Search

This paper is concerned with the critical sharp traveling wave for doubly nonlinear diffusion equation with time delay, where the doubly nonlinear degenerate diffusion is defined by $\Big(\big|(u^m)_x\big|^{p-2}(u^m)_x\Big)_x$ with $m>0$ and $p>1$. The doubly nonlinear diffusion equation is proved to admit a unique sharp type traveling wave for the degenerate case $m(p-1)>1$, the so-called slow-diffusion case. This sharp traveling wave associated with the minimal wave speed $c^*(m,p,r)$ is monotonically increasing, where the minimal wave speed satisfies $c^*(m,p,r)0$. The sharp front is $C^1$-smooth for $\frac{1}{p-1}, Comment: arXiv admin note: text overlap with arXiv:1909.11751

We are concerned with a class of degenerate diffusion equations with time delay describing population dynamics with age structure. In our recent study [{\em Nonlinearity}, 33 (2020), 4013--4029], we established the existence and uniqueness of critical traveling wave for the time-delayed degenerate diffusion equations, and obtained the reducing mechanism of time delay on critical wave speed. In this paper, we now are able to show the asymptotic spreading speed and its coincidence with the critical wave speed $c^*(m,r)$ of sharp wave, and prove that the initial perturbation or the boundary of the compact support of the solution propagates at the critical wave speed $c^*(m,r)$ for the time-delayed degenerate diffusion equations. Remarkably, different from the existing studies related to spreading speeds, the time delay and the degenerate diffusion lead to some essential difficulties in the analysis of the spreading speed, because the time-delay makes the critical speed of traveling waves slow down, and the degenerate diffusion causes the loss of regularity for the solutions. By a phase transform technique combined with the monotone method, we can determine the asymptotic spreading speed. Furthermore, we propose a brand-new sharp-profile-based difference scheme to handle large variation of degenerate diffusion $(u^m)_{xx}$ near the sharp edge and carry out some numerical simulations which perfectly confirm our theoretical results.

We consider a population dynamics model with degenerate diffusion and time delay. We discover sharp-oscillatory waves with sharp edges and non-decaying oscillations arising from density-dependent dispersal and reproduction with age structure. Degenerate diffusion and bad effect of time delay prevent the use of existing approaches. Here, we develop a new delayed iteration framework to show the existence of these peculiar waves. In particular, the estimate of the admissible wave speed is highly nontrivial. We employ a new phase transform method coupled with the detailed analysis of phase energy. Furthermore, we give a complete characterization of the dynamical behaviors of various kinds of waves. Our results indicate that simple invasion rules can generate complex wave patterns and provide some interesting insights into the ecological dynamics.

The boundary value problem for the three-dimensional steady viscous compressible Navier-Stokes/Allen-Cahn (NSAC) system is considered. We establish the existence of a weak solution for the adiabatic index γ > 2 with the phase function belonging to [ − 1 , 1 ] . Moreover, we give further analysis on the weak solution. More specifically, we prove that the steady NSAC system degenerates into Navier-Stokes system if the phase function is positive (negative) on Ω ‾ .

For the classical reaction diffusion equation, the a priori speed of fronts is determined exactly in the pioneering paper (Benguria and Depassier 1996 Commun. Math. Phys. 175 221–227) by variational characterization method. In this paper, we study the age-structured population dynamics using a degenerate diffusion equation with time delay. We show the existence and uniqueness of sharp critical fronts, where the sharp critical front is C 1-smooth when the diffusion degeneracy is weaker with 1 < m < 2, and the sharp critical front is non-C 1-smooth (piecewise smooth) when the diffusion degeneracy is stronger with m ≥ 2, and the non-critical waves are C 2-smooth. We give a new variational approach for the critical wave speed and investigate how the time delay affects the propagation mechanism of fronts. It is shown that the time delay slows down the critical wave speed.

