Intrinsic electric fields and proton diffusion in immobilized protein membranes. Effects of electrolytes and buffers.

We present a theory for proton diffusion through an immobilized protein membrane perfused with an electrolyte and a buffer. Using a Nernst-Planck equation for each species and assuming local charge neutrality, we obtain two coupled nonlinear diffusion equations with new diffusion coefficients dependent on the concentration of all species, the diffusion constants or mobilities of the buffers and salts, the pH-derivative of the titration curves of the mobile buffer and the immobilized protein, and the derivative with respect to ionic strength of the protein titration curve. Transient time scales are locally pH-dependent because of protonation-deprotonation reactions with the fixed protein and are ionic strength-dependent because salts provide charge carriers to shield internal electric fields. Intrinsic electric fields arise proportional to the gradient of an "effective" charge concentration. The field may reverse locally if buffer concentrations are large (greater to or equal to 0.1 M) and if the diffusivity of the electrolyte species is sufficiently small. The "ideal" electrolyte case (where each species has the same diffusivity) reduces to a simple form. We apply these theoretical considerations to membranes composed of papain and bovine serum albumin (BSA) and show that intrinsic electric fields greatly enhance the mobility of protons when the ionic strength of the salts is smaller than 0.1 M. These results are consistent with experiments where pH changes are observed to depend strongly on buffer, salt, and proton concentrations in baths adjacent to the membranes.     

Calcium binding to bile salts

Calcium binding to bile salt monomers and micelles is an important issue with respect to the possible (but rare) precipitation of calcium bile salts in the gallbladder. In the present work the binding of Ca2+ to six bile salts was measured in solutions containing 2 to 100 mM bile salts by means of a calcium-sensitive dye, murexide, which determines the ionic calcium concentration. In solutions containing bile salt at concentration higher than 20 mM most, if not all, of the bound Ca2+ is associated with micellar surfaces. The results were analyzed by employing a model which combines specific binding with electrostatic equations and accounts for the system being a closed one. The analysis of Ca2+ binding data considered explicitly the presence of Na+ ions and yielded intrinsic binding coefficients for Ca2+ and Na+ which were utilized to explain and predict binding results for various concentrations of Ca2+, Na+ and bile salts. The calculations indicate that in saline solutions most of the surface sites were bound by Na+, whereas less than 10% were bound by Ca2+ even in the presence of 8 mM Ca2+. The binding of Ca2+ to bile salt micelles increases with pH. An increase in temperature results in reduced binding affinity of Ca2+ to the bile salt micelles.     

The Non-Steady-State Membrane Potential of Ion Exchangers with Fixed Sites

A system of equations, based upon the assumption that the only force acting on each ionic species is due to the gradient of its electrochemical potential, is used to deduce, in the non-steady state for zero net current, the expression of the difference of electric potential between two solutions separated by an ion exchange membrane with fixed monovalent sites. The membrane is assumed to be solely permeable to cations or anions, depending on whether the charge of the sites is -1 or +1, and not to permit any flow of solvent. Under the assumptions that the difference of standard chemical potentials of any pair of permeant monovalent species and the ratio of their mobilities are constant throughout the membrane, even when the spacing of sites is variable, explicit expressions are derived for the diffusion potential and total membrane potential as functions of time and of solution activities. The expressions are valid for any number of permeant monovalent species having ideal behavior and for two permeant monovalent species having “n-type” non-ideal behavior. The results show that for a step change in solution composition the observable potential across a membrane having fixed, but not necessarily uniformly spaced, sites becomes independent of time once equilibria are established at the boundaries of the membrane and attains its steady-state value even while the ionic concentration profiles and the electric potential profile within the membrane are changing with time.     

