Rule-Based Modeling of Signal Transduction: A Primer

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(34!R(lig,ch~closed)9!L#+#%(/%07!.-)!/)('.(3.!,(..)/3!L(rec)!+(.'-)*!.-)!/)('.(3.!*,)'#)*!L(rec)9!

P(..)/3!+(.'-#3&!.$!&)3)/(.)!/)('.#$3*!#*!*2++(/#=)4!#3!F68#&)!ED!

! gU!

P(..)/3*!%#)!(.!.-)!-)(/.!$1!/2%)@8(*)4!+$4)%#3&9!P(..)/3*!'(3!8)!*(#4!.$!*)%)'.!*,)'#)*!.-(.!,$**)**!(!

+(.'-#3&!*28*./2'.2/)9!G!&)%:06+5!&#2)!6-!)//):06H)2'!%!-)0!+/!&)%:0%50!4%00)&5-!%5,!%!-)0!+/!

0&%5-/+&$%06+5-!%4426),!0+!0I+-)!4%00)&5-D!K!/)('.#$3!#*!&)3)/(.)4!80!*)%)'.#3&!*,)'#)*!.-(.!+(.'-!.-)!

/)('.(3.!,(..)/3*!(34!(,,%0#3&!.-)!./(3*1$/+(.#$3!.$!.-)+!.$!&).!.-)!,/$42'.!*,)'#)*9!

B@> FD($3G'D#$(*:(30!8#$%$&#'(%!)>,)/#+)3.*!#3;$%;)!1$%%$5#3&!.-)!.#+)@'$2/*)*!$1!)>,)/#+)3.(%!$2.,2.*7!$1.)3!/)1)//)4!

.$!(*!0&%J):0+&6)-9!S('-!$2.,2.!#*!2*2(%%0!*,)'#1#'!.$!(!*#3&%)!'$%%)'.#$3!$1!*,)'#)*9!M$/!)>(+,%)7!#3!(!MWS?!

)>,)/#+)3.!$3!/)'),.$/!(&&/)&(.#$37!$3)!+#&-.!4)*#&3!.-)!)>,)/#+)3.!*2'-!.-(.!$3%0!4#+)/*!'(3!

,/$42')!1%2$/)*')3')7!(34!.-)!1%2$/)*')3.!$2.,2.!#*!(!123'.#$3!$1!.-)!.$.(%!'$3')3./(.#$3!$1!(%%!4#+)/!

*,)'#)*9!L#+#%(/%0!#3!(!I)*.)/3!8%$.!)>,)/#+)3.!2*#3&!(3!(3.#8$40!*,)'#1#'!.$!(!,(/.#'2%(/!,/$.)#37!.-)!

+)(*2/)+)3.!(.!4#11)/)3.!.#+)!,$#3.*!#*!,/$,$/.#$3(%!.$!.-)!.$.(%!'$3')3./(.#$3!$1!.-)!,/$.)#3!(;(#%(8%)!

1$/!8#34#3&9!G3!(!"AB!+$4)%7!$3)!'(3!*#+#%(/%0!4)1#3)!*,)'#1#'!*2+*!$1!'$3')3./(.#$3*!$1!*,)'#)*!.-(.!(/)!

$1!#3.)/)*.!(34!3))4!.$!+$3#.$/)4!$/!./('6)4!.-/$2&-!.-)!*#+2%(.#$3!$1!.-)!+$4)%9!L2'-!*2+*!(/)!'(%%)4!

+B-)&H%B2)-!(34!(/)!$1!.5$!.0,)*T!+$%)'2%)*@$8*)/;(8%)*!(34!*,)'#)*@$8*)/;(8%)*9!

F$3*#4)/!.-)!+$%)'2%)!.0,)*!A(b,b,c)7!B(a)!(34!C(a)9!K!'(3!8#34!.5$!"!(34!$3)!F9!?-#*!/)*2%.*!#3!.-)!

1$%%$5#3&!*,)'#)*T!

"! B(a)

F! C(a)

K! A(b,b,c)

K"! A(b!0,b,c).B(a!0)!

"K"! A(b!0,b!1,c).B(a!0).B(a!1)!

KF! A(b,b,c!2).C(a!2)!

K"F! A(b!0,b,c!2).B(a!0).C(a!2)!

! g[!

"K"F! A(b!0,b!1,c!2).B(a!0).B(a!1).C(a!2)!

K!-4):6)-K+B-)&H%B2)!#*!(3!235)#&-.)4!*2+!$1!.-)!'$3')3./(.#$3*!$1!*,)'#)*!+(.'-)4!.$!(!,(..)/3!C$/!(!

%#*.!$1!,(..)/3*D9!M$/!)>(+,%)7!%).!2*!4)1#3)!(!*,)'#)*@$8*)/;(8%)!.$!8)!.-)!,(..)/3T!A(b)9!?-#*!,(..)/3!

+(.'-)*!(30!*,)'#)*!.-(.!'$3.(#3*!(3!A!+$%)'2%)!5#.-!(3!238$234!b!'$+,$3)3.9!?-)!*,)'#)*!K!(34!KF!

-(;)!.5$!238$234!8!'$+,$3)3.*!)('-!(34!.-)!*,)'#)*!K"!(34!K"F!-(;)!$3)!238$234!8!'$+,$3)3.!

)('-9!?-2*!.-)!$8*)/;(8%)!5$2%4!+(.'-!(%%!1$2/!$1!.-)*)!*,)'#)*!C82.!3$.!.-)!*,)'#)*!"K"FD9!?-)!;(%2)!$1!

.-#*!$8*)/;(8%)!5$2%4!8)!&#;)3!80!.-)!*2+!kKlikK"likKFlikK"Fl7!5-#'-!5$2%4!;(/0!$;)/!.-)!'$2/*)!$1!(!

*#+2%(.#$39!

K!$+2):#2)-K+B-)&H%B2)!5)#&-.*!.-)!'$3')3./(.#$3*!$1!.-)!*,)'#)*!80!.-)!32+8)/!$1!+(.'-)*!.$!(!

,(..)/3!C$/!(!%#*.!$1!,(..)/3*D9!M$/!)>(+,%)7!%).!2*!4)1#3)!(!+$%)'2%)*@$8*)/;(8%)!5#.-!.-)!*(+)!,(..)/3T!

A(b)9!?-#*!5$2%4!+(.'-!*,)'#)*!K"!(34!K"F!$3')!)('-!(34!.-)!*,)'#)*!K!(34!KF!.5#')!C*#3')!.-)0!-(;)!

.5$!238$234!b!*#.)*D9!?-)!;(%2)!$1!.-#*!$8*)/;(8%)!5$2%4!8)!&#;)3!80!.-)!*2+!JmkKl!i!JmkKFl!igmkK"l!i!

gmkK"Fl9!!

B@B !$'45-,.*A$.5$3*E*A,.5$H5*F$3*#4)/!.-)!/)('.#$3!/2%)T!


?-)!./(3*1$/+(.#$3!(,,%#)4!#3!.-#*!/2%)!#*!.-)!'/)(.#$3!$1!.-)!lig-rec!8$349!?-)!'$+,$3)3.*!.-(.!

,(/.#'#,(.)!#3!.-)!./(3*1$/+(.#$3C*D!'(//#)4!$2.!80!(!/)('.#$3!(/)!'$%%)'.#;)%0!'(%%)4!.-)!&)%:06+5!:)50)&9!

<)/)7!.-)!/)('.#$3!')3.)/!#*!.-)!*).!$1!'$+,$3)3.*!lig!(34!rec9!!

A$5!'$3*#4)/!(3$.-)/!/)('.#$3!/2%)T!

R(lig,ch~open) + L(rec) -> R(lig!0,ch~open).L(rec!0) k1

! g\!

<)/)7!.-)!*(+)!./(3*1$/+(.#$3!#*!8)#3&!(,,%#)47!#9)9!.-)!lig-rec 8$347!(34!.-)/)1$/)!#.!-(*!.-)!*(+)!

/)('.#$3!')3.)/!C234)/%#3)4!1$/!)+,-(*#*D9!<$5);)/7!.-)!(44#.#$3(%!ch!'$+,$3)3.!#3!.-)!open!*.(.)!#*!

/)O2#/)4!.$!#34#'(.)!.-(.!#1!.-)!'-(33)%!#*!$,)37!.-)3!.-)!/)('.#$3!/(.)!*-$2%4!8)!6g9!?-)!'$+,$3)3.*!

.-(.!4$!3$.!,(/.#'#,(.)!#3!.-)!/)('.#$37!82.!(/)!3);)/.-)%)**!/)O2#/)4!(34!#31%2)3')!.-)!/)('.#$3!/(.)!

'$3*.(3.!(/)!'$%%)'.#;)%0!'(%%)4!.-)!&)%:06+5!:+50)L0D!!

M#3(%%07!'$3*#4)/!.-)!/)('.#$3!/2%)T!

R(lig,ch~closed) + L(rec) ->R(lig!0,ch~closed).L(rec!0) k2

?-#*!/2%)!(%*$!-(*!(!/)('.#$3!')3.)/!#4)3.#'(%!.$!.-)!,/);#$2*!/2%)*!C234)/%#3)4!1$/!)+,-(*#*D9!<$5);)/7!

.-)!/)('.#$3!'$3.)>.!#*!3$5!ch~closed (34!.-)!/(.)!'$3*.(3.!#*!6J9!

I-)3!(!/)('.#$3!/2%)!#*!2*)4!.$!&)3)/(.)!/)('.#$3*7!.-)!/)('.#$3!'$3.)>.!,/$;#4)*!+#3#+2+!'$+,2%*$/0!

'$34#.#$3*!.-(.!3))4!.$!8)!$8)0)4!80!.-)!&)3)/(.)4!/)('.#$3*9!G3!.-)!(8*)3')!$1!(30!/)('.#$3!'$3.)>.7!

.-)!/)('.#$3!/2%)!#*!&)3)/(%!(34!+(.'-)*!(%%!,$**#8%)!/)('.#$3*!-(;#3&!.-)!*(+)!./(3*1$/+(.#$39!K44#3&!

+$/)!'$3.)>.!d*,)'#(%#=)*e!.-)!/)('.#$3!/2%)!.$!+(.'-!1)5)/!/)('.#$3*!.-(.!$8)0!.-)!'$34#.#$3*!#+,$*)4!

80!.-)!'$3.)>.9!?-)!/)('.#$3!#.*)%1!'(3!8)!'$3*#4)/)4!(*!(!-#&-%0!*,)'#(%#=)4!/)('.#$3!/2%)!5#.-!);)/0!

'$+,$3)3.!#3!.-)!#3.)/('.#3&!*,)'#)*!(44)4!(*!'$3.)>.9!

A$.)!.-(.!#3!8#4#/)'.#$3(%!/)('.#$3!/2%)*7!.-)!'$3.)>.!#*!,/)*)/;)4!#3!8$.-!4#/)'.#$3*9!M$/!)>(+,%)7!

'$3*#4)/!.-)!8#4#/)'.#$3(%!/2%)!C5#.-!/)('.#$3!')3.)/!234)/%#3)4!1$/!)+,-(*#*DT!

R(lig,ch~closed) + L(rec) <-> R(lig!0,ch~closed).L(rec!0) k2,kr

?-#*!#*!)O2#;(%)3.!.$!.-)!.5$!/)('.#$3!/2%)*7!8$.-!5#.-!ch~closed!(*!'$3.)>.T!

R(lig,ch~closed) + L(rec) -> R(lig!0,ch~closed).L(rec!0) k2

R(lig!0,ch~closed).L(rec!0)-> R(lig,ch~closed) + L(rec) kr

B@I 1J.5K$(-(*'.)*L$/3')'5-,.*

! ga!

I-)3!5/#.#3&!(!/)('.#$3!/2%)!#3!"ABH7!$3)!+2*.!+(6)!*2/)!.-(.!.-)/)!#*!(.!%)(*.!$3)!/)('.(3.!,(..)/3!

(34!$3)!,/$42'.!,(..)/39!<$5);)/7!.-)/)!(/)!(!32+8)/!$1!*#.2(.#$3*!5-)/)!.-)!32+8)/!$1!+$%)'2%)*!$3!

)#.-)/!.-)!/)('.(3.!*#4)!$/!.-)!,/$42'.!*#4)!$1!.-)!/)('.#$3!#*!=)/$9!?$!#34#'(.)!=)/$!*.$#'-#$+)./07!$3)!

'(3!2*)!.-)!*0+8$%!h!C=)/$D9!

I-)3!.-)!/)('.(3.!*#4)!$1!(!/)('.#$3!/2%)!-(*!=)/$!*.$#'-#$+)./07!.-)!/)('.#$3!#*!./)(.)4!(*!(!=)/$@$/4)/!

*03.-)*#*!/)('.#$37!1$/!)>(+,%)T!

0 -> L(rec) k_syn

?-#*!/)('.#$3!/2%)!*-$2%4!,/$42')!.-)!%#&(34!+$%)'2%)!(.!(!'$3*.(3.!=)/$@$/4)/!/(.)7!5-#'-!#*!)O2(%!.$!

k_syn!C.0,#'(%!23#.*!:!*@gD9!n)/$@$/4)/!*03.-)*#*!#*!2*)12%!.$!+$4)%!.-)!'(*)!5-)/)!(!/)('.#3&!(&)3.!#*!

