Enumeration of minimal stoichiometric precursor sets in metabolic networks

Background: What an organism needs at least from its environment to produce a set of metabolites, e.g. target(s) of interest and/or biomass, has been called a minimal precursor set. Early approaches to enumerate all minimal precursor sets took into account only the topology of the metabolic network (topological precursor sets). Due to cycles and the stoichiometric values of the reactions, it is often not possible to produce the target(s) from a topological precursor set in the sense that there is no feasible flux. Although considering the stoichiometry makes the problem harder, it enables to obtain biologically reasonable precursor sets that we call stoichiometric. Recently a method to enumerate all minimal stoichiometric precursor sets was proposed in the literature. The relationship between topological and stoichiometric precursor sets had however not yet been studied. Results: Such relationship between topological and stoichiometric precursor sets is highlighted. We also present two algorithms that enumerate all minimal stoichiometric precursor sets. The first one is of theoretical interest only and is based on the above mentioned relationship. The second approach solves a series of mixed integer linear programming problems. We compared the computed minimal precursor sets to experimentally obtained growth media of several Escherichia coli strains using genome-scale metabolic networks. Conclusions: The results show that the second approach efficiently enumerates minimal precursor sets taking stoichiometry into account, and allows for broad in silico studies of strains or species interactions that may help to understand e.g. pathotype and niche-specific metabolic capabilities. sasita is written in Java, uses cplex as LP solver and can be downloaded together with all networks and input files used in this paper at http://www.sasita.gforge.inria.fr

Conclusion: Contributions of Multiple Representations to Biological Education

Our book project began in 2009 with the intent to bring together international biology educators and biology education researchers who are involved in improving biological education from the perspective of multiple representations. It was also our goal that this volume would be able to address how biological education could meet the challenges of the twenty-first century, in which the breakthroughs in biological research would necessitate the integration of research and education with global economics and human social structures

Double deprotonation of ruthenium(II) cations containing 1,2-dimethyl-substituted η6-arenes. Protonation of the resulting exo-coordinated (o-xylylene)ruthenium(0) complexes and X-ray crystal structures of the agostic (η3-pentamethylbenzyl)ruthenium(II)

Treatment of the various ruthenium(II) salts [Ru(ONO2)(eta-6-1,2-dimethylarene)L2]NO3 and [Ru(O2CCF3)(eta-6-1,2-dimethylarene)L2]PF6 with KO-t-Bu or (Me3Si)2NNa in the presence of a ligand L' gives o-xylylene (o-quinodimethane) complexes of zerovalent ruthenium, i.e. Ru{eta-4-(CH2)2C6Me4}L2L' (L = L' = PMe2Ph, P(CD3)2Ph, PMePh2, P(OMe)3, P(OCH2)3CMe; L2 = Ph2PCH2CH2PPh2, L' = PMe2Ph; L2 = (Z)-Ph2PCH=CHPPh2, L' = PMe2Ph, P(CD3)2Ph), Ru{eta-4-(CH2)2C6H2Me2}L2L' (L = L' = PMe2Ph, PMePh2), and Ru{eta-4-(CH2)2C6H4}(PMe2Ph)3, in good to moderate yields. In all cases the o-xylylene group is coordinated through its exo pair of double bonds. The reactions are proposed to proceed via the undetected intermediates Ru(o-xylylene)L2 (L = monodentate P-donor ligand, L2 = bidentate P-donor ligand) in which the ruthenium atom can migrate from the endo to the exo pair of double bonds before ligand L' attacks. On treatment with HPF6, Ru{eta-4-(CH2)2C6Me4}L2L' and Ru(eta-4-(CH2)2C6H4}(PMe2Ph)3 give (eta-3-benzyl)ruthenium(II) salts [Ru{eta-3-(HCH2)(CH2)C6Me4}L2L']PF6 (L = Ph2PCH2CH2PPh2, L' = PMe2Ph (1); L = (Z)-Ph2PCH=CHPPh2, L' = PMe2Ph (2), P(CD3)2Ph (2a); L = L' = PMe2Ph (3), P(CD3)2Ph (3a)) and [Ru{eta-3-(HCH2)-(CH2)C6H4}(PMe2Ph)3]PF6 (4) in which the added proton bridges the metal atom and a terminal methylene group. Crystals of 2 are monoclinic, space group P2(1)/n, with a = 18.88.4 (3) angstrom, b = 18.612 (3) angstrom, c = 12.361 (1) angstrom, beta = 90.40 (1)-degrees, and Z = 4; those of 3 are monoclinic, space group C2/c, with a = 21.220 (8) angstrom, b = 23.412 (10) angstrom, c = 18.580 (7) angstrom, beta = 126.05 (1)-degrees, and Z = 8. The structures were solved by heavy-atom methods and refined by least-squares analysis to R = 0.042 and R(w) = 0.053 for 5787 independent reflections (I greater-than-or-equal-to 3-sigma) (2) and R = 0.053 and R(w) = 0.076 for 5832 independent reflections (I > 3-sigma) (3). Both cations contain a ruthenium atom coordinated in a distorted-octahedral arrangement by a eta-3-pentamethylbenzyl group, which occupies two sites, three phosphorus atoms, and an agostic methyl hydrogen atom that has been directly located in 2 but not 3. The eta-3-benzyl interaction in 2 shows the usual asymmetry, the shortest Ru-C bond being to the terminal CH2 group (Ru-C(22) = 2.164 (5) angstrom, Ru-C(2) = 2.342 (4) angstrom, Ru-C(1) = 2.358 (4) angstrom). The metrical parameters defining the agostic Ru-H-CH2 interaction in 2 are r(Ru-C) = 2.416 (5) angstrom, r(Ru-H) = 1.92 (4) angstrom, r(C-H) = 1.01 (5) angstrom, and angle C-H-Ru = 107 (3)-degrees. The distances from ruthenium to the terminal carbon atoms in 3 (Ru-C(11) = 2.333 (9) angstrom, Ru-C(22) = 2.283 (10) angstrom) are almost equal within experimental error, in contrast with the corresponding distances in 2, and indicate that the solid-state structure of 3 is an average in which either C(11) or C(22) is protonated. Variable-temperature NMR (H-1, P-31) spectra of complexes 1, 2, 2a, 3, 3a, and 4 show these molecules to be fluxional as a consequence of three processes: (1) reversible Ru-H (agostic) bond breaking, which cannot be frozen out, even at -100-degrees-C; (2) reversible eta-3 reversible eta-1 interconversions of the benzyl group, for which the estimated DELTA-G(double dagger) values are ca. 13 kcal/mol at 303 K for 2 and ca