The Toll signaling pathway was initially identified for its involvement in the control of early embryogenesis. It was later shown to be also part of a major innate immune pathway controlling the expression of anti-microbial peptides in many eukaryotes including humans; cactus, the essential negative regulator of this pathway in flies, was found to be induced in parallel to the Toll-dependent activation process during immune defenses. We were interested in the mechanisms of this dual effect and provide here evidence that upon pathogenic stimuli, dorsal, one of the transcription factors of the fly Toll pathway, can induce the expression of the E3 ligase Bre1. We further show that Bre1 complexes with the E2 Rad6 to mono-ubiquitinate histone H2B and to promote the transcription of cactus to achieve homeostasis of the Toll immune response. Our studies characterize a Toll signal-dependent regulatory machinery in governing the Toll pathway in Drosophila.

We investigate the propagating profiles of a degenerate chemotaxis model describing the bacteria chemotaxis and consumption of oxygen by aerobic bacteria, in particular, the effect of the initial attractant distribution on bacterial clustering. We prove that the compact support of solutions may shrink if the signal concentration satisfies a special structure, and show the finite speed propagating property without assuming the special structure on attractant concentration, and obtain an explicit formula of the population spreading speed in terms of model parameters. The presented results suggest that bacterial cluster formation can be affected by chemotactic attractants and density-dependent dispersal.

Summary Black tea is the most widely consumed tea drink in the world and has consistently been reported to possess anti-aging benefits. However, whether theaflavins, one type of the characteristic phytochemicals in black tea extracts, are involved in regulating aging and lifespan in consumers remains largely unknown. In this study, we show that theaflavins play a beneficial role in preventing age-onset intestinal leakage and dysbiosis, thus delaying aging in Drosophila. Mechanistically, theaflavins regulate the condensate assembly of Imd to negatively govern the overactivation of Imd signals in fruit fly intestines. In addition, theaflavins prevent DSS-induced colitis in mice, suggesting theaflavins play a role in modulating intestinal integrity. Overall, our study reveals a molecular mechanism by which theaflavins regulate gut homeostasis likely through controlling Imd coalescence., Graphical abstract, Highlights • Theaflavins extend Drosophila lifespan and increase climbing ability • Theaflavins prevent age-onset microbiota dysbiosis and intestinal leakage • Theaflavins downregulate Imd signals maybe through controlling Imd condensation • Theaflavins alleviate DSS-induced colitis in CD-1 mice, Animal Physiology; Molecular Biology; Immunology

The intestine, a high-turnover tissue, plays a critical role in regulating aging and health in both vertebrates and invertebrates. Maintaining the epithelial barrier function of the intestine by preserving innate immune homeostasis significantly delays aging and prevents mortality. In an effort to explore effective chemicals and materials that can improve intestinal integrity, we performed a nonbiased screen utilizing Drosophila as an animal model. We showed that long-term uptake of aspirin markedly prevented age-onset gut leakage, the over-proliferation of intestinal stem cells, and the dysbiosis of commensal microbiota in fruit flies. Mechanistically, aspirin efficiently downregulated chronic activation of intestinal immune deficiency signaling during aging. Furthermore, our in vivo and in vitro biochemical analyses indicated that aspirin is a negative modulator in control of the K63-linked ubiquitination of Imd. Our findings uncover a novel regulatory mechanism by which aspirin positively modulates intestinal homeostasis, thus delaying aging, in Drosophila.

This paper is concerned with time-delayed reaction–diffusion equations with degenerate diffusion. When the term for birth rate is a nonlocal integral with a heat kernel, the family of minimum wave speeds corresponding to all the degenerate diffusion coefficients is proved to admit a uniform positive infimum. However, when the term for birth rate is local, there is no positive infimum of all the minimum wave speeds. This difference indicates that the nonlocal effect plays a role as Laplacian such that a positive lower bound independent of the degenerate diffusion exists for the minimum wave speeds. The approach adopted for the proof is the monotone technique with the viscosity vanishing method. The degeneracy of diffusion for the equation causes us essential difficulty in the proof. A number of numerical simulations are also carried out at the end of the paper, which further numerically confirm our theoretical results.

