The Coupling of Protonation and Reduction in Proteins with Multiple Redox Centers: Theory, Computational Method, and Application to Cytochrome c3

Virtual Model Compound Approach for Calculating Redox Potentials of [Fe2S2]-Cys4 Centers in Proteins - Structure Quality Matters

The midpoint potential of the [Fe2S2]-Cys4-cluster in proteins is known to vary between -200 and -450 mV. This variation is caused by the different electrostatic environment of the cluster in the respective proteins. Continuum electrostatics can quantify the impact of the protein environment on the redox potential. Thus, if the redox potential of a [Fe2S2]-Cys4-cluster model compound in aqueous solution would be known, then redox potentials in various protein complexes could be calculated. However, [Fe2S2]-Cys4-cluster models are not water-soluble, and thus, their redox potential can not be measured in aqueous solution. To overcome this problem, we introduce a method that we call Virtual Model Compound Approach (VMCA) to extrapolate the model redox potential from known redox potentials of proteins. We carefully selected high-resolution structures for our analysis and divide them into a fit set, for fitting the model redox potential, and an independent test set, to check the validity of the model redox potential. However, from our analysis, we realized that the some structures can not be used as downloaded from the PDB but had to be re-refined in order to calculate reliable redox potentials. Because of the re-refinement, we were able to significantly reduce the standard deviation of our derived model redox potential for the [Fe2S2]-Cys4-cluster from 31 mV to 10 mV. As the model redox potential, we obtained -184 mV. This model redox potential can be used to analyze the redox behavior of [Fe2S2]-Cys4-clusters in larger protein complexes.

Exploring Coupled Redox and pH Processes with a Force-Field-Based Approach: Applications to Five Different Systems

Coupled redox and pH-driven processes are at the core of many important biological mechanisms. As the distribution of protonation and redox states in a system is associated with the pH and redox potential of the solution, having efficient computational tools that can simulate under these conditions becomes very important. Such tools have the potential to provide information that complement and drive experiments. In previous publications we have presented the implementation of the constant pH and redox potential molecular dynamics (C(pH,E)MD) method in AMBER and we have shown how multidimensional replica exchange can be used to significantly enhance the convergence efficiency of our simulations. In the current work, after an improvement in our C(pH,E)MD approach that allows a given residue to be simultaneously pH- and redox-active, we have employed our methodologies to study five different systems of interest in the literature. We present results for capped tyrosine dipeptide, two maquette systems containing one pH- and redox-active tyrosine (α₃Y and peptide A), and two proteins that contain multiple heme groups (diheme cytochrome c from Rhodobacter sphaeroides and Desulfovibrio vulgaris Hildenborough cytochrome c₃). We show that our results can provide new insights into previous theoretical and experimental findings by using a fully force-field-based and GPU-accelerated approach, which allows the simulations to be executed with high computational performance.

Computational Biochemistry-Enzyme Mechanisms Explored

Understanding enzyme mechanisms is a major task to achieve in order to comprehend how living cells work. Recent advances in biomolecular research provide huge amount of data on enzyme kinetics and structure. The analysis of diverse experimental results and their combination into an overall picture is, however, often challenging. Microscopic details of the enzymatic processes are often anticipated based on several hints from macroscopic experimental data. Computational biochemistry aims at creation of a computational model of an enzyme in order to explain microscopic details of the catalytic process and reproduce or predict macroscopic experimental findings. Results of such computations are in part complementary to experimental data and provide an explanation of a biochemical process at the microscopic level. In order to evaluate the mechanism of an enzyme, a structural model is constructed which can be analyzed by several theoretical approaches. Several simulation methods can and should be combined to get a reliable picture of the process of interest. Furthermore, abstract models of biological systems can be constructed combining computational and experimental data. In this review, we discuss structural computational models of enzymatic systems. We first discuss various models to simulate enzyme catalysis. Furthermore, we review various approaches how to characterize the enzyme mechanism both qualitatively and quantitatively using different modeling approaches.

Redox induced protonation of heme propionates in cytochrome c oxidase: Insights from surface enhanced resonance Raman spectroscopy and QM/MM calculations

Understanding the coupling between heme reduction and proton translocation in cytochrome c oxidase (CcO) is still an open problem. The propionic acids of heme a₃ have been proposed to act as a proton loading site (PLS) in the proton pumping pathway, yet this proposal could not be verified by experimental data so far. We have set up an experiment where the redox states of the two hemes in CcO can be controlled via external electrical potential. Surface enhanced resonance Raman (SERR) spectroscopy was applied to simultaneously monitor the redox state of the hemes and the protonation state of the heme propionates. Simulated spectra based on QM/MM calculations were used to assign the resonant enhanced CH₂ twisting modes of the propionates to the protonation state of the individual heme a and heme a₃ propionates respectively. The comparison between calculated and measured H₂OD₂O difference spectra allowed a sound band assignment. In the fully reduced enzyme at least three of the four heme propionates were found to be protonated whereas in the presence of a reduced heme a and an oxidized heme a₃ only protonation of one heme a₃ propionates was observed. Our data supports the postulated scenario where the heme a₃ propionates are involved in the proton pathway.

Energy-converting respiratory Complex I: on the way to the molecular mechanism of the proton pump

In respiring organisms the major energy transduction flux employs the transmembrane electrochemical proton gradient as a physical link between exergonic redox reactions and endergonic ADP phosphorylation. Establishing the gradient involves electrogenic, transmembrane H(+) translocation by the membrane-embedded respiratory complexes. Among others, Complex I (NADH:ubiquinone oxidoreductase) is the most structurally complex and functionally enigmatic respiratory enzyme; its molecular mechanism is as yet unknown. Here we highlight recent progress and discuss the catalytic events during Complex I turnover in relation to their role in energy conversion and to the enzyme structure.

