The modelling of electrostatic interactions in the function of globular proteins

Formulation and characterization of liposomes containing drug absorption enhancers for optimized anti-HIV and antimalarial drug delivery

Most of the current clinically used anti-HIV and antimalarial drugs have low bioavailability, either due to poor solubility and permeability, rapid clearance from anatomical reservoirs and poor retention at their site of action (e.g. due to the p-glycoprotein efflux system), and extreme first-pass metabolism (e.g. by the cytochrome P450 enzymes). Hence, new approaches such as the incorporation of drug absorption enhancers (DAEs) (also referred to as bioenhancers) into dosage forms, and exploration of nanocarriers such as liposomes as novel dosage forms, are needed and may provide a viable means that could improve the bioavailability of both anti-HIV and antimalarial drugs. Liposomes loaded with efavirenz or mefloquine in combination with drug absorption enhancers, as well as placebo dosage forms, were prepared using a thin-lipid film hydration technique and characterized for their particle size and zeta potentials, entrapment efficiency, in vitro drug release, and in vitro drug permeability. Liposomes were further investigated for their biocompatibility (safety) using H-4-II-E liver cells in vitro. Drug-loaded liposomes prepared using l-α-phospatidylcholine, dioleoyl (DOPC) and cholesterol (CHOL) (1:1 mol/mol) as well as liposomes made of 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC), CHOL, and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) (4:6:26 mol/mol/mol) exhibited the best results in terms of their entrapment efficiency, particle size, zeta potential, in vitro drug release, and permeability. DSPC:CHOL:DPPC liposomes released EFV-based formulations better than DPPC:CHOL liposomes for immediate release behaviour. DOPC:CHOL liposomes produced a controlled release and more drug was released in the presence of DAEs for both EFV (0.4-fold higher) and MQ-based (sevenfold higher) formulations in the first 2 h. However, these liposomes were less biocompatible (< 50% cell viability) with liver cells. DOPC:CHOL and DSPC:CHOL:DPPC liposomes could provide a useful nano-formulation platform, which could ensure drug loading, followed by sustained release of both anti-HIV and antimalaria drugs.

Influential Mutations in the SMAD4 Trimer Complex Can Be Detected from Disruptions of Electrostatic Complementarity

This article examines three techniques for rapidly assessing the electrostatic contribution of individual amino acids to the stability of protein-protein complexes. Whereas the energetic minimization of modeled oligomers may yield more accurate complexes, we examined the possibility that simple modeling may be sufficient to identify amino acids that add to or detract from electrostatic complementarity. The three methods evaluated were (a) the elimination of entire side chains (e.g., glycine scanning), (b) the elimination of the electrostatic contribution from the atoms of a side chain, called nullification, and (c) side chain structure prediction using SCWRL4. These techniques generate models in seconds, enabling large-scale mutational scanning. We evaluated these techniques on the SMAD2/SMAD4 heterotrimer, whose formation plays a crucial role in antitumor pathways. Many studies have documented the clinical and structural effect of specific mutations on trimer formation. Our results describe how glycine scanning yields more specific predictions, although nullification may be more sensitive, and how side chain structure prediction enables the identification of uncharged-to-charge mutations.

VASP-E: specificity annotation with a volumetric analysis of electrostatic isopotentials

Algorithms for comparing protein structure are frequently used for function annotation. By searching for subtle similarities among very different proteins, these algorithms can identify remote homologs with similar biological functions. In contrast, few comparison algorithms focus on specificity annotation, where the identification of subtle differences among very similar proteins can assist in finding small structural variations that create differences in binding specificity. Few specificity annotation methods consider electrostatic fields, which play a critical role in molecular recognition. To fill this gap, this paper describes VASP-E (Volumetric Analysis of Surface Properties with Electrostatics), a novel volumetric comparison tool based on the electrostatic comparison of protein-ligand and protein-protein binding sites. VASP-E exploits the central observation that three dimensional solids can be used to fully represent and compare both electrostatic isopotentials and molecular surfaces. With this integrated representation, VASP-E is able to dissect the electrostatic environments of protein-ligand and protein-protein binding interfaces, identifying individual amino acids that have an electrostatic influence on binding specificity. VASP-E was used to examine a nonredundant subset of the serine and cysteine proteases as well as the barnase-barstar and Rap1a-raf complexes. Based on amino acids established by various experimental studies to have an electrostatic influence on binding specificity, VASP-E identified electrostatically influential amino acids with 100% precision and 83.3% recall. We also show that VASP-E can accurately classify closely related ligand binding cavities into groups with different binding preferences. These results suggest that VASP-E should prove a useful tool for the characterization of specific binding and the engineering of binding preferences in proteins.

