A method to determine dielectric constants in nonhomogeneous systems: application to biological membranes

Influences of membrane mimetic environments on membrane protein structures

The number of membrane protein structures in the Protein Data Bank is becoming significant and growing. Here, the transmembrane domain structures of the helical membrane proteins are evaluated to assess the influences of the membrane mimetic environments. Toward this goal, many of the biophysical properties of membranes are discussed and contrasted with those of the membrane mimetics commonly used for structure determination. Although the mimetic environments can perturb the protein structures to an extent that potentially gives rise to misinterpretation of functional mechanisms, there are also many structures that have a native-like appearance. From this assessment, an initial set of guidelines is proposed for distinguishing native-like from nonnative-like membrane protein structures. With experimental techniques for validation and computational methods for refinement and quality assessment and enhancement, there are good prospects for achieving native-like structures for these very important proteins.

Surface electrostatics of lipid bilayers by EPR of a pH-sensitive spin-labeled lipid

Many biophysical processes such as insertion of proteins into membranes and membrane fusion are governed by bilayer electrostatic potential. At the time of this writing, the arsenal of biophysical methods for such measurements is limited to a few techniques. Here we describe a, to our knowledge, new spin-probe electron paramagnetic resonance (EPR) approach for assessing the electrostatic surface potential of lipid bilayers that is based on a recently synthesized EPR probe (IMTSL-PTE) containing a reversibly ionizable nitroxide tag attached to the lipids' polar headgroup. EPR spectra of the probe directly report on its ionization state and, therefore, on electrostatic potential through changes in nitroxide magnetic parameters and the degree of rotational averaging. Further, the lipid nature of the probe provides its full integration into lipid bilayers. Tethering the nitroxide moiety directly to the lipid polar headgroup defines the location of the measured potential with respect to the lipid bilayer interface. Electrostatic surface potentials measured by EPR of IMTSL-PTE show a remarkable (within ±2%) agreement with the Gouy-Chapman theory for anionic DMPG bilayers in fluid (48°C) phase at low electrolyte concentration (50 mM) and in gel (17°C) phase at 150-mM electrolyte concentration. This agreement begins to diminish for DMPG vesicles in gel phase (17°C) upon varying electrolyte concentration and fluid phase bilayers formed from DMPG/DMPC and POPG/POPC mixtures. Possible reasons for such deviations, as well as the proper choice of an electrostatically neutral reference interface, have been discussed. Described EPR method is expected to be fully applicable to more-complex models of cellular membranes.

Models of membrane electrostatics

Formulas are derived for the electrostatic potential of a charge in or near a membrane modeled as one or more dielectric slabs lying between two semi-infinite dielectrics. One can use these formulas in Monte Carlo codes to compute the distribution of ions near cell membranes more accurately than by using Poisson-Boltzmann theory or its linearized version. Here I use them to discuss the electric field of a uniformly charged membrane, the image charges of an ion, the distribution of salt ions near a charged membrane, the energy of a zwitterion near a lipid slab, and the effect of including the phosphate head groups as thin layers of high electric permittivity.

Electrostatics in proteins and protein-ligand complexes

Accurate computational methods for predicting electrostatic energies are of major importance for our understanding of protein energetics in general for computer-aided drug design as well as for the design of novel biocatalysts and protein therapeutics. Electrostatic energies are of particular importance in such applications as virtual screening, drug design and protein-protein docking due to the high charge density of protein ligands and small-molecule drugs, and the frequent protonation state changes observed when drugs bind to their protein targets. Therefore, the development of a reliable and fast algorithm for the evaluation of electrostatic free energies, as an important contributor to the overall protein energy function, has been the focus for many scientists over the past three decades. In this review we describe the current state-of-the-art in modeling electrostatic effects in proteins and protein-ligand complexes. We focus mainly on the merits and drawbacks of the continuum methodology, and speculate on future directions in refining algorithms for calculating electrostatic energies in proteins using experimental data.