STUDIES IN THE PHYSICAL CHEMISTRY OF AMINO ACIDS,PEPTIDES, AND RELATED SUBSTANCES : XI. THE SOLUBILITY OF CYSTINE IN THE PRESENCE OF IONS AND ANOTHER DIPOLAR ION

1. As an introduction to the relations that obtain in biochemical systems containing several components, some ionic, some dipolar ionic, the solubility of cystine has been investigated in the presence of glycine and neutral salts. 2. Both glycine and sodium chloride increase cystine solubility at all concentrations. The interaction between cystine and ions is, however, diminished with increase in glycine concentration, and the interaction between cystine and glycine with increase in ionic strength. 3. Sodium sulfate also increases the solubility of cystine, but at concentrations greater than one molal its solvent action is smaller than its salting-out effect, which is greater at all concentrations than that of sodium chloride, and greater the higher the glycine concentration. 4. These interactions are defined by an equation giving the solubility ratio of cystine in terms of salting-out constants, constants related to the electric moments of cystine, and to the ionic strength and dielectric constant of the solution. 5. The higher the concentration of glycine and therefore the dielectric constant of the solution, the smaller that part of the interaction between ions and dipolar ions which depends upon Coulomb forces and the greater appears the salting-out effect. 6. Conversely, the greater the ionic strength and the salting-out effect the smaller the interaction between dipolar ions in solution.     

The permeability of the endplate channel to organic cations in frog muscle

The relative permeability of endplate channels to many organic cations was determined by reversal-potential criteria. Endplate currents induced by iontophoretic "puffs" of acetylcholine were studied by a Vaseline gap, voltage clamp method in cut muscle fibers. Reversal potential changes were measured as the NaCl of the bathing medium was replaced by salts of organic cations, and permeability ratios relative to Na+ ions were calculated from the Goldman-Hodgkin-Katz equation. 40 small monovalent organic cations had permeability ratios larger than 0.1. The most permeant including NH4+, hydroxylamine, hydrazine, methylamine, guanidine, and several relatives of guanidine had permeability ratios in the range 1.3--2.0. However, even cations such as imidazole, choline, tris(hydroxymethyl)aminomethane, triethylamine, and glycine methylester were appreciably permeant with permeability ratios of 0.13--0.95. Four compounds with two charged nitrogen groups were also permeant. Molecular models of the permeant ions suggest that the smallest cross-section of the open pore must be at least as large as a square, 6.5 A x 6.5 A. Specific chemical factors seem to be less important than access or friction in determining the ionic selectivity of the endplate channel.     

Ionic selectivity, saturation, and block in sodium channels. A four- barrier model

Ionic fluxes in Na channels of myelinated axons show ionic competition, block, and deviations from simple flux independence. These phenomena are particularly evident when external Na+ ions are replaced by other permeant or impermeant ions. The observed currents require new flux equations not based on the concepts of free diffusion. A specific permeability model for the Na channel is developed from Eyring rate theory applied to a chain of saturable binding sites. There are four energy barriers in the pore and only one ion is allowed inside at a time. Deviations from independence arise from saturation. The model shows that ionic permeability ratios measured from zero-current potentials can differ from those measured from relative current amplitudes or conductances. The model can be fitted to experiments with various external sodium substitutes by varying only two parameters: For each ion the height of the major energy barrier (the selectivity filter) determines the biionic zero-current potential and the depth of the energy well (binding site) just external to that barrier then determines the current amplitudes. Voltage clamp measurements with myelinated nerve fibers are given showing numerous examples of deviations from independence in ionic fluxes. Strong blocks of ionic currents by guanidinium compounds and Tl+ ions are fitted by binding within the channel with apparent dissociation constants in the range 50-122 mM. A small block with high Na+ concentrations can be fitted by Na+ ion binding with a dissociation constant of 368 mM. The barrier model is given a molecular interpretation that includes stepwise dehydration of the permeating ion as it interacts with an ionized carboxylic acid.     

