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Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks

Yıl 2022, , 366 - 375, 30.12.2022
https://doi.org/10.47000/tjmcs.901339

Öz

In the biological systems, Monte Carlo approaches are used to provide the stochastic simulation of the chemical reactions. The major stochastic simulation algorithms (SSAs) are the direct method, also known as the Gillespie algorithm, the first reaction method and the next reaction method. While these methods give accurate generation of the results, they are computationally demanding for large complex systems. To increase the computational efficiency of SSAs, approximate SSAs can be option. The approximate methods rely on the leap condition. This condition means that the propensity function during the time interval $ t $ to $[ t+\tau ]$ should not be altered for the chosen time step $\tau$. Here, to proceed with the system's history axis from one time step to the next, we compute how many times each reaction can be realized in each small time interval $\tau$ so that we can observe plausible simultaneous reactions. Hence, this study aims to generate a realistic and close confidence interval for the parameter which denotes the underlying numbers of simultaneous reactions in the system by satifying the leap condition. For this purpose, the poisson $\tau$-leap algorithm and the approximate Gillespie algorithm, as the extension of the Gillespie algorithm, are handled. In the estimation for the associated parameters in both algorithms, we derive their maximum likelihood estimators, moment estimatora and bayesian estimators. From the derivations, we theoretically show that our novel confidence intervals are narrower than the current confidence intervals under the leap condition.

Destekleyen Kurum

Middle East Technical University

Proje Numarası

10282

Kaynakça

  • Demirb\"{u}ken S. and Purut\c{c}uo\u{g}lu V. (2020). Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks. Proceeding of the 4th International Conference on Mathematics, 288-298.
  • Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry, 81(25):2340–2361.
  • Gibson, M. A. and Bruck, J. (2000). Efficient exact stochastic simulation of chemical systems with many species and many channels. Journal of Physical Chemistry, A (104):1876-1889.
  • Gillespie T. and Petzold L.R. Improved Leap-Size Selection for Accelerated Stochastic Simulation. Journal of Chemical Physics, 119, 8229-8234, (2003).
  • Gillespie D. T. (2001). Approximate accelerated stochastic simulation of chemically reacting systems. Journal of Chemical Physics, 115:1716–1733.
  • Gillespie D.T.(2006).Stochastic Simulation of Chemical Kinetics. Annual Review Physical Chemistry, 58:35-55.
  • Lee J. Bain and Max Engelhardt, Introduction to Probability and Mathematical Statistics, 382-383. Duxbury Press, (1992).
  • Purut\c{c}uo\u{g}lu V. and Wit E. (2006).Exact and Approximate Stochastic Simulations of theMAPK Pathway and Comparisons of Simulations Results. Journal of Integrative Bioinformatics, 3, 1-13.
  • Purut\c{c}uo\u{g}lu, V. and Wit, E. (2008). An approximation algorithm based on leap condition for stochastical simulation of biomedical systems. Proceeding of the 4th International Conference ``Inverse problems: Modelling and Simulation", 151-152.
Yıl 2022, , 366 - 375, 30.12.2022
https://doi.org/10.47000/tjmcs.901339

Öz

Proje Numarası

10282

Kaynakça

  • Demirb\"{u}ken S. and Purut\c{c}uo\u{g}lu V. (2020). Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks. Proceeding of the 4th International Conference on Mathematics, 288-298.
  • Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry, 81(25):2340–2361.
  • Gibson, M. A. and Bruck, J. (2000). Efficient exact stochastic simulation of chemical systems with many species and many channels. Journal of Physical Chemistry, A (104):1876-1889.
  • Gillespie T. and Petzold L.R. Improved Leap-Size Selection for Accelerated Stochastic Simulation. Journal of Chemical Physics, 119, 8229-8234, (2003).
  • Gillespie D. T. (2001). Approximate accelerated stochastic simulation of chemically reacting systems. Journal of Chemical Physics, 115:1716–1733.
  • Gillespie D.T.(2006).Stochastic Simulation of Chemical Kinetics. Annual Review Physical Chemistry, 58:35-55.
  • Lee J. Bain and Max Engelhardt, Introduction to Probability and Mathematical Statistics, 382-383. Duxbury Press, (1992).
  • Purut\c{c}uo\u{g}lu V. and Wit E. (2006).Exact and Approximate Stochastic Simulations of theMAPK Pathway and Comparisons of Simulations Results. Journal of Integrative Bioinformatics, 3, 1-13.
  • Purut\c{c}uo\u{g}lu, V. and Wit, E. (2008). An approximation algorithm based on leap condition for stochastical simulation of biomedical systems. Proceeding of the 4th International Conference ``Inverse problems: Modelling and Simulation", 151-152.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Saliha Demirbüken Bu kişi benim 0000-0002-1394-8621

Vilda Purutcuoglu 0000-0002-3913-9005

Proje Numarası 10282
Yayımlanma Tarihi 30 Aralık 2022
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

APA Demirbüken, S., & Purutcuoglu, V. (2022). Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks. Turkish Journal of Mathematics and Computer Science, 14(2), 366-375. https://doi.org/10.47000/tjmcs.901339
AMA Demirbüken S, Purutcuoglu V. Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks. TJMCS. Aralık 2022;14(2):366-375. doi:10.47000/tjmcs.901339
Chicago Demirbüken, Saliha, ve Vilda Purutcuoglu. “Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks”. Turkish Journal of Mathematics and Computer Science 14, sy. 2 (Aralık 2022): 366-75. https://doi.org/10.47000/tjmcs.901339.
EndNote Demirbüken S, Purutcuoglu V (01 Aralık 2022) Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks. Turkish Journal of Mathematics and Computer Science 14 2 366–375.
IEEE S. Demirbüken ve V. Purutcuoglu, “Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks”, TJMCS, c. 14, sy. 2, ss. 366–375, 2022, doi: 10.47000/tjmcs.901339.
ISNAD Demirbüken, Saliha - Purutcuoglu, Vilda. “Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks”. Turkish Journal of Mathematics and Computer Science 14/2 (Aralık 2022), 366-375. https://doi.org/10.47000/tjmcs.901339.
JAMA Demirbüken S, Purutcuoglu V. Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks. TJMCS. 2022;14:366–375.
MLA Demirbüken, Saliha ve Vilda Purutcuoglu. “Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks”. Turkish Journal of Mathematics and Computer Science, c. 14, sy. 2, 2022, ss. 366-75, doi:10.47000/tjmcs.901339.
Vancouver Demirbüken S, Purutcuoglu V. Extension of Leap Condition in Approximate Stochastic Simulation Algorithms of Biological Networks. TJMCS. 2022;14(2):366-75.

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