Thermodynamic linkage between the binding of protons and inhibitors to HIV-1 protease

The aspartyl dyad of free HIV-1 protease has apparent pK(a)s of approximately 3 and approximately 6, but recent NMR studies indicate that the aspartyl dyad is fixed in the doubly protonated form over a wide pH range when cyclic urea inhibitors are bound, and in the monoprotonated form when the inhibitor KNI-272 is bound. We present computations and measurements related to these changes in protonation and to the thermodynamic linkage between protonation and inhibition. The Poisson-Boltzmann model of electrostatics is used to compute the apparent pK(a)s of the aspartyl dyad in the free enzyme and in complexes with four different inhibitors. The calculations are done with two parameter sets. One assigns epsilon = 4 to the solute interior and uses a detailed model of ionization; the other uses epsilon = 20 for the solute interior and a simplified representation of ionization. For the free enzyme, both parameter sets agree well with previously measured apparent pK(a)s of approximately 3 and approximately 6. However, the calculations with an internal dielectric constant of 4 reproduce the large pKa shifts upon binding of inhibitors, but the calculations with an internal dielectric constant of 20 do not. This observation has implications for the accurate calculation of pK(a)s in complex protein environments. Because binding of a cyclic urea inhibitor shifts the pK(a)s of the aspartyl dyad, changing the pH is expected to change its apparent binding affinity. However, we find experimentally that the affinity is independent of pH from 5.5 to 7.0. Possible explanations for this discrepancy are discussed.     

Electrostatic effects in proteins: comparison of dielectric and charge models.

Two approaches for calculating electrostatic effects in proteins are compared and ana analysis is presented of the dependence of calculated properties on the model used to define the charge distribution. Changes in electrostatic free energy have been calculated using a screened Coulomb potential (SCP) with a distance-dependent effective dielectric permittivity to model bulk solvent effects and a finite difference approach to solve the Poisson-Boltzmann (FDPB) equation. The properties calculated include shifts in dissociation constants of ionizable groups, the effect of annihilating surface charges on the binding of metals, and shifts in redox potentials due to changes in the charge of ionizable groups. In the proteins considered the charged sites are separated by 3.5-12 A. It is shown that for the systems studied in this distance range the SCP yields calculated values which are at least as accurate as those obtained from solution of the FDPB equation. In addition, in the distance range 3-5 A the SCP gives substantially better results than the FDPB equation. Possible sources of this difference between the two methods are discussed. Shifts in binding constants and redox potentials were calculated with several standard charge sets, and the resulting values show a variation of 20-40% between the 'best' and 'worst' cases. From this study it is concluded that in most applications, changes in electrostatic free energies can be calculated economically and reliably using an SCP approach with a single functional form of the screening function.     

Distance dependence and salt sensitivity of pairwise, coulombic interactions in a protein

Histidine pK(a) values were measured in charge-reversal (K78E, K97E, K127E, and K97E/K127E) and charge-neutralization (E10A, E101A, and R35A) mutants of staphylococcal nuclease (SNase) by (1)H-NMR spectroscopy. Energies of interaction between pairs of charges (DeltaG(ij)) were obtained from the shifts in pK(a) values relative to wild-type values. The data describe the distance dependence and salt sensitivity of pairwise coulombic interactions. Calculations with a continuum electrostatics method captured the experimental DeltaG(ij) when static structures were used and when the protein interior was treated empirically with a dielectric constant of 20. The DeltaG(ij) when r(ij) < or = 10 A were exaggerated slightly in the calculations. Coulomb's law with a dielectric constant near 80 and a Debye-Hückel term to account for screening by the ionic strength reproduced the salt sensitivity and distance dependence of DeltaG(ij) as well as the structure-based method. In their interactions with each other, surface charges behave as if immersed in water; the Debye length describes realistically the distance where interactions become negligible at a given ionic strength. On average, charges separated by distances (r(ij)) approximately 5 A interacted with DeltaG(ij) approximately 0.6 kcal/mole in 0.01 M KCl, but DeltaG(ij) decayed to < or =0.10 kcal/mole when r(ij) = 20 A. In 0.10 M KCl, DeltaG(ij) approximately 0.10 kcal/mole when r(ij) = 10 A. In 1.5 M KCl, only short-range interactions with r(ij) < or = 5 A persisted. Although at physiological ionic strengths the interactions between charges separated by more than 10 A are extremely weak, in situations where charge imbalance exists many weak interactions can cumulatively produce substantial effects.     

