pH-dependent redox potential: how to use it correctly in the activation energy analysis

The activation barrier (the activation free energy) for the reaction's elementary act proper does not depend on the presence of reactants outside the reaction complex. The barrier is determined directly by the concentration-independent configurational free energy. In the case of redox reactants with pH-dependent redox potential, only the pH-independent quantity, the configurational redox potential enters immediately into expression for activation energy. Some typical cases of such reactions have been discussed (e.g., simultaneous proton and electron detachment, acid dissociation followed by oxidation, dissociation after oxidation, and others). For these mechanisms, the algorithms for calculation of the configurational redox potential from the experimentally determined redox potentials have been described both for the data related to a dissolved reactant or to a prosthetic group of an enzyme. Some examples of pH-dependent enzymatic redox reactions, in particular for the Rieske iron-sulfur protein, have been discussed.     

Modelling of the electron transfer reactions in Photosystem I by electron tunnelling theory: The phylloquinones bound to the PsaA and the PsaB reaction centre subunits of PS I are almost isoenergetic to the iron-sulfur cluster FX

Photosystem I is a large macromolecular complex located in the thylakoid membranes of chloroplasts and in cyanobacteria that catalyses the light driven reduction of ferredoxin and oxidation of plastocyanin. Due to the very negative redox potential of the primary electron transfer cofactors accepting electrons, direct estimation by redox titration of the energetics of the system is hampered. However, the rates of electron transfer reactions are related to the thermodynamic properties of the system. Hence, several spectroscopic and biochemical techniques have been employed, in combination with the classical Marcus theory for electron transfer tunnelling, in order to access these parameters. Nevertheless, the values which have been presented are very variable. In particular, for the case of the tightly bound phylloquinone molecule A₁, the values of the redox potentials reported in the literature vary over a range of about 350 mV. Previous models of Photosystem I have assumed a unidirectional electron transfer model. In the present study, experimental evidence obtained by means of time resolved absorption, photovoltage, and electron paramagnetic resonance measurements are reviewed and analysed in terms of a bi-directional kinetic model for electron transfer reactions. This model takes into consideration the thermodynamic equilibrium between the iron-sulfur centre F_X and the phylloquinone bound to either the PsaA (A_1A) or the PsaB (A_1B) subunit of the reaction centre and the equilibrium between the iron-sulfur centres F_A and F_B. The experimentally determined decay lifetimes in the range of sub-picosecond to the microsecond time domains can be satisfactorily simulated, taking into consideration the edge-to-edge distances between redox cofactors and driving forces reported in the literature. The only exception to this general behaviour is the case of phylloquinone (A₁) reoxidation. In order to describe the reported rates of the biphasic decay, of about 20 and 200 ns, associated with this electron transfer step, the redox potentials of the quinones are estimated to be almost isoenergetic with that of the iron sulfur centre F_X. A driving force in the range of 5 to 15 meV is estimated for these reactions, being slightly exergonic in the case of the A_1B quinone and slightly endergonic, in the case of the A_1A quinone. The simulation presented in this analysis not only describes the kinetic data obtained for the wild type samples at room temperature and is consistent with estimates of activation energy by the analysis of temperature dependence, but can also explain the effect of the mutations around the PsaB quinone binding pocket. A model of the overall energetics of the system is derived, which suggests that the only substantially irreversible electron transfer reactions are the reoxidation of A₀ on both electron transfer branches and the reduction of F_A by F_X.     

Protonmotive pathways and mechanisms in the cytochrome bc1 complex

The cytochrome bc(1) complex catalyzes electron transfer from ubiquinol to cytochrome c by a protonmotive Q cycle mechanism in which electron transfer is linked to proton translocation across the inner mitochondrial membrane. In the Q cycle mechanism proton translocation is the net result of topographically segregated reduction of quinone and reoxidation of quinol on opposite sides of the membrane, with protons being carried across the membrane as hydrogens on the quinol. The linkage of proton chemistry to electron transfer during quinol oxidation and quinone reduction requires pathways for moving protons to and from the aqueous phase and the hydrophobic environment in which the quinol and quinone redox reactions occur. Crystal structures of the mitochondrial cytochrome bc(1) complexes in various conformations allow insight into possible proton conduction pathways. In this review we discuss pathways for proton conduction linked to ubiquinone redox reactions with particular reference to recently determined structures of the yeast bc(1) complex.     

