Mathematical Modeling of Biochemical Reactions Under Random Effects
Mathematical Modeling of Biochemical Reactions Under Random Effects
In this study, random effects are added to the parameters of the deterministic Biochemical ReactionModel (BRM) to form a system of random differential equations. A random model is built with these equations todescribe the random behavior of biochemical reactions. Gaussian and Beta distributions are used for the randomeffect terms. Numerical characteristics of the random model are investigated using the simulations of the randomequation system. Characteristics of the model components under Gaussian and Beta distributed effects are comparedand comments are made on the difference in these two cases. The results are also used to explore the differences inthe deterministic and random models of BRM and to study the random behavior of the model components.
Keywords:
Random Differential Equation, Biochemical Reaction Model Beta Distribution, Gaussian Distribution, Random Effect, Runge Kutta Method,
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- Batiha, A., Batiha, B., Di erential transformation method for a reliable treatment of the nonlinear biochemical reaction model, Advanced Studied in Biology, 3(2011), 355–360. 2
- Bekiryazici, Z., Merdan, M., Kesemen, T., Khaniyev, T., Random modeling of biochemical reactions under Gaussian random e ects, Abstracts Book: International Conference on Mathematics and Mathematics Education, (2016), 192–193. 4.1
- Feller,W., An Introduction to Probability Theory and Its Applications, Advanced Studied in Biology, JohnWiley & Sons Inc., New York, 1968. 3.2
- Goh, S.M., Noorani, M.S.M., Hashim, I., Introducing variational iteration method to a biochemical reaction model, Nonlinear Analysis: Real World Applications, 11(2010), 2264–2272. 2
- Goutsias, J., Classical versus stochastic kinetics modeling of biochemical reaction systems, Biophysical Journal, 92(2007), 2350–2365. 3
- Haskett, J.D., Pachepsky, Y.A., Acock, B., Use of the beta distribution for parameterizing variability of soil properties at the regional level for crop yield estimation, Agricultural Systems, 48(1995), 73–86. 3.2
- Kierzek, A.M., STOCKS: Stochastic kinetic simulations of biochemical systems with Gillespie algorithm, Bioinformatics, 18(2002), 470–481. 3
- Kurtz, T.G., The Relationship between stochastic and deterministic models for chemical reactions, The Journal of Chemical Physics, 57(1972), 2976. 3
- Malik, S.A., Qureshi, I.M., Amir, M., Haq, I., Numerical solution to nonlinear biochemical reaction model using hybrid polynomial basis di erential evolution technique, Advanced Studied in Biology, 6(2014), 99–113. 2
- Merdan, M., Khaniyev, T., On the behavior of solutions under the influence of stochastic e ect of avian-human influenza epidemic model, International Journal of Biotechnology and Biochemistry, 4(2008), 75–100. 3
- Michaelis, L., Menten, M.L., Die kinetik der interwirkung, Biochemische Zeitschrift, 49(1913), 333. 1, 2
- Sen, A. K., An Application of the adomian decomposition method to the transient behavior of a model biochemical reaction, Journal of Mathematical Analysis and Applications, 131(1988), 232–245. 2, 4.3.1
- Soong, T.T., Random Di erential Equations in Science and Engineering, Academic Press Inc., New York, 1973. 3
- Suleiman, M.Y., Hlaing Oo,W.M.,Wahab, M.A., Zakaria, A., Application of beta distribution to Malaysian sunshine data, Renewable Energy, 18(1999), 573–579. 3.2
- Wiley, J.A., Herschkorn, S.J., Padian, N.S., Heterogeneity in the probability of HIV transmission per sexual contact: The case of male-to-female transmission in penile–vaginal intercourse, Statistics in Medicine, 8(1989), 93–102. 3.2
- Yildirim, A., Gokdogan, A., Merdan, M., Numerical approximations to solution of biochemical reaction model, International Journal of Chemical Reactor Engineering, 9(2011). 2, 2, 3, 4.3.3
- ISSN: 2148-1830
- Yayın Aralığı: 2
- Başlangıç: 2013
- Yayıncı: MATEMATİKÇİLER DERNEĞİ