Before revision:  To overcome this issue , this paper proposes a computational method for predicting rigorous upper and lower bounds of dynamic moments . We combine the differential equation model of the moment dynamics with a so-called moment condition to derive linear matrix inequalities that the moments of molecular copy numbers must satisfy . Using these conditions, we formulate a semidefinite program that efficiently and rigorously computes the bounds of transient moment dynamics.
After revision:  To overcome this issue , this paper proposes a computational method for predicting rigorous upper and lower bounds of transient moments for reactions governed by the law of mass action. We first derive an equation that transient moments must satisfy based on the moment equation. Although this equation is underdetermined, we introduce a set of semidefinite constraints known as moment condition to derive linear matrix inequalities that the moments of molecular copy numbers must satisfy . Using these conditions, we formulate a semidefinite program that efficiently and rigorously computes the bounds of transient moment dynamics.