title: 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.
authors: Beijing International Center for Mathematical Research, Beijing 100871, People's Republic of China.
authors: Chen
authors: C
authors: Jia
authors: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China.
authors: Minping
authors: M
authors: Qian
authors: Center for Statistical Science, Peking University, Beijing 100871, People's Republic of China. jiangdq@math.pku.edu.cn.
authors: Daquan
authors: D
authors: Jiang
mesh_terms: D001943:Breast Neoplasms / Q000473:pathology / Q000503:physiopathology*; D049109:Cell Proliferation; D002471:Cell Transformation, Neoplastic / Q000378:metabolism* / Q000473:pathology; D003198:Computer Simulation; D004734:Energy Metabolism; D006801:Humans; D008390:Markov Chains; D008954:Models, Biological; D015233:Models, Statistical; D014411:Neoplastic Stem Cells / Q000473:pathology / Q000502:physiology*; D013816:Thermodynamics; D014407:Tumor Cells, Cultured