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Article

Mathematical modeling for enzyme inhibitors with slow and fast subsystems

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Pages 442-449 | Received 23 Jul 2020, Accepted 18 Oct 2020, Published online: 10 Nov 2020

References

  • Akgül, A., Khoshnaw, S. H., & Rasool, H. M. (2020). Minimizing cell signalling pathway elements using lumping parameters. Alexandria Engineering Journal, 59(4), 2161–2169. doi:10.1016/j.aej.2020.01.041
  • Ali, M., Hamza, S., Aldila, D., Sultan, F., Mustafa, S., & Shahzad, M. (n.d.). Evaluation of steady-state to identify the fast-slow completion-route in the multi-route reaction mechanism. 1–6. doi:10.1007/s13204-020-01455-2.
  • Almeida, R. (2018). Analysis of a fractional SEIR model with treatment. Applied Mathematics Letters, 84, 56–62. doi:10.1016/j.aml.2018.04.015
  • Area, I., Batarfi, H., Losada, J., Nieto, J.J., Shammakh, W., & Torres, Á. (2015). On a fractional order Ebola epidemic model. Advances in Difference Equations, 2015(1). doi:10.1186/s13662-015-0613-5
  • Atangana, A., & Alabaraoye, E. (2013). Solving a system of fractional partial differential equations arising in the model of HIV infection of CD4+ cells and attractor one-dimensional Keller–Segel equations. Advances in Difference Equations, 2013(1). doi:10.1186/1687-1847-2013-94
  • Atangana, A., & Alqahtani, R.T. (2016). Modelling the spread of river blindness disease via the caputo fractional derivative and the beta-derivative. Entropy, 18(2), 40. doi:10.3390/e18020040
  • Atangana, A., & Goufo, E. F. D. (2014). On the mathematical analysis of Ebola hemorrhagic fever: Deathly infection disease in West African countries. BioMed Research International, 2014, 261383–261387. doi:10.1155/2014/261383
  • Atangana, A., Goufo, D., & Franc, E. (2014). Computational analysis of the model describing HIV infection of CD4 + T cells. BioMed Research International, 2014, 618404. doi:10.1155/2014/618404
  • Baker, R. E. (2011). Mathematical biology and ecology lecture notes. University of Oxford, Oxford.
  • Bartocci, E., & Lió, P. (2016). Computational modeling, formal analysis, and tools for systems biology. PLoS Computational Biology, 12(1), e1004591. doi:10.1371/journal.pcbi.1004591
  • Briggs, G. E., & Haldane, J. B. (1925). A note on the kinetics of enzyme action. The Biochemical Journal, 19(2), 338–339. doi:10.1042/bj0190338
  • Eilertsen, J., & Schnell, S. (2020). The quasi-steady-state approximations revisited: Timescales, small parameters, singularities, and normal forms in enzyme kinetics. Mathematical Biosciences, 325, 108339. doi:10.1016/j.mbs.2020.108339
  • Fang, X., Wallqvist, A., & Reifman, J. (2009). A systems biology framework for modeling metabolic enzyme inhibition of Mycobacterium tuberculosis. BMC Systemic Biology, 3(1), 92. doi:10.1186/1752-0509-3-92
  • Fenichel, N. (1979). Geometric singular perturbation theory for ordinary differential equations. Journal of Differential Equations, 31(1), 53–98. doi:10.1016/0022-0396(79)90152-9
  • Frenzen, C. L., & Maini, P. K. (1988). Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme–substrate ratios. Journal of Mathematical Biology, 26(6), 689–703. doi:10.1007/BF00276148
  • Gan, Q., Allen, S.J., & Taylor, G. (2003). Kinetic dynamics in heterogeneous enzymatic hydrolysis of cellulose: An overview, an experimental study and mathematical modelling. Process Biochemistry, 38(7), 1003–1018. doi:10.1016/S0032-9592(02)00220-0
  • Giersch, C. (2000). Mathematical modelling of metabolism. Current Opinion in Plant Biology, 3 (3), 249–253. doi:10.1016/S0958-1669(00)00079-3
  • Gombert, A.K., & Nielsen, J. (2000). Mathematical modelling of metabolism. Current Opinion in Biotechnology, 11(2), 180–186. doi:10.1016/S0958-1669(00)00079-3
  • Heineken, F. G., Tsuchiya, H. M., & Aris, R. (1967). On the mathematical status of the pseudo-steady state hypothesis of biochemical kinetics. Mathematical Biosciences, 1(1), 95–113. doi:10.1016/0025-5564(67)90029-6
  • Ingalls, B. (2012). Mathematical modelling in systems biology: An introduction. University of Waterloo, Waterloo.