Monitoring membrane binding and insertion of peptides by two-color fluorescent label

Herein, we developed an approach for monitoring membrane binding and insertion of peptides using a fluorescent environment-sensitive label of the 3-hydroxyflavone family. For this purpose, we labeled the N-terminus of three synthetic peptides, melittin, magainin 2 and poly-l-lysine capable to interact with lipid membranes. Binding of these peptides to lipid vesicles induced a strong fluorescence increase, which enabled to quantify the peptide-membrane interaction. Moreover, the dual emission of the label in these peptides correlated well with the depth of its insertion measured by the parallax quenching method. Thus, in melittin and magainin 2, which show deep insertion of their N-terminus, the label presented a dual emission corresponding to a low polar environment, while the environment of the poly-l-lysine N-terminus was rather polar, consistent with its location close to the bilayer surface. Using spectral deconvolution to distinguish the non-hydrated label species from the hydrated ones and two photon fluorescence microscopy to determine the probe orientation in giant vesicles, we found that the non-hydrated species were vertically oriented in the bilayer and constituted the best indicators for evaluating the depth of the peptide N-terminus in membranes. Thus, this label constitutes an interesting new tool for monitoring membrane binding and insertion of peptides.

Influence of solubilizing environments on membrane protein structures

Membrane protein structures are stabilized by weak interactions and are influenced by additional interactions with the solubilizing environment. Structures of influenza virus A M2 protein, a proven drug target, have been determined in three different environments, thus providing a unique opportunity to assess environmental influences. Structures determined in detergents and detergent micelles can have notable differences from those determined in lipid bilayers. These differences make it imperative to validate membrane protein structures.

Modulation of the cytochrome P450 reductase redox potential by the phospholipid bilayer

Cytochrome P450 reductase (CPR) is a tethered membrane protein which transfers electrons from NADPH to microsomal P450s. We show that the lipid bilayer has a role in defining the redox potential of the CPR flavin domains. In order to quantitate the electrochemical behavior of this central redox protein, full-length CPR was incorporated into soluble nanometer scale discoidal membrane bilayers (nanodiscs), and potentials were measured using spectropotentiometry. The redox potentials of both FMN and FAD were found to shift to more positive values when in a membrane bilayer as compared to a solubilized version of the reductase. The potentials of the semiquinone/hydroquinone couple of both FMN and FAD are altered to a larger extent than the oxidized/semiquinone couple which is understood by a simple electrostatic model. When anionic lipids were used to change the membrane composition of the CPR-nanodisc, the redox potential of both flavins became more negative, favoring electron transfer from CPR to cytochrome P450.

Continuum theory of lipid bilayer electrostatics

In order to address the concerns about the applicability of the continuum theory of lipid bilayers, we generalize it by including a film with uniaxial dielectric properties representing the polar head groups of the lipid molecules. As a function of the in-plane dielectric constant κ|| of this film, we encounter a sequence of different phases. For low values of κ||, transmembrane pores have aqueous cores, ions are repelled by the bilayer, and the ion permeability of the bilayer is independent of the ion radius as in the existing theory. For increasing κ||, a threshold is reached--of the order of the dielectric constant of water--beyond which ions are attracted to the lipid bilayer by generic polarization attraction, transmembrane pores collapse, and the ion permeability becomes sensitively dependent on the ion radius, results that are more consistent with experimental and numerical studies of the interaction of ions with neutral lipid bilayers. At even higher values of κ||, the ion/pore complexes are predicted to condense in the form of extended arrays. The generalized continuum theory can be tested quantitatively by studies of the ion permeability as a function of salt concentration and co-surfactant concentration.

Backbone structure of a small helical integral membrane protein: A unique structural characterization

The structural characterization of small integral membrane proteins pose a significant challenge for structural biology because of the multitude of molecular interactions between the protein and its heterogeneous environment. Here, the three-dimensional backbone structure of Rv1761c from Mycobacterium tuberculosis has been characterized using solution NMR spectroscopy and dodecylphosphocholine (DPC) micelles as a membrane mimetic environment. This 127 residue single transmembrane helix protein has a significant (10 kDa) C-terminal extramembranous domain. Five hundred and ninety distance, backbone dihedral, and orientational restraints were employed resulting in a 1.16 A rmsd backbone structure with a transmembrane domain defined at 0.40 A. The structure determination approach utilized residual dipolar coupling orientation data from partially aligned samples, long-range paramagnetic relaxation enhancement derived distances, and dihedral restraints from chemical shift indices to determine the global fold. This structural model of Rv1761c displays some influences by the membrane mimetic illustrating that the structure of these membrane proteins is dictated by a combination of the amino acid sequence and the protein's environment. These results demonstrate both the efficacy of the structural approach and the necessity to consider the biophysical properties of membrane mimetics when interpreting structural data of integral membrane proteins and, in particular, small integral membrane proteins.

