Continuous-Time Markov Chain–Based Flux Analysis in Metabolism

Abstract

Metabolic flux analysis (MFA), a key technology in bioinformatics, is an effective way of analyzing the entire metabolic system by measuring fluxes. Many existing MFA approaches are based on differential equations, which are complicated to be solved mathematically. So MFA requires some simple approaches to investigate metabolism further. In this article, we applied continuous-time Markov chain to MFA, called MMFA approach, and transformed the MFA problem into a set of quadratic equations by analyzing the transition probability of each carbon atom in the entire metabolic system. Unlike the other methods, MMFA analyzes the metabolic model only through the transition probability. This approach is very generic and it could be applied to any metabolic system if all the reaction mechanisms in the system are known. The results of the MMFA approach were compared with several chemical reaction equilibrium constants from early experiments by taking pentose phosphate pathway as an example.

Continuous Description of Discrete Biological Data

“…Toillustratesomepossibleapplicationsofthemethodwewillconsidertwo-dimensionalnonlinear models that can be represented in the form of the equation (1). Naturally, there are numerous biologicalmodels,whicharedescribingbyordinarydifferentialequationsandincludessomeelements of stochastic processes (Huo, 2014;Rowe, 1994;Smitalova, Sujan, 1991). Here, to illustrate the methodology,webaseonclassicalVolterramodels,whichareverypopularinpopulationbiology, biochemistry,biophysicsandother.TheclassicVolterra"predator-prey"modelisasystemofquadratic ordinarydifferentialequationsandhasseveralforms (MaynardSmith,1974;Volterra,1931).The "predator-prey"versionhasaform:…”