  • Jones, C. K. (1995). Geometric singular perturbation theory. Dynamical Systems. Lecture Notes in Mathematics, 1609, 44–118. doi:10.1007/BFb0095239
  • Kang, H. W., KhudaBukhsh, W. R., Koeppl, H., & Rempała, G. A. (2019). Quasi-steady-state approximations derived from the stochastic model of enzyme kinetics. Bulletin of Mathematical Biology, 81(5), 1303–1336. doi:10.1007/s11538-019-00575-3
  • Kapteijn, F., Gascon, J., & Nijhuis, T. A. (2018). Chemical kinetics of catalyzed reactions. Catalysis: An integrated textbook for students. doi:10.1007/978-1-4020-4547-9_6
  • Khazaaleh, M. (2018). Two reduction methods to simplify complex ODE mathematical models of biological networks and a case study: The G1/S checkpoint/DNA-damage signal transduction pathways [Doctoral dissertation]. Lincoln University, Lincoln.
  • Khoshnaw, S. H. (2013). Iterative approximate solutions of kinetic equations for reversible enzyme reactions. Natural Science, 05(06), 740–755. doi:10.4236/ns.2013.56091
  • Khoshnaw, S.H.A. (2015b). Reduction of a kinetic model of active export of importins. Dynamical Systems, Differential Equations & Applications, 705–722. doi:10.3934/proc.2015.0705
  • Khoshnaw, S. H. A., Mohammad, N. A., & Salih, R. H. (2017). Identifying critical parameters in SIR model for spread of disease. Open Journal of Modelling & Simulation, 05(01), 32–46. doi:10.4236/ojmsi.2017.51003
  • Khoshnaw, S. H. A., & Rasool, H. M. (2019). Model reduction for non-linear protein translation pathways using slow and fast subsystems. Zanco Journal of Pure & Applied Sciences, 31(2), 14–24. doi:10.21271/zjpas.31.2.3
  • Khoshnaw, S. H. (2015a). Model reductions in biochemical reaction networks (PhD thesis). University of Leicester, Leicester.
  • Khoshnaw, S. H., & Rasool, H. M. (2019). Mathematical Modelling for complex biochemical networks and identification of fast and slow reactions. The international conference on mathematical and related sciences (pp. 55–69). Antalya: Springer. doi:10.1007/s13204-020-01455-2
  • Klonowski, W. (1983). Simplifying principles for chemical and enzyme reaction kinetics. Biophysical Chemistry, 18(2), 73–87. doi:10.1016/0301-4622(83)85001-7
  • Kot, M. (2001). Elements of mathematical ecology. Cambridge: Cambridge University Press.
  • Lawson, D., & Glenn, M. (2008). An introduction to mathematical modeling. Bioinformatics & Statistics Scotland, 3–13.