Thermodynamics of transport through the ammonium transporter Amt-1 investigated with free energy calculations

Amt-1 from Archaeoglobus fulgidus (AfAmt-1) belongs to the Amt/Rh family of ammonium/ammonia transporting membrane proteins. The transport mode and the precise microscopic permeation mechanism utilized by these proteins are intensely debated. Open questions concern the identity of the transported substrate (ammonia and/or ammonium) and whether the transport is passive or active. To address these questions, we studied the overall thermodynamics of the different transport modes as a function of the environmental conditions. Then, we investigated the thermodynamics of the underlying microscopic transport mechanisms with free energy calculations within a continuum electrostatics model. The formalism developed for this purpose is of general utility in the calculation of binding free energies for ligands with multiple protonation forms or other binding forms. The results of our calculations are compared to the available experimental and theoretical data on Amt/Rh proteins and discussed in light of the current knowledge on the physiological conditions experienced by microorganisms and plants. We found that microscopic models of electroneutral and electrogenic transport modes are in principle thermodynamically viable. However, only the electrogenic variants have a net thermodynamic driving force under the physiological conditions experienced by microorganisms and plants. Thus, the transport mechanism of AfAmt-1 is most likely electrogenic.

GMCT : a Monte Carlo simulation package for macromolecular receptors

Generalized Monte Carlo titration (GMCT) is a versatile suite of computer programs for the efficient simulation of complex macromolecular receptor systems as for example proteins. The computational model of the system is based on a microstate description of the receptor and an average description of its surroundings in terms of chemical potentials. The receptor can be modeled in great detail including conformational flexibility and many binding sites with multiple different forms that can bind different ligand types. Membrane embedded systems can be modeled including electrochemical potential gradients. Overall properties of the receptor as well as properties of individual sites can be studied with a variety of different Monte Carlo (MC) simulation methods. Metropolis MC, Wang-Landau MC and efficient free energy calculation methods are included. GMCT is distributed as free open source software at www.bisb.uni-bayreuth.de under the terms of the GNU Affero General Public License.

Histidine in continuum electrostatics protonation state calculations

A modification to the standard continuum electrostatics approach to calculate protein pK(a)s, which allows for the decoupling of histidine tautomers within a two-state model, is presented. Histidine with four intrinsically coupled protonation states cannot be easily incorporated into a two-state formalism, because the interaction between the two protonatable sites of the imidazole ring is not purely electrostatic. The presented treatment, based on a single approximation of the interrelation between histidine's charge states, allows for a natural separation of the two protonatable sites associated with the imidazole ring as well as the inclusion of all protonation states within the calculation.

Analysis of the electrochemistry of hemes with E(m)s spanning 800 mV

The free energy of heme reduction in different proteins is found to vary over more than 18 kcal/mol. It is a challenge to determine how proteins manage to achieve this enormous range of E(m)s with a single type of redox cofactor. Proteins containing 141 unique hemes of a-, b-, and c-type, with bis-His, His-Met, and aquo-His ligation were calculated using Multi-Conformation Continuum Electrostatics (MCCE). The experimental E(m)s range over 800 mV from -350 mV in cytochrome c(3) to 450 mV in cytochrome c peroxidase (vs. SHE). The quantitative analysis of the factors that modulate heme electrochemistry includes the interactions of the heme with its ligands, the solvent, the protein backbone, and sidechains. MCCE calculated E(m)s are in good agreement with measured values. Using no free parameters the slope of the line comparing calculated and experimental E(m)s is 0.73 (R(2) = 0.90), showing the method accounts for 73% of the observed E(m) range. Adding a +160 mV correction to the His-Met c-type hemes yields a slope of 0.97 (R(2) = 0.93). With the correction 65% of the hemes have an absolute error smaller than 60 mV and 92% are within 120 mV. The overview of heme proteins with known structures and E(m)s shows both the lowest and highest potential hemes are c-type, whereas the b-type hemes are found in the middle E(m) range. In solution, bis-His ligation lowers the E(m) by approximately 205 mV relative to hemes with His-Met ligands. The bis-His, aquo-His, and His-Met ligated b-type hemes all cluster about E(m)s which are approximately 200 mV more positive in protein than in water. In contrast, the low potential bis-His c-type hemes are shifted little from in solution, whereas the high potential His-Met c-type hemes are raised by approximately 300 mV from solution. The analysis shows that no single type of interaction can be identified as the most important in setting heme electrochemistry in proteins. For example, the loss of solvation (reaction field) energy, which raises the E(m), has been suggested to be a major factor in tuning in situ E(m)s. However, the calculated solvation energy vs. experimental E(m) shows a slope of 0.2 and R(2) of 0.5 thus correlates weakly with E(m)s. All other individual interactions show even less correlation with E(m). However the sum of these terms does reproduce the range of observed E(m)s. Therefore, different proteins use different aspects of their structures to modulate the in situ heme electrochemistry. This study also shows that the calculated E(m)s are relatively insensitive to different heme partial charges and to the protein dielectric constant used in the simulation.

Investigating the mechanisms of photosynthetic proteins using continuum electrostatics

Computational methods based on continuum electrostatics are widely used in theoretical biochemistry to analyze the function of proteins. Continuum electrostatic methods in combination with quantum chemical and molecular mechanical methods can help to analyze even very complex biochemical systems. In this article, applications of these methods to proteins involved in photosynthesis are reviewed. After giving a short introduction to the basic concepts of the continuum electrostatic model based on the Poisson-Boltzmann equation, we describe the application of this approach to the docking of electron transfer proteins, to the comparison of isofunctional proteins, to the tuning of absorption spectra, to the analysis of the coupling of electron and proton transfer, to the analysis of the effect of membrane potentials on the energetics of membrane proteins, and to the kinetics of charge transfer reactions. Simulations as those reviewed in this article help to analyze molecular mechanisms on the basis of the structure of the protein, guide new experiments, and provide a better and deeper understanding of protein functions.

