The NMR structure of the oxidised wild-type cytochrome c3 from Desulfovibrio vulgaris Hildenborough was determined in solution. Using a newly developed methodology, NMR data from the K45Q mutant was then grafted onto data from the wild-type protein to determine the structure in the region of the mutation. The structural origins of the redox-Bohr effect and haem–haem cooperativities are discussed with respect to the redox-related conformational changes observed in solution.

The facultative aerobic bacterium Geobacter sulfurreducens produces a small periplasmic c-type triheme cytochrome with 71 residues (PpcA) under anaerobic growth conditions, which is involved in the iron respiration. The thermodynamic properties of the PpcA redox centers and of a protonatable center were determined using NMR and visible spectroscopy techniques. The redox centers have negative and different reduction potentials (−162, −143, and −133 mV for heme I, III, and IV, respectively, for the fully reduced and protonated protein), which are modulated by redox interactions among the hemes (covering a range from 10 to 36 mV) and by redox−Bohr interactions (up to −62 mV) between the hemes and a protonatable center located in the proximity of heme IV. All the interactions between the four centers are dominated by electrostatic effects. The microscopic reduction potential of heme III is the one most affected by the oxidation of the other hemes, whereas heme IV is the most affected by the protonation state of the molecule. The thermodynamic properties of PpcA showed that pH strongly modulates the redox behavior of the individual heme groups. A preferred electron transfer pathway at physiologic pH is defined, showing that PpcA has the necessary thermodynamic properties to perform e-/H+ energy transduction, contributing to a H+ electrochemical potential gradient across the periplasmic membrane that drives ATP synthesis. PpcA is 46% identical in sequence to and shares a high degree of structural similarity with a periplasmic triheme cytochrome c7 isolated from Desulfuromonas acetoxidans, a bacterium closely related to the Geobacteracea family. However, the results obtained for PpcA are quite different from those published for D. acetoxidans c7, and the physiological consequences of these differences are discussed.

The relation showing that the Grunwald-Letnikov and generalised Cauchy derivatives are equal is presented. This establishes a bridge between two different formulations and simultaneously between the classic integer order derivatives and the fractional ones. Starting from the generalised Cauchy derivative formula, new relations are obtained, namely a regularised version that makes the concept of pseudo-function appear naturally without the need for a rejection of any infinite part. From the regularised derivative, new formulations are deduced and specialised first for the real functions and afterwards for functions with Laplace transforms obtaining the definitions proposed by Lionville. With these tools suitable definitions of fractional linear systems are obtained.

The foresight and scenario building methods can be an interesting reference for social sciences, especially in terms of innovative methods for labour process analysis. A scenario – as a central concept for the prospective analysis – can be considered as a rich and detailed portrait of a plausible future world. It can be a useful tool for policy-makers to grasp problems clearly and comprehensively, and to better pinpoint challenges as well as opportunities in an overall framework. The features of the foresight methods are being used in some labour policy making experiences. Case studies developed in Portugal will be presented, and some conclusions will be drawn in order to organise a set of principles for foresight analysis applied to the European project WORKS on the work organisation re-structuring in the knowledge society, and on the work design methods for new management structures of virtual organisations.

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