Mammalian mitochondrial and microsomal cytochromes b(5) exhibit divergent structural and biophysical characteristics

The only outer mitochondrial membrane cytochrome b(5) examined to date, from rat (rOM b(5)), exhibits greater stability than known mammalian microsomal (Mc) isoforms, as well as a much higher kinetic barrier for hemin dissociation and a more negative reduction potential. A BlastP search of available databases using the protein sequence of rOM b(5) as template revealed entries for analogous proteins from human (hOM b(5)) and mouse (mOM b(5)). We prepared a synthetic gene coding for the heme-binding domain of hOM b(5), and expressed the protein to high levels. The hOM protein exhibits stability, hemin-binding, and redox properties similar to those of rOM b(5), suggesting that they are characteristic of the OM b(5) subfamily. The divergence in properties between the OM and Mc b(5) isoforms in mammals can be attributed, at least in part, to the presence of two extended hydrophobic patches in the former. The biophysical properties characteristic of the OM proteins may be important in facilitating the two functions proposed for them so far, reduction of ascorbate radical and stimulation of androgen synthesis.     

How rapid are the internal reactions of the ubiquinol:cytochrome c 2 oxidoreductase?

The temperature dependence of the partial reactions leading to turn-over of the UQH₂:cyt c ₂ oxidoreductase of Rhodobacter sphaeroides have been studied. The redox properties of the cytochrome components show a weak temperature dependence over the range 280–330 K, with coefficients of about 1 m V per degree; our results suggest that the other components show similar dependencies, so that no significant change in the gradient of standard free-energy between components occurs over this temperature range. The rates of the reactions of the high potential chain (the Rieske iron sulfur center, cytochromes c ₁ and c ₂, reaction center primary donor) show a weak temperature dependence, indicating an activation energy < 8 kJ per mole for electron transfer in this chain. The oxidation of ubiquinol at the Q_z-site of the complex showed a strong temperature dependence, with an activation energy of about 32 kJ mole^–1. The electron transfer from cytochrome b-566 to cytochrome b-561 was not rate determining at any temperature, and did not contribute to the energy barrier. The activation energy of 32 kJ mole^–1 for quinol oxidation was the same for all states of the quinone pool (fully oxidized, partially reduced, or fully reduced before the flash). We suggest that the activation barrier is in the reaction by which ubiquinol at the catalytic site is oxidized to semiquinone. The most economical scheme for this reaction would have the semiquinone intermediate at the energy level indicated by the activation barrier. We discuss the plausibility of this simple model, and the values for rate constants, stability constant, the redox potentials of the intermediate couples, and the binding constant for the semiquinone, which are pertinent to the mechanism of the ubiquinol oxidizing site.Abbreviations (BChl)₂ P870, primary donor of the photochemical reaction center - b/c ₁ complex ubiquinol: cytochrome c ₂ oxidoreductase - cyt b _H cytochrome b-561 or higher potential cytochrome b - cyt b _L cytochrome b-566, or low potential cytochrome b - cyt c ₁, cyt c ₂, cyt c _t cytochromes c ₁ and c ₂, and total cytochrome c (cyt c ₁ and cyt c ₂) - Fe.S Rieske-type iron sulfur center, Q - QH₂ ubiquinone, ubiquinol - Q_z, Q_zH₂, Q_z ^– ubiquinone, ubiquinol, and semiquinone anion of ubiquinone, bound at quinol oxidizing site - Q_z-site ubiquinol oxidizing site (also called Q_o-(outside) - Q_o (Oxidizing) - Q_P (Positive proton potential) site) - Q_c-site uubiquinone reductase site (also called the Q_i-(inside) - Q_R (Reducing), or - Q_N (Negative proton potential) site) - UHDBT 5-(n-undecyl)-6-hydroxy-4,7-dioxobenzothiazol     