Proteins, the ubiquitous worker molecules of the cell, are a diverse class of molecules that perform very specific tasks. Understanding how proteins achieve specificity is a critical step towards understanding biological systems and a key prerequisite for rationally engineering new proteins. To examine electrostatic influences on specificity in proteins, this paper presents VASP-E, a software tool that generates solid representations of the electrostatic potential fields that surround proteins. VASP-E compares solids with constructive solid geometry, a class of techniques developed first for modeling complex machine parts. We observed that solid representations could quantify the degree of charge complementarity in protein-protein interactions and identify key residues that strengthen or weaken them. VASP-E correctly identified amino acids with established experimental influences on protein-protein binding specificity. We also observed that solid representations of electrostatic fields could identify electrostatic conservations and variations that relate to similarities and differences in binding specificity between proteins and small molecules.

Isolating influential regions of electrostatic focusing in protein and DNA structure

Electrostatic focusing is a general phenomenon that occurs in cavities and grooves on the molecular surface of biomolecules. Narrow surface features can partially shield charged atoms from the high-dielectric solvent, enhancing electrostatic potentials inside the cavity and projecting electric field lines outward into the solvent. This effect has been observed in many instances and is widely considered in the human examination of molecular structure, but it is rarely integrated into the digital representations used in protein structure comparison software. To create a computational representation of electrostatic focusing, that is compatible with structure comparison algorithms, this paper presents an approach that generates three-dimensional solids that approximate regions where focusing occurs. We verify the accuracy of this representation against instances of focusing in proteins and DNA. Noting that this representation also identifies thin focusing regions on the molecular surface that are unlikely to affect binding, we describe a second algorithm that conservatively isolates larger focusing regions. The resulting 3D solids can be compared with Boolean set operations, permitting a new range of analyses on the regions where electrostatic focusing occurs. They also represent a novel integration of molecular shape and electrostatic focusing into the same structure comparison framework.

Implicit solvent models

Implicit solvent models for biomolecular simulations are reviewed and their underlying statistical mechanical basis is discussed. The fundamental quantity that implicit models seek to approximate is the solute potential of mean force, which determines the statistical weight of solute conformations, and which is obtained by averaging over the solvent degrees of freedom. It is possible to express the total free energy as the reversible work performed in two successive steps. First, the solute is inserted in the solvent with zero atomic partial charges; second, the atomic partial charges of the solute are switched from zero to their full values. Consequently, the total solvation free energy corresponds to a sum of non-polar and electrostatic contributions. These two contributions are often approximated by simple geometrical models (such as solvent exposed area models) and by macroscopic continuum electrostatics, respectively. One powerful route is to approximate the average solvent density distribution around the solute, i.e. the solute-solvent density correlation functions, as in statistical mechanical integral equations. Recent progress with semi-analytical approximations makes continuum electrostatics treatments very efficient. Still more efficient are fully empirical, knowledge-based models, whose relation to explicit solvent treatments is not fully resolved, however. Continuum models that treat both solute and solvent as dielectric continua are also discussed, and the relation between the solute fluctuations and its macroscopic dielectric constant(s) clarified.

Modeling electrostatic effects in proteins

Electrostatic energies provide what is perhaps the most effective tool for structure-function correlation of biological molecules. This review considers the current state of simulations of electrostatic energies in macromolecules as well as the early developments of this field. We focus on the relationship between microscopic and macroscopic models, considering the convergence problems of the microscopic models and the fact that the dielectric 'constants' in semimacroscopic models depend on the definition and the specific treatment. The advances and the challenges in the field are illustrated considering a wide range of functional properties including pK(a)'s, redox potentials, ion and proton channels, enzyme catalysis, ligand binding and protein stability. We conclude by pointing out that, despite the current problems and the significant misunderstandings in the field, there is an overall progress that should lead eventually to quantitative descriptions of electrostatic effects in proteins and thus to quantitative descriptions of the function of proteins.

Study of the insulin dimerization: binding free energy calculations and per-residue free energy decomposition

A calculation of the binding free energy for the dimerization of insulin has been performed using the molecular mechanics-generalized Born surface area approach. The calculated absolute binding free energy is -11.9 kcal/mol, in approximate agreement with the experimental value of -7.2 kcal/mol. The results show that the dimerization is mainly due to nonpolar interactions. The role of the hydrogen bonds between the 2 monomers appears to give the direction of the interactions. A per-atom decomposition of the binding free energy has been performed to identify the residues contributing most to the self association free energy. Residues B24-B26 are found to make the largest favorable contributions to the dimerization. Other residues situated at the interface between the 2 monomers were found to make favorable but smaller contributions to the dimerization: Tyr B16, Val B12, and Pro B28, and to an even lesser extent, Gly B23. The energy decomposition on a per-residue basis is in agreement with experimental alanine scanning data. The results obtained from a single trajectory (i.e., the dimer trajectory is also used for the monomer analysis) and 2 trajectories (i.e., separate trajectories are used for the monomer and dimer) are similar.

