Well-balanced and asymptotic preserving schemes for kinetic models

In this paper, we propose a general framework for designing numerical schemes that have both well-balanced (WB) and asymptotic preserving (AP) properties, for various kinds of kinetic models. We are interested in two different parameter regimes, 1) When the ratio between the mean free path and the characteristic macroscopic length $\epsilon$ tends to zero, the density can be described by (advection) diffusion type (linear or nonlinear) macroscopic models; 2) When $\epsilon$ = O(1), the models behave like hyperbolic equations with source terms and we are interested in their steady states. We apply the framework to three different kinetic models: neutron transport equation and its diffusion limit, the transport equation for chemotaxis and its Keller-Segel limit, and grey radiative transfer equation and its nonlinear diffusion limit. Numerical examples are given to demonstrate the properties of the schemes

To the uniqueness problem for nonlinear elliptic equations

We prove existence, boundedness and uniqueness of solutions to nonlinear elliptic boundary of second order under nonstandard assumptions with respect to the coefficients. Our assumptions are natural in view of drift diffusion processes for example in semiconductors and chemotaxi

Observation of external environment influence on living cells with holographic microscope

Předmětem diplomové práce je pozorování vnějšího vlivu na buňky za použití multimodálního holografického mikroskopu. Teoretická část práce pojednává nejdříve o vývoji holografické mikroskopie na ÚFI FSI VUT v Brně. Dále se práce zaměřuje na multimodální holografický mikroskop, který umožňuje neinvazivně pozorovat živé buňky. V diplomové práci je také uveden jeho popis, postup práce a zpracování hologramu. Stěžejní částí je i rešerše na téma chemotaxe buněk a osmotické jevy v buňkách. V rámci práce byly na tato témata navrženy příslušné experimenty. V experimentální části je nejdříve popsána kultivace buněk, poté příprava vzorku a komůrek pro pozorování a následně zpracování dat. Druhá polovina experimentální části je zaměřena přímo na provedená měření. Ve všech experimentech byly pozorovány buňky K2 (plné označení LW13K2).Subject of this master's thesis is the observation of influence of external environment on the living cells with the use of multimodal holographic microscope. The theoretical part is summarising the development of the holographic microscopy at IPE FME BUT. The theoretical part also describes multimodal holographic microscope, which allows non-invasive observing of living cells. The thesis also covers construction of the microscope, basic working instructions and the hologram processing method. The main subject of the thesis is the research on the topic of chemotaxis and osmotic processes in the cells. Experiments were designed for the purpose of this thesis to cover topics mentioned above. The experimental part of the thesis deals with cultivation of the cells, preparation of the sample and observation chambers and processing of the data. This part later focuses directly on the laboratory measurements. In all experiments, cells K2 (full name LW13K2) were observed.

The role of protein tyrosine phosphatase CD45 in neutrophil granulocytes

Strict regulation of the immune response is critical for appropriate protection against in- fection, preventing tissue damage, and maintaining homeostasis. A significant part of this regulation is mediated at the level of signaling pathways in which tyrosine phosphorylati- on plays a key role. It is regulated by the action of protein tyrosine kinases and protein tyrosine phosphatases (PTP). An important PTP expressed on all nucleated hematopoie- tic cells is the CD45. Its role has been studied primarily in T- and B-lymphocytes. There CD45 plays an important role in antigen-induced signaling and signaling triggered by other stimuli. It becomes apparent that also in neutrophils CD45 plays an importat role in many mechanisms that contribute to appropriate protection against infection. These include, for example, adhesion, extravasation, chemotaxis, phagocytosis, production of cytokines and oxidative burst. In many cases, CD45 affects these processes by regulating Src family kinases. Other means of CD45 participation in specific pathways are often not clear. This thesis summarizes our current understanding of role of CD45 in neutrophil granulocytes and its effects on the function of these cells. 1Pro dostatečnou obranu proti infekci, zamezení tkáňovému poškození a udržení home- ostázy je nutná přísná regulace imunitní odpovědi. Významná část této regulace probíhá na úrovni signálních drah, v nichž hraje důležitou roli tyrozinová fosforylace. Ta je regu- lována prostřednictvím protein tyrozin kináz a protein tyrozin fosfatáz (PTP). Klíčovou PTP jaderných hematopoetických buněk je CD45. Její role byla studována především v T- a B-lymfocytech, kde je důležitá pro signalizaci vyvolanou antigenem a dalšími sti- muly. Ukazuje se, že také u neutrofilů hraje CD45 důležitou roli v mnoha mechanismech, které přispívají k adekvátní obraně proti infekci. Jsou jimi například adheze, diapedéza, chemotaxe, fagocytóza, produkce cytokinů a oxidační vzplanutí. V řadě případů CD45 ovlivňuje tyto procesy prostřednictvím regulace kináz rodiny Src. O dalších způsobech zapojení CD45 do jednotlivých drah často není mnoho známo. Tato práce shrnuje dosa- vadní poznatky studia CD45 v neutrofilních granulocytech a jejím vlivu na funkci těchto buněk. 1Department of Cell BiologyKatedra buněčné biologieFaculty of SciencePřírodovědecká fakult

