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Computational Modeling of Reaction and Diffusion Processes in Mammalian Cell
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
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: urn:nbn:se:kth:diva-93466ISBN: 978-91-7501-315-2 (print)OAI: oai:DiVA.org:kth-93466DiVA: diva2:516283
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
List of papers
1. A Method for Efficient Calculation of Diffusion and Reactions of Lipophilic Compounds in Complex Cell Geometry
Open this publication in new window or tab >>A Method for Efficient Calculation of Diffusion and Reactions of Lipophilic Compounds in Complex Cell Geometry
Show others...
2011 (English)In: PLoS ONE, ISSN 1932-6203, E-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.

Keyword
POLYCYCLIC AROMATIC-HYDROCARBONS, REGION DIOL EPOXIDES, BREAST-CANCER CELLS, GLUTATHIONE TRANSFERASES, ELECTRON-MICROSCOPY, MEMBRANES, CONJUGATION, METABOLISM, ACTIVATION, TOPOTECAN
National Category
Health Sciences
Identifiers
urn:nbn:se:kth:diva-41300 (URN)10.1371/journal.pone.0023128 (DOI)000294680800004 ()2-s2.0-80052334702 (Scopus ID)
Funder
Swedish Research CouncilSwedish e‐Science Research Center
Note
QC 20110927Available from: 2011-09-27 Created: 2011-09-26 Last updated: 2017-12-08Bibliographically approved
2. On the numerical approximation of drug diffusion in complex cell geometry
Open this publication in new window or tab >>On the numerical approximation of drug diffusion in complex cell geometry
2009 (English)In: Proceedings of the 6th International Conference on Frontiers of Information Technology, FIT '09, Abbottabad, 2009Conference paper, Published paper (Other academic)
Abstract [en]

The mathematical modeling of a mammalian cell is a very tedious work due to its very complex geometry. Especially, taking into account the spatial distribution and the inclusion of lipophilic toxic compounds greatly increases its complexity. The nonhomogeneity and the different cellular architecture of the cell certainly affect the diffusion of these compounds. The complexity of the whole system can be reduced by a homogenization technique. To see the effect of these compounds on different cell architectures, we have implemented a mathematical model. The work has been done in 2-dimensional space. The simulation results have been qualitatively verified using compartmental modeling approach. This work can be extended with a more complex reaction-diffusion system and to 3-dimensional space as well. Copyright 2009 ACM.

Place, publisher, year, edition, pages
Abbottabad: , 2009
Keyword
Approximation of complex geometry, Homogenization, Metabolism in biological cells, Reaction-Diffusion system, 3-dimensional, Cell architectures, Cell geometries, Cellular architecture, Compartmental modeling, Complex geometries, Complex reactions, Dimensional spaces, Drug diffusion, Homogenization techniques, Mammalian cells, Mathematical modeling, Nonhomogeneity, Numerical approximations, Reaction diffusion systems, Simulation result, Spatial distribution, Toxic compounds, Whole systems, Diffusion in liquids, Dynamic models, Homogenization method, Information technology, Mammals, Metabolism, Computational geometry
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-32389 (URN)10.1145/1838002.1838021 (DOI)2-s2.0-77956295910 (Scopus ID)9781605586427 (ISBN)
Note
QC 20110413Available from: 2011-04-13 Created: 2011-04-13 Last updated: 2012-04-19Bibliographically approved
3. Influence of Biological Cell Geometry on Reaction and Diffusion Simulation
Open this publication in new window or tab >>Influence of Biological Cell Geometry on Reaction and Diffusion Simulation
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:nbn:se:kth:diva-93462 (URN)
Funder
Swedish e‐Science Research Center
Note

QC 20120418

Available from: 2012-04-17 Created: 2012-04-17 Last updated: 2013-04-09
4. In silico Modeling of Intracellular Diffusion and Reaction of Benzo[a]pyrene Diol Epoxide
Open this publication in new window or tab >>In silico Modeling of Intracellular Diffusion and Reaction of Benzo[a]pyrene Diol Epoxide
Show others...
2012 (English)Report (Other academic)
Abstract [en]

