Overshoot in biological systems modelled by Markov chains: a non‐equilibrium dynamic phenomenon

Abstract

A number of biological systems can be modelled by Markov chains. Recently, there has been an increasing concern about when biological systems modelled by Markov chains will perform a dynamic phenomenon called overshoot. In this study, the authors found that the steady-state behaviour of the system will have a great effect on the occurrence of overshoot. They showed that overshoot in general cannot occur in systems that will finally approach an equilibrium steady state. They further classified overshoot into two types, named as simple overshoot and oscillating overshoot. They showed that except for extreme cases, oscillating overshoot will occur if the system is far from equilibrium. All these results clearly show that overshoot is a non-equilibrium dynamic phenomenon with energy consumption. In addition, the main result in this study is validated with real experimental data.

Mapping the functional versatility and fragility of Ras GTPase signaling circuits through in vitro network reconstitution

“…The transient response of the wild-type GTPase in the high-GAP network context was unanticipated, as this phenomenon cannot be explained by the simplest model of effector/GTPase binding in which the GTPase toggles ON and OFF with rates directly proportional to [GAP] and [GEF] ( Figure 3—figure supplement 2 ). Indeed, this is consistent with analytic results that state that two-state systems cannot show overshoot behavior ( Jia et al, 2014 ). However, transient overshoot could be easily introduced into the system by two non-mutually exclusive mechanisms: (1) competition between effectors and GAP molecules; and (2) the existence of a post-hydrolysis GTPase state that is refractory to GEF stimulation.…”

A multi-phenotypic cancer model with cell plasticity

“…That is, the proportion of stem-like cells is rapidly elevated by de-differentiation to the value above the equilibrium level, and then returns towards the final equilibrium as time passes. It has been reported that CSC-NSCC model can never perform overshooting [27,45], which implies that the overshooting phenomenon are rooted in the diversity of phenotype in the multi-phenotypic model. Moreover, note that overshooting behavior is a result of biological response to environmental stimulus through evolution [46], cancer cell plasticity may have meaningful implications for the evolution of cancer.…”

“…In particular, an interesting overshooting phenomenon of CSCs proportion arises in S-B-L model with cell plasticity. Note that two-phenotypic models never perform overshooting [27,45], overshooting can be a result of interplay between cell plasticity and diversity of phenotype. Moreover, it has been investigated in ecology and population genetics that phenotypic variability can serve as an advantageous strategy for biological populations in fluctuating environments [31,32,33,34,35], our findings thus enrich this idea that cell plasticity as a surviving strategy might be more essential in maintaining the phenotype diversity (heterogeneity) of cancer especially during transient dynamics.…”

A solution to the reversible embedding problem for finite Markov chains

“…Therefore, the generator estimation problem in statistics is naturally related to embedding problem for finite Markov chains. Recently, the generator estimation problem has been widely studied in biology [26,27], since a number of biochemical systems can be modeled by continuous-time Markov chains. In general, there are two types of Markov chains that must be distinguished, reversible chains and irreversible chains.…”