Electrostatic field effects on membrane domain segregation and on lateral diffusion

Natural membranes are organized structures of neutral and charged molecules bearing dipole moments which generate local non-homogeneous electric fields. When subjected to such fields, the molecules experience net forces that can modify the lipid and protein organization, thus modulating cell activities and influencing (or even dominating) the biological functions. The energetics of electrostatic interactions in membranes is a long-range effect which can vary over distance within r⁻¹ to r⁻³. In the case of a dipole interacting with a plane of dipoles, e.g. a protein interacting with a lipid domain, the interaction is stronger than two punctual dipoles and depends on the size of the domain. In this article, we review several contributions on how electrostatic interactions in the membrane plane can modulate the phase behavior, surface topography and mechanical properties in monolayers and bilayers.     

An evaluation of Poisson-Boltzmann electrostatic free energy calculations through comparison with experimental mutagenesis data

For systems involving highly and oppositely charged proteins, electrostatic forces dominate association and contribute to biomolecular complex stability. Using experimental or theoretical alanine-scanning mutagenesis, it is possible to elucidate the contribution of individual ionizable amino acids to protein association. We evaluated our electrostatic free energy calculations by comparing calculated and experimental data for alanine mutants of five protein complexes. We calculated Poisson-Boltzmann electrostatic free energies based on a thermodynamic cycle, which incorporates association in a reference (Coulombic) and solvated (solution) state, as well as solvation effects. We observe that Coulombic and solvation free energy values correlate with experimental data in highly and oppositely charged systems, but not in systems comprised of similarly charged proteins. We also observe that correlation between solution and experimental free energies is dependent on dielectric coefficient selection for the protein interior. Free energy correlations improve as protein dielectric coefficient increases, suggesting that the protein interior experiences moderate dielectric screening, despite being shielded from solvent. We propose that higher dielectric coefficients may be necessary to more accurately predict protein-protein association. Additionally, our data suggest that Coulombic potential calculations alone may be sufficient to predict relative binding of protein mutants.     

On the calculation of electrostatic interactions in proteins

In this paper we present a classical treatment of electrostatic interactions in proteins. The protein is treated as a region of low dielectric constant with spherical charges embedded within it, surrounded by an aqueous solvent of high dielectric constant, which may contain a simple electrolyte. The complete analysis includes the effects of solvent screening, polarization forces, and self energies, which are related to solvation energies. Formulae, and sample calculations of forces and energies, are given for the special case of a spherical protein. Our analysis and model calculations point out that any consistent treatment of electrostatic interactions in proteins should account for the following. Solvent polarization is an important factor in the calculation of pairwise electrostatic interactions. Solvent polarization substantially affects both electrostatic energies and forces acting upon charges. No simple expression for the effective dielectric constant, Deff, can generally be valid, since Deff is a sensitive function of position. Solvent screening of pairwise interactions involving dipolar groups is less effective than the screening of charges. In fact for many interactions involving dipoles, solvent screening can be essentially ignored. The self energy of charges makes a large contribution to the total electrostatic energy of a protein. This must be compensated by specific interactions with other groups in the protein. Strategies for applying our analysis to proteins whose structures are known are discussed.     

The structure and dipole moment of globular proteins in solution and crystalline states: use of NMR and X-ray databases for the numerical calculation of dipole moment

The large dipole moment of globular proteins has been well known because of the detailed studies using dielectric relaxation and electro-optical methods. The search for the origin of these dipolemoments, however, must be based on the detailed knowledge on protein structure with atomic resolutions. At present, we have two sources of information on the structure of protein molecules: (1) x-ray databases obtained in crystalline state; (2) NMR databases obtained in solution state. While x-ray databases consist of only one model, NMR databases, because of the fluctuation of the protein folding in solution, consist of a number of models, thus enabling the computation of dipole moment repeated for all these models. The aim of this work, using these databases, is the detailed investigation on the interdependence between the structure and dipole moment of protein molecules. The dipole moment of protein molecules has roughly two components: one dipole moment is due to surface charges and the other, core dipole moment, is due to polar groups such as N--H and C==O bonds. The computation of surface charge dipole moment consists of two steps: (A) calculation of the pK shifts of charged groups for electrostatic interactions and (B) calculation of the dipole moment using the pK corrected for electrostatic shifts. The dipole moments of several proteins were computed using both NMR and x-ray databases. The dipole moments of these two sets of calculations are, with a few exceptions, in good agreement with one another and also with measured dipole moments.     

