Printer Friendly


Byline: N. Abid Q. A. Chaudhry M. Gul and S. Zahid

ABSTRACT:The manifold cell organization permitted extraneous hydrophobic compounds to react with the existing compounds inside the cell. The carcinogenic and lipophilic environmental toxins PAH provoked detrimental and noxious compounds in the interior of the cell. The cell sustained reaction and diffusion mechanism with those lipophilic compounds. The heterogeneous cell configuration grew into mosaic by virtue of the membranous architectures in the vicinity of the cytoplasm. The establishment of those conglomerate cytoplasmic membranous organelles in 2D axisymmetric geometry was absurd therefore 3D geometry was constructed. The model had been formulated in ComsolMultiphysics by adopting the homogenization approach. The counter collation of the simulated results of 3D and 2D axisymmetric model were investigated. The commendable affinity demonstrated by the results encouraged to extend the model by introducing diminutive cytoplasmic organelles in addition with more convoluted reaction chains.

Key words:Lipophilic Reaction-diffusion mechanism Polycyclicaromatic hydrocarbons Heterogeneous.


The primitive entity of the mosaic and minute composition of living organisms christened as cell are microscopic as they ranges few micrometers. Intracellular membranes establish the heterogeneous cell architecture. Despite the fact that the cell itself is few micrometers it also accommodates numerous miniature and complicated architectures. The primary components of cell are: cellular membrane cytoplasm nuclear membrane and nucleus. The tiny organelles i.e. mitochondria endoplasmic reticulum golgi apparatus etc. inhabit the cytoplasm embedded in aqueous region (Campbellet al. 2006) attributes also membranous in architecture in consequence of which the mathematical modeling of the heterogeneous cell eventually turns out complex provided that the above mentioned complex cytoplasmic membranous structures i.e. the tiny organelles inside the cytoplasm are comprehended the model will turn out more intricate.

The conferred model is inquired by the reaction and diffusion of Po1lycyclic Aromatic Hydrocarbons in cell. 2D axisymmetric model was promoted by (Dreij et al. 2011) comprehending reaction- diffusion mechanism. Taking into account the earlier model the subsequent model is progressed to 3D inclusive of the entire processes incorporated by (Dreij et al. 2011). MATERIALS AND METHODS

In the model discussed in this paper some basic assumptions were used the details of which can be found in (Dreij et al. 2011). Homogenization approach was emphasized for the cytoplasm in the interest to attenuate the intricacy of the model. Partial Differential Equations were formulated and were solved in the software named ComsolMultiphysics along with the geometry. Moreover the results of the preceding (2D axisymmetric) and subsequent (3D) models were compared adjacently for the affirmation of the commenced 3D model.

The nature was encompassed by peculiar environmental toxins and lethal compounds among which PAHs were most familiar. These lipophilic attributed environmental toxins acknowledged the cell to react with DNA of the cell where it formed DNA adduct. When coal oil fuel and natural gas encountered partial burning it yielded PAHs which were carcinogenic (Moiz and George 1995). In extra-cellular medium cytoplasm and nucleus PAH diolepoxide endured the hydrolysis process resulting in the production of PAH tetrol. Unaccompanied by the reaction the membranes sustained alone the diffusion process where themembranes were partitioned by partition coefficient. Thecytosol permittedPAH diol epoxide to react with glutathione conjugate (GSH) giving rise to diol epoxide conjugates (Dreijet al. 2011). Involving the DNA inside nucleus PAH diolepoxide counteredwith the DNA forming DNA adduct which can alter the behavior of DNA and can be the cause of destruction of the cell (Thakkeret al.1985).

Table-1.Showing mathematical symbols/notations

###Symbol###Description/ Chemical Name

###L###PAH diol epoxide



###PAH tetrol

###Glutathione conjugate

###Y###DNA adduct



The term eff " used in the subscripts of the terms of above equations denoted the effective terms obtained by homogenization procedure the details of which can be found in the study conducted by (Dreij et al. 2011).

Initial conditions: At initial time we assumed that only L was added to the system where its value in extra- cellular region was non-zero. The initial condition is presented below.Equation

The quantitative model along with the boundary and initial conditions as discussed abovewere formulated in Comsol Multiphysics 3.5 and Reaction Engineering Lab 1.5. This software worked on the principles of Finite Element Method (Chaskalovic 2008). The model was generated in Chemical Engineering Module. The Direct Pardiso method was used for solving the problem.


The mathematical model wasdesigned in Comsol Multiphysics 3.5 and Reaction Engineering Lab 1.5 the details of which were described in previous section. The geometric and chemical

Table-2. Geometric constants


Volume of one cell[m3]###3x10-15

Volume of nucleus[m3]###7.5x10-16

Volume of cell medium[m3]###10-5

Thickness of membrane [m]###1.127x10-8

Radius of cell [m]###8.947x10-6

constantsderived here are in line with studies carried out by (Dreij et al. 2011; JernstrAlm et al. 1996;Sundberg et al. 2002) and are summarized in Table-2 and 3 respectively.

