An electrostatic model for the dielectric effects,the adsorption of multivalent ions,and the bending of B-DNA

We have studied electrostatic properties of DNA with a discrete charge model consisting of a cylindrical dielectric core with a radius of 8 Å and a dielectric constant D_i = 4, surrounded by two helical strings of phosphate point charges at 10 Å from the axis, immersed in an aqueous medium with dielectric constant D_w = 78.54. Eliminating the dielectric core makes potentials in the phosphate surface less negative by about 0.5 kT/e. Salt effects are evaluated for the model without a dielectric core, using the shielded Coulomb potential. Smearing the phosphate charges increases their potential by about 2.5 kT/e, due mostly to the self-potential of the smeared charge. Potentials in the center of the minor and major grooves vary less than 0.02 kT/e along their helical path. The potential in the center of the minor groove is from 1.0 to 1.7 kT/e, more negative than in the center of the major groove, depending on dielectric core and salt concentration. So multivalent cations and also larger cationic ligands, such as some antibiotics, are likely to adsorb in the minor groove, in agreement with earlier computations by A. and B. Pullman. Dielectric effects on the surface potential and the local potential variations are found to be relatively small. Bending of DNA is studied by placing a multivalent cation, M^Z+, in the center of the minor or major groove, curving DNA around it for a certain length, and calculating the free energy difference between the bent and the straight configuration. Boltzmann averaged bending angles, 〈β〉, are found to be maximal in 0.03M monovalent salt, for a length of about 50 or 25 Å of curved DNA when an M^Z+ ion is adsorbed in the minor or the major groove, respectively. When the dielectric constant of water is used throughout the calculation, we find maximal bends of 〈β〉 = 11° for M²⁺ and 〈β〉 = 16° for M³⁺ in the minor groove, 〈β〉 = 13° for M³⁺ in the major groove. The absence of bends in DNA adsorbed to mica in the presence of Mg salts supports the role of Mg²⁺ in “ion bridging” between DNA and mica. The treatment of the effective dielectric constant between two points outside a dielectric cylinder in water is appended. © 1998 John Wiley & Sons, Inc. Biopoly 46: 503–516, 1998     

Reaction Field Effects on the Simulated Properties of Liquid Water

Abstract

The effects of including a reaction field contribution on the structure and dynamics of liquid water have been investigated using molecular dynamics simulations. Reaction field effects are determined for two models of water, the simple point charge (SPC) model and the extended simple point charge (SPC/E) model, and at two temperatures (277 K and 300 K). Inclusion of the reaction field leads to a reduced system density, an increase in translational diffusion, which is model dependent, an increase in internal energy, and an increase in rotational diffusion rates, in addition to the large (known) changes in the dielectric properties of liquid water. It is concluded that continued use of the reaction field technique should involve a reparameterization of the water model and not merely a merging with the original model parameters.     

Computer Simulation of the Dielectric Properties of Liquid Water

Abstract

Monte Carlo simulations of water in the NVT ensemble using three models (SPC, TIP4P and TIPS2) are reported. The internal energy, dielectric constant, and the site-site radial distribution functions of liquid water (temperature 300 K and mass density 1 gm cc^?1) were calculated and compared with experiment. It was found that of the three intermolecular potential models, SPC gives the best dielectric constant. Since SPC also yields acceptable results for the energy and structure, it is judged to be the best among the three models studied.     

Visualization of Drug-Nucleic Acid Interactions At Atomic Resolution. VIII. Structures of Two Ethidium/Dinucleoside Monophosphate Crystalline Complexes Containing Ethidium: Cytidylyl(3′-5′) Guanosine

Abstract

This paper describes two complexes containing ethidium and the dinucleoside monophosphate, cytidylyl(3′-5′)guanosine (CpG). Both crystals are monoclinic, space group P2₁, with unit cell dimensions as follows: modification 1: a = 13.64 Å, b = 32.16 Å, c - 14.93 Å, β = 114.8° and modification 2: a = 13.79 Å, b = 31.94 Å, c = 15.66 Å, β = 117.5°. Each structure has been solved to atomic resolution and refined by Fourier and least squares methods; the first has been refined to a residual of 0.187 on 1,903 reflections, while the second has been refined to a residual of 0.187 on 1,001 reflections. The asymmetric unit in both structures contains two ethidium molecules and two CpG molecules; the first structure has 30 water molecules (a total of 158 non-hydrogen atoms), while the second structure has 19 water molecules (a total of 147 non-hydrogen atoms). Both structures demonstrate intercalation of ethidium between base-paired CpG dimers. In addition, ethidium molecules stack on either side of the intercalated duplex, being related by a unit cell translation along the a axis.