In this paper we study the existence of time periodic solutions for the evolutionary weighted \begin{document}$p$\end{document} -Laplacian with a nonlinear periodic source in a bounded domain containing the origin. We show that there is a critical exponent \begin{document}$q_c = q_c(α,β) = \frac{(N+β)p}{N+α-p}-1$\end{document} and a singular exponent \begin{document}$q_s = p-1$\end{document} : there exists a positive periodic solution when \begin{document}$0 and \begin{document}$q\ne q_s$\end{document} ; while there is no positive periodic solution when \begin{document}$q≥ q_c$\end{document} . The case when \begin{document}$q = q_s$\end{document} is completely different from the remaining case \begin{document}$q\ne q_s$\end{document} , the problem may or may not have solutions depending on the coefficients of the equation.

This paper deals with the existence and the asymptotic behavior of discontinuous traveling wave entropy solutions for a modified Allen-Cahn model, in which, the usual Ficken-based model for phase transition is replaced with a more physical model with nonlinear diffusive flux. The discontinuous traveling waves correspond to the discontinuous phase transition phenomena.

Significance Inhibitory Smads (I-Smads) play important roles to negatively regulate TGF-β/BMP (bone morphogenetic protein) signaling, thus controlling numerous cellular and developmental processes. Recent studies have suggested that Smad7, a member of I-Smads, is overexpressed in numerous cancer types and its abundance is positively correlated to the malignancy. However, the molecular mechanism underlying action of I-Smads in cells remains poorly understood. Here we show that the Drosophila I-Smad, Dad, accesses the membrane via palmitoylation to target the BMP type I receptor for ubiquitination. Importantly, we show that the palmitoyltransferase dHIP14 catalyzes Dad palmitoylation and antagonizes BMP/Dpp signaling. Our findings uncover a mechanism by which I-Smad controls TGF-β/BMP signaling., TGF-β/BMP (bone morphogenetic protein) signaling pathways play conserved roles in controlling embryonic development, tissue homeostasis, and stem cell regulation. Inhibitory Smads (I-Smads) have been shown to negatively regulate TGF-β/BMP signaling by primarily targeting the type I receptors for ubiquitination and turnover. However, little is known about how I-Smads access the membrane to execute their functions. Here we show that Dad, the Drosophila I-Smad, associates with the cellular membrane via palmitoylation, thereby targeting the BMP type I receptor for ubiquitination. By performing systematic biochemistry assays, we characterized the specific cysteine (Cys556) essential for Dad palmitoylation and membrane association. Moreover, we demonstrate that dHIP14, a Drosophila palmitoyl acyl-transferase, catalyzes Dad palmitoylation, thereby inhibiting efficient BMP signaling. Thus, our findings uncover a modification of the inhibitory Smads that controls TGF-β/BMP signaling activity.

This paper deals with a mathematical model of gravitational sedimentation–consolidation processes, for which the existence of discontinuous traveling wave entropy solutions is established by using the phase plane analysis method.

Drosophila germ-line stem cells (GSCs) provide an excellent model to study the regulatory mechanisms of stem cells in vivo. Bag of marbles (bam) has been demonstrated to be necessary and sufficient to promote GSC and cystoblast differentiation. Despite extensive investigation of its regulation and genetic functions, the biochemical nature of the Bam protein has been unknown. Here, we report that Bam is an ubiquitin-associated protein and controls the turnover of cyclin A (CycA). Mechanistically, we found that Bam associated with Otu to form a deubiquitinase complex that stabilized CycA by deubiquitination, thus providing a mechanism to explain how ectopic expression of Bam in GSCs promotes differentiation. Collectively, our findings not only identify a biochemical function of Bam, which contributes to GSC fate determination, but also emphasizes the critical role of proper expression of cyclin proteins mediated by both ubiquitination and deubiquitination pathways in balancing stem cell self-renewal and differentiation.

This paper is concerned with traveling wave solutions for a chemotaxis model with degenerate diffusion of porous medium type. We establish the existence of semi-finite traveling waves, including the sharp type and $$C^1$$ type semi-finite waves. Our results indicate that chemotaxis slows down the wave speed of semi-finite traveling wave, that is, the traveling wave speed for chemotaxis with porous medium (degenerate) diffusion is smaller than that for the porous medium equation without chemotaxis. As we know, this is a new result not shown in the existing literature. The result appears to be a little surprising since chemotaxis is a convective force. We prove our results by the Schauder’s fixed point theorem and estimate the wave speed by a variational approach.

