The Molecular Determinants of the Increased Reduction Potential of the Rubredoxin Domain of Rubrerythrin Relative to Rubredoxin

Based on the crystal structures, three possible sequence determinants have been suggested as the cause of a 285 mV increase in reduction potential of the rubredoxin domain of rubrerythrin over rubredoxin by modulating the polar environment around the redox site. Here, electrostatic calculations of crystal structures of rubredoxin and rubrerythrin and molecular dynamics simulations of rubredoxin wild-type and mutants are used to elucidate the contributions to the increased reduction potential. Asn¹⁶⁰ and His¹⁷⁹ in rubrerythrin versus valines in rubredoxins are predicted to be the major contributors, as the polar side chains contribute significantly to the electrostatic potential in the redox site region. The mutant simulations show both side chains rotating on a nanosecond timescale between two conformations with different electrostatic contributions. Reduction also causes a change in the reduction energy that is consistent with a linear response due to the interesting mechanism of shifting the relative populations of the two conformations. In addition to this, a simulation of a triple mutant indicates the side-chain rotations are approximately anticorrelated so whereas one is in the high potential conformation, the other is in the low potential conformation. However, Ala¹⁷⁶ in rubrerythrin versus a leucine in rubredoxin is not predicted to be a large contributor, because the solvent accessibility increases only slightly in mutant simulations and because it is buried in the interface of the rubrerythrin homodimer.     

Characterizing the effects of the protein environment on the reduction potentials of metalloproteins

The reduction potentials of electron transfer proteins are critically determined by the degree of burial of the redox site within the protein and the degree of permanent polarization of the polypeptide around the redox site. Although continuum electrostatics calculations of protein structures can predict the net effect of these factors, quantifying each individual contribution is a difficult task. Here, the burial of the redox site is characterized by a dielectric radius R _p (a Born-type radius for the protein), the polarization of the polypeptide is characterized by an electret potential ? _p (the average electrostatic potential at the metal atoms), and an electret-dielectric spheres (EDS) model of the entire protein is then defined in terms of R _p and ? _p. The EDS model shows that for a protein with a redox site of charge Q, the dielectric response free energy is a function of Q ², while the electret energy is a function of Q. In addition, R _p and ? _p are shown to be characteristics of the fold of a protein and are predictive of the most likely redox couple for redox sites that undergo different redox couples.     

Molecular dynamics simulations of rubredoxin from Clostridium pasteurianum: Changes in structure and electrostatic potential duringredox 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 Å, 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 Å). 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 kcall/mol/e) and the polar sidechains 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. © 1995 Wiley-Liss, Inc.     

Experimental evaluation of the effective dielectric constant of proteins

Chemical modifications that alter the net charge of residues in reduction-oxidation proteins influence the redox potential of the protein by changing the electrostatic potential at the redox center. If the locations of the modified charges are known, the shift in redox potential may be used to determine the effective dielectric constant for the interactions between the redox center and modified residues. From the shift in redox potential upon charge neutralization of specific lysines in the hemoprotein cytochrome c, an effective dielectric constant of approximately 50 is calculated for the electrostatic interaction between the modified lysines and heme iron in the native protein.     

The redox potentials of the two-iron plant algal ferredoxins. An electrostatic model

The two-iron-sulphur co-ordination centre in plant and algal ferredoxins is considered as a collection of charged ions whose net negative charge is twice that of the one-iron-sulphur protein rubredoxin. Calculation of the electrostatic free-energy changes for reduction of the two types of proteins indicates that the redox potential of the two-iron-sulphur proteins should be more negative than that of the one-iron-sulphur protein and that in biological systems the ferredoxins should function as one-electron transfer proteins.     

Protein contributions to redox potentials of homologous rubredoxins: an energy minimization study.