'$3.#32$2*%0!1%$5#3&!#3.$!.-)!*0*.)+!1/$+!.-)!$2.*#4)7!1$/!)>(+,%)7!.-)!'$3.#32$2*!+$;)+)3.!$1!

&/$5.-!1('.$/*!1/$+!.-)!8%$$4!.$!(30!8$40!.#**2)!$/!.-)!'$3./$%%)4!1%$5!$1!32./#)3.*!#3!(!8#$/)('.$/9!

I-)/)!.-)!*03.-)*#*!4),)34*!$3!.-)!'$3')3./(.#$3*!$1!*,)'#1#'!+$%)'2%)*7!#.!#*!8)..)/!.$!2*)!1#/*.@$/4)/!

(34!*)'$34@$/4)/!)%)+)3.(/0!/)('.#$3*9!M$/!)>(+,%)7!.-)!,/$42'.#$3!$1!+WAK!1/$+!(!&)3)!4),)34*!$3!

.-)!32+8)/!$1!('.#;)%0!./(3*'/#8#3&!'$,#)*!$1!.-)!&)3)!#3!(!')%%T!

Gene() -> Gene() + mRNA k_transcription

I-)3!.-)!,/$42'.!*#4)!$1!(!/)('.#$3!/2%)!-(*!=)/$!*.$#'-#$+)./07!#.!-(*!3$!8)(/#3&!$3!.-)!/(.)!$1!.-)!

/)('.#$3!*#3')!.-)!/(.)!#*!4).)/+#3)4!$3%0!80!.-)!/)('.(3.!'$3')3./(.#$3*9!L2'-!/)('.#$3*!(/)!.0,#'(%%0!

2*)4!.$!+$4)%!*,$3.(3)$2*!$/!8('6&/$234!4)&/(4(.#$37!5-#'-!$''2/*!#3!*$+)!1$/+!$/!.-)!$.-)/!5#.-!

+$*.!8#$+$%)'2%)*9!M$/!)>(+,%)7!.$!+$4)%!*,$3.(3)$2*!4)&/(4(.#$3!$1!.-)!/)'),.$/T!

R() -> 0 k_degr

?-)!#3.)/3(%!(34!8#34#3&!*.(.)*!$1!'$+,$3)3.*!'(3!8)!+)3.#$3)4!.$!/)*./#'.!.-)!4)&/(4(.#$3!.$!$3%0!

')/.(#3!.0,)*!$1!+$%)'2%)*9!M$/!)>(+,%)7!#1!.-)!$3%0!/)'),.$/*!4)&/(4)4!5)/)!.-$*)!#3!.-)!'%$*)4!*.(.)T!

! gc!

R(ch~closed) -> 0 k_degr

G.!#*!#+,$/.(3.!.$!3$.)!.-(.!#3!(!4)&/(4(.#$3!/)('.#$3!/2%)7!.-)!'$+,%).)!+(.'-)4!/)('.(3.!*,)'#)*!#*!

4)&/(4)4!(34!3$.!V2*.!.-)!+$%)'2%)*!+)3.#$3)4!#3!.-)!/2%)9!?-)!(8$;)!/)('.#$3!/2%)!5#%%!&)3)/(.)!.-)!

1$%%$5#3&!/)('.#$3*T!

R(lig,ch~closed) -> 0 k_degr

R(lig!0,ch~closed).L(rec) -> 0 k_degr

?$!4)%).)!$3%0!.-)!+$%)'2%)*!'$3')/3)4!C(34!3$.!.-)!5-$%)!*,)'#)*D7!2*)!.-)!DeleteMolecules!

6)05$/4T!

R(ch~closed) -> 0 k_degr DeleteMolecules

G3!.-#*!'(*)!.-)!'$33)'.)4!+$%)'2%)*!(/)!3$.!4)%).)4!(34!.-#*!5$2%4!&)3)/(.)!.-)!1$%%$5#3&!/)('.#$3*T!

R(lig,ch~closed) -> 0 k_degr

R(lig!0,ch~closed).L(rec) -> L(rec) k_degr

B@M 1J99$53JN*+"#5-?#-4-5J*'.)*!'5$*7))-5-,.*F$3*#4)/!.-)!1$%%$5#3&!*#.2(.#$3T!?-)!K!+$%)'2%)!'(3!4#+)/#=)9!G.!)>#*.*!#3!.5$!4#11)/)3.!#*$1$/+*!Kg!(34!

KJ!(34!8$.-!-).)/$@!(34!-$+$@4#+)/#=(.#$3!$''2/9!S>,/)**#3&!.-#*!#3!.-)!./(4#.#$3(%!1/(+)5$/67!.-#*!

#+,%#)*!.-)!)>#*.)3')!$1!.-/))!4#11)/)3.!/)('.#$3*T!!

Kg!i!KJ!@j!`gJ!

Kg!i!Kg!@j!`gg!

KJ!i!KJ!@j!`JJ!

S;)3!#1!8$.-!-).)/$@!(34!-$+$@4#+)/#=(.#$3!-(;)!#4)3.#'(%!#3.)/('.#$3!*./)3&.-*!C(11#3#.#)*D7!.-)!-$+$@

4#+)/#=(.#$3!5$2%4!,/$'))4!(.!-(%1!.-)!/(.)!$1!.-)!-).)/$@4#+)/#=(.#$3!42)!.$!.-)!*0++)./0!#3!,#'6#3&!

$2.!(!-$+$@4#+)/#=#3&!+$%)'2%)!,(#/9!?-)/)1$/)7!.-)!/(.)!'$3*.(3.*!(/)!2*2(%%0!)>,/)**)4!(*T!

! gf!

Kg!i!KJ!@j!`gJ! !!!!!!!!!!!!!!!!!!6!

Kg!i!Kg!@j!`gg! ! 6]J!

KJ!i!KJ!@j!`JJ! ! 6]J!

<)/)7!$3)!'(3!.-#36!$1!X6Y!(*!.-)!(*0++)./#'!/)('.#$3!/(.)!'$3*.(3.!(34!.-)!Cg]JD!+2%.#,%0#3&!1('.$/!(*!

8)#3&!42)!.$!.-)!-'$$)0&'!)//):09!S>,/)**#3&!.-)*)!/)('.#$3*!2*#3&!"AB!*,)'#)*!(34!/),/)*)3.#3&!.-)!

.5$!#*$1$/+*!(*!.5$!4#11)/)3.!*.(.)*7!

A(iso~a1) + A(iso~a2) -> A(iso~a1!0).A(iso~a2!0) k

A(iso~a1) + A(iso~a1) -> A(iso~a1!0).A(iso~a1!0) 0.5*k

A(iso~a2) + A(iso~a2) -> A(iso~a2!0).A(iso~a2!0) 0.5*k

"#$A).B)3!(2.$+(.#'(%%0!4).)'.*!/)('.#$3!*0++)./#)*!(34!(,,%#)*!.-)!*0++)./0!1('.$/!);)3!#1!.-)!

/)('.#$3!/2%)*!.-)+*)%;)*!(/)!(*0++)./#'9!I-)3!5/#.#3&!(!/)('.#$3!/2%)7!.-)!+$4)%)/!+2*.!(%5(0*!

,/$;#4)!.-)!%-'$$)0&6:!&)%:06+5!&%0)!:+5-0%509!K%%!.-/))!/)('.#$3*!(8$;)!'(3!8)!&)3)/(.)4!5#.-!.-)!

/#&-.!/)('.#$3!/(.)!'$3*.(3.*!2*#3&!$3%0!.-)!*#3&%)!/2%)T!

A(iso!0) + A(iso!0) -> A(iso!0).A(iso!0) k

?-)!*.(.)*!$1!.-)!iso!'$+,$3)3.!(/)!%)1.!23+)3.#$3)4!#3!.-)!/)('.#$3!/2%)!*#3')!.-)0!4$!3$.!(11)'.!.-)!

(*0++)./#'!/)('.#$3!/(.)!'$3*.(3.9!"#$A).B)3!4).)'.*!.-(.!*$+)!$1!.-)!&)3)/(.)4!/)('.#$3*!(/)!

*0++)./#'!(34!*$+)!(/)!3$.9!G.!.-)3!(2.$+(.#'(%%0!(**#&3*!.-)!Cg]JD!+2%.#,%0#3&!1('.$/!.$!.-)!*0++)./#'!

/)('.#$3*9!

?-)!$#206426:60'!)//):0!#*!*))3!5-)3!#3.)/('.#$3*!(/)!+2%.#;(%)3.9!L2,,$*)!.-)!+$%)'2%)!K!-(*!.5$!

#4)3.#'(%!*#.)*!1$/!8#34#3&!.-)!+$%)'2%)!"9!?-)37!#3!.-)!./(4#.#$3(%!1/(+)5$/67!$3)!5$2%4!5/#.)!.-)!

1$%%$5#3&!/)('.#$3*9!

! Jh!

K!i!"!@j!K"!

K"!i!"!@j!"K"!

S;)3!.-$2&-!.-)!.5$!8#34#3&!*#.)*!-(;)!#4)3.#'(%!(34!#34),)34)3.!'-)+#'(%!#3.)/('.#$3*7!.-)!1#/*.!

/)('.#$3!*-$2%4!,/$'))4!(.!.5#')!.-)!/(.)!$1!.-)!*)'$34!8)'(2*)!K!-(*!.5#')!.-)!32+8)/!$1!8#34#3&!*#.)*!

(*!K"9!?-#*!#*!2*2(%%0!)>,/)**)4!(*T!

K!i!"!@j!K"! ! Jm6!

K"!i!"!@j!"K"! !!!!!! !!!!!6!

L#3')!"ABH!(%%$5*!+2%.#,%)!#4)3.#'(%!'$+,$3)3.*!#3!(!+$%)'2%)7!#.!(2.$+(.#'(%%0!(''$23.*!1$/!.-)!

+2%.#,%#'#.0!1('.$/!5-)3!&)3)/(.#3&!.-)!/)('.#$3*9!?-)!+$4)%)/!+2*.!(%5(0*!,/$;#4)!.-)!4)&K-60)!

&)%:06+5!&%0)!:+5-0%509!G1!.-)!+$%)'2%)!.0,)*!(/)!A(b,b) (34!B(a)7!.-)3!#.!#*!*211#'#)3.!.$!5/#.)!.-)!

1$%%$5#3&!/)('.#$3!/2%)T!

A(b) + B(a) -> A(b!0).B(a!0) k

?-#*!5$2%4!(2.$+(.#'(%%0!&)3)/(.)!.-)!1$%%$5#3&!/)('.#$3*9!

A(b,b) + B(a) -> A(b,b!0).B(a!0) 2*k

A(b,b!0).B(a!0) + B(a) -> A(b!1,b!0).B(a!0).B(b!1) k

H(*.%07!#1!+2%.#,%)!/)('.#$3!/2%)*!&)3)/(.)!.5$!;)/*#$3*!$1!.-)!*(+)!/)('.#$37!8$.-!(/)!6),.!#3!.-)!

/)('.#$3!3).5$/6!8)'(2*)!.-)0!+(0!-(;)!4#11)/)3.!/(.)!'$3*.(3.*!$/!/(.)!%(5*9!`2/#3&!*#+2%(.#$37!.-)!

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.-)!)11#'#)3.!,(/.#'%)@8(*)4!*.$'-(*.#'!*#+2%(.$/!&/)(.%0!)>,(34*!.-)!/(3&)!$1!+$4)%*!.-(.!'(3!8)!

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M !$4$?5,3*Q-/'.)*;.5$3'45-,.(*U*7*&-,V$5S$.*2"5,3-'#*G3!.-#*!*)'.#$37!5)!5#%%!5(%6!.-/$2&-!.-)!,/$')**!$1!'$3*./2'.#3&7!*#+2%(.#3&7!(34!(3(%0=#3&!(!"ABH!

+$4)%9!!I)!'$3*#4)/!.-)!)>(+,%)!$1!.-)!-2+(3!),#4)/+(%!&/$5.-!1('.$/!CSBMD!%#&(34!8#34#3&!*,)'#1#'(%%0!

.$!.-)!),#4)/+(%!&/$5.-!1('.$/!/)'),.$/!CSBMW7!(%*$!63$53!(*!<SWg!(34!SW""gD9!?-#*!#3.)/('.#$3!#*!

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,/$%#1)/(.#$3!#3!8$.-!-)(%.-0!(34!'(3')/$2*!')%%*9!?-)!+$4)%!,/)*)3.)4!-)/)!'(3!8)!2*)4!.$!#3;)*.#&(.)!

-$5!-0,$.-)*#=)4!#3.)/('.#$3*!(11)'.!(&&/)&(.)!4#*./#82.#$3*!$1!/)'),.$/*9!

! Ra!

I)!1$/+2%(.)!.-)!+$4)%!80!4/(5#3&!4)*'/#,.#$3*!$1!8#$'-)+#'(%!#3.)/('.#$3*!1/$+!.-)!)>#*.#3&!

