  A number of biological systems can be modeled by Markov chains. Recently,
there has been an increasing concern about when biological systems modeled by
Markov chains will perform a dynamic phenomenon called overshoot. In this
article, we found that the steady-state behavior of the system will have a
great effect on the occurrence of overshoot. We confirmed that overshoot in
general cannot occur in systems which will finally approach an equilibrium
steady state. We further classified overshoot into two types, named as simple
overshoot and oscillating overshoot. We 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 nonequilibrium dynamic
phenomenon with energy consumption. In addition, the main result in this
article is validated with real experimental data.

Quantitative Methods