Energy contribution of the solvent to the charge migration in DNA

The authors have investigated the interactions of the reaction centers, participating in the charge transfer reaction within the DNA molecule with the phosphate backbones and the solvent molecules, and have estimated the contribution of these interactions into the charge migration in DNA. They have determined the unequal shift of the energy surfaces of the initial and final transition states of the transfer reaction along the energy axis and the dependence of the magnitude of the energy shift on the nature of the reaction centers and the surrounding environment. The nonuniform distribution of the negative charge in the DNA phosphate backbones results in an increase of the positive shift of the energy surface of the DNA base pairs in the center of the structure, where the maximum density of the negative charge is concentrated. Localization of the positive charge on the guanine and the adenine in the DNA base pairs in the oxidized state results in a dependence of the free energy of reaction in the solvent on the pair sequences and their arrangement in the DNA chain. As an example, for the G-C/A-T configuration the positive charges are localized on the same strand that results in a decrease of the free energy of reaction in the solvent for charge migration from G-C to A-T pair by 0.125 eV.

pH modulates the quinone position in the photosynthetic reaction center from Rhodobacter sphaeroides in the neutral and charge separated states

The structure of the photosynthetic reaction-center from Rhodobacter sphaeroides has been determined at four different pH values (6.5, 8.0, 9.0, 10.0) in the neutral and in charge separated states. At pH 8.0, in the neutral state, we obtain a resolution of 1.87 A, which is the best ever reported for the bacterial reaction center protein. Our crystallographic data confirm the existence of two different binding positions of the secondary quinone (QB). We observe a new orientation of QB in its distal position, which shows no ring-flip compared to the orientation in the proximal position. Datasets collected for the different pH values show a pH-dependence of the population of the proximal position. The new orientation of QB in the distal position and the pH-dependence could be confirmed by continuum electrostatics calculations. Our calculations are in agreement with the experimentally observed proton uptake upon charge separation. The high resolution of our crystallographic data allows us to identify new water molecules and external residues being involved in two previously described hydrogen bond proton channels. These extended proton-transfer pathways, ending at either of the two oxo-groups of QB in its proximal position, provide additional evidence that ring-flipping is not required for complete protonation of QB upon reduction.

Evidence for Delocalized Anticooperative Flash Induced Proton Binding as Revealed by Mutants at the M266His Iron Ligand in Bacterial Reaction Centers

Bacterial reaction centers (RCs) convert light energy into chemical free energy via the double reduction and protonation of the secondary quinone electron acceptor, QB, to the dihydroquinone QBH2. Two RC mutants (M266His --> Leu and M266His --> Ala) with a modified ligand of the non-heme iron have been studied by flash-induced absorbance change spectroscopy. No important changes were observed for the rate constants of the first and second electron transfers between the first quinone electron acceptor, QA, and QB. However, in the M266HL mutant a destabilization of approximately 40 meV of the free energy level of QA- was observed, at variance with the M266HA mutant. The superposition of the three-dimensional X-ray structures of the three proteins in the QA region provides no obvious explanation for the energy modification in the M266HL mutant. The shift of the midpoint redox potential of QA/QA- in M266HL caused accelerated recombination of the charges in the P+ QA- state of the RCs where the native QA was replaced by a low potential anthraquinone (AQA). As previously reported for the native RCs, in the M266HL we observed a biphasicity of the P+ AQA- --> P AQA charge recombination. Interestingly, both phases present a similar acceleration in the M266HL mutant with respect to the wild type. The pH dependencies of the proton uptake upon QA- and QB- formations are superimposable in both mutants but very different from those of native RCs. The data measured in mutants are similar to those that we previously obtained on strains modified at various sites of the cytoplasmic region. The similarity of the response to these different mutations is puzzling, and we propose that it arises from a collective behavior of multiple acidic residues resulting in strongly anticooperative proton binding. The unspecific disappearance of the high pH band of proton uptake observed in all these mutants appears as the natural consequence of removing any member of an interactive proton cluster. This long range interaction also accounts for the similar responses to mutations of the proton uptake pattern induced by either QA- or QB-. We surmise that the presence of an extended protonated water H-bond network providing protons to QB is responsible for these effects.

Simulation of the Electron Transfer between the Tetraheme Subunit and the Special Pair of the Photosynthetic Reaction Center Using a Microstate Description

Charge transfer through biological macromolecules is essential for many biological processes such as, for instance, photosynthesis and respiration. Protons or electrons are transferred between titratable residues or redox-active cofactors, respectively. Transfer rates between these sites depend on the current charge configuration of neighboring sites. Here, we formulate the kinetics of charge-transfer systems in a microstate formalism. A unique transfer rate constant can be assigned to the interconversion of microstates. Mutual interactions between sites participating in the transfer reactions are naturally taken into account. The formalism is applied to the kinetics of electron transfer in the tetraheme subunit and the special pair of the reaction center of Blastochloris viridis. It is shown that continuum electrostatic calculations can be used in combination with an existing empirical rate law to obtain electron-transfer rate constants. The re-reduction kinetics of the photo-oxidized special pair simulated in a microstate formalism is shown to be in good agreement with experimental data. A flux analysis is used to follow the individual electron-transfer steps.

