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A Method for Efficient Calculation of Diffusion and Reactions of Lipophilic Compounds in Complex Cell Geometry
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA. (Numerical Analysis)
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2011 (English)In: PLoS ONE, ISSN 1932-6203, Vol. 6, no 8, e23128- p.Article in journal (Refereed) Published
Abstract [en]

A general description of effects of toxic compounds in mammalian cells is facing several problems. Firstly, most toxic compounds are hydrophobic and partition phenomena strongly influence their behaviour. Secondly, cells display considerable heterogeneity regarding the presence, activity and distribution of enzymes participating in the metabolism of foreign compounds i.e. bioactivation/biotransformation. Thirdly, cellular architecture varies greatly. Taken together, complexity at several levels has to be addressed to arrive at efficient in silico modelling based on physicochemical properties, metabolic preferences and cell characteristics. In order to understand the cellular behaviour of toxic foreign compounds we have developed a mathematical model that addresses these issues. In order to make the system numerically treatable, methods motivated by homogenization techniques have been applied. These tools reduce the complexity of mathematical models of cell dynamics considerably thus allowing to solve efficiently the partial differential equations in the model numerically on a personal computer. Compared to a compartment model with well-stirred compartments, our model affords a more realistic representation. Numerical results concerning metabolism and chemical solvolysis of a polycyclic aromatic hydrocarbon carcinogen show good agreement with results from measurements in V79 cell culture. The model can easily be extended and refined to include more reactants, and/or more complex reaction chains, enzyme distribution etc, and is therefore suitable for modelling cellular metabolism involving membrane partitioning also at higher levels of complexity.

Place, publisher, year, edition, pages
2011. Vol. 6, no 8, e23128- p.
Keyword [en]
National Category
Health Sciences
URN: urn:nbn:se:kth:diva-41300DOI: 10.1371/journal.pone.0023128ISI: 000294680800004ScopusID: 2-s2.0-80052334702OAI: diva2:444061
Swedish Research CouncilSwedish e‐Science Research Center
QC 20110927Available from: 2011-09-27 Created: 2011-09-26 Last updated: 2012-05-24Bibliographically approved
In thesis
1. Computational Modeling of Reaction and Diffusion Processes in Mammalian Cell
Open this publication in new window or tab >>Computational Modeling of Reaction and Diffusion Processes in Mammalian Cell
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

PAHs are the reactive toxic chemical compounds which are present as environmental pollutants. These reactive compounds not only diffuse through the membranes of the cell but also partition into the membranes. They react with the DNA of the cell giving rise to toxicity and may cause cancer. To understand the cellular behavior of these foreign compounds, a mathematical model including the reaction-diffusion system and partitioning phenomenon has been developed. In order to reduce the complex structure of the cytoplasm due to the presence of many thin membranes, and to make the model less computationally expensive and numerically treatable, homogenization techniques have been used. The resulting complex system of PDEs generated from the model is implemented in Comsol Multiphysics. The numerical results obtained from the model show a nice agreement with the in vitro cell experimental results. Then the model was reduced to a system of ODEs, a compartment model (CM). The quantitative analysis of the results of the CM shows that it cannot fully capture the features of metabolic system considered in general. Thus the PDE model affords a more realistic representation. In order to see the influence of cell geometry in drug diffusion, the non-spherical axi-symmetric cell geometry is considered, where we showed that the cellular geometry plays an important role in diffusion through the membranes. For further reduction of complexity of the model, another simplified model was developed. In the simplified model, we used PDEs for the extracellular domain, cytoplasm and nucleus, whereas the plasma and nuclear membranes were taken away, and replaced by the membrane flux, using Fick's Law. We further extended the framework of our previously developed model by benchmarking against the results from four different cell lines. Global optimization techniques are used for the parameters describing the diffusion and reaction to fit the measured data. Numerical results were in good agreement with the in vitro results. For the further development of the model, the process of surface bound reactions were added, thus developing a new cell model. The effective equations were derived using iterative homogenization for this model. The numerical results of some of the species were qualitatively verified against the in vitro results found in literature.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. xiii, 52 p.
Trita-CSC-A, ISSN 1653-5723 ; 2012:03
National Category
Computational Mathematics
urn:nbn:se:kth:diva-93466 (URN)978-91-7501-315-2 (ISBN)
Public defence
2012-05-15, E2, Lindstedsvägen 3, KTH, Stockholm, 10:00 (English)
QC 20120419Available from: 2012-04-19 Created: 2012-04-17 Last updated: 2012-04-19Bibliographically approved

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Chaudhry, Qasim AliHanke, Michael
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