Intelligent host engineering for metabolic flux optimisation in biotechnology

Optimising the function of a protein of length N amino acids by directed evolution involves navigating a ‘search space’ of possible sequences of some 20N. Optimising the expression levels of P proteins that materially affect host performance, each of which might also take 20 (logarithmically spaced) values, implies a similar search space of 20P. In this combinatorial sense, then, the problems of directed protein evolution and of host engineering are broadly equivalent. In practice, however, they have different means for avoiding the inevitable difficulties of implementation. The spare capacity exhibited in metabolic networks implies that host engineering may admit substantial increases in flux to targets of interest. Thus, we rehearse the relevant issues for those wishing to understand and exploit those modern genome-wide host engineering tools and thinking that have been designed and developed to optimise fluxes towards desirable products in biotechnological processes, with a focus on microbial systems. The aim throughput is ‘making such biology predictable’. Strategies have been aimed at both transcription and translation, especially for regulatory processes that can affect multiple targets. However, because there is a limit on how much protein a cell can produce, increasing kcat in selected targets may be a better strategy than increasing protein expression levels for optimal host engineering.

Volumes of Polyhedra in Non-Euclidean Spaces of Constant Curvature

Computation of the volumes of polyhedra is a classical geometry problem known since ancient mathematics and preserving its importance until present time. Deriving volume formulas for 3-dimensional non-Euclidean polyhedra of a given combinatorial type is a very difficult problem. Nowadays, it is fully solved for a tetrahedron, the most simple polyhedron in the combinatorial sense. However, it is well known that for a polyhedron of a special type its volume formula becomes much simpler. This fact was noted by Lobachevsky who found the volume of the so-called ideal tetrahedron in hyperbolic space (all vertices of this tetrahedron are on the absolute).In this survey, we present main results on volumes of arbitrary non-Euclidean tetrahedra and polyhedra of special types (both tetrahedra and polyhedra of more complex combinatorial structure) in 3-dimensional spherical and hyperbolic spaces of constant curvature K = 1 and K = -1, respectively. Moreover, we consider the new method by Sabitov for computation of volumes in hyperbolic space (described by the Poincare model in upper half-space). This method allows one to derive explicit volume formulas for polyhedra of arbitrary dimension in terms of coordinates of vertices. Considering main volume formulas for non-Euclidean polyhedra, we will give proofs (or sketches of proofs) for them. This will help the reader to get an idea of basic methods for computation of volumes of bodies in non-Euclidean spaces of constant curvature.

Verb classifiers in East Asia

Many linguists define classification systems in terms of semantic profiling. The classifier profiles a semantic trait common to all the classified items. This paper rejects semantic profiling in favor of a combinatorial definition of classification and evaluates verb classification in five languages of the Sinitic, Tai-Kadai, Miao-Yao and Tibeto-Burman families. Only sortal verb classifiers in Sinitic, Tai-Kadai, Miao-Yao (not Tibeto-Burman) are classificatory in the combinatorial sense. Sortal verb classifiers stand for a lexical classification technique in which the classifiers are derived from adjunct noun phrases. Cross-linguistically, the technique contrasts with other techniques such as the classification of verbs by incorporated core arguments found in Native American languages. This paper also evaluates mensural verb classifiers and auto-classifiers which are generally not classificatory in the combinatorial sense.

Freely Solvable Graphs in Peg Solitaire

In a 2011 paper, the game of peg solitaire is generalized to arbitrary boards, which are treated as graphs in the combinatorial sense. Of particular interest are graphs that are freely solvable, that is, graphs that can be solved from any starting position. In this paper we give several examples of freely solvable graphs including all such trees with ten vertices or less, numerous cycles with a subdivided chord, meshes, and generalizations of the wheel, helm, and web.

ON PRIMENESS OF LABELED ORIENTED TREES

Knot complements are aspherical. Whether this extends to ribbon disc complements, or, equivalently, to standard 2-complexes of labeled oriented trees, remains unresolved. It is known that prime injective labeled oriented trees are diagrammatically reducible, that is, aspherical in a strong combinatorial sense. We show that arbitrary prime labeled oriented trees need not be DR. We conjecture that all injective labeled oriented trees are aspherical and prove the conjecture under natural conditions.

Bicyclopropylidene. A unique tetrasubstituted alkene and versatile C6-building block for organic synthesis

Bicyclopropylidene (4), now readily available in preparatively viable quantities, is evolving as a useful C6 building block for organic synthesis due to its enhanced reactivity at the C-H, the C=C, as well as both types of C-C single bonds. Monosubstituted derivatives are accessible by deprotonation/electrophilic substitution. Di- and tetrasubstituted bicyclopropylidenes are best made by copper-mediated reductive dimerization of bromolithiocarbenoids. The 1,3-dipolar cycloadducts of nitrones rearrange to spirocyclopropanated piperidones, palladium-catalyzed codimerizations with acrylates occur with opening of one of the rings to yield precursors to bicyclo[3.3.0]octene and bicyclo[5.3.0]decene skeletons. Silicon-heteroatom bonds can be added across the double bond of 4 under palladium catalysisjust like across a C텡C triple bond, and carbopalladation of the double bond in 4 occurs more rapidly than that in an acrylate. A variety of new three-component reactions of 4 with alkenyl as well as aryl halides and dienophiles have been developed and extended to be carried out in a combinatorial sense, even on a polymer support, with an additional dimension added in the cleavage step. Most of the reported reactions of bicyclopropylidene (4) proceed with good to excellent yields.