosphatidylglycerol vesicle fluidity and Mn2+ binding were also studied with EPR. A large reduction in the measured Mn2+ affinity accompained melting of the phospholipid, but observed hysteresis in the temperature dependence of the binding render uncertain any simple explanation based on changes in surface potential. Supplementary light scattering data indicated that vesicle aggregation was involved in the hysteresis phenomena.     

Binding of peptides with basic residues to membranes containing acidic phospholipids.

There are clusters of basic amino acids on many cytoplasmic proteins that bind transiently to membranes (e.g., protein kinase C) as well as on the cytoplasmic domain of many intrinsic membrane proteins (e.g., glycophorin). To explore the possibility that these basic residues bind electrostatically to monovalent acidic lipids, we studied the binding of the peptides Lysn and Argn (n = 1-5) to bilayer membranes containing phosphatidylserine (PS) or phosphatidylglycerol (PG). We made electrophoretic mobility measurements using multilamellar vesicles, fluorescence and equilibrium binding measurements using large unilamellar vesicles, and surface potential measurements using monolayers. None of the peptides bound to vesicles formed from the zwitterionic lipid phosphatidylcholine (PC) but all bound to vesicles formed from PC/PS or PC/PG mixtures. None of the peptides exhibited specificity between PS and PG. Each lysine residue that was added to Lys2 decreased by one order of magnitude the concentration of peptide required to reverse the charge on the vesicle; equivalently it increased by one order of magnitude the binding affinity of the peptides for the PS vesicles. The simplest explanation is that each added lysine binds independently to a separate PS with a microscopic association constant of 10 M-1 or a free energy of approximately 1.4 kcal/mol. Similar, but not identical, results were obtained with the Argn peptides. A simple theoretical model combines the Gouy-Chapman theory (which accounts for the nonspecific electrostatic accumulation of the peptides in the aqueous diffuse double layer adjacent to the membrane) with mass action equations (which account for the binding of the peptides to greater than 1 PS). This model can account qualitatively for the dependence of binding on both the number of basic residues in the peptides and the mole fraction of PS in the membrane.     

The protein-mediated transfer of phosphatidylcholine between membranes. The effect of membrane lipid composition and ionic composition of the medium.

The phosphatidylcholine exchange protein from bovine liver catalyzes the transfer of phosphatidylcholine between rat liver mitochondria and sonicated liposomes. The effect of changes in the liposomal lipid composition and ionic composition of the medium on the transfer have been determined. In addition, it has been determined how these changes affected the electrophoretic mobility i.e. the surface charge of the membrane particles involved. Transfer was inhibited by the incorporation of negatively charged phosphatidic acid, phosphatidylserine, phosphatidylglycerol and phosphatidylinositol into the phosphatidylcholine-containing vesicles; zwitterionic phosphatidyl-ethanolamine had much less of an inhibitory effect while positively charged stearylamine stimulated. The cation Mg2+ and, to a lesser extent, K+ overcame the inhibitory effect exerted by phosphatidic acid, in that concentration range where these ions neutralized the negative surface charge most effectively. Under conditions where Mg2+ and K+ affected the membrane surface charge relatively little inhibition was observed. In measuring the protein-mediated transfer between a monolayer and vesicles consisting of only phosphatidylcholine, cations inhibited the transfer in the order La3+ greater than Mg2+ larger than or equal to Ca2+ greater than K+ = Na+. Inhibition was not related to the ionic strength, and very likely reflects an interference of these cations with an electrostatic interaction between the exchange protein and the polar head group of phosphatidylcholine.     

Sterically stabilized liposomes. Reduction in electrophoretic mobility but not electrostatic surface potential.

The electrophoretic mobility of liposomes containing a negatively charged derivative of phosphatidylethanolamine with a large headgroup composed of the hydrophilic polymer polyethylene glycol (PEG-PE) was determined by Doppler electrophoretic light scattering. The results show that this method is improved by the use of measurements at multiple angles to eliminate artifacts and that very small mobilities can be measured. The electrophoretic mobility of liposomes with 5 to 10 mol% PEG-PE is approximately -0.5 mu ms-1/Vcm-1 regardless of PEG-PE content compared with approximately -2 mu ms-1/Vcm-1 for similar liposomes but containing 7.5% phosphatidylglycerol (PG) instead of PEG-PE. Measurements of surface potential by distribution of an anionic fluorescent probe show that the PEG-PE imparts a negative charge identical to that by PG, consistent with the expectation of similar locations of the ionized phosphate responsible for the charge. The reduced mobility imparted by the surface bound PEG is attributed to a mechanism similar to that described for colloidal steric stabilization: hydrodynamic drag moves the hydrodynamic plane of shear, or the hydrodynamic radius, away from the charge-bearing plane, that of the phosphate moities. An extended length of approximately 50 A for the 2,000 molecular weight PEG is estimated from the reduction in electrophoretic mobility.     

