Electrostatic effects in unfolded staphylococcal nuclease

Structure-based calculations of pKa values and electrostatic free energies of proteins assume that electrostatic effects in the unfolded state are negligible. In light of experimental evidence showing that this assumption is invalid for many proteins, and with increasing awareness that the unfolded state is more structured and compact than previously thought, a detailed examination of electrostatic effects in unfolded proteins is warranted. Here we address this issue with structure-based calculations of electrostatic interactions in unfolded staphylococcal nuclease. The approach involves the generation of ensembles of structures representing the unfolded state, and calculation of Coulomb energies to Boltzmann weight the unfolded state ensembles. Four different structural models of the unfolded state were tested. Experimental proton binding data measured with a variant of nuclease that is unfolded under native conditions were used to establish the validity of the calculations. These calculations suggest that weak Coulomb interactions are an unavoidable property of unfolded proteins. At neutral pH, the interactions are too weak to organize the unfolded state; however, at extreme pH values, where the protein has a significant net charge, the combined action of a large number of weak repulsive interactions can lead to the expansion of the unfolded state. The calculated pKa values of ionizable groups in the unfolded state are similar but not identical to the values in small peptides in water. These studies suggest that the accuracy of structure-based calculations of electrostatic contributions to stability cannot be improved unless electrostatic effects in the unfolded state are calculated explicitly.     

Transfer RNAs: electrostatic patterns and an early stage of recognition by synthetases and elongation factor EF-Tu

Distributions of phosphate backbone-produced electrostatic potentials around several tRNAs were calculated by solving the nonlinear Poisson-Boltzmann equation. The tRNAs were either free or bound to the proteins involved in translation: aminoacyl-tRNA and elongation factor EF-Tu. We identified several regions of strong negative potential related to typical structural patterns of tRNA and invariant throughout the tRNAs. The patterns are conserved upon binding of tRNAs to the synthetase and the EF-Tu. Variation of tRNA charge in our theoretical calculations of electrostatic potential-mediated pK shifts of pH-dependent labels attached to tRNA, compared to experimentally observed pK shifts for those labels, shows that the total charge of tRNA is large, within the interval of -40 to -70 proton charges. The electrostatic field of tRNA is sufficient to cause ionization of histidine residues of ARSase, causing additional free energy of ARSase-tRNA interaction of at least several kcal/mol. This may discriminate proteins with respect to the particular tRNA at large distances. Two types of tRNA-protein electrostatic recognition mechanisms are discussed. One, more specific, involves charges induced on protein by the large electrostatic potential of tRNA, while the other, less specific, does not involve induced charges.     

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.     

Calbindin D(9k): a protein optimized for calcium binding at neutral pH.

The binding of calcium ions by EF-hand proteins depends strongly on the electrostatic interactions between Ca(2+) ions and negatively charged residues of these proteins. We have investigated the pH dependence of the binding of Ca(2+) ions by calbindin D(9k). This protein offers a unique possibility for interpretation of such data since the pK(a) values of all ionizable groups are known. The binding is independent of pH between 7 and 9, where maximum calcium affinity is observed. An abrupt decrease in the binding affinity is observed at pH values below 7. This decrease is due to protonation of acidic groups, leading to modification of protein charges. The pH dependence of the product of the two macroscopic Ca(2+)-binding constants can be formally described by the involvement of two acidic groups with pK(a) = 6.6. Monte Carlo calculations show that the reduction of Ca(2+) binding is strictly determined by variable electrostatic interactions due to pH-dependent changes not only in the binding sites, but also of the overall charge of the protein.     