Influence of the solvent structure on the electrostatic interactions in proteins

The proper estimation of the influence of the many-body dynamic solvent microstructure on a pairwise electrostatic interaction (PEI) at the protein-solvent interface is very important for solving many biophysical problems. In this work, the PEI energy was calculated for a system that models the interface between a protein and an aqueous solvent. The concept of nonlocal electrostatics for interfacial electrochemical systems was used to evaluate the contribution of a solvent orientational polarization, correlated by the network of hydrogen bonds, into the PEI energy in proteins. The analytical expression for this energy was obtained in the form of Coulomb's law with an effective distance-dependent dielectric function. The asymptotic and numerical analysis carried out for this function revealed several features of dielectric heterogeneity at the protein-solvent interface. For charges located in close proximity to this interface, the values of the dielectric function for the short-distance electrostatic interactions were found to be remarkably smaller than those determined by the classical model, in which the solvent was considered as the uniform dielectric medium of high dielectric constant. Our results have shown that taking into consideration the dynamic solvent microstructure remarkably increases the value of the PEI energy at the protein-solvent interface.

Engineering the pH-optimum of a triglyceride lipase: from predictions based on electrostatic computations to experimental results

The optimisation of enzymes for particular purposes or conditions remains an important target in virtually all protein engineering endeavours. Here, we present a successful strategy for altering the pH-optimum of the triglyceride lipase cutinase from Fusarium solani pisi. The computed electrostatic pH-dependent potentials in the active site environment are correlated with the experimentally observed enzymatic activities. At pH-optimum a distinct negative potential is present in all the lipases and esterases that we studied so far. This has prompted us to propose the "The Electrostatic Catapult Model" as a model for product release after cleavage of the ester bond. The origin of the negative potential is associated with the titration status of specific residues in the vicinity of the active site cleft. In the case of cutinase, the role of Glu44 was systematically investigated by mutations into Ala and Lys. Also, the neighbouring Thr45 was mutated into Proline, with the aim of shifting the spatial location of Glu44. All the charge mutants displayed altered titration behaviour of active site electrostatic potentials. Typically, the substitution of the residue Glu44 pushes the onset of the active site negative potential towards more alkaline conditions. We, therefore, predicted more alkaline pH optima, and this was indeed the experimentally observed. Finally, it was found that the pH-dependent computed Coulombic energy displayed a strong correlation with the observed melting temperatures of native cutinase.

Redox properties of cytochrome c

The redox properties of cytochromes (cyt) c, a ubiquitous class of heme-containing electron transport proteins, have been extensively investigated over the last two decades. The reduction potential (E degrees') is central to the chemistry of cyt c for two main reasons. First, E degrees' influences both the thermodynamic and kinetic aspects of the electron exchange reaction with redox partners. Second, this thermodynamic parameter is remarkably sensitive to changes in the properties of the heme and the protein matrix, and hence can be profitably used for the investigation of the solution chemistry of cyt c. This research area owes much to the exploitation of voltammetric techniques for the determination of E degrees' for metalloproteins, which dates back to the late 1970s. Since then, much effort has been devoted to the comprehension of the molecular factors that control E degrees' in cyt c, which include first coordination sphere effects on the heme iron, the interactions of the heme group with the surrounding polypeptide chain and the solvent, and also include medium effects related to the nature and ionic composition of the solvent, pH, the presence of potential protein ligands, and the temperature. This article provides an overview of the most significant advances made in this field recently.

Binding free energies and free energy components from molecular dynamics and Poisson-Boltzmann calculations. Application to amino acid recognition by aspartyl-tRNA synthetase

