Abstract
We perform a Gillespie simulation for a simple auto-catalytic gene regulatory network with a positive feedback loop. The chemical master equation for the same model has been solved directly, and after a transient period, proteins were shown to go extinct due to a rare event. We find these features are reproduced with the Gillespie simulation, and the time-dependent frequency of protein numbers shows excellent agreement with the time-dependent probability obtained by solving the master equation directly. The reproduction of the probability for a rare event with the Gillespie simulation reconfirms the feasibility of using the method for modelling the stochastic dynamics of more complex gene regulatory networks, where the direct solution of the master equation is no longer feasible due to computational costs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. de Jong, J. Comput. Biol. 9, 67 (2000).
A. D. Keller, J. Theor. Biol. 170, 175 (1994).
E. Plahte, T. Mestl and S. W. Omholt, J. Biol. Syst. 3, 409 (1995).
E. H. Snoussi, J. Biol. Syst. 6, 3 (1998).
J.-L. Gouzé, J. Biol. Syst. 6, 11 (1998).
O. Cinquin and J. Demongeot, J. Theor. Biol. 216, 229 (2002).
J. Hasty, J. Pradines, M. Dolnik and J. J. Collins, Proc. Natl. Acad. Sci. 97, 2075 (2000).
P. Smolen, D. A. Baxter and J. H. Byrne, Bull. Math. Biol. 62, 247 (2000).
D. Angeli, J. E. Ferrell and E. D. Sontag, Proc. Natl. Acad. Sci. 101, 1822 (2004).
N. Radde, Bioinformatics 26, 2874 (2010).
J. Lee, AIP Advances 6, 055013 (2016).
T. B. Kepler and T. C. Elston, Biophys. J. 81, 3116 (2001).
A. M. Walczak, J. N. Onuchic and P. G. Wolynes, Proc. Natl. Acad. Sci. 102, 18926 (2005).
N. Friedman, L. Cai and X. S. Xie, Phys. Rev. Lett. 97, 168302 (2006).
A. Loinger, A. Lipshtat, N. Q. Balaban and O. Biham, Phys. Rev. E 75, 021904 (2007).
A. Ochab-Marcinek and M. Tabaka, Proc. Natl. Acad. Sci. 107, 22096 (2010).
D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977).
Y. Cao and J. Liang, BMC Syst. Biol. 2, 30 (2008).
Y. Cao, H.-M. Lu and J. Liang, Proc. Natl. Acad. Sci. 107, 18445 (2010).
Y. Cao, A. Terebus and J. Liang, Bull. Math. Biol. 78, 617 (2016).
Y. Cao, A. Terebus and J. Liang, Multiscale Model. Simul. 14, 923 (2016).
J. Lee and J. Lee, Phys. Rev. E 98, 062404 (2018).
D. L. Isaacson and R. W. Madsen, Markov Chains, Theory and Applications (Wiley, New York, 1976).
G. S. Fisherman, A First Course in Monte Carlo (Duxbury Press, Pacific Grove, USA, 2005).
Acknowledgments
This work was supported by the National Research Foundation of Korea, funded by the Ministry of Education (NRF-2017R1D1A1B03031344).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, Y.J., Lee, J.J. & Lee, J. Gillespie Simulation of Rare Events in a Genetic Regulatory Network. J. Korean Phys. Soc. 74, 907–911 (2019). https://doi.org/10.3938/jkps.74.907
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3938/jkps.74.907