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1
Content available remote Some remarks on well-posedness of the higher-dimensional chemorepulsion system
EN
We consider a fully parabolic system of chemorepulsion in higher dimensions. We introduce a new energy-like identity and comment on its relation to the Li-Yau-Hamilton inequalities. Next, we show that for the chemorepellent moving much more slowly than the cells, the time global well-posedness holds.
PL
W artykule przedstawiono urządzenie lab-on-a-chip do hodowli i badań potencjału biologicznego mikroorganizmów. Szczegółowo opisano konstrukcję i technologię lab-chipa wykonanego ze szkła borokrzemowego. Użyteczność zaproponowanego rozwiązania sprawdzono w badaniach dwóch gatunków eugleny: Eugleny gracilis oraz Eugleny viridis. W ramach przeprowadzonych doświadczeń mikroorganizmy te poddano oddziaływaniu powietrza, azotu i dwutlenku węgla. Na podstawie otrzymanych wyników określono wzrost populacji euglen stymulowanych światłem i dwutlenkiem węgla (fotosynteza). Udokumentowano również pozytywną chemotaksję E. gracilis w kierunku powietrza. Doświadczenia wykazały, że konstrukcja lab-chipa umożliwia uzyskanie długoterminowej hodowli euglen i może znaleźć w przyszłości zastosowanie w badaniach potencjału biologicznego innych mikroorganizmów, komórek, czy oocytów.
EN
In the paper, the lab-on-a-chip for culturing and microorganisms’ investigation has been presented. The construction and technology of borosilicate glass chip has been described in details. Utility of the device has been verified in the study of Euglena vridis and Euglena gracilis. The selected microorganisms have been subjected to air, nitrogen and carbon dioxide stimulation. In the experiments, the population growth based on the photosynthesis process of two euglena species has been investigated. In addition, a repeatable, positive chemotaxis of Euglena gracilis towards air in the lab-on-a-chip device has been observed. The conducted experiments have proved that the lab-on-a-chip construction enables for a long term culturing of the chosen microorganisms and may be used to provide reliable cell or oocyte study in the near future.
EN
A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than 8π as the initial data is given. This result was obtained by Senba and Suzuki (2002) and Bedrossian and Masmoudi (2014) using different arguments. Moreover, we show a uniform bound for the existence time of solutions as well as an optimal hypercontractivity estimate.
EN
In the case of producing large amounts of hydrogenous gas, currently there are no problems related to basic techniques of hydrogen production and distribution, but the main technological problem will consists of storing it in order to regulate the difference between permanent or increasing gas production and seasonally modulated gas consumption. The most efficient and most inexpensive method of storing large amounts of hydrogen is to inject them in geological formations like aquifers, depleted gas reservoirs, or salt caverns (Zittel and Wurster 1996). The cost is of order $ 3.5 per 1 GJ (Taylor et al. 1986). Several underground storages of hydrogen (USH) or town gas exist in the word, as for instance, Teeside in the UK, in Texas, in Russia, Kiel in Germany, Lobodice in Czechoslovakia, Beynes - an ex-storage in France. During several tens of years the storage of hydrogen was considered as something deja-vu, to be similar to that of natural gas, which is amplified by the chemical inactivity of hydrogen and its very low solvability in groundwater [Bulatov 1979; Carden and Paterson 1979; Lindblom 1985; Paterson 1983]. Nevertheless, quite unusual behaviour of UHS was discovered by in situ monitoring of the gas composition extracted during the cycle "production" which followed the cycle "injection". These observations (Smigai et al. 1990; Buzek et al. 1994) revealed high variations of gas composition in time and space. In particular, a significant reduction in the H2 and CO2 contents and a simultaneous increase in CH4 contents were observed in the Lobodice town gas storage facility (Smigai et al. 1990). Similar phenomena were recorded in Beynes. After several months of injection and storage, at the beginning of the cycle "production" the twofold increase of the methane contents in the reservoir gas and the twofold reduction of the CO2 CO contents was observed. The contents of hydrogen decreased by 1.4. The explanation to these observations has been done in (Buzek et al. 1994) in terms of the in situ methane generators by methanogenic bacteria which catalyse the reaction between hydrogen and CO2/CO, by producing methane and water. Further observations have revealed even more unusual effects within the storage facility, such as creating a spatial alternation of the areas saturated preferably by hydrogen or methane. This proved an in situ natural separation of chemical components in space. Thus, we are dealing with a natural reactor which partially destroys CO2 and H2 and doubles the mass of methane. It is clear that the problem is important for industry as it concerns both the energy sector and ecology. The resulting economical efficiency of such a process can be estimated only after the physical and mathematical modeling of all possible scenarios of the reservoir behaviour. The development of such a model represents the main objective of this paper.
EN
In this paper we investigate a mathematical model of cancer invasion of tissue, which incorporates haptotaxis, chemotaxis, proliferation and degradation rates for cancer cells and the extracellular matrix, kinetics of urokinase receptor, and urokinase plasminogen activator cycle. We solve the model using spectrally accurate approximations and compare its numerical solutions with laboratory data. The spectral accuracy allows to use low-dimensional matrices and vectors, which speeds up the computations of the numerical solutions and thus to estimate the parameter values for the model equations. Our numerical results demonstrate correlations between numerical data computed from the mathematical model and in vivo tumour growth rates from prostate cell lines.
6
Content available remote Cells and attractant masses related by chemotactic aggregation
EN
The active role played by chemotactic current density of the migrating cells in order to overcome its diffusion current, leads to a spatially - non-homogeneous and time - presistent distribution of the cells. We show that independently of the initial attractant concentration, its quantity tends exponentially to the concentration of cells as the system approaches a steady state.
PL
Chemotaksja w kolonii komórkowej wywołana sygnałami biochemicznymi wydzielanymi przez komórki prowadzi do złożonych zachowań takiej zbiorowości, które można badać za pomocą metod multiagentowych. W pracy opisano agentowy model kolonii oraz przeprowadzone na nim eksperymenty symulacyjne. Obserwowana populacja wykazywała tendencję do samorzutnego wytwarzania skupisk. Wyniki doświadczeń wskazują, że zbiorowość organizmów może prezentować zachowania pozornie celowe pomimo braku jawnie określonej strategii kierującej zachowaniem poszczególnych osobników.
EN
Biochemical signals produced by colony of unicellular organisms can induce complex movements of cells caused by their chemotaxis. This behaviour can be modelled with the use of multiagent dynamic system. This paper describes multiagent model of a cellular colony and presents the results of performed simulations, which reveal agents' spontaneous tendency to aggregate into clusters. Analysis of model dynamics leads to conclusion that apparently intentional behaviour can emerge in population consisted of simple agents lacking ability to make strategic decisions.
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