Divalent cation binding to phospholipid vesicles. Dependence on temperature and lipid fluidity

Mn²⁺ binding to vesicles prepared from several different species of anionic phospholipids was determined as a function of temperature by electron paramagnetic resonance (EPR). The Mn²⁺ affinities of phosphatidylserine, cardiolipin and egg yolk phosphatidylglycerol all increased monitonically with temperature.Vesicles prepared from hydrogenated and natural (bovine) phosphatidylserine were monitored with respect to hydrocarbon chain fluidity as well as Mn²⁺ binding. Contrary to expectations based on surface potential considerations, the affinity of phosphatidylserine for divalent cations was apparently not lowered in going from the gel state to the liquid crystalline state of the bilayer. The results are instead consistent with an enhancement in cation affinity with increased lipid fluidity.Dipalmitoyl phosphatidylglycerol vesicle fluidity and Mn²⁺ binding were also studied with EPR. A large reduction in the measured Mn²⁺ affinity accompanied melting of the phospholipid, but observed hysteresis in the temperature dependence of the binding render uncertain any simple explanation based on changes in surface potential. Supplementary light scattering data indicated that vesicle aggregation was involved in the hysteresis phenomena.     

Influence of lipid membranes on the conformational transitions of nucleic acids

The conformational transitions of nucleic acids which were enclosed in reverse phase evaporation vesicles (REV) were studied by thermal denaturation with optical recording. Cloned fragments of double-stranded DNA containing 179 base pairs and 187 base pairs, respectively, and polyA.polyU were enclosed in REV with a yield up to every vesicle containing 50 nucleic acid molecules. With the 179 base pairs DNA enclosed in the vesicle from egg lecithin two well resolved helix-coil transitions could be measured; one is very similar in the midpoint-temperature Tm and halfwidth delta T1/2 to the transition of the free nucleic acid, and the other transition occurs stabilized at a 3.5 degrees C higher Tm-value and with a broader delta T1/2, 2.7 degrees C instead of 0.6 degree C. Both transitions are from nucleic acids inside the vesicles. Varying the surface charge of the lipid membrane by adding the negatively charged phosphatidylserine or phosphatidylglycerol, an optimum in the yield of enclosure and a maximum in the increase in Tm (4.5 degrees C) and delta T1/2 (5.5 degrees C instead of 1.0 degrees C) was obtained at 20% phosphatidylserine or phosphatidylglycerol. In vesicles from pure negatively charged lipids no second population of nucleic acids was observed. Qualitatively, similar effects were observed with polyA.polyU. Stabilization and broadening of the second transition is higher for nucleic acids inside vesicles from lipids with unsaturated fatty acids, as dioleoyl-phosphatidylcholine, than with saturated fatty acids, dipalmitoyl-phosphatidylcholine. Stabilization and broadening decrease with increasing ionic strength, whereas the relative contributions of both transitions to the total hypochromicity remain unchanged; the second transition coincides with the first at 90 mM Na+. From the experimental results it was concluded that the interaction of nucleic acids and lipid membranes is mainly of electrostatic nature. The nucleic acids exist inside the vesicles in two populations, one behaving like nucleic acid free in solution and one influenced by the contact with the membrane. All results are in accordance with a model in which the interaction between the nucleic acid and the membrane is in competition with the dipole-dipole interaction inside the membrane surface.     

