Vladimir L. Popov

Homogeneous spaces and equivariant embeddings

Introduction.- 1 Algebraic Homogeneous Spaces.- 2 Complexity and Rank.- 3 General Theory of Embeddings.- 4 Invariant Valuations.- 5 Spherical Varieties.- Appendices.- Bibliography.- Indices

Structure‐guided alteration of coenzyme specificity of formate dehydrogenase by saturation mutagenesis to enable efficient utilization of NADP+

Formate dehydrogenase from Candida boidinii (CboFDH) catalyses the oxidation of formate anion to carbon dioxide with concomitant reduction of NAD+ to NADH. CboFDH is highly specific to NAD+ and virtually fails to catalyze the reaction with NADP+. Based on structural information for CboFDH, the loop region between β‐sheet 7 and α‐helix 10 in the dinucleotide‐binding fold was predicted as a principal determinant of coenzyme specificity. Sequence alignment with other formate dehydrogenases revealed two residues (Asp195 and Tyr196) that could account for the observed coenzyme specificity. Positions 195 and 196 were subjected to two rounds of site‐saturation mutagenesis and screening and enabled the identification of a double mutant Asp195Gln/Tyr196His, which showed a more than 2 × 107‐fold improvement in overall catalytic efficiency with NADP+ and a more than 900‐fold decrease in the efficiency with NAD+ as cofactors. The results demonstrate that the combined polar interactions and steric factors comprise the main structural determinants responsible for coenzyme specificity. The double mutant Asp195Gln/Tyr196His was tested for practical applicability in a cofactor recycling system composed of cytochrome P450 monooxygenase from Bacillus subtilis, (CYP102A2), NADP+, formic acid and ω‐(p‐nitrophenyl)dodecanoic acid (12‐pNCA). Using a 1250‐fold excess of 12‐pNCA over NADP+ the first order rate constant was determined to be equal to kobs = 0.059 ± 0.004 min−1.

Representations with a free module of covariants

i. From here on k is a ground field, k = k, char k = 0. Let G be a connected simplyconnected semisimple group; 0 be its representation in kn = V without nonzero fixed points; k[V] G be the subalgebra of G-invariants in the algebra k[V] of polynomials on V; V/G and ~: V + V/G be the variety of orbits and the orbit morphism [I]; mG be the maximum of the numbers dim p(G).v, v ~ V. The k[V]G-module k[V] is called the module of covariants.

Groups, generators, syzygies, and orbits in invariant theory

* Introduction* Notation and terminology* The role of reductive groups in invariant theory* Constructive invariant theory* The degree of the Poincare series of the algebra of invariants and a finiteness theorem for representations with free algebra of invariants* Syzygies in invariant theory* Representations with free modules of covariants* A classification of normal affine quasihomogeneous varieties of SL2* Quasihomogeneous curves, surfaces, and solids* Appendices* Bibliography* Subject index

Jordan Groups and Automorphism Groups of Algebraic Varieties

The first section of this paper is focused on Jordan groups in abstract setting, the second on that in the settings of automorphisms groups and groups of birational self-maps of algebraic varieties. The appendix contains formulations of some open problems and the relevant comments.

Comparative structural and functional analysis of two octaheme nitrite reductases from closely related Thioalkalivibrio species

Octaheme nitrite reductase from the haloalkaliphilic bacterium Thioalkalivibrio paradoxus was isolated and characterized. A comparative structural and functional analysis of two homologous octaheme nitrite reductases from closely related Thioalkalivibrio species was performed. It was shown that both enzymes have similar catalytic properties, owing to high structural similarity. Both enzymes are characterized by specific structural features distinguishing them from pentaheme cytochrome c nitrite reductases, such as the Tyr‐Cys bond in the active site, the hexameric structure resulting in the formation of a void space inside the hexamer, and the product channel that opens into the void interior space of the hexamer. It is suggested that these specific structural features are responsible for the higher nitrite reductase activity, the greater preference for nitrite than for sulfite as a substrate, and the wider pH range of the catalytic activity of octaheme nitrite reductases than of pentaheme homologs.

Finite subgroups of diffeomorphism groups

We prove the following: (1) the existence, for every integer n ≥ 4, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem for finite simple subgroups of diffeomorphism groups of compact smooth topological manifolds.

Two Orbits: When is one in the closure of the other?

AbstractLet G be a connected linear algebraic group, let V be a finite dimensional algebraic G-module, and let

Tensor product decompositions and open orbits in multiple flag varieties

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