Energetics of charge-charge interactions in proteins

Electrostatic interactions between pairs of atoms in proteins are calculated with a model based on the linearized Poisson-Boltzmann equation. The equation is solved accurately by a method that takes into account the detailed shape of the protein. This paper presents applications to several systems. Experimental data for the interaction of ionized residues with an active site histidine in subtilisin BPN' allow the model to be tested, using various assumptions for the electrical properties of the protein and solvent. The electrostatic stabilization of the active site thiolate of rhodanese is analyzed, with attention to the influence of alpha-helices. Finally, relationships between electrostatic potential and charge-charge distance are reported for large and small globular proteins. The above results are compared with those of simpler electrostatic models, including Coulomb's law with both a distance-dependent dielectric constant (epsilon = R) and a fixed dielectric constant (epsilon = 2), and Tanford-Kirkwood theory. The primary conclusions are as follows: 1) The Poisson-Boltzmann model agrees with the subtilisin data over a range of ionic strengths; 2) two alpha-helices generate a large potential in the active site of rhodanese; 3) epsilon = R overestimates weak electrostatic interactions but yields relatively good results for strong ones; 4) Tanford-Kirkwood theory is a useful approximation to detailed solutions of the linearized Poisson-Boltzmann equation in globular proteins; and 5) the modified Tanford-Kirkwood theory over-screens the measured electrostatic interactions in subtilisin.     

Electrostatic environment of hemes in proteins: pK(a)s of hydroxyl ligands

The pK(a)s of ferric aquo-heme and aquo-heme electrochemical midpoints (E(m)s) at pH 7 in sperm whale myoglobin, Aplysia myoblogin, hemoglobin I, heme oxygenase 1, horseradish peroxidase and cytochrome c oxidase were calculated with Multi-Conformation Continuum Electrostatics (MCCE). The pK(a)s span 3.3 pH units from 7.6 in heme oxygenase 1 to 10.9 in peroxidase, and the E(m)s range from -250 mV in peroxidase to 125 mV in Aplysia myoglobin. Proteins with higher in situ ferric aquo-heme pK(a)s tend to have lower E(m)s. Both changes arise from the protein stabilizing a positively charged heme. However, compared with values in solution, the protein shifts the aquo-heme E(m)s more than the pK(a)s. Thus, the protein has a larger effective dielectric constant for the protonation reaction, showing that electron and proton transfers are coupled to different conformational changes that are captured in the MCCE analysis. The calculations reveal a breakdown in the classical continuum electrostatic analysis of pairwise interactions. Comparisons with DFT calculations show that Coulomb's law overestimates the large unfavorable interactions between the ferric water-heme and positively charged groups facing the heme plane by as much as 60%. If interactions with Cu(B) in cytochrome c oxidase and Arg 38 in horseradish peroxidase are not corrected, the pK(a) calculations are in error by as much as 6 pH units. With DFT corrected interactions calculated pK(a)s and E(m)s differ from measured values by less than 1 pH unit or 35 mV, respectively. The in situ aquo-heme pK(a) is important for the function of cytochrome c oxidase since it helps to control the stoichiometry of proton uptake coupled to electron transfer [Song, Michonova-Alexova, and Gunner (2006) Biochemistry 45, 7959-7975].     

Charge-charge interactions are key determinants of the pK values of ionizable groups in ribonuclease Sa (pI=3.5) and a basic variant (pI=10.2)