This paper is concerned with the multi-dimensional compressible Euler equations with time-dependent over-damping of the form $-\frac{\mu}{(1+t)^\lambda}\rho\boldsymbol u$ in $\mathbb R^n$, where $n\ge2$, $\mu>0$, and $\lambda\in[-1,0)$. This continues our previous work dealing with the under-damping case for $\lambda\in[0,1)$. We show the optimal decay estimates of the solutions such that for $\lambda\in(-1,0)$ and $n\ge2$, $\|\rho-1\|_{L^2(\mathbb R^n)}\approx(1+t)^{-\frac{1+\lambda}{4}n}$ and $\|\boldsymbol u\|_{L^2(\mathbb R^n)}\approx (1+t)^{-\frac{1+\lambda}{4}n-\frac{1-\lambda}{2}}$, which indicates that a stronger damping gives rise to solutions decaying optimally slower. For the critical case of $\lambda=-1$, we prove the optimal logarithmical decay of the perturbation of density for the damped Euler equations such that $\|\rho-1\|_{L^2(\mathbb R^n)}\approx |\ln(e+t)|^{-\frac{n}{4}}$ and $\|\boldsymbol u\|_{L^2(\mathbb R^n)}\approx (1+t)^{-1}\cdot|\ln(e+t)|^{-\frac{n}{4}-\frac{1}{2}}$ for $n\ge7$. The over-damping effect reduces the decay rates of the solutions to be slow, which causes us some technical difficulty in obtaining the optimal decay rates by the Fourier analysis method and the Green function method. Here, we propose a new idea to overcome such a difficulty by artfully combining the Green function method and the time-weighted energy method.

In this paper we are interested in studying singular periodic solutions for the p-Laplacian in a punctured domain. We find an interesting phenomenon that there exists a critical exponent pc = N and a singular exponent qs = p-1. Precisely speaking, only if p > pc can singular periodic solutions exist; while if 1

The intestine, a high-turnover tissue, plays a critical role in regulating aging and health in both vertebrates and invertebrates. Maintaining the epithelial barrier function of the intestine by preserving innate immune homeostasis significantly delays aging and prevents mortality. In an effort to explore effective chemicals and materials that can improve intestinal integrity, we performed a nonbiased screen utilizing Drosophila as an animal model. We showed that long-term uptake of aspirin markedly prevented age-onset gut leakage, the over-proliferation of intestinal stem cells, and the dysbiosis of commensal microbiota in fruit flies. Mechanistically, aspirin efficiently downregulated chronic activation of intestinal immune deficiency signaling during aging. Furthermore, our in vivo and in vitro biochemical analyses indicated that aspirin is a negative modulator in control of the K63-linked ubiquitination of Imd. Our findings uncover a novel regulatory mechanism by which aspirin positively modulates intestinal homeostasis, thus delaying aging, in Drosophila.

The Budyko–Sellers climate model with mushy region is considered in this paper. We prove the existence and uniqueness of the initial value problem and the periodic problem, the attractivity of periodic solutions. We also study the asymptotic behavior of the model as the width of mushy region tends to zero.

The polytropic filtration equation with generalized Fisher–KPP sources is considered. We will show that the equation may have finite times oscillatory traveling waves, and try to give a complete classification by virtue of a singular exponent in the source according to the finiteness of the oscillatory times of traveling waves.

In eukaryotic cells, RNA-binding proteins (RBPs) interact with RNAs to form ribonucleoprotein complexes (RNA granules) that have long been thought to regulate RNA fate or activity. Emerging evidence suggests that some RBPs not only bind RNA but also possess enzymatic activity related to ubiquitin regulation, raising important questions of whether these RBP-formed RNA granules regulate ubiquitin signaling and related biological functions. Here, we show that Drosophila Otu binds RNAs and coalesces to membrane-less biomolecular condensates via its intrinsically disordered low-complexity domain, and coalescence represents a functional state for Otu exerting deubiquitinase activity. Notably, coalescence-mediated enzymatic activity of Otu is positively regulated by its bound RNAs and co-partner Bam. Further genetic analysis reveals that the Otu/Bam deubiquitinase complex and dTraf6 constitute a feedback loop to maintain intestinal immune homeostasis during aging, thereby controlling longevity. Thus, regulated biomolecular condensates may represent a mechanism that controls dynamic enzymatic activities and related biological processes.