INVESTIGATION OF A FACTOR RELEASED BY NEOPLASTIC CELLS WHICH PRODUCES A CHEMOKINETIC RESPONSE IN ACTIVATED MACROPHAGES

The increase in rate of random migration (chemokinesis) of C. parvum activated macrophages in media conditioned by Lewis Lung (LL) carcinoma cells was attributed to a trypsin sensitive, heat stable, high molecular weight factor released from the membrane of the tumor cells. A capillary tube assay was developed to expediently monitor the chemokinetic activity of macrophages incubated in whole and fractionated media. The capillary tube assay was found to be capable of detecting both chemokinetic and chemotactic (directional movement) factors present in the test media. Statistical analysis revealed the capillary tube assay provided reproducible data both within and between experiments. Media conditioned by 6 different syngeneic and allogeneic mouse tumor cell lines demonstrated significantly higher chemokinetic activity compared to unconditioned or normal fibroblast conditioned media. The release of the chemokinetic factor (CKF) by Lewis Lung cultures was demonstrated to be maximum during the logarithmic growth phase of these neoplastic cells. Molecular seive chromatography of the Lewis Lung conditioned media revealed the CKF to have a molecular weight of approximately 360,000 daltons. Similarly to the C. parvum activated macrophages, the pyran activated macrophages responded chemokinetically to LL conditioned media. However oyster glycogen and thioglycolate elicited macrophages demonstrated no significant chemokinetic response in the presence of the LL-CKF. The Lewis Lung chemokinetic factor demonstrated no chemotactic activity in the Boyden chamber assay. In fact, the CKF actually inhibited the response of these macrophages to a known chemotactic factor. Indirect immunofluorescent staining of the CKF indicated that it was a membrane protein shed by the LL cells and bound by activated macrophages. The possibility is discussed that CKF may be a glycocalyx protein shed by tumor cells which interferes with macrophage- neoplastic cell interactions involved in the tumoricidal activity of macrophages

Dimension estimate of global attractors for a chemotaxis-growth system and its discretizations

Nakaguchi Etsushi. Dimension estimate of global attractors for a chemotaxis-growth system and its discretizations. 数理解析研究所講究録. No.1693, 2009, p. 143-150

Excisional Wound Healing and the Role of Homeobox Genes

The biochemical and physiologic mechanisms responsible for excisional wound contraction have been extensively studied but are not completely understood. Furthermore, the genes that regulate these processes are unknown. As a result, there are limited treatment options available for patients with diseases or conditions characterized by abnormal tissue contraction. In an attempt to improve our understanding of these mechanisms and identify some of the putative regulatory genes, we studied excisional wound healing in the mid-gestational fetal rabbit. These wounds normally do not contract nor are they associated with inflammation, fibrosis, or scar formation. However, we have been able to induce contraction, with and without inflammation and fibrosis, by providing sustained levels of exogenous TGF-βl and -β3, respectively, at the excisional wound site. In addition to learning more about the role of the TGF-β isoforms in tissue repair, we utilized our model to identify some of the regulatory genes responsible for contraction. We theorized that homeobox genes direct the mechanisms of excisional wound contraction. These genes encode for a family of transcription factors that are known to regulate cellular differentiation and tissue migration during development. We demonstrated that homeobox genes are expressed in normal fetal and adult rabbit skin and their pattern of expression varies for several of these genes. There was a 2-fold increase for Hoxa-5, yet a moderate decrease in Hoxc-6 transcripts in the contracting versus non-contracting fetal group. In addition, there was a greater than 3-fold increase in Hoxd-8 transcripts in the adult excisional wound group compared to the normal adult skin group. Using a ribonuclease protection assay, we confirmed that the level of Hoxd-8 expression was significantly greater at the site of adult excisional wounds than in the normal skin. These findings suggest that this homeobox gene may regulate some aspect of the mechanisms responsible for excisional wound contraction. Further studies may delineate the role of Hoxa-8 and other homeobox genes in the mechanisms of excisional wound contraction. If they are determined to direct various aspects of the contractile process, future therapeutic interventions targeting these genes may improve the healing of many abnormal wound healing conditions and diseases

A pathway-based mean-field model for E. coli chemotaxis: Mathematical derivation and Keller-Segel limit

A pathway-based mean-field theory (PBMFT) was recently proposed for E. coli chemotaxis in [G. Si, T. Wu, Q. Quyang and Y. Tu, Phys. Rev. Lett., 109 (2012), 048101]. In this paper, we derived a new moment system of PBMFT by using the moment closure technique in kinetic theory under the assumption that the methylation level is locally concentrated. The new system is hyperbolic with linear convection terms. Under certain assumptions, the new system can recover the original model. Especially the assumption on the methylation difference made there can be understood explicitly in this new moment system. We obtain the Keller-Segel limit by taking into account the different physical time scales of tumbling, adaptation and the experimental observations. We also present numerical evidence to show the quantitative agreement of the moment system with the individual based E. coli chemotaxis simulator.Comment: 21 pages, 3 figure