DAPI binding to the DNA minor groove: a continuum solvent analysis

A continuum solvent model based on the generalized Born (GB) or finite-difference Poisson-Boltzmann (FDPB) approaches has been employed to compare the binding of 4'-6-diamidine-2-phenyl indole (DAPI) to the minor groove of various DNA sequences. Qualitative agreement between the results of GB and FDPB approaches as well as between calculated and experimentally observed trends regarding the sequence specificity of DAPI binding to B-DNA was obtained. Calculated binding energies were decomposed into various contributions to solvation and DNA-ligand interaction. DNA conformational adaptation was found to make a favorable contribution to the calculated total interaction energy but did not change the DAPI binding affinity ranking of different DNA sequences. The calculations indicate that closed complex formation is mainly driven by nonpolar contributions and was found to be disfavored electrostatically due to a desolvation penalty that outbalances the attractive Coulomb interaction. The calculated penalty was larger for DAPI binding to GC-rich sequences compared with AT-rich target sequences and generally larger for the FDPB vs the GB continuum model. A radial interaction profile for DAPI at different distances from the DNA minor groove revealed an electrostatic energy minimum a few Angstroms farther away from the closed binding geometry. The calculated electrostatic interaction up to this distance is attractive and it may stabilize a nonspecific binding arrangement.     

静电和疏水效应对胰岛素二聚体稳定性的影响

从猪胰岛素二聚体的结构出发,着重研究了胰岛素二聚体单体之间的静电和疏水相互作用,用连续介质模型的有限差分方法计算得到胰岛素二聚体的静电势,用溶剂可接近表面（ASA）模型分析了分子表面积及疏水性,还考察了不同pH值对胰岛素二聚体静电和疏水相互作用的影响。结果分析表明,当pH值处于弱酸弱碱范围内时（4．6－8．5）,静电相 互作用能和疏水自由能都呈现出较小的值,当pH为6．2时,疏水性出现一个明显的峰值,这与胰岛素二聚体结晶的实验条件相吻合。     

The effect of heme-linked ionizable groups on cyanide binding to methemoglobin

The pH dependence of the kinetics of the binding of cyanide ion to methemoglobins A and S and to guinea pig and pigeon methemoglobins appears to be not directly correlated with the net charges on the proteins. The kinetics can, however, be adequately explained in terms of three sets of heme-linked ionizable groups with pK1 ranging between 4.9 and 5.3, pK2 between 6.2 and 7.9, and pK3 between 8.0 and 8.5 at 20 degrees C. pK1 is assigned to carboxylic acid groups, pK2 to histidines and terminal amino groups, and pK3 to the acid-alkaline methemoglobin transition. Kinetic second order rate constants have also been determined for the binding of cyanide ion by the four sets of methemoglobin species present in solution. The pKi values and the rate constants of methemoglobin S are strikingly different from those of methemoglobin A. This result is explained in terms of different electrostatic contributions to the free energy of heme linkage arising from differences in the environments of ionizable groups at the surfaces of the two molecules.     

Lipid demixing and protein-protein interactions in the adsorption of charged proteins on mixed membranes

The adsorption free energy of charged proteins on mixed membranes, containing varying amounts of (oppositely) charged lipids, is calculated based on a mean-field free energy expression that accounts explicitly for the ability of the lipids to demix locally, and for lateral interactions between the adsorbed proteins. Minimization of this free energy functional yields the familiar nonlinear Poisson-Boltzmann equation and the boundary condition at the membrane surface that allows for lipid charge rearrangement. These two self-consistent equations are solved simultaneously. The proteins are modeled as uniformly charged spheres and the (bare) membrane as an ideal two-dimensional binary mixture of charged and neutral lipids. Substantial variations in the lipid charge density profiles are found when highly charged proteins adsorb on weakly charged membranes; the lipids, at a certain demixing entropy penalty, adjust their concentration in the vicinity of the adsorbed protein to achieve optimal charge matching. Lateral repulsive interactions between the adsorbed proteins affect the lipid modulation profile and, at high densities, result in substantial lowering of the binding energy. Adsorption isotherms demonstrating the importance of lipid mobility and protein-protein interactions are calculated using an adsorption equation with a coverage-dependent binding constant. Typically, at bulk-surface equilibrium (i.e., when the membrane surface is "saturated" by adsorbed proteins), the membrane charges are "overcompensated" by the protein charges, because only about half of the protein charges (those on the hemispheres facing the membrane) are involved in charge neutralization. Finally, it is argued that the formation of lipid-protein domains may be enhanced by electrostatic adsorption of proteins, but its origin (e.g., elastic deformations associated with lipid demixing) is not purely electrostatic.     