Several studies has suggested that glutathione conjugation of polycyclicaromatic hydrocarbons (PAHs) catalyzed by glutathione transferases (GSTs)are important factors in protecting cells against toxicity and DNA damagederived from these compounds. To further characterize the intracellular dynamicsof PAH DEs and the role of GSTs in protection against DNA damage,we recently developed a PDE model using techniques for mathematicalhomogenization (Dreij K et al. PLoS One 6(8), 2011). In this study, wewanted to further develop our model by benchmarking against results fromfour V79 cell lines; control cells and cells overexpressing human GSTs A1-1, M1-1 and P1-1. We used an approach of global optimization of the parametersdescribing the diffusion and reaction of the ultimate carcinogenic PAHmetabolite benzo[a]pyrene diol epoxide to fit measured values from the fourV79 cell lines. Numerical results concerning the formation of glutathioneconjugates and hydrolysis were in good agreement with results from measurementsin V79 cell culture. Cellular results showed significant protectionby GST expression against formation of DNA adducts with more than 10-fold reduced levels compared to control cells. Results from the model usingglobally optimized parameters showed that the model cannot predict theprotective effects of GSTs. Extending the model to also include effects fromprotein interactions and GST localization showed the same discrepancy. Insummary, the results show that we have an incomplete understanding of theintracellular dynamics of the interaction between BPDE and GST that warrantsfurther investigation and development of the model.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2012. 28 p.
Series
TRITA-NA, 2012:3
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-93464 (URN)
Funder
Swedish e‐Science Research Center
Note

QC 20120418

Available from: 2012-04-17 Created: 2012-04-17 Last updated: 2013-04-09Bibliographically approved
5. Mathematical Modeling of Reaction and Diffusion Systems in a Cell Including Surface Reactions on the Cytoplasmic Membranes
Open this publication in new window or tab >>Mathematical Modeling of Reaction and Diffusion Systems in a Cell Including Surface Reactions on the Cytoplasmic Membranes
2012 (English)Report (Other academic)
Abstract [en]

Benzo[a]pyrene (BP) is a toxic polycyclic aromatic hydrocarbon (PAH) whichis found in our environment. These BPs are metabolized to benzo[a]pyrene diol(BPD) by enzymes bound to the cytoplasmic membranes e.g. members of thecytochrome P450 protein family and epoxide hydrolyses. BPDs are further metabolizedto two stereochemical variants of Benzo[a]pyrene diol expoxide (BPDE) bythe cytochrome P450 family of proteins. These are the two steps of metabolismcategorized as Phase I. In Phase II, BPDEs are further metabolized by soluble enzymesin the cytoplasm e.g. members of the glutathione transferase protein familyto GSH conjugates. BPDE can also diffuse into the cellular nucleus and reactwith DNA forming mutagenic DNA adducts. The formation of GSH conjugatesand DNA adducts, was earlier studied by us by developing a mathematical modeldescribing the intracellular reaction and diffusion of lipophilic PAHs taking intoaccount the partitioning phenomenon (Dreij K et al. PLoS One 6(8), 2011). In thispaper part of Phase I metabolism i.e formation of BPDE metabolites, will be addedto the model, thus enhancing the previous model. These cytochrome P450 reactionstake place on the intracellular membranes, and are modeled as a membranesurface reaction within the cytoplasm using the standard process of adsorption anddesorption. The effective equations are derived using iterative homogenization forthe numerical treatment of the cytoplasm including surface effects. The numericalresults of some of the species have been qualitatively verified against in vitroresults found in the literature.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2012. 24 p.
Series
TRITA-NA, 2012:4
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-93465 (URN)
Funder
Swedish e‐Science Research Center
Note

QC 20120418

Available from: 2012-04-17 Created: 2012-04-17 Last updated: 2014-01-29Bibliographically approved

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Citation style
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  • modern-language-association-8th-edition
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  • en-US
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Output format
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