DYNAMICS FOR A CHEMOTAXIS MODEL WITH GENERAL LOGISTIC DAMPING AND SIGNAL DEPENDENT MOTILITY

In this paper,we consider the fully parabolic Chemotaxis system with the general logistic source{ut=Δ(γ(v)u)+λu-μu^(k),x∈Ω,t>0,vt=△v+wz,x∈Ω,t>0,wt=-wz,x∈Ω,t>0,zt=△z-z+u,x∈Ω,t>0 whereΩ⊂ℝn(n≥1)is a smooth and bounded domain,λ≥0,μ≥0,κ>1,and the motility function satisfies thatγ(v)∈C3([0,∞)),γ(v)>0,γ′(v)≤0 for all v≥0.Considering the Neumann boundary condition,we obtain the global boundedness of solutions if one of the following conditions holds:(i)λ=μ=0,1≤nλ3;(ii)λ>0,μ>0,combined withκ>1,1≤n≤3 or k>n+2/4,,n>3.Moreover,we prove that the solution (u, v, w, z) exponentially converges to the constant steady state ((λ/μ)1/k-1,∫Ωv0dx+∫Ωw0dx/|Ω|,0,(λ/μ)1/k-1).

High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models

In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.

THE SHOCK WAVES FOR A MIXED-TYPE SYSTEM FROM CHEMOTAXIS

In this paper,we study the shock waves for a mixed-type system from chemotaxis.We are concerned with the jump conditions for the left state which is located in the elliptical region and the right state in the hyperbolic region.Under the generalized entropy conditions,we find that there are different shock wave structures for different parameters.To guarantee the uniqueness of the solutions,we obtain the admissible shock waves which satisfy the generalized entropy condition in both parameters.Finally,we construct the Riemann solutions in some solvable regions.

THE SINGULAR CONVERGENCE OF A CHEMOTAXIS-FLUID SYSTEM MODELING CORAL FERTILIZATION

The singular convergence of a chemotaxis-fluid system modeling coral fertilization is justified in spatial dimension three.More precisely,it is shown that a solution of parabolic-parabolic type chemotaxis-fluid system modeling coral fertilization■converges to that of the parabolic-elliptic type chemotaxis-fluid system modeling coral fertiliz ation■in a certain Fourier-Herz space asε^(-1)→0.

BOUNDEDNESS OF A CHEMOTAXIS-CONVECTION MODEL DESCRIBING TUMOR-INDUCED ANGIOGENESIS

This paper is concerned with the parabolic-parabolic-elliptic system■in a bounded domainΩ?Rnwith a smooth boundary,where the parametersχ,ζ1,ζ2are positive constants and m≥1.Based on the coupled energy estimates,the boundedness of the global classical solution is established in any dimensions(n≥1)provided that m>1.

一类非线性chemotaxis系统的局部零能控性

本文研究了一类非线性chemotaxis系统的能控性问题.利用这类线性化结合不动点的方法,获得了非线性系统的局部零能控性结果,推广了非线性抛物-椭圆型方程能控性的结果.

3维chemotaxis-fluid方程弱解的整体存在性

针对具有非线性3维扩散chemotaxis-fluid模型,在其初边值问题基础上,提出了在m>7/6时该模型具有弱解整体存在性的论断。利用正则化问题的先验估计方法,给出了基于chemotaxis-fluid模型的5个引理并进行了证明,在此证明基础上,对所提论断进行了证明。

两类Chemotaxis模型解的性质

本文讨论了抛物-双曲和抛物-常微两个Chemotaxis模型初边值问题解的性质.利用形式级数展开的方法,得到全局解在微小扰动下,导致解在有限时间内爆破,并对爆破时间进行了估计.因此说明了这种模型空间齐性解的不稳定性.

SOLVABILITY OF A PARABOLIC-HYPERBOLIC TYPE CHEMOTAXIS SYSTEM IN 1-DIMENSIONAL DOMAIN

In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-dimensional domain. In addition, local solvability of the free boundary problem is considered by straightening the free boundary.

