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Influence of Biological Cell Geometry on Reaction and Diffusion Simulation
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).ORCID iD: 0000-0003-4950-6646
2012 (English)Report (Other academic)
Abstract [en]

Mathematical modeling of reaction-diffusion system in a biological cellis an important and difficult task, especially when the chemical compoundsare lipophilic. The difficulty level increases, when we take into account theheterogeneity of the cell, and the variation of cellular architecture. Mathematicalmodeling of reaction-diffusion systems in spherical cell geometryhas earlier been performed by us. In the present paper, we have workedwith non-spherical cell geometry, because the cellular geometry can play animportant role for drug diffusion in the cell. Homogenization techniques,which were earlier applied in the case of a spherical cell model, have beenused for the numerical treatment of the model. This technique considerablyreduces the complexity of the model. To further reduce the complexity ofthe model, a simplified model was also developed. The key idea of this simplifiedmodel has been advocated in Virtual Cell, where PDEs are used forthe extracellular domain, cytoplasm and nucleus, whereas the plasma andnuclear membranes have been taken away, and replaced by membrane flux,using Fick’s Law of diffusion. The numerical results of the non-sphericalcell model have been compared with the results of the spherical cell model,where the numerical results of spherical cell model have already been validatedagainst in vitro cell experimental results. From the numerical results,we conclude that the plasma and nuclear membranes can be protective reservoirsof significance. The numerical results of the simplified model werecompared against the numerical results of our detailed model, revealing theimportance of detailed modeling of membranes in our model.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2012. , 28 p.
Series
TRITA-NA, 2012:2
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-93462OAI: oai:DiVA.org:kth-93462DiVA: diva2:516281
Funder
Swedish e‐Science Research Center
Note

QC 20120418

Available from: 2012-04-17 Created: 2012-04-17 Last updated: 2013-04-09
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.
Series
Trita-CSC-A, ISSN 1653-5723 ; 2012:03
National Category
Computational Mathematics
Identifiers
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)
Opponent
Supervisors
Note
QC 20120419Available from: 2012-04-19 Created: 2012-04-17 Last updated: 2012-04-19Bibliographically approved

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