Table 3.

Summary of different methods used in dynamic network.

Method	Description	Reaction	Equation	Advantages	Disadvantages
ODEs	Series of reaction-rate equations solved using numerical methods	$\mathrm{A}\stackrel{k_1}{\to }\mathrm{B}$	$\begin{array}{l}\frac{d\left[A\right]}{dt}=-k_1\left[A\right]\\ \frac{d\left[B\right]}{dt}=k_1\left[A\right]\end{array}$	Well understood formalism	Limited to temporal modeling
				Deterministic	Assumed high concentrations and uniform mixing
	Produces graphs or tables of reagent production and consumption			Fast	Brittle
				Mathematically robust
PDEs	Expresses spatial and temporal dependence through partial derivatives	$\mathrm{A}+\mathrm{B}\stackrel{k_1}{\to }\mathrm{C}$	$\begin{array}{l}\frac{\partial \left[A\right]}{\partial t}=D_1{\nabla }^2\left[\mathrm{A}\right]-{\mathrm{k}}_1\left[\mathrm{A}\right]\left[\mathrm{B}\right]\\ \frac{\partial \left[\mathrm{B}\right]}{\partial t}=D_1{\nabla }^2\left[\mathrm{B}\right]-{\mathrm{k}}_1\left[\mathrm{A}\right]\left[\mathrm{B}\right]\\ \frac{\partial \left[\mathrm{C}\right]}{\partial t}=-D_1{\nabla }^2\left[\mathrm{C}\right]+{\mathrm{k}}_1\left[\mathrm{A}\right]\left[\mathrm{B}\right]\\ \text{Note}:{\nabla }^2\left[\mathrm{A}\right]=\frac{{\partial }^2\left[A\right]}{\partial {\mathrm{x}}^2}+\frac{{\partial }^2\left[A\right]}{\partial {\mathrm{y}}^2}+\frac{{\partial }^2\left[A\right]}{\partial {\mathrm{z}}^2}\end{array}$	Well understood formalism	Complicated
				Possible to be fast	Difficult to implement or generalize
	Bases on numerical methods	With diffusion of molecules at rate D1		Mathematically robust	Unable to model state of discontinuous transitions
	Produces numeric output of concentrations and x, y, z coordinates			Enables modeling of time- and space-dependent process	Brittle