Physico-chemical model of a voltage-gated sodium channel

A permeant ion is known to create in the channel pore a local electrical field, the intensity of which exceeds the intensity of an electrical field produced by the membrane potential. In our study, we consider a sodium channel model, in which the effects of a permeant ion, an inactivating particle, and pharmacological agents on mobile charged groups of the channel are semi-phenomenologically taken into account by using motion equations for a generalized structural variable. Stationary solutions for the equation correspond to “open,” “closed,” and “inactivated” channel states. Because of this, the channel free energy profile, as a function of the structural variable, has three local minima. The three energy values of these states depend both on the electrical field applied externally and on the near-membrane concentrations of permeant ions and acting pharmacological agents. Sodium channel activation and inactivation kinetics are considered resulting from relative changes of the free energy typical of the above three states of the channel. The results we obtained in the course of channel activation and inactivation modeling and their voltage dependence are qualitatively consistent with the commonly known experimental data. The proposed model allows one to qualitatively predict the dependence of the sodium channel kinetic characteristics on the concentrations of permeant ions and pharmacological agents.     

Theory for carrier-mediated zero-current conductance of bilayers extended to allow for nonequilibrium of interfacial reactions,spatially dependent mobilities and barrier shape

Summary A generalized form of the electrodiffusion equation, allowing for any shape of symmetrical energy barrier and any spatial dependence of the diffusion coefficient, is used to deduce theoretically the carrier-mediated conductance for thin (e.g., bilayer) membranes in the limit of low applied current. Both the Nernst-Planck and the Eyring single-barrier treatments are special cases of this more general approach, which allows for the effect of non-uniform properties of the lipid and non-uniform profiles of the forces acting within the membrane interior. Two independent mechanisms for ions to cross the membrane-solution interfaces are considered; namely, (1) the reaction at the interface between ions from solution and carriers from the membrane, and (2) the partition across the interfaces of complexes already formed in the solution. The rates of these reactions are taken into account using the rate equations of chemical kinetics; and the Poisson-Boltzmann equation is integrated in the aqueous solutions to evaluate the effect of charged polar head groups of the lipid. The analysis leads to an expression for the conductance, which, in the approximation of constant field, is an explicit function of such experimentally variable parameters as the concentrations and types of permeant ions and carriers in the aqueous phases, the total ionic strength and the nature of the polar head groups of the lipid. The functional relationship observable in an unknown membrane can, in principle, enable one to deduce such information as the mechanism of ion permeation across the interfaces, the magnitude of the surface charge, and the degree of ion-carrier complexation in the aqueous solutions.     

Flow limits of Kedem-Katchalsky equations for fluid flux

The Kedem-Katchalsky equations for fluid flux across membranes may not be adequate for large solvent flows. In particular, for an example of two membranes in series, it is argued that they would predict physically unreasonable behavior. An alternate equation for solute flow is proposed for a simple sieving membrane. For the same example, this equation predicts more physically reasonable results.     

The Effect of Applied Suctions and 2,4-Dichlorophenoxyacetic Acid on Water and Salt Efflux from the Cut Ends of Excised Maize Roots

Solution flux and the potassium concentration of the emergentfluid from young excised maize roots was measured at variousapplied suctions both for control and 2,4-D-treated roots. Non-linearvolume flow versus pressure curves were obtained and the xylemsap ionic concentration fell only slightly if at all with increasingsuctions. Salt flux and volume flow were linearly related. An operational value of the hydraulic conductance of each rootwas obtained and shown to decrease after treatment with 2,4-D.It was concluded that an increase in transpiration was unlikelyto overcome the lowered flux of salts to aerial parts of theplant induced by 2,4-D. The filtration properties of the root are discussed in relationto the possible pathways of ions and water to the xylem vessels.It is concluded that the location of the outside compartmentcorresponding to the concentration C° in the usual phenomenologicalflux equations depends on whether one is considering salt orwater flow through the root.     