The basic feature of the sugar-phosphate chains accompanying ethidium intercalation in both structures is: C3′ endo (3′-5′) C2′ endo. This mixed sugar-puckering pattern has been observed in all previous studies of ethidium intercalation and is a feature common to other drug-nucleic acid structural studies carried out in our laboratory. We discuss this further in this paper and in the accompanying papers.     

Crystal structure of Escherichia coli TEM1 β-lactamase at 1.8 Å resolution

The X-ray structure of Escherichia coli TEM1β-lactamase has been refined to a crystallorgphic R-factor of 16.4% for 22,510 reflections between 5.0 and 1.8 Å resolution; 199 water molecules and 1 sulphate ion were included in refinement. Except for the tips of a few solvent-exposed side chains, all protein atoms have clear electron density and refined to an average atomic temperature factor of 11 Ų. The estimated coordinates error is 0.17 Å. The substrate binding site is located at the interface of the two domains of the protein and contains 4 water molecules and the sulphate anion. One of these solvent molecules is found at hydrogen bond distance from S70 and E166. S70 and S130 are hydrogen bonded to K73 and K234, respectively. It was found that the E. coli TEM1 and Staphylococcus aureus PC1 β-lactamases crystal structures differ in the relative orientations of the two domains composing the enzymes, which result in a narrowed substrate binding cavity in the TEM1 enzyme. Local but significant differences in the vicinity of this site may explain the occurrence of TEM1 natural mutants with extended substrate specificities. © 1993 Wiley-Liss, Inc.     

Visualization of Drug-Nucleic Acid Interactions at Atomic Resolution. IX. Structures of Two N,N-Dimethylproflavine: 5-Iodocytidylyl (3′-5′) Guanosine Crystalline Complexes

Abstract

This paper describes two complexes containing N,N-dimethylproflavine and the dinucleoside monophosphate, 5-iodocytidylyl(3′-5′)guanosine (iodoCpG). The first complex is triclinic, space group PI, with unit cell dimensions a = 11.78 Å, b = 14.55 Å, c = 15.50 Å, a = 89.2°, β = 86.2°, γ = 96.4°. The second complex is monoclinic, space group P2₁, with a = 14.20 Å, b = 19.00 Å, c = 20.73 Å, β = 103.6°. Both structures have been solved to atomic resolution and refined by Fourier and least squares methods. The first structure has been refined anisotropically to a residual of 0.09 on 5,025 observed reflections using block diagonal least squares, while the second structure has been refined isotropically to a residual of 0.13 on 2,888 reflections with full matrix least squares. The asymmetric unit in both structures contains two dimethylproflavine molecules and two iodoCpG molecules; the first structure has 16 water molecules (a total of 134 non-hydrogen atoms), while the second structure has 18 water molecules (a total of 136 non-hydrogen atoms). Both structures demonstrate intercalation of dimethylproflavine between base-paired iodoCpG dimers. In addition, dimethylproflavine molecules stack on either side of the intercalated duplex, being related by a unit cell translation along b and a axes, respectively.

The basic structural feature of the sugar-phosphate chains accompanying dimethylproflavine intercalation in both structures is the mixed sugar puckering pattern: C3′ endo (3′-5′) C2′ endo. This same structural information is again demonstrated in the accompanying paper, which describes a complex containing dimethylproflavine with deoxyribo-CpG.

Similar information has already appeared for other “simple” intercalators such as ethidium, acridine orange, ellipticine, 9-aminoacridine, N-methyl-tetramethylphenanthrolinium and terpyridine platinum. “Complex” intercalators, however, such as proflavine and daunomycin, have given different structural information in model studies. We discuss the possible reasons for these differences in this paper and in the accompanying paper.     