Specific amino acid binding by aminoacyl-tRNA synthetases (aaRS) is necessary for correct translation of the genetic code. Engineering a modified specificity into aminoacyl-tRNA synthetases has been proposed as a means to incorporate artificial amino acid residues into proteins in vivo. In a previous paper, the binding to aspartyl-tRNA synthetase of the substrate Asp and the analogue Asn were compared by molecular dynamics free energy simulations. Molecular dynamics combined with Poisson-Boltzmann free energy calculations represent a less expensive approach, suitable for examining multiple active site mutations in an engineering effort. Here, Poisson-Boltzmann free energy calculations for aspartyl-tRNA synthetase are first validated by their ability to reproduce selected molecular dynamics binding free energy differences, then used to examine the possibility of Asn binding to native and mutant aspartyl-tRNA synthetase. A component analysis of the Poisson-Boltzmann free energies is employed to identify specific interactions that determine the binding affinities. The combined use of molecular dynamics free energy simulations to study one binding process thoroughly, followed by molecular dynamics and Poisson-Boltzmann free energy calculations to study a series of related ligands or mutations is proposed as a paradigm for protein or ligand design. The binding of Asn in an alternate, "head-to-tail" orientation observed in the homologous asparagine synthetase is analyzed, and found to be more stable than the "Asp-like" orientation studied earlier. The new orientation is probably unsuitable for catalysis. A conserved active site lysine (Lys198 in Escherichia coli) that recognizes the Asp side-chain is changed to a leucine residue, found at the corresponding position in asparaginyl-tRNA synthetase. It is interesting that the binding of Asp is calculated to increase slightly (rather than to decrease), while that of Asn is calculated, as expected, to increase strongly, to the same level as Asp binding. Insight into the origin of these changes is provided by the component analyses. The double mutation (K198L,D233E) has a similar effect, while the triple mutation (K198L,Q199E,D233E) reduces Asp binding strongly. No binding measurements are available, but the three mutants are known to have no ability to adenylate Asn, despite the "Asp-like" binding affinities calculated here. In molecular dynamics simulations of all three mutants, the Asn ligand backbone shifts by 1-2 A compared to the experimental Asp:AspRS complex, and significant side-chain rearrangements occur around the pocket. These could reduce the ATP binding constant and/or the adenylation reaction rate, explaining the lack of catalytic activity in these complexes. Finally, Asn binding to AspRS with neutral K198 or charged H449 is considered, and shown to be less favorable than with the charged K198 and neutral H449 used in the analysis.

Description of hydration free energy density as a function of molecular physical properties

A method to calculate the solvation free energy density (SFED) at any point in the cavity surface or solvent volume surrounding a solute is proposed. In the special case in which the solvent is water, the SFED is referred to as the hydration free energy density (HFED). The HFED is described as a function of some physical properties of the molecules. These properties are represented by simple basis functions. The hydration free energy of a solute was obtained by integrating the HFED over the solvent volume surrounding the solute, using a grid model. Of 34 basis functions that were introduced to describe the HFED, only six contribute significantly to the HFED. These functions are representations of the surface area and volume of the solute, of the polarization and dispersion of the solute, and of two types of electrostatic interactions between the solute and its environment. The HFED is described as a linear combination of these basis functions, evaluated by summing the interaction energy between each atom of the solute with a grid point in the solvent, where each grid point is a representation of a finite volume of the solvent. The linear combination coefficients were determined by minimizing the error between the calculated and experimental hydration free energies of 81 neutral organic molecules that have a variety of functional groups. The calculated hydration free energies agree well with the experimental results. The hydration free energy of any other solute molecule can then be calculated by summing the product of the linear combination coefficients and the basis functions for the solute.

Cooperative charge fluctuations by migrating protons in globular proteins

A review of the hydrogen bonded network on the protein surface shows the presence of a charged complex system with parallel and competitive interactions, including ionizable side-chains, migrating protons, bound water and nearby backbone peptides. This system displays cooperative effects of dynamical nature, reviewed for lysozyme as a case. By increasing the water coverage of the protein powder, the bound water cluster exhibits a percolative transition, detectable by the onset of large water-assisted displacements of migrating protons, with a parallel emergence of protein mobility and biological function. By lowering the temperature, migrating protons exhibit a glassy dielectric relaxation in the low frequency range, pointing to a frustration by competing interactions similar to that observed in spin glasses and fragile glass forming liquids. The observation of these dissipative processes implies the occurrence of spontaneous charge fluctuations. A simplified model of the protein surface, where conformational and ionizable side-chain fluctuations are averaged out, is used to discuss the statistical physics of these cooperative effects. Some biological implications of this dynamical cooperativity for enzymatic activity are briefly suggested at the end.

Intrinsic protein electric fields: basic non-covalent interactions and relationship to protein-induced Stark effects

Knowledge of the interactions involving charged, polar and polarizable groups in proteins is fundamental, not only because they are important determinants for gaining insight into biophysical molecular recognition and assembly processes, but also for understanding how the matrix of a protein can be viewed as an electric field capable of inducing Stark perturbations on the spectral properties of biological optical centers. This review describes the essential features of noncovalent interactions in protein systems and discusses the concept of the dielectric constant of a protein in the context of different microscopic and macroscopic modeling approaches. It also provides an account of a specific type of high resolution vibrational and optical Stark spectroscopy attempting to correlate the observed spectral properties of biological optical centers to the intrinsic protein fields induced by the matrix in which they reside.