Redox infrared markers of the heme and axial ligands in microperoxidase: bases for the analysis of c-type cytochromes

Structural changes accompanying the change in the redox state of microperoxidase-8 (MP8), the heme-octapeptide obtained from cytochrome c, and its complexes with (methyl)imidazole ligands were studied by electrochemically induced Fourier transform IR (FTIR) difference spectroscopy. To correlate with confidence IR modes with a specific electronic state of the iron, we used UV-vis and electron paramagnetic resonance spectroscopy to define precisely the heme spin state in the samples at the millimolar concentration of MP8 required for FTIR difference spectroscopy. We identified four intense redox-sensitive IR heme markers, nu38 at 1,569 cm(-1) (ox)/1,554 cm(-1) (red), nu42 at 1,264 cm(-1) (ox)/1,242 cm(-1) (red), nu43 at 1,146 cm(-1) (ox), and nu44 at 1,124-1,128 cm(-1) (ox). The intensity of nu42 and nu43 was clearly enhanced for low-spin imidazole-MP8 complexes, while that of nu44 increased for high-spin MP8. These modes can thus be used as IR markers of the iron spin state in MP8 and related c-type cytochromes. Moreover, one redox-sensitive band at 1,044 cm(-1) (red) is attributed to an IR marker specific of c-type hemes, possibly the delta(CbH3)(2,4) heme mode. Other redox-sensitive IR bands were assigned to the MP8 peptide backbone and to the fifth and sixth axial heme ligands. The distinct IR frequencies for imidazole (1,075 cm(-1)) and histidine (1,105 cm(-1)) side chains in the imidazole-MP8 complex allowed us to provide the first direct determination of their pKa at pH 9 and 12, respectively.

Physical Gelation of Chitosan in the Presence of β-Glycerophosphate: The Effect of Temperature

When adding beta-glycerophosphate (beta-GP), a weak base, to chitosan aqueous solutions, the polymer remains in solution at neutral pH and room temperature, while homogeneous gelation of this system can be triggered upon heating. It is therefore one of the rare true physical chitosan hydrogels. In this study, physicochemical and rheological properties of chitosan solutions in the presence of acetic acid and beta-GP were investigated as a function of temperature in order to gain a better understanding of the gelation mechanisms. The gel structure formed at high temperature was only partially thermoreversible upon cooling to 5 degrees C because of the existence of remaining associations, confirmed by the spontaneous recovery of the gel after breakup at low temperature. Increasing temperature had no effect on the pH values of this system, while conductivity (and calculated ionic strength) increased. Values from the pH measurements were used to estimate the degree of protonation of each species as a function of temperature. The decreasing ratio of -NH3+ in chitosan and -OPO(O-)2 in beta-GP suggested reduced chitosan solubility along with a diminution of ionic interactions such as ionic bridging with increasing temperature. On the other hand, the increased ionic strength as a function of temperature, in the presence of beta-GP, enhanced screening of electrostatic repulsion and increased hydrophobic effect, resulting in favorable conditions for gel formation. Therefore, our study suggests that hydrophobic interactions and reduced solubility are the main driving force for chitosan gelation at high temperature in the presence of beta-GP.

One-Electron Reduction Potential for Oxygen- and Sulfur-Centered Organic Radicals in Protic and Aprotic Solvents

We estimated one-electron reduction potentials of redox-active organic molecules for a spectrum of eight different functional groups (phenoxyl, p-benzoquinone, phenylthiyl, p-benzodithiyl, carboxyl, benzoyloxyl, carbthiyl, and benzoylthiyl) in protic (water) and aprotic (acetonitrile, N,N-dimethylacetamide) solvents. Electron affinities (EA) were evaluated in a vacuum with high level quantum chemical methods using Gaussian3-MP2 (G3MP2) and Becke 3 Lee, Yang, and Parr functional B3LYP with aug-cc-pVTZ basis set. To evaluate one-electron redox potentials, gas-phase free energies were combined with solvation energies obtained in a two-step computational approach. First, atomic partial charges were determined in a vacuum by the quantum chemical method B3LYP/6-31G(d,p). Second, solvation energies were determined, solving the Poisson equation with these atomic partial charges. Redox potentials computed this way, compared to experimental data for the 21 considered organic compounds in different solvents, yielded overall root-mean-square deviations of 0.058 and 0.131 V using G3MP2 or B3LYP to compute electronic energies, respectively, while B3LYP/6-31G(d,p) was used to compute solvation energies.

On the Use of Different Dielectric Constants for Computing Individual and Pairwise Terms in Poisson−Boltzmann Studies of Protein Ionization Equilibrium

Poisson-Boltzmann (PB) models are a fast and common tool for studying electrostatic processes in proteins, particularly their ionization equilibrium (protonation and/or reduction), often yielding quite good results when compared with more detailed models. Yet, they are conceptually very simple and necessarily approximate, their empirical character being most evident when it comes to the choice of the dielectric constant assigned to the protein region. The present study analyzes several factors affecting the ability of PB-based methods to model protein ionization equilibrium. We give particular attention to a suggestion made by Warshel and co-workers (e.g., Sham et al. J. Phys. Chem. B 1997, 101, 4458) of using different protein dielectric constants for computing the individual (site) and the pairwise (site-site) terms of the ionization free energies. Our prediction of pK(a) values for several proteins indicates that no advantage is obtained by such a procedure, even for sites that are buried and/or display large pK(a) shifts relative to the solution values. In particular, the present methodology gives the best predictions using a dielectric constant around 20, for shifted/buried and nonshifted/exposed sites alike. The similarities and differences between the PB model and Warshel's PDLD/S model are discussed, as well as the reasons behind their apparently discrepant results. The present PB model is shown to predict also good reduction potentials in redox proteins.