Exploring the effect of confinement on water clusters in carbon nanotubes

Using armchair-type single-walled carbon nanotubes (SWCNTs) of different sizes as model compounds for lignite, the effect of water molecule confinement on the water-holding capacity of lignite pores was investigated. Results indicated that the water-holding capacity of pores with diameters of <10 nm was eight times larger than that of pores with diameters of 100 nm. The configuration of the cluster of water molecules in each SWCNT and the binding energy between each SWCNT and the water molecules within it were calculated by means of density functional theory using a hybrid functional: M06-2X/6-311+G**, 6-31G*. The results prove that the configurations of the water molecules in the SWCNTs are very different to their configuration in the unconfined state. In vacuum, the cluster of three water molecules adopted a trimer configuration, while they presented a linear configuration in the 6.78 Å SWCNT. Similarly, in vacuum, the cluster of five water molecules formed a five-membered ring, while they favored a linear configuration in the 6.78 Å SWCNT, a zigzag configuration in the 8.14 Å SWCNT, and a trimer?+?1?+?1 configuration (i.e., a trimer plus two isolated water molecules) in the 9.49 Å, 10.85 Å, and 13.75 Å SWCNTs. There was found to be a degree of competition between the coupling energy of the water molecules with the SWCNT and the hydrogen bonding among the water molecules. When the diameter of the SWCNT was >1 nm, the hydrogen bonding among the water molecules dominated, while the coupling energy of the water molecules with the SWCNT amounted to only 30–40% of the total interaction energy of the water molecules.

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Graphical Abstract Computed equilibrium structures of five water molecules confined in SWCNTs with diameters of 6.78 Å, 8.14 Å, 9.49 Å, 10.85 Å, and 13.75 Å, and in vacuum

     

Simple combined explicit/implicit water model

A simple combined water model (SCW model) for the calculation of the hydration free energy is presented. In the frame of the model a solute is placed in the centre of the spherical cavity with explicit water molecules, which are considered at the atomistic level. Rigid wall potential at the boundary of the cavity restricts the moving of the explicit water molecules. Water outside the sphere is considered as the conducting continuum (implicit part of the model). Simulation is performed in the frame of the NVT ensemble (constant number of particles, volume and temperature), density of water is fixed and equal to experimental value 1 g/cm³. The energy of electrostatic interaction of atomic point charges of the explicit water molecules with conducting continuum is calculated analytically by means of the image charges method. It provides high computational efficiency of the SCW model. For the averaging of the calculated thermodynamic and structural values over microstates of the system the thermodynamic integration method is used. The possible using of SCW for the docking problem is discussed.     

Modification of the erythrocyte membrane dielectric constant by alcohols

Summary Aliphatic alcohols are found to stimulate the transmembrane fluxes of a hydrophobic cation (tetraphenylarsonium, TPA) and anion (AN-12) 5–20 times in red blood cells. The results are analyzed using the Born-Parsegian equation (Parsegian, A., 1969,Nature (London) 221:844–846), together with the Clausius-Mossotti equation to calculate membrane dielectric energy barriers. Using established literature values of membrane thickness, native membrane dielectric constant, TPA ionic radius, and alcohol properties (partition coefficient, molar volume, dielectric constant), the TPA permeability data is predicted remarkably well by theory. If the radius of AN-12 is taken as 1.9 Å, its permeability in the presence of butanol is also described by our analysis. Further, the theory quantitatively accounts for the data of Gutknecht and Tosteson (Gutknecht, J., Tosteson, D.C., 1970,J. Gen. Physiol. 55:359–374) covering alcohol-induced conductivity changes of 3 orders of magnitude in artificial bilayers. Other explanations including perturbations of membrane fluidity, surface charge, membrane thickness, and dipole potential are discussed. However, the large magnitude of the stimulation, the more pronounced effect on smaller ions, and the acceleration of both anions and cations suggest membrane dielectric constant change as the primary basis of alcohol effects.     

Cation transport in nanopores

Using periodic boundary conditions and external electric potential field, we have simulated an ion current flow through a flexible nanopore using cations and an explicit extended simple point charge (SPC/E) water with molecular dynamics simulation. The simulation voltages range goes beyond the usual ionic channel measurements ( ± 1 V) and yields useful information about density profiles, current density distribution and current–voltage (I–V) characteristics.     