63$5%)4&)!8(*)!#3!.-)!8#$+)4#'(%!%#.)/(.2/)!(34!/),/)*)3.#3&!.-)*)!(*!"AB!+$%)'2%)*!(34!/2%)*9!!?-)*)!

4)*'/#,.#$3*!*-$2%4!3$.!8)!'$3*#4)/)4!)*.(8%#*-)4!1('.*7!82.!/(.-)/!*-$2%4!8)!'$3*#4)/)4!-0,$.-)*)*!

(8$2.!.-)!*0*.)+!*./2'.2/)7!5-#'-!'(3!8)!.)*.)4!80!'$+,(/#3&!+$4)%!,/)4#'.#$3*!5#.-!)>,)/#+)3.(%!

$8*)/;(.#$3*!(34!4(.(9!

?-)!+$4)%!#*!5/#..)3!#3!(!3$/+(%!.)>.!1#%)!5#.-!.-)!)>.)3*#$3!XDB582Y9!?-)!+$4)%!'$+,/#*)*!(!*)/#)*!$1!

.)>.!8%$'6*7!3(+)%0!,(/(+).)/*7!+$%)'2%)!.0,)*7!$8*)/;(8%)*7!*))4!*,)'#)*7!/)('.#$3!/2%)*!(34!('.#$3*9!

?-)!8%$'6*!123'.#$3*!(34!'$+,(/.+)3.*!+(0!(%*$!8)!,/$;#4)4!#3!+$/)!'$+,%)>!+$4)%*9!K%%!8%$'6*!(/)!

'$3*./2'.)4!(*T!

begin block-name

[blocktext]

[blocktext]

[blocktext]

end block-name

K30!.)>.!$3!(!%#3)!1$%%$5#3&!(!r!C-(*-D!*0+8$%!#*!'$3*#4)/)4!(!'$++)3.!(34!#*!#&3$/)49!G1!(!%#3)!8)'$+)*!

.$$!%$3&7!.-)!s!C8('6*%(*-D!*0+8$%!'(3!8)!2*)4!.$!)>.)34!(!*.(.)+)3.!.$!.-)!3)>.!%#3)9!L28*)O2)3.!.(8*!

(34!*,(')*!(/)!./)(.)4!(*!(!*#3&%)!5-#.)*,(')9!

M@: 1$$)-./*2K$*+,)$#*Knowledge Base: The ligand EGF monovalently binds the receptor EGFR. The extracellular domain of EGFR

has a binding site for EGF and a domain that mediates dimerization with other receptor molecules (35).

EGFR autophosphorylates at multiple amino acid positions, including Y1068 (tyrosine at position 1068 in the

amino acid sequence of human EGFR) and Y1173 (reviewed in (36)).

?/(3*%(.#3&!.-#*!#31$/+(.#$3!1/$+!.-)!%#.)/(.2/)7!5)!'(3!'$3*./2'.!.-)!+$%)'2%)!.0,)*!(*!1$%%$5*T!

L(rec)!Q!H#&(34!5#.-!(!/)'),.$/!8#34#3&!*#.)!

! Rc!

R(lig,dim,y1068~0~p,y1173~0~p)!Q!W)'),.$/!5#.-!(!%#&(34!8#34#3&!*#.)7!(!4#+)/#=(.#$3!4$+(#3!(34!

.5$!.0/$*#3)*!.-(.!'(3!8)!#3!23,-$*,-$/0%(.)4!$/!,-$*,-$/0%(.)4!*.(.)*9!

?-)!+$%)'2%)!.0,)*!(/)!4)1#3)4!#3!(!+$%)'2%)!.0,)*!8%$'67!#9)9!

begin molecule types

L(rec)

R(lig,dim,y1068~0~p,y1173~0~p)

end molecule types

I)!(%*$!3))4!.$!4)1#3)!.-)!*.(/.#3&!*,)'#)*!(34!.-)#/!'$3')3./(.#$3*!1$/!.-)!+$4)%9!?-#*!#*!,/$;#4)4!

2*#3&!.-)!*))4!*,)'#)*!8%$'69!?-)!'$+,%).)!*,)'#)*!*,)'#1#'(.#$3*!*-$2%4!8)!,/$;#4)49!G3!.-#*!'(*)7!.-)!

*.(/.#3&!*,)'#)*!(/)!*#+,%0!1/))!%#&(34!(34!+$3$+)/#'!23,-$*,-$/0%(.)4!/)'),.$/9!G.!#*!(!&$$4!

'$3;)3.#$3!.$!,/$;#4)!,$,2%(.#$3!32+8)/*!1$/!.-)!*))4!*,)'#)*!(34!2*)!+#'/$*'$,#'!/(.)!'$3*.(3.*!#3!

.-)!/)('.#$3!/2%)*9!

begin seed species

R(lig,dim, y1068~0,y1173~0) R0

L(rec) L0

end seed species

R0!(34!L0!(/)!,(/(+).)/*!.-(.!(/)!.$!8)!4)1#3)4!*),(/(.)%0!#3!.-)!,(/(+).)/*!8%$'69!G3!.-)!,(/(+).)/*!

8%$'67!(!,(/(+).)/!3(+)!#*!(**#&3)4!(!/)(%!32+8)/!$/!(!*.(34(/4!+(.-)+(.#'(%!)>,/)**#$3!#3;$%;#3&!

$.-)/!,(/(+).)/*9!M$/!)>(+,%)7!R0!'(3!8)!4)1#3)4!4#/)'.%0!(*!(!32+8)/!(34!L0!'(3!8)!4)1#3)4!#3!.)/+*!

$1!'$3')3./(.#$3!'$3;)/.)4!.$!,$,2%(.#$3!32+8)/9!?-)!23#.*!$1!.-)!,(/(+).)/*!'(3!8)!&#;)3!#3!

'$++)3.*!1$/!'%(/#.0T!

begin parameters

V_ext 1.6e-9 #liters

N_Avo 6.022e23 #molecule number per mole

R0 1e5 #molecule number per cell

! Rf!

L0 L_conc*V_ext*N_Avo #molecule number

end parameters

P(/(+).)/*!2*)4!)%*)5-)/)!#3!.-#*!.2.$/#(%!(/)!(**2+)4!.$!-(;)!8))3!4)1#3)4!#3!.-)!,(/(+).)/*!8%$'6!

)#.-)/!5#.-!32+)/#'(%!;(%2)*!$/!(*!)>,/)**#$3*!$1!$.-)/!,(/(+).)/*9!

M#3(%%07!5)!3))4!.$!4)1#3)!.-)!$8*)/;(8%)*!1$/!.-)!+$4)%9!?-#*!+$4)%!./)(.*!/)'),.$/!(&&/)&(.#$3!(34!

,-$*,-$/0%(.#$39!A$.!$3%0!(/)!5)!#3.)/)*.)4!#3!.-)!32+8)/!$1!4#+)/!*,)'#)*7!82.!(%*$!#3!.-)!32+8)/!$1!

/)'),.$/*!#3!4#+)/*9!?-)*)!'(3!8)!/),/)*)3.)4!2*#3&!*,)'#)*@$8*)/;(8%)*!(34!+$%)'2%)*@$8*)/;(8%)*!

/)*,)'.#;)%0!#3!.-)!$8*)/;(8%)*!8%$'6!C3$.)!.-)!2*)!$1!5#%4'(/4*!#3!$8*)/;(8%)*D9!

begin observables

Molecules BoundLigand L(rec!+)

Molecules BoundReceptor R(lig!+)

Species Dimer R(dim!0).R(dim!0)

Species UnligatedSpecies R(lig,dim),R(lig,dim!0).R(lig,dim!0)

Species PhosphSpecies R(y1068~p),R(y1173~p)

end observables

?-)!Molecules/Species!6)05$/4!#34#'(.)*!.-)!.0,)!$1!$8*)/;(8%)9!?-#*!#*!1$%%$5)4!80!.-)!3(+)!

(**#&3)4!.$!.-)!$8*)/;(8%)!(34!.-)3!.-)!%#*.!$1!,(..)/3*!.$!+(.'-!.-)!*,)'#)*!*2++)4!2,!#3!.-)!

$8*)/;(8%)9!

K3!$,.#$3(%!123'.#$3*!8%$'6!'(3!8)!2*)4!.$!4)1#3)!&%$8(%!123'.#$3*!$1!.-)!$8*)/;(8%)*9!?-)*)!123'.#$3*!

'(3!8)!2*)4!.$!./('6!6)0!;(/#(8%)*!#3!.-)!*#+2%(.#$3!$/!1$/!+$4#1#)4!/(.)!%(5*!#3!/)('.#$3!/2%)*!C*))!

"):06+5!PDCD9!?-)!$8*)/;(8%)*!/)1)/)3')4!80!(!&%$8(%!123'.#$3!+2*.!8)!4)1#3)4!#3!.-)!$8*)/;(8%)*!8%$'69!

?-)!123'.#$3!#.*)%1!#*!4)1#3)4!#3!.-)!123'.#$3*!8%$'69!?-)!$8*)/;(8%)*!8%$'6!+2*.!,/)')4)!.-)!123'.#$3*!

8%$'6!1$/!.-)!$8*)/;(8%)*!.$!8)!2*)4!#3!.-)!123'.#$3*9!

! Uh!

K3!)>(+,%)!123'.#$3!#3;$%;#3&!.-)!*,)'#)*@$8*)/;(8%)!SubstrateSum!5$2%4!8)!4)1#3)4!#3!.-)!123'.#$3*!

8%$'6!(*T!

begin functions

k_func kcat*E_tot/(KM + SubstrateSum)

end functions

K%.-$2&-!#.!#*!3$.!2*)4!#3!.-#*!,(/.#'2%(/!+$4)%7!k_func!4)1#3)4!-)/)!'(3!8)!2*)4!#3*.)(4!$1!.-)!L(.!/(.)!

%(5!#3!(!/)('.#$3!/2%)9!

M@< &"-#)-./*5K$*+,)$#*G3!.-#*!*)'.#$37!5)!'/)(.)!*);)/(%!-0,$.-)*)*!(8$2.!.-)!/)'),.$/!(&&/)&(.#$3!+)'-(3#*+!(34!.-)3!

#+,%)+)3.!/)('.#$3!/2%)*!8(*)4!$3!)('-!-0,$.-)*#*9!

?-)!/2%)*!(/)!)3'%$*)4!#3!(!/)('.#$3!/2%)*!8%$'6!(*T!

begin reaction rules

[reaction_rule]

[reaction_rule]

end reaction rules

M@<@: L-9$3%L$?$.)$.5*8K,(?K,3J#'5-,.*

Knowledge Base: The kinase on EGFR is inactive in monomers and is activated by dimerization (37).

G1!8$.-!,-$*,-$/0%(.#$3!*#.)*!5)/)!/),/)*)3.)4!(*!#4)3.#'(%7!C1$/!)>(+,%)7!#1!.-)!+$%)'2%)!.0,)!5)/)!

R(lig,dim,y~0~p,y~0~p)!#3*.)(4D7!.-)3!5)!5$2%4!$3%0!3))4!(!*#3&%)!/2%)!.$!/),/)*)3.!#.9!?-)!

4#+)/#=(.#$3!#*!&#;)3!(*!'$3.)>.!(34!.-)!./(3*1$/+(.#$3!#*!,-$*,-$/0%(.#$39!

R(dim!0).R(dim!0,y~0) -> R(dim!0).R(dim!0,y~p) k_ph

! Ug!

<$5);)/7!5)!-(;)!'-$*)3!.$!+$4)%!.-)!.5$!,-$*,-$/0%(.#$3!*#.)*!4#*.#3'.%09!?-)/)1$/)!5)!5$2%4!3))4!

.5$!4#11)/)3.!/2%)*9!?-)!6#3).#'*!'(3!*.#%%!8)!+(4)!#4)3.#'(%!5#.-!#4)3.#'(%!/(.)!'$3*.(3.*7!$/!3$3@#4)3.#'(%!

5#.-!4#11)/)3.!/(.)!'$3*.(3.*9!!

R(dim!0).R(dim!0,y1068~0) -> R(dim!0).R(dim!0,y1068~p) k_ph1

R(dim!0).R(dim!0,y1173~0) -> R(dim!0).R(dim!0,y1173~p) k_ph2

L#3')!.-)!$3%0!(;(#%(8%)!8#34#3&!,(/.3)/!$3!dim!'$+,$3)3.!#*!(3$.-)/!dim!'$+,$3)3.!C#9)9!5)!(/)!3$.!

5/#.#3&!(30!/)('.#$3!/2%)*!5-)/)!dim!8#34*!.$!(30.-#3&!)%*)D7!5)!'(3!*-$/.)3!.-)!'$3.)>.!/),/)*)3.(.#$3!

2*#3&!.-)!i!5#%4'(/4!$3!.-)!8$349!

R(dim!+,y1068~0) -> R(dim!+,y1068~p) k_ph1

R(dim!+,y1173~0) -> R(dim!+,y1173~p) k_ph2

A$.!4),-$*,-$/0%(.#3&!.-)!.0/$*#3)!*#.)*!5$2%4!/)*2%.!#3!/23(5(0!,-$*,-$/0%(.#$37!5-#'-!#*!234)*#/(8%)9!