Lipases and esterases: a review of their sequences, structure and evolution

This chapter aims to provide a brief review on the enzyme family of lipases and esterases. The sequences, 3D structures and pH dependent electrostatic signatures are presented and analyzed. Since the family comprises more than 100 sequences, we have tried to focus on the most interesting features from our perspective, which translates into finding similarities and differences between members of this family, in particular in and around the active sites, and to identify residues that are partially or totally conserved. Such residues we believe are either important for maintaining the structural scaf-fold of the protein or to maintain activity or specificity. The structure function relationship for these proteins is therefore of central interest. Can we uniquely identify a protein from this large family of sequences--and if so, what is the identifier? The protein family displays some highly complex features: many of the proteins are interfacially activated, i.e. they need to be in physical contact with the aggregated substrate. Access to the active site is blocked with either a loop fragment or an alpha-helical fragment in the absence of interfacial contact. Although the number of known, relevant protein 3D structures is growing steadily, we are nevertheless faced with a virtual explosion in the number of known or deduced amino acid sequences. It is therefore unrealistic to expect that all protein sequences within the foreseeable future will have their 3D structure determined by X-ray diffractional analysis or through other methods. When feasible the gene and/or the amino acid sequences will be analyzed from an evolutionary perspective. As the 3D folds are often remarkably similar, both among the triglyceride lipases as well as among the esterases, the functional diversities (e.g. specificity) must originate in differences in surface residue utilization, in particular of charged residues. The pH variations in the isopotential surfaces of some of the most interesting lipases are presented and a qualitative interpretation proposed. Finally we illustrate that NMR has potential for becoming an important tool in the study of lipases, esterases and their kinetics.

Hydration and conformational equilibria of simple hydrophobic and amphiphilic solutes

We consider whether the continuum model of hydration optimized to reproduce vacuum-to-water transfer free energies simultaneously describes the hydration free energy contributions to conformational equilibria of the same solutes in water. To this end, transfer and conformational free energies of idealized hydrophobic and amphiphilic solutes in water are calculated from explicit water simulations and compared to continuum model predictions. As benchmark hydrophobic solutes, we examine the hydration of linear alkanes from methane through hexane. Amphiphilic solutes were created by adding a charge of +/-1e to a terminal methyl group of butane. We find that phenomenological continuum parameters fit to transfer free energies are significantly different from those fit to conformational free energies of our model solutes. This difference is attributed to continuum model parameters that depend on solute conformation in water, and leads to effective values for the free energy/surface area coefficient and Born radii that best describe conformational equilibrium. In light of these results, we believe that continuum models of hydration optimized to fit transfer free energies do not accurately capture the balance between hydrophobic and electrostatic contributions that determines the solute conformational state in aqueous solution.

The partial charge of the nitrogen atom in peptide bonds

A majority of the standard texts dealing with proteins portray the peptide link as a mixture of two resonance forms, in one of which the nitrogen atom has a positive charge. As a consequence, it is often believed that the nitrogen atom has a net positive charge. This is in apparent contradiction with the partial negative charge on the nitrogen that is used in force fields for molecular modeling. However, charges on resonance forms are best regarded as formal rather than actual charges and current evidence clearly favors a net negative charge for the nitrogen atom. In the course of the discussion, new ideas about the electronic structure of amides and the peptide bond are presented.

Electric fields at the plasma membrane level: a neglected element in the mechanisms of cell signalling

Membrane proteins possess certain features that make them susceptible to the electric fields generated at the level of the plasma membrane. A reappraisal of cell signalling, taking into account the protein interactions with the membrane electrostatic profile, suggests that an electrical dimension is deeply involved in this fundamental aspect of cell biology. At least three types of potentials can contribute to this dimension: (1) the potential across the compact layer of water adherent to membrane surfaces; this potential is affected by classical inducers of cell differentiation, like dimethylsulfoxide and hexamethylenebisacetamide; (2) the potential across the Gouy-Chapman double layer, which accounts for the effects of extracellular cations in the modulation of differentiation; and (3) the resting potential. This last potential and its governing ion currents can be exploited in localised mechanisms of cell signalling centred on the functional association of integrin receptors with ion channels.

The blind watchmaker and rational protein engineering

In the present review some scientific areas of key importance for protein engineering are discussed, such as problems involved in deducting protein sequence from DNA sequence (due to posttranscriptional editing, splicing and posttranslational modifications), modelling of protein structures by homology, NMR of large proteins (including probing the molecular surface with relaxation agents), simulation of protein structures by molecular dynamics and simulation of electrostatic effects in proteins (including pH-dependent effects). It is argued that all of these areas could be of key importance in most protein engineering projects, because they give access to increased and often unique information. In the last part of the review some potential areas for future applications of protein engineering approaches are discussed, such as non-conventional media, de novo design and nanotechnology.