The dipole moment of the electron carrier adrenodoxin is not critical for redox partner interaction and electron transfer

Dipole moments of proteins arise from helical dipoles, hydrogen bond networks and charged groups at the protein surface. High protein dipole moments were suggested to contribute to the electrostatic steering between redox partners in electron transport chains of respiration, photosynthesis and steroid biosynthesis, although so far experimental evidence for this hypothesis was missing. In order to probe this assumption, we changed the dipole moment of the electron transfer protein adrenodoxin and investigated the influence of this on protein-protein interactions and electron transfer. In bovine adrenodoxin, the [2Fe-2S] ferredoxin of the adrenal glands, a dipole moment of 803 Debye was calculated for a full-length adrenodoxin model based on the Adx(4-108) and the wild type adrenodoxin crystal structures. Large distances and asymmetric distribution of the charged residues in the molecule mainly determine the observed high value. In order to analyse the influence of the resulting inhomogeneous electric field on the biological function of this electron carrier the molecular dipole moment was systematically changed. Five recombinant adrenodoxin mutants with successively reduced dipole moment (from 600 to 200 Debye) were analysed for their redox properties, their binding affinities to the redox partner proteins and for their function during electron transfer-dependent steroid hydroxylation. None of the mutants, not even the quadruple mutant K6E/K22Q/K24Q/K98E with a dipole moment reduced by about 70% showed significant changes in the protein function as compared with the unmodified adrenodoxin demonstrating that neither the formation of the transient complex nor the biological activity of the electron transfer chain of the endocrine glands was affected. This is the first experimental evidence that the high dipole moment observed in electron transfer proteins is not involved in electrostatic steering among the proteins in the redox chain.     

Reproduction of correct electrostatic field by charges and dipoles on a closed surface

A general algorithm based on the Green function theorem has been developed to correctly reproduce electrostatic fields inside a closed space by point charges and point dipoles on the surface surrounding the space. For actual computations, limited numbers of point charges, including charge pairs replacing point dipoles, are enough to approximate the inner fields. As examples, reaction fields were reproduced by the current surface charges and dipoles for the dielectric models, where a monopole, dipole, or quadrupole was individually set at the center in a vacuum sphere surrounded by high dielectric continuum. The potentials due to those reaction fields agree well with the analytical ones. As an application of this method to the analysis of the electronic structure of the active site of a protein, a combination of the continuum dielectric model and ab initio molecular orbital calculation was carried out. Other applications to molecular dynamics and quantum mechanical calculations are also discussed.     

Calculation of pigment transition energies in the FMO protein

The Fenna-Matthews-Olson (FMO) protein of green sulfur bacteria represents an important model protein for the study of elementary pigment-protein couplings. We have previously used a simple approach [Adolphs and Renger (2006) Biophys J 91:2778-2797] to study the shift in local transition energies (site energies) of the FMO protein of Prosthecochloris aestuarii by charged amino acid residues, assuming a standard protonation pattern of the titratable groups. Recently, we have found strong evidence that besides the charged amino acids also the neutral charge density of the protein is important, by applying a combined quantum chemical/electrostatic approach [Müh et al. (2007) Proc Natl Acad Sci USA, in press]. Here, we extract the essential parts from this sophisticated method to obtain a relatively simple method again. It is shown that the main contribution to the site energy shifts is due to charge density coupling (CDC) between the pigments and their pigment, protein and water surroundings and that polarization effects for qualitative considerations can be approximated by screening the Coulomb coupling by an effective dielectric constant.     

Calculation and measurement of the dipole moment of small proteins: Use of protein data base

The dipole moments of small protein molecules were determined experimentally in order to validate the calculated dipole moments by previous investigators. We found that the agreements are satisfactory for some proteins. There are, however, many proteins for which the agreement is less than satisfactory. In order to find the cause of the disagreement, the dipole moments of these proteins were recalculated using the Brookhaven Protein Data Bank. We calculated the dipole moment due to fixed surface charges and the bond moments of all the carbonyl groups in main chain and side chains. The calculation consists of the mean moments and their mean square fluctuations. In addition, we investigated the effect of electrostatic interactions between charged sites for several proteins. These results show that incorporation of the interactions does not affect substantially the calculated dipole moments. The rms fluctuation of the dipole moment is found to be small but not negligible. In conclusion, recalculated dipole moments are in good agreement with the observed values. © 1993 John Wiley & Sons, Inc.     