Electron transfer between flavodoxin semiquinone and c-type cytochromes: correlations between electrostatically corrected rate constants, redox potentials, and surface topologies

We have measured the ionic strength dependence of the rate constants for electron transfer from the semiquinone of Clostridium pasteurianum flavodoxin to 12 c-type cytochromes and several inorganic oxidants using stopped-flow methodology. The experimental data were fit quite well by an electrostatic model that represents the interaction domains as parallel disks with a point charge equal to the charge within this region of the protein. The analysis provides an evaluation of the electrostatic interaction energy and the rate constant at infinite ionic strength (k affinity). The electrostatic charge on the oxidant within the interaction site can be obtained from the electrostatic energy, and for most of those reactants for which structures are available, the results are in good agreement with expectation. The k affinity values were found to correlate with redox potential differences, as expected from the theory of adiabatic (or nonadiabatic) outer-sphere electron-transfer reactions. Deviations from the theoretical curves are interpreted in terms of the influence of surface topology on reaction rate constants. In general, we find that electrostatic effects, steric influences, and redox potential all exert a much larger effect on reaction rate constants for the flavodoxin-cytochrome system than has been previously observed for free flavin-cytochrome interactions. The implications of this for determining biological specificity are discussed.     

Criteria that discriminate between native proteins and incorrectly folded models

Various theoretical concepts, such as free energy potentials, electrostatic interaction potentials, atomic packing, solvent-exposed surface, and surface charge distribution, were tested for their ability to discriminate between native proteins and misfolded protein models. Misfolded models were constructed by introducing incorrect side chains onto polypeptide backbones: side chains of the alpha-helical hemerythrin were modeled on the beta-sheeted backbone of immunoglobulin VL domain, whereas those of the VL domain were similarly modeled on the hemerythrin backbone. CONGEN, a conformational space sampling program, was used to construct the side chains, in contrast to the previous work, where incorrect side chains were modeled in all trans conformations. Capability of the conformational search procedure to reproduce native conformations was gauged first by rebuilding (the correct) side chains in hemerythrin and the VL domain: constructs with r.m.s. differences from the x-ray side chains 2.2-2.4 A were produced, and many calculated conformations matched the native ones quite well. Incorrectly folded models were then constructed by the same conformational protocol applied to incorrect amino acid sequences. All CONGEN constructs, both correctly and incorrectly folded, were characterized by exceptionally small molecular surfaces and low potential energies. Surface charge density, atomic packing, and Coulomb formula-based electrostatic interactions of the misfolded structures and the correctly folded proteins were similar, and therefore of little interest for diagnosing incorrect folds. The following criteria clearly favored the native structures over the misfolded ones: 1) solvent-exposed side-chain nonpolar surface, 2) number of buried ionizable groups, and 3) empirical free energy functions that incorporate solvent effects.     

Optimized atomic radii for protein continuum electrostatics solvation forces

Recently, we presented a Green's function approach for the calculation of analytic continuum electrostatic solvation forces based on numerical solutions of the finite-difference Poisson-Botzmann (FDPB) equation [Im et al., Comp. Phys. Comm. 111 (1998) 59]. In this treatment the analytic forces were explicitly defined as the first derivative of the FDPB continuum electrostatic free energy with respect to the coordinates of the solute atoms. A smooth intermediate region for the solute-solvent dielectric boundary needed to be introduced to avoid abrupt discontinuous variations in the solvation free energy and forces as a function of the atomic positions. In the present paper we extend the set of optimized radii, which was previously parametrized from molecular dynamics free energy simulations of the 20 standard amino acids with explicit solvent molecules [Nina et al., J. Phys. Chem. 101 (1997) 5239], to yield accurate solvation free energy by taking the influence of the smoothed dielectric region into account.     

