On negative flows of the AKNS hierarchy and a class of deformations of bihamiltonian structure of hydrodynamic type

A deformation parameter of a bihamiltonian structure of hydrodynamic type is shown to parameterize different extensions of the AKNS hierarchy to include negative flows. This construction establishes a purely algebraic link between, on the one hand, two realizations of the first negative flow of the AKNS model and, on the other, two-component generalizations of Camassa-Holm and Dym type equations. The two-component generalizations of Camassa-Holm and Dym type equations can be obtained from the negative order Hamiltonians constructed from the Lenard relations recursively applied on the Casimir of the first Poisson bracket of hydrodynamic type. The positive order Hamiltonians, which follow from Lenard scheme applied on the Casimir of the second Poisson bracket of hydrodynamic type, are shown to coincide with the Hamiltonians of the AKNS model. The AKNS Hamiltonians give rise to charges conserved with respect to equations of motion of two-component Camassa-Holm and two-component Dym type equations.Comment: 20 pages, Late

Vertex Operators and Soliton Solutions of Affine Toda Model with U(2) Symmetry

The symmetry structure of non-abelian affine Toda model based on the coset $SL(3)/SL(2)\otimes U(1)$ is studied. It is shown that the model possess non-abelian Noether symmetry closing into a q-deformed $SL(2)\otimes U(1)$ algebra. Specific two vertex soliton solutions are constructed.Comment: 17 pages, latex, misprints corrected, version to appear in J.Phys

Substrate Adhesion Regulates Sealing Zone Architecture and Dynamics in Cultured Osteoclasts

The bone-degrading activity of osteoclasts depends on the formation of a cytoskeletal-adhesive super-structure known as the sealing zone (SZ). The SZ is a dynamic structure, consisting of a condensed array of podosomes, the elementary adhesion-mediating structures of osteoclasts, interconnected by F-actin filaments. The molecular composition and structure of the SZ were extensively investigated, yet despite its major importance for bone formation and remodelling, the mechanisms underlying its assembly and dynamics are still poorly understood. Here we determine the relations between matrix adhesiveness and the formation, stability and expansion of the SZ. By growing differentiated osteoclasts on micro-patterned glass substrates, where adhesive areas are separated by non-adhesive PLL-g-PEG barriers, we show that SZ growth and fusion strictly depend on the continuity of substrate adhesiveness, at the micrometer scale. We present a possible model for the role of mechanical forces in SZ formation and reorganization, inspired by the current data

Paxillin and Hic-5 Interaction with Vinculin Is Differentially Regulated by Rac1 and RhoA

Cell migration is of paramount importance to organism development and maintenance as well as multiple pathological processes, including cancer metastasis. The RhoGTPases Rac1 and RhoA are indispensable for cell migration as they regulate cell protrusion, cell-extracellular matrix (ECM) interactions and force transduction. However, the consequences of their activity at a molecular level within the cell remain undetermined. Using a combination of FRET, FRAP and biochemical analyses we show that the interactions between the focal adhesion proteins vinculin and paxillin, as well as the closely related family member Hic-5 are spatially and reciprocally regulated by the activity of Rac1 and RhoA. Vinculin in its active conformation interacts with either paxillin or Hic-5 in adhesions in response to Rac1 and RhoA activation respectively, while inactive vinculin interacts with paxillin in the membrane following Rac1 inhibition. Additionally, Rac1 specifically regulates the dynamics of paxillin as well as its binding partner and F-actin interacting protein actopaxin (α-parvin) in adhesions. Furthermore, FRET analysis of protein:protein interactions within cell adhesions formed in 3D matrices revealed that, in contrast to 2D systems vinculin interacts preferentially with Hic-5. This study provides new insight into the complexity of cell-ECM adhesions in both 2D and 3D matrices by providing the first description of RhoGTPase-coordinated protein:protein interactions in a cellular microenvironment. These data identify discrete roles for paxillin and Hic-5 in Rac1 and RhoA-dependent cell adhesion formation and maturation; processes essential for productive cell migration

Myosin II Motor Proteins with Different Functions Determine the Fate of Lamellipodia Extension during Cell Spreading

Non-muscle cells express multiple myosin-II motor proteins myosin IIA, myosin IIB and myosin IIC transcribed from different loci in the human genome. Due to a significant homology in their sequences, these ubiquitously expressed myosin II motor proteins are believed to have overlapping cellular functions, but the mechanistic details are not elucidated. The present study uncovered a mechanism that coordinates the distinctly localized myosin IIA and myosin IIB with unexpected opposite mechanical roles in maneuvering lamellipodia extension, a critical step in the initiation of cell invasion, spreading, and migration. Myosin IIB motor protein by localizing at the front drives lamellipodia extension during cell spreading. On the other hand, myosin IIA localizes next to myosin IIB and attenuates or retracts lamellipodia extension. Myosin IIA and IIB increase cell adhesion by regulating focal contacts formation in the spreading margins and central part of the spreading cell, respectively. Spreading cells expressing both myosin IIA and myosin IIB motor proteins display an organized actin network consisting of retrograde filaments, arcs and central filaments attached to focal contacts. This organized actin network especially arcs and focal contacts formation in the spreading margins were lost in myosin IIÂ cells. Surprisingly, myosin IIB̂ cells displayed long parallel actin filaments connected to focal contacts in the spreading margins. Thus, with different roles in the regulation of the actin network and focal contacts formation, both myosin IIA and IIB determine the fate of lamellipodia extension during cell spreading