Determination of the dipole moments of RNAse SA wild type and a basic mutant

In this study, we report the effects of acidic to basic residue point mutations (5K) on the dipole moment of RNAse SA at different pHs. Dipole moments were determined by measuring solution capacitance of the wild type (WT) and the 5K mutant with an impedance analyzer. The dipole moments were then (1) compared with theoretically calculated dipole moments, (2) analyzed to determine the effect of the point mutations, and (3) analyzed for their contribution to overall protein-protein interactions (PPI) in solution as quantitated by experimentally derived second virial coefficients. We determined that experimental and calculated dipoles were in reasonable agreement. Differences are likely due to local motions of residue side chains, which are not accounted for by the calculated dipole. We observed that the proteins' dipole moments increase as the pH is shifted further from their isoelectric points and that the wild-type dipole moments were greater than those of the 5K. This is likely due to an increase in the proportion of one charge (either negative or positive) relative to the other. A greater charge disparity corresponded to a larger dipole moment. Finally, the larger dipole moments of the WT resulted in greater attractive overall PPI for that protein as compared to the 5K.     

Evaluation of the influence of the internal aqueous solvent structure on electrostatic interactions at the protein-solvent interface by nonlocal continuum electrostatic approach

The dielectric properties of the polar solvent on the protein-solvent interface at small intercharge distances are still poorly explored. To deconvolute this problem and to evaluate the pair-wise electrostatic interaction (PEI) energies of the point charges located at the protein-solvent interface we used a nonlocal (NL) electrostatic approach along with a static NL dielectric response function of water. The influence of the aqueous solvent microstructure (determined by a strong nonelectrostatic correlation effect between water dipoles within the orientational Debye polarization mode) on electrostatic interactions at the interface was studied in our work. It was shown that the PEI energies can be significantly higher than the energies evaluated by the classical (local) consideration, treating water molecules as belonging to the bulk solvent with a high dielectric constant. Our analysis points to the existence of a rather extended, effective low-dielectric interfacial water shell on the protein surface. The main dielectric properties of this shell (effective thickness together with distance- and orientation-dependent dielectric permittivity function) were evaluated. The dramatic role of this shell was demonstrated when estimating the protein association rate constants.     

Dielectric properties of hemoglobin and myoglobin. II. Dipole moment of sperm whale myoglobin

This paper is concerned with the molecular origin of the dipole moment of sperm whale myoglobin as it can be calculated from the dielectric dispersion at 1 Mcps on the basis of a mechanism of orientational polarization. It was possible to compare the dielectric increment of native myoglobin and its change during the reaction with bromo acetate with dipole moments calculated according to the known coordinates of the charged groups of the molecule. The agreement between the two shows that in myoglobin only the permanent dipole moment due to these charged groups is important, and that contributions from other possible sources remain within the limits of experimental error.     

Effects of aligned α‐helix peptide dipoles on experimental electrostatic potentials

Aligned protein α‐helix dipoles have been implicated in protein function and structure. The recent breakthroughs in high‐resolution electron microscopy (EM) of macromolecules makes it possible to explore fundamental aspects of structural biology at the detailed molecular level. The electrostatic potential (ESP) generated by aligned protein α‐helix dipole should be observable in high‐resolution EM maps despite the fact that the effect may be partially screened by induced electric fields. Here, we show that aligned backbone dipoles in protein α‐helices account for long‐range features in the protein ESP functions. Our results are consistent with experimental EM maps and density functional theory calculations, including direct Fourier summation for proper calculation of the ESP due to the nonlocal nature of the ESP function from aligned dipoles and other partial atomic charges.     