Identification and analysis of long-range electrostatic effects in proteins by computer modeling:Aspartate transcarbamylase

While ion pairs are readily identified in crystal structures, longer range electrostatic interactions cannot be identified from the three-dimensional structure alone. These interactions are likely to be important in large, multisubunit proteins that are regulated by allosteric interactions. In this paper, we show that these interactions are readily detected by electrostatic modeling, using, as an example, unliganded Escherichia coli aspartate transcarbamylase, a widely studied allosteric enzyme with 12 subunits and a molecular weight of 310 kD. The Born, dipolar, and site-site interaction terms of the free energy of protonation of the 810 titratable sites in the holoenzyme were calculated using the multigrid solution of the nonlinear Poisson-Boltzmann equation. Calculated titration curves are in good agreement with experimental titration curves, and the structural asymmetry observed in the crystal structure is readily apparent in the calculated free energies and pK_1/2 values. Most of the residues with pK_1/2 values that differ substantially from those of model compounds are buried in the low dielectric medium of the protein, particularly at the intersubunit interfaces. The dependence of the site-site interaction free energies on distance is complex, with a steep dependence at distances less than 5 Å and a more shallow dependence at longer distances. Interactions over distances of 6 to 15 Å require a bridging residue and are often not apparent in the structure. The network of interactions between ionizable groups extends across and between subunits and provides a potential mechanism for transmitting long-range structural effects and allosteric signals. © 1996 Wiley-Liss, Inc.     

Are unit charges always negligible?

 The electrostatic contribution to the reduction potentials due to the unit charges of ionizable residues largely explains the span in redox potentials in a series of high-potential Fe₄S₄ iron-sulfur proteins and mutants. This appears to be a lucky case in which other contributions (in general) larger than that due to unit charges cancel out. Received, accepted: 26 November 1996     

Coupling between conformation and proton binding in proteins

Interest centers here on whether the use of a fixed charge distribution of a protein solute, or a treatment that considers proton-binding equilibria by solving the Poisson equation, is a better approach to discriminate native from non-native conformations of proteins. In this analysis of the charge distribution of 7 proteins, we estimate the solvation free energy contribution to the total free energy by exploring the 2(zeta) possible ionization states of the whole molecule, with zeta being the number of ionizable groups in the amino acid sequence, for every conformation in the ensembles of 7 proteins. As an additional consideration of the role of electrostatic interactions in determining the charge distribution of native folds, we carried out a comparison of alternative charge assignment models for the ionizable residues in a set of 21 native-like proteins. The results of this work indicate that (1) for 6 out of 7 proteins, estimation of solvent polarization based on the Generalized Born model with a fixed charge distribution provides the optimal trade-off between accuracy, with respect to the Poisson equation, and speed when compared to the accessible surface area model; for the seventh protein, consideration of all possible ionization states of the whole molecule appears to be crucial to discriminate the native from non-native conformations; (2) significant differences in the degree of ionization and hence the charge distribution for native folds are found between the different charge models examined; (3) the stability of the native state is determined by a delicate balance of all the energy components, and (4) conformational entropy, and hence the dynamics of folding, may play a crucial role for a successful ab initio protein folding prediction.     

Electrostatic screening in molecular dynamics simulations.