The pK values of the titratable groups in ribonuclease Sa (RNase Sa) (pI=3.5), and a charge-reversed variant with five carboxyl to lysine substitutions, 5K RNase Sa (pI=10.2), have been determined by NMR at 20 degrees C in 0.1M NaCl. In RNase Sa, 18 pK values and in 5K, 11 pK values were measured. The carboxyl group of Asp33, which is buried and forms three intramolecular hydrogen bonds in RNase Sa, has the lowest pK (2.4), whereas Asp79, which is also buried but does not form hydrogen bonds, has the most elevated pK (7.4). These results highlight the importance of desolvation and charge-dipole interactions in perturbing pK values of buried groups. Alkaline titration revealed that the terminal amine of RNase Sa and all eight tyrosine residues have significantly increased pK values relative to model compounds.A primary objective in this study was to investigate the influence of charge-charge interactions on the pK values by comparing results from RNase Sa with those from the 5K variant. The solution structures of the two proteins are very similar as revealed by NMR and other spectroscopic data, with only small changes at the N terminus and in the alpha-helix. Consequently, the ionizable groups will have similar environments in the two variants and desolvation and charge-dipole interactions will have comparable effects on the pK values of both. Their pK differences, therefore, are expected to be chiefly due to the different charge-charge interactions. As anticipated from its higher net charge, all measured pK values in 5K RNase are lowered relative to wild-type RNase Sa, with the largest decrease being 2.2 pH units for Glu14. The pK differences (pK(Sa)-pK(5K)) calculated using a simple model based on Coulomb's Law and a dielectric constant of 45 agree well with the experimental values. This demonstrates that the pK differences between wild-type and 5K RNase Sa are mainly due to changes in the electrostatic interactions between the ionizable groups. pK values calculated using Coulomb's Law also showed a good correlation (R=0.83) with experimental values. The more complex model based on a finite-difference solution to the Poisson-Boltzmann equation, which considers desolvation and charge-dipole interactions in addition to charge-charge interactions, was also used to calculate pK values. Surprisingly, these values are more poorly correlated (R=0.65) with the values from experiment. Taken together, the results are evidence that charge-charge interactions are the chief perturbant of the pK values of ionizable groups on the protein surface, which is where the majority of the ionizable groups are positioned in proteins.     

Microwave dielectric relaxation in muscle. A second look.

The dielectric permittivity and conductivity of muscle fibers from the giant barnacle, Balanus nubilus, have been measured at 1, 25, and 37 degrees C, between 10 MHz and 17 GHz. The dominant microwave dielectric relaxation process in these fibers is due to dipolar relaxation of the tissue water, which shows a characteristic relaxation frequency equal to that of pure water, ranging from 9 GHz (1 degree C) to 25 GHz (37 degree C). The total permittivity decrease, epsilon 0 -- epsilon infinity, due to this process accounts for approximately 95% of the water content of the tissue; thus, the major fraction of tissue water is dielectrically identical to the pure fluid on a picosecond time scale. A second dielectric process contributes significantly to the tissue dielectric properties between 0.1 and 1--5 GHz, and arises in part form Maxwell-Wagner effects due to the electrolyte content of the tissue, and in part from dielectric relaxation of the tissue proteins themselves.     

Correlation of electron transfer rate in photosynthetic reaction centers with intraprotein dielectric properties

A number of the electrogenic reactions in photosystem I, photosystem II, and bacterial reaction centers (RC) were comparatively analyzed, and the variation of the dielectric permittivity (epsilon) in the vicinity of electron carriers along the membrane normal was calculated. The value of epsilon was minimal at the core of the complexes and gradually increased towards the periphery. We found that the rate of electron transfer (ET) correlated with the value of the dielectric permittivity: the fastest primary ET reactions occur in the low-polarity core of the complexes within the picosecond time range, whereas slower secondary reactions take place at the high-polarity periphery of the complexes within micro- to millisecond time range. The observed correlation was quantitatively interpreted in the framework of the Marcus theory. We calculated the reorganization energy of ET carriers using their van der Waals volumes and experimentally determined epsilon values. The electronic coupling was calculated by the empirical Moser-Dutton rule for the distance-dependent electron tunneling rate in nonadiabatic ET reactions. We concluded that the local dielectric permittivity inferred from the electrometric measurements could be quantitatively used to estimate the rate constant of ET reactions in membrane proteins with resolved atomic structure with the accuracy of less than one order of magnitude.     