Adverse effects of metal exposure on chemotaxis towards water-soluble attractants regulated mainly by ASE sensory neuron in nematode Caenorhabditis elegans

Chemotaxis to water-soluble attractants is mainly controlled by ASE sensory neuron whose specification is regulated by che-1 in Caenorhabditis elegans. Our data suggested that exposure to high concentrations of metals, such as Pb, Cu, Ag, and Cr, would result in severe defects of chemotaxis to water-soluble attractants of NaCl, cAMP, and biotin. Moreover, the morphology of ASE neuron structures as observed by relative fluorescent intensities and relative size of fluorescent puncta of cell bodies, relative lengths of sensory endings in ASE neurons, and the expression patterns of che-1 were obviously altered in metal exposed animals when they meanwhile exhibited obvious chemotaxis defects to water-soluble attractants. In addition, the dendrite morphology could be noticeably changed in animals exposed to 150 μmol/L of Pb, Cu, and Ag. Furthermore, we observed significant decreases of chemotaxis to water-soluble attractants in Pb exposed che-1 mutant at concentrations more than 2.5 μmol/L, and in Cu, Ag, and Cr exposed che-1 mutant at concentrations more than 50 μmol/L. Therefore, impairment of the ASE neuron structures and functions may largely contribute to the appearance of chemotaxis defects to water-soluble attractants in metal exposed nematodes.

BOUNDEDNESS OF THE HIGHER-DIMENSIONAL QUASILINEAR CHEMOTAXIS SYSTEM WITH GENERALIZED LOGISTIC SOURCE

This article considers the following higher-dimensional quasilinear parabolic-parabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),x∈Ω,t>0 vt=Δv+w−v,x∈Ω,t>0,wt=u−w,x∈Ω,t>0,in a bounded domainΩ⊂R^n(n≥2)with smooth boundary ∂Ω,where the diffusion coefficient D(u)and the chemotactic sensitivity function S(u)are supposed to satisfy D(u)≥M1(u+1)^−αand S(u)≤M2(u+1)^β,respectively,where M1,M2>0 and α,β∈R.Moreover,the logistic source f(u)is supposed to satisfy f(u)≤a−μu^γ with μ>0,γ≥1,and a≥0.Asα+2β<γ−1+2γ/n,we show that the solution of the above chemotaxis system with sufficiently smooth nonnegative initial data is uniformly bounded.

Construction and Expression of Eukaryotic Expressing Vector pCH510 of Polypeptide CH50 and Its Chemotaxis and Antitumor Function by in vivo Transfection

To construct an eukaryotic expressing vector that expresses CH50, a recombinant CellⅠ HepⅡ bifunctional domain polypeptide of human fibronectin, and to investigate the chemotaxis to immune cells and the inhibitory effect on the growth of tumor by the expression of the plasmid in vivo , the plasmid was constructed by DNA recombination. Gene transfection was performed in vitro and in vivo . The expressed product was identified by Western blot. The chemotaxis after gene transfection in vivo was observed by histotomy and staining of muscle tissues. The inhibition of gene transfection on solid tumor was observed in mice. The results showed that plasmid pCH510 was constructed by the recombination of the 5′ terminal noncoding region and signal peptide coding region of human fibronectin cDNA and cDNA fragment coding CH50 polypeptide with a 3′ terminal noncoding region of human FN cDNA, and the insertion of the recombinated fragment into plasmid pcDNA3.1. After transfection with plasmid pCH510, NIH3T3 cells could produce CH50 polypeptide. The transfection of plasmid pCH510 by the injection in muscle of mouse could produce the effects of chemotaxis on immune cells and the inhibition on the growth of solid tumor. It is concluded that plasmid pCH510 can express in cells and in vivo in mouse. The expression of the plasmid in vivo has a chemotactic effect on immune cells and can inhibit the growth of solid tumor.

Metabolism-independent chemotaxis of Pseudomonas sp. strain WBC-3 toward aromatic compounds

Pseudomonas sp. strain WBC-3 utilized methyl parathion or para-nitrophenol (PNP) as the sole source of carbon, nitrogen, and energy, and methyl parathion hydrolase had been previously characterized. Its chemotactic behaviors to aromatics were investigated. The results indicated that strain WBC-3 was attracted to multiple aromatic compounds, including metabolizable or transformable substrates PNP, 4-nitrocatechol, and hydroquinone. Disruption of PNP catabolic genes had no e?ect on its chemotactic behaviors w...