An X-ray diffraction study of poly-L-arginine hydrochloride

An x-ray study has been made of polyarginine hydrochloride to investigate whether, like polylysine hydrochloride, it can undergo conformational changes merely from variations in the degree of hydration. X-ray powder and fiber photographs of specimens containing up to about five molecules of water per arginine residue show features characteristic of α-helical structures including a 5.4-Å layer line and a meridional 1.5-Å reflection. Increasing the water content from ¹/₂ to 6¹/₂ molecules per residue causes the a axis of the hexagonal unit cell to increase from 14.4 Å to 15.8 Å, with no appreciable change in the 27.0 Å c axis. Removal of the last half molecule of water results in a very diffuse α pattern, but on rehydration the sharp pattern reappears. Specimens containing five to twenty water molecules per residue show quite a different pattern, the spacing of which do not vary appreciably with hydration. This pattern includes a meridional 3.4-Å reflection, a feature commonly shown by β structures, and indeed all the reflections can be satisfactorily indexed in terms of a monoclinic unit cell with a = 9.26 Å, b = 22.05 Å, c = 6.76 Å, and γ = 108.9°. These dimensions are shown by models to be compatible with a β pleated-sheet structure.     

Structure of a Novel Drug-Nucleic Acid Crystalline Complex: 1,10-Phenanthroline-Platinum(II) Ethylenediamine—5′-Phosphoryl-Thymidylyl(3′-5′) Deoxyadenosine

Abstract

1,10-Phenanthroline-platinum (II) ethylenediamine (PEPt) forms a 1:2 crystalline complex with 5′-phosphorylthymidylyl (3′-5′) deoxyadenosine (d-pTpA). Crystals are monoclinic, P2₁, with a - 10.204 Å, b =24.743 Å, c = 21.064 Å, β = 94.6°. The structure has been determined by Patterson and Fourier methods, and refined by least squares to a residual of 0.128 on 2,367 observed reflections.

PEPt molecules form sandwich-like stacks with adenine-thymine hydrogen-bonded pairs along the a axis. Intercalation in the classic sense is not observed in this structure. Instead, d-pTpA molecules form an open chain structure in which adenine-thymine residues hydrogen- bond together with the reversed Hoogsteen type base-pairing configuration. Deoxyadenosine residues exist in the syn conformation and are C3′ endo and C1′ exo. Thymidine residues are in the high anti conformation with C2′ endo puckers. The structure is heavily hydrated, forming a channel-like water network along the a axis. Other features of the structure are described.     

Channel‐like crystal structure of cinchoninium L‐O‐phosphoserine salt dihydrate

Studies on the interactions between L ‐O‐ phosphoserine, as one of the simplest fragments of membrane components, and the Cinchona alkaloid cinchonine, in the crystalline state were performed. Cinchoninium L ‐O‐phosposerine salt dihydrate (PhSerCin) crystallizes in a monoclinic crystal system, space group P2₁, with unit cell parameters: a = 8.45400(10) Å, b = 7.17100(10) Å, c = 20.7760(4) Å, α = 90°, β = 98.7830(10)°, γ = 90°, Z = 2. The asymmetric unit consists of the cinchoninium cation linked by hydrogen bonds to a phosphoserine anion and two water molecules. Intermolecular hydrogen bonds connecting phosphoserine anions via water molecules form chains extended along the b axis. Two such chains symmetrically related by twofold screw axis create a “channel.” On both sides of this channel cinchonine cations are attached by hydrogen bonds in which the atoms N1, O12, and water molecules participate. This arrangement mimics the system of bilayer biological membrane. Chirality 2010. © 2009 Wiley‐Liss, Inc.     

Simulation of protein diffusion: a sensitive probe of protein–solvent interactions

Aqueous solutions of Candida antarctica lipase B (CALB) were simulated considering three different water models (SPC/E, TIP3P, TIP4P) by a series of molecular dynamics (MD) simulations of three different box sizes (L = 9, 14, and 19 nm) to determine the diffusion coefficient, the water viscosity and the protein density. The protein–water systems were equilibrated for 500 ns, followed by 100 ns production runs which were analysed. The diffusional properties of CALB were characterized by the Stokes radius (R_S), which was derived from the diffusion coefficient and the viscosity. R_S was compared to the geometric radius (R_G) of CALB, which was derived from the protein density. R_S and R_G differed by 0.27 nm for SPC/E and by 0.40 and 0.39 nm for TIP3P and TIP4P, respectively, which characterizes the thickness of the diffusive hydration layer on the protein surface. The simulated hydration layer of CALB resulted in agreement with those experimentally determined for other seven different proteins of comparable size. By avoiding the most common pitfalls, protein diffusion can be reliably simulated: simulating different box sizes to account for the finite size effect, equilibrating the protein–water system sufficiently, and using the complete production run for the determination of the diffusion coefficient.     