Table-3. Chemical Constants for the Model


D1###Diffusion coefficient in extracellular medium [m2s-1]###10-9

D2D4###Diffusion coefficient in cell/nuclear membrane [m2s-1]###10-12

D5###Diffusion coefficient in nucleus [m2s-1]###2.5x10-10

KpL###Partition coefficient for BPDE###1.2x10-3

KpR###Partition coefficient for BPT###8.3x10-3

kR###Solvolytic reactivity forming Z [s-1]###7.7x10-3

kY###DNA adduct formation rate [s-1]###6.2x10-3

kG###Formation rate of J###3.7x103

The numerical results were computed for a time span of 600sec. The results obtained from the 3D model discussed in this paper were compared with the numerical results of 2D axi-symmetric model which were found from (Dreij et al. 2011). Figure-2 showed the comparison of degradation of PAH diol epoxides in extracellular medium of both models.Figure-3 represented the comparison of the formation of PAH tetrols whereas in Figure-4 the comparison of PAH conjugated in nucleus was seen. Earlier the study of computing the PAH diol epoxides in extracellular medium PAH tetrols in extra and intra-cellular medium and glutathione conjugate in cytoplasm was carried out by (Chaudhry et al. 2014) using the technique of differential transformation method but in the current study the model developed was spatially distributed which resembled the in-vitro and in-vivo situation.

The bracketed letters p and n in the legends of the graphs represented the preceding 2D axi-symmetric model and subsequent 3D model respectively. L (p) R (p) and G (p) served as the results of 2D axi-symmetric in graph while L (n) R (n) and G (n) served as the graphs of 3D. The adjacent comparisons of graphs of both the models were coincidental.

The meager difference in the value of glutathione conjugate in graph in Figure-4 exhibitedmight be due to the modification in the dimension or the mesh establishment. These results represented the commendable affinity which stated that the model was valid for future consideration.

Concerning the former model we can extend it in either ways by recognizing these organelles as separate subdomains or inserting more reactions or membranes. To find the optimal parameter for the model using optimization approach is an important work to be done as discussed by (Dreij et al. 2012; Chaudhryet al. 2009).


Campbell N. A. B. Williamson R. J. Heyden. Biology: Exploring Life.Pearson Prentice Hall Boston Massachusetts (2006). Chaskalovic J. Finite element methods for engineering sciences. Springer Berlin Heidelberg (2008).

Chaudhry N. A. M. O. Ahmad and J. Ali. Constraint handling in genetic algorithms by a 2-parameter- exponential penalty function approach. Pak. J. Sci 61(3): 122-129 (2009).

Chaudhry Q. A. M. O. Ahmad F. Ashraf R. Ashraf and N. A. Chaudhry. Mathematical modeling of reaction-diffusion mechanism of PAH diol epoxides in a cell. Pak. J. Sci 66(3): 209-213 (2014). Thakker D.R. H. Yagi W. Levin A.W. Wood A.H. Conney and D. M. Jerina. Polycyclic aromatic hydrocarbons: Metabolic activation to ultimate carcinogens. Academic Press UK (1985). Dreij K. Q. A. Chaudhry B. JernstrAlm R. Morgenstern and M. Hanke. A Method for Efficient Calculation of Diffusion and Reactions of Lipophilic Compounds in Complex Cell Geometry. PLoS ONE 6(8): e23128 (2011).

Dreij K. Q. A. Chaudhry J. Zhang K. Sundberg B. JernstrAlm M. Hanke and R. Morgenstern. In silico modeling of the intracellular dynamics of polycyclic aromatic hydrocarbons. Toxicol Lett 211: S60S61 (2012). JernstrAlm B. M. Funk H. Frank B. Mannervik and A.

Seidel. Glutathione Stransferase A1-1-catalysed conjugation of bay and fjord region diol epoxides or polycyclic aromatic hydrocarbons with glutathione. Carcinogenesis 17(7): 1491 1498 (1996).

Moiz M. and J. George. Toxicological Profile for Polycyclic Aromatic Hydrocarbons. Revised ed. ATSDR (1995). Sundberg K. K. Dreij A. Seidel and B. JernstrAlm.

Glutathione conjugation and DNA adduct formation of dibenzo[al]pyrene and benzo[a]pyrene diol epoxides in V79 cells stably expressing different human glutathione transferases. Chem Res Toxicol 15(2): 170179 (2002).
COPYRIGHT 2014 Asianet-Pakistan
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2014 Gale, Cengage Learning. All rights reserved.

Article Details
Printer friendly Cite/link Email Feedback
Publication:Pakistan Journal of Science
Date:Dec 31, 2014

Terms of use | Privacy policy | Copyright © 2019 Farlex, Inc. | Feedback | For webmasters