The Influence of a Transmembrane pH Gradient on Protonation Probabilities of Bacteriorhodopsin: The Structural Basis of the Back-Pressure Effect

Bacteriorhodopsin pumps protons across a membrane using the energy of light. The proton pumping is inhibited when the transmembrane proton gradient that the protein generates becomes larger than four pH units. This phenomenon is known as the back-pressure effect. Here, we investigate the structural basis of this effect by predicting the influence of a transmembrane pH gradient on the titration behavior of bacteriorhodopsin. For this purpose we introduce a method that accounts for a pH gradient in protonation probability calculations. The method considers that in a transmembrane protein, which is exposed to two different aqueous phases, each titratable residue is accessible for protons from one side of the membrane depending on its hydrogen-bond pattern. This method is applied to several ground-state structures of bacteriorhodopsin, which residues already present complicated titration behaviors in the absence of a proton gradient. Our calculations show that a pH gradient across the membrane influences in a non-trivial manner the protonation probabilities of six titratable residues which are known to participate in the proton transfer: D85, D96, D115, E194, E204, and the Schiff base. The residues connected to one side of the membrane are influenced by the pH on the other side because of their long-range electrostatic interactions within the protein. In particular, D115 senses the pH at the cytoplasmic side of the membrane and transmits this information to D85 and the Schiff base. We propose that the strong electrostatic interactions found between D85, D115, and the Schiff base as well as the interplay of their respective protonation states under the influence of a transmembrane pH gradient are responsible for the back-pressure effect on bacteriorhodopsin.

Specific ion effects: Role of salt and buffer in protonation of cytochrome c

Changes in background salt and buffer are known to influence the properties of proteins. The reasons have remained obscure. The challenge posed by many such problems is this. Can physical chemistry contribute any predictive quantitative insights to what is in effect the simplest macromolecular solution behavior? Or must all remain specific? Our thesis is that it can. For definiteness we consider here as an illustrative example: surface pH and protonation equilibria of cytochrome c. We demonstrate an important role for ionic dispersion forces, missing from previous theoretical treatments. Unlike charge interactions these are different for each ionic species, and act between a protein and both salt and buffer ions. The charge of proteins depends not only on pH, ionic charge, and salt concentration. Taking ionic dispersion forces into account goes some way towards explaining the dependence on ionic species. We demonstrate why the addition of buffer can have profound effects, including reversal of the salt dependence of the protein charge.

Tuning heme redox potentials in the cytochrome C subunit of photosynthetic reaction centers

The photosynthetic reaction center (RC) from Rhodopseudomonas viridis contains four cytochrome c hemes. They establish the initial part of the electron transfer (ET) chain through the RC. Despite their chemical identity, their midpoint potentials cover an interval of 440 mV. The individual heme midpoint potentials determine the ET kinetics and are therefore tuned by specific interactions with the protein environment. Here, we use an electrostatic approach based on the solution of the linearized Poisson-Boltzmann equation to evaluate the determinants of individual heme redox potentials. Our calculated redox potentials agree within 25 meV with the experimentally measured values. The heme redox potentials are mainly governed by solvent accessibility of the hemes and propionic acids, by neutralization of the negative charges at the propionates through either protonation or formation of salt bridges, by interactions with other hemes, and to a lesser extent, with other titratable protein side chains. In contrast to earlier computations on this system, we used quantum chemically derived atomic charges, considered an equilibrium-distributed protonation pattern, and accounted for interdependencies of site-site interactions. We provide values for the working potentials of all hemes as a function of the solution redox potential, which are crucial for calculations of ET rates. We identify residues whose site-directed mutation might significantly influence ET processes in the cytochrome c part of the RC. Redox potentials measured on a previously generated mutant could be reproduced by calculations based on a model structure of the mutant generated from the wild type RC.

Investigation of protonatable residues in Rhodothermus marinus caa3 haem-copper oxygen reductase: comparison with Paracoccus denitrificans aa3 haem-copper oxygen reductase

The Rhodothermus marinus caa(3 )haem-copper oxygen reductase contains all the residues of the so-called D- and K-proton channels, with the notable exception of the helix VI glutamate residue (Glu278(I) in Paracoccus denitrificans aa(3)), being nevertheless a true oxygen reductase reducing O(2) to water, and an efficient proton pump. Instead, in the same helix, but one turn below, it has a tyrosine residue (Tyr256(I), R. marinus caa(3) numbering), whose hydroxyl group occupies the same spatial position as the carboxylate group of Glu278(I), as deduced by comparative modelling techniques. Therefore, we proposed previously that this tyrosine residue could play an important role in the proton pathway. In this article we further study this hypothesis, by investigating the equilibrium thermodynamics of protonation in R. marinus caa(3), using theoretical methodologies based on the structural model previously obtained. Control calculations are also performed for the P. denitrificans aa(3) oxygen reductase. In both oxygen reductases we find several residues that are proton active (i.e., that display partial protonation) at physiological pH, some of them being redox sensitive (i.e., sensitive to the protein redox state). However, the caa(3 )Tyr256(I) is not proton active at physiological pH, in contrast to the aa(3) Glu278(I) which is both proton active at physiological pH and shows a high redox sensitivity. In R. marinus caa(3) we do not find any other residues in the same protein zone that can have this property. Therefore, there are no putative D-channel residues that are proton active in this oxidase. The protonatable residues of the K-channel are much more functionally conserved in both oxygen reductases than the same type of residues in the D-channel. Two (Tyr262(I) and Lys336(I), caa(3) numbering) out of three protonatable K-channel residues are proton active and redox sensitive in both proteins.