The screened Coulombic potential has been shown to describe satisfactorily equilibrium properties like pK shifts, the effects of charged groups on redox potentials and binding constants of metal ions. To test how well the screening of the electrostatic potential describes the dynamical trajectory of a macromolecular system, a series of comparative simulations have been carried out on a protein system which explicitly included water molecules and a system in vacuo. For the system without solvent the results of using (i) the standard potential form were compared with results of (ii) the potential where the Coulomb term was modified by the inclusion of a distance dependent dielectric, epsilon (r), to model the screening effect of bulk water, and (iii) standard potential modified by reducing the charge on ionized residue side chains. All molecular dynamics simulations have been carried out on bovine pancreatic trypsin inhibitor. Comparisons between the resulting trajectories, averaged structures, hydrogen bonding patterns and properties such as solvent accessible surface area and radius of gyration are described. The results show that the dynamical behaviour of the protein calculated with a screened electrostatic term compares more favourably with the time-dependent structural changes of the full system with explicitly included water than the standard vacuum simulation.     

Binding free energy calculations of adenosine deaminase inhibitors

The interactions between four inhibitors and adenosine deaminase (ADA) were examined by calculating their binding free energies after molecular dynamics simulations. A bonded model was used to represent the electrostatic potentials of the zinc coordination site. The charge distribution of the model was derived by using a two-stage electrostatic potential fitting calculations. The calculated binding free energies are in good agreement with the experimental data and the ranking of binding affinities is well reproduced. Notably, our findings suggest that non-polar contributions play an important role for ADA-inhibitor interactions.     

Do salt bridges stabilize proteins? A continuum electrostatic analysis

The electrostatic contribution to the free energy of folding was calculated for 21 salt bridges in 9 protein X-ray crystal structures using a continuum electrostatic approach with the DELPHI computer-program package. The majority (17) were found to be electrostatically destabilizing; the average free energy change, which is analogous to mutation of salt bridging side chains to hydrophobic isosteres, was calculated to be 3.5 kcal/mol. This is fundamentally different from stability measurements using pKa shifts, which effectively measure the strength of a salt bridge relative to 1 or more charged hydrogen bonds. The calculated effect was due to a large, unfavorable desolvation contribution that was not fully compensated by favorable interactions within the salt bridge and between salt-bridge partners and other polar and charged groups in the folded protein. Some of the salt bridges were studied in further detail to determine the effect of the choice of values for atomic radii, internal protein dielectric constant, and ionic strength used in the calculations. Increased ionic strength resulted in little or no change in calculated stability for 3 of 4 salt bridges over a range of 0.1-0.9 M. The results suggest that mutation of salt bridges, particularly those that are buried, to "hydrophobic bridges" (that pack at least as well as wild type) can result in proteins with increased stability. Due to the large penalty for burying uncompensated ionizable groups, salt bridges could help to limit the number of low free energy conformations of a molecule or complex and thus play a role in determining specificity (i.e., the uniqueness of a protein fold or protein-ligand binding geometry).     

The uptake of protons by heme-linked ionizable groups on azide binding to methemoglobin

When azide ion reacts with methemoglobin in unbuffered solution the pH of the solution increases. This phenomenon is associated with increases in the pK values of heme-linked ionizable groups on the protein which give rise to an uptake of protons from solution. We have determined as a functional of pH the proton uptake, delta h+, on azide binding to methemoglobin at 20 degrees C. Data for methemoglobins A (human), guinea pig and pigeon are fitted to a theoretical expression based on the electrostatic effect of these sets of heme-linked ionizable groups on the binding of the ligand. From these fits the pK values of heme-linked ionizable groups are obtained for liganded and unliganded methemoglobins. In unliganded methemoglobin pK1, which is associated with carboxylic acid groups, ranges between 4.0 and 5.5 for the three methemoglobins; pK2, which is associated with histidines and terminal amino groups, ranges from 6.2 to 6.7. In liganded methemoglobin pK1 lies between 5.8 and 6.3 and pK2 varies from 8.1 to 8.5. The pH dependences of the apparent equilibrium constants for azide binding to the three methemoglobins at 20 degrees C are well accounted for with the pK values calculated from the variation of delta h+ with pH.     

