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Salt-promoted protein folding, preferential binding, or electrostatic screening?

The extended coil/molten globule conformational equilibrium exhibited by ferricytochrome c in 10 to 20 mM HCl was examined using free boundary capillary electrophoresis. Addition of the osmolyte glucitol, also called sorbitol, to shift the conformational equilibrium toward the molten globule markedly diminished the mobility of the protein. This diminution can be entirely assigned to the relative viscosity of the added glucitol. The insensitivity of the viscosity corrected protein mobility to added glucitol suggests that both the extended coil and molten globule conformations of cytochrome c are free draining in an electrophoresis measurement. Addition of a neutral salt to shift the conformational equilibrium toward the molten globule conformation also markedly diminished the mobility of the protein. This diminution can be entirely assigned to the electrostatic screening afforded by the added salt. The onset of the conformational transition observed by optical measurements and the onset of electrostatic screening observed by mobility measurements appear to be in common for some but not all neutral salts. The exception suggests that preferential binding of the anion of a neutral salt to the molten globule conformation and not electrostatic screening is principally responsible for the shift in the conformational equilibrium of cytochrome c in acidic solutions.

Animals↗

An empirical model for electrostatic interactions in proteins incorporating multiple geometry-dependent dielectric constants.

Here we introduce an electrostatic model that treats the complexity of electrostatic interactions in a heterogeneous protein environment by using multiple parameters that take into account variations in protein geometry, local structure, and the type of interacting residues. The optimal values for these parameters were obtained by fitting the model to a large dataset of 260 experimentally determined pK(a) values distributed over 41 proteins. We obtain fits between the calculated and observed values that are significantly better than the null model. The model performs well on the groups that exhibit large pK(a) shifts from solution values in response to the protein environment and compares favorably with other, successful continuum models. The empirically determined values of the parameters correlate well with experimentally observed contributions of hydrogen bonds and ion pairs as well as theoretically predicted magnitudes of charge-charge and charge-polar interactions. The magnitudes of the dielectric constants assigned to different regions of the protein rank according to the strength of the relaxation effects expected for the core, boundary, and surface. The electrostatic interactions in this model are pairwise decomposable and can be calculated rapidly. This model is therefore well suited for the large computations required for simulating protein properties and especially for prediction of mutations for protein design.

Algorithms↗

Comparison of different schemes to treat long-range electrostatic interactions in molecular dynamics simulations of a protein crystal.

Eight molecular dynamics simulations of a ubiquitin crystal unit cell were performed to investigate the effect of different schemes to treat the long-range electrostatic interactions as well as the need to include counter ions. A crystal system was chosen as the test system, because the higher charge density compared with a protein in solution makes it more sensitive to the way of treating the electrostatic interactions. Three different schemes of treating the long-range interactions were compared: straight cutoff, reaction-field approximation, and a lattice-sum method (P3M). For each of these schemes, two simulations were performed, one with and one without the counter ions. Two additional simulations with a reaction-field force and different initial placements of the counter ions were performed to examine the effect of the initial positions of the ions. The inclusion of long-range electrostatic interactions using either a reaction-field or a lattice-sum method proved to be necessary for the simulation of crystals. These two schemes did not differ much in their ability to reproduce the crystallographic structure. The inclusion of counter ions, on the other hand, seems not necessary for obtaining a stable simulation. The initial positions of the ions have a visible but small effect on the simulation.

Amino Acid Sequence↗

Rational proteomics II: electrostatic nature of cofactor preference in the short-chain oxidoreductase (SCOR) enzyme family.

The dominant role of long-range electrostatic interatomic interactions in nicotinamide adenine dinucleotide/nicotinamide adenine dinucleotide phosphate (NAD/NADP) cofactor recognition has been shown for enzymes of the short-chain oxidoreductase (SCOR) family. An estimation of cofactor preference based only on the contribution of the electrostatic energy term to the total energy of enzyme-cofactor interaction has been tested for approximately 40 known three-dimensional (3D) crystal complexes and approximately 330 SCOR enzymes, with cofactor preference predicted by the presence of Asp or Arg recognition residues at specific 3D positions in the beta2alpha3 loop (Duax et al., Proteins 2003;53:931-943). The results obtained were found to be consistent with approximately 90% reliable cofactor assignments for those subsets. The procedure was then applied to approximately 170 SCOR enzymes with completely uncertain NAD/NADP dependence, due to the lack of Asp and Arg marker residues. The proposed 3D electrostatic approach for cofactor assignment ("3D_DeltaE(el)") has been implemented in an automatic screening procedure, and together with the use of marker residues proposed earlier (Duax et al., Proteins 2003;53:931-943), increases the level of reliable predictions for the putative SCORs from approximately 70% to approximately 90%. It is expected to be applicable for any NAD/NADP-dependent enzyme subset having at least 25-30% sequence identity, with at least one enzyme of known 3D crystal structure.