Molecular basis for redox-Bohr and cooperative effects in cytochrome c3 from Desulfovibrio desulfuricans ATCC 27774: Crystallographic and modeling studies of oxidized and reduced high-resolution structures at pH 7.6

The tetraheme cytochrome c3 is a small metalloprotein with ca. 13,000 Da found in sulfate-reducing bacteria, which is believed to act as a partner of hydrogenase. The three-dimensional structure of the oxidized and reduced forms of cytochrome c3 from Desulfovibrio desulfuricans ATCC 27774 at pH 7.6 were determined using high-resolution X-ray crystallography and were compared with the previously determined oxidized form at pH 4.0. Theoretical calculations were performed with both structures, using continuum electrostatic calculations and Monte Carlo sampling of protonation and redox states, in order to understand the molecular basis of the redox-Bohr and cooperativity effects related to the coupled transfer of electrons and protons. We were able to identify groups that showed redox-linked conformational changes. In particular, Glu61, His76, and propionate D of heme II showed important contributions to the redox-cooperativity, whereas His76, propionate A of heme I, and propionate D of heme IV were the key residues for the redox-Bohr effect. Upon reduction, an important movement of the backbone region surrounding hemes I and II was also identified, that, together with a few redox-linked conformational changes in side-chain residues, results in a significant decrease in the solvent accessibility of hemes I and II.

Redox-Bohr and other cooperativity effects in the nine-heme cytochrome C from Desulfovibrio desulfuricans ATCC 27774: crystallographic and modeling studies

The nine-heme cytochrome c is a monomeric multiheme cytochrome found in Desulfovibrio desulfuricans ATCC 27774. The polypeptide chain comprises 296 residues and wraps around nine hemes of type c. It is believed to take part in the periplasmic assembly of proteins involved in the mechanism of hydrogen cycling, receiving electrons from the tetraheme cytochrome c3. With the purpose of understanding the molecular basis of electron transfer processes in this cytochrome, we have determined the crystal structures of its oxidized and reduced forms at pH 7.5 and performed theoretical calculations of the binding equilibrium of protons and electrons in these structures. This integrated study allowed us to observe that the reduction process induced relevant conformational changes in several residues, as well as protonation changes in some protonatable residues. In particular, the surroundings of hemes I and IV constitute two areas of special interest. In addition, we were able to ascertain the groups involved in the redox-Bohr effect present in this cytochrome and the conformational changes that may underlie the redox-cooperativity effects on different hemes. Furthermore, the thermodynamic simulations provide evidence that the N- and C-terminal domains function in an independent manner, with the hemes belonging to the N-terminal domain showing, in general, a lower redox potential than those found in the C-terminal domain. In this way, electrons captured by the N-terminal domain could easily flow to the C-terminal domain, allowing the former to capture more electrons. A notable exception is heme IX, which has low redox potential and could serve as the exit path for electrons toward other proteins in the electron transfer pathway.

How cytochromes with different folds control heme redox potentials

The electrochemical midpoint potentials (E(m)'s) of 13 cytochromes, in globin (c, c(2), c(551), c(553)), four-helix bundle (c', b(562)), alpha beta roll (b(5)), and beta sandwich (f) motifs, with E(m)'s spanning 450 mV were calculated with multiconformation continuum electrostatics (MCCE). MCCE calculates changes in oxidation free energy when a heme-axial ligand complex is moved from water into protein. Calculated and experimental E(m)'s are in good agreement for cytochromes with His-Met and bis-His ligated hemes, where microperoxidases provide reference E(m)'s. In all cytochromes, E(m)'s are raised by 130-260 mV relative to solvated hemes by the loss of reaction field (solvation) energy. However, there is no correlation between E(m) and heme surface exposure. Backbone amide dipoles in loops or helix termini near the axial ligands raise E(m)'s, but amides in helix bundles contribute little. Heme propionates lower E(m)'s. If the propionic acids are partially protonated in the reduced cytochrome, protons are released on heme oxidation, contributing to the pH dependence of the E(m). In all cytochromes studied except b(5)'s and low potential globins, buried side chains raise E(m)'s. MCCE samples ionizable group protonation states, heme redox states, and side chain rotamers simultaneously. Globins show the largest structural changes on heme oxidation and four-helix bundles the least. Given the calculated protein-induced E(m) shift and measured cytochrome E(m) the five-coordinate, His heme in c' is predicted to have a solution E(m) between that of isolated bis-His and His-Met hemes, while the reference E(m) for His-Ntr ligands in cytochrome f should be near that of His-Met hemes.

The position of QB in the photosynthetic reaction center depends on pH: a theoretical analysis of the proton uptake upon QB reduction

Electrostatics-based calculations have been performed to examine the proton uptake upon reduction of the terminal electron acceptor Q(B) in the photosynthetic reaction center of Rhodobacter sphaeroides as a function of pH and the associated conformational equilibrium. Two crystal structures of the reaction center were considered: one structure was determined in the dark and the other under illumination. In the two structures, the Q(B) was found in two different positions, proximal or distal to the nonheme iron. Because Q(B) was found mainly in the distal position in the dark and only in the proximal position under illumination, the two positions have been attributed mostly to the oxidized and the reduced forms of Q(B), respectively. We calculated the proton uptake upon Q(B) reduction by four different models. In the first model, Q(B) is allowed to equilibrate between the two positions with either oxidation state. This equilibrium was allowed to vary with pH. In the other three models the distribution of Q(B) between the proximal position and the distal position was pH-independent, with Q(B) occupying only the distal position or only the proximal position or populating the two positions with a fixed ratio. Only the first model, which includes the pH-dependent conformational equilibrium, reproduces both the experimentally measured pH dependence of the proton uptake and the crystallographically observed conformational equilibrium at pH 8. From this model, we find that Q(B) occupies only the distal position below pH 6.5 and only the proximal position above pH 9.0 in both oxidation states. Between these pH values both positions are partially occupied. The reduced Q(B) has a higher occupancy in the proximal position than the oxidized Q(B). In summary, the present results indicate that the conformational equilibrium of Q(B) depends not only on the redox state of Q(B), but also on the pH value of the solution.

