Information entropy in cosmology.

The effective evolution of an inhomogeneous cosmological model may be described in terms of spatially averaged variables. We point out that in this context, quite naturally, a measure arises which is identical to a fluid model of the Kullback-Leibler relative information entropy, expressing the distinguishability of the local inhomogeneous mass density field from its spatial average on arbitrary compact domains. We discuss the time evolution of "effective information" and explore some implications. We conjecture that the information content of the Universe-measured by relative information entropy of a cosmological model containing dust matter-is increasing.

Cosmological parameters are dressed.

In the context of the averaging problem in relativistic cosmology, we provide a key to the interpretation of cosmological parameters by taking into account the actual inhomogeneous geometry of the Universe. We discuss the relation between "bare" cosmological parameters determining the cosmological model and the parameters interpreted by observers with a "Friedmannian bias," which are "dressed" by the smoothed-out geometrical inhomogeneities of the surveyed spatial region.

The function of the [4Fe-4S] clusters and FAD in bacterial and archaeal adenylylsulfate reductases. Evidence for flavin-catalyzed reduction of adenosine 5'-phosphosulfate.

The iron-sulfur flavoenzyme adenylylsulfate (adenosine 5'-phosphosulfate, APS) reductase catalyzes reversibly the 2-electron reduction of APS to sulfite and AMP, a key step in the biological sulfur cycle. APS reductase from one archaea and three different bacteria has been purified, and the molecular and catalytic properties have been characterized. The EPR parameters and redox potentials (-60 and -520 mV versus NHE) have been assigned to the two [4Fe-4S] clusters I and II observed in the three-dimensional structure of the enzyme from Archaeoglobus fulgidus (Fritz, G., Roth, A., Schiffer, A., Büchert, T., Bourenkov, G., Bartunik, H. D., Huber, H., Stetter, K. O., Kroneck, P. M. H., and Ermler, U. (2002) Proc. Natl. Acad. Sci. U. S. A. 99, 1836-1841). Sulfite binds to FAD to form a covalent FAD N(5)-sulfite adduct with characteristic UV/visible spectra, in accordance with the three-dimensional structure of crystalline enzyme soaked with APS. UV/visible monitored titrations reveal that the substrates AMP and APS dock closely to the FAD cofactor. These results clearly document that FAD is the site of the 2-electron reduction of APS to sulfite and AMP. Reaction of APS reductase enzyme with sulfite and AMP leads to partial reduction of the [4Fe-4S] centers and formation of the anionic FAD semiquinone. Thus, both [4Fe-4S] clusters function in electron transfer and guide two single electrons from the protein surface to the FAD catalytic site.

The presence of an iron-sulfur cluster in adenosine 5'-phosphosulfate reductase separates organisms utilizing adenosine 5'-phosphosulfate and phosphoadenosine 5'-phosphosulfate for sulfate assimilation.

It was generally accepted that plants, algae, and phototrophic bacteria use adenosine 5'-phosphosulfate (APS) for assimilatory sulfate reduction, whereas bacteria and fungi use phosphoadenosine 5'-phosphosulfate (PAPS). The corresponding enzymes, APS and PAPS reductase, share 25-30% identical amino acids. Phylogenetic analysis of APS and PAPS reductase amino acid sequences from different organisms, which were retrieved from the GenBank(TM), revealed two clusters. The first cluster comprised known PAPS reductases from enteric bacteria, cyanobacteria, and yeast. On the other hand, plant APS reductase sequences were clustered together with many bacterial ones, including those from Pseudomonas and Rhizobium. The gene for APS reductase cloned from the APS-reducing cyanobacterium Plectonema also clustered together with the plant sequences, confirming that the two classes of sequences represent PAPS and APS reductases, respectively. Compared with the PAPS reductase, all sequences of the APS reductase cluster contained two additional cysteine pairs homologous to the cysteine residues involved in binding an iron-sulfur cluster in plants. Mössbauer analysis revealed that the recombinant APS reductase from Pseudomonas aeruginosa contains a [4Fe-4S] cluster with the same characteristics as the plant enzyme. We conclude, therefore, that the presence of an iron-sulfur cluster determines the APS specificity of the sulfate-reducing enzymes and thus separates the APS- and PAPS-dependent assimilatory sulfate reduction pathways.

Structure of adenylylsulfate reductase from the hyperthermophilic Archaeoglobus fulgidus at 1.6-A resolution.

The iron-sulfur flavoenzyme adenylylsulfate (adenosine 5'-phosphosulfate, APS) reductase catalyzes reversibly the reduction of APS to sulfite and AMP. The structures of APS reductase from the hyperthermophilic Archaeoglobus fulgidus in the two-electron reduced state and with sulfite bound to FAD are reported at 1.6- and 2.5- resolution, respectively. The FAD-sulfite adduct was detected after soaking the crystals with APS. This finding and the architecture of the active site strongly suggest that catalysis involves a nucleophilic attack of the N5 atom of reduced FAD on the sulfur atom of APS. In view of the high degree of similarity between APS reductase and fumarate reductase especially with regard to the FAD-binding alpha-subunit, it is proposed that both subunits originate from a common ancestor resembling archaeal APS reductase. The two electrons required for APS reduction are transferred via two [4Fe-4S] clusters from the surface of the protein to FAD. The exceptionally large difference in reduction potential of these clusters (-60 and -500 mV) can be explained by interactions of the clusters with the protein matrix.