In this paper, we establish the existence of radially symmetric solutions of the p-Laplacian with a concave term and critical Sobolev–Hardy exponent in a perforated-like domain. Copyright © 2011 John Wiley & Sons, Ltd.

A polyphasic taxonomic approach was used to study strain 12116T, which was isolated from desert sand in Xinjiang, China. Cells of the isolate were Gram-negative, non-motile, rod-shaped and aerobic. MK-7 was the predominant respiratory menaquinone. The DNA G+C content was 46.3 mol%. A phylogenetic analysis based on 16S rRNA gene sequences showed that the isolate was most closely related to the members of the genus Dyadobacter, with similarities ranging from 94.7 to 96.6 %. Therefore, on the basis of genotypic and phenotypic data, strain 12116T represents a novel species of the genus Dyadobacter, for which the name Dyadobacter alkalitolerans sp. nov. is proposed. The type strain is 12116T (=CCTCC AB 207176T =NRRL B-51268T).

Many stem cell populations are tightly regulated by their local microenvironment (niche), which comprises distinct types of stromal cells. However, little is known about mechanisms by which niche subgroups coordinately determine the stem cell fate. Here we identify that Yki, the key Hippo pathway component, is essential for escort cell (EC) function in promoting germline differentiation in Drosophila ovary. We found that Hedgehog (Hh) signals emanating primarily from cap cells support the function of ECs, where Cubitus interruptus (Ci), the Hh signaling effector, acts to inhibit Hippo kinase cascade activity. Mechanistically, we found that Ci competitively interacts with Hpo and impairs the Hpo-Wts signaling complex formation, thereby promoting Yki nuclear localization. The actions of Ci ensure effective Yki signaling to antagonize Sd/Tgi/Vg-mediated default repression in ECs. This study uncovers a mechanism explaining how subgroups of niche cells coordinate to determine the stem cell fate via Hh-Hippo signaling crosstalk, and enhances our understanding of mechanistic regulations of the oncogenic Yki/YAP signaling.

In this paper we consider the time-periodic Allen-Cahn equation subject to homogeneous boundary value condition and time-periodic condition. For the case of a smooth bounded domain with spatial dimension $N\leq 3$ , we prove the existence of classical nontrivial periodic solutions. For the case of a star shaped domain with $N\geq4$ , we prove the nonexistence of nontrivial periodic solutions. For the case of an annulus domain with $N \geq3 $ , we prove the existence of nontrivial radial periodic solutions. Some numerical simulations are also presented to illustrate our results.

Innate immunity mediated by Toll signalling has been extensively studied, but how Toll signalling is precisely controlled in balancing innate immune responses remains poorly understood. It was reported that the plasma membrane localization of Drosophila MyD88 is necessary for the recruitment of cytosolic adaptor Tube to the cell surface, thus contributing to Toll signalling transduction. Here we demonstrate that Drosophila Pellino functions as a negative regulator in Toll-mediated signalling. We show that Pellino accumulates at the plasma membrane upon the activation of Toll signalling in a MyD88-dependent manner. Moreover, we find that Pellino is associated with MyD88 via its CTE domain, which is necessary and sufficient to promote Pellino accumulation at the plasma membrane where it targets MyD88 for ubiquitination and degradation. Collectively, our study uncovers a mechanism by which a feedback regulatory loop involving MyD88 and Pellino controls Toll-mediated signalling, thereby maintaining homeostasis of host innate immunity., Toll signalling activates the innate immune response; however, it remains unclear how this pathway is suppressed to avoid excessive inflammatory responses. Here, the authors report that Pellino, a RING domain-containing ubiquitin E3 ligase, is a negative regulator of Toll signalling in Drosophila.