I)!'(3!2*)!(!23#1$/+!1#/*.@$/4)/!8('6&/$234!4),-$*,-$/0%(.#$3T!

R(y1068~p) -> R(y1068~0) k_deph

R(y1173~p) -> R(y1173~0) k_deph

?-#*!#*!(!;(%#4!(**2+,.#$3!.$!+(6)!5-)3!.-)!,-$*,-(.(*)*!(/)!-#&-%0!('.#;)!(34!3$3@*,)'#1#'9!

M@<@< Q-/'.)%L$?$.)$.5*L-9$3-W'5-,.*

Hypothesis: Ligand binding initiates receptor dimerization.

S>,/)**)4!(*!(!./(4#.#$3(%!)O2#%#8/#2+!+$4)%7!

! ! ! !!"#$ !"!!!!!

!" ! !" !!"# !""!!

! UJ!

<)/)7!.-)!/)('.#$3*!(/)!/),/)*)3.)4!(*!8#4#/)'.#$3(%!)O2#%#8/#2+!/)('.#$3*!4)1#3)4!80!)X#626B&6#$!

%--+:6%06+5!:+5-0%50-7!5-#'-!(/)!/(.#$*!$1!.-)!1$/5(/4!(34!/);)/*)!/(.)!'$3*.(3.*9!"ABH!/)O2#/)*!.-(.!

.-)!+$4)%!8)!*,)'#1#)4!#3!.)/+*!$1!#34#;#42(%!/(.)!'$3*.(3.*7!#9)9!

! ! !!!!!!!!"!!!!!!!!"#$#!!!"#$ !

!!!!!!!!!

!" ! !"!!"!!!!!"

!""!!!!!!!!!"#$#!!!"# ! !!"!!!!"

!

?-)!.5$!8#4#/)'.#$3(%!/)('.#$3*!'(3!8)!4#/)'.%0!./(3*%(.)4!#3.$!8#4#/)'.#$3(%!/)('.#$3!/2%)*9!

R(lig,dim) + L(rec) <-> R(lig!0,dim).L(rec!0) k_f,k_r

R(lig!+,dim) + R(lig!+,dim) <-> R(lig!+,dim!0).R(lig!+,dim!0) k_f_d,k_r_d

A$.)!.-(.!.-)!8#+$%)'2%(/!(**$'#(.#$3!#3!.-)!*)'$34!/2%)!#*!*0++)./#'!(34!#3!.-)!./(4#.#$3(%!)>,/)**#$3!

5$2%4!/)O2#/)!(!Cg]JD!+2%.#,%#'(.#$3!1('.$/9!<$5);)/7!(*!+)3.#$3)4!)(/%#)/7!"#$A).B)3!/)O2#/)*!.-)!

+$4)%)/!.$!2*)!.-)!(*0++)./#'!/)('.#$3!/(.)!'$3*.(3.9!N3!,/$')**#3&!.-)!/2%)7!"#$A).B)3!4#*'$;)/*!.-)!

*0++)./0!(34!(2.$+(.#'(%%0!(**#&3*!.-)!+2%.#,%#'(.#$3!1('.$/9!

Knowledge Base: Both singly-ligated and unligated dimers have been discovered to exist (38).

?-)!+$4)%!(*!#.!*.(34*!/),/)*)3.*!.-)!.0,#'(%!+(33)/!#3!5-#'-!%#&(34@#342')4!4#+)/#=(.#$3!(34!

,-$*,-$/0%(.#$3!#*!+$4)%)4!)9&9!#3!/)1*9!!$$#%2#'3&9!<$5);)/!.-#*!+$4)%!#*!4)1#'#)3.!8)'(2*)!#.!4$)*!3$.!

'(,.2/)!.-)!12%%!3(.2/)!$1!.-)!#3.)/('.#$3!8).5))3!%#&(34@8#34#3&!(34!4#+)/#=(.#$3!,/$')**)*9!G3!.-)!

'2//)3.!+$4)%!-0,$.-)*#*7!.-)!4#+)/!*.(.)!#*!#3)>./#'(8%0!%#36)4!.$!.-)!%#&(34@8$234!*.(.)7!5-#'-!#*!3$.!

./2)!#3!.-)!%#&-.!$1!.-)!(8$;)!);#4)3')9!?-)!)>,)/#+)3.(%!);#4)3')!$1!)>#*.)3')!$1!*#3&%0@%#&(.)4!(34!

23%#&(.)4!4#+)/*!)3(8%)*!&)J):0658!.-)!'2//)3.!+$4)%!-0,$.-)*#*9!

M@<@> Q-/'.)%;.)$?$.)$.5*L-9$3-W'5-,.*

! UR!

?$!)>,%(#3!.-)!)>#*.)3')!$1!*#3&%0@%#&(.)4!(34!23%#&(.)4!4#+)/*7!5)!#3./$42')!(3!(%.)/3(.)!-0,$.-)*#*9!

Hypothesis: Ligand binding and receptor dimerization are independent of each other.

S>,/)**)4!(*!(!./(4#.#$3(%!)O2#%#8/#2+!+$4)%!C5#.-!)O2#%#8/#2+!(**$'#(.#$3!'$3*.(3.*D7!

!!!! !! ! !!"#$ !!!"! ! !!"#$ !"!!"!!!"# !!!"# !!!"#

!!! !! ! !!"#$ !!"! ! !!"#$ !""!!

G3!.)/+*!$1!/)('.#$3*T!

!!!! !! !!!!!!

!!!"! !!!!!!

!"!!"

!!"!!!!" !!"!!!!" !!"!!!!"

!!! !! !!!!!!

!!"! !!!!!!

!""!

!

!"#$#!!!"#$ !!!!!!!!"#!!!"# ! !!"

!!"!

L#3')!.-)!4#+)/#=(.#$3!(34!%#&(34!8#34#3&!/)('.#$3*!(/)!'$+,%).)%0!#34),)34)3.!$1!)('-!$.-)/!#3!.-#*!

+$4)%7!5)!'(3!+$4)%!.-#*!*0*.)+!2*#3&!.5$!'$3.)>.@1/))!/2%)*T!

R(lig) + L(rec) <-> R(lig!0).L(rec!0) k_f,k_r

R(dim) + R(dim) <-> R(dim!2).R(dim!2) k_f_d,k_r_d

A$.)!.-(.!80!/)+$;#3&!'$3.)>.7!5)!-(;)!)3(8%)4!.-)!/)('.#$3!/2%)!.$!&)3)/(.)!(44#.#$3(%!/)('.#$3*9!?-)!

4#+)/#=(.#$3!/2%)!#3!.-)!)(/%#)/!-0,$.-)*#*!&)3)/(.)4!$3%0!$3)!/)('.#$3T!WH!5#.-!WH9!<)/)7!#.!&)3)/(.)*!

.-/))!4#+)/#=(.#$3!/)('.#$3*T!W!5#.-!W7!W!5#.-!WH!(34!WH!5#.-!WH9!

Knowledge Base: Phosphorylation of receptor increases on ligand addition (reviewed in (36)).

! UU!

G3!.-#*!+$4)%7!5)!-(;)!4)%#36)4!.-)!4#+)/#=(.#$3!1/$+!%#&(34@8#34#3&7!#9)9!%#&(34!8#34#3&!4$)*!3$.!

#31%2)3')!.-)!)O2#%#8/#2+!'$3')3./(.#$3*!$1!.-)!4#+)/!C(34!;#')!;)/*(D9!L#3')!,-$*,-$/0%(.#$3!#*!4#+)/@

4),)34)3.7!.-#*!#+,%#)*!.-(.!%#&(34@8#34#3&!'(33$.!4#/)'.%0!#31%2)3')!,-$*,-$/0%(.#$39!?-)!+$4)%!

8)-(;#$/!#*!(.!$44*!5#.-!)>,)/#+)3.(%!);#4)3')9!<)3')!.-#*!+$4)%!-0,$.-)*#*!#*!(%*$!&)J):0),9!

M@<@B A,,?$3'5-G$*Q-/'.)*&-.)-./*'.)*L-9$3-W'5-,.*

?5$!);)3.*!(/)!*(#4!.$!)>-#8#.!:++4)&%06H60'!#1!.-)!*)O2)3')!$1!$''2//)3')!$1!.-$*)!.5$!);)3.*!(11)'.*!

.-)!#3./#3*#'!/(.)*!(.!5-#'-!.-)0!$''2/9!N3)!,%(2*#8%)!+$4)%!1$/!4#+)/!1$/+(.#$3!,$*#.*!.-(.!.-)!

+$3$+)/7!23%#&(.)4!4#+)/!(34!*#3&%0@%#&(.)4!4#+)/!(%%!-(;)!4#11)/)3.!(11#3#.#)*!1$/!.-)!%#&(34!!'"&9!

Hypothesis: Ligand binding and receptor dimerization are mutually cooperative.

S>,/)**#3&!.-#*!(*!(!./(4#.#$3(%!)O2#%#8/#2+!+$4)%!C5#.-!)O2#%#8/#2+!(**$'#(.#$3!'$3*.(3.*D7!

!!!! !! !!!"#$!! !!!"! !

!!"#$!! !"!!"!!!"#!! !!!"#!! !!!"#!!!!! !! !

!!"#$!! !!"! !!!"#$!! !""!

!

F$$,)/(.#;#.0!#+,$*)*!.-)/+$403(+#'!'$3*./(#3.*!$3!.-)!+$4)%9!G1!.-)/)!#*!3$!)>.)/3(%!)3)/&0!*$2/')!$/!

*#367!(!*0*.)+!$1!/);)/*#8%)!/)('.#$3*!*-$2%4!$8)0!+(**!(34!)3)/&0!'$3*)/;(.#$39!G1!.-)/)!(/)!+2%.#,%)!

,(.-*!1/$+!.-)!*(+)!*).!$1!/)('.(3.*!.$!.-)!*(+)!*).!$1!,/$42'.*7!.-)3!.-)!,/$42'.!$1!.-)!)O2#%#8/#2+!

'$3*.(3.*!(%$3&!(%%!,(.-*!*-$2%4!8)!#4)3.#'(%9!G3!$.-)/!5$/4*7!.-)!,/$42'.!$1!)O2#%#8/#2+!'$3*.(3.*!$;)/!(!

'%$*)4!%$$,!$1!/);)/*#8%)!/)('.#$3*!*-$2%4!8)!23#.09!?-#*!)11)'.!#*!'(%%)4!,)0%62),!B%2%5:)!(34!,%(')*!

'$3*./(#3.*!$3!.-)!,(/(+).)/*!(34!/2%)*!2*)4!.$!+$4)%!.-)!*0*.)+!C)9&9!#3!!%2&D9!G3!.-#*!'(*)7!.-)/)!(/)!(.!

%)(*.!.5$!'%$*)4!%$$,*7!/)*2%.#3&!#3!.-)!1$%%$5#3&!'$3*./(#3.*T!

!!"#$!!!!"#!! ! !!!"#$!!!!"#!!!

!!"#$!!!!"#!! ! !!!"#$!!!!"#!!!

! U[!

?$!*#+,%#10!,(/(+).)/*7!5)!4)*'/#8)!.-)!.-/))!%#&(34!8#34#3&!)O2#%#8/#2+!'$3*.(3.*!2*#3&!+2%.#,%#'(.#;)!

1('.$/*!!!(34!"!$3!.-)!+$3$+)/!%#&(34!8#34#3&!)O2#%#8/#2+!'$3*.(3.!E8#347!#9)9!

!!"#$!! ! !!"#$!

!!"#$!! ! !!!"#$!!!

!!"#$!! ! !!!"#$!!!

Z*#3&!.-)*)!/)%(.#$3*!(34!.-)!'$3*./(#3.*!$8.(#3)4!,/);#$2*%07!5)!'(3!4)*'/#8)!.-)!4#+)/#=(.#$3!

)O2#%#8/#2+!'$3*.(3.*!(*!+2%.#,%#'(.#;)!1('.$/*!$3!.-)!23%#&(.)4!4#+)/#=(.#$3!)O2#%#8/#2+!'$3*.(3.!E4#+T!

!!"#!! ! !!"#!!

!!"#!! ! !!!"#!

!!"#!! ! !"!!"#!

?-)!3).5$/6!'(3!8)!/)5/#..)3!(*T!

!!!! !! ! !!"#$ !!!"! ! !!"#$ !"!!!!!!"# !!!!"# !!"!!"#

!!! !! ! !!!"#$ !!"! ! !!!"#$ !""!!

A$.)!.-(.!"#$A).B)3!/)O2#/)*!/)('.#$3!/(.)!'$3*.(3.*7!5-)/)(*!-)/)!5)!-(;)!$3%0!+(3(&)4!.$!$8.(#3!

+2%.#,%#'(.#;)!1('.$/*!1$/!.-)!)O2#%#8/#2+!'$3*.(3.*9!I)!4$!3$.!63$5!-$5!.-)!1('.$/!4#*./#82.)*!8).5))3!

.-)!1$/5(/4!/)('.#$3!(34!.-)!/);)/*)!/)('.#$3!(34!+2*.!+(6)!(**2+,.#$3*!(8$2.!#.9!

