Kinetic Treatment of Coupled Electron and Proton Transfer in Flash-Photolysis Experiments on Carbon Monoxide-Inhibited Mixed-Valence Cytochrome c Oxidase

ELECTRON TRANSFER REACTIONS COUPLED TO PROTON TRANSLOCATION: CYTOCHROME OXIDASE, PROTON PUMPS, AND BIOLOGICAL ENERGY TRANSDUCTION

Cytochrome oxidase (COX) is the terminal component of electron transport chain of the respiratory system in mitochondria, and one of the key enzymes responsible for energy generation in cells. COX functions as a proton pump that utilizes free energy of oxygen reduction for translocation of protons across the mitochondrion membrane. The proton gradient created in the process is later utilized to drive synthesis of ATP. Although the structure of COX has been recently resolved, the molecular mechanism of proton pumping remains unknown. In this paper, general principles and possible molecular mechanisms of energy transformations in this enzyme will be discussed. The main question is how exactly chemical energy of oxygen reduction and water formation is transformed into a proton gradient; or, how exactly electron transfer reactions are utilized to translocate protons across the mitochondrion membrane against the electrochemical gradient. A key to the solution of this problem is in understanding correlated transport of electrons and protons. Here, theoretical models are discussed for coupled electron and proton transfer reactions in which an electron is tunneling over long distance between two redox cofactors, and a coupled proton is moving along a proton conducting channel in a classical, diffusion-like random walk fashion. Such reactions are typical for COX and other enzymes involved in biological energy transformations.

Proton diffusion along biological membranes

Biological surfaces are known to be capable of retaining protons and facilitating their lateral diffusion. Since the surface dynamically exchanges protons with the bulk, the proton movement from a source to a target at the surface acquires a complicated pattern of coupled surface and bulk (2D + 3D) diffusion of which the main feature is that the surface acts as a proton-collecting antenna enhancing the proton flux from the bulk. A phenomenological model of this process is reviewed and its applications to recent experiments on lipid bilayers and small unilaminar vesicles are discussed. The model (i) introduces the important notions of the fast and slow regimes of proton exchange between the surface and the bulk, (ii) permits evaluation of the antenna radius and amplification coefficient in both regimes, (iii) explains the observed macroscopically large distances (in the micrometer range; Antonenko and Pohl 1998 FEBS Lett. 429 197) that the proton can travel along lipid membranes embedded into pure aqueous solutions, and (iv) predicts the dependence of the steady-state proton flux and the kinetics of the non-stationary diffusion upon the buffer concentration in buffered solutions. The surface diffusion coefficient for small unilaminar vesicles is calculated from experimental data (Sandén et al 2010 Proc. Natl Acad. Sci. USA 107 4129) to be 1 × 10(-5) cm(2) s(-1). The dependence of the shape of the kinetic curves representing protonation/deprotonation of a lipid-bound pH-sensitive dye attached to a planar bilayer lipid membrane upon the buffer concentration (Serowy et al 2003 Biophys. J. 84 1031) and the effect of changing the membrane composition (Antonenko and Pohl 2008 Eur. Biophys. J. 37 865) are explained.

Hydrogen atom transfer reactions of a ruthenium imidazole complex: hydrogen tunneling and the applicability of the Marcus cross relation