A connected-cluster of hydration around myoglobin: correlation between molecular dynamics simulations and experiment

An analysis of a molecular dynamics simulation of metmyoglobin in an explicit solvent environment of 3,128 water molecules has been performed. Both statics and dynamics of the protein-solvent interface are addressed in a comparison with experiment. Three-dimensional density distributions, temperature factors, and occupancy weights are computed for the solvent by using the trajectory coordinates. Analysis of the hydration leads to the localization of more than 500 hydration sites distributed into multiple layers of solvation located between 2.6 and 6.8 A from the atomic protein surface. After locating the local solvent density maxima or hydration sites we conclude that water molecules of hydration positions and hydration sites are distinct concepts. Both global and detailed properties of the hydration cluster around myoglobin are compared with recent neutron and X-ray data on myoglobin. Questions arising from differences between X-ray and neutron data concerning the locations of the protein-bound water are investigated. Analysis of water site differences found from X-ray and neutron experiments compared with our simulation shows that the simulation gives a way to unify the hydration picture given by the two experiments.

Hydrophilic surface maps of channel-forming peptides: analysis of amphipathic helices

Ion channels may be formed by bundles of amphipathic alpha-helices aligned parallel to one another and spanning a lipid bilayer membrane, with the hydrophilic faces of the helices lining a central pore. In order to provide insight into the packing of such helices in bundles, a method has been developed to evaluate hydrophilic surface maps of amphipathic alpha-helices and to display these surfaces in a readily interpretable form. The procedure is based upon empirical energy calculations of interactions of a water molecule with an amphipathic alpha-helix. The method has been applied to three channel-forming peptides: Staphylococcal delta-toxin; alamethicin; and a synthetic leucine- and serine-containing peptide. Particular emphasis is placed upon the effects of sidechain conformational flexibility on hydrophilic surface maps. A family of models of the delta-toxin helix is generated by a simulated annealing procedure. The results of hydrophilic surface map analyses provide more exact definition of the centre of the hydrophilic face of amphipathic helices, and of the variation of the position of the centre in response to changes in sidechain conformation. This information is used to define families of preliminary models for a given ion channel, as is illustrated for delta-toxin.

Multigrid solution of the nonlinear Poisson-Boltzmann equation and calculation of titration curves

Although knowledge of the pKa values and charge states of individual residues is critical to understanding the role of electrostatic effects in protein structure and function, calculating these quantities is challenging because of the sensitivity of these parameters to the position and distribution of charges. Values for many different proteins which agree well with experimental results have been obtained with modified Tanford-Kirkwood theory in which the protein is modeled as a sphere (reviewed in Ref. 1); however, convergence is more difficult to achieve with finite difference methods, in which the protein is mapped onto a grid and derivatives of the potential function are calculated as differences between the values of the function at grid points (reviewed in Ref. 6). Multigrid methods, in which the size of the grid is varied from fine to coarse in several cycles, decrease computational time, increase rates of convergence, and improve agreement with experiment. Both the accuracy and computational advantage of the multigrid approach increase with grid size, because the time required to achieve a solution increases slowly with grid size. We have implemented a multigrid procedure for solving the nonlinear Poisson-Boltzmann equation, and, using lysozyme as a test case, compared calculations for several crystal forms, different refinement procedures, and different charge assignment schemes. The root mean square difference between calculated and experimental pKa values for the crystal structure which yields best agreement with experiment (1LZT) is 1.1 pH units, with the differences in calculated and experimental pK values being less than 0.6 pH units for 16 out of 21 residues. The calculated titration curves of several residues are biphasic.

The redox properties of cytochromes b imposed by the membrane electrostatic environment

The effect of the dipole potential field of extended membrane spanning alpha-helices on the redox potentials of b cytochromes in energy transducing membranes has been calculated in the context of a three phase model for the membrane. In this model, the membrane contains three dielectric layers; (i) a 40-A hydrophobic membrane bilayer, with dielectric constant em = 3-4, (ii) 10-20-A interfacial layers of intermediate polarity, ein = 12-20, that consist of lipid polar head groups and peripheral protein segments, and (iii) an external infinite water medium, ew = 80. The unusually positive midpoint potential, Em = +0.4 V, of the "high potential" cytochrome b-559 of oxygenic photosynthetic membranes, a previously enigmatic property of this cytochrome, can be explained by (i) the position of the heme in the positive dipole potential region near the NH2 termini of the two parallel helices that provide its histidine ligands, and (ii) the loss of solvation energy of the heme ion due to the low dielectric constant of its surroundings, leading to an estimate of +0.31 to +0.37 V for the cytochrome Em. The known tendency of this cytochrome to undergo a large -delta Em shift upon exposure of thylakoid membranes to proteases or damaging treatments is explained by disruption of the intermediate polarity (ein) surface dielectric layer and the resulting contact of the heme with the external water medium. Application of this model to the two hemes (bn and bp) of cytochrome b of the cytochrome bc1 complex, with the two hemes placed symmetrically in the low dielectric (em) membrane bilayer, results in Em values of hemes bn and bp that are, respectively, somewhat too negative (approximately -0.1 V), and much too positive (approximately +0.3 V), leading to a potential difference, Em(bp) - Em(bn), with the wrong sign and magnitude, +0.25 V instead of -0.10 to -0.15 V. The heme potentials can only be approximately reconciled with experiment, if it is assumed that the two hemes are in different dielectric environments, with that of heme bp being more polar.