The energetic contributions of the protein to the redox potential in an iron-sulfur protein are studied via energy minimization, comparing homologous rubredoxins from Clostridium pasteurianum, Desulfovibrio gigas, Desulfovibrio vulgaris, and Pyrococcus furiosus. The reduction reaction was divided into 1) the change in the redox site charge without allowing the protein to respond and 2) the relaxation of the protein in response to the new charge state, focusing on the latter. The energy minimizations predict structural relaxation near the redox site that agrees well with that in crystal structures of oxidized and reduced P. furiosus rubredoxin, but underpredicts it far from the redox site. However, the relaxation energies from the energy-minimized structures agree well with those from the crystal structures, because the polar groups near the redox site are the main determinants and the charged groups are all located at the surface and thus are screened dielectrically. Relaxation energies are necessary for good agreement with experimentally observed differences in reduction energies between C. pasteurianum and the other three rubredoxins. Overall, the relaxation energy is large (over 500 mV) from both the energy-minimized and the crystal structures. In addition, the range in the relaxation energy for the different rubredoxins is large (300 mV), because even though the structural perturbations of the polar groups are small, they are very near the redox site. Thus the relaxation energy is an important factor to consider in reduction energetics.     

Can a simple function for the dielectric response model electrostatic effects in globular proteins?

The relationship between the effective dielectric constant that models the electrostatic effect from a charged side chain in a protein was evaluated both experimentally and theoretically. Experimental values were obtained from the shifts in pKa that resulted from point mutations of side chains in subtilisin. Theoretical values were obtained from an iterative solution to Poisson's equation that considers the dielectric response of the protein and the solvent together with charge positions. There is no simple relationship between the effective dielectric constant and the distance from the charge responsible for the interactions. For some charge positions a linear but not a direct proportional relationship of the effective dielectric with distance of separation was observed. Thus, simple models such as a linear distance-dependence for the dielectric response are not suitable to evaluate electrostatic effects in proteins.     

Redox properties of mesophilic and hyperthermophilic rubredoxins as a function of pressure and temperature.

The formal equilibrium reduction potentials of recombinant electron transport protein, rubredoxin (MW = 7500 Da), from both the mesophilic Clostridium pasteurianum (Topt = 37 degrees C) and hyperthermophilic Pyrococcus furiosus (Topt = 95 degrees C) were recorded as a function of pressure and temperature. Measurements were made utilizing a specially designed stainless steel electrochemical cell that easily maintains pressures between 1 and 600 atm and a temperature-controlled cell that maintains temperatures between 4 and 100 degrees C. The reduction potential of P. furiosus rubredoxin was determined to be 31 mV at 25 degrees C and 1 atm, -93 mV at 95 degrees C and 1 atm, and 44 mV at 25 degrees C and 400 atm. Thus, the reduction potential of P. furiosus rubredoxin obtained under standard conditions is likely to be dramatically different from the reduction potential obtained under its normal operating conditions. Thermodynamic parameters associated with electron transfer were determined for both rubredoxins (for C. pasteurianum, DeltaV degrees = -27 mL/mol, DeltaS degrees = -36 cal K-1 mol-1, and DeltaH degrees = -10 kcal/mol, and for P. furiosus, DeltaV degrees = -31 mL/mol, DeltaS degrees = -41 cal K-1 mol-1, and DeltaH degrees = -13 kcal/mol) from its pressure- and temperature-reduction potential profiles. The thermodynamic parameters for electron transfer (DeltaV degrees, DeltaS degrees, and DeltaH degrees ) for both proteins were very similar, which is not surprising considering their structural similarities and sequence homology. Despite the fact that these two proteins exhibit dramatic differences in thermostability, it appears that structural changes that confer dramatic differences in thermostability do not significantly alter electron transfer reactivity. The experimental changes in reduction potential as a function of pressure and temperature were simulated using a continuum dielectric electrostatic model (DELPHI). A reasonable estimate of the protein dielectric constant (epsilonprotein) of 6 for both rubredoxins was determined from these simulations. A discussion is presented regarding the analysis of electrostatic interaction energies of biomolecules through pressure- and temperature-controlled electrochemical studies.     

Electrostatic potential energy within a protein monitored by metal charge-dependent hydrogen exchange

Hydrogen exchange measurements on Zn(II)-, Ga(III)-, and Ge(IV)-substituted Pyrococcus furiosus rubredoxin demonstrate that the log ratio of the base-catalyzed rate constants (Delta log k(ex)) varies inversely with the distance out to at least 12 A from the metal. This pattern is consistent with the variation of the amide nitrogen pK values with the metal charge-dependent changes in the electrostatic potential. Fifteen monitored amides lie within this range, providing an opportunity to assess the strength of electrostatic interactions simultaneously at numerous positions within the structure. Poisson-Boltzmann calculations predict an optimal effective internal dielectric constant of 6. The largest deviations between the experimentally estimated and the predicted DeltapK values appear to result from the conformationally mobile charged side chains of Lys-7 and Glu-48 and from differential shielding of the peptide units arising from their orientation relative to the metal site.     