Molecular dynamics study of Desulfovibrio africanus cytochrome c3 in oxidized and reduced forms

A 5-ns molecular dynamics study of a tetraheme cytochrome in fully oxidized and reduced forms was performed using the CHARMM molecular modeling program, with explicit water molecules, Langevin dynamics thermalization, Particle Mesh Ewald long-range electrostatics, and quantum mechanical determination of heme partial charges. The simulations used, as starting points, crystallographic structures of the oxidized and reduced forms of the acidic cytochrome c(3) from Desulfovibrio africanus obtained at pH 5.6. In this paper we also report structures for the two forms obtained at pH 8. In contrast to previous cytochrome c(3) dynamics simulations, our model is stable. The simulation structures agree reasonably well with the crystallographic ones, but our models show higher flexibility and the water molecules are more labile. We have compared in detail the differences between the simulated and experimental structures of the two redox states and observe that the hydration structure is highly dependent on the redox state. We have also analyzed the interaction energy terms between the hemes, the protein residues, and water. The direct electrostatic interaction between hemes is weak and nearly insensitive to the redox state, but the remaining terms are large and contribute in a complex way to the overall potential energy differences that we see between the redox states.

Energetics of radical transfer in DNA photolyase

Charge separation and radical transfer in DNA photolyase from Escherichia coli is investigated by computing electrostatic free energies from a solution of the Poisson-Boltzmann equation. For the initial charge separation 450 meV are available. According to recent experiments [Aubert et al. Nature 2000, 405, 586-590] the flavin receives an electron from the proximal tryptophan W382, which consequently forms a cationic radical WH(*)(+)382. The radical state is subsequently transferred along the triad W382-W359-W306 of conserved tryptophans. The radical transfer to the intermediate tryptophan W359 is nearly isoenergetic (58 meV uphill); the radical transfer from the intermediate W359 to the distal W306 is 200 meV downhill in energy, funneling and stabilizing the radical state at W306. The resulting cationic radical WH(*)(+)306 is further stabilized by deprotonation, yielding the neutral radical W(*)306, which is 214 meV below WH(*)(+)306. The time scale of the charge recombination process yielding back the resting enzyme with FADH(*) is governed by reprotonation of W306, with a calculated lifetime of 1.2 ms that correlates well with the measured lifetime of 17 ms. In photolyase from Anacystis nidulans the radical state is partially transferred to a tyrosine [Aubert et al. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 5423-5427]. In photolyase from Escherichia coli, there is a tyrosine (Y464) close to the distal tryptophan W306 that could play this role. We show that this tyrosine cannot be involved in radical transfer, because the electron transfer from tyrosine to W306 is much too endergonic (750 meV) and a direct hydrogen transfer is likely too slow. Coupling of specific charge states of the tryptophan triad with protonation patterns of titratable residues of photolyase is small.

Continuum electrostatic analysis of irregular ionization and proton allocation in proteins

Irregular (nonsigmoidal) ionization behavior of titratable groups in proteins is analyzed theoretically, using a computational algorithm designed to count explicitly for tautomers of titratable groups and different locations of polar hydrogens. On the basis of calculations for different model systems (acid-acid, base-base, acid-base pairs, and cluster of three strongly interacting groups), it is demonstrated that the pK values, extracted from nonsigmoidal titration curves by fitting to a sum of Henderson-Hasselbalch equations, do not describe the ionization equilibrium correctly. The conditions for observation of irregular titration curves are derived analytically for the case of arbitrary couple of interacting ionizable groups. A possible relation between irregularly shaped titration curves and tautomerization is also illustrated. The protonation-deprotonation equilibrium of Asp76 in ribonuclease T1 is shown to be coupled to dipole reorientation of a water molecule bound at the protein-solvent interface. This finding provides a new interpretation of the experimentally observed chemical shift of this residue.

Effects of pH on protein association: modification of the proton-linkage model and experimental verification of the modified model in the case of cytochrome c and plastocyanin

Effects of pH on protein association are not well understood. To understand them better, we combine kinetic experiments, calculations of electrostatic properties, and a new theoretical treatment of pH effects. The familiar proton-linkage model, when used to analyze the dependence of the association constant K on pH, reveals little about the individual proteins. We modified this model to allow determination not only of the numbers of the H+ ions involved in the association but also of the pK(a) values, in both the separate and the associated proteins, of the side chains that are responsible for the dependence of K on pH. Some of these side chains have very similar pK(a) values, and we treat them as a group having a composite pK(a) value. Use of these composite pK(a) values greatly reduces the number of parameters and allows meaningful interpretation of the experimental results. We experimentally determined the variation of K in the interval 5.4 < or = pH < or = 9.0 for four diprotein complexes, those that the wild-type cytochrome c forms with the wild-type plastocyanin and its mutants Asp42Asn, Glu59Gln, and Glu60Gln. The excellent fittings of the experimental results to the modified model verified this model and revealed some unexpected and important properties of these prototypical redox metalloproteins. Protein association causes a decrease in the pK(a) values of the acidic side chains and an increase in the pK(a) values of the basic side chains. Upon association, three carboxylic side chains in wild-type plastocyanin each release a H+ ion. These side chains in free plastocyanin have an anomalously high composite pK(a) value, approximately 6.3. Upon association, five or six side chains in cytochrome c, likely those of lysine, each take up a H+ ion. Some of these side chains have anomalously low pK(a) values, less than 7.0. The unusual pK(a) values of the residues in the recognition patches of plastocyanin and cytochrome c may be significant for the biological functions of these proteins. Although each mutation in plastocyanin markedly, and differently, changed the dependence of K on pH, the model consistently gave excellent fittings. They showed decreased numbers of H+ ions released or taken up upon protein association and altered composite pK(a) values of the relevant side chains. Comparisons of the fitted composite pK(a) values with the theoretically calculated pK(a) values for plastocyanin indicated that Glu59 and Asp61 in the wild-type plastocyanin each release a H+ ion upon association with cytochrome c. Information of this kind cannot readily be obtained by spectroscopic methods. Our modification of the proton-linkage model is a general one, applicable also to ligands other than H+ ion and to processes other than association.