Estimation of thickness of concentration boundary layers by osmotic volume flux determination

The estimation method of the concentration boundary layers thicknesses (δ) in a single-membrane system containing non-electrolytic binary or ternary solutions was devised using the Kedem-Katchalsky formalism. A square equation used in this method contains membrane transport (L(p), σ, ω) and solution (D, C) parameters as well as a volume osmotic flux (J(v)). These values can be determined in a series of independent experiments. Calculated values δ are nonlinearly dependent on the concentrations of investigated solutions and the membrane system configuration. These nonlinearities are the effect of a competition between spontaneously occurring diffusion and natural convection. The mathematical model based on Kedem-Katchalsky equations and a concentration Rayleigh number (R(C)) was presented. On the basis of this model we introduce the dimensionless parameter, called by us a Katchalsky number (Ka), modifies R(C) of membrane transport. The critical value of this number well describes a moment of transition from the state of diffusion into convective diffusion membrane transport.     

Modification of the Kedem-Katchalsky equations

The presented modification of the transport equations of Kedem-Katchalsky resulted in the introduction of (omega s/omega) and omega/(omega-Lp sigma[(1-sigma)C1-(1-sigma s)C2]) factors into the Kedem-Katchalsky equations. The above factors determine the influence of boundary layers on transport across the membrane. The modified Kedem-Katchalsky equations were verified for synthetic membranes and it was shown that the value of the (omega s/omega) factor depended on the type of membrane and the membrane configuration system. This modification facilitated a wider range of application of the Kedem-Katchalsky equations to systems in which the solutions were stirred or unstirred.     

The Relation between Salt and Ionic Transport Coefficients

The reflection coefficient was originally introduced by Staverman to describe the movement of nonelectrolytes through membranes. When this coefficient is extended to salts, one has a choice of defining this term for the whole salt moving as a single electrically neutral component or for the individual ions of the salt. The latter definition is meaningful only in the absence of an electric field across the permeability barrier. This condition may be achieved with the voltage clamp or short-circuit technique and is especially useful in dealing with biological systems in which one rarely has only a single salt or even equal concentrations of the major anion and cation. The relations between the transport coefficients for the salt and its individual ions are derived. The special conditions which may result in negative osmosis through a charged membrane in the presence of a salt are discussed.     

Dependence of the intracellular concentrations of univalent ions and hydrogenase activity on the salt composition and pH of the medium in the haloalkaliphilic sulfate-reducing bacterium Desulfonatronum thiodismutans

It has been shown that the intracellular concentrations of Na+, K+, and Cl- ions in Desulfonatronum thiodismutans depend on the extracellular concentration of Na' ions. An increase in the extracellular concentration of Na+ results in the accumulation of K+ ions in cells, which points to the possibility that these ions perform an osmoprotective function. When the concentration of the NaCI added to the medium was increased to 4%, the concentration gradient of Cl- ions changed insignificantly. It was found that D. thiodismutans contains two forms of hydrogenase--periplasmic and cytoplasmic. Both enzymes are capable of functioning in solutions with high ionic force; however they exhibit different sensitivities to Na+, K+, and Li+ salts and pH. The enzymes were found to be resistant to high concentrations of Na+ and K+ chlorides and Na+ bicarbonate. The cytoplasmic hydrogenase differed significantly from the periplasmic one in having much higher salt tolerance and lower pH optimum. The activity of these enzymes depended on the nature of both the cationic and anionic components of the salts. For instance, the inhibitory effect of NaCl was less pronounced than that of LiCl, whereas Na+ and Li+ sulfates inhibited the activity of both hydrogenase types to an equal degree. The highest activity of these enzymes was observed at low Na+ concentrations, close to those typical of cells growing at optimal salt concentrations.     