Mutations in cytochrome b that affect kinetics of the electron transfer reactions at center N in the yeast cytochrome bc1 complex

We have examined the pre-steady-state kinetics and thermodynamic properties of the b hemes in variants of the yeast cytochrome bc₁ complex that have mutations in the quinone reductase site (center N). Trp-30 is a highly conserved residue, forming a hydrogen bond with the propionate on the high potential b heme (b_H heme). The substitution by a cysteine (W30C) lowers the redox potential of the heme and an apparent consequence is a lower rate of electron transfer between quinol and heme at center N. Leu-198 is also in close proximity to the b_H heme and a L198F mutation alters the spectral properties of the heme but has only minor effects on its redox properties or the electron transfer kinetics at center N. Substitution of Met-221 by glutamine or glutamate results in the loss of a hydrophobic interaction that stabilizes the quinone ligands. Ser-20 and Gln-22 form a hydrogen-bonding network that includes His-202, one of the carbonyl groups of the ubiquinone ring, and an active-site water. A S20T mutation has long-range structural effects on center P and thermodynamic effects on both b hemes. The other mutations (M221E, M221Q, Q22E and Q22T) do not affect the ubiquinol oxidation kinetics at center P, but do modify the electron transfer reactions at center N to various extents. The pre-steady reduction kinetics suggest that these mutations alter the binding of quinone ligands at center N, possibly by widening the binding pocket and thus increasing the distance between the substrate and the b_H heme. These results show that one can distinguish between the contribution of structural and thermodynamic factors to center N function.     

Exploring gas permeability of cellular membranes and membrane channels with molecular dynamics

Aquaporins are a family of membrane proteins specialized in rapid water conduction across biological membranes. Whether these channels also conduct gas molecules and the physiological significance of this potential function have not been well understood. Here we report 140 ns of molecular dynamics simulations of membrane-embedded AQP1 and of a pure POPE bilayer addressing these questions. The permeability of AQP1 to two types of gas molecules, O2 and CO2, was investigated using two complementary methods, namely, explicit gas diffusion simulation and implicit ligand sampling. The simulations show that the central (tetrameric) pore of AQP1 can be readily used by either gas molecule to permeate the channel. The two approaches produced similar free energy profiles associated with gas permeation through the central pore: a -0.4 to -1.7 kcal/mol energy well in the middle, and a 3.6-4.6 kcal/mol energy barrier in the periplasmic vestibule. The barrier appears to be mainly due to a dense cluster of water molecules anchored in the periplasmic mouth of the central pore by four aspartate residues. Water pores show a very low permeability to O2, but may contribute to the overall permeation of CO2 due to its more hydrophilic nature. Although the central pore of AQP1 is found to be gas permeable, the pure POPE bilayer provides a much larger cross-sectional area, thus exhibiting a much lower free energy barrier for CO2 and O2 permeation. As such, gas conduction through AQP1 may only be physiologically relevant either in membranes of low gas permeability, or in cells where a major fraction of the cellular membrane is occupied by AQPs.     

The dynamic complex of cytochrome c6 and cytochrome f studied with paramagnetic NMR spectroscopy

The rapid transfer of electrons in the photosynthetic redox chain is achieved by the formation of short-lived complexes of cytochrome b₆f with the electron transfer proteins plastocyanin and cytochrome c₆. A balance must exist between fast intermolecular electron transfer and rapid dissociation, which requires the formation of a complex that has limited specificity. The interaction of the soluble fragment of cytochrome f and cytochrome c₆ from the cyanobacterium Nostoc sp. PCC 7119 was studied using NMR spectroscopy and X-ray diffraction. The crystal structures of wild type, M58H and M58C cytochrome c₆ were determined. The M58C variant is an excellent low potential mimic of the wild type protein and was used in chemical shift perturbation and paramagnetic relaxation NMR experiments to characterize the complex with cytochrome f. The interaction is highly dynamic and can be described as a pure encounter complex, with no dominant stereospecific complex. Ensemble docking calculations and Monte-Carlo simulations suggest a model in which charge–charge interactions pre-orient cytochrome c₆ with its haem edge toward cytochrome f to form an ensemble of orientations with extensive contacts between the hydrophobic patches on both cytochromes, bringing the two haem groups sufficiently close to allow for rapid electron transfer. This model of complex formation allows for a gradual increase and decrease of the hydrophobic interactions during association and dissociation, thus avoiding a high transition state barrier that would slow down the dissociation process.     