Semi-continuum electrostatic calculations of redox potentials in photosystem I

The midpoint redox potentials (E(m)) of all cofactors in photosystem I from Synechococcus elongatus as well as of the iron-sulfur (Fe(4)S(4)) clusters in two soluble ferredoxins from Azotobacter vinelandii and Clostridium acidiurici were calculated within the framework of a semi-continuum dielectric approach. The widely used treatment of proteins as uniform media with single dielectric permittivity is oversimplified, particularly, because permanent charges are considered both as a source for intraprotein electric field and as a part of dielectric polarizability. Our approach overcomes this inconsistency by using two dielectric constants: optical epsilon(o)=2.5 for permanent charges pre-existing in crystal structure, and static epsilon(s) for newly formed charges. We also take into account a substantial dielectric heterogeneity of photosystem I revealed by photoelectric measurements and a liquid junction potential correction for E(m) values of relevant redox cofactors measured in aprotic solvents. We show that calculations based on a single permittivity have the discrepancy with experimental data larger than 0.7 V, whereas E(m) values calculated within our approach fall in the range of experimental estimates. The electrostatic analysis combined with quantum chemistry calculations shows that (i) the energy decrease upon chlorophyll dimerization is essential for the downhill mode of primary charge separation between the special pair P(700) and the primary acceptor A(0); (ii) the primary donor is apparently P(700) but not a pair of accessory chlorophylls; (iii) the electron transfer from the A branch quinone Q(A) to the iron-sulfur cluster F(X) is most probably downhill, whereas that from the B branch quinone Q(B) to F(X) is essentially downhill.     

Electrostatic screening in molecular dynamics simulations.

The screened Coulombic potential has been shown to describe satisfactorily equilibrium properties like pK shifts, the effects of charged groups on redox potentials and binding constants of metal ions. To test how well the screening of the electrostatic potential describes the dynamical trajectory of a macromolecular system, a series of comparative simulations have been carried out on a protein system which explicitly included water molecules and a system in vacuo. For the system without solvent the results of using (i) the standard potential form were compared with results of (ii) the potential where the Coulomb term was modified by the inclusion of a distance dependent dielectric, epsilon (r), to model the screening effect of bulk water, and (iii) standard potential modified by reducing the charge on ionized residue side chains. All molecular dynamics simulations have been carried out on bovine pancreatic trypsin inhibitor. Comparisons between the resulting trajectories, averaged structures, hydrogen bonding patterns and properties such as solvent accessible surface area and radius of gyration are described. The results show that the dynamical behaviour of the protein calculated with a screened electrostatic term compares more favourably with the time-dependent structural changes of the full system with explicitly included water than the standard vacuum simulation.     

Spatial distribution of dielectric shielding in the interior of Pyrococcus furiosus rubredoxin as sampled in the subnanosecond timeframe by hydrogen exchange

Experimental pK values of ionizable sidechains provide the most direct test for models representing dielectric shielding within the interior of a protein. However, only the strongly shifted pK values are particularly useful for discriminating among models. NMR titration studies have usually found only one or two such shifted pK values in each protein, so that the fitting of the experimental data to a uniform internal dielectric (epsilon(int)) model is not well constrained. The observed variation among proteins for such epsilon(int) estimates may reflect nonuniformity of dielectric shielding within each protein interior or qualitative differences between individual proteins. The differential amide kinetic acidities for a series of metal-substituted rubredoxins are shown to be consistent with Poisson-Boltzmann predictions of dielectric shielding that is relatively uniform for all of the amides that are sensitive to the metal charge, a region which corresponds to roughly 1/3 of the internal volume. The effective epsilon(int) values near 6 that are found in this study are significantly lower than many such estimates derived from sidechain pK measurements. The differing timeframes in which dielectric relaxation can respond to the highly transient peptide anion as compared to the longer lived states of the charged sidechains offers an explanation for the lower apparent dielectric constant deduced from these measurements.     

Combining conformational flexibility and continuum electrostatics for calculating pK(a)s in proteins

Protein stability and function relies on residues being in their appropriate ionization states at physiological pH. In situ residue pK(a)s also provides a sensitive measure of the local protein environment. Multiconformation continuum electrostatics (MCCE) combines continuum electrostatics and molecular mechanics force fields in Monte Carlo sampling to simultaneously calculate side chain ionization and conformation. The response of protein to charges is incorporated both in the protein dielectric constant (epsilon(prot)) of four and by explicit conformational changes. The pK(a) of 166 residues in 12 proteins was determined. The root mean square error is 0.83 pH units, and >90% have errors of <1 pH units whereas only 3% have errors >2 pH units. Similar results are found with crystal and solution structures, showing that the method's explicit conformational sampling reduces sensitivity to the initial structure. The outcome also changes little with protein dielectric constant (epsilon(prot) 4-20). Multiconformation continuum electrostatics titrations show coupling of conformational flexibility and changes in ionization state. Examples are provided where ionizable side chain position (protein G), Asn orientation (lysozyme), His tautomer distribution (RNase A), and phosphate ion binding (RNase A and H) change with pH. Disallowing these motions changes the calculated pK(a).     