Artificial cytochrome b: computer modeling and evaluation of redox potentials

We generated atomic coordinates of an artificial protein that was recently synthesized to model the central part of the native cytochrome b (Cb) subunit consisting of a four-helix bundle with two hemes. Since no X-ray structure is available, the structural elements of the artificial Cb were assembled from scratch using all known chemical and structural information available and avoiding strain as much as possible. Molecular dynamics (MD) simulations applied to this model protein exhibited root-mean-square deviations as small as those obtained from MD simulations starting with the crystal structure of the native Cb subunit. This demonstrates that the modeled structure of the artificial Cb is relatively rigid and strain-free. The model structure of the artificial Cb was used to determine the redox potentials of the two hemes by calculating the electrostatic energies from the solution of the linearized Poisson-Boltzmann equation (LPBE). The calculated redox potentials agree within 20 meV with the experimentally measured values. The dependence of the redox potentials of the hemes on the protein environment was analyzed. Accordingly, the total shift in the redox potentials is mainly due to the low dielectric medium of the protein, the protein backbone charges, and the salt bridges formed between the arginines and the propionic acid groups of the hemes. The difference in the shift of the redox potentials is due to the interactions with the hydrophilic side chains and the salt bridges formed with the propionic acids of the hemes. For comparison and to test the computational procedure, the redox potentials of the two hemes in the native Cb from the cytochrome bc(1) (Cbc(1)) complex were also calculated. Also in this case the computed redox potentials agree well with experiments.

Macromolecular electrostatics: continuum models and their growing pains

Theoretical understanding of macromolecular electrostatics has advanced substantially over the past year. Continuum models have given promising results for calculating protein-ligand binding free energy differences, as well as pK(a)s and redox properties, particularly with explicit treatment of multiple conformers. Generalized Born and other techniques have led to the first molecular dynamics simulations of proteins and RNA with continuum solvent. Continuum and microscopic descriptions of dielectric relaxation have been critically compared.

A novel view of pH titration in biomolecules

When individual titratable sites in a molecule interact with each other, their pH titration can be considerably more complex than that of an independent site described by the classical Henderson-Hasselbalch equation. We propose a novel framework that decomposes any complex titration behavior into simple standard components. The approach maps the set of N interacting sites in the molecule onto a set of N independent, noninteracting quasi-sites, each characterized by a pK'(a) value. The titration curve of an individual site in the molecule is a weighted sum of Henderson-Hasselbalch curves corresponding to the quasi-sites. The total protonation curve is the unweighted sum of these Henderson-Hasselbalch curves. We show that pK'(a) values correspond to deprotonation constants available from methods that can be used to assess total proton uptake or release, and establish their connection to protonation curves of individual residues obtained by NMR or infrared spectroscopy. The new framework is tested on a small molecule diethylenetriaminepentaacetate (DTPA) exhibiting nonmonotonic titration curves, where it gives an excellent fit to experimental data. We demonstrate that the titration curve of a site in a group of interacting sites can be accurately reconstructed, if titration curves of the other sites are known. The application of the new framework to the protein rubredoxin demonstrates its usefulness in calculating and interpreting complicated titration curves.

Electron transfer between the quinones in the photosynthetic reaction center and its coupling to conformational changes

The electron transfer between the two quinones Q(A) and Q(B) in the bacterial photosynthetic reaction center (bRC) is coupled to a conformational rearrangement. Recently, the X-ray structures of the dark-adapted and light-exposed bRC from Rhodobacter sphaeroides were solved, and the conformational changes were characterized structurally. We computed the reaction free energy for the electron transfer from to Q(B) in the X-ray structures of the dark-adapted and light-exposed bRC from Rb. sphaeroides. The computation was done by applying an electrostatic model using the Poisson-Boltzmann equation and Monte Carlo sampling. We accounted for possible protonation changes of titratable groups upon electron transfer. According to our calculations, the reaction energy of the electron transfer from to Q(B) is +157 meV for the dark-adapted and -56 meV for the light-exposed X-ray structure; i.e., the electron transfer is energetically uphill for the dark-adapted structure and downhill for the light-exposed structure. A common interpretation of experimental results is that the electron transfer between and Q(B) is either gated or at least influenced by a conformational rearrangement: A conformation in which the electron transfer from to Q(B) is inactive, identified with the dark-adapted X-ray structure, changes into an electron-transfer active conformation, identified with the light-exposed X-ray structure. This interpretation agrees with our computational results if one assumes that the positive reaction energy for the dark-adapted X-ray structure effectively prevents the electron transfer. We found that the strongly coupled pair of titratable groups Glu-L212 and Asp-L213 binds about one proton in the dark-adapted X-ray structure, where the electron is mainly localized at Q(A), and about two protons in the light-exposed structure, where the electron is mainly localized at Q(B). This finding agrees with recent experimental and theoretical studies. We compare the present results for the bRC from Rb. sphaeroides to our recent studies on the bRC from Rhodopseudomonas viridis. We discuss possible mechanisms for the gated electron transfer from to Q(B) and relate them to theoretical and experimental results.