Redox potential of the Rieske iron-sulfur protein: Quantum-chemical and electrostatic study

Quantum-chemical study of structures, energies, and effective partial charge distribution for several models of the Rieske protein redox center is performed in terms of the B3LYP density functional method in combination with the broken symmetry approach using three different atomic basis sets. The structure of the redox complex optimized in vacuum differs markedly from that inside the protein. This means that the protein matrix imposes some stress on the active site resulting in distortion of its structure. The redox potentials calculated for the real active site structure are in a substantially better agreement with the experiment than those calculated for the idealized structure. This shows an important role of the active site distortion in tuning its redox potential. The reference absolute electrode potential of the standard hydrogen electrode is used that accounts for the correction caused by the water surface potential. Electrostatic calculations are performed in the framework of the polarizable solute model. Two dielectric permittivities of the protein are employed: the optical permittivity for calculation of the intraprotein electric field, and the static permittivity for calculation of the dielectric response energy. Only this approach results in a reasonable agreement of the calculated and experimental redox potentials.     

Microscopic and semimacroscopic redox calculations: what can and cannot be learned from continuum models

 The major role of electrostatic effects in the control of redox potentials in proteins is now widely appreciated. However, the evaluation and conceptualization of the actual electrostatic contributions is far from trivial, and some models still overlook the nature of electrostatic effects in proteins. This commentary considers different contributions to redox potentials of proteins and discusses the ability of different models to capture these contributions. It is pointed out that macroscopic models which consider the protein as a medium of uniform low dielectric constant cannot reproduce the proper physics of redox proteins. In particular, it is pointed out that the crucial effects of the protein permanent dipoles must be taken into account explicitly and that these permanent dipoles involve effective dielectric constants that are different from those for ionized residues. It is also argued that the reorganization of the protein upon change of oxidation states or ionization of protein residues should be taken into account in redox calculations. The role of water penetration and the inadequacy of describing electrostatic effects by solvent accessibility is briefly mentioned. The nature and the meaning of the "dielectric constant" that should be used in redox calculations are also discussed. It is pointed out that the "dielectric constant" ε_p used in current discretized continuum (DC) models is simply a representation of the contributions which are treated implicitly and not the proper dielectric constant of the protein. It is then explained that the need to use a large "dielectric constant" in DC models reflects, among other factors, the implicit representation of the reorganization of permanent dipoles, and that even an explicit treatment of the fluctuations of ionized surface residues will lead to incorrect results when one uses ε_p=εˉ in continuum treatments. Finally, it is suggested that although the discussion and classification of different contributions to redox potentials is very useful, only the evaluation of the totality of the protein contributions (rather than an arbitrary subset) can lead to a quantitative understanding of redox proteins. Received, accepted: 26 November 1996     

Molecular interpretation of kinetic-ionic strength effects

A recent and important approach to investigating electron transfer mechanisms of redox proteins has been through kinetic-ionic strength studies. There is, however, significant controversy as to whether such studies (1) yield information regarding the charge (or location) of the electron transfer site or (2) more simply reflect the influence of net or overall protein charge on the electrostatic interactions. A critical analysis using different theoretical approaches is made of our recent work and of the bulk of the published non-physiological small molecule-protein and protein-protein kinetic ionic strength studies; it is concluded that (1) the approximated Bronsted-Debye-Huckel equation can not be used at all for protein redox reactions, (2) irrespective of the theoretical approaches discussed, such studies do not provide information regarding the charge of the electron transfer site, (3) it is the net charge of the reactants that control the electrostatic interactions, (4) both the equation derived by Wherland and Gray and the full Bronsted-Debye-Huckel equation provide reasonably good approximations of net protein charge, (5) pH changes quantitatively modulate net protein charge, and (6) thus, protein redox rates need to be electrostatically corrected if relevant interpretations of kinetic-ionic strength experiments are to be made.     

