The discrete Chemical Master Equation (dCME) provides a fundamental framework to study stochasticity in reaction networks. However, solving dCMEs is challenging, as it is often unknown if the computed probability peaks are complete and nothing important is missing. It is also difficult to accurately estimate probabilities of rare events.<br/>Here we discuss how time-evolving and steady state probability landscape can be exactly computed using the n-simplex optimal state numeration algorithm and the ACME (accurate chemical master equation) method (www.bioacme.org, DOI. 10.1137/15M1034180), without Monte Carlo simulation or Fokker-Planck/Langevin approximation. We also discuss how to guarantee small errors and how to estimate the best achievable accuracy with a given laptop/supercomputer, through an a priori calculated error bound when truncation of the state space inevitabley occurs for complex networks. In addition, we describe a new formulation of discrete probability flux and velocity under proper boundary conditions and how their global flow maps can be exactly computed. We give examples on analysis of phenomenological characterization of cellular decision networks, including bi-stability, epigenetic states, and the robustness of wild type versus mutants networks. Furthermore, we discuss how ACME computation can reveal the origin of the reservoir of HIV latently infected cells and uncover detailed mechanism of probabilistic intra-cellular control of latency and transactivation. Moreover, we discuss how new approaches for health intervention can been formulated based on large scale computation exploring changes in the probability landscapes of networks under different perturbations, in the context of clinical treatment of the “shock and kill” and the “block and lock” strategies.

Exact construction of probability landscapes and global flow maps of discrete flux of stochastic networks without Monte Carlo sampling or Fokker-Planck approximations

2019 Spring National Meeting

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