Note: NAMD–LP: Filtering and Translating NAMD-generated Files

Abstract

We have empirically tested limits of the magnitude of multiple time steps in molecular dynamics simulations of aqueous systems, and the extent to which these offer a means to shorten computation time. Three different steps were employed, δ₀t for calculation of “bonded” forces, δ₁t for calculations of short-range (< 6 Å) non-bonded forces, and δ₂t for long-range (< 10 Å) non-bonded forces. Each longer step was a multiple of the shortest one. The leap-frog integration algorithm was used with SHAKE for restraint of all bond lengths and water molecules. For a system of SPC water molecules, calculation of short-range non-bonded forces could be done with a time step δ₁t = 10 fs, without appreciable change of the average temperature and energy, radial distribution function or diffusion coefficient. These properties were found to be insensitive to the inclusion of long-range non-bonded forces. A multiple-step protocol with δ₀t = 2, δ₁t = 4 and δ₂t = 16 fs has been compared with a single-step procedure with δt 2 fs for small polypeptides in water. The exploration of conformation space, with crossing of low energy barriers, was tested with the glycine dipeptide and was found to proceed at similar rates. Mean, hysteresis and statistical error of the free energy for changing alanine to α-amino butyric acid in the dipeptide, calculated by the slow-growth method, proved independent of the cutoff distance or exact protocol, within 1 kJ/mol. In conclusion, we recommend, instead of use of a single time step of 2 fs at a 10 Å cutoff, use of a time step δ_t = 4 fs for short-range nonbonded forces and a time step δ₂t = 16 fs for long-range nonbonded forces for a 60% reduction of computation time.     

Theoretical Study of the Conformations of Pustulan [(1⇒6)-β-D)-Glucan]

Abstract

The total potential energy including nonbondedJuntorsional and hydrogen bond contributions has been computed for pustulan, a (1?6) linked β-D-glucan polysaccharide, as a function of rotational angles φ, ψ, and ω The (φ, ψ, ω)-space contains many local minima and at least three distinct deep minima. Two minima at (φ, ψ, ω)=(25°,190°,gg) and (φ, ψ, ω)=(65°,150°,gg) of almost equal energies have helical parameters (n=5.2, A=1.0Å) and (n=3.2, h= 1.5Å), respectively. A third minimum at (φ, ψ, ω)=(40°,70°gt) leads to an extended zig-zag structure (n=2.2, h=2.2Å). Energy maps obtained for gentiobiose, the disaccharide of pustulan, also reveal many local minima and the small energy differences among them indicate that gentiobiose is extremely flexible. Gentiodextrins, a family of cyclic molecules of (l?6)-β-D- glucose residues, were also studied. Conformations free from steric hindrance were found for cyclic molecules with three to six glucose residues.     

Visualization of Drug-Nucleic Acid Interactions at Atomic Resolution. X. Structure of a N,N-Dimethylproflavine: Deoxycytidylyl(3′-S′)Deoxyguanosine Crystalline Complex

Abstract

N,N-dimethylproflavine forms a crystalline complex with deoxycytidylyl(3′-5′)deoxyguanosine (d-CpG), space group P2₁,2₁2, with a = 21.37 Å, b = 34.05 Å, c = 13.63 Å. The structure has been solved to atomic resolution and refined by Fourier and least squares methods to a residual of 0.18 on 2,032 observed reflections. The structure consists of two N,N- dimethylproflavine molecules, two deoxycytidylyl (3′-5′)deoxyguanosine molecules and 16 water molecules, a total of 128 nonhydrogen atoms. As with other structures of this type, N,N-dimethylproflavine molecules intercalate between base-paired d-CpG dimers. In addition, dimethylproflavine molecules stack on either side of the intercalated duplex, being related by a unit cell translation along the c axis.