Electrostatic and redox potential effects on the rat of electron-transfer reaction of nicotinamide adenine dinucleotides with 1-substituted 5-ethylphenazines

The effects of redox potential and electric charge on the rate of electron-transfer reaction by a two-electron process were investigated. For electron donors, beta-NADH, beta-NADPH and alpha-NADH were used; they have similar structures but different charges and different redox potentials. For electron acceptors, the following 5-ethylphenazine derivatives were used: 1-(3-carboxypropyloxy)-5-ethylphenazine, 1-(3-ethoxycarbonylpropyloxy)-5-ethylphenazine, and 1-[N-(2-aminoethyl)carbamoylpropyloxy]-5-ethylphenazine. They have similar structures and different charges. Using these donors and acceptors, the potential and the charge effects were estimated separately. In the potential effect, a linear free energy relationship was observed for the change in the redox potential of the donor with a Br?nsted slope of about unity. On the other hand, the slope for the change in the potential of the acceptor was about 0.5. These results show that the potential effect due to electron donors is different from that due to electron acceptors. A linear relationship was also observed between activation free energy and electrostatic force (or potential). The redox potential effect and the electrostatic effect are independent and additive. New theory for the mechanism of electron-transfer reactions is needed to explain these results.     

Leucine 41 is a gate for water entry in the reduction of Clostridium pasteurianum rubredoxin

Biological electron transfer is an efficient process even though the distances between the redox moieties are often quite large. It is therefore of great interest to gain an understanding of the physical basis of the rates and driving forces of these reactions. The structural relaxation of the protein that occurs upon change in redox state gives rise to the reorganizational energy, which is important in the rates and the driving forces of the proteins involved. To determine the structural relaxation in a redox protein, we have developed methods to hold a redox protein in its final oxidation state during crystallization while maintaining the same pH and salt conditions of the crystallization of the protein in its initial oxidation state. Based on 1.5 A resolution crystal structures and molecular dynamics simulations of oxidized and reduced rubredoxins (Rd) from Clostridium pasteurianum (Cp), the structural rearrangements upon reduction suggest specific mechanisms by which electron transfer reactions of rubredoxin should be facilitated. First, expansion of the [Fe-S] cluster and concomitant contraction of the NH...S hydrogen bonds lead to greater electrostatic stabilization of the extra negative charge. Second, a gating mechanism caused by the conformational change of Leucine 41, a nonpolar side chain, allows transient penetration of water molecules, which greatly increases the polarity of the redox site environment and also provides a source of protons. Our method of producing crystals of Cp Rd from a reducing solution leads to a distribution of water molecules not observed in the crystal structure of the reduced Rd from Pyrococcus furiosus. How general this correlation is among redox proteins must be determined in future work. The combination of our high-resolution crystal structures and molecular dynamics simulations provides a molecular picture of the structural rearrangement that occurs upon reduction in Cp rubredoxin.     

Kinetics of reduction of high redox potential ferredoxins by the semiquinones of Clostridium pasteurianum flavodoxin and exogenous flavin mononucleotide. Electrostatic and redox potential effects

We have measured the ionic strength dependence of the rate constants for the electron-transfer reactions of flavin mononucleotide (FMN) and flavodoxin semiquinones with 10 high redox potential ferredoxins (HiPIP's). The rate constants were extrapolated to infinite ionic strength by using a theoretical model of electrostatic interactions developed in our laboratory. In all cases, the sign of the electrostatic interaction was the same as the protein net charge, but the magnitudes were much smaller. The results are consistent with a model in which the electrical charges are approximately uniformly distributed over the HiPIP surface and in which there are both short- and long-range electrostatic interactions. An electrostatic field calculation for Chromatium vinosum HiPIP is consistent with this. The presumed site of electron transfer includes that region of the protein surface to which the iron-sulfur cluster is nearest and appears to be relatively hydrophobic. The principal short-range electrostatic interaction would involve the negative charge on the iron-sulfur cluster. For some net negatively charged proteins, this effect is magnified, and for net positively charged HiPIP's, it is counterbalanced. The rate constants extrapolated to infinite ionic strength can be correlated with redox potential differences between the reactants, as has previously been shown for cytochrome-flavin semiquinone reactions. Both electrostatic and redox potential effects are magnified for the flavodoxin semiquinone as compared to the FMN semiquinone-HiPIP reactions. This was also observed previously for the flavin semiquinone-cytochrome reactions.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Differential electrostatic stabilization of A-, B-, and Z-forms of DNA

