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Year 2016, Volume: 5 , 8 - 18, 30.12.2016

Abstract

References

  • 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

Mathematical Modeling of Biochemical Reactions Under Random Effects

Year 2016, Volume: 5 , 8 - 18, 30.12.2016

Abstract

In this study, random effects are added to the parameters of the deterministic Biochemical Reaction

Model (BRM) to form a system of random differential equations. A random model is built with these equations to

describe the random behavior of biochemical reactions. Gaussian and Beta distributions are used for the random

effect terms. Numerical characteristics of the random model are investigated using the simulations of the random

equation system. Characteristics of the model components under Gaussian and Beta distributed effects are compared

and comments are made on the difference in these two cases. The results are also used to explore the differences in

the deterministic and random models of BRM and to study the random behavior of the model components.

References

  • 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
There are 16 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Zafer Bekiryazıcı

Mehmet Merdan

Tülay Kesemen

Tahir Khaniyev

Publication Date December 30, 2016
Published in Issue Year 2016 Volume: 5

Cite

APA Bekiryazıcı, Z., Merdan, M., Kesemen, T., Khaniyev, T. (2016). Mathematical Modeling of Biochemical Reactions Under Random Effects. Turkish Journal of Mathematics and Computer Science, 5, 8-18.
AMA Bekiryazıcı Z, Merdan M, Kesemen T, Khaniyev T. Mathematical Modeling of Biochemical Reactions Under Random Effects. TJMCS. December 2016;5:8-18.
Chicago Bekiryazıcı, Zafer, Mehmet Merdan, Tülay Kesemen, and Tahir Khaniyev. “Mathematical Modeling of Biochemical Reactions Under Random Effects”. Turkish Journal of Mathematics and Computer Science 5, December (December 2016): 8-18.
EndNote Bekiryazıcı Z, Merdan M, Kesemen T, Khaniyev T (December 1, 2016) Mathematical Modeling of Biochemical Reactions Under Random Effects. Turkish Journal of Mathematics and Computer Science 5 8–18.
IEEE Z. Bekiryazıcı, M. Merdan, T. Kesemen, and T. Khaniyev, “Mathematical Modeling of Biochemical Reactions Under Random Effects”, TJMCS, vol. 5, pp. 8–18, 2016.
ISNAD Bekiryazıcı, Zafer et al. “Mathematical Modeling of Biochemical Reactions Under Random Effects”. Turkish Journal of Mathematics and Computer Science 5 (December 2016), 8-18.
JAMA Bekiryazıcı Z, Merdan M, Kesemen T, Khaniyev T. Mathematical Modeling of Biochemical Reactions Under Random Effects. TJMCS. 2016;5:8–18.
MLA Bekiryazıcı, Zafer et al. “Mathematical Modeling of Biochemical Reactions Under Random Effects”. Turkish Journal of Mathematics and Computer Science, vol. 5, 2016, pp. 8-18.
Vancouver Bekiryazıcı Z, Merdan M, Kesemen T, Khaniyev T. Mathematical Modeling of Biochemical Reactions Under Random Effects. TJMCS. 2016;5:8-18.