Search

This paper is a continuation of the previous work (Pusateri, in: Forum of mathematics, Cambridge University Press) by the first two authors. We focus on 1-dimensional quadratic Klein–Gordon equations with a potential, under some assumptions that are less general than (Pusateri, in: Forum of mathematics, Cambridge University Press), but that allow us to present some simplifications in the proof of the global existence with decay for small solutions. In particular, we can propagate a stronger control on a basic L2-weighted-type norm while providing some shorter and less technical proofs for some of the arguments.

Inoculation of plants with plant growth-promoting bacteria (PGPB) is an ecological approach to improve plants growth and yield. The objective of this study was to screen native PGPBs in tomato root rhizosphere and evaluate their performance in germination and growth of seedlings in the greenhouse in the western region of Cameroon. Isolates were selected based on their ability to solubilize phosphate, produce indole-3-acetic acid, and improve seed germination and seedling growth under laboratory conditions. Following this screening, eight bacteria were selected (S1, S4, S13, S14, S16, B9, B11, and B15) to assess their performance on seedling growth in greenhouse. Seeds of two tomato varieties (one improved, Raja, and the local one, Foolewouh) were used in this study. The experiment was performed in sterilized and non-sterilized soils. Phylogenetic analysis of the 16S rRNA sequence showed that these bacteria belong to the genus Bacillus, including B. thuringiensis, B. cereus, B. pacificus, and B. aerius. The bacterial performance depended on the variety and conditions of soil treatment. Isolates improved seed germination (up to 31.93%) and seeding strength (up to 78.59%) in vitro. In greenhouse, inoculation with PGPB significantly increased stem height, root length, and weight of fresh and dry stems and roots. Raja variety was more sensitive to bacteria and performed better than the Foolewouh variety. Bacterial isolates on sterilized soil allowed to better seedling growth compared to non-sterilized soil. The study showed that B. thuringiensis (strain B9), B. pacificus (strain B11), and Bacillus sp. (strain B15) can be used as inoculant formulations to improve seedling growth of tomato plant.

We investigate norms of spectral projectors on thin spherical shells for the Laplacian on generic tori, including generic rectangular tori. We state a conjecture and partially prove it, improving on previous results concerning arbitrary tori.

Retinoid X receptors (RXRα, β, and γ) are essential members of the nuclear receptor (NR) superfamily of ligand-dependent transcriptional regulators that bind DNA response elements and control the expression of large gene networks. As obligate heterodimerization partners of many NRs, RXRs are involved in a variety of pathophysiological processes. However, despite this central role in NR signaling, there is still no consensus regarding the precise biological functions of RXRs and the putative role of the endogenous ligands (rexinoids) previously proposed for these receptors. Based on available crystal structures, we introduced a series of amino acid substitutions into the ligand-binding pocket of all three RXR subtypes in order to alter their binding properties. Subsequent characterization using a battery of cell-based and in vitro assays led to the identification of a double mutation abolishing the binding of any ligand while keeping the other receptor functions intact and a triple mutation that selectively impairs interaction with natural rexinoids but not with some synthetic ligands. We also report crystal structures that help understand the specific ligand-binding capabilities of both variants. These RXR variants, either fully disabled for ligand binding or retaining the property of being activated by synthetic compounds, represent unique tools that could be used in future studies to probe the presence of active endogenous rexinoids in tissues/organs and to investigate their role in vivo. Last, we provide data suggesting a possible involvement of fatty acids in the weak interaction of RXRs with corepressors.

We construct forward self-similar solutions (expanders) for the compressible Navier–Stokes equations. Some of these self-similar solutions are smooth, while others exhibit a singularity due to cavitation at the origin.

We prove essentially optimal bounds for norms of spectral projectors on thin spherical shells for the Laplacian on the cylinder (R/Z)*R. In contrast to previous investigations into spectral projectors on tori, having one unbounded dimension available permits a compact self-contained proof.

This article is devoted to backward self-similar blow up solutions of the compressible Navier–Stokes equations with radial symmetry. We show that such solutions cannot exist if they either have finite energy, or satisfy appropriate smallness conditions. Furthermore, numerical simulations lead us to the conjecture that such solutions do not exist.

Retinoids are a family of compounds that include both vitamin A (all-trans retinol) and its naturally occurring metabolites such as retinoic acids (e.g. all-trans retinoic acid) as well as synthetic analogs. They are critically involved in the regulation of a wide variety of essential biological processes, such as embryogenesis and organogenesis, apoptosis, reproduction, vision, and the growth and differentiation of normal and neoplastic cells in vertebrates. The ability of these small molecules to control the expression of several hundred genes through binding to nuclear ligand-dependent transcription factors accounts for most of their functions. Three retinoic acid receptor (RARα,β,γ) and three retinoid X receptor (RXRα,β,γ) subtypes form a variety of RXR–RAR heterodimers that have been shown to mediate the pleiotropic effects of retinoids through the recruitment of high-molecular weight co-regulatory complexes to response-element DNA sequences found in the promoter region of their target genes. Hence, heterodimeric retinoid receptors are multidomain entities that respond to various incoming signals, such as ligand and DNA binding, by allosteric structural alterations which are the basis of further signal propagation. Here, we provide an overview of the current state of knowledge with regard to the structural mechanisms by which retinoids and DNA response elements act as allosteric effectors that may combine to finely tune RXR–RAR heterodimers activity.

