FEMLAB - KTH

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5.9 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 6 Conclusion 22 References 24 List of Abbreviations 25
Chapter 1 Introduction The aim of this work is to develop a mathematical model for the in vitro chemical reactions and diffusion of carcinogenic compounds in cells, and then create a computer programme based on the model. Consequently, by using different parameters the programme will enable us to carry out these experiments virtually, and thus predict the risk of cancer in living humans and animals. The primary carcinogenic substrate, in the form of diol epoxides (C), is initially outside the cell. Outside the cell, some of this substrate reacts with water to form tetrols (U), which do not cause cancer, although it diffuses everywhere in the cell. When the remaining substrate C diffuses through the outer membrane of the cell, it still reacts with water within the cytoplasm, while some of it is converted into glutathione conjugates (B) by an enzyme called GST . B does not cause cancer either, but remains in the cytoplasm, where it is pumped out. The remaining C will reach the nucleus, where it still reacts with water in the nucleus to form U, as well as with DNA to form DNA adducts (A). It is this A that causes cancer. It will stay in the nucleus without diffusing into the other parts of the cell. Each cell in the cell culture used in the study is surrounded by about 168 times its volume of medium. The substrate was then added in the medium for the reactions and diffusion to begin. There are no reactions in the membranes, or so-called lipid compartment of the cell. Reaction only takes place in the aqueous compartment of the cell: In the cytoplasm the reaction of substrate C with water is slow but the enzymatic reaction is much faster. In the nucleus, the reaction of C with DNA is the same rate as the reaction with water in the cytoplasm. Figure 1.1 illustrates the diffusion and reactions in and out of a cell. The partition coefficient, Kp, which is the equilibrium ratio of the concentration C or U between any aqueous compartment of the cell and its neighbouring lipid compartment, is 1 × 10 −3 . Kp depends on the substrate. The complexity of this work lies on the complex geometry, as well as the fact 1
Page 1 and 2: Mathematical Modelling and Numerica
Page 3 and 4: Abstract In order to shed more ligh
Page 5: Contents 1 Introduction 1 2 The Phy
Page 9 and 10: Chapter 2 The Physical Problem and
Page 11 and 12: Ci + water −→ Ui at rate kiCi (
Page 13 and 14: Chapter 3 Scaling and Reformulation
Page 15 and 16: Chapter 4 Simplification of problem
Page 17 and 18: and since ▽ 2 φ is constant over
Page 19 and 20: 4.3 Solving for concentration; Frac
Page 21 and 22: Chapter 5 Model Implementation with
Page 23 and 24: Figure 5.1. The computational Domai
Page 25 and 26: Physical subdomain Femlab Subdomain
Page 27 and 28: Figure 5.3. C in solution plotted a
Page 29 and 30: Figure 6.1. Concentration of A in t
Page 31: List of Abbreviations A . . . . . .

FEMLAB - KTH

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