How do calcium ions induce free radical oxidation of hydroxy-1,4-naphthoquinone? Ca2+ stabilizes the naphthosemiquinone anion-radical of echinochrome A

A surprising effect is the direct action of Ca(2+) on redox reactions of ortho-quinoid compounds. The effect of Ca(2+) on oxidation of the sea urchin pigment 6-ethyl-2,3,5,7,8-pentahydroxy-1,4-naphthoquinone (echinochrome A) has been studied by electron paramagnetic resonance (EPR) spectroscopy, by UV/VIS absorbance spectroscopy, and by measurement of oxygen consumption. Echinochrome A per se reacted with dioxygen only in an alkaline solution; 2,3-semiquinone anion-radical of echinochrome A and superoxide anion-radical were the intermediates of the oxidation. Addition of calcium ions sharply increased the rate of echinochrome A autooxidation at alkaline pH and provoked oxidation at neutral pH. To explain this phenomenon we have focused on changes of the acid-base properties of echinochrome A in the presence of calcium and on stabilization of 2,3-semiquinone anion-radical of echinochrome A by Ca(2+). Dissociation constants (pK(a1), pK(a2), and pK(a3)) of echinochrome A determined by potentiometric titration were 5.20, 6.78, and >10 in calcium-free solution and 5.00, 6.10, and 7.15 in the presence of Ca(2+). We have found that Ca(2+) forms an insoluble adduct with the 2,3-semiquinone anion-radical. Thus, the effect of redox-inert calcium on the free radical reactions could be explained (i) by additional deprotonation of echinochrome A and (ii) by formation of a Ca(2+)-naphtho-2,3-semiquinone complex (calcium semiquinonate). Additionally, we have shown that the dried red spines from Strongylocentrotus intermedius possess paramagnetic properties; the EPR signal of the natural spines was similar to that of calcium semiquinonate obtained in our artificial chemical system.     

The relationship between ligand-binding thermodynamics and protein-ligand interaction forces measured by atomic force microscopy.

The interaction forces between biotin and a set of streptavidin site-directed mutants with altered biotin-binding equilibrium and activation thermodynamics have been measured by atomic force microscopy. The AFM technique readily discriminates differences in interaction force between the site-directed (Trp to Phe or Ala) mutants. The interaction force is poorly correlated with both the equilibrium free energy of biotin binding and the activation free energy barrier to dissociation of the biotin-streptavidin complex. The interaction force is generally well correlated with the equilibrium biotin-binding enthalpy as well as the enthalpic activation barrier, but in the one mutant where these two parameters are altered in opposite directions, the interaction force is clearly correlated with the activation enthalpy of dissociation. These results suggest that the AFM force measurements directly probe the enthalpic activation barrier to ligand dissociation.     

Kinetics and mechanism of Ru(III) and Hg(II) co-catalyzed oxidation of D-galactose and D-ribose by N-bromoacetamide in perchloric acid

Kinetics of oxidation of reducing sugars D-galactose (Gal) and D-ribose (Rib) by N-bromoacetamide (NBA) in the presence of ruthenium(III) chloride as a homogeneous catalyst and in perchloric acid medium, using mercuric acetate as a scavenger for Br(minus sign) ions, as well as a co-catalyst, have been investigated. The kinetic results indicate that the first-order kinetics in NBA at lower concentrations tend towards zero order at its higher concentrations. The reactions follow identical kinetics, being first order in the [sugar] and [Ru(III)]. Inverse fractional order in [H(+)] and [acetamide] were observed. A positive effect of [Hg(OAc)(2)] and [Cl(minus sign)] was found, whereas a change in ionic strength (mu) has no effect on oxidation velocity. Formic acid and D-lyxonic acid (for Gal) and formic acid and L-erythronic acid (for Rib) were identified as main oxidation products of reactions. The various activation parameters have been computed and recorded. A suitable mechanism consistent with experimental findings has been proposed.     