Binding of monovalent cations to phosphatidylserine and modulation of Ca2+- and Mg2+-induced vesicle fusion

The effect of several monovalent cations on the Ca2+-induced aggregation and fusion of sonicated phosphatidylserine (PS) vesicles is studied by monitoring the mixing of internal compartments of the fusing vesicles using the Tb/dipicolinic acid assay. The dissociation of the fluorescent Tb-dipicolinate complex which accompanies Ca2+-induced vesicle fusion is determined directly and is due to leakage of contents and entry of medium into vesicles. PS vesicles do not fuse when the medium contains only monovalent cations (at pH 7.4), regardless of the cation concentration or whether there is aggregation of the vesicles. A mass-action kinetic analysis of the data provides estimates for the rate of aggregation, C11, and for the rate of fusion per se, f11. Values of f11 increase dramatically with reduction in monovalent cation concentration and are primarily determined by binding ratios of Ca2+ or Mg2+ per PS. With 300 mM of monovalent cations, the fusion per se is essentially rate-limiting to the overall fusion process and values of f11 are significantly larger with the monovalent cations which bind the least, i.e., according to the sequence tetramethylammonium greater than K+ greater than Na+ greater than Li+. With monovalent cations in concentrations of 100 mM or less, the aggregation is rate-limiting to the fusion and the overall initial fusion rates are determined by an interplay between aggregation and fusion rates. Under conditions of fast aggregation, the Ca2+-induced fusion of small PS vesicles can occur within milliseconds or less.     

Stoichiometric and electrostatic characterization of calcium binding to native and lipid-substituted adenosinetriphosphatase of sarcoplasmic reticulum

The stoichiometry of calcium binding to specific sites (i.e., those producing enzyme activation) was found to be 8-10 nmol/mg protein in native sarcoplasmic reticulum vesicles, and 13.9-15.4 nmol/mg of ATPase purified by non-ionic detergent solubilization and anion exchange chromatography. Parallel measurements of phosphoenzyme yielded levels of 4.0-4.9 and 6.0-7.7 nmol/mg of protein in the two preparations, respectively, demonstrating that each 115 kDa ATPase chain includes one catalytic site and two calcium binding sites. The apparent association constant, K = (6 +/- 2) X 10(5) M-1, and the binding cooperativity, nH = 1.9, were unchanged when measurements were carried out with native sarcoplasmic reticulum vesicles and when the membrane surface charge was altered by lipid substitution with phosphatidylcholine or phosphatidylserine, at neutral pH in the presence of 10 mM MgCl2 and 80 mM KCl. On the other hand, the apparent association constant was increased in the absence of Mg2+ or, to a lesser extent, in the absence of monovalent cations. It was also observed that the cooperative character of the calcium binding isotherms was reduced in low ionic-strength media. Analysis of the electrostatic effects indicates that the calcium-binding domain is shielded from the membrane phospholipid surface charge by virtue of its location within the ATPase protein. The effects of various electrolytes are attributed to monovalent-cation binding in the calcium-binding domain. The apparent loss of cooperativity of the calcium binding isotherms at low ionic strength is attributed to a progressive displacement of the titration curve which is minimal at low degrees of saturation and becomes larger at higher degrees of saturation. This behavior is described quantitatively by the progressive effect of calcium binding on an electrostatic potential generated by localized protein charge densities within, or near, the calcium-binding domain.     

Adsorption of monovalent and divalent cations by phospholipid membranes. The monomer-dimer problem.

A generalization of the Stern theory is derived to treat the simultaneous adsorption of monovalent cations and divalent cations by single-component phospholipid membranes, where the ion:phospholipid binding stoichiometries are 1:1 for the monovalent cations and 1:1 and/or 1:2 for the divalent cations. This study treats both the situation in which the monovalent and divalent cations compete for membrane binding sites and that in which they do not compete. The general formalism of the screening/binding problem is reviewed, and it is shown how the adsorption problem can be isolated from the electrostatics. The statistical mechanics of mixed 1:1- and 1:2-stoichiometric adsorption (the monomer-dimer problem) is treated, and the problem of simultaneous 1:1 and 1:2 binding is solved. A simple expression for this solution, given in the Bethe approximation, is combined with the electrostatics to yield an adsorption isotherm encompassing both 1:1 monovalent-cation, and 1:1 and 1:2 divalent-cation, binding to charged membranes. A comparison with the simplified treatment of previous authors is made and the significance of their assumptions clarified in light of the present result. The present and previous treatments are plotted for a representative case of Na+ and Ca++ binding to a phosphatidylserine membrane. Criteria are established to permit unambiguous experimental testing of the present vs. previous treatments.