Open-Boundary Molecular Dynamics of a DNA Molecule in a Hybrid Explicit/Implicit Salt Solution

The composition and electrolyte concentration of the aqueous bathing environment have important consequences for many biological processes and can profoundly affect the behavior of biomolecules. Nevertheless, because of computational limitations, many molecular simulations of biophysical systems can be performed only at specific ionic conditions: either at nominally zero salt concentration, i.e., including only counterions enforcing the system’s electroneutrality, or at excessive salt concentrations. Here, we introduce an efficient molecular dynamics simulation approach for an atomistic DNA molecule at realistic physiological ionic conditions. The simulations are performed by employing the open-boundary molecular dynamics method that allows for simulation of open systems that can exchange mass and linear momentum with the environment. In our open-boundary molecular dynamics approach, the computational burden is drastically alleviated by embedding the DNA molecule in a mixed explicit/implicit salt-bathing solution. In the explicit domain, the water molecules and ions are both overtly present in the system, whereas in the implicit water domain, only the ions are explicitly present and the water is described as a continuous dielectric medium. Water molecules are inserted and deleted into/from the system in the intermediate buffer domain that acts as a water reservoir to the explicit domain, with both water molecules and ions free to enter or leave the explicit domain. Our approach is general and allows for efficient molecular simulations of biomolecules solvated in bathing salt solutions at any ionic strength condition.     

Kinetics and thermodynamics of thermal denaturation in acyl carrier protein.

The denaturation of Escherichia coli acyl carrier protein (ACP) in buffers containing both monovalent and divalent cations was followed by variable-temperature NMR and differential scanning calorimetry. Both high concentrations of monovalent salts (Na+) and moderate concentrations of divalent salts (Ca2+) raise the denaturation temperature, but calorimetry indicates that a significant increase in the enthalpy of denaturation is obtained only with the addition of a divalent salt. NMR experiments in both low ionic strength monovalent buffers and low ionic strength monovalent buffers containing calcium ions show exchange between native and denatured forms to be slow on the NMR time scale. However, in high ionic strength monovalent buffers, where the temperature of denaturation is elevated as it is in the presence of Ca2+, the transition is fast on the NMR time scale. These results suggest that monovalent and divalent cations may act to stabilize ACP in different ways. Monovalent ions may nonspecifically balance the intrinsic negative charge of this protein in a way that is similar for native, denatured, and intermediate forms. Divalent cations provide stability by binding to specific sites present only in the native state.     

On the theory of diffusion of electrolytes

In the theory of diffusion of electrolytes the following assumptions are frequently made: (i) the electrolytic solution is electrically neutral everywhere, (ii) the ionic concentrations and the electric potential all depend on a single Cartesian coordinate as the only space variable. Often the electric potential of the solution is determined on the basis of the Poisson equation alone, disregarding any other relation between this potential and the ionic concentrations. Since the Poisson equation only represents a condition which the potential fulfills, the use of this equation alone may lead to error unless the explicit relation for the potential involving a space integration of ionic concentrations is also taken into account. But if this relation is used the Poisson equation becomes redundant and, more important, assumptions (i) and (ii) appear unacceptable, the former because it leads to a zero electric potential everywhere, the latter because it is mathematically incorrect. The present paper is based on general equations of diffusion of ions, excluding the Poisson equation. These equations form a system of nonlinear integrodifferential quations whose number equals the number of ionic species present in the solution. It appears that when all ions are distributed symmetrically around a point all functions related to the above system of equations can be made dependent on a single space coordinate: the distance from the center of symmetry. Two methods of successive approximations are given for the solution of the equations in the case of spherical symmetry with limitation to the steady state. These methods are then applied to the study of the distribution of ionic concentrations and electrical potentials inside a cell of spherical shape in equilibrium with its surroundings. These methods are rapidly convergent; exact theoretical values of the electric potential are calculable on the boundary of the cell. It appears that the potential at the center of the cell is not more than ∼50% higher than at its boundary and that variation of concentration inside the cell is not very large. For instance, with 100 mV on the boundary the ionic concentration there is about four times higher than at the center. Calculations show that extremely small amounts of electricity are sufficient to account for the electric potentials currently observed. In a cell of 100 micra diameter an average concentration of only 10⁻¹⁴ mole/cm³ of a monovalent ion would be sufficient to give 1 millivolt on the boundary. This concentration is directly proportional to the voltage and inversely proportional to the square of the cell diameter. Most of the numerical results given above are obtained by considering only those ions whose electrical charge is not compensated for by ions of an opposite sign. The total concentrations may be much higher than those quoted. The theory does not take into account possible effects of structural heterogeneities which may exist in the cell, particularly of various phase boundaries. An incidental result shows that the Boltzmann distribution function in the form employed in modern theory of electrolytes is fundamentally a consequence of the mathematical theory of diffusion alone. It is pointed out, however, that Boltzmann distribution is not always compatible with the definition of the electric potential.     