Regulatory interactions in the dimeric cytochrome bc1 complex: The advantages of being a twin

The dimeric cytochrome bc₁ complex catalyzes the oxidation-reduction of quinol and quinone at sites located in opposite sides of the membrane in which it resides. We review the kinetics of electron transfer and inhibitor binding that reveal functional interactions between the quinol oxidation site at center P and quinone reduction site at center N in opposite monomers in conjunction with electron equilibration between the cytochrome b subunits of the dimer. A model for the mechanism of the bc₁ complex has emerged from these studies in which binding of ligands that mimic semiquinone at center N regulates half-of-the-sites reactivity at center P and binding of ligands that mimic catalytically competent binding of ubiquinol at center P regulates half-of-the-sites reactivity at center N. An additional feature of this model is that inhibition of quinol oxidation at the quinone reduction site is avoided by allowing catalysis in only one monomer at a time, which maximizes the number of redox acceptor centers available in cytochrome b for electrons coming from quinol oxidation reactions at center P and minimizes the leakage of electrons that would result in the generation of damaging oxygen radicals.     

Redox properties of components I and IV of trout hemoglobins: kinetic and potentiometric studies

Redox properties of component I and IV from trout hemoglobin (Salmo irideus) have been studied kinetically and at equilibrium. In the case of component I of trout hemoglobin, the mid-point potential (Eh) is pH independent below the acid-alkaline transition (pKa approximately equal to 8.6) and decreases at higher pH, following the deprotonation of the water molecule. Similarly to human hemoglobin, the mid-point potential of component IV of trout hemoglobin is pH-dependent, but the redox Bohr effect is extended to more acid pH. Moreover, the cooperativity of the redox equilibrium process is higher than in human hemoglobin. These features parallel the oxygen-binding properties of the same hemoglobin components from trout hemolysate. Differently from human hemoglobin, the oxidation kinetics of the two hemoglobins from trout by potassium ferricyanide show markedly biphasic progress curves with pH-independent second-order rate constants. This behavior suggests a different energy barrier for the interaction with ferricyanide in the two types of subunit of both Hb components from trout.     

Structure at 1.3 A resolution of Rhodothermus marinus caa(3) cytochrome c domain

The cytochrome c domain of subunit II from the Rhodothermus marinus caa(3) HiPIP:oxygen oxidoreductase, a member of the superfamily of heme-copper-containing terminal oxidases, was produced in Escherichia coli and characterised. The recombinant protein, which shows the same optical absorption and redox properties as the corresponding domain in the holo enzyme, was crystallized and its structure was determined to a resolution of 1.3 A by the multiwavelength anomalous dispersion (MAD) technique using the anomalous dispersion of the heme iron atom. The model was refined to final R(cryst) and R(free) values of 13.9% and 16.7%, respectively. The structure reveals the insertion of two short antiparallel beta-strands forming a small beta-sheet, an interesting variation of the classical all alpha-helical cytochrome c fold. This modification appears to be common to all known caa(3)-type terminal oxidases, as judged by comparative modelling and by analyses of the available amino acid sequences for these enzymes. This is the first high-resolution crystal structure reported for a cytochrome c domain of a caa(3)-type terminal oxidase. The R.marinus caa(3) uses HiPIP as the redox partner. The calculation of the electrostatic potential at the molecular surface of this extra C-terminal domain provides insights into the binding to its redox partner on one side and its interaction with the remaining subunit II on the other side.     