Statistics and Physical Origins of pK and Ionization State Changes upon Protein-Ligand Binding

This work investigates statistical prevalence and overall physical origins of changes in charge states of receptor proteins upon ligand binding. These changes are explored as a function of the ligand type (small molecule, protein, and nucleic acid), and distance from the binding region. Standard continuum solvent methodology is used to compute, on an equal footing, pK changes upon ligand binding for a total of 5899 ionizable residues in 20 protein-protein, 20 protein-small molecule, and 20 protein-nucleic acid high-resolution complexes. The size of the data set combined with an extensive error and sensitivity analysis allows us to make statistically justified and conservative conclusions: in 60% of all protein-small molecule, 90% of all protein-protein, and 85% of all protein-nucleic acid complexes there exists at least one ionizable residue that changes its charge state upon ligand binding at physiological conditions (pH = 6.5). Considering the most biologically relevant pH range of 4-8, the number of ionizable residues that experience substantial pK changes (ΔpK > 1.0) due to ligand binding is appreciable: on average, 6% of all ionizable residues in protein-small molecule complexes, 9% in protein-protein, and 12% in protein-nucleic acid complexes experience a substantial pK change upon ligand binding. These changes are safely above the statistical false-positive noise level. Most of the changes occur in the immediate binding interface region, where approximately one out of five ionizable residues experiences substantial pK change regardless of the ligand type. However, the physical origins of the change differ between the types: in protein-nucleic acid complexes, the pK values of interface residues are predominantly affected by electrostatic effects, whereas in protein-protein and protein-small molecule complexes, structural changes due to the induced-fit effect play an equally important role. In protein-protein and protein-nucleic acid complexes, there is a statistically significant number of substantial pK perturbations, mostly due to the induced-fit structural changes, in regions far from the binding interface.     

Redox potential of quinones in photosynthetic reaction centers from Rhodobacter sphaeroides: dependence on protonation of Glu-L212 and Asp-L213

The absolute values of the one-electron redox potentials of the two quinones (Q(A) and Q(B)) in bacterial photosynthetic reaction centers from Rhodobacter sphaeroides were calculated by evaluating the electrostatic energies from the solution of the linearized Poisson-Boltzmann equation at pH 7.0. The redox potential for Q(A) was calculated to be between -173 and -160 mV, which is close to the lowest measured values that are assumed to refer to nonequilibrated protonation patterns in the redox state Q(A)(-). The redox potential of quinone Q(B) is found to be about 160-220 mV larger for the light-exposed than for the dark-adapted structure. These values of the redox potentials are obtained if Asp-L213 is nearly protonated (probability 0.75-1.0) before and after electron transfer from Q(A) to Q(B), while Glu-L212 is partially protonated (probability 0.6) in the initial state Q(A)(-)Q(B)(0) and fully protonated in the final state Q(A)(0)Q(B)(-). Conversely, if the charge state of the quinones is varied from Q(A)(-)Q(B)(0) to Q(A)(0)Q(B)(-) corresponding to the electron transfer from Q(A) to Q(B), Asp-L213 remains protonated, while Glu-L212 changes its protonation state from 0.15 H(+) to fully protonated. In agreement with results from FTIR spectra, there is proton uptake at Glu-L212 going along with the electron transfer, whereas Asp-L213 does not change its protonation state. However, in our simulations Asp-L213 is considered to be protonated rather than ionized as deduced from FTIR spectra. The calculated redox potential of Q(A) shows little dependence on the charge state of Asp-L213, which is due to a strong coupling with the protonation state of Asp-M17 but increases by 50 mV if Glu-L212 changes from the ionized to the protonated charge state. Both are in agreement with fluorescence measurements observing the decay of SP(+)Q(A)(-) in a wide pH regime. The computed difference in redox potential of Q(B) in the light-exposed and dark-adapted structure was traced back to the hydrogen bond of Q(B) with His-L190 that is lost in the dark-adapted structure and the charge of the non-heme iron atom, which is closer to Q(B) in the light-exposed than in the dark-adapted structure.