Topological data analysis of high dimensional probability landscapes of biochemical reaction networks using persistent homology

Abstract

Biomolecular species such as proteins, DNAs, and RNA interact in cell to form reaction networks that regulate cellular functions. At small copy numbers, stochasticity arises from thermal fluctuations and plays important roles on cellular phenotypes. The underlying stochastic chemical kinetics (SCK) is governed by the discrete chemical master equation (dCME). Recent developments of the ACME algorithm enables the exact solution to dCME. With the constructions of exactly computed time-evolving and steady state probability landscapes, it is now possible to investigate the landscape properties of many stochastic networks, including where the probability basins are located, their significance, how they are connected, and where cycles of various dimensions appear.