Energy landscape of the trpzip2 peptide

Replica exchange simulations are used to study the energy landscape of trpzip2, a model beta-hairpin system, using the AMBER99sb force field and explicit solvent. The total simulation time is 300 ns per replica (approximately 10 mus total). The trp side chains are observed to adopt multiple packing arrangements with a freezing temperature below 273 K in the simulated system. The secondary structure and native hydrogen bonds melt out cooperatively around 273 K. The residual beta-strand structure and antiparallel bonding persist at high temperature. These results provide a model for the three apparent melting transitions observed experimentally in this system. The dominant folding mechanism of trpzip2 in this model appears to be zipping, which is consistent with recent measurements on similar hairpins. Structures for which the turn is native-like and the termini are non-native-like collectively form a metastable intermediate. Most of the stabilizing enthalpy is gained after the formation of the turn. Equilibrium thermodynamic quantities are compared against experiment. Although the AMBER99sb force field reproduces the native structure with good fidelity, the stability of the native state is significantly underpredicted with a melting temperature near 273 K, and the relative heat capacity is only about one tenth of its experimental value.

Charge equilibration force fields for lipid environments: applications to fully hydrated DPPC bilayers and DMPC-embedded gramicidin A

Polarizable force fields for lipid and solvent environments are used for molecular dynamics simulations of a fully hydrated dipalmitoylphosphatidylcholine (DPPC) bilayer and gramicidin A (gA) dimer embedded in a dimyristoylphosphatidylcholine (DMPC) bilayer. The lipid bilayer is modeled using the CHARMM charge equilibration (CHEQ) polarizable force field for lipids and the TIP4P-FQ force field to represent solvent. For the DPPC bilayer system, results are compared to the same system simulated using the nonpolarizable CHARMM27r (C27r) force field and TIP3P water. Calculated atomic and electron density profiles, head group orientations as measured by the phosphorus-nitrogen vector orientation, and deuterium order parameters are found to be consistent with previous simulations and with experiment. The CHEQ model exhibits greater water penetration into the bilayer interior, as demonstrated by the potential of mean force calculated from the water density profile. This is a result of the variation of the water molecular dipole from 2.55 D in the bulk to 1.88 D in the interior. We discuss this finding in the context of previous studies (both simulation and experiment) that have investigated the extent of penetration of water into DPPC bilayers. We also discuss the effects of including explicit polarization on the water dipole moment variation as a function of distance from the bilayer. We show distributions of atomic charges over the course of the simulation since the CHEQ model allows the charges to fluctuate. We have calculated the interfacial dipole potential, which the CHEQ model predicts to be 0.95 V compared to 0.86 V as predicted by the C27r model. We also discuss dielectric permittivity profiles and the differences arising between the two models. We obtain bulk values of 72.77 for the CHEQ model (TIP4P-FQ water) and 91.22 for C27r (TIP3P), and values approaching unity in the membrane interior. Finally, we present results of simulations of gA embedded in a DMPC bilayer using the CHEQ model and discuss structural properties.

Interfacial structure, thermodynamics, and electrostatics of aqueous methanol solutions via molecular dynamics simulations using charge equilibration models

We present results from molecular dynamics simulations of methanol-water solutions using charge equilibration force fields to explicitly account for nonadditive electronic interaction contributions to the potential energy. We study solutions across the concentration range from 0.1 to 0.9 methanol mole fraction. At dilute concentrations, methanol density is enhanced at the liquid-vapor interface, consistent with previous molecular dynamics and experimental studies. Interfacial thickness exhibits a monotonic increase with increasing methanol mole fraction, while surface tensions display monotonic decrease with methanol concentration, in qualitative agreement with experimental data and previous molecular dynamics predictions using polarizable force fields. In terms of interfacial structure, in keeping with predictions of traditional force fields, there is a unique preferential orientation of methanol molecules at the interface. Moreover, there is a free energetic preference for methanol molecules at the interface as evidenced by potential of mean force calculations. The pmf calculations suggest an interfacial state with 0.8 kcal/mol stability relative to the bulk, again in qualitative agreement with previous simulation and experimental studies. Interfacial potentials based on double integration of total charge density range from -610 to -330 mV over the dilute to concentrated regimes, respectively. The preponderance of methanol at the interface at all mole fractions gives rise to a dominant methanol contribution to the total interfacial potential. Interestingly, there is a transition of the water surface potential contribution from negative to positive upon the transition from methanol mole fraction of 0.1 to 0.2. The dipole and quadrupole contributions to the water component of the total interfacial potential are effectively of equal magnitude and opposite sign, thus cancelling one another. We compute the in-plane component of the dielectric permittivity along the interface normal. We observe a nonmonotonic behavior of the methanol in-plane dielectric permittivity that tracks the methanol density profiles at low methanol mole fractions. At higher methanol mole fractions, the total in-plane permittivity is dominated by methanol and displays a monotonic decrease from bulk to vapor. We finally probe the nature of hydration of water in the bulk versus interfacial regions for methanol mole fractions of 0.1 and 0.2. In the bulk, methanol perturbs water structure so as to give rise to water hydrogen bond excesses. Moreover, we observe negative hydrogen bond excess in the vicinity of the alkyl group, as reported by Zhong et al. for bulk ethanol-water solutions using charge equilibration force fields, and positive excess in regions hydrogen bonding to nearest-neighbor methanol molecules. Within the interfacial region, water and methanol density reduction lead to concomitant water hydrogen bond deficiencies (negative hydrogen-bond excess).