The reaction of Ru(II)(acac)2(py-imH) (Ru(II)imH) with TEMPO(*) (2,2,6,6-tetramethylpiperidine-1-oxyl radical) in MeCN quantitatively gives Ru(III)(acac)2(py-im) (Ru(III)im) and the hydroxylamine TEMPO-H by transfer of H(*) (H(+) + e(-)) (acac = 2,4-pentanedionato, py-imH = 2-(2'-pyridyl)imidazole). Kinetic measurements of this reaction by UV-vis stopped-flow techniques indicate a bimolecular rate constant k(3H) = 1400 +/- 100 M(-1) s(-1) at 298 K. The reaction proceeds via a concerted hydrogen atom transfer (HAT) mechanism, as shown by ruling out the stepwise pathways of initial proton or electron transfer due to their very unfavorable thermochemistry (Delta G(o)). Deuterium transfer from Ru(II)(acac)2(py-imD) (Ru(II)imD) to TEMPO(*) is surprisingly much slower at k(3D) = 60 +/- 7 M(-1) s(-1), with k(3H)/k(3D) = 23 +/- 3 at 298 K. Temperature-dependent measurements of this deuterium kinetic isotope effect (KIE) show a large difference between the apparent activation energies, E(a3D) - E(a3H) = 1.9 +/- 0.8 kcal mol(-1). The large k(3H)/k(3D) and DeltaE(a) values appear to be greater than the semiclassical limits and thus suggest a tunneling mechanism. The self-exchange HAT reaction between Ru(II)imH and Ru(III)im, measured by (1)H NMR line broadening, occurs with k(4H) = (3.2 +/- 0.3) x 10(5) M(-1) s(-1) at 298 K and k(4H)/k(4D) = 1.5 +/- 0.2. Despite the small KIE, tunneling is suggested by the ratio of Arrhenius pre-exponential factors, log(A(4H)/A(4D)) = -0.5 +/- 0.3. These data provide a test of the applicability of the Marcus cross relation for H and D transfers, over a range of temperatures, for a reaction that involves substantial tunneling. The cross relation calculates rate constants for Ru(II)imH(D) + TEMPO(*) that are greater than those observed: k(3H,calc)/k(3H) = 31 +/- 4 and k(3D,calc)/k(3D) = 140 +/- 20 at 298 K. In these rate constants and in the activation parameters, there is a better agreement with the Marcus cross relation for H than for D transfer, despite the greater prevalence of tunneling for H. The cross relation does not explicitly include tunneling, so close agreement should not be expected. In light of these results, the strengths and weaknesses of applying the cross relation to HAT reactions are discussed.

Dynamics of Radiationless Transitions: Effects of Displacement−Distortion−Rotation of Potential Energy Surfaces on Internal Conversion Decay Rate Constants,

General expressions for calculating the internal conversion decay rate constants between two adiabatic electronic states and between two diabatic electronic states are derived. The expressions include the displacements, distortions, and rotations of potential energy surfaces as well as the temperature. For illustration, internal conversion rate constants between various singlet electronic states of ethylene and between the first excited S1 and the ground S0 singlet electronic states of azulene are calculated.

Analysis of the kinetics of the membrane potential generated by cytochrome c oxidase upon single electron injection

In a recent work from this group (Popovic, D. M.; Stuchebrukhov A. A. FEBS Lett. 2004, 566, 126), a model of proton pumping by cytochrome c oxidase (CcO) was proposed. The key element of the model is His291 (bovine notation), a histidine ligand to enzyme's CuB redox center, which plays the role of the pump element. The model assumes that upon electron transfer between heme a and the binuclear catalytic center of the enzyme, two sequential proton transfers occur: First, a proton from Glu242 is transferred to an unprotonated His291, then a second proton, after reprotonation of Glu242 from the negative side of the membrane, is transferred to a hydroxyl group in the binuclear center, a water molecule is formed, and the first proton, due to proton-proton repulsion, is expelled from His291 to the positive side of the membrane, resulting in a pumping event. In the process the free energy of water formation (i.e., reduction of oxygen) is transformed into a proton gradient across the membrane. The model possesses specific kinetic features. It assumes, for example, that upon electron transfer the first proton is transferred to the proton-loading site of the pump, His291, and not to the catalytic center of the enzyme. Here, we analyze the kinetic properties of the proposed model, and calculate the time dependence of the membrane potential generated by CcO upon a single electron injection into the enzyme. These data are directly compared with recent experimental measurements of the membrane potential generated by CcO. Specifically, F to O, and O to E transitions will be discussed. Several enzymes from different organisms (bovine, two bacterial enzymes, and several mutants) are compared and discussed in detail. The kinetic description, however, is phenomenological, and does not include explicitly the nature of the groups involved in proton translocation, except in terms of their position depth within the membrane; thus, the kinetic equations developed here are in fact describe a generic model, similar, e.g., to that proposed earlier by Peter Rich (P.R. Rich, Towards an understanding of the chemistry of oxygen reduction and proton translocation in the iron-copper respiratory oxidases. Aust. J. Plant Physiol. 22 (1995) 479-486), and which is based on the idea of displacement of the pumped protons by the chemical ones.

