From polygons and symbols to polylogarithmic functions

We present a review of the symbol map, a mathematical tool that can be useful in simplifying expressions among multiple polylogarithms, and recall its main properties. A recipe is given for how to obtain the symbol of a multiple polylogarithm in terms of the combinatorial properties of an associated rooted decorated polygon. We also outline a systematic approach to constructing a function corresponding to a given symbol, and illustrate it in the particular case of harmonic polylogarithms up to weight four. Furthermore, part of the ambiguity of this process is highlighted by exhibiting a family of non-trivial elements in the kernel of the symbol map for arbitrary weight.Comment: 75 pages. Mathematica files with the expression of all HPLs up to weight 4 in terms of the spanning set are include

Endothelial progenitor cells and integrins: adhesive needs

In the last decade there have been multiple studies concerning the contribution of endothelial progenitor cells (EPCs) to new vessel formation in different physiological and pathological settings. The process by which EPCs contribute to new vessel formation in adults is termed postnatal vasculogenesis and occurs via four inter-related steps. They must respond to chemoattractant signals and mobilize from the bone marrow to the peripheral blood; home in on sites of new vessel formation; invade and migrate at the same sites; and differentiate into mature endothelial cells (ECs) and/or regulate pre-existing ECs via paracrine or juxtacrine signals. During these four steps, EPCs interact with different physiological compartments, namely bone marrow, peripheral blood, blood vessels and homing tissues. The success of each step depends on the ability of EPCs to interact, adapt and respond to multiple molecular cues. The present review summarizes the interactions between integrins expressed by EPCs and their ligands: extracellular matrix components and cell surface proteins present at sites of postnatal vasculogenesis. The data summarized here indicate that integrins represent a major molecular determinant of EPC function, with different integrin subunits regulating different steps of EPC biology. Specifically, integrin α4β1 is a key regulator of EPC retention and/or mobilization from the bone marrow, while integrins α5β1, α6β1, αvβ3 and αvβ5 are major determinants of EPC homing, invasion, differentiation and paracrine factor production. β2 integrins are the major regulators of EPC transendothelial migration. The relevance of integrins in EPC biology is also demonstrated by many studies that use extracellular matrix-based scaffolds as a clinical tool to improve the vasculogenic functions of EPCs. We propose that targeted and tissue-specific manipulation of EPC integrin-mediated interactions may be crucial to further improve the usage of this cell population as a relevant clinical agent

The disruption of proteostasis in neurodegenerative diseases

Cells count on surveillance systems to monitor and protect the cellular proteome which, besides being highly heterogeneous, is constantly being challenged by intrinsic and environmental factors. In this context, the proteostasis network (PN) is essential to achieve a stable and functional proteome. Disruption of the PN is associated with aging and can lead to and/or potentiate the occurrence of many neurodegenerative diseases (ND). This not only emphasizes the importance of the PN in health span and aging but also how its modulation can be a potential target for intervention and treatment of human diseases.info:eu-repo/semantics/publishedVersio