Stochastic simulation algorithm can appropriately describe the probabilistic nature of the biological chemical reactions, which is caused by the low abundance of mRNA and some proteins. Gillespie algorithm is a comprehensive sampling method without any approximations. We will introduce the algorithm, especially converting concentrations and rate constants to particle numbers and reaction propensity. We will also demonstrate the noise size affected by the volume of the system.

Next, we will introduce the burst Langevin algorithm for systems with either or both mRNA and protein burst productions. Burst productions of mRNA (protein) can be regarded as the noise propagation from its upstream DNA (mRNA). For a full-described gene expression model, the burst Langevin algorithm neglects the fast-fluctuating upstream reactants tracking and introduces a parameter for the noise size of the downstream. Therefore, we can modify the noise size for the downstream’s burst production. Burst Langevin algorithm also increases the time step length, thus, it is an efficient and versatile means to simulate such huge abundance. Hopefully, we can demonstrate stochastic simulation algorithms for further analysis of biological networks with noise effects.

 

References:

1. Gillespie, D. T. J. Comput. Phys. 1977, 22, 403.

2. Yan, C.-C. S.; Chepyala, S. R.; Yen, C.-M.; Hsu, C.-P. Sci. Rep. 2017, 7, 16851.