Surface-mediated proton-transfer reactions in membrane-bound proteins

As outlined by Peter Mitchell in the chemiosmotic theory, an intermediate in energy conversion in biological systems is a proton electrochemical potential difference ("proton gradient") across a membrane, generated by membrane-bound protein complexes. These protein complexes accommodate proton-transfer pathways through which protons are conducted. In this review, we focus specifically on the role of the protein-membrane surface and the surface-bulk water interface in the dynamics of proton delivery to these proton-transfer pathways. The general mechanisms are illustrated by experimental results from studies of bacterial photosynthetic reaction centres (RCs) and cytochrome c oxidase (CcO).

Water-hydroxide exchange reactions at the catalytic site of heme-copper oxidases

Membrane-bound heme-copper oxidases catalyze the reduction of O(2) to water. Part of the free energy associated with this process is used to pump protons across the membrane. The O(2) reduction reaction results in formation of high-pK(a) protonatable groups at the catalytic site. The free energy associated with protonation of these groups is used for proton pumping. One of these protonatable groups is OH(-), coordinated to the heme and Cu(B) at the catalytic site. Here we present results from EPR experiments on the Rhodobacter sphaeroides cytochrome c oxidase, which show that at high pH (9) approximately 50% of oxidized heme a(3) is hydroxide-ligated, while at low pH (6.5), no hydroxide is bound to heme a(3). The kinetics of hydroxide binding to heme a(3) were investigated after dissociation of CO from heme a(3) in the enzyme in which the heme a(3)-Cu(B) center was reduced while the remaining redox sites were oxidized. The dissociation of CO results in a decrease of the midpoint potential of heme a(3), which results in electron transfer (tau approximately equal 3 micros) from heme a(3) to heme a in approximately 100% of the enzyme population. At pH >7.5, the electron transfer is followed by proton release from a H(2)O molecule to the bulk solution (tau approximately equal 2 ms at pH 9). This reaction is also associated with absorbance changes of heme a(3), which on the basis of the results from the EPR experiments are attributed to formation of hydroxide-ligated heme a(3). The OH(-) bound to heme a(3) under equilibrium conditions at high pH is also formed transiently after O(2) reduction at low pH. It is proposed that the free energy associated with electron transfer to the binuclear center and protonation of this OH(-) upon reduction of the recently oxidized enzyme provides the driving force for the pumping of one proton.

Electron and hydrogen-atom self-exchange reactions of iron and cobalt coordination complexes

Reported here are self-exchange reactions between iron 2,2'-bi(tetrahydro)pyrimidine (H(2)bip) complexes and between cobalt 2,2'-biimidazoline (H(2)bim) complexes. The (1)H NMR resonances of [Fe(II)(H(2)bip)(3)](2+) are broadened upon addition of [Fe(III)(H(2)bip)(3)](3+), indicating that electron self-exchange occurs with k(Fe,e)(-) = (1.1 +/- 0.2) x 10(5) M(-1) s(-1) at 298 K in CD(3)CN. Similar studies of [Fe(II)(H(2)bip)(3)](2+) plus [Fe(III)(Hbip)(H(2)bip)(2)](2+) indicate that hydrogen-atom self-exchange (proton-coupled electron transfer) occurs with k(Fe,H.) = (1.1 +/- 0.2) x 10(4) M(-1) s(-1) under the same conditions. Both self-exchange reactions are faster at lower temperatures, showing small negative enthalpies of activation: DeltaH++(e(-)) = -2.1 +/- 0.5 kcal mol(-1) (288-320 K) and DeltaH++(H.) = -1.5 +/- 0.5 kcal mol(-1) (260-300 K). This behavior is concluded to be due to the faster reaction of the low-spin states of the iron complexes, which are depopulated as the temperature is raised. Below about 290 K, rate constants for electron self-exchange show the more normal decrease with temperature. There is a modest kinetic isotope effect on H-atom self-exchange of 1.6 +/- 0.5 at 298 K that is close to that seen previously for the fully high-spin iron biimidazoline complexes.(12) The difference in the measured activation parameters, E(a)(D) - E(a)(H), is -1.2 +/- 0.8 kcal mol(-1), appears to be inconsistent with a semiclassical view of the isotope effect, and suggests extensive tunneling. Reactions of [Co(H(2)bim)(3)](2+)-d(24) with [Co(H(2)bim)(3)](3+) or [Co(Hbim)(H(2)bim)(2)](2+) occur with scrambling of ligands indicating inner-sphere processes. The self-exchange rate constant for outer-sphere electron transfer between [Co(H(2)bim)(3)](2+) and [Co(H(2)bim)(3)](3+) is estimated to be 10(-)(6) M(-1) s(-1) by application of the Marcus cross relation. Similar application of the cross relation to H-atom transfer reactions indicates that self-exchange between [Co(H(2)bim)(3)](2+) and [Co(Hbim)(H(2)bim)(2)](2+) is also slow, < or =10(-3) M(-1) s(-1). The slow self-exchange rates for the cobalt complexes are apparently due to their interconverting high-spin [Co(II)(H(2)bim)(3)](2+) with low-spin Co(III) derivatives.