The molecular mechanism of action of the proton ionophore FCCP (carbonylcyanide p-trifluoromethoxyphenylhydrazone).

We propose a simple model that accounts for the ability of the weak acid FCCP (Carbonylcyanide-p-trifluoromethoxyphenylhydrazone) to both transport protons across phospholipid bilayer membranes and uncouple oxidation from phosphorylation in mitochondria. Four parameters are required to characterize this model: the rate constant for the movement of A- across the membrane, kA, the rate constant for the movement of HA across the membrane, kHA, the adsorption coefficient of A- onto the membrane-solution interface, beta A, and the surface pK. These four parameters were determined from kinetic measurements on planar bilayer membranes using the charge-pulse and voltage-clamp techniques. We confirmed the adequacy of the model by determining each of these parameters independently, utilizing equilibrium dialysis, zeta potential, membrane potential, spectrophotometric, and conductance measurements. For a phosphatidylethanolamine bilayer the values of the parameters are kHA = 10(4)S-1, beta A = 3 10(-3) cm, and 6.0 less than pK less than 6.4. As predicted theoretically, the value of KA depends on both the applied voltage, V, and dielectric constant of the membrane, epsilon r; when V approaches zero and the membrane contains chlorodecane (epsilon r congruent to 2.7) kA = 700 s-1. If oxidation is coupled to phosphorylation by means of a delta microH+, and V er congruent to 2.7 for the inner membrane of the mitochondrion, the model predicts that FCCP should exert maximal uncoupling activity at a pH congruent to pK. This prediction agrees with the published experimental results.     

Direct proton magnetic resonance determination of the pKa of the active center histidine in thiolsubtilisin

The serine proteases constitute a group of endopeptidases whose members owe their catalytic activity to the presence of a catalytic triad of amino acids consisting of a serine, a histidine and an aspartate. The pK(a) values for this histidine have been determined for several cases in which there is a negative charge installed at the serine to mimic the oxyanionic intermediate and related transition state for the catalytic pathway. Instances from this laboratory include (1) replacement of the serine by a cysteine in subtilisin to create a thiolate; (2) formation of monoisopropylphosphoryl-Ser 195 monoanionic phosphodiesters (in trypsin and chymotrypsin, Ser 221 in subtilisins); and (3) tetrahedral boronates formed with peptide boronic acids. The nuclear magnetic resonance (NMR) signals pertinent to this histidine, or signals indirectly reflecting the state of ionization of this histidine, have been used effectively to monitor changes in the active center ionization state. In every case studied, there is elevation of the pK(a) at the histidine when the negative charge is installed at the serine position. Herein is reported the first NMR measurement of the active center His 63 pK(a) in thiolsubtilisin Carlsberg; it is elevated by 3 units compared with the parent enzyme. Using a numerical solution (finite difference) of the Poisson-Boltzmann equation, a protein dielectric constant of 4 provides a good estimate of the experimentally observed pK(a) elevations. Very significantly, a very low protein dielectric constant (epsilon(p) = 3-5) is required in all of the comparisons, and for all three enzymes used (chymotrypsin, trypsin, and subtilisin). Finally, we discuss why the electrostatic perturbation sensed at His of the active center is more amplified by a negative charge on the Ser side than the same charge on the Asp side. A plausible explanation is that the positive charge on the imidazolium ring of the His is localized, with the N(delta 1) carrying a smaller fraction, the N(epsilon 2) carrying the bulk of the positive charge.     

A fast and simple method to calculate protonation states in proteins.

A simple model for electrostatic interactions in proteins, based on a distance and position dependent screening of the electrostatic potential, is presented. It is applied in conjunction with a Monte Carlo algorithm to calculate pK(alpha) values of ionizable groups in proteins. The purpose is to furnish a simple, fast, and sufficiently accurate model to be incorporated into molecular dynamic simulations. This will allow for dynamic protonation calculations and for coupling between changes in structure and protonation state during the simulation. The best method of calculating protonation states available today is based on solving the linearized Poisson-Boltzmann equation on a finite difference grid. However, this model consumes far too much computer time to be a practical alternative. Tests are reported for fixed structures on bacteriorhodopsin, lysozyme, myoglobin, and calbindin. The studies include comparisons with Poisson-Boltzmann calculations with dielectric constants 4 and 20 inside the protein, a model with uniform dielectric constant 80 and distance-dependent dielectric models. The accuracy is comparable to that of Poisson-Boltzmann calculations with dielectric constant 20, and it is considerably better than that with epsilon = 4. The time to calculate the protonation at one pH value is at least 100 times less than that of a Poisson-Boltzmann calculation. Proteins 1999;36:474-483.     