Analysis of ordered arrays of adsorbed lysozyme by scanning tunneling microscopy

Scanning tunneling microscopy (STM) has been used to observe lysozyme at a graphite surface directly in order to gain mechanistic information about the molecular events involved in protein adsorption. The experiments were performed using an insulated tip in an aqueous protein solution, allowing the time course of the adsorption process to be followed, including the evolution of ordered arrays. Ordered arrays of protein molecules were observed, with lattice spacings that varied with bulk protein concentration and salt strength. Fourier analysis was used to determine the average cell dimensions of an array. From the observed lattice spacings, it was possible to estimate the surface coverage of the protein, and thus, by varying the conditions, adsorption isotherms could be obtained. These isotherms compare well with adsorption isotherms measured using total internal reflectance fluorescence (TIRF) spectroscopy on a hydrophobic surface. Since the protein is charged and the electrolyte has an effect on the isotherms, electrostatics are a likely controlling factor. Molecular electrostatics computations were thus used to investigate the possible origins of the lattice structure, and they suggest that favorable intermolecular interactions among adsorbed molecules are consistent with hydrophobically dominated protein-surface interactions.

Reduction kinetics of the four hemes of cytochrome c3 from Desulfovibrio vulgaris by flash photolysis

The reduction of the tetraheme cytochrome c3 (from Desulfovibrio vulgaris, strains Miyazaki F and Hildenbourough) by flavin semiquinone and reduced methyl viologen follows a monophasic kinetic profile, even though the four hemes do not have equivalent reduction potentials. Rate constants for reduction of the individual hemes are obtained subsequent to incrementally reducing the cytochrome by phototitration. The dependence of each rate constant on the reduction potential difference between the heme and the reductant can be described by outer sphere electron transfer theroy. Thus, the very low reduction potentials of the cytochrome c3 hemes compensate for the very large solvent accessibility of the hemes. The relative rate constants for electron transfer to the four hemes of cytochrome c3 are consistent with the assignments of reduction potential to hemes previously made by Park et al. (Park, J.-S., Kano, K., Niki, S. and Akutsu, H. (1991) FEBS Lett. 285, 149-151) using NMR techniques. The ionic strength dependence of the observed rate constant for reduction by the methyl viologen radical cation indicates that ionic strength substantially alters the structure and/or the heme reduction potentials of the cytochrome. This result is confirmed by reduction with a neutral flavin species (5-deazariboflavin semiquinone) in which the reactivity of the highest potential heme decreases and the reactivity of the lowest potential heme increases at high (500 mM) ionic strength, and by the sensitivity of heme methyl resonances to ionic strength as observed by 1H-NMR. These unusual ionic strength-dependent effects may be due to a combination of structural changes in the cytochrome and alterations of the electrostatic fields at elevated ionic strengths.

The roles of serine and threonine sidechains in ion channels: a modelling study

The ion channel of the nicotinic acetylcholine receptor (nAChR) is believed to be lined by transmembrane M2 helices. A "4-8-12" sequence motif, comprising serine (S) or threonine (T) residues at positions 4, 8 and 12 of M2, is conserved between different members, anion and cation selective, of the nAChR superfamily. Parallel bundles of 4-8-12 motif-containing helices are considered as simplified models of ion channels. The relationship between S and T sidechain conformations and channel-ion interactions is explored via evaluation of interaction energies of K+ and of Cl- ions with channel models. Energy calculations are used to determine optimal chi 2 (C alpha-C beta-O gamma-H gamma) values in the presence of K+ or Cl- ions. 4-8-12 motif-containing bundles may form favourable interactions with either cations or anions, dependent upon the chi 2 values adopted. Parallel-helix and tilted-helix bundles are considered, as are heteromeric models designed to mimic the Torpedo nAChR. The main conclusion of the study is that conformational flexibility at chi 2 enables both S and T residues to form favourable interactions with anions or cations. Consequently, there is apparently no difference between S and T residues in their interactions with permeant ions, which suggests that the presence of T vs. S residues within the 4-8-12 motif is not a major mechanism whereby anion/cation selectivity may be generated. The implications of these studies with respect to more elaborate models of nAChR and related receptors are considered.

