Accurate Chemical Master Equation (ACME) method

Direct Solution of Chemical Master Equation for Probability Landscapes

ACME provides an efficient and optimal algorithm for enumerating state spaces and directly solving discrete Chemical Master Equations, which is a fundamental method for modeling stochastic gene regulatory networks in systems biology. Instead of running millions of stochastic simulation trajectories using Gillespie's algorithm (Gillespie, 1977), Finite Buffer method can accurately and efficiently capture the important rare events in biological networks by directly solving full stochastic probability landscapes for both time evolution and steady state of reaction networks with arbitrary stoichiometry. Finite Buffer method has been successfully applied to study many critical biological processes, such as the cell fate determination and switching efficiency and stability issues in the epigenetic circuits of phage lambda, a virus to E. coli cell (Cao et al. 2010). Finite Buffer dCME can be applied to study broad issues in systems biology, such as the regulation of stem cell development and differentiation, and cell cancerogenesis. It has also been used to identify key interactions in a complex regulatory network (Cao et al. 2010), which can potentially be used to aid in discovering novel drug targets and designing/optimizing genetic circuits in synthetic biology. 


(Please cite following papers for using ACME method)

  1. Youfang Cao, Anna Terebus and Jie Liang (2016). State space truncation with quantified errors for accurate solutions to discrete chemical master equation. Bulletin of Mathematical Biology. 78:617–661. (PDF)
  2. Youfang Cao, Anna Terebus and Jie Liang (2016). Accurate Chemical Master Equation solution using multi-finite buffers. SIAM: Multiscale Modeling and Simulation. 14(2): 923–963. (PDF)
  3. Youfang Cao, Hsiao-Mei Lu and Jie Liang (2010). Probability landscape of heritable and robust epigenetic state of lysogeny in phage lambda. Proceedings of the National Academy of Sciences USA, 107(43), 18445–18450.
  4. Youfang Cao and Jie Liang (2008). Optimal enumeration of state space of finitely buffered stochastic molecular networks and accurate computation of steady state landscape probability. BMC Systems Biology 2:30.