Animals↗

Electrostatic interactions in the assembly of Escherichia coli aspartate transcarbamylase.

Although ionizable groups are known to play important roles in the assembly, catalytic, and regulatory mechanisms of Escherichia coli aspartate transcarbamylase, these groups have not been characterized in detail. We report the application of static accessibility modified Tanford-Kirkwood theory to model electrostatic effects associated with the assembly of pairs of chains, subunits, and the holoenzyme. All of the interchain interfaces except R1-R6 are stabilized by electrostatic interactions by -2 to -4 kcal-m-1 at pH 8. The pH dependence of the electrostatic component of the free energy of stabilization of intrasubunit contacts (C1-C2 and R1-R6) is qualitatively different from that of intersubunit contacts (C1-C4, C1-R1, and C1-R4). This difference may allow the transmission of information across subunit interfaces to be selectively regulated. Groups whose calculated pK or charge changes as a result of protein-protein interactions have been identified and the results correlated with available information about their function. Both the 240s loop of the c chain and the region near the Zn(II) ion of the r chain contain clusters of ionizable groups whose calculated pK values change by relatively large amounts upon assembly. These pK changes in turn extend to regions of the protein remote from the interface. The possibility that networks of ionizable groups are involved in transmitting information between binding sites is suggested.

Amino Acids↗

The frequency of ion-pair substructures in proteins is quantitatively related to electrostatic potential: a statistical model for nonbonded interactions.

A statistical analysis of ion pairs in protein crystal structures shows that their abundance with respect to uncharged controls is accurately predicted by a Boltzmann-like function of electrostatic potential. It appears that the mechanisms of protein folding and/or evolution combine to produce a "thermal" distribution of local nonbonded interactions, as has been suggested by statistical-mechanical theories. Using this relationship, we develop a maximum likelihood methodology for estimation of apparent energetic parameters from the data base of known structures, and we derive electrostatic potential functions that lead to optimal agreement of observed and predicted ion-pair frequencies. These are similar to potentials of mean force derived from electrostatic theory, but departure from Coulombic behavior is less than has been suggested.

Biological Evolution↗

Modelling the three-dimensional structure and electrostatic potential field of the two Cu,Zn superoxide dismutase variants from Xenopus laevis.

The crystallographic structure of bovine superoxide dismutase has been used as a template for the graphic reconstruction of the three-dimensional structures of the two Xenopus laevis variants (Schininà, M.E. et al. Arch. Biochem. Biophys. 272:507-515, 1989). In these models the structure-essential residues maintain their position and their structural role, and the interactions between the subunits and the close packing within the beta-barrel are maintained with conservative substitutions and even increased with "aromatic pairs." Because of the same topological motif and surface location of charges, arising from the model building of the two variants with respect to the bovine enzyme, we have calculated the electrostatic potential fields around the models of the two Xenopus laevis variants by numerically solving the Poisson-Boltzmann equation. We show that conservation of a specific space-relationship of charges maintains the potential field pattern already observed in the bovine enzyme, where a negative potential field surrounds the protein surface and specific positive regions wrap up the copper center active site. This electrostatic potential field distribution supports the idea that electrostatic interactions control, like in the bovine enzyme, the mechanism of enzyme-substrate recognition in the Xenopus laevis Cu,Zn superoxide dismutases, suggesting that coordinated mutation of charged residues has occurred in the evolution of this enzyme.

Amino Acid Sequence↗

The electrostatic potential of Escherichia coli dihydrofolate reductase.

