Analytical study of the effect of recombination on evolution via DNA shuffling

We investigate a multi-locus evolutionary model which is based on the DNA shuffling protocol widely applied in \textit{in vitro} directed evolution. This model incorporates selection, recombination and point mutations. The simplicity of the model allows us to obtain a full analytical treatment of both its dynamical and equilibrium properties, for the case of an infinite population. We also briefly discuss finite population size corrections

Control of Oxo-Group Functionalization and Reduction of the Uranyl Ion

yesUranyl complexes of a large, compartmental N8-macrocycle adopt a rigid, “Pacman” geometry that stabilizes the UV oxidation state and promotes chemistry at a single uranyl oxo-group. We present here new and straightforward routes to singly reduced and oxo-silylated uranyl Pacman complexes and propose mechanisms that account for the product formation, and the byproduct distributions that are formed using alternative reagents. Uranyl(VI) Pacman complexes in which one oxo-group is functionalized by a single metal cation are activated toward single-electron reduction. As such, the addition of a second equivalent of a Lewis acidic metal complex such as MgN″2 (N″ = N(SiMe3)2) forms a uranyl(V) complex in which both oxo-groups are Mg functionalized as a result of Mg−N bond homolysis. In contrast, reactions with the less Lewis acidic complex [Zn(N″)Cl] favor the formation of weaker U−O−Zn dative interactions, leading to reductive silylation of the uranyl oxo-group in preference to metalation. Spectroscopic, crystallographic, and computational analysis of these reactions and of oxo-metalated products isolated by other routes have allowed us to propose mechanisms that account for pathways to metalation or silylation of the exo-oxogroup