Both sugar-phosphate chains demonstrate the mixed sugar puckering geometry: C3′ endo (3′-5′) C2′ endo. This same intercalative geometry has been seen in two other complexes containing N,N-dimethylproflavine and iodoCpG, described in the accompanying paper. Taken together, these studies indicate a common intercalative geometry present in both RNA- and DNA- model systems. Again, N,N-dimethylproflavine behaves as a simple intercalator, intercalating asymmetrically between guanine-cytosine base-pairs. The free amino- group on the intercalated dimethylproflavine molecule does not hydrogen bond directly to the phosphate oxygen. Other aspects of the structure will be presented.     

Molecular Mechanics Studies of Molybdenum Disulphide Catalysts Parameterisation of Molybdenum and Sulphur

Abstract

A method for the parameterisation of molybdenum disulphide is presented which reproduces the crystal structure accurately. The method involves calculating parameters such that there is no net force contribution from any individual term of the potential on any atom. Ideal bond lengths and bond angles are taken from the X-ray crystal structure; stretching and bending force constants are calculated from a combination of spectroscopic data and quantum mechanics calculations, whereby the energy function with bond length or bond angle is calculated and fitted with an harmonic potential. For the non-bonded Lennard-Jones parameters, the dispersion coefficient C was calculated by an interpolation of existing published parameters using a multiple regression and then the crystal energy was minimised with respect to the van der Waals radius r₀ using a fixed crystal fragment.

These parameters were tested for various models of the hexagonal and rhombohedral forms of MoS₂. RMS fits between structures minimised with molecular mechanics and experimental models ranged from 0.006 Å to 0.012 Å.     

Probing the effect of nitro groups in nitramine based energetic molecules: a DFT and charge density study

The structure, electron density distribution, energetic and electrostatic properties of simple nitramine based energetic TMA, DMNA, MDA and TNA molecules were determined using density functional theory (B3LYP) with the 6-311G^** and aug-cc-pVDZ basis sets coupled with Bader's theory of atoms in molecules. In the NO₂ group substituted molecules, the N–N bond distance increases with the increase of NO₂ groups, whereas in C–N bonds, this effect is relatively less, and the distances are almost equal. The topological analysis of electron density reveals that the electron density ρ_bcp(r) of C–N and N–N bonds are significantly decreasing with the increase of NO₂ groups in the nitramine molecules. The Laplacian of electron density ▽²ρ_bcp(r) of N–NO₂ bonds [DMNA: ? 16.7 eÅ^? 5, MDA: ? 12.8 eÅ^? 5 and TNA: ? 7.9 eÅ^? 5] of the molecules are relatively less negative, and the values also decrease with the increase of NO₂ groups; this implies that the charge concentration decreases with the increase of NO₂ groups, which leads to weakening the N–N bonds of the molecules. The isosurface of molecular electrostatic potential displays high electronegative regions around the NO₂ groups. The oxygen balance OB₁₀₀ of the molecules increases as the number of NO₂ group increases in the molecules, in which, the TNA molecule having maximum OB₁₀₀ value [+7.89]. The band gap, heat of detonation, bond dissociation energy and charge imbalance are predominantly depends on the number of NO₂ group present in the molecule. The charge imbalance parameter (ν) has been calculated for all molecules, which reveals that TNA is a highly sensitive molecule, the corresponding ν value is 0.047.     

Quantitative analysis of the binding of melittin to planar lipid bilayers allowing for the discrete-charge effect

The interaction of melittin with lecithin bilayers was studied using the resulting surface potentials at the bilayer/water interfaces to monitor the association. Melittin added to the aqueous phase binds strongly to the interface but remains localized on that side of the bilayer to which it is added. The analysis of the binding curves reveals the inadequacy of the Gouy-Chapman theory for the fixed-charge surface potential in describing the electrostatic potential experienced by the adsorbed molecules. Calculations based on the Stern equation, modified for a discrete charge distribution, give a good fit to the experimental data. The thermodynamic analysis revealed different binding energies, Δ$\text{G}$°, at 10 and 100 mM ionic strength (?7.85 and ?8.26 kcal/mol, respectively). Binding saturates at an area of 650 Ų per melittin molecule. A change in the surface dipole potential corresponding to ?1.1 debye/?_a ($\text{?}{}_{\mathrm{a}}\text{= dielectric constant of the adsorption region}$) had to be postulated. The Debye-Hückel length for a charge bound to the membrane/solution interface was found to be about one-third smaller than in bulk solution.