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 ...