Prolongation Loop Algebras for a Solitonic System of Equations

We consider an integrable system of reduced Maxwell-Bloch equations that describes the evolution of an electromagnetic field in a two-level medium that is inhomogeneously broadened. We prove that the relevant Backlund transformation preserves the reality of the n-soliton potentials and establish their pole structure with respect to the broadening parameter. The natural phase space of the model is embedded in an infinite dimensional loop algebra. The dynamical equations of the model are associated to an infinite family of higher order Hamiltonian systems that are in involution. We present the Hamiltonian functions and the Poisson brackets between the extended potentials.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

A new age in functional genomics using CRISPR/Cas9 in arrayed library screening

CRISPR technology has rapidly changed the face of biological research, such that precise genome editing has now become routine for many labs within several years of its initial development. What makes CRISPR/Cas9 so revolutionary is the ability to target a protein (Cas9) to an exact genomic locus, through designing a specific short complementary nucleotide sequence, that together with a common scaffold sequence, constitute the guide RNA bridging the protein and the DNA. Wild-type Cas9 cleaves both DNA strands at its target sequence, but this protein can also be modified to exert many other functions. For instance, by attaching an activation domain to catalytically inactive Cas9 and targeting a promoter region, it is possible to stimulate the expression of a specific endogenous gene. In principle, any genomic region can be targeted, and recent efforts have successfully generated pooled guide RNA libraries for coding and regulatory regions of human, mouse and Drosophila genomes with high coverage, thus facilitating functional phenotypic screening. In this review, we will highlight recent developments in the area of CRISPR-based functional genomics and discuss potential future directions, with a special focus on mammalian cell systems and arrayed library screening

The Toda lattice is super-integrable

We prove that the classical, non-periodic Toda lattice is super-integrable. In other words, we show that it possesses 2N-1 independent constants of motion, where N is the number of degrees of freedom. The main ingredient of the proof is the use of some special action--angle coordinates introduced by Moser to solve the equations of motion.Comment: 8 page

A reversible phospho-switch mediated by ULK1 regulates the activity of autophagy protease ATG4B

Upon induction of autophagy, the ubiquitin-like protein LC3 is conjugated to phosphatidylethanolamine (PE) on the inner and outer membrane of autophagosomes to allow cargo selection and autophagosome formation. LC3 undergoes two processing steps, the proteolytic cleavage of pro-LC3 and the de-lipidation of LC3-PE from autophagosomes, both executed by the same cysteine protease ATG4. How ATG4 activity is regulated to co-ordinate these events is currently unknown. Here we find that ULK1, a protein kinase activated at the autophagosome formation site, phosphorylates human ATG4B on serine 316. Phosphorylation at this residue results in inhibition of its catalytic activity in vitro and in vivo. On the other hand, phosphatase PP2A-PP2R3B can remove this inhibitory phosphorylation. We propose that the opposing activities of ULK1-mediated phosphorylation and PP2A-mediated dephosphorylation provide a phospho-switch that regulates the cellular activity of ATG4B to control LC3 processing

A symplectic realization of the Volterra lattice

We examine the multiple Hamiltonian structure and construct a symplectic realization of the Volterra model. We rediscover the hierarchy of invariants, Poisson brackets and master symmetries via the use of a recursion operator. The rational Volterra bracket is obtained using a negative recursion operator.Comment: 8 page

Multiscale expansion and integrability properties of the lattice potential KdV equation

We apply the discrete multiscale expansion to the Lax pair and to the first few symmetries of the lattice potential Korteweg-de Vries equation. From these calculations we show that, like the lowest order secularity conditions give a nonlinear Schroedinger equation, the Lax pair gives at the same order the Zakharov and Shabat spectral problem and the symmetries the hierarchy of point and generalized symmetries of the nonlinear Schroedinger equation.Comment: 10 pages, contribution to the proceedings of the NEEDS 2007 Conferenc

On ATG4B as Drug Target for Treatment of Solid Tumours-The Knowns and the Unknowns

Autophagy is an evolutionary conserved stress survival pathway that has been shown to play an important role in the initiation, progression, and metastasis of multiple cancers; however, little progress has been made to date in translation of basic research to clinical application. This is partially due to an incomplete understanding of the role of autophagy in the different stages of cancer, and also to an incomplete assessment of potential drug targets in the autophagy pathway. While drug discovery efforts are on-going to target enzymes involved in the initiation phase of the autophagosome, e.g., unc51-like autophagy activating kinase (ULK)1/2, vacuolar protein sorting 34 (Vps34), and autophagy-related (ATG)7, we propose that the cysteine protease ATG4B is a bona fide drug target for the development of anti-cancer treatments. In this review, we highlight some of the recent advances in our understanding of the role of ATG4B in autophagy and its relevance to cancer, and perform a critical evaluation of ATG4B as a druggable cancer targe

A discrete linearizability test based on multiscale analysis

In this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad-graph by the multiple scale reduction around their harmonic solution. We show that the A1, A2 and A3 linearizability conditions restrain the number of the parameters which enter into the equation. A subclass of the equations which pass the A3 C-integrability conditions can be linearized by a Möbius transformation

Multiscale reduction of discrete nonlinear Schroedinger equations

We use a discrete multiscale analysis to study the asymptotic integrability of differential-difference equations. In particular, we show that multiscale perturbation techniques provide an analytic tool to derive necessary integrability conditions for two well-known discretizations of the nonlinear Schroedinger equation.Comment: 12 page

Discrete Multiscale Analysis: A Biatomic Lattice System

We discuss a discrete approach to the multiscale reductive perturbative method and apply it to a biatomic chain with a nonlinear interaction between the atoms. This system is important to describe the time evolution of localized solitonic excitations. We require that also the reduced equation be discrete. To do so coherently we need to discretize the time variable to be able to get asymptotic discrete waves and carry out a discrete multiscale expansion around them. Our resulting nonlinear equation will be a kind of discrete Nonlinear Schr\"odinger equation. If we make its continuum limit, we obtain the standard Nonlinear Schr\"odinger differential equation