Integrin betal mediates hepatocellular carcinoma cells chemotaxis to laminin

BACKGROUND: Chemotaxis is an important step durin the invasion of carcinoma cells. And integrins are most im portant receptors mediating interaction between cells an extracellular matrix ( ECM). This study was designed t study integrin betal mediating chemotaxis of hepatocellula carcinoma (HCC) cells to laminin (LN). METHODS: A micropipette technique was adopted to in vestigate the effect of blockade of integrin betal on pseudo pod protrusion of HCC cells in response to LN stimulation Chemotactic pseudopod protrusion of a HCC cell was eva luated using a dual-pipette set-up, in which two pipette filled with LN solution were positioned in close contact wit the same cell, and pseudopod protrusion into each pipett was viewed dynamically and recorded with a tape recorder The lengths of pseudopods were measured and plotte against time to obtain a pseudopod growth curve. The in tegrin betal subunit on the surfaces of HCC cells were ana lyzed by flow cytometry. RESULTS: In dual pipette chemotaxis experiment, whe the two pipettes were filled with LN(50 μg/ml, 200 μg/ml) pseudopods extended from the HCC cell into each of th pipettes nearly symmetrically, ie, with nearly identica maximum pseudopod length and similar pseudopod growth curves. Upon addition of anti-CD29 (20 μg/ml) to one o the pipettes, pseudopod protrusion was blocked nearly completely while protrusion into the opposite pipette be came more evidently, with a larger maximum length. Ex pression of integrin betal was up to 95.78% to cells chosen in the experiment. CONCLUSION: Integrin betal subunit was an importan constituent receptor subunit for mediating chemotactic pseudopod protrusion of HCC cell to LN.

Expression of Metadherin/AEG-1 Gene Is Positively Related to Orientation Chemotaxis and Adhesion of Human Hepatocellular Carcinoma Cell Lines of Different Metastatic Potentials

Metastasis contributes to the poor prognosis of hepatocellular carcinoma （HCC）. However, the mechanism through which a primary HCC cell develops into a metastatic phenotype is not well understood. The purpose of this study was to examine the correlation between metadherin （MTDH）/ astrocyte elevated gene-1 （AEG-1） expression in HCC cell lines of different metastatic potentials and such metastatic phenotypes as orientation chemotaxis and adhesion. MTDH/AEG-1 expression was detected by RT-PCR and western blotting in HCC cell lines （HepG2, Huh7, Sk-HEP-1, MHCC-97H）. Distribution of MTDH/AEG-1 was observed by immunofluorescence staining and confocal laser scanning microscopy. The abilities of orientation chemotaxis and adhesion and the index of interaction between HCC cell lines and microvascular endothelial cell lines （MVECs, including HUVECs and HPMECs） were measured by chemotaxis assay and adhesion assay, respectively. The results showed that MTDH/AEG-1 protein expression was significantly higher in high metastatic potential cancer cell lines （Sk-HEP-1, MHCC-97H ） than in low metastatic potential cell lines （HepG2, Huh7） （P〈0.05）. The MTDH/AEG-1 protein was localized in the perinuclear region of HCC cells. Furthermore, the abilities of orientation chemotaxis and adhesion of HCC cells to HPMECs were increased as compared with those of HCC cells to HUVECs （P〈0.05）. The abilities of orientation chemotaxis and adhesion were much stronger in Sk-HEP-1 and MHCC-97H cells with MTDH/AEG-1 highly expressed than in HepG2 and Huh7 cells with MTDH/AEG-1 lowly expressed （P〈0.05）. These results suggested that the expression of MTDH/AEG-1 gene in HCC cell lines of different metastatic potentials was closely positively related to the abilities of orientation chemotaxis and adhesion of HCC cells. It was deduced that MTDH/AEG-1 might play a pivotal role in the lung-specific metastasis of HCC, which may be medi-ated through orientation chemotaxis and adhesion abilities of HCC cells. MTDH/AEG-1 may serve as a potential therapeutic target for HCC.