Electrostatic forces in two lysozymes: calculations and measurements of histidine pKa values

In order to examine the electrostatic forces in globular proteins, pKa values and their ionic strength dependence of His residues of hen egg white lysozyme (HEWL) and human lysozyme (HUML) were measured, and they were compared with those calculated numerically. pKa values of His residues in HEWL, HUML, and short oligopeptides were determined from chemical shift changes of His side chains by 1H-nmr measurements. The associated changes in pKa values in HEWL and HUML were calculated by solving the Poisson-Boltzmann equations numerically for macroscopic dielectric models. The calculated pKa changes and their ionic strength dependence agreed fairly well with the observed ones. The contribution from each residue of each alpha-helix dipole to the pKa values and their ionic strength dependence was analyzed using Green's reciprocity theorem. The results indicate that (1) the pKa of His residues are largely affected by surrounding ionized and polar groups; (2) the ionic strength dependence of the pKa values is determined by the overall charge distributions and their accessibilities to solvent; and (3) alpha-helix dipoles make a significant contribution to the pKa, when the His residue is close to the helix terminus and not fully exposed to the solvent.

Solvent dielectric effects on protein dynamics

Electron paramagnetic resonance (EPR) spectroscopy and molecular dynamics (MD) simulations were used to investigate the dynamics of alpha-chymotrypsin in solvents ranging in dielectric constant from 72 to 1.9. EPR measurements showed that motions in the vicinity of two spin-labeled amino acids (Met-192 and Ser-195) decreased dramatically with decreasing solvent dielectric constant, a trend consistent with changes in the electrostatic force between charged residues of the protein. EPR results and MD simulations revealed a very similar functional dependence between rates of motion in the protein and the dielectric constant of the bulk solvent; however, predicted motions of protein atoms were markedly faster than measured motions of the spin labels. MD calculations for dielectric constants of 5 and 72 showed the greatest differences near the outer surface of the protein. In general, at the lower dielectric constant many atoms of the protein move more slowly, and many of the slowest residues are near the exterior. These results suggest that altered dynamics may contribute to the unusual properties--e.g., modified stereoselectivities--of enzymes in nearly dry organic solvents.

Electrostatic fields at the active site of ribulose-1,5-bisphosphate carboxylase

A macroscopic approach has been employed to calculate the electrostatic potential field of nonactivated ribulose-1,5-bisphosphate carboxylase and of some complexes of the enzyme with activator and substrate. The overall electrostatic field of the L2-type enzyme from the photosynthetic bacterium Rhodospirillum rubrum shows that the core of the dimer, consisting of the two C-terminal domains, has a predominantly positive potential. These domains provide the binding sites for the negatively charged phosphate groups of the substrate. The two N-terminal domains have mainly negative potential. At the active site situated between the C-terminal domain of one subunit and the N-terminal domain of the second subunit, a large potential gradient at the substrate binding site is found. This might be important for polarization of chemical bonds of the substrate and the movement of protons during catalysis. The immediate surroundings of the activator lysine, K191, provide a positive potential area which might cause the pK value for this residue to be lowered. This observation suggests that the electrostatic field at the active site is responsible for the specific carbamylation of the epsilon-amino group of this lysine side chain during activation. Activation causes a shift in the electrostatic potential at the position of K166 to more positive values, which is reflected in the unusually low pK of K166 in the activated enzyme species. The overall shape of the electrostatic potential field in the L2 building block of the L8S8-type Rubisco from spinach is, despite only 30% amino acid homology for the L-chains, strikingly similar to that of the L2-type Rubisco from Rhodospirillum rubrum. A significant difference between the two species is that the potential is in general more positive in the higher plant Rubisco. In particular, the second phosphate binding site has a considerably more positive potential, which might be responsible for the higher affinity for the substrate of L8S8-type enzymes. The higher potential at this site might be due to two remote histidine residues, which are conserved in the plant enzymes.

Ion channels formed by amphipathic helical peptides. A molecular modelling study

Channel forming peptides (CFPs) are amphipathic peptides, of length ca. 20 residues, which adopt an alpha-helical conformation in the presence of lipid bilayers and form ion channels with electrophysiological properties comparable to those of ion channel proteins. We have modelled CFP channels as bundles of parallel trans-bilayer helices surrounding a central ion-permeable pore. Ion-channel interactions have been explored via accessible surface area calculations, and via evaluation of changes in van der Waals and electrostatic energies as a K+ ion is translated along the length of the pore. Two CFPs have been modelled: (a) zervamicin-A1-16, a synthetic apolar peptaibol related to alamethicin, and (b) delta-toxin from Staphylococcus aureus. Both of these CFPs have previously been shown to form ion channels in planar lipid bilayers, and have been shown to have predominantly helical conformations. Zervamicin-A1-16 channels were modelled as bundles of 4 to 8 parallel helices. Two related helix bundle geometries were explored. K(+)-channel interactions have been shown to involve exposed backbone carbonyl oxygen atoms. delta-Toxin channels were modelled as bundles of 6 parallel helices. Residues Q3, D11 and D18 generate favourable K(+)-channel interactions. Rotation of W15 about its C beta-C gamma bond has been shown to be capable of occluding the central pore, and is discussed as a possible model for sidechain conformational changes in relation to ion channel gating.