Determination of electric parameters of cell membranes by a dielectrophoresis method.

Marszalek, P., J. J. Zielinsky, and M. Fikus (1989. Bioelectrochem. Bioenerg. 22:289-298) have described a novel design for measuring the complete dielectrophoretic spectrum of a single cell. From the analysis of the dielectrophoretic spectrum, the membrane conductivity, sigma membr, and the membrane dielectric permittivity, epsilon membr, of the cell may be determined according to the theory of dielectrophoresis described by Sauer, F. A. (1985. Interactions between Electromagnetic Field and Cells. A. Chiabrera, C. Nicolini, and H.P. Schwan, editors. Plenum Publishing Corp., New York. 181-202). At Fo, the net force experienced by a single shell sphere in a nonuniform periodic field is zero, and the sphere ceases to move in the field. In other words, at Fo, the effective polarizability, chi eff, of the sphere (the polarizability of sphere minus the polarizability of the medium) is equal to zero. For biological cells in high conductivity medium, e.g., the isotonic saline, sigma membr falls below 2 x 10(-6) S m-1, where Fo becomes insensitive to sigma membr, and the method becomes impractical. In a low conductivity medium, 0.3 M sucrose, sigma membr of cells is generally higher and the method may be applied. Assuming a membrane thickness of 9 nm, epsilon membr of Neurospora crassa slime cells was determined to be in the range of 8.3-9.4 epsilon o, and of myeloma Tib9 to be 9.4 epsilon o, epsilon o being the dielectric permittivity of the free space. The values for the slime cells were compared with values obtained by the dielectric spectroscopy method which measures average values for cells in suspension.     

THE AUTODESTRUCTION OF PEPSIN IN RELATION TO ITS IONIZATION

1. Evidence is presented that pepsin is a univalent acid with a value for pK of 6.85 (or a base, with pK 7.39). 2. The autodestruction of the pepsin is shown to be dependent in part upon an instantaneous irreversible change occurring in the ionized form of the enzyme (if it be an acid) or in the unionized form (if it be a base). 3. A further progressive autodestruction of pepsin at any given hydrogen ion concentration and temperature is defined by the mass law equation for a monomolecular reaction 4. The velocity of autodestruction of pepsin is directly proportional to the hydroxyl ion concentration. It is much less in the range of hydroxyl ion concentration from pOH 9.89-7.7, than in the range greater than pOH 7.7. In both of these ranges variations in pK with pOH may be represented by straight lines.     

Single file ion diffusion and the Schmoluchowski equation

The Schmoluchowski equation is introduced into the problem of single file ion diffusion in a channel. The ions mutually interact due to coulomb repulsion and are also subject to a single ion potential due to the channel. The positions of the ions are represented by a continuous co-ordinate. The problem is reduced to the solution of a pair of transfer integral equations. The resistivity of finite and infinite channels is calculated for various dielectric constants and mean ionic separations. The ionic density for finite channels is also calculated. The results clearly demonstrate that strong coulomb interaction leads to a co-operative motion of the ions across channels.     

Dielectric properties of proteins from simulation: the effects of solvent, ligands, pH, and temperature

We have used a standard Fr?hlich-Kirkwood dipole moment fluctuation model to calculate the static dielectric permittivity, epsilon(0), for four different proteins, each of which was simulated under at least two different conditions of pH, temperature, solvation, or ligand binding. For the range of proteins and conditions studied, we calculate values for epsilon(0) between 15 and 40. Our results show, in agreement with prior work, that the behavior of charged residues is the primary determinant of the effective permittivity. Furthermore, only environmental changes that alter the properties of charged residues exert a significant effect on epsilon. In contrast, buried water molecules or ligands have little or no effect on protein dielectric properties.     

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.