The thermodynamic properties of the Desulfovibrio vulgaris (Hildenborough) tetrahaem cytochrome c3 (Dvc,) are rationalised by a model which involves both homotropic (e-/e-) and heterotropic (e-/H+) cooperativity. The paramagnetic shifts of a methyl group from each haem of the DVC, have been determined in each stage of oxidation at several pH values by means of two-dimensional exchange NMR. The thermodynamic parameters are obtained by fitting the model to the NMR data and to redox titrations followed by visible spectroscopy. They show significant positive cooperativity between two of the haems whereas the remaining interactions appear to be largely electrostatic in origin. These parameters imply that the protein undergoes a proton-assisted two-electron transfer which can be used for energy transduction. Comparison with the crystal structure together with measurement of the kinetics of proton exchange suggest that the pH dependence is mediated by a charged residue(s) readily acessible to the solvent and close to haem I.Keywords: cooperativity ; energy transduction ; multiheme cytochrome ; NMR ; redox-Bohr.The functional cooperativity between different regions of some proteins [ l ] is a fundamental property to control and coordinate important chemical events in the living cell. Although the molecular basis for the fine regulation of several types of cooperativity mechanisms has been successfully established [2], little is known about the structural basis for electron/electron and electron/proton cooperativities and their role either in electron transfer or in energy transduction [3].Desulfovibrio spp. cytochrome c, is a small (=14 m a ) , monomeric tetrahaem protein which exhibits cooperativity between the four haems and acidmase group(s): the haem redox potentials are pH dependent (redox-Bohr effect) and each haem redox potential is dependent on the oxidation state of the other three haems (redox interaction potentials) [4-61. Due to its small size and the fact that the haems are diamagnetic in the reduced state and paramagnetic in the oxidised one, NMR is particularly well suited to characterise this protein from the structural and thermodynamic point of view [4,[7][8][9][10][11][12][13][14][15].Furthermore, several X-ray structures are available for cytochromes c3 from Desulfovibrio spp. [16-231.The thermodynamic properties of cytochrome c, have been analysed by previous NMR studies [4,5,8,15, 241. In the first of these studies an NMR data set obtained at two discrete pH values for Desulfovibrio gigas cytochrome c, was used to calculate nine parameters (three relative microscopic redox potentials and six haem-haem redox interactions) for each pH value, independently treated. The redox interaction potentials were fixed according to the maximum concentration reached by the intermediate oxidation stages (defined according to the number of oxidised haems) in redox titrations followed by NMR [4]. Using the same NMR data set, a second study proposed a model with 21 parameters in which the four haem redox potentials ...

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The assignment of 13C resonances of nuclei alpha to the haem in horse ferricytochrome c is completed and the Fermi contact shifts are evaluated at 30 degrees C and 50 degrees C using empirical magnetic susceptibility tensors to correct for dipolar interactions. The Fermi contact shifts are fitted to a model of molecular orbitals of eg symmetry, which are subject to a rhombic perturbation. A similar analysis is performed using published data for Pseudomonas aeruginosa cytochrome c551. The relationship between the orientation of the effective g tensor and that of the rhombic perturbation in these proteins is shown to agree with theoretical predictions. A comparison between the orientation of the rhombic perturbations and the crystal structures of horse cytochrome c and P. aeruginosa cytochrome c551 reveals that the orientation of the histidine and methionine axial ligands dominates the rhombic perturbation and that the two ligands have approximately equal influence. The magnitude of the perturbation shows that the orientation of the axial ligands has little effect on the haem redox potential. However, the relationship that is established between the magnetic susceptibility tensor, the partially filled haem molecular orbitals, and the orientation of the haem ligands offers a new source of precise structural information.

Many ferricytochromes c exhibit a peculiar effect in which the 'H chemical shifts of the haem methyl groups appear in pairs and, although the paramagnetic shifts of the two groups with the larger shifts decrease with temperature, those of the pair with the smaller shifts actually increase. Recent NMR studies [Santos, H. and Turner, D. L. (1992) Eur. J. Biochem. 206, 721 -7281 gave ' H and I3C assignments for most of the haem substituents and the axial ligands in horse cytochrome c at 30°C and 50°C in both oxidation states. These data are used together with an empirically determined magnetic susceptibility tensor to evaluate the F e d contact contribution to the paramagnetic shift and hence map the delocalisation of the unpaired electron. The anti-Curie effect is explained by a Boltzmann distribution between partially filled porphyrin 3e(n) molecular orbitals with an energy difference of 3 W/mol. The fact that the energy gap is small with respect to the energy of binding to the electron transfer partners calls into question the significance of the asymmetry of the electron distribution in the electron transfer process.The 'H-NMR spectrum of horse ferricytochrome c takes on a dramatic appearance because two of the haem methyl resonances are shifted by about 30 ppm to low field while the other two are shifted only by about 5 ppm and barely emerge from the main envelope of signals. The large shifts have been assigned to methyls 3 and 8, situated in diametrically opposed pyrroles, and are assumed to be generated largely by the Fermi contact interaction [l]. This implies a strong asymmetry in the distribution of the delocalised unpaired electron which had been the subject of speculation concerning the pathway for electron transfer [2J. Fermi contact shifts are expected to show an inverse temperature dependence, and methyls 3 and 8 exhibit such Curie law behaviour approximately, but methyls 1 and 5 have paramagnetic shifts which actually increase with temperature. Such anticurie behaviour has been observed for many c-type ferricytochromes, including those from horse [3], Pseudomonas aeruginosa [41, Rhodospirillum rubrum [5], Rhodopseudomonas gelatinosa [6], Paracoccus denitrijicans [7], and Methylophilus methylotrophus cytochrome cL which is illustrated in Fig.l. The effect has become accepted as a characteristic for identifying haem methyl resonances close to the main envelope of signals, and yet it seems never to have been explained.Anti-Curie behaviour has also been observed in ferredoxins, in which the effect is caused by thermal population of excited electronic spin states [8]. A similar effect has been observed in horse ferricytochrome c at elevated temperatures when the native low-spin protein is in fast chemical exchange with partially denatured high-spin forms [9]. This work, however, concerns only the region of linear temperature dependence of chemical shifts in which protein remains in a pure low-spin (S = '/z) state.