Functional and topological aspects of pH-dependent regulation of electron and proton transport in chloroplasts in silico

In this work, we summarize results of computer simulation of electron and proton transport processes coupled to ATP synthesis in chloroplasts performed within the frames of a mathematical model developed as a system of differential equations for concentrations of electron carriers and hydrogen ion inside and outside the granal and stromal thylakoids. The model takes into account topological peculiarities and lateral heterogeneity of the chloroplast lamellar system. This allowed us to analyze the influence of restricted diffusion of protons inside small compartments of a chloroplast (e.g., in the narrow inter-thylakoid gap) on electron transport processes. The model adequately describes two modes of pH-dependent feedback control of electron transport associated with: (i) the acidification of the thylakoid lumen, which causes the slowing down of plastoquinol oxidation and stimulates an increase in dissipation of excess energy in PS2, and (ii) the alkalization of stroma, inducing the activation of the BBC (Bassham-Benson-Calvin) cycle and intensified consumption of ATP and NADPH. The influence of ATP on electron transport is mediated by modulation of the thylakoid membrane conductivity to protons through the ATP synthase complexes. We also analyze the contribution of alternative electron transport pathways to the maintenance of optimal balance between the energy donating and energy consuming stages of the light-induced photosynthetic processes.     

The local electric field within phospholipid membranes modulates the charge transfer reactions in reaction centres

Three different cholesterol derivatives and phloretin, known to affect the local electric field in phospholipid membranes, have been introduced into Rhodobacter sphaeroides reaction centre-containing phospholipid liposomes. We show that cholesterol and 6-ketocholestanol significantly slow down the interquinone first electron transfer (∼ 10 times), whereas phloretin and 5-cholesten-3β-ol-7-one leave the kinetics essentially unchanged. Interestingly, the two former compounds have been shown to increase the dipole potential, whereas the two latter decrease it. We also measured in isolated RCs the rates of the electron and proton transfers at the first flash. Over the pH range 7-10.5 both reactions display biphasic behaviors with nearly superimposable rates and amplitudes, suggesting that the gating process limiting the first electron transfer is indeed the coupled proton entry. We therefore interpret the effects of cholesterol and 6-ketocholestanol as due to dipole concentration producing an increased free energy barrier for protons to enter the protein perpendicular to the membrane. We also report for the first time in R. sphaeroides RCs, at room temperature, a biphasicity of the P⁺Q_A⁻ charge recombination, induced by the presence of cholesterol derivatives in proteoliposomes. We propose that these molecules decrease the equilibration time between two RC conformations, therefore revealing their presence.     

Oxidoreduction of cytochrome b in the presence of antimycin

1. The effect of oxidizing equivalents on the redox state of cytochrome b in the presence of antimycin has been studied in the presence and absence of various redox mediators.

2. The antimycin-induced extra reduction of cytochrome b is always dependent on the initial presence of an oxidant such as oxygen. After removal of the oxidant this effect remains or is partially (under some conditions even completely) abolished depending on the redox potential of the substrate used and the leak through the antimycin-inhibited site.

3. The increased reduction of cytochrome b induced by oxidant in the presence of antimycin involves all three spectroscopically resolvable b components (b-562, b-566 and b-558.

4. Redox mediators with an actual redox potential of less than 100–170 mV cause the oxidation of cytochrome b reduced under the influence of antimycin and oxidant.

5. Redox titrations of cytochrome b with the succinate/fumarate couple were performed aerobically in the presence of cyanide. In the presence of antimycin two b components are separated potentiometrically, one with an apparent midpoint potential above 80 mV (at pH 7.0), outside the range of the succinate/fumurate couple, and one with an apparent midpoint potential of 40 mV and an n value of 2. In the absence of antimycin cytochrome b titrates essentially as one species with a midpoint potential of 39 mV (at pH 7.0) and n = 1.14.

6. The increased reducibility of cytochrome b induced by antimycin plus oxidant is considered to be the result of two effects: inhibition of oxidation of ferrocytochrome b by ferricytochrome c₁ (the effect of antimycin), and oxidation of the semiquinone form of a two-equivalent redox couple such as ubiquinone/ubiquinol by the added oxidant, leading to a decreased redox potential of the QH₂/QH^• couple and reduction of cytochrome b.