Nanoscopic description of biomembrane electrostatics: results of molecular dynamics simulations and fluorescence probing

Electrostatic fields generated on and inside biological membranes are recognized to play a fundamental role in key processes of cell functioning. Their understanding requires an adequate description on the level of elementary charges and the reconstruction of electrostatic potentials by integration over all elementary interactions. Out of all the available research tools, only molecular dynamics simulations are capable of this, extending from the atomic to the mesoscopic level of description on the required time and space scale. A complementary approach is that offered by molecular probe methods, with the application of electrochromic dyes. Highly sensitive to intermolecular interactions, they generate integrated signals arising from electric fields produced by elementary charges at the sites of their location. This review is an attempt to provide a critical analysis of these two approaches and their present and potential applications. The results obtained by both methods are consistent in that they both show an extremely complex profile of the electric field in the membrane. The nanoscopic view, with two-dimensional averaging over the bilayer plane and formal separation of the electrostatic potential into surface (Psi(s)), dipole (Psi(d)) and transmembrane (Psi(t)) potentials, is constructive in the analysis of different functional properties of membranes.

Molecular dynamics simulations of a DMPC bilayer using nonadditive interaction models

We present a polarizable force field based on the charge-equilibration formalism for molecular dynamics simulations of phospholipid bilayers. We discuss refinement of headgroup dihedral potential parameters to reproduce ab initio conformational energies of dimethylphosphate calculated at the MP2/cc-pVTZ level of theory. We also address the refinement of electrostatic and Lennard-Jones (van der Waals) parameters to reproduce ab initio polarizabilities and water interaction energies of dimethylphosphate and tetramethylammonium. We present results of molecular dynamics simulations of a solvated dimyristoylphosphatidylcholine bilayer using this polarizable force field as well as the nonpolarizable, fixed-charge CHARMM27 and CHARMM27r force fields for comparison. Calculated atomic and electron-density profiles, deuterium order parameters, and headgroup orientations are found to be consistent with previous simulations and with experiment. Polarizable interaction models for solvent and lipid exhibit greater water penetration into the lipid interior; this is due to the variation of water molecular dipole moment from a bulk value of 2.6 Debye to a value of 1.9 Debye in the membrane interior. The reduction in the electrostatic component of the desolvation free-energy penalty allows for greater water density. The surface dipole potential predicted by the polarizable model is 0.95 V compared to the value of 0.8 V based on nonpolarizable force-field calculations. Effects of inclusion of explicit polarization are discussed in relation to water dipole moment and varying charge distributions. Dielectric permittivity profiles for polarizable and nonpolarizable interactions exhibit subtle differences arising from the nature of the individual component parameterizations; for the polarizable force field, we obtain a bulk dielectric permittivity of 79, whereas the nonpolarizable force field plateaus at 97 (the value for pure TIP3P water). In the membrane interior, both models predict unit permittivities, with the polarizable models contributing from one to two more units due to the optical dielectric (high-frequency dipole fluctuations). This contribution is a step toward the continuing development of a CHARMM (Chemistry at Harvard Molecular Mechanics) polarizable force field for simulations of biomacromolecular systems.

Test of the Gouy-Chapman theory for a charged lipid membrane against explicit-solvent molecular dynamics simulations

A wealth of experimental data has verified the applicability of the Gouy-Chapman (GC) theory to charged lipid membranes. Surprisingly, a validation of GC by molecular dynamics (MD) simulations has been elusive. Here, we report a test of GC against extensive MD simulations of an anionic lipid bilayer solvated by water at different concentrations of NaCl or KCl. We demonstrate that the ion distributions from the simulations agree remarkably well with GC predictions when information on the adsorption of counterions to the bilayer is incorporated.