Measurement and computation of the dipole moment of globular proteins III: Chymotrypsin

The dipole moments of alpha- and gamma-chymotrypsin are determined experimentally using the dielectric constant measuring method. The values thus obtained are compared with the results of the electric dichroism measurements for alpha-chymotrypsins by other investigators. The agreement is reasonably good, if not satisfactory. The cause of difference appears to be due to the difficulty of finding the correct internal field. The interaction between two neighboring dipoles is found to be a minor component of the local fields. Secondly, the dipole moment of alpha-chymotrypsin was computed using Protein Data Bases. The dipole moment of proteins consists of two major components, the moment due to fixed surface charges and the core moment due to polar chemical bonds. The method of calculation was described in detail in previous papers. The pK shifts of polar side chains were calculated using the methods of Tanford et al. and its modification by Warshel et al. The agreement between measured and calculated dipole moments is satisfactory.     

Mapping the electrostatic potential within the ribosomal exit tunnel

Electrostatic potentials influence interactions among proteins and nucleic acids, the orientation of dipoles and quadrupoles, and the distribution of mobile charges. Consequently, electrostatic potentials can modulate macromolecular folding and conformational stability, as well as rates of catalysis and substrate binding. The ribosomal exit tunnel, along with its resident nascent peptide, is no less susceptible to these consequences. Yet, the electrostatics inside the tunnel have never been measured. Here we map both the electrostatic potential and accessibilities along the length of the tunnel and determine the electrostatic consequences of introducing a charged amino acid into the nascent peptide. To do this we developed novel probes and strategies. Our findings provide new insights regarding the dielectric of the tunnel and the dynamics of its local electric fields.     

The activation of the nicotinic acetylcholine receptor by the transmitter

Experimental evidence has been published from isolated guinea pig muscle in vitro, and from direct ligand binding to receptors from T. californica, indicating that two agonist ions react with the nicotinic receptor by exchanging for one magnesium ion. It is the basis of the ion exchange receptor pair model, in which two acetylcholine ions exchange for one magnesium ion in contact with and between a pair of negatively charged receptor groups about 4 A apart. In the resting state the electrostatic attraction between the negatively charged receptor groups and the Mg2+ ion exerts a binding force. This binding force is opposed by the quantum mechanical repulsions of the electron clouds of the charged groups and ions in contact, together with the mutual repulsion of the pair of receptor oxyanions. When the Mg2+ ion is replaced by two acetylcholine ions the quaternary heads of the latter are positioned so that they form two mutually repelling ACh+ receptor group dipoles. As the Mg2+ ion leaves, its rehydration energy contributes to the sum of the electron cloud repulsions and the ACh+ receptor group dipole repulsions, causing the receptor groups to be forced apart activating the receptor macromolecule. The subsequent decrease in ACh+ concentration results in the reestablishment of the resting state. The coulombic electrostatic energy, the Born repulsion energy, the London attraction energy and the oxyanion ACh+ dipole repulsion energies have been calculated and shown to be consistent with the model. The displacement of the Mg2+ by two ACh+ ions makes several hundred kcals of energy available for receptor group separation and receptor activation.     

Control of the redox potential of cytochrome c and microscopic dielectric effects in proteins

X-ray structural information provides the opportunity to explore quantitatively the relation between the microenvironments of heme proteins and their redox potentials. This can be done by considering the protein as a "solvent" for its redox center and calculating the difference between the electrostatic energy of the reduced and oxidized heme. Such calculations are presented here, applying the protein dipoles-Langevin dipoles (PDLD) model to cytochrome c. The calculations focus on an evaluation of the difference between the redox potentials of cytochrome c and the octapeptide-methionine complex formed by hydrolysis of cytochrome c. The corresponding difference (approximately 7 kcal/mol) is accounted for by the PDLD calculations. It is found that the protein provides basically a low dielectric environment for the heme, which destabilizes the oxidized heme (relative to its energy in water). The effect of the charged propionic acids on the heme is examined in a preliminary way. It is found that the negative charges of these groups are in a hydrophilic rather than a hydrophobic environment and that the protein-water system provides an effective high dielectric constant for their interaction with the heme. The dual nature of the dielectric effect of the cytochrome (a low dielectric constant for the self-energy of the heme and a high dielectric constant for charge-charge interactions) is discussed. The findings of this work are consistent with the difference between the folding energies of the reduced and oxidized cytochrome c.     

