Drug efflux pumps play a key role in drug resistance and also serve other functions in bacteria. There has been a growing list of multidrug and drug-specific efflux pumps characterized from bacteria of human, animal, plant and environmental origins. These pumps are mostly encoded on the chromosome, although they can also be plasmid-encoded. A previous article in this journal provided a comprehensive review regarding efflux-mediated drug resistance in bacteria. In the past 5 years, significant progress has been achieved in further understanding of drug resistance-related efflux transporters and this review focuses on the latest studies in this field since 2003. This has been demonstrated in multiple aspects that include but are not limited to: further molecular and biochemical characterization of the known drug efflux pumps and identification of novel drug efflux pumps; structural elucidation of the transport mechanisms of drug transporters; regulatory mechanisms of drug efflux pumps; determining the role of the drug efflux pumps in other functions such as stress responses, virulence and cell communication; and development of efflux pump inhibitors. Overall, the multifaceted implications of drug efflux transporters warrant novel strategies to combat multidrug resistance in bacteria.

Efflux-Mediated Drug Resistance in Bacteria

Functions of One Complex Variable

Bacteria produce a wide range of exopolysaccharides which are synthesized via different biosynthesis pathways. The genes responsible for synthesis are often clustered within the genome of the respective production organism. A better understanding of the fundamental processes involved in exopolysaccharide biosynthesis and the regulation of these processes is critical toward genetic, metabolic and protein-engineering approaches to produce tailor-made polymers. These designer polymers will exhibit superior material properties targeting medical and industrial applications. Exploiting the natural design space for production of a variety of biopolymer will open up a range of new applications. Here, we summarize the key aspects of microbial exopolysaccharide biosynthesis and highlight the latest engineering approaches toward the production of tailor-made variants with the potential to be used as valuable renewable and high-performance products for medical and industrial applications.

/pdf/bacterial-exopolysaccharides-biosynthesis-pathways-and-3t1hslwdme.pdf

Bacterial exopolysaccharides: biosynthesis pathways and engineering strategies

Compact Lie groups are ‘perfect’ entities in modern mathematics because: 

(a)

They are differentiable (and even analytical) manifolds of finite dimension and therefore can be analysed with the help of the most powerful tool of mathematics: ordinary and partial differential operators (equations);




(b)

Denoting by £(G) or L(G) = T e (G) the tangent space to G in unity e, we find that L(G) can be identified with the set of left-invariant vector fields on G (or with the set of appropriate differential operators of order one). Thus L(G) naturally becomes a Lie algebra: on L(G) there exists a structure [·, ·] which satisfies the axioms of Lie algebra (see below);




(c)

This rich algebraic structure, in turn, makes it possible to apply the powerful algebraic tools (theory of Lie algebras);




(d)

An abstract (finite dimensional) Lie algebra g defines (up to an isomorphism) a simply connected Lie group G such that £(G) = g. Therefore investigations of the Lie group G can be to large extent replaced by investigations of its Lie algebra g;




(e)

Compactness of a Lie group G makes it possible to use the theory of representations of compact groups developed by Weyl and Peter. This theory is extraordinarily beautiful and simple: it reduces to large extend to the spectral theory of compact operators;




(f)

And finally every complex, compact (connected) commutative Lie group is a torus. Moreover, as it was shown by E. Cartan, every compact Lie group contains a maximal torus T (any other such a torus is conjugated T 1 = gTg −1 ); and any point g 0 of the group G belongs to some maximal torus: G = U g gTg −1. This fundamental Cartan theorem makes it possible to apply to T (and thus to the whole of G) the theory of representations of abelian groups: every representation of the torus T decomposes into the finite (and orthogonal) sum of unit representations (over ℂ), the so called weights. Thus the knowledge of these weights is the fundamental element of the theory of representations of compact Lie groups.

Representations of Compact Lie Groups

Epithelial sodium channel (ENaC) family: Phylogeny, structure-function, tissue distribution, and associated inherited diseases.

We introduce the $k$-generalized gamma function $\Gamma_k$, beta function $B_k$, and Pochhammer $k$-symbol $(x)_{n,k}$. We prove several identities generalizing those satisfied by the classical gamma function, beta function and Pochhammer symbol. We provided integral representation for the $\Gamma_k$ and $B_k$ functions.

On hypergeometric functions and Pochhammer $k$-symbol

We introduce the q,k-generalized Pochhammer symbol. We construct Γ q,k and B q,k , the q,k-generalized gamma and beta functions, and show that they satisfy properties that generalize those satisfied by the classical gamma and beta functions. Moreover, we provide integral representations for Γ q,k and B q,k .

/pdf/q-k-generalized-gamma-and-beta-functions-b53cugqa61.pdf

q,k-Generalized Gamma and Beta Functions

On the Gaussian q-distribution

We study quantum deformations of Poisson orbivarieties. Given a Poisson manifold (ℝ m , α) we consider the Poisson orbivariety ( . The Kontsevich star product on functions on (ℝ m ) n induces a star product on functions on ( . We provide explicit formulae for the case &#x1d525;×&#x1d525;/&#x1d4b2;, where &#x1d525; is the Cartan subalgebra of a classical Lie algebra &#x1d524; and &#x1d4b2; is the Weyl group of &#x1d525;. We approach our problem from a fairly general point of view, introducing Polya functors for categories over nonsymmetric Hopf operads.

Quantum Symmetric Functions

We study quantum deformations of Poisson orbivarieties. Given a Poisson manifold $(\mathbb{R}^{m},\alpha)$ we consider the Poisson orbivariety $(\mathbb{R}^{m})^{n}/S_{n}$. The Kontsevich star product on functions on $(\mathbb{R}^{m})^{n}$ induces a star product on functions on $(\mathbb{R}^{m})^{n}/S_{n}$. We provide explicit formulae for the case ${{\mathfrak h} \times {\mathfrak h}}/\mathcal{W}$, where ${\mathfrak h}$ is the Cartan subalgebra of a classical Lie algebra ${\mathfrak g}$ and $\mathcal{W}$ is the Weyl group of ${\mathfrak h}$. We approach our problem from a fairly general point of view, introducing Polya functors for categories over non-symmetric Hopf operads.

Quantum symmetric functions

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