K!&)3)/(%!5(0!$1!/)*$%;#3&!.-#*!#**2)!5$2%4!8)!.$!4#*./#82.)!.-)!+2%.#,%#'(.#;)!1('.$/*!#3!.-)!1$%%$5#3&!

+(33)/!!'$&T!

!"!!! ! !!!!!!! !! ! ! !!

!!!

!!! ! !!!!!

! U\!

!!! ! !!!!!!!

! ! ! ! !!

A$57!80!'-(3&#3&!#7!5)!'(3!'$3./$%!.-)!4#*./#82.#$3!$1!.-)!+2%.#,%#'(.#;)!1('.$/!$;)/!.-)!1$/5(/4!(34!

/);)/*)!/)('.#$3!/(.)!'$3*.(3.*!#3!.-)!+$*.!&)3)/(%!5(09!?-)/)!#*!3$!*#3&%)!8)*.!;(%2)!1$/!#9!G3!.-#*!

.2.$/#(%7!5)!2*)!#oh7!'(2*#3&!.-)!+2%.#,%#'(.#;)!1('.$/!.$!(11)'.!$3%0!.-)!/);)/*)!/(.)!(34!3$.!.-)!1$/5(/4!

/(.)7!#9)9!

!!! ! !!!

!!! ! !!!!! !!!! !

W)5/#.#3&!.-)!)O2#%#8/#2+!+$4)%!#3!.)/+*!$1!/)('.#$3*!(34!#+,%)+)3.#3&!.-)!+2%.#,%#'(.#;)!1('.$/*!C1$/!

.-)!)O2#%#8/#2+!'$3*.(3.*D!(*!4#;#*#;)!1('.$/*!$3!.-)!/);)/*)!/(.)T!

!!!! !! !!!!!!

!!!"! !!!!!!

!"!!"

!!"!!!!" !!"!!!!!" ! !!"!!!!!" ! !

!!! !! !!!!!! !

!!"! !!!!!! !

!""!

!

!"#$#!!!"#$ !!!!!!!!"#!!!"# ! !!"

!!"!

?-)*)!/)('.#$3*!(/)!3$5!'$3*#*.)3.!5#.-!4).(#%)4@8(%(3')9!`),)34#3&!$3!.-)!;(%2)*!'-$*)3!1$/!!!(34!"7!

$3)!'(3!'(2*)!.-)!*0*.)+!.$!)>-#8#.!+2%.#,%)!'$$,)/(.#;)!8)-(;#$/*9!

Knowledge Base: Dimerization is enhanced by ligand-binding. However, the two ligand-binding sites on the

dimer are negatively cooperative (43).

! Ua!

G1!.-)!23%#&(.)4!4#+)/!-(*!(!-#&-)/!(11#3#.0!1$/!%#&(34!.-(3!.-)!+$3$+)/7!.-)!,/)*)3')!$1!%#&(34!*-#1.*!

.-)!4#+)/@+$3$+)/!)O2#%#8/#2+!.$5(/4*!.-)!4#+)/7!5-#'-!(%*$!#3'/)(*)*!/)'),.$/!,-$*,-$/0%(.#$39!G3!

.-#*!+$4)%!%#&(34!8#34#3&!'$$,)/(.)*!,$*#.#;)%0!5#.-!4#+)/!1$/+(.#$3!%)(4#3&!.$!(3!#3'/)(*)!#3!

4#+)/#=(.#$3!5-)3!%#&(34!#*!(44)49!!K3$.-)/!1)(.2/)!$1!.-#*!*0*.)+7!-$5);)/7!(,,)(/*!.$!8)!.-(.!$3')!

$3)!/)'),.$/!#3!(!4#+)/!8#34*!%#&(347!.-)!*)'$34!/)'),.$/!)>-#8#.*!(!'$3*#4)/(8%0!/)42')4!(11#3#.0!1$/!

%#&(34!!'"&9!G3!$.-)/!5$/4*7!%#&(34!8#34#3&!#*!5)8%06H)2'!:++4)&%06H)!$3!.-)!4#+)/9!L./2'.2/(%!);#4)3')!

*./$3&%0!*2,,$/.#3&!3)&(.#;)!'$$,)/(.#;#.0!-(*!)+)/&)4!/)')3.%0!!''&9!

"(*)4!$3!.-)!)O2#%#8/#2+!'$3*.(3.*!4).)/+#3)4!1/$+!)>,)/#+)3.!C!'%&7!M#&!RD7!5)!2*)!.-)!;(%2)*!!!o!gJh!

(34!"!o!h9ha9!?-)*)!;(%2)*!(/)!'$3*#*.)3.!5#.-!$2/!,/);#$2*!4#*'2**#$3!.-(.!%#&(34!8#34#3&!)3-(3')*!

4#+)/#=(.#$3!CE4#+7JogJhE4#+7g!(34!E4#+7Roc9UE4#+7gD!5-)/)(*!.-)!%#&(34!8#34#3&!.$!.-)!4#+)/!#*!3)&(.#;)%0!

'$$,)/(.#;)!CE8#347Roh9haE8#347JD!

:$4)%#3&!.-#*!*')3(/#$!/)O2#/)*!+$/)!/)('.#$3!/2%)*!.-(3!.-)!,/);#$2*!+$4)%9!?-#*!#*!(!'-(/('.)/#*.#'!

1)(.2/)!$1!/2%)@8(*)4!+$4)%#3&9!G34),)34)3.!,/$')**)*7!%('6#3&!/)('.#$3!'$3.)>.7!(/)!.-)!)(*#)*.!.$!

)>,/)**!5#.-!.-)!1)5)*.!32+8)/!$1!/2%)*9!Z3#4#/)'.#$3(%!#31%2)3')*7!#3!5-#'-!$3)!,/$')**!(11)'.*!.-)!/(.)!

$1!(3$.-)/!82.!3$.!;#')!;)/*(7!/)O2#/)!(44#.#$3(%!'$3.)>.9!"#4#/)'.#$3(%!#31%2)3')*7!#3!5-#'-!.5$!

,/$')**)*!+2.2(%%0!(11)'.!.-)#/!/(.)*!&#;#3&!/#*)!.$!'$$,)/(.#;#.07!/),/)*)3.!.-)!+$*.!'$+,%)>!%#36(&)!

8).5))3!.5$!'$+,$3)3.*9!!F(/)!+2*.!8)!.(6)3!#3!+$4)%#3&!*2'-!#3.)/('.#$3*!.$!)3*2/)!.-(.!4).(#%)4!

8(%(3')!#*!$8)0)49!!

M$/!.-)!'2//)3.!-0,$.-)*#*7!5)!'(3!5/#.)!.-)!/2%)*!(*!1$%%$5*T!

# Ligand association

R(lig)+L(rec) -> R(lig!1).L(rec!1) k_f

# Ligand dissociation for monomer, singly-ligated dimer and doubly-ligated dimer

R(dim,lig!1).L(rec!1) -> R(dim,lig)+L(rec) k_r

! Uc!

R(dim!2,lig).R(dim!2,lig!1).L(rec!1) -> \

R(dim!2,lig).R(dim!2,lig) + L(rec) k_r/alpha

R(dim!2,lig!+).R(dim!2,lig!1).L(rec!1) -> \

R(dim!2,lig!+).R(dim!2,lig) + L(rec) k_r/beta

# Dimer association

R(dim) + R(dim) -> R(dim!1).R(dim!1) k_f_d

#Dimer dissociation for unligated/singly-ligated/doubly-ligated dimers

R(lig,dim!1).R(lig,dim!1) -> R(lig,dim) + R(lig,dim) k_r_d

R(lig!+,dim!1).R(lig,dim!1) -> R(lig!+,dim) + R(lig,dim) k_r_d/alpha

R(lig!+,dim!1).R(lig!+,dim!1) -> R(lig!+,dim) + R(lig!+,dim) k_r_d/(alpha*beta)

?-#*!+$4)%!$1!/)'),.$/!(&&/)&(.#$3!'$//)*,$34*!'%$*)%0!5#.-!.-)!)>,)/#+)3.(%!(34!*./2'.2/(%!);#4)3')9!

<)3')!5)!(''),.!.-)*)!/2%)*!(34!,/$'))4!.$!*#+2%(.)!.-)!+$4)%9!?-)!'-$#')!$1!/(.)!,(/(+).)/*!#*!

4#*'2**)4!#3!&)3)/(%!#3!"):06+5!Y9!

M@> 1-9"#'5-./*5K$*9,)$#*?-)!+$%)'2%)!.0,)*7!,(/(+).)/*7!*))4!*,)'#)*!(34!/)('.#$3!/2%)*!'$3*.#.2.)!.-)!+$4)%9!_(/#$2*!('.#$3*!

'(3!.-)3!8)!,)/1$/+)4!$3!.-)!+$4)%!2*#3&!.-)!('.#$3*!8%$'69!K'.#$3*!(/)!,/)@)>#*.#3&!"ABH!/$2.#3)*!

.-(.!'(3!8)!'(%%)4!(.!5#%%!80!.-)!+$4)%)/9!?0,#'(%%07!('.#$3*!/)O2#/)!('.#$3@,(/(+).)/*!(34!1%(&*!(34!

*-$2%4!8)!.)/+#3(.)4!5#.-!.-)!*)+#'$%$3!*0+8$%9!

begin actions

[action];

[action];

end actions

M@>@: V$5=,3P*S$.$3'5-,.*

! Uf!

?-)!3).5$/6!&)3)/(.#$3!('.#$3!*.(/.*!5#.-!.-)!*))4!*,)'#)*!(34!#.)/(.#;)%0!(,,%#)*!.-)!/)('.#$3!/2%)*!.$!

.-)!*,)'#)*!*).!.$!&)3)/(.)!3)5!/)('.#$3*!(34!*,)'#)*9!?-#*!'(3!,/$'))4!.#%%!.-)!3).5$/6!*#=)!*.$,*!

#3'/)(*#3&7!#3!5-#'-!.-)!'(*)!.-)!5-$%)!3).5$/6!-(*!8))3!&)3)/(.)49!N/7!.-)!*#=)!$1!.-)!3).5$/6!'(3!8)!

(/8#./(/#%0!%#+#.)4!80!%#+#.#3&!.-)!32+8)/!$1!#.)/(.#$3*!C2*#3&!max_iter!1%(&D!$/!.-)!+(>#+2+!32+8)/!$1!

+$%)'2%)*!C2*#3&!max_stoichD!#3!(!'$+,%)>9!?-)!3).5$/6!#*!,/#3.)4!$2.!#3!(!.)>.!1#%)!5#.-!ZD5)0[!

)>.)3*#$39!?-)!3(+)!$1!.-)!DB582!1#%)!#*!2*)4!(*!.-)!8(*)!3(+)!1$/!.-)!D5)0!1#%)9!!

?-)!4#11)/)3.!*,)'#)*!(/)!(**#&3)4!32+8)/*!80!4)1(2%.!.$!'$+,('.%0!/),/)*)3.!.-)!/)('.#$3*7!82.!.-)!12%%!

'$31#&2/(.#$3!'(3!(%*$!8)!5/#..)3!$2.!#3*.)(4!2*#3&!(!TextReaction!1%(&9!?-)!overwrite!1%(&!#*!2*)4!.$!

#34#'(.)!5-).-)/!.$!$;)/5/#.)!(!,/)@)>#*.#3&!1#%)!$1!.-)!*(+)!3(+)9!K!.0,#'(%!generate_network!

'$++(34!5$2%4!%$$6!%#6)!.-#*T!

generate_network({overwrite=>1,max_stoich=>{“R”,”2”},max_iter=>20,TextReaction=>1});

G3!.-#*!*.(.)+)3.7!.-)!generate_network!/$2.#3)!#*!'(%%)4!5-#'-!&)3)/(.)*!.-)!/)('.#$3!3).5$/6!*28V)'.!

.$!.-)!'$34#.#$3!.-(.!.-)!+(>#+2+!32+8)/!$1!/)'),.$/!+$%)'2%)*!#*!J!#3!(30!'$+,%)>!(34!.-(.!.-)!/2%)*!

(/)!#.)/(.#;)%0!(,,%#)4!(.!+$*.!Jh!.#+)*9!I-)3!.-)!3).5$/6!#*!8)#3&!5/#..)3!#3!.-)!D5)0!1#%)7!.-)!/$2.#3)!#*!

(%%$5)4!.$!$;)/5/#.)!)>#*.#3&!1#%)*!$1!.-)!*(+)!3(+)!(34!#*!.$%4!.$!5/#.)!4$53!.-)!12%%!*,)'#)*!

*,)'#1#'(.#$3*!#3!.-)!/)('.#$3*9!

M$/!.-)!,2/,$*)*!$1!.-#*!+$4)%7!5)!'$2%4!*#+,%0!2*)T!

generate_network({overwrite=>1,TextReaction=>1});

M$/!%(/&)!3).5$/6*7!#.!#*!(4;#*(8%)!.$!&)3)/(.)!.-)!3).5$/6!$3%0!$3')!2*#3&!.-)!generate_network!

'$++(34!(34!.-)3!1$/!*28*)O2)3.!*#+2%(.#$3!/)2*)!.-)!3).5$/6!2*#3&!.-)!readFile ('.#$3!$/!80!&#;#3&!

