Soliton surfaces via zero-curvature representation of differential equations

The main aim of this paper is to introduce a new version of the Fokas-Gel'fand formula for immersion of soliton surfaces in Lie algebras. The paper contains a detailed exposition of the technique for obtaining exact forms of 2D-surfaces associated with any solution of a given nonlinear ordinary differential equation (ODE) which can be written in zero-curvature form. That is, for any generalized symmetry of the zero-curvature condition of the associated integrable model, it is possible to construct soliton surfaces whose Gauss-Mainardi-Codazzi equations are equivalent to infinitesimal deformations of the zero-curvature representation of the considered model. Conversely, it is shown (Proposition 1) that for a given immersion function of a 2D-soliton surface in a Lie algebra, it possible to derive the associated generalized vector field in evolutionary form which characterizes all symmetries of the zero-curvature condition. The theoretical considerations are illustrated via surfaces associated with the Painlev\'e equations P1, P2 and P3, including transcendental functions, the special cases of the rational and Airy solutions of P2 and the classical solutions of P3.Comment: 28 pages, 2 figure

Reorganization of the nuclear lamina and cytoskeleton in adipogenesis

A thorough understanding of fat cell biology is necessary to counter the epidemic of obesity. Although molecular pathways governing adipogenesis are well delineated, the structure of the nuclear lamina and nuclear-cytoskeleton junction in this process are not. The identification of the ‘linker of nucleus and cytoskeleton’ (LINC) complex made us consider a role for the nuclear lamina in adipose conversion. We herein focused on the structure of the nuclear lamina and its coupling to the vimentin network, which forms a cage-like structure surrounding individual lipid droplets in mature adipocytes. Analysis of a mouse and human model system for fat cell differentiation showed fragmentation of the nuclear lamina and subsequent loss of lamins A, C, B1 and emerin at the nuclear rim, which coincides with reorganization of the nesprin-3/plectin/vimentin complex into a network lining lipid droplets. Upon 18 days of fat cell differentiation, the fraction of adipocytes expressing lamins A, C and B1 at the nuclear rim increased, though overall lamin A/C protein levels were low. Lamin B2 remained at the nuclear rim throughout fat cell differentiation. Light and electron microscopy of a subcutaneous adipose tissue specimen showed striking indentations of the nucleus by lipid droplets, suggestive for an increased plasticity of the nucleus due to profound reorganization of the cellular infrastructure. This dynamic reorganization of the nuclear lamina in adipogenesis is an important finding that may open up new venues for research in and treatment of obesity and nuclear lamina-associated lipodystrophy

Control of Metabolic Homeostasis by Stress Signaling Is Mediated by the Lipocalin NLaz

Metabolic homeostasis in metazoans is regulated by endocrine control of insulin/IGF signaling (IIS) activity. Stress and inflammatory signaling pathways—such as Jun-N-terminal Kinase (JNK) signaling—repress IIS, curtailing anabolic processes to promote stress tolerance and extend lifespan. While this interaction constitutes an adaptive response that allows managing energy resources under stress conditions, excessive JNK activity in adipose tissue of vertebrates has been found to cause insulin resistance, promoting type II diabetes. Thus, the interaction between JNK and IIS has to be tightly regulated to ensure proper metabolic adaptation to environmental challenges. Here, we identify a new regulatory mechanism by which JNK influences metabolism systemically. We show that JNK signaling is required for metabolic homeostasis in flies and that this function is mediated by the Drosophila Lipocalin family member Neural Lazarillo (NLaz), a homologue of vertebrate Apolipoprotein D (ApoD) and Retinol Binding Protein 4 (RBP4). Lipocalins are emerging as central regulators of peripheral insulin sensitivity and have been implicated in metabolic diseases. NLaz is transcriptionally regulated by JNK signaling and is required for JNK-mediated stress and starvation tolerance. Loss of NLaz function reduces stress resistance and lifespan, while its over-expression represses growth, promotes stress tolerance and extends lifespan—phenotypes that are consistent with reduced IIS activity. Accordingly, we find that NLaz represses IIS activity in larvae and adult flies. Our results show that JNK-NLaz signaling antagonizes IIS and is critical for metabolic adaptation of the organism to environmental challenges. The JNK pathway and Lipocalins are structurally and functionally conserved, suggesting that similar interactions represent an evolutionarily conserved system for the control of metabolic homeostasis