Copia Retrotransposon in the Zaprionus Genus: Another Case of Transposable Element Sharing with the Drosophila melanogaster Subgroup

Copia is a retrotransposon that appears to be distributed widely among the Drosophilidae subfamily. Evolutionary analyses of regulatory regions have indicated that the Copia retrotransposon evolved through both positive and purifying selection, and that horizontal transfer (HT) could also explain its patchy distribution of the among the subfamilies of the melanogaster subgroup. Additionally, Copia elements could also have transferred between melanogaster subgroup and other species of Drosophilidae-D. willistoni and Z. tuberculatus. In this study, we surveyed seven species of the Zaprionus genus by sequencing the LTR-ULR and reverse transcriptase regions, and by using RT-PCR in order to understand the distribution and evolutionary history of Copia in the Zaprionus genus. The Copia element was detected, and was transcriptionally active, in all species investigated. Structural and selection analysis revealed Zaprionus elements to be closely related to the most ancient subfamily of the melanogaster subgroup, and they seem to be evolving mainly under relaxed purifying selection. Taken together, these results allowed us to classify the Zaprionus sequences as a new subfamily-ZapCopia, a member of the Copia retrotransposon family of the melanogaster subgroup. These findings indicate that the Copia retrotransposon is an ancient component of the genomes of the Zaprionus species and broaden our understanding of the diversity of retrotransposons in the Zaprionus genus.

Non-autonomous semilinear evolution equations with almost sectorial operators

Inspired by the theory of semigroups of growth a, we construct an evolution process of growth alpha. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that. under natural assumptions. a reasonable concept of solution can be given to Such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Holder continuous functions and to a parabolic problem in a domain Omega subset of R(n) with a one dimensional handle.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

A Single Mutation at the Sheet Switch Region Results in Conformational Changes Favoring lambda 6 Light-Chain Fibrillogenesis

Systemic amyloid light-chain (LC) amyloidosis is a disease process characterized by the pathological deposition of monoclonal LCs in tissue. All LC subtypes are capable of fibril formation although lambda chains, particularly those belonging to the lambda 6 type, are overrepresented. Here, we report the thermodynamic and in vitro fibrillogenic properties of several mutants of the lambda 6 protein 6aJL2 in which Pro7 and/or His8 was substituted by Ser or Pro. The H8P and H8S mutants were almost as stable as the wildtype protein and were poorly fibrillogenic. In contrast, the P7S mutation decreased the thermodynamic stability of 6aJL2 and greatly enhanced its capacity to form amyloid-like fibrils in vitro. The crystal structure of the P7S mutant showed that the substitution induced both local and long-distance effects, such as the rearrangement of the V(L) (variable region of the light chain)-V(L) interface. This mutant crystallized in two orthorhombic polymorphs, P2(1)2(1)2(1) and C222(1). In the latter, a monomer that was not arranged in the typical Bence-Jones dimer was observed for the first time. Crystal-packing analysis of the C222(1) lattice showed the establishment of intermolecular beta-beta interactions that involved the N-terminus and beta-strand B and that these could be relevant in the mechanism of LC fibril formation. Our results strongly suggest that Pro7 is a key residue in the conformation of the N-terminal sheet switch motif and, through long-distance interactions, is also critically involved in the contacts that stabilized the V(L) interface in lambda 6 LCs. (C) 2009 Elsevier Ltd. All rights reserved.

Density-Profile Processes Describing Biological Signaling Networks: Almost Sure Convergence to Deterministic Trajectories

We introduce jump processes in R(k), called density-profile processes, to model biological signaling networks. Our modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. We are mostly interested on the multi-dimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-intervals, its path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting. We present a simple example of spin-flip stochastic model, associated to a synthetic biology model known as repressilator, which leads to a dynamical system with Hopf and pitchfork bifurcations. Depending on the parameter values, the magnetization random path can either converge to a unique stable fixed point, converge to one of a pair of stable fixed points, or asymptotically evolve close to a deterministic orbit in Rk. We also discuss a simple signaling pathway related to cancer research, called p53 module.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

On the composite of irreducible morphisms in almost sectional paths

We study here when the composite of it irreducible morphisms in almost sectional paths is non-zero and lies in Rn+1 (C) 2007 Elsevier B.V. All rights reserved.

The bar-radical of a class of almost alternative baric algebras

In this article we prove that, if (U, ) is a finite dimensional baric algebra of (gamma, delta) type over a field F of characteristic not equal 2,3,5 such that gamma(2) - delta(2) + delta = 1 and 0,1, then rad(U) = R(U)boolean AND(bar(U))(2), where R(U) is the nilradical (maximal nil ideal) of U.

Geodesics and Almost Geodesic Cycles in Random Regular Graphs

A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and v in C, the distance d(G)(u, v) is at least d(C)(u, v) - e(n). Let omega(n) be any function tending to infinity with n. We consider a random d-regular graph on n vertices. We show that almost all pairs of vertices belong to an almost geodesic cycle C with e(n)= log(d-1)log(d-1) n+omega(n) and vertical bar C vertical bar =2 log(d-1) n+O(omega(n)). Along the way, we obtain results on near-geodesic paths. We also give the limiting distribution of the number of geodesics between two random vertices in this random graph. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 66: 115-136, 2011