.-)!D5)0!1#%)!3(+)!(*!(!,(/(+).)/!#3!$.-)/!('.#$3*!C*))!$3%#3)!4$'2+)3.(.#$3!(.!-..,T]]8#$3).&)39$/&!1$/!

+$/)!4).(#%D9!

! [h!

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#*!.0,#'(%%0!(!,/)@)>#*.#3&!)O2#%#8/(.)4!'$3./$%!*.(.)!(34!.-)!,)/.2/8(.#$3!#*!.0,#'(%%0!.-)!(44#.#$3!$1!*$+)!

'-)+#'(%!*,)'#)*!$/!('.#;(.#$3!$1!*$+)!/)('.#$39!?-)3!(1.)/!(!4)1#3)4!.#+)!$/!(.!+(30!.#+)@,$#3.*7!.-)!

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23.#%!)O2#%#8/#2+!$/!*.)(40!*.(.)!#*!('-#);)49!?-#*!*.),!#*!'(%%)4!.-)!)X#626B&%06+5!*.),9!K!d&$$4e!+$4)%7!

#9)9!$3)!5-#'-!'%$*)%0!'$//)*,$34*!.$!/)(%#.07!#*!$3)!5-)/)!(%%!./(3*1$/+(.#$3*!(/)!'$+,%)+)3.(/0!(34!#3!

.-)!(8*)3')!$1!(!,)/.2/8#3&!(&)3.7!.-)!*0*.)+!)O2#%#8/(.)*9!M$%%$5#3&!)O2#%#8/(.#$37!.-)!,)/.2/8#3&!(&)3.!

#*!(44)4!.$!.-)!*0*.)+!(34!*28*)O2)3.!*#+2%(.#$3!#*!'(%%)4!4)&0#&B%06+5\!$/!,%(#3%0!-6$#2%06+5!C5-#'-!

'(3!8)!+#*%)(4#3&D9!

M$/!.-)!/)'),.$/!(&&/)&(.#$3!+$4)%7!.-)!&/$234!*.(.)!#3;$%;)*!/)'),.$/!(**$'#(.#$3!(34!4#**$'#(.#$3!#3!

.-)!(8*)3')!$1!%#&(34!(34!.-)!,)/.2/8)4!*.(.)!#3;$%;)*!(44#.#$3!$1!%#&(34!(34!+$3#.$/#3&!.-)!

(&&/)&(.#$39!?-)!+$3$+)/#'!/)'),.$/*!.-(.!*))4!.-)!+$4)%!5$2%4!3)')**(/#%0!8)!1(/!(5(0!1/$+!

)O2#%#8/#2+9!Z*#3&!('.#$3*!5)!'(3!*).!.-)!%#&(34!'$3')3./(.#$3!.$!=)/$!(34!.-)3!2*)!32+)/#'(%!N`S!

#3.)&/(.#$3!.$!)O2#%#8/(.)!.-)!+$4)%9!

simulate_ode({suffix=>ode,t_start=>0,t_end=>200,n_steps=>100});

?-)!suffix!$,.#$3!#*!2*)4!.$!(,,)34!.-)!XtY!(34!.-)3!X$4)Y!.$!.-)!8(*)!3(+)7!5-#'-!#*!.(6)3!1/$+!.-)!

3(+)!$1!.-)!DB582!1#%)9!t_start!(34!t_end!#34#'(.)!.-)!.$.(%!.#+)!$;)/!5-#'-!.-)!+$4)%!#*!)O2#%#8/(.)4!

(34!n_steps!#34#'(.)*!.-)!32+8)/!$1!.#+)@,$#3.*!(.!5-#'-!'$3')3./(.#$3*!(/)!/)'$/4)49!!

! [g!

M$%%$5#3&!)O2#%#8/(.#$37!5)!5#*-!.$!(44!%#&(34!(34!,)/.2/8!.-)!+$4)%9!?$!4$!.-#*7!1#/*.!5)!3))4!.$!*(;)!

.-)!'$3')3./(.#$3*!1/$+!.-)!)O2#%#8/(.#$3!*.),!(34!.-)3!(44!3)5!%#&(349!?-#*!#*!(''$+,%#*-)4!2*#3&T!

saveConcentrations();

setConcentration("L(rec)","L0_temp");

?-)!continue!1%(&!'(3!8)!2*)4!.$!.2/3!'$3'(.)3(.)!(!3)5!*#+2%(.#$3!5#.-!.-)!)(/%#)/!$3)9!N3)!+2*.!

+(6)!*2/)!.-(.!.-)!t_start!$1!.-)!3)5!*#+2%(.#$3!#*!.-)!*(+)!(*!.-)!t_end!$1!.-)!)(/%#)/!*#+2%(.#$3!(34!

.-(.!.-)!suffix!;(%2)!#*!3$.!'-(3&)49!K30!32+8)/!$1!*#+2%(.#$3*!'(3!8)!*$!'$3'(.)3(.)49!

simulate_ode({suffix=>ode,continue=>1,t_start=>200,t_end=>500,n_steps=>100});

G3;$'(.#$3!$1!.-)!LLK!*#+2%(.$/!1$%%$5*!.-)!*(+)!*03.(>7!82.!.-)!simulate_ssa!'$++(34!#*!2*)4!

#3*.)(49!M$/!.-)!LLK!(34!N`S!*#+2%(.#$3*7!.-)!)3.#/)!3).5$/6!#*!&)3)/(.)4!C(34!*(;)4!#3!.-)!D5)0!1#%)D!

(34!.-)!./(V)'.$/#)*!C'$3')3./(.#$3!;*9!.#+)D!$1!(%%!*,)'#)*!(/)!/)'$/4)4!#3!.-)!D:,%0!.)>.!1#%)9!?-)!

./(V)'.$/#)*!$1!.-)!$8*)/;(8%)*!C5-#'-!(/)!5)#&-.)4!*2+*!$1!*,)'#1#'!*,)'#)*D!(/)!/)'$/4)4!#3!.-)!D8,%0!

.)>.!1#%)9!?-)!AM*#+!+).-$4!4$)*!3$.!&)3)/(.)!.-)!3).5$/6!(34!.-)/)1$/)!5/#.)*!$3%0!(!D8,%0!1#%)9!L#3')!

+2%.#,%)!*#+2%(.#$3*!'(3!8)!'$3'(.)3(.)4!#3!(!*#3&%)!('.#$3*!8%$'67!2*)!$1!(,,/$,/#(.)!*211#>)*!#*!

)3'$2/(&)4!.$!4#*.#3&2#*-!8).5))3!4(.(!1#%)*9!!

G1!.-)!continue!1%(&!5(*!*).!.$!g!(34!.-)!*211#>!5(*!3$.!'-(3&)47!.-)3!.-)!./(V)'.$/0!$1!.-)!*#+2%(.#$3!#*!

'$3'(.)3(.)4!5#.-!.-)!,/);#$2*!*#+2%(.#$39!M$/!(!*#3&%)!*)O2)3')!$1!'$3'(.)3(.)4!*#+2%(.#$3*7!(!*#3&%)!

D:,%0!1#%)!(34!(!*#3&%)!D8,%0!1#%)!(/)!&)3)/(.)49!G1!.-)!continue!1%(&!5(*!*).!.$!h!C5-#'-!#*!.-)!4)1(2%.!

;(%2)D!$/!#1!.-)!*211#>!2*)4!1$/!.-)!*#+2%(.#$3!*.),!#*!'-(3&)47!.-)3!)('-!*#+2%(.#$3!$2.,2.!#*!5/#..)3!.$!(!

*),(/(.)!*).!$1!4(.(!1#%)*9!

?$!*#+2%(.)!.-)!*(+)!,)/.2/8(.#$3!2*#3&!LLK7!5)!5$2%4!3))4!.$!/)*).!.-)!*,)'#)*!'$3')3./(.#$3*!.$!.-)!

)O2#%#8/(.)4!*.(.)9!?-#*!#*!,)/1$/+)4!80!.-)!resetConcentrations()!+).-$4!5-#'-!'-(3&)*!(%%!.-)!

*,)'#)*!'$3')3./(.#$3*!.$!5-(.!.-)0!5)/)!42/#3&!.-)!%(*.!saveConcentrations()!'(%%9!M$%%$5#3&!.-)!

! [J!

/)*).7!%#&(34!#*!#3./$42')4!2*#3&!.-)!setConcentration()!+).-$4!(34!LLK!#*!2*)4!.$!*#+2%(.)!.-)!

+$4)%9!!

AM*#+!'(3!8)!#3;$6)4!2*#3&!.-)!simulate_nf!'$++(347!,/$;#4)4!.-)!8#3(/0!1$/!AM*#+!)>#*.*!#3!.-)!8#3!

*281$%4)/!$1!.-)!"#$A).B)3!#3*.(%%(.#$39!?-)!('.#$3*!.-(.!'(3!8)!2*)4!#3!.-)!('.#$3*!8%$'6!(34!.-)#/!

/)*,)'.#;)!*03.(>!(/)!,$*.)4!5#.-!.-)!4$'2+)3.(.#$3!$3!.-)!"#$A).B)3!5)8*#.)!C-..,T]]8#$3).&)39$/&D9!

M@>@> TH$4"5-,.*

?-)!('.#$3*!8%$'6!#*!2*)4!.$!%#*.!.-)!*)O2)3')!$1!'$++(34*!.-(.!.-)!+$4)%)/!5#*-)*!.$!#+,%)+)3.!5-)3!

"#$A).B)3!)>)'2.)*!.-)!+$4)%9!?-)!+$4)%)/!*-$2%4!*(;)!.-)!'$+,%).)!+$4)%!(*!(!DB582!1#%)!C*(0!

+$4)%983&%D7!$,)3!(!.)/+#3(%!$/!'$++(34!,/$+,.!(34!)3.)/!.-)!4#/)'.$/0!#3!5-#'-!.-)!"ABH!1#%)!

/)*#4)*9!?-)3!.-)!1$%%$5#3&!'$++(34!*-$2%4!8)!#**2)4T!

perl /…/BioNetGen/Perl2/BNG2.pl model.bngl

5-)/)!]u]!#*!(!,%(')-$%4)/!1$/!.-)!,(.-!.$!.-)!,(/)3.!1$%4)/!5-)/)!"#$A).B)3!#*!#3*.(%%)49!?-)!*%(*-!

'$3;)3.#$3!2*)4!C8('6*%(*-7!1$/5(/4!*%(*-D!+#&-.!4#11)/!4),)34#3&!$3!.-)!.)/+#3(%!2*)49!M$/!)>(+,%)7!

$3!(!I#34$5*!'$++(34!,/$+,.7!.-)!'$++(34!5$2%4!%$$6!%#6)T!

perl “C:\BioNetGen\Perl2\BNG2.pl” model.bngl

N3!(!Z3#>!.)/+#3(%!*2'-!(*!8(*-!C1$234!#3!NL!v!(34!H#32>D7!.-)!'$++(34!5$2%4!%$$6!%#6)T!

perl /Users/username/BioNetGen/Perl2/BNG2.pl model.bngl

P)/%!#*!/)O2#/)4!.$!/23!"#$A).B)3!(34!+#&-.!3))4!.$!8)!*),(/(.)%0!#3*.(%%)4!$3!')/.(#3!,%(.1$/+*9!?-)!

'$++(34!'(3!(%*$!8)!)+8)44)4!#3!.)/+#3(%!*'/#,.*!(34!$.-)/!*'/#,.#3&!)3;#/$3+)3.*!*2'-!(*!W7!N'.(;)7!

:(.H(8!$/!:(.-)+(.#'(9!

N3!)>)'2.#$37!"#$A).B)3!/)(4*!.-)!"ABH!1#%)!(34!*)O2)3.#(%%0!#+,%)+)3.*!.-)!('.#$3*!#3!.-)!('.#$3*!

8%$'69!M#%)*!5/#..)3!80!.-)!('.#$3*!C*(07!3).5$/6!&)3)/(.#$3!$/!*#+2%(.#$3D!(/)!*(;)4!#3!.-)!*(+)!1$%4)/9!

! [R!

M@>@B 7.'#J(-(*

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4#11)/)3.!*$1.5(/)!1$/!*.(.#*.#'(%!(3(%0*#*!(34!;#*2(%#=(.#$37!#3'%24#3&!C82.!3$.!%#+#.)4!.$D!*,/)(4*-)).!

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'$+,2.#3&!)3;#/$3+)3.*!C:(.%(87!N'.(;)7!W7!:(.-)+(.#'(D9!?-)!+$4)%*!.-)+*)%;)*!'(3!8)!)>,$/.)4!.$!

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*'/#,.#3&!)3;#/$3+)3.*!C*2'-!(*!!:(.%(8D!+(0!8)!2*)4!.$!/)(47!+$4#10!(34!*#+2%(.)!"ABH!+$4)%*!1/$+!

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1#..#3&!+$4)%*!.$!)>,)/#+)3.(%!4(.(7!*'(33#3&!32+)/#'(%!/(3&)*!1$/!,(/(+).)/*7!'-)'6#3&!%$'(%!(34!