Escherichia coli dihydrofolate reductase (DHFR) carries a net charge of -10 electrons yet it binds ligands with net charges of -4 (NADPH) and -2 (folate or dihydrofolate). Evaluation and analysis of the electrostatic potential of the enzyme give insight as to how this is accomplished. The results show that the enzyme is covered by an overall negative potential (as expected) except for the ligand binding sites, which are located inside "pockets" of positive potential that enable the enzyme to bind the negatively charged ligands. The electrostatic potential can be related to the asymmetric distribution of charged residues in the enzyme. The asymmetric charge distribution, along with the dielectric boundary that occurs at the solvent-protein interface, is analogous to the situation occurring in superoxide dismutase. Thus DHFR is another case where the shape of the active site focuses electric fields out into solution. The positive electrostatic potential at the entrance of the ligand binding site in E. coli DHFR is shown to be a direct consequence of the presence of three positively charged residues at positions 32, 52, and 57--residues which have also been shown recently to contribute significantly to electronic polarization of the ligand folate. The latter has been postulated to be involved in the catalytic process. A similar structural motif of three positively charged amino acids that gives rise to a positive potential at the entrance to the active site is also found in DHFR from chicken liver, and is suggested to be a common feature in DHFRs from many species. It is noted that, although the net charges of DHFRs from different species vary from +3 to -10, the enzymes are able to bind the same negatively charged ligands, and perform the same catalytic function.

Amino Acids↗

Treatment of electrostatic effects in proteins: multigrid-based Newton iterative method for solution of the full nonlinear Poisson-Boltzmann equation.

The nonlinear Poisson-Boltzmann equation (NPBE) provides a continuum description of the electrostatic field in an ionic medium around a macromolecule. Here, a novel approach to the solution of the full NPBE is developed. This robust and efficient algorithm combines multilevel techniques with a damped inexact Newton's method. The CPU time required for solution of the full NPBE, which is less than that for standard single-grid approaches in solving the corresponding linearized equation, is proportional to the number of unknowns enabling applications to very large macromolecular systems. Convergence of the method is demonstrated for a variety of protein systems. Comparison of the solutions to the linearized Poisson-Boltzmann equation shows that the damping of the electrostatic field around the charge is increased and that the potential scales logarithmically with charge. The inclusion of the full nonlinearity thus reduces the impact of highly charged residues on protein surfaces and provides a more realistic representation of electrostatic effects. This is demonstrated through calculation of potential around the active site regions of the 1,266-residue tryptophan synthase dimer and in the computation of rate constants from Brownian dynamics calculations in the superoxide dismutase-superoxide and antibody-antigen systems.

Algorithms↗

Molecular dynamics simulations of rubredoxin from Clostridium pasteurianum: changes in structure and electrostatic potential during redox reactions.

Molecular dynamics simulations of Clostridium pasteurianum rubredoxin in the oxidized and reduced forms have been performed. Good agreement between both forms and crystal data has been obtained (rms deviation of backbone atoms of 1.06 and 1.42 A, respectively), which was due in part to the use of explicit solvent and counterions. The reduced form exhibits an unexpected structural change: the redox site becomes much more solvent-accessible, so that water enters a channel between the surface and the site, but with little actual structural rearrangement (the rms deviation of backbone atoms between the oxidized and reduced is 0.77 A). The increase in solvent accessibility is also seen, although to a much lesser extent, between the oxidized and reduced crystal structures of Pyrococcus furiosus rubredoxin, but no high resolution crystal or nuclear magnetic resonance solution data exist for reduced C. pasteurianum rubredoxin. The electrostatic potential at the iron site and fluctuations in the potential, which contribute to both the redox and electron transfer properties, have also been evaluated for both the oxidized and the reduced simulations. These results show that the backbone plays a significant role (62-70 kcal/mol/e) and the polar side chains contribute relatively little (0-4 kcal/mol/e) to the absolute electrostatic potential at the iron of rubredoxin for both forms. However, both groups contribute significantly to the change in redox state by becoming more polarized and more densely packed around the redox site upon reduction. Furthermore, these results show that the solvent becomes much more polarized in the reduced form than in the oxidized form, even excluding the penetrating water. Finally, the simulation indicates that the contribution of the charged side chains to the electrostatic potential is largely canceled by that of the counterions.

