Table S1.

Reactions and typical parameter values used in a reduced model comprising DUSP5, ERK, and an upstream kinase (K) without cellular compartmentalization

No.	Reaction	Rate	Value
1	ERK activation	$k_{\text{act}}$	$k_{\text{act}}=0.5$
	$\text{ERK}\hspace{0.17em}+{\text{K}}^{*}\to {\text{ERK}}^{*}+{\text{K}}^{*}$
2	DUSP synthesis	$k_{\text{D}}$	$k_{\text{D}}=0.5,\hspace{0.17em}\tau =3$
	${\text{ERK}}^{*}\to {\text{ERK}}^{*}+\text{DUSP}\hspace{0.17em}\left(\text{delay}\hspace{0.17em}:\hspace{0.17em}\tau \right)$
3	Sequestration	$k_{\text{sq}}$	$k_{\text{sq}}=1$
	${\text{ERK}}^{*}\hspace{0.17em}+\text{DUSP}\to \text{ERK}:\text{DUSP}$
4	Release	${\gamma }_{\text{ERK:DUSP}}$	${\gamma }_{\text{ERK:DUSP}}=1$
	$\text{ERK}:\text{DUSP}\to \text{ERK}$
5	Upstream input	$e^{-{\gamma }_{i}t}$	${\gamma }_i=1$
	$\text{K}\to {\text{K}}^{*}$
6	Upstream negative feedback	${\gamma }_{\text{K}}+k_{\text{fb}}\frac{{\left[{\text{ERK}}^{*}\right]}^n}{{\theta }^n+{\left[{\text{ERK}}^{*}\right]}^n}$	${\gamma }_{\text{K}}=1,\hspace{0.17em}{k}_{\text{fb}}=1,$
	${\text{K}}^{*}\to \text{K}$		$\theta =0.5,\hspace{0.17em}n=4$
7	ERK deactivation	${\gamma }_{\text{ERK}}$	${\gamma }_{\text{ERK}}=0.1$
	${\text{ERK}}^{*}\hspace{0.17em}\to \text{ERK}$
8	DUSP degradation	${\gamma }_{\text{DUSP}}$	${\gamma }_{\text{DUSP}}=0.5$
	$\text{DUSP}\to \varnothing$