Biyokimyasal Reaksiyonlar için Stokastik Simülasyon Algoritmalarına Genel Bir Bakış

Öz

Biyolojik bir sistemi anlayabilmek için hangi genlerin/proteinlerin organizmanın neresinde, ne zaman ve nasıl reaksiyonda olduğunu bilmemiz gerekmektedir. Bu kadar detaylı, karmaşık ve metabolik seviyede rassal olan reaksiyonları içeren biyokimyasal bir mekanizmada, hücresel aktivitelerin deneysel olarak ispatlanması, teknolojik imkanların sınırlı olması sebebiyle çoğu kez mümkün olmamakta veya yüksek deney maliyetine sebep olmaktadır. Biyokimyasal modelleme; bir sistemin elemanlarının farklı zaman ve şartlar altındaki durumunu, sistemi oluşturan proteinler ve moleküller arasındaki etkileşimi sistemin bilinen özellikleri yardımıyla ifade etmenin matematiksel yoludur. Bu çalışmada; reaksiyonların nasıl formülize edildiği ve bu reaksiyonlardan oluşan sistemin stokastik modellemelerinin biyoinformatik ve matematiksel biyoloji alanlarında hangi simülasyon algoritmalarıyla yapıldığı tanıtılmaktadır.

Anahtar Kelimeler

• Matematiksel modelleme
• Simülasyon
• Stokastik algoritmalar

An Overview to Stochastic Simulation Algorithms for Biochemical Systems

Öz

In order to understand a biological system, we should know which genes/proteins react together, where, when, and how they react in the organisms. In such a biochemical mechanism which is detailed, complex, and stochastic in metabolic level, the experimental validations of cellular activations cannot be typically applicable due to the current technological limitations or the high expenses of the possible experiments. The biochemical modelling is a mathematical way to describe the elements of a system, their proteomic and metabolic interactions, their states under different time points and various conditions by using the known theories about that system. In this study we review how formalize the biochemical reactions and which simulation algorithms can be performed to stochastically model a system whose components are described by these biochemical reactions in the frameworks of bioinformatics and mathematical biology.

Anahtar Kelimeler

• Mathematical modelling
• Simulation
• Stochastic algorithms

Kaynakça

1. Auger, A., Chatelain, P., Koumoutsakos, P., 2006. R-leaping: Accelerating the stochastic simulation algorithm by reaction leaps.
2. Bower, J. M., Bolouri, H., 2001. Computational modelling of genetic and biochemical networks. Massachusetts Institute of Technology.
3. Brent, R., 2004. A partnership between biology and engineering. Nature Biotechnology, 22:469–482.
4. Cao, Y., Gillespie, D. T., Petzold, L. R., 2005. Avoiding negative populations in explicit poisson Tau-Leaping. Journal of Chemical Physics, 123:054104.1-054104.8.
5. Cao, Y., Li, H., Petzold, L., 2006. Efficient formulation of the stochastic simultion algorithm for chemically reacting system. Journal of Chemical Physics, 121 (9): 4059-4067.
6. Endy, D., Brent, R., 2001. Modelling cellular behaviour. Nature, 409:391–395.
7. Fedoroff, N., Fontana, W., 2002. Genetic networks: Small numbers of big molecules. Science, 297:1129–1131.
8. Gibson, M. A., Bruck, J., 2000. Efficient exact stochastic simulation of chemical systems with many species and many channels. Journal of Physical Chemistry, A(104):1876–1889.

9. Gillespie, D. T., 1977. Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry, 81(25):2340–2361.
10. Gillespie, D. T., 1992. A rigorous derivation of the chemical master equation. Physica A, 188:404–425.
11. Hume, D. A., 2000. Probability in transcriptional regulation and its implications for leukocyte differention and inducible gene expression. Blood, 96:2323–2328.
12. Jong, H. D., 2002. Modeling and simulation of genetic regulatory systems: A literatüre review. Journal of Computational Biology, 9 (1), 67-103.
13. Kampen, N. G. V., 1981. Stochastic Processes in physics and chemistry. Elsevier.
14. Khanin, R., Wit, E., 2006. How scale-free are biological networks. Journal of Computational Biology, 13 (3), 810-818.
15. Kitano, H., 2001. Foundations of systems biology. Massachusetts Institute of Technology.
16. Lok, L., 2002. Pathfinder and other tools for analyzing signal transduction networks. Ann. N.Y. Acad. Sci., 971:589-594.
17. Lok, L., Brent, R., 2005. Automatic generation of cellular reaction networks with moleculizer 1.0. Nature Biotechnology, 23(1):131–136.
18. Morton-Firth, C., Bray, D., 1998. Predicting temporal fluctuations in an signalling pathway. Journal of Theoretical Biology, 192:117–128.
19. Purutçuoğlu, V., Wit, E., 2006. Exact and approximate stochastic simulations of the APK pathway and comparisons of simulations’ results. Journal of Integrative Bioinformatics, 3, 231-243.
20. Purutçuoğlu, V., Wit, E., 2008. Bayesian inference for the MAPK/ERK pathway by considering the dependency of the kinetic parameters. Bayesian Analysis, 3 (4), 851-886.
21. Purutçuoğlu, V., 2010. Stochastic simulation of large biochemical systems by approximate Gillespie algorithm. Proceeding of the 5rd International Symposium on Health, Informatics and Bioinformatics, IEEE Xplore, 181-186.
22. Turner, T. E., Schnell, S., Burrage, K., 2004. Stochastic approaches for modelling in vivo reactions. Computational Biology and Chemistry, 28:165–178.
23. Wilkinson, D.J., 2006. Stochastic modelling for systems biology. Chapman and Hall/CRC.