Table 1.

This table assumed that the designer has already selected a value of R for the subnetwork.

Operation	Componentpathways	Constraint equations	Free parameters
Addition	Syn. 1,	${\mathit{g}}_{\mathit{s}\text{,1}}=\frac{{\mathit{k}}_{\mathit{syn}\text{,1}}\cdot \mathit{R}}{\mathrm{\Delta }{\mathit{E}}_{\mathit{s}\text{,1}}-{\mathit{k}}_{\mathit{syn}\text{,1}}\cdot \mathit{R}}$	ksyn,1
	transmission	ΔEs,1 − ksyn,1⋅R > 0	ΔEs,1, maximize
	Syn. 2,	${\mathit{g}}_{\mathit{s}\text{,2}}=\frac{{\mathit{k}}_{\mathit{syn}\text{,2}}\cdot \mathit{R}}{\mathrm{\Delta }{\mathit{E}}_{\mathit{s}\text{,2}}-{\mathit{k}}_{\mathit{syn}\text{,2}}\cdot \mathit{R}}$	ksyn,2
	transmission	ΔEs,2 − ksyn,2⋅R > 0	ΔEs,2, maximize
Subtraction	Syn. 1,	${\mathit{g}}_{\mathit{s}\text{,1}}=\frac{{\mathit{k}}_{\mathit{syn}}\cdot \mathit{R}}{\mathrm{\Delta }{\mathit{E}}_{\mathit{s}\text{,1}}-{\mathit{k}}_{\mathit{syn}}\cdot \mathit{R}}$	ksyn
	transmission	ΔEs,1 − ksyn⋅R > 0	ΔEs,1, maximize
	Syn. 2,	${\mathit{g}}_{\mathit{s}\text{,2}}=\frac{\mathrm{\Delta }{\mathit{E}}_{\mathit{s}\text{,1}}}{\mathrm{\Delta }{\mathit{E}}_{\mathit{s}\text{,2}}}\cdot \frac{-{\mathit{k}}_{\mathit{syn}}\cdot \mathit{R}}{\mathrm{\Delta }{\mathit{E}}_{\mathit{s}\text{,1}}-{\mathit{k}}_{\mathit{syn}}\cdot \mathit{R}}$	ΔEs,2, minimize
	transmission
Division	Syn. 1,	${\mathit{g}}_{\mathit{s}\text{,1}}=\frac{{\mathit{k}}_{\mathit{syn}}\cdot \mathit{R}}{\mathrm{\Delta }{\mathit{E}}_{\mathit{s}\text{,1}}-{\mathit{k}}_{\mathit{syn}}\cdot \mathit{R}}$	csyn
	transmission	ksyn = 1	ΔEs,1, maximize
		ΔEs,1 − ksyn⋅R > 0
	Syn. 2,	${\mathit{g}}_{\mathit{s}\text{,2}}=\frac{{\mathit{c}}_{\mathit{syn}}\cdot \mathit{R}-\mathit{R}}{\mathrm{\Delta }{\mathit{E}}_{\mathit{s}\text{,2}}-{\mathit{c}}_{\mathit{syn}}\cdot \mathit{R}}$
	modulation	ΔEs,2 = 0
		0 < csyn < 1
Multiplication	Syn. 1,	${\mathit{g}}_{\mathit{s}\text{,1}}=\frac{{\mathit{k}}_{\mathit{syn}}\cdot \mathit{R}}{\mathrm{\Delta }{\mathit{E}}_{\mathit{s}\text{,1}}-{\mathit{k}}_{\mathit{syn}}\cdot \mathit{R}}$
	transmission	ksyn = 1
		ΔEs,1 − ksyn⋅R > 0	ΔEs,1, maximize
	Syn. 2,	${\mathit{g}}_{\mathit{s}\text{,2}}=\frac{-\mathit{R}}{\mathrm{\Delta }{\mathit{E}}_{\mathit{s}\text{,2}}}$
	modulation	ΔEs,2 < 0	ΔEs,2, maximize
	Syn. 3,	gs,3 = gs,2
	modulation	ΔEs,3 = ΔEs,2

In this table, “minimize” refers to making a value as negative as possible and “maximize” refers to making a value as positive as possible.