Asymptotic expansions of the solutions of the Cauchy problem for nonlinear parabolic equations

Let $u$ be a solution of the Cauchy problem for the nonlinear parabolic equation $$\partial_t u=\Delta u+F(x,t,u,\nabla u) \quad in \quad{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad in \quad{\bf R}^N,$$ and assume that the solution $u$ behaves like the Gauss kernel as $t\to\infty$. In this paper, under suitable assumptions of the reaction term $F$ and the initial function $\varphi$, we establish the method of obtaining higher order asymptotic expansions of the solution $u$ as $t\to\infty$. This paper is a generalization of our previous paper, and our arguments are applicable to the large class of nonlinear parabolic equations

Nonlinear characterizations of stochastic completeness

We prove that conservation of probability for the free heat semigroup on a Riemannian manifold M (namely stochastic completeness), hence a linear property, is equivalent to uniqueness of positive, bounded solutions to nonlinear evolution equations of fast diffusion type on M of the form ut=Δϕ(u), ϕ being an arbitrary concave, increasing, positive function, regular outside the origin and with ϕ(0)=0. Either property is also equivalent to nonexistence of nonnegative, nontrivial, bounded solutions to the elliptic equation ΔW=ϕ−1(W), with ϕ as above. As a consequence, explicit criteria for uniqueness or nonuniqueness of bounded solutions to fast diffusion-type equations on manifolds are given, these being the first results on such issues

Distinct cellular pathways select germline-encoded and somatically mutated antibodies into immunological memory

One component of memory in the antibody system is long-lived memory B cells selected for the expression of somatically mutated, high-affinity antibodies in the T cell-dependent germinal center (GC) reaction. A puzzling observation has been that the memory B cell compartment also contains cells expressing unmutated, low-affinity antibodies. Using conditional Bcl6 ablation, we demonstrate that these cells are generated through proliferative expansion early after immunization in a T cell-dependent but GC-independent manner. They soon become resting and long-lived and display a novel distinct gene expression signature which distinguishes memory B cells from other classes of B cells. GC-independent memory B cells are later joined by somatically mutated GC descendants at roughly equal proportions and these two types of memory cells efficiently generate adoptive secondary antibody responses. Deletion of T follicular helper (Tfh) cells significantly reduces the generation of mutated, but not unmutated, memory cells early on in the response. Thus, B cell memory is generated along two fundamentally distinct cellular differentiation pathways. One pathway is dedicated to the generation of high-affinity somatic antibody mutants, whereas the other preserves germ line antibody specificities and may prepare the organism for rapid responses to antigenic variants of the invading pathogen

Antiparkinson Drug Benztropine Suppresses Tumor Growth, Circulating Tumor Cells, and Metastasis by Acting on SLC6A3/DAT and Reducing STAT3

Tumor growth, progression, and therapy resistance are crucial factors in the prognosis of cancer. The properties of three-dimensional (3D) tumor-like organoids (tumoroids) more closely resemble in vivo tumors compared to two-dimensionally cultured cells and are therefore effectively used for assays and drug screening. We here established a repurposed drug for novel anticancer research and therapeutics using a 3D tumoroid-based screening system. We screened six pharmacologically active compounds by using an original tumoroid-based multiplex phenotypic screening system with a matrix metalloproteinase 9 (MMP9) promoter-driven fluorescence reporter for the evaluation of both tumoroid formation and progression. The antiparkinson drug benztropine was the most effective compound uncovered by the screen. Benztropine significantly inhibited in vitro tumoroid formation, cancer cell survival, and MMP9 promoter activity. Benztropine also reduced the activity of oncogenic signaling transducers and trans-activators for MMP9, including STAT3, NF-kappa B, and beta-catenin, and the properties of cancer stem cells/cancer-initiating cells. Benztropine and GBR-12935 directly targeted the dopamine transporter DAT/SLC6A3, whose genetic alterations such as amplification were correlated with poor prognosis for cancer patients. Benztropine also inhibited the tumor growth, circulating tumor cell (CTC) number, and rate of metastasis in a tumor allograft model in mice. In conclusion, we propose the repurposing of benztropine for anticancer research and therapeutics that can suppress tumor progression, CTC, and metastasis of aggressive cancers by reducing key pro-tumorigenic factors

High cocoa polyphenol rich chocolate may reduce the burden of the symptoms in chronic fatigue syndrome

<p>Abstract</p> <p>Background</p> <p>Chocolate is rich in flavonoids that have been shown to be of benefit in disparate conditions including cardiovascular disease and cancer. The effect of polyphenol rich chocolate in subjects with chronic fatigue syndrome (CFS) has not been studied previously.</p> <p>Methods</p> <p>We conducted a double blinded, randomised, clinical pilot crossover study comparing high cocoa liquor/polyphenol rich chocolate (HCL/PR) in comparison to simulated iso-calorific chocolate (cocoa liquor free/low polyphenols(CLF/LP)) on fatigue and residual function in subjects with chronic fatigue syndrome. Subjects with CFS having severe fatigue of at least 10 out of 11 on the Chalder Fatigue Scale were enrolled. Subjects had either 8 weeks of intervention in the form of HCL/PR or CLF/LP, with a 2 week wash out period followed by 8 weeks of intervention with the other chocolate.</p> <p>Results</p> <p>Ten subjects were enrolled in the study. The Chalder Fatigue Scale score improved significantly after 8 weeks of the HCL/PR chocolate arm [median (range) Exact Sig. (2-tailed)] [33 (25 - 38) vs. 21.5 (6 - 35) 0.01], but that deteriorated significantly when subjects were given simulated iso-calorific chocolate (CLF/CP) [ 28.5 (17 - 20) vs. 34.5 (13-26) 0.03]. The residual function, as assessed by the London Handicap scale, also improved significantly after the HCL/PR arm [0.49 (0.33 - 0.62) vs. 0.64 (0.44 - 0.83) 0.01] and deteriorated after iso-calorific chocolate [00.44 (0.43 - 0.68) vs. 0.36 (0.33 - 0.62)0.03]. Likewise the Hospital Anxiety and Depression score also improved after the HCL/PR arm, but deteriorated after CLF/CP. Mean weight remained unchanged throughout the trial.</p> <p>Conclusion</p> <p>This study suggests that HCL/PR chocolate may improve symptoms in subjects with chronic fatigue syndrome.</p