The static accessibility discrete charge algorithm for protein charge interactions is extended to the case of linear polyelectrolytes. In this model, the effective dielectric value between surface charge sites depends predominantly on the solvent ionic strength and the solvent accessibilities of the charge sites. This treatment accounts for the phenomena of specific ion binding in the context of a general electrostatic effect [Matthew and Richards (1982) Biochemistry 21 , 4989]. Specific ion sites are determined by locating areas of high electrostatic potential at the solvent interface of the macromolecule. At a given ionic strength the calculated potential at a site is taken to describe a binding constant and therefore the ion site occupancy. For a 20-base-pair fragment of B-DNA, net charge of ?40, 16 ion sites are indicated in the minor groove. The partial occupancy of each site increases from 0.2 to 0.5 as the ionic strength is increased from 0.01 to 0.50. Over the same range of ionic strength, the electrostatic free energy of this charge array is calculated to change from +0.6 to ?0.05 kcal/bp. Parallel behavior is predicted for A- and Z-DNA charge geometries. The most stable configuration, based on electrostatic criteria, at high ionic strength (I = 0.1–0.5) is that of Z-DNA. In this range, the ratio of “bound” sodium to phosphate is predicted to be less than 0.4.     

Probing protein electrostatic interactions through temperature/reduction potential profiles

 The change in the equilibrium reduction potentials of the iron-sulfur proteins, Pyrococcus furiosus rubredoxin and P. furiosus ferredoxin, and heme protein, horse cytochrome c, has been calculated as a function of temperature using a numerical solution to the Poisson-Boltzman equation. Working curves for different internal dielectric constants were generated to best reproduce experimental observation. Based on a comparison of the experimental and simulated change in reduction potential with temperature, it is concluded that the dielectric constant of proteins is temperature-dependent and varies from protein to protein. For example, the temperature-dependent reduction potential of cytochrome c can only be simulated using a different temperature-dependent dielectric constant for each oxidation state, but this was not the case for rubredoxin or ferredoxin. The role of changes in ionization states of cytochrome c at alkaline pHs, where the reduction potential is known to be pH-dependent at room temperature, is also discussed in terms of electrostatic interaction energies as a function of temperature. It appears that temperature/reduction potential profiles may provide a direct method for measuring relative changes in internal protein dielectric constants. Received: 29 April 1996 / Accepted: 1 August 1996     

A new method for computing the macromolecular electric potential

A general methodology is developed for the rigorous computation of the electrostatic potential for a protein of arbitrary shape, assuming the presence of linear dielectric media. The theory proceeds by considering the distribution of induced polarization charge at the dielectric interface, rather than by attempting a direct solution of Poisson's equation (as in the finite-difference approach of Warwicker & Watson). The method is applied to a study of two-dimensional model proteins, where it is shown that the presence of a cleft is associated with a region of relatively high potential in the solvent medium. The results of a preliminary calculation in three dimensions for the protein lysozyme are also discussed; again, a region of enhanced potential is observed near the cleft at the active site. Our computational evidence supports the suggestion of Warwicker & Watson that clefts are associated with important electrostatic effects.     

The de novo design of a rubredoxin-like Fe site.

A redox center similar to that of rubredoxin was designed into the 56 amino acid immunoglobulin binding B1 domain of Streptococcals protein G. The redox center in rubredoxin contains an iron ion tetrahedrally coordinated by four cysteine residues, [Fe(S-Cys)4](-1),(-2). The design criteria for the target site included taking backbone movements into account, tetrahedral metal-binding, and maintaining the structure and stability of the wild-type protein. The optical absorption spectrum of the Co(II) complex of the metal-binding variant is characteristic of tetrahedral chelation by four cysteine residues. Circular dichroism and nuclear magnetic resonance measurements reveal that the metal-free and Cd(II)-bound forms of the variant are folded correctly and are stable. The Fe(III) complex of the metal-binding mutant reproduces the optical and the electron paramagnetic resonance spectra of oxidized rubredoxin. This demonstrates that the engineered protein chelates Fe(III) in a tetrahedral array, and the resulting center is similar to that of oxidized rubredoxin.