Proton-coupled electron transfer versus hydrogen atom transfer in benzyl/toluene, methoxyl/methanol, and phenoxyl/phenol self-exchange reactions

Degenerate hydrogen atom exchange reactions have been studied using calculations, based on density functional theory (DFT), for (i) benzyl radical plus toluene, (ii) phenoxyl radical plus phenol, and (iii) methoxyl radical plus methanol. The first and third reactions occur via hydrogen atom transfer (HAT) mechanisms. The transition structure (TS) for benzyl/toluene hydrogen exchange has C(2)(h)() symmetry and corresponds to the approach of the 2p-pi orbital on the benzylic carbon of the radical to a benzylic hydrogen of toluene. In this TS, and in the similar C(2) TS for methoxyl/methanol hydrogen exchange, the SOMO has significant density in atomic orbitals that lie along the C-H vectors in the former reaction and nearly along the O-H vectors in the latter. In contrast, the SOMO at the phenoxyl/phenol TS is a pi symmetry orbital within each of the C(6)H(5)O units, involving 2p atomic orbitals on the oxygen atoms that are essentially orthogonal to the O.H.O vector. The transferring hydrogen in this reaction is a proton that is part of a typical hydrogen bond, involving a sigma lone pair on the oxygen of the phenoxyl radical and the O-H bond of phenol. Because the proton is transferred between oxygen sigma orbitals, and the electron is transferred between oxygen pi orbitals, this reaction should be described as a proton-coupled electron transfer (PCET). The PCET mechanism requires the formation of a hydrogen bond, and so is not available for benzyl/toluene exchange. The preference for phenoxyl/phenol to occur by PCET while methoxyl/methanol exchange occurs by HAT is traced to the greater pi donating ability of phenyl over methyl. This results in greater electron density on the oxygens in the PCET transition structure for phenoxyl/phenol, as compared to the PCET hilltop for methoxyl/methanol, and the greater electron density on the oxygens selectively stabilizes the phenoxyl/phenol TS by providing a larger binding energy of the transferring proton.

Proton transport via the membrane surface

Some proton pumps, such as cytochrome c oxidase (C(c)O), translocate protons across biological membranes at a rate that considerably exceeds the rate of proton transport to the entrance of the proton-conducting channel via bulk diffusion. This effect is usually ascribed to a proton-collecting antenna surrounding the channel entrance. In this paper, we consider a realistic phenomenological model of such an antenna. In our model, a homogeneous membrane surface, which can mediate proton diffusion toward the channel entrance, is populated with protolytic groups that are in dynamic equilibrium with the solution. Equations that describe coupled surface-bulk proton diffusion are derived and analyzed. A general expression for the rate constant of proton transport via such a coupled surface-bulk diffusion mechanism is obtained. A rigorous criterion is formulated of when proton diffusion along the surface enhances the transport. The enhancement factor is found to depend on the ratio of the surface and bulk diffusional constants, pK(a) values of surface protolytic groups, and their concentration. A capture radius for a proton on the surface and an effective size of the antenna are found. The theory also predicts the effective distance that a proton can migrate on the membrane surface between a source (such as CcO) and a sink (such as ATP synthase) without fully equilibrating with the bulk. In pure aqueous solutions, protons can travel over long distances (microns). In buffered solutions, the travel distance is much shorter (nanometers); still the enhancement effect of the surface diffusion on the proton flow to a target on the surface can be tens to hundreds at physiological buffer concentrations. These results are discussed in a general context of chemiosmotic theory.