Table 2.

Methods of mathematical modeling.

Method	Dynamic variables	Time	Example
Boolean networks	X(t) = 0 or 1 Y(t) = 0 or 1	t = integer (0, 1, 2, …)	X inhibits synthesis of Y and Y inhibits synthesis of X X (t + 1)=¬Y (t) Y (t + 1)=¬X (t)
Ordinary differential equations	X(t) = positive real number Y(t)= positive real number	t= real number (t ≥ 0)	X inhibits synthesis of Y and Y inhibits synthesis of X $\frac{dX}{dt}=\frac{k_{\text{sx}}}{1+Y^p}-k_{\text{dx}}X$ $\frac{dY}{dt}=\frac{k_{\text{sy}}}{1+X^q}-k_{\text{dy}}Y$
Stochastic models	M(t) = positive integer	t= real number (t ≥ 0)	Propensity of mRNA synthesis = ksm Propensity of mRNA degradation = kdmM Probability density function for number of mRNA molecules in the cell is $P(M)=e^{-\lambda }\frac{{\lambda }^M}{M!}$, where $\lambda =\frac{k_{\text{sm}}}{k_{\text{dm}}}$
Hybrid deterministic-stochastic models	M(t) = positive integer P(t) = positive real number	t = real number (t ≥ 0)	Genetic regulatory network: Simulate mRNA fluctuations, M(t), with a stochastic model and protein dynamics, P(t), with ordinary differential equations