&%$8(%!,(/(+).)/!*)3*#.#;#.07!2*#3&!"ABH!+$4)%*!(*!+$42%)*!#3!(!-#)/(/'-#'(%!1/(+)5$/67!).'9!

O A,9?'359$.5'#*+,)$#-./*

! [U!

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;$%2+)*7!.-)!2*)/!'(3!+(32(%%0!+$4)%!.-)!%$'(.#$3!(*!(!*),(/(.)!'$+,$3)3.!*.(.)!(34!,/$;#4)!#.!(*!

'$3.)>.!1$/!)('-!/)('.#$3!/2%)9!?-)!2*)/!5$2%4!(%*$!3))4!.$!#3'%24)!.-)!'$//)'.!;$%2+)@*'(%#3&!1('.$/!1$/!

)('-!/)('.#$3!/2%)7!-$5);)/7!(34!.-#*!O2#'6%0!&).*!.)4#$2*!(*!.-)!32+8)/!$1!'$+,(/.+)3.*!#3'/)(*)*7!

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! [[!

?-)!'$+,(/.+)3.*!8%$'6!#*!2*)4!.$!)3'$4)!.-)!'$+,(/.+)3.!-#)/(/'-0!(34!'$+,(/.+)3.!;$%2+)*9!G.!#*!

(3!$,.#$3(%!8%$'6!.-(.!./#&&)/*!.-)!2*)!$1!'"ABH!1/(+)5$/6!(34!*03.(>9!F$3*#4)/!.-)!-#)/(/'-0!

4)*'/#8)4!#3!F68#&)!P9!?-#*!'(3!8)!)3'$4)4!#3!(!'$+,(/.+)3.*!8%$'6!(*!1$%%$5*T!

begin compartments

Ext 3 V_ext # External milieu

Plm 2 V_plm Ext # Plasma Membrane, enclosed by Ext

Cyt 3 V_cyt Plm # Cytosol, enclosed by Plm

Enm 2 V_enm Cyt # Endosomal Membrane, enclosed by Cyt

Num 2 V_num Cyt # Nuclear Membrane, enclosed by Cyt

End 3 V_end Enm # Endosome, enclosed by Enm

Nuc 3 V_nuc Num # Nucleus, enclosed by Num

end compartments

S('-!%#3)!#34#'(.)*!.-)!3(+)!$1!.-)!'$+,(/.+)3.7!.-)!4#+)3*#$3!CJ`!$/!R`D7!.-)!;$%2+)!$1!.-)!

'$+,(/.+)3.!(34!.-)!3(+)!$1!.-)!,(/)3.!'$+,(/.+)3.9!K!*-$/.!4)*'/#,.#$3!'(3!8)!&#;)3!(*!(!'$++)3.!

1$/!'%(/#.09!

O@< +,#$4"#$*Q,4'5-,.*:$%)'2%)!%$'(.#$3!#*!&#;)3!80!(!,$*.1#>!5#.-!.-)!w!*0+8$%!#3!8$.-!,(..)/3*!(34!*,)'#)*9!M$/!)>(+,%)7!.$!

/),/)*)3.!(!+$3$+)/#'!/)'),.$/!,/)*)3.!#3!.-)!,%(*+(!+)+8/(3)!'$+,(/.+)3.!CPlmD7!5)!2*)T!

R(dim)@Plm

G3!,(..)/3*!(34!*,)'#)*!5#.-!+2%.#,%)!+$%)'2%)*7!);)/0!+$%)'2%)e*!%$'(.#$3!'(3!8)!#34#'(.)4!80!(3!w!

,$*.1#>9!M$/!)>(+,%)7!.$!/),/)*)3.!(!4#+)/!$1!/)'),.$/*!,/)*)3.!#3!.-)!,%(*+(!+)+8/(3)7!5)!2*)T!

R(dim!0)@Plm.R(dim!0)@Plm

! [\!

:$%)'2%)*!'(3!1$/+!8$34*!5#.-!+$%)'2%)*!#3!.-)!*(+)!'$+,(/.+)3.*!$/!#3!(4V(')3.!'$+,(/.+)3.*9!

?-2*!(!*#3&%)!*,)'#)*!'(3!*,(3!+2%.#,%)!'$+,(/.+)3.*9!M$/!)>(+,%)7!.$!/),/)*)3.!(!/)'),.$/!$3!.-)!

,%(*+(!+)+8/(3)!.-(.!8#34*!(!%#&(34!$2.*#4)!.-)!')%%7!5)!2*)T!

R(lig!0)@Plm.L(rec!0)@Ext

K!0+4+2+86:%22'!:+5-6-0)50!-4):6)-!4$)*!3$.!*,(3!+$/)!.-(3!$3)!*2/1(')!(34!4$)*!3$.!-(;)!8$34*!.-(.!

3))4!.$!,(**!.-/$2&-!'$+,(/.+)3.*9!S>(+,%)*!(/)!*-$53!#3!F68#&)!O9!

G1!'"AB!#*!#3;$6)4!2*#3&!.-)!'$+,(/.+)3.*!8%$'67!.-)3!.-)!*))4@*,)'#)*!8%$'6!*-$2%4!'$3.(#3!

.$,$%$&#'(%%0!'$3*#*.)3.!*,)'#)*!5#.-!.-)#/!12%%!'$+,(/.+)3.(%!*,)'#1#'(.#$37!1$/!)>(+,%)7!

begin seed species

R(lig,dim)@Plm R0

L(rec)@Ext L0

end seed species

O@> Q,4'5-,.*-.*8'55$3.(*'"AB!,/$;#4)*!(!%$.!$1!1%)>#8#%#.0!#3!.(#%$/#3&!,(..)/3*!.$!+(.'-!*,)'#)*!8(*)4!$3!.-)!%$'(.#$3!$1!.-)#/!

+$%)'2%)*9!!

?-)!%88&)8%0)!2+:%06+5!$1!(!*,)'#)*!'(3!8)!#31)//)4!1/$+!.-)!%$'(.#$3!$1!#.*!+$%)'2%)*T!!

• G1!(%%!.-)!+$%)'2%)*!#3!(!*,)'#)*!(/)!#3!(!;$%2+)!'$+,(/.+)3.7!.-)3!.-)#/!(&&/)&(.)!%$'(.#$3!#*!.-(.!

;$%2+)!'$+,(/.+)3.9!

• G1!(%%!.-)!+$%)'2%)*!#3!(!*,)'#)*!(/)!#3!(!*2/1(')!'$+,(/.+)3.7!.-)3!.-)#/!(&&/)&(.)!%$'(.#$3!#*!.-(.!

*2/1(')!'$+,(/.+)3.9!

• G1!.-)!*,)'#)*!*,(3*!$3)!*2/1(')!(34!$3)!$/!.5$!;$%2+)*7!.-)3!.-)!(&&/)&(.)!%$'(.#$3!#*!.-(.!

*2/1(')!'$+,(/.+)3.9!

!!

! [a!

L,)'#)*!'(3!8)!/)1)//)4!.$!80!.-)#/!(&&/)&(.)!%$'(.#$3!2*#3&!(3!w!,/)1#>!$3!(!,(..)/39!M$/!)>(+,%)7!

'$3*#4)/!.-)!4#+)/!,(..)/3!C$3!.-)!,%(*+(@+)+8/(3)D7!!!R(dim!0)@Plm.R(dim!0)@Plm

?-)!*(+)!,(..)/3!'(3!8)!/)1)//)4!.$!2*#3&!.-)!(&&/)&(.)!%$'(.#$3!(*!@Plm:R(dim!0).R(dim!0)

M$/!*,)'#)*!.-(.!8/#4&)!'$+,(/.+)3.*7!.-)!(&&/)&(.)!%$'(.#$3!C.-)!*2/1(')D!'(3!*.#%%!8)!,/$;#4)4!(*!w!

,/)1#>!5-)/)(*!.-)!'$33)'.)4!+$%)'2%)*!#3!.-)!(4V(')3.!'$+,(/.+)3.*!'(3!8)!.(&&)4!5#.-!.-)!w!

,$*.1#>!(*!)>'),.#$3*!.$!.-)!/2%)9!

M$/!)>(+,%)7!'$3*#4)/!.-)!/)'),.$/!4#+)/!$3!.-)!,%(*+(!+)+8/(3)!'$33)'.)4!.$!(!*#3&%)!%#&(34!

+$%)'2%)!#3!.-)!)>.)/3(%!'$+,(/.+)3.T!!R(dim!0,lig!1)@Plm.L(rec!1)@Ext.R(dim!0)@Plm.!

?-)!(&&/)&(.)!%$'(.#$3!#*!.-)!Plm!*2/1(')9!?$!+(.'-!.-#*!*,)'#)*!2*#3&!(!,(..)/37!5)!'(3!2*)!.-)!@Plm!

,/)1#>!(34!,/$;#4)!.-)!Ext!%$'(.#$3*!(*!,$*.1#>!C234)/%#3)4!1$/!)+,-(*#*D7!#9)9!

@Plm:R(dim!0,lig!1).R(dim!0).L(rec!1)@Ext

_$%2+)!+$%)'2%)*!8$234!.$!(!*2/1(')!'(3!8)!+(.'-)4!80!,/)1#>!%$'(.#$3!.(&*!$1!.-)!(&&/)&(.)!%$'(.#$39!

M$/!)>(+,%)7!'$3*#4)/!.-)!*,)'#)*T!! R(dim,lig!1)@Plm.L(rec!0)@Ext

?-)!(&&/)&(.)!%$'(.#$3!$1!.-)!*,)'#)*!#*!Plm9!

G.!'(3!8)!+(.'-)4!80!8$.-!,(..)/3*T! L(rec!+)@Ext!(34!@Plm:L(rec!+)

?-)!+(.'-)4!/)&#$3!#*!234)/%#3)4!1$/!)+,-(*#*9

O@B !$'45-,.*!"#$(*-.*5K$*A,9?'359$.5'#*Y3'9$=,3P*

O@B@: 7"5,9'5-4*Z,#"9$*14'#-./*

G1!'"AB!#*!3$.!#3;$6)47!#9)9!#1!.-)!'$+,(/.+)3.*!8%$'6!#*!3$.!2*)47!.-)!+$4)%)/!+2*.!+(32(%%0!,/$;#4)!

.-)!;$%2+)!1('.$/!(34!K;$&(4/$!32+8)/!1('.$/!1$/!.-)!+#'/$*'$,#'!/)('.#$3!/(.)!'$3*.(3.7!1$/!)>(+,%)T!

A(b) + B(a) -> A(b!0).B(a) k/(N_Avo*V_cyt)

! [c!

G1!'"AB!#*!#3;$6)47!#9)9!.-)!'$+,(/.+)3.*!(34!;$%2+)*!(/)!*,)'#1#)4!#3!.-)!'$+,(/.+)3.*!8%$'67!.-)3!

.-)!;$%2+)!*'(%#3&!#*!,(/.!$1!.-)!'"AB!,/$')**#3&!(34!.-)!+$4)%)/!3))4!$3%0!,/$;#4)!.-)!K;$&(4/$!

32+8)/!1('.$/9!M$/!)>(+,%)7!.-)!*(+)!/)('.#$3!/2%)!5$2%4!8)!+$4)%)4!#3!.-)!'"AB!1/(+)5$/6!(*T!

A(b) + B(a) -> A(b!0).B(a) k/N_Avo

'"AB!5$2%4!(2.$+(.#'(%%0!*'(%)!#.!.$!k/(N_Avo*V_cyt)!#1!#.!4).)'.*!.-(.!.-)!8#+$%)'2%(/!/)('.#$3!'(3!

$''2/!#3!.-)!'0.$,%(*+!(34!V_cyt!#*!*,)'#1#)4!(*!.-)!;$%2+)!$1!.-)!'0.$,%(*+#'!'$+,(/.+)3.!#3!.-)!

'$+,(/.+)3.*!8%$'69!

G3!(''$/4(3')!5#.-!.-)!)>,%(3(.#$3!&#;)3!#3!"):06+5!PDE7!23#+$%)'2%(/!/)('.#$3*!(/)!3);)/!*'(%)4!80!

;$%2+)7!)#.-)/!#3!*2/1(')*!$/!;$%2+)*9!"#+$%)'2%(/!/)('.#$3*!#3!X;$%2+)*Y!(34!X*2/1(')*Y!(/)!

(2.$+(.#'(%%0!*'(%)4!80!.-)!/)*,)'.#;)!'$+,(/.+)3.(%!;$%2+)9!:$%)'2%)*!#3!*2/1(')*!(/)!(**2+)4!.$!8)!

/)*./#'.)4!.$!(!*+(%%!;$%2+)!)3;)%$,#3&!.-)!*2/1(')!C#9)9!.-)!*2/1(')!;$%2+)!#*!)O2(%!.$!.-)!*2/1(')!(/)(!

+2%.#,%#)4!80!(!*2/1(')!.-#'63)**D!,/$;#4)4!80!.-)!+$4)%)/9!G.!#*!3$.!/)'$++)34)4!.$!+$4)%!/)('.#$3!

$/4)/*!-#&-)/!.-(3!8#+$%)'2%(/!#3!.-)!'$+,(/.+)3.(%!1/(+)5$/69!

