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River flows have been known to be scaling for over 40 years and scaling notions have developed rapidly since the 1980s. Using the framework of universal multifractals and time series of rainfall and river runoff for 30 French catchments (basin sizes of 40 km2 to 200 km2) from 1 day to 30 years, we quantify types and extent of the scaling regimes. For both flow and rain series, we observed a scale break at roughly 16 days, which we associate with the “synoptic maximum”; the time scale of structures of planetary spatial extent. For the two scaling regimes in both series, we estimate the universal multifractal parameters as well as the critical exponents associated with multifractal phase transitions. Using these exponents, we perform (causal) multifractal time series simulations and show how a simple (linear) scaling transfer function can be used to relate the low‐frequency rainfall series to the corresponding river flow series. The high‐frequency regime requires nonlinear transforms.

Growth factors mediate their diverse biologic responses (regulation of cellular proliferation, differentiation, migration and survival) by binding to and activating cell-surface receptors with intrinsic protein kinase activity named receptor tyrosine kinases (RTKs). About 60 RTKs have been identified and can be classified into more than 16 different receptor families. Their activity is normally tightly controlled and regulated. Overexpression of RTK proteins or functional alterations caused by mutations in the corresponding genes or abnormal stimulation by autocrine growth factor loops contribute to constitutive RTK signaling, resulting in alterations in the physiological activities of cells. The ErbB receptor family of RTKs comprises four distinct receptors: the EGFR (also known as ErbB1/HER1), ErbB2 (neu, HER2), ErbB3 (HER3) and ErbB4 (HER4). ErbB family members are often overexpressed, amplified, or mutated in many forms of cancer, making them important therapeutic targets. EGFR has been found to be amplified in gliomas and non-small-cell lung carcinoma while ErbB2 amplifications are seen in breast, ovarian, bladder, non-small-cell lung carcinoma, as well as several other tumor types. Several data have shown that ErbB receptor family and its downstream pathway regulate epithelial-mesenchymal transition, migration, and tumor invasion by modulating extracellular matrix (ECM) components. Recent findings indicate that ECM components such as matrikines bind specifically to EGF receptor and promote cell invasion. In this review, we will present an in-depth overview of the structure, mechanisms, cell signaling, and functions of ErbB family receptors in cell adhesion and migration. Furthermore, we will describe in a last part the new strategies developed in anti-cancer therapy to inhibit ErbB family receptor activation.

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Receptor tyrosine kinases have a single transmembrane (TM) segment that is usually assumed to play a passive role in ligand-induced dimerization and activation of the receptor. However, mutations within some of these receptors, and recent studies with the epidermal growth factor (EGF) and ErbB2 receptors have indicated that interactions between TM domains do contribute to stabilization of ligand-independent and/or ligand-induced receptor dimerization and activation. One consequence of the importance of these interactions is that short hydrophobic peptides corresponding to these domains should act as specific inhibitors. To test this hypothesis, we constructed expression vectors encoding short fusion peptides encompassing native or mutated TM domains of the EGF, ErbB2, and insulin receptors. In human cell lines overexpressing the wild-type EGF receptor or ErbB2, we observed that the peptides are expressed at the cell surface and that they inhibit specifically the autophosphorylation and signaling pathway of their cognate receptor. Identical results were obtained with peptides chemically synthesized. Mechanism of action involves inhibition of dimerization of the receptors as shown by the lack of effects of mutant nondimerizing sequences, completed by density centrifugation and covalent cross-linking experiments. Our findings stress the role of TM domain interactions in ErbB receptor function, and possibly for other single-spanning membrane proteins.