Multiplicities and tensor product coefficients for ArA_r

We apply some recent developments of Baldoni-DeLoera-Vergne on vector partition functions, to Kostant and Steinberg formulas, in the case of $A_r$. We therefore get a fast {\sc Maple} program that computes for $A_r$: the multiplicity $c_{\lambda,\mu}$ of the weight $\mu$ in the representation $V(\lambda)$ of highest weight $\lambda$; the multiplicity $c_{\lambda,\mu,\nu}$ of the representation $V(\nu)$ in $V(\lambda)\otimes V(\mu)$. The computation also gives the locally polynomial functions $c_{\lambda,\mu}$ and $c_{\lambda,\mu,\nu}$

Volume computation for polytopes and partition functions for classical root systems

This paper presents an algorithm to compute the value of the inverse Laplace transforms of rational functions with poles on arrangements of hyperplanes. As an application, we present an efficient computation of the partition function for classical root systems.Comment: 55 pages, 14 figures. Maple programs available at http://www.math.polytechnique.fr/~vergne/work/IntegralPoints.htm

Border forces and friction control epithelial closure dynamics

Epithelization, the process whereby an epithelium covers a cell-free surface, is not only central to wound healing but also pivotal in embryonic morphogenesis, regeneration, and cancer. In the context of wound healing, the epithelization mechanisms differ depending on the sizes and geometries of the wounds as well as on the cell type while a unified theoretical decription is still lacking. Here, we used a barrier-based protocol that allows for making large arrays of well-controlled circular model wounds within an epithelium at confluence, without injuring any cells. We propose a physical model that takes into account border forces, friction with the substrate, and tissue rheology. Despite the presence of a contractile actomyosin cable at the periphery of the wound, epithelization was mostly driven by border protrusive activity. Closure dynamics was quantified by an epithelization coefficient $D = \sigma_p/\xi$ defined as the ratio of the border protrusive stress $\sigma_p$ to the friction coefficient $\xi$ between epithelium and substrate. The same assay and model showed a high sensitivity to the RasV12 mutation on human epithelial cells, demonstrating the general applicability of the approach and its potential to quantitatively characterize metastatic transformations.Comment: 44 pages, 17 figure

The Rance Tidal Power Plant Model

Water Qualit

Tissue fusion over non-adhering surfaces

Tissue fusion eliminates physical voids in a tissue to form a continuous structure and is central to many processes in development and repair. Fusion events in vivo, particularly in embryonic development, often involve the purse-string contraction of a pluricellular actomyosin cable at the free edge. However in vitro, adhesion of the cells to their substrate favors a closure mechanism mediated by lamellipodial protrusions, which has prevented a systematic study of the purse-string mechanism. Here, we show that monolayers can cover well-controlled mesoscopic non-adherent areas much larger than a cell size by purse-string closure and that active epithelial fluctuations are required for this process. We have formulated a simple stochastic model that includes purse-string contractility, tissue fluctuations and effective friction to qualitatively and quantitatively account for the dynamics of closure. Our data suggest that, in vivo, tissue fusion adapts to the local environment by coordinating lamellipodial protrusions and purse-string contractions

Pharmacological Or Genetic Targeting Of Transient Receptor Potential (TRP) Channels Can Disrupt The Planarian Escape Response

In response to noxious stimuli, planarians cease their typical ciliary gliding and exhibit an oscillatory type of locomotion called scrunching. We have previously characterized the biomechanics of scrunching and shown that it is induced by specific stimuli, such as amputation, noxious heat, and extreme pH. Because these specific inducers are known to activate Transient Receptor Potential (TRP) channels in other systems, we hypothesized that TRP channels control scrunching. We found that chemicals known to activate TRPA1 (allyl isothiocyanate (AITC) and hydrogen peroxide) and TRPV (capsaicin and anandamide) in other systems induce scrunching in the planarian species Dugesia japonica and, except for anandamide, in Schmidtea mediterranea. To confirm that these responses were specific to either TRPA1 or TRPV, respectively, we tried to block scrunching using selective TRPA1 or TRPV antagonists and RNA interference (RNAi) mediated knockdown. Unexpectedly, co-treatment with a mammalian TRPA1 antagonist, HC-030031, enhanced AITC-induced scrunching by decreasing the latency time, suggesting an agonistic relationship in planarians. We further confirmed that TRPA1 in both planarian species is necessary for AITC-induced scrunching using RNAi. Conversely, while co-treatment of a mammalian TRPV antagonist, SB-366791, also enhanced capsaicin-induced reactions in D. japonica, combined knockdown of two previously identified D. japonica TRPV genes (DjTRPVa and DjTRPVb) did not inhibit capsaicin-induced scrunching. RNAi of DjTRPVa/DjTRPVb attenuated scrunching induced by the endocannabinoid and TRPV agonist, anandamide. Overall, our results show that although scrunching induction can involve different initial pathways for sensing stimuli, this behavior’s signature dynamical features are independent of the inducer, implying that scrunching is a stereotypical planarian escape behavior in response to various noxious stimuli that converge on a single downstream pathway. Understanding which aspects of nociception are conserved or not across different organisms can provide insight into the underlying regulatory mechanisms to better understand pain sensation