We analyze the stationary and traveling wave solutions to a family of degenerate dispersive equations of KdV and NLS-type. In stark contrast to the standard soliton solutions for non-degenerate KdV and NLS equations, the degeneracy of the elliptic operators studied here allows for compactly supported steady or traveling states. As we work in $1$ dimension, ODE methods apply, however the models considered have formally conserved Hamiltonian, Mass and Momentum functionals, which allow for variational analysis as well., Comment: 26 pages, 6 figures, comments welcome!!

Sans vouloir traiter de façon exhaustive des normes internationales de catalogage, l’auteur en donne néanmoins les lignes générales. On retrouve donc exposés l’origine et le développement de ces normes élaborées au cours de diverses rencontres internationales; suivent la mention des buts principaux qu’elles poursuivent et celle de leurs caractéristiques; un bref panorama de la situation actuelle termine cet article., Without treating the subject of international cataloguing standards exhaustively, the author nevertheless traces the main lines. Thus, we find exposed the origin and development of these standards which were elaborated in various international meetings; followed by the mention of their principal aims and characteristics; and finally, the article ends on a brief overview of the actual situation., Sin hacer un estudio exhaustivo de las normas internacionales de catalogación, el autor presenta sus líneas generales. Describe el origen y desarrollo de las normas elaboradas durante varias reuniones internacionales; expone también sus objetivos principales y características. El artículo termina con una breve descripción de la situación actual.

We consider the cubic nonlinear Schrodinger equation with a potential in one space dimension. Under the assumptions that the potential is generic, sufficiently localized, with no bound states, we obtain the long-time asymptotic behavior of small solutions. In particular, we prove that, as time goes to infinity, solutions exhibit nonlinear phase corrections that depend on the scattering matrix associated to the potential. The proof of our result is based on the use of the distorted Fourier transform – the so-called Weyl–Kodaira–Titchmarsh theory – a precise understanding of the “nonlinear spectral measure” associated to the equation, and nonlinear stationary phase arguments and multilinear estimates in this distorted setting.

Retinoic acid receptors (RARs) and retinoid X receptors (RXRs) form heterodimers that activate target gene transcription by recruiting co-activator complexes in response to ligand binding. The nuclear receptor (NR) co-activator TIF2 mediates this recruitment by interacting with the ligand-binding domain (LBD) of NRs trough the nuclear receptor interaction domain (TIF2NRID) containing three highly conserved α-helical LxxLL motifs (NR-boxes). The precise binding mode of this domain to RXR/RAR is not clear due to the disordered nature of TIF2. Here we present the structural characterization of TIF2NRID by integrating several experimental (NMR, SAXS, CD, SEC-MALS) and computational data. Collectively, the data are in agreement with a largely disordered protein with partially structured regions, including the NR-boxes and their flanking regions, which are evolutionary conserved. NMR and X-ray crystallographic data on TIF2NRID in complex with RXR/RAR reveal a cooperative binding of the three NR-boxes as well as an active role of their flanking regions in the interaction.

We develop a unified approach to proving $L^p-L^q$ boundedness of spectral projectors, the resolvent of the Laplace-Beltrami operator and its derivative on $\mathbb{H}^d.$ In the case of spectral projectors, and when $p$ and $q$ are in duality, the dependence of the implicit constant on $p$ is shown to be sharp. We also give partial results on the question of $L^p-L^q$ boundedness of the Fourier extension operator. As an application, we prove smoothing estimates for the free Schr\"{o}dinger equation on $\mathbb{H}^d$ and a limiting absorption principle for the electromagnetic Schr\"{o}dinger equation with small potentials., Comment: Final version, to appear

The three retinoic acid receptor subtypes (RARα, RARβ and RARγ) act as ligand-inducible transcription factors binding to DNA regulatory elements in the promoter regions of target genes by forming heterodimers with the retinoid X receptors (RXRα, RXRβ and RXRγ). They act as ligand-dependent transcription factors that regulate a large variety of genes involved in cell growth, differentiation, survival and death. The (patho)physiological functions of RAR-RXR heterodimers rely on a dynamic sequence of protein-protein interactions, many of which being modulated by natural (retinoic acid) or synthetic ligands. Direct protein-protein interactions include heterodimerization between RARs and RXRs, recruitment (and release) of transcriptional coactivators and corepressors, cross-talk with other transcription factors, including nuclear receptors, or transient association with many enzymes involved in post-translational modifications to cite the most prominent ones. This chapter describes structural, biochemical, biophysical and cell-based assays to monitor protein-protein interactions relevant to the retinoic acid signaling pathways with a focus on those for which a structural description has been provided.