  • Li, B., & Li, B. (2013). Quasi-steady-state laws in reversible model of enzyme kinetics. Journal of Mathematical Chemistry, 51(10), 2668–2686. doi:10.1007/s10910-013-0229-5
  • Li, B., Shen, Y., & Li, B. (2008). Quasi-steady-state laws in enzyme kinetics. The Journal of Physical Chemistry: A, 112(11), 2311–2321. doi:10.1021/jp077597q
  • López Zazueta, C., Bernard, O., & Gouzé, J. L. (2019). Dynamical reduction of linearized metabolic networks through quasi steady state approximation. AIChE Journal, 65(1), 18–31. doi:10.1002/aic.16406
  • Moayyedi, M. K. (2019). Extension ability of reduced order model of unsteady incompressible flows using a combination of POD and Fourier modes. Journal of Applied & Computational Mechanics, 5(1), 1–12. doi:10.22055/JACM.2018.24099.1171
  • Mohan, C., Long, K. D., & Mutneja, M. (2013). An introduction to inhibitors and their biological applications, pp. 3–13.
  • Murray, J. D. (2001). Mathematical biology: I: An introduction. Berlin: Springer.
  • Özöğür, S. (2009). Mathematical modelling of enzymatic reactions, simulation and parameter estimation. Saarbrucken: VDM Verlag.
  • Palsson, B.O., Palsson, H., & Lightfoot, E.N. (1985). Mathematical modelling of dynamics and control in metabolic networks. III. Linear reaction sequences. Journal of Theoretical Biology, 113(2), 231–259. doi:10.1016/S0022-5193(85)80226-5
  • Pedersen, M. G., Bersani, A. M., & Bersani, E. (2008). Quasi steady-state approximations in complex intracellular signal transduction networks: A word of caution. Journal of Mathematical Chemistry, 43(4), 1318–1344. doi:10.1007/s10910-007-9248-4
  • Rahmanzadeh, M., Asadi, T., & Atashafrooz, M. (2020). The development and application of the RCW method for the solution of the Blasius problem. Journal of Applied & Computational Mechanics, 6(1), 105–111. doi:10.22055/JACM.2019.28250.1469
  • Schnell, S., & Maini, P. K. (2002). Enzyme kinetics far from the standard quasi-steady-state and equilibrium approximations. Mathematical & Computer Modelling, 35(1–2), 137–144. doi:10.1016/S0895-7177(01)00156-X
  • Segel, L. A. (1988). On the validity of the steady state assumption of enzyme kinetics. Bulletin of Mathematical Biology, 50(6), 579–593. doi:10.1016/S0092-8240(88)80057-0
  • Segel, I. H., & Martin, R. L. (1988). The general modifier (“allosteric”) unireactant enzyme mechanism: Redundant conditions for reduction of the steady state velocity equation to one that is first degree in substrate and effector. Journal of Theoretical Biology, 135(4), 445–453. doi:10.1016/s0022-5193(88)80269-8
  • Segel, L. A., & Slemrod, M. (1989). The quasi-steady-state assumption: A case study in perturbation. SIAM Review, 31(3), 446–477. doi:10.1137/1031091
  • Shin, S. Y., & Nguyen, L. K. (2017). Dissecting cell-fate determination through integrated mathematical modeling of the ERK/MAPK signaling pathway. In ERK signaling. Totowa Press: Humana Press.
  • Snowden, T. J., van der Graaf, P. H., & Tindall, M. J. (2017). Methods of model reduction for large-scale biological systems: A survey of current methods and trends. Bulletin of Mathematical Biology, 79(7), 1449–1486. doi:10.1007/s11538-017-0277-2
  • Snowden, T. J., van der Graaf, P. H., & Tindall, M. J. (2018). Model reduction in mathematical pharmacology: Integration, reduction and linking of PBPK and systems biology models. Journal of Pharmacokinetics & Pharmacodynamics, 45(4), 537–555. doi:10.1007/s10928-018-9584-y
  • Sontag, E. D. (2014). Lecture notes on mathematical systems biology. New Brunswick: Rutgers University.
  • Volk, L., Richardson, W., Lau, K. H., Hall, M., & Lin, S. H. (1977). Steady state and equilibrium approximations in reaction kinetics. Journal of Chemical Education, 95(2), 95–97. doi:10.1021/ed054p95