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

Year 2022, , 366 - 375, 30.12.2022

Saliha Demirbüken Vilda Purutcuoglu

https://doi.org/10.47000/tjmcs.901339

Cited By: 1

Abstract

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.

Keywords

Approximate stochastic simulation algorithms, leap condition, confidence interval

Supporting Institution

Middle East Technical University

Project Number

10282

References

• 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.