The three retinoic acid receptor subtypes (RARα, RARβ and RARγ) act as ligand-inducible transcription factors binding to DNA regulatory elements in the promoter regions of target genes by forming heterodimers with the retinoid X receptors (RXRα, RXRβ and RXRγ). They act as ligand-dependent transcription factors that regulate a large variety of genes involved in cell growth, differentiation, survival and death. The (patho)physiological functions of RAR-RXR heterodimers rely on a dynamic sequence of protein-protein interactions, many of which being modulated by natural (retinoic acid) or synthetic ligands. Direct protein-protein interactions include heterodimerization between RARs and RXRs, recruitment (and release) of transcriptional coactivators and corepressors, cross-talk with other transcription factors, including nuclear receptors, or transient association with many enzymes involved in post-translational modifications to cite the most prominent ones. This chapter describes structural, biochemical, biophysical and cell-based assays to monitor protein-protein interactions relevant to the retinoic acid signaling pathways with a focus on those for which a structural description has been provided.

This paper proposes a fairly general new point of view on the question of asymptotic stability of (topological) solitons. Our approach is based on the use of the distorted Fourier transform at the nonlinear level; it does not rely on Strichartz or virial estimates and is therefore able to treat low power nonlinearities (hence also non-localized solitons) and capture the global (in space and time) behavior of solutions. More specifically, we consider quadratic nonlinear Klein-Gordon equations with a potential in one space dimension. The potential is assumed to be regular, decaying, and either generic or exceptional (with some additional parity assumptions). Assuming that the associated Schr\"odinger operator has no negative eigenvalues, we obtain global-in-time bounds, including sharp pointwise decay and modified asymptotics, for small solutions. These results have implications for the asymptotic stability of solitons, or topological solitons, for a variety of problems. For instance, we obtain full asymptotic stability of kinks with respect to odd perturbations for the double Sine-Gordon problem (in an appropriate range of the deformation parameter). For the $\phi^4$ problem, we obtain asymptotic stability of the kink (with respect to odd perturbations) when the coupling to the internal mode appearing in the linearization around it is neglected. Our results also go beyond these examples since our approach allows for the presence of a fully coherent phenomenon at the level of quadratic interactions, which creates a degeneracy in distorted Fourier space. We devise a suitable framework that incorporates this, and use multilinear harmonic analysis in the distorted setting to control all nonlinear interactions., Comment: 152 pages. v2: abstract revised. Minor changes in the presentation. Some typos corrected. Added an application to the asymptotic stability of kinks for the double sine-Gordon equation, inspired by the work of Kowalczyk, Martel, Mu\~noz and Van Den Bosch (arXiv:2008.01276). v3: Expanded parts of introduction and minor corrections

We examine the question of uniqueness for the equivariant reduction of the harmonic map heat flow in the energy supercritical dimension. It is shown that, generically, singular data can give rise to two distinct solutions which are both stable, and satisfy the local energy inequality. We also discuss how uniqueness can be retrieved., 43 pages; typos corrected

The retinoic acid receptors (RARs) form heterodimers with retinoid X receptors (RXRs) and control gene transcription in response to ligand binding and via allosteric activation of the C-termini helix (helix H12) of its ligand-binding domain. Herein we show that in the absence of ligand, helices H12 of RXR and RAR are disordered. The selective RAR agonist, Am580, induces folding of H12, whereas in the presence of the inverse agonist BMS493, H12 stays mostly disordered. These results substantiate a link between the structural dynamics of H12 and RXR/RAR heterodimer biological functions, and highlight disordered-to-order transition as an essential mechanism for retinoic acid mediated regulation. Unliganded RAR exerts a strong repressive activity allowed by the recruitment of transcriptional corepressors and establishment of a corepressor complex in the promoter region of target genes. The human regulatory complex of the RARα bound to the full-length interaction domain of the corepressor N-CoR was studied by integrating several experimental (SAXS, X-ray crystallography, NMR, CD, AUC) and computational data. Unexpectedly, we found that, while mainly intrinsically disordered, the N-CoR presents partially evolutionary conserved structured regions that are involved in transient intramolecular contacts. In the presence of RXR/RAR, we show that N-CoR exploits its multivalency to form a multi-site complex that diplays an equilibrium between different conformational states. This conformational equilibrium is modulated by cognate ligands, RAR point mutation and RXR H12 deletion. Now, we can state that, in addition to NR conformation and ligand-induced allosteric changes, intrinsic disorder is substantially embedded in the synergetic regulation of RXR/RAR activity and its resulting abilities to communicate with the intracellular components.