GLOBALLY BOUNDED IN-TIME SOLUTIONS TO A PARABOLIC-ELLIPTIC SYSTEM MODELLING CHEMOTAXIS

In this article, the globally bounded in-time pointwise estimate of solutions to the simplified Keller-Segel system modelling chemotaxis are derived. Moreover, a local existence theorem is obtained.

Induction of chemotaxis to sodium chloride and diacetyl and thermotaxis defects by microcystin-LR exposure in nematode Caenorhabditis elegans

Apart from the liver disruption, embryotoxicity and genotoxicity, microcystin （MC）-LR also could cause neurotoxicity. Nematode Caenorhabditis elegans was explored as a model to study the neurotoxicity. In the present study, we provided evidence to indicate the neurotoxicity on chemotaxis to NaCl and diacetyl, and thermotaxis from MC-LR exposure to C. elegans. As a result, higher concentrations of MC-LR caused significantly severe defects of chemotaxis to NaCl and diacetyl, and thermotaxis. The neurotoxicity on chemotaxis to NaCl and diacetyl, and thermotaxis from MC-LR exposure might be largely mediated by the damage on the corresponding sensory neurons （ASE, AWA, and AFD） and interneuron AIY. The expression levels ofche-1 and odr-7 were significantly decreased （P 〈 0.01） in animals exposed to MC-LR at concentrations lower than 10 μg/L, whereas the expression levels of ttx-1 and ttx-3 could be significantly （P 〈 0.01） lowered in animals even exposed to 1 μg/L of MC-LR. Moreover, both the chemotaxis to NaCl and diacetyl and the thermotaxis were more significantly reduced in MC-LR exposed mutants of che-1（p674）, odr-7（ky4）, ttx-1（p767）, and ttx-3（ks5） than those in exposed wild-type N2 animals at the same concentrations.

BOUNDEDNESS AND ASYMPTOTIC STABILITY IN A PREDATOR-PREY CHEMOTAXIS SYSTEM WITH INDIRECT PURSUIT-EVASION DYNAMICS

This work explores the predator-prey chemotaxis system with two chemicals {u_(t) = Δu + ∇ ・ (u∇v) + μ_(1)u(1 − u − α_(1)w), x ∈ Ω, t > 0,v_(t )= Δv −α_(1)v + β_(1)w, x ∈ Ω, t > 0,w_(t) = Δw − ξ∇ ・ (w∇z) + μ_(2)w(1 + α_(2)u − w), x ∈ Ω, t > 0,z_(t) =Δz −α_(2)z +β_(2)u, x ∈ Ω, t > 0, in an arbitrary smooth bounded domainΩ■R^(n) under homogeneous Neumann boundary conditions.The parameters in the system are positive.We first prove that if n≤3,the corresponding initial-boundary value problem admits a unique global bounded classical solution,under the assumption thatχ,ξ,μ_(i),a_(i),α_(i) andβ_(i)(i=1,2)satisfy some suitable conditions.Subsequently,we also analyse the asymptotic behavior of solutions to the above system and show that·when a_(1)<1 and bothμ1/χ^(2) andμ2/ξ^(2) are sufficiently large,the global solution(u,v,w,z)of this system exponentially converges to(1-a_(1)/1+a_(1)a_(2),β_(1)(1+a_(2))/α_(1)(1+a_(1)a_(2)),1+a_(2)/1+a_(1)a_(2),β_(2)(1-a_(1))/α_(2)(1+a_(1)a_(2)))as t→∞;·when a1>1 andμ_(2)/ξ_(2) is sufficiently large,the global bounded classical solution(u,v,w,z)of this system exponentially converges to(0,α_(1)/β_(1),1,0)as t→∞;·when a1=1 andμ_(2)/ξ_(2) is sufficiently large,the global bounded classical solution(u,v,w,z)of this system polynomially converges to(0,α_(1)/β_(1),1,0)as t→∞.

On Solutions of Generalized Bacterial Chemotaxis Model in a Semi-Solid Medium

In this paper, the Adomian’s decomposition method has been developed to yield approximate solution of bacterial chemotaxis model of fractional order in a semi-solid medium. The fractional derivatives are described in the Caputo sense. The method introduces a promising tool for solving many linear and nonlinear fractional differential equations.