Physical chemistry and evolution of salt tolerance in halobacteria

The cellular constituents of extremely halophilic bacteria not only tolerate high salt concentration, but in many cases require it for optical functioning. The characteristics affected by salt include enzyme activity, stability, allosteric regulation, conformation and subunit association. The salt effects are of two major kinds: electrostatic shielding of negative charges by cations at low salt concentration, and hydrophobic stabilization by salting-out type salts at high salt concentration. The composition of halobacterial proteins shows an excess of acidic amino acids and a deficiency of nonpolar amino acids, which accounts for these effects. Since the cohesive forces are weaker and the repulsing forces are stronger in these proteins, preventing aggregation in salt, these structures are no longer suited for functioning in the absence of high salt concentrations. Unlike these nonspecific effects, ribosomes in halobacteria show marked preference for potassium over sodium ions. To ensure the proper intracellular ionic composition, powerful ion transport systems have evolved in the halobacteria, resulting in the extrusion of sodium ions and their replacement by potassium. It is likely that such membrane transport system for ionic movements is a necessary requisite for salt tolerance.Proceedings of the Fourth College Park Colloquium on Chemical Evolution:Limits of Life, University of Maryland, College Park, 18–20 October 1978.     

Self-association of human apolipoproteins A-I and A-II and interactions of apolipoprotein A-I with bile salts: quasi-elastic light scattering studies

We employed quasi-elastic light scattering (QLS) to systematically study the aqueous self-association of human apolipoproteins A-I and A-II (apo A-I and apo A-II) and the interactions of apo A-I with common taurine-conjugated bile salts. Self-association of apo A-I was promoted by increases in apolipoprotein concentration (0.09-2.2 mg/mL) and ionic strength (0.15-2.0 M NaCl), inhibited by increases in temperature (5-50 degrees C) and guanidine hydrochloride concentration (0-2.0 M), and unaffected by hydrostatic pressures up to 500 atm. The mean hydrodynamic radius (Rh) of apo A-I micelles ranged from 38 A to a maximum asymptotic value of 68 A. We examined several possible models of apo A-I self-association; the model that best fitted the Rh values assumed that apo A-I monomers first interacted at low concentrations to form dimers, which then further associated to form ring-shaped limiting octamers. Comparison of the temperature-dependent and ionic strength dependent free energy changes for the formation of octamers from apo A-I dimers suggested that hydrophobic forces strongly favored self-association and that electrostatic repulsive forces were only weakly counteractive. Apo A-II self-association was also promoted by increases in apolipoprotein concentration (0.2-1.8 mg/mL) and inhibited by increases in guanidine hydrochloride concentration (0-1.0 M) but was unaffected by variations in temperature (10-37 degrees C): the largest Rh values observed were consistent with limiting tetramers. As demonstrated by equilibrium dialysis, bile salts in concentrations below their critical micellar concentrations (cmc) bound to apo A-I micelles but had no effect upon apo A-I self-association, as inferred from constant Rh values. When bile salt concentrations exceeded their aqueous cmc values, a dissociation of apo A-I micelles resulted with the formation of mixed bile salt/apo A-I micelles. These studies support the concepts that apo A-I and apo A-II form small dimeric micelles at low concentrations that grow sharply to reach limiting sizes over a narrow concentration range. The influences of bile salt concentration and species upon these micelles have relevance to the plasma transport of bile salts in high-density lipoproteins and to the physical-chemical state of apo A-I and apo A-II molecules in native biles.