Algorithms↗

Potential-derived point-charge model study of electrostatic interaction energies in some hydrogen-bonded systems.

Mulliken's atomic changes (MC) and potential derived (PD) point charges obtained from STO-3G wave functions are used to study the electrostatic interaction energies for a series of representative hydrogen-bonded complexes. The results of the above-mentioned models are compared with the more accurate results of segmental multipole moment (SMM) expansion, and it is shown that the PD model is superior to the MC model. The results of PD model are shown to be well correlated with the results of SMM expansion technique. Results of our calculations using 6-31G and 6-31G** PD charges are also reported here. Electrostatic interaction energies obtained using 6-31G** PD charges are compared with the 6-31G** SCF interaction energies available for the nine hydrogen-bonded dimers of ammonia, water, and hydrogen fluoride and a good correlation between the two is shown. The interrelationship between the results of different basis sets are also examined for the PD point-charge model. The electrostatic interaction energies obtained using STO-3G PD model are shown to be well correlated to the results of 6-31G and 6-31G** PD models.

Ammonia↗

Electrostatic recognition in redox copper proteins: a 1H NMR study of the protonation behavior of His 19 in oxidized and reduced Cu,Zn superoxide dismutase.

The pK shift of the His 19 residue in bovine Cu,Zn superoxide dismutase was carefully measured by nuclear magnetic resonance spectroscopy as a function of the change of the copper oxidation state. The measured pK values were identical within experimental error, at variance with results obtained with other copper proteins under similar conditions. The DelPhi program, based on a macroscopic dielectric model for the electrostatic interactions in proteins, was used to calculate pK shifts, as a function of charge perturbation introduced by metal oxidation, between the oxidized and the reduced enzyme, which are assumed to have the same structure on the basis of previous spectroscopic data. A nice fit with the experimental pK values was obtained protonating the imidazole of the copper-zinc bridging His 61, which is known to release the copper in the reduced enzyme. Protonation of His 61 in the reduced state gives rise to an electrostatic potential distribution around the protein almost identical to that observed in the oxidized one. These results suggest that a major role for the bridging histidine in Cu,Zn superoxide dismutase is to provide identical electrostatic steering of the substrate in the two oxidation states of the enzyme by redox-linked protonation-deprotonation processes. This property is discussed in comparison with the effect of copper reduction on the distribution of the electric field in small blue copper proteins.

Acids↗

Quantitation of electrostatic and hydrophobic membrane interactions by equilibrium dialysis and reverse-phase HPLC.

Equilibrium dialysis and reverse-phase HPLC have been used for the sensitive and precise quantitation of both electrostatic and hydrophobic interactions of peptides and small molecules with lipid bilayers. We show that hydrophobic solutes are rapidly and quantitatively released from lipid dispersions when loaded onto a C4 reverse-phase HPLC column equilibrated in water+0.1% trifluoroacetic acid and that the lipid molecules have no interfering effect on the chromatography. Peptides interacting electrostatically with bilayers are released quantitatively when a higher ionic strength buffer (water+2% ammonium acetate) is used. As little as 50 ng of solute can be accurately quantitated even in the presence of milligram amounts of lipid. We demonstrate the application of these methods to the hydrophobic interactions between indoles and lipid bilayers and to the electrostatic interaction between defensins, which are cationic antibiotic peptides, and anionic bilayers. The high sensitivity allows nondestructive quantitation of submicrogram amounts of precious solutes and the high precision allows the heat capacity change, an important thermodynamic parameter, to be obtained from the partitioning data.

Antifungal Agents↗

The Osmotic Pressure of Electrostatically Stabilized Colloidal Dispersions

A mathematical model for predicting the osmotic pressure of electrostatically stabilized colloids has been developed. The model is based on detailed descriptions of the colloidal interactions within an electrostatically stabilized dispersion. Electrostatic interactions are accounted for by a Wigner-Seitz cell approach including a numerical solution of the nonlinear Poisson-Boltzmann equation. London-van der Waals forces are calculated using a computationally efficient means of approximating screened, retarded Lifshitz-Hamaker constants. Configurational entropy effects are calculated using an equation of state giving excellent agreement with molecular dynamic data. These descriptions of colloidal interactions are used to develop an a priori model, with no adjustable parameters, that allows quantitative prediction of the osmotic pressure of colloidal dispersions as a function of zeta potential (and hence pH), colloid size, ionic strength, and colloid concentration. The model shows good agreement with literature experimental data for the osmotic pressure of the protein bovine serum albumin (BSA). A charge regulation model for the BSA surface has also been developed from knowledge of the amino acid groups giving rise to the protein charge. A comparison of zeta potentials calculated from this model with experimentally determined values for dilute BSA dispersions shows good agreement for a wide range of conditions. The charge regulation model has also been incorporated into the osmotic pressure prediction, resulting in excellent agreement between theory and experiment.