Effective activation energy of enzymatic and nonenzymatic reactions. Evolution-imposed requirements to enzyme structure

The difference of the activation energies in a protein globule and water has been treated in terms of the theory of an elementary act of charge transfer reaction with regards to the energy spent on the transfer of charged reactants from water into the protein. The protein was treated as a structureless dielectric with a given optical and static dielectric constants surrounded by the aqueous phase. Reactions of different types (charge exchange between reactants, charge separation, neutralization, etc.) have been analyzed both under prevalence of purely electrostatic effects and under considerable nonelectrostatic contributions to the activation energies. It is shown that for all one-electron and most multi-electron reactions involving two reaction centres the energy spent for charged reactant transfer from water into protein is greater than the concomitant activation energy gain. The same effect takes place in a number of cases for multi-centre processes as well. To overcome the entropy hindrances, the reactants and catalysts must combine into multiparticle complexes, i.e. form microscopic regions of low dielectric constant. This results in increased effective activation energy as compared to reactions in water. It has been hypothesized that in order to make up for this loss the evolution has selected the proteins which are characterized by considerable intraglobular permanent electric fields. The presence in proteins of high concentrations of strongly polar peptide groups renders them advantageous in this respect over other polymers that are less polar.     

The role of proteins in a dipole model for steady-state ionic transport through biological membranes.

The steady-state current-voltage characteristics of biological membranes are analyzed for means of an application of the electrodiffusion theory to the passage of ions through "dielectric pores", with orientable dipoles at the pore-water interfaces. A detailed evaluation of the electrostatic potential barrier shows, indeed, that the ions have practically no chance to penetrate into the phospholipid bilayer, but that they can cross the membrane through local protein inclusions, of high dielectric constant. A "gating mechanism" can be provided, moreover, by a change of the potential barrier, resulting from a dipole reorientation at the pore-water interface. Dipole-dipole interactions are opposed to the orienting effect of an applied field, but they can be neglected when the separation between the dipoles exceeds a certain critical value. The high polarizability of the pore material leads to an amplification of the effect of an applied field on the orientable dipoles. It is therefore possible to achieve a satisfactory agreement with the experimental results of Gilbert and Ehrenstein (Biophys. J., 9: 447, 1969) for the squid axon, and, in particular, to account for the width of the negative resistance regions with a relatively small value for the length of the orientable dipoles.     

Calculation of the electric potential in the active site cleft due to alpha-helix dipoles

A macroscopic dielectric model has been used to set up the electrostatic equation for the protein-solvent system. A numerical method of solution has been applied, enabling calculation of the electric potential outside a protein due to the charges within the protein. The glycolytic enzyme phosphoglycerate mutase, which is an α/β protein binding negatively charged substrates, has been studied. Modelling the helix dipoles with positive and negative charges shows that the α-helical structure could stabilize negatively charged substrates in the active site cleft of an enzyme with an energy of a few kT.     

Protein stabilization by salt bridges: concepts, experimental approaches and clarification of some misunderstandings

Salt bridges in proteins are bonds between oppositely charged residues that are sufficiently close to each other to experience electrostatic attraction. They contribute to protein structure and to the specificity of interaction of proteins with other biomolecules, but in doing so they need not necessarily increase a protein's free energy of unfolding. The net electrostatic free energy of a salt bridge can be partitioned into three components: charge-charge interactions, interactions of charges with permanent dipoles, and desolvation of charges. Energetically favorable Coulombic charge-charge interaction is opposed by often unfavorable desolvation of interacting charges. As a consequence, salt bridges may destabilize the structure of the folded protein. There are two ways to estimate the free energy contribution of salt bridges by experiment: the pK(a) approach and the mutation approach. In the pK(a) approach, the contribution of charges to the free energy of unfolding of a protein is obtained from the change of pK(a) of ionizable groups caused by altered electrostatic interactions upon folding of the protein. The pK(a) approach provides the relative free energy gained or lost when ionizable groups are being charged. In the mutation approach, the coupling free energy between interacting charges is obtained from a double mutant cycle. The coupling free energy is an indirect and approximate measure of the free energy of charge-charge interaction. Neither the pK(a) approach nor the mutation approach can provide the net free energy of a salt bridge. Currently, this is obtained only by computational methods which, however, are often prone to large uncertainties due to simplifying assumptions and insufficient structural information on which calculations are based. This state of affairs makes the precise thermodynamic quantification of salt bridge energies very difficult. This review is focused on concepts and on the assessment of experimental methods and does not cover the vast literature.