Journal Article↗

Charge Regulation and Electrostatic Interactions for a Spherical Particle in a Cylindrical Pore

Previous theoretical analyses of electrostatic interactions for proteins in porous media have assumed that the protein (and pore) surface maintains either constant charge or constant potential during the interaction; however, the actual surface charge is determined by the extent of the surface ionization and binding reactions, both of which are altered when the protein enters the pore due to the change in the local ionic environment caused by the distortion of the electrical potential field. Theoretical calculations for the electrostatic potential are performed for a spherical particle in a cylindrical pore, accounting for this charge regulation phenomenon using a linearized form of the charge regulation boundary condition. The equilibrium partition coefficient in the pore is then evaluated from the free energy of interaction. Specific calculations are provided for the protein bovine serum albumin, with the charge regulation parameters evaluated from a model for the detailed protein charge characteristics. Model predictions are compared with experimental data for the bovine serum albumin sieving coefficient at different pH and ionic strength. These results provide important insights into the effects of charge regulation on the magnitude of the electrostatic interactions between charged proteins and charged pores. Copyright 1997Academic Press

Journal Article↗

The Electrostatic Interaction of Rigid, Globular Proteins with Arbitrary Charge Distributions.

We use the linearized Poisson-Boltzmann equation to construct an analytical estimate of the electrostatic interaction energy for two rigid, globular proteins with arbitrary charge distributions represented by spherical multipole moments. Our analysis avoids invoking the superposition approximation and therefore is not limited to weakly interacting double layers. The interaction energy is a function of the protein properties (radii, multipole moments, and dielectric constant); the geometry (protein separation and orientations); and the solution properties (Debye screening length and dielectric constant). The proteins may be different. This is an extension of previous treatments for constant surface charge or for constant surface potential particles that are more applicable to isotropic colloids. We give example calculations for the interactions of Ribonuclease A molecules interacting in an electrolyte. These results suggest that electrostatic effects may be largely responsible for attractions between proteins, even if they are like charged. A set of routines using MATHEMATICA is available for performing the interaction energy and electrostatic potential calculations. Copyright 1998 Academic Press.

Journal Article↗

Electrostatic Contribution to the Enthalpy of Charging at Hematite/Electrolyte Interface.

A calorimetry study of hematite surface reactions is reported, with special emphasis on the estimation of the electrostatic contribution to the enthalpy of charging. The calorimetry titrations were performed outside the point of zero charge region where the electrostatic contribution is significant. The results were interpreted by the surface complexation model. The interpretation enabled the evaluation of standard protonation and deprotonation enthalpies as well as the electrostatic contribution to these quantities. Copyright 1999 Academic Press.

Journal Article↗

Electrostatic Interaction and Partitioning of Ion-Penetrable Spheres.

Electrostatic interaction between two ion-penetrable spheres near a horizontal plate or in a slit pore is investigated theoretically. The orientation of the line connecting the two particle centers can be arbitrary relative to the plate(s). The electrostatic interaction energy and force on each particle are obtained analytically by the method of images. Emphasis is placed on the effect of the presence of the second particle, compared to the case of a single particle or the case without any plate(s). It is found that the horizontal electrical force on each particle is always repulsive. This repulsive force is enhanced by the plate(s) of constant surface charge density, while it is reduced by the plate(s) of constant surface potential. The electrostatic interaction together with the steric effect is used to determine the partition coefficient for the case of a slit pore, correct to O(C(infinity)), where C(infinity) is the volume fraction of particles in the bulk solution. The positive correction coefficient is larger for conducting plates than for insulating plates. Copyright 2001 Academic Press.

Journal Article↗