O@B@< [.-G$3('#*!$'45-,.*!"#$(*

"#$%$&#'(%!/)('.#$3*!'(3!-(,,)3!8).5))3!/)('.(3.*!(*!%$3&!(*!.-)0!(/)!#3!.-)!*(+)!$/!(4V(')3.!

'$+,(/.+)3.*9!N1.)37!.-)!#4)3.#.0!$1!.-)!'$+,(/.+)3.*!'$2%4!8)!#//)%);(3.!.$!.-)!/(.)!'$3*.(3.!C)>'),.!

1$/!.-)!;$%2+)!*'(%#3&!1('.$/D9!M$/!)>(+,%)7!+2%.#,%)!')%%!.0,)*!'(3!,/$42')!4#11)/)3.!32+8)/*!$1!.-)!

*(+)!/)'),.$/!$3!.-)#/!,%(*+(!+)+8/(3)*7!82.!.-)*)!/)'),.$/*!8#34!5#.-!.-)!*(+)!#3./#3*#'!(11#3#.0!.$!

(3!)>.)/3(%!%#&(349!L2'-!23#;)/*(%!,-)3$+)3(!'(3!8)!5/#..)3!(*!23#;)/*(%!/)('.#$3!/2%)*7!#9)9!5#.-$2.!(30!

'$+,(/.+)3.(%!'$3.)>.9!!

N3!,/$')**#3&!(!23#;)/*(%!/)('.#$3!/2%)7!'"AB!'(3!#4)3.#10!.-)!'$+,(/.+)3.*!#3!5-#'-!.-)!/)('.(3.*!'(3!

$''2/9!?-)37!'"AB!(2.$+(.#'(%%0!&)3)/(.)*!/)('.#$3*!+(.'-#3&!.-)!/)('.#$3!/2%)7!82.!(,,%#'(8%)!.$!.-)!

! [f!

*,)'#1#'!'$+,(/.+)3.*!C$/!,(#/*!$1!(4V(')3.!'$+,(/.+)3.*D!5-)/)!.-)!/)('.(3.*!(/)!#3!,/$>#+#.09!M$/!

8#+$%)'2%(/!(34!-#&-)/!/)('.#$3*7!'"AB!(2.$+(.#'(%%0!*'(%)*!.-)!/)('.#$3!/(.)!80!.-)!(,,/$,/#(.)!

;$%2+)9!

M$/!)>(+,%)7!/)'),.$/!4#+)/#=(.#$3!'(3!$''2/!$3!8$.-!,%(*+(!+)+8/(3)*!CPlmD!(34!)34$*$+(%!

+)+8/(3)*!CEnmD9!?-#*!'(3!8)!/),/)*)3.)4!80!(!23#;)/*(%!/2%)T!

R(dim) + R(dim) -> R(dim!0).R(dim!0) k

?-#*!/2%)!5$2%4!&)3)/(.)!4#+)/#=(.#$3!/)('.#$3*!#3!8$.-!Plm!(34!Enm!'$+,(/.+)3.*!

R(dim)@Plm + R(dim)@Plm -> R(dim!0)@Plm.R(dim!0)@Plm k/V_Plm

R(dim)@Enm + R(dim)@Enm -> R(dim!0)@Enm.R(dim!0)@Enm k/V_Enm

G1!(!*,)'#1#'!/)('.#3&!,(#/!$''2/*!$3%0!#3!$3)!%$'(.#$3!C$/!$3)!,(#/!$1!(4V(')3.!%$'(.#$3*D7!.-)3!#.!#*!

*211#'#)3.!.$!2*)!(!23#;)/*(%!/2%)!.$!+$4)%!.-)!/)('.#$39!!

O@B@> 14,?$*!$(53-45$)*!$'45-,.*!"#$(*

L'$,)!/)*./#'.)4!/)('.#$3*!(/)!/)('.#$3*!5-$*)!8)-(;#$/!.-)!+$4)%)/!5#*-)*!.$!/)*./#'.!4),)34#3&!$3!

5-)/)!.-)!%$'(.#$3!$1!.-)!/)('.#$3!#*9!M$/!)>(+,%)7!.-)!*(+)!/)('.#$3*!'(3!$''2/!#3!.-/))!4#11)/)3.!

'$+,(/.+)3.*7!82.!.-)!+$4)%)/!+#&-.!5#*-!.$!(**#&3!4#11)/)3.!+#'/$*'$,#'!/(.)*!1$/!.-)!/)('.#$3!#3!.5$!

'$+,(/.+)3.*!(34!4#*(%%$5!.-)!/)('.#$3!#3!.-)!.-#/49!!

Z3#;)/*(%!/2%)*!'(33$.!8)!)+,%$0)4!1$/!.-)*)!,2/,$*)*9!G3!'"ABH7!80!2*#3&!.-)!w!*0+8$%7!+$4)%)/*!

-(;)!.-)!,$5)/!.$!*,)'#10!)>('.%0!5-)/)!(!,(/.#'2%(/!/)('.#$3!$''2/*9!M$/!)>(+,%)7!*2,,$*)!/)'),.$/*!

5)/)!4)&/(4)4!(.!.5$!4#11)/)3.!/(.)*!4),)34#3&!$3!.-)!%$'(.#$37!#9)9!/(,#4%0!#3!)34$*$+)*7!82.!$3%0!;)/0!

*%$5%0!#3!.-)!,%(*+(!+)+8/(3)7!.-)3!5)!'(3!2*)!*'$,)@/)*./#'.)4!/2%)*!.$!*-$5!.-#*T!

R()@End -> 0 k_degr_fast DeleteMolecules

R()@Plm -> 0 k_degr_slow DeleteMolecules

! \h!

K,,/$,/#(.)!;$%2+)@*'(%#3&!#*!4$3)!1$/!8#+$%)'2%(/!(34!-#&-)/!$/4)/!/)('.#$3*9!

O@B@B 23'.(?,35*!"#$(*

?-)!'"ABH!*,)'#1#'(.#$3!(%%$5*!+$%)'2%)*!(34!*,)'#)*!.$!8)!+$;)4!8).5))3!'$+,(/.+)3.*!#3!(!32+8)/!

$1!5(0*!(*!%$3&!(*!.-)!/)*2%.#3&!*,)'#)*!#*!.$,$%$&#'(%%0!'$3*#*.)3.9!!G1!(!./(3*,$/.!/)('.#$3!&)3)/(.)4!80!(!

./(3*,$/.!/2%)!'/)(.)*!(!.$,$%$&#'(%%0!#3'$3*#*.)3.!*,)'#)*7!"#$A).B)3!5#%%!4).)'.!#.!(34!4#*'(/4!.-)!

/)('.#$39!!

:$%)'2%)*!'(3!8)!+$;)4!#34#;#42(%%0!1/$+!.-)#/!%$'(.#$3!.$!(30!(4V(')3.!'$+,(/.+)3.!C;$%2+)!.$!

*2/1(')!$/!*2/1(')!.$!;$%2+)D!*#+,%0!80!'-(3&#3&!.-)!w@,$*.1#>9!M$/!)>(+,%)7!+$;#3&!(!-0,$.-).#'(%!K!

+$%)'2%)!1/$+!.-)!,%(*+(!+)+8/(3)!.$!.-)!'-#%4!'$+,(/.+)3.!'0.$,%(*+T!

A(x)@Plm -> A(x)@Cyt

?-#*!#*!%,J%:)50K:+$4%&0$)50!$+2):#2%&!0&%5-4+&09!!

:$;#3&!(!+$%)'2%)!8).5))3!(4V(')3.!'$+,(/.+)3.*!4$)*!3$.!(11)'.!.-)!,$*.1#>!%$'(.#$3!.(&!$1!$.-)/!

+$%)'2%)*!#3!.-)!*(+)!*,)'#)*9!M$/!)>(+,%)7!#1!(!"!+$%)'2%)!5)/)!'$33)'.)4!.$!K7!.-)3!#.!5$2%4!*.(0!#3!

Plm9!?-)!(8$;)!/2%)!5$2%4!&)3)/(.)!.-)!/)('.#$3!C5#.-!./(3*,$/.)4!+$%)'2%)!234)/%#3)4!1$/!)+,-(*#*DT!

A(x,b!0)@Plm.B(a!0)@Plm -> A(x,b!0)@Cyt.B(a!0)@Plm k

K3!)>(+,%)!5-)/)!*2'-!(!./(3*,$/.!/2%)!5$2%4!8)!2*)12%!#*!.$!+$4)%!+)+8/(3)!#3*)/.#$3!$1!,/$.)#3*7!

#9)9!5-)3!(!,/$.)#3!1/))%0!4#112*#3&!#3!.-)!'0.$,%(*+!#*!./(3*,$/.)4!.$!(!+)+8/(3)!'$+,(/.+)3.9!

K4V(')3.@'$+,(/.+)3.!+$%)'2%(/!./(3*,$/.!'(33$.!8)!)>.)34)4!.$!*,)'#)*!./(3*,$/.!80!2*#3&!.-)!w@

,/)1#>!#3*.)(4!$1!.-)!,$*.@1#>9!!

G34#;#42(%!+$%)'2%)*!'(3!8)!+$;)4!1/$+!$3)!;$%2+)!.$!(3$.-)/!;$%2+)!.-/$2&-!(!8/#4&#3&!*2/1(')9!M$/!

)>(+,%)7!.-)0!'(3!8)!+$;)4!8).5))3!.-)!'0.$,%(*+!(34!.-)!32'%)2*7!5-#'-!(/)!8/#4&)4!80!.-)!32'%)(/!

+)+8/(3)9!?-#*!#*!B&6,8),KH+2#$)!$+2):#2%&!0&%5-4+&0D!

! \g!

A(x)@Cyt -> A(x)@Nuc k

K3!)>(+,%)!5-)/)!*2'-!(!./(3*,$/.!+)'-(3#*+!5$2%4!8)!2*)12%!#*!./(3*,$/.!.-/$2&-!(!'-(33)%!#3!.-)!

*2/1(')7!*2'-!(*!.-)!1%$5!$1!'-%$/#4)!#$3*!1/$+!.-)!)>.)/3(%!;$%2+)!.$!.-)!'0.$,%(*+!.-/$2&-!(!'-%$/#4)!

'-(33)%!#3!.-)!+)+8/(3)9!

"/#4&)4@;$%2+)!+$%)'2%(/!./(3*,$/.!-(*!.-)!,$.)3.#(%!.$!'/)(.)!.$,$%$&#'(%%0!#3'$3*#*.)3.!'$+,%)>)*9!

L2'-!/)('.#$3*7!#1!.-)0!'$2%4!8)!&)3)/(.)4!1/$+!.-)!/)('.#$3!/2%)*7!5#%%!8)!(2.$+(.#'(%%0!4#*'(/4)49!

Z3%#6)!(4V(')3.@'$+,(/.+)3.!./(3*,$/.7!8/#4&)4@;$%2+)!+$%)'2%(/!./(3*,$/.!'(3!8)!)>.)34)4!.$!

B&6,8),KH+2#$)!-4):6)-!0&%5-4+&0!80!2*#3&!.-)!w@,/)1#>!#3*.)(4!$1!.-)!,$*.@1#>9!?-#*!5$2%4!*#+,%0!+$;)!

.-)!)3.#/)!*,)'#)*!+(.'-)4!80!.-)!,(..)/3!(*!%$3&!(*!#.!#*!12%%0!'$3.(#3)4!#3!.-)!8/#4&)4@;$%2+)9!!

M$/!)>(+,%)7!'$3*#4)/!.-)!/2%)T!

@Cyt:A(x) -> @Nuc:A(x) k

I-)3!.-#*!/2%)!#*!(,,%#)4!.$!.-)!@Cyt:A(x,b!0).B(a!0)!*,)'#)*7!.-)!1$%%$5#3&!/)('.#$3!#*!&)3)/(.)4T!

A(x,b!0)@Cyt.B(a!0)@Cyt -> A(x,b!0)@Nuc.B(a!0)@Nuc k

K*!$3)!'(3!*))7!.-)!%$'(.#$3!.(&*!$1!(%%!+$%)'2%)*!#3!.-)!*,)'#)*!-(;)!8))3!'$3;)/.)4!1/$+!Cyt!.$!Nuc9!!

?-)!/)('.#$3!+)'-(3#*+!4$)*!3$.!-(;)!.$!8)!23#+$%)'2%(/7!1$/!)>(+,%)7!(!;(%#4!8/#4&)4@;$%2+)!

./(3*,$/.!/2%)!5$2%4!8)T!

@Cyt:A(x)+B()@Num -> @Nuc:A(x) + B()@Num k

<)/)7!(!+$%)'2%)!B()!$3!.-)!8/#4&#3&!*2/1(')!Num!)3(8%)*!.-)!./(3*,$/.!$1!*$+)!*,)'#)*!+(.'-#3&!A(x)!

8).5))3!.-)!8/#4&)4!;$%2+)*!Cyt!(34!Nuc9!?-)!/(.)!'$3*.(3.!6!#*!8#+$%)'2%(/!/(.)!'$3*.(3.!*'(%)4!$3%0!

80!.-)!K;$&(4/$!32+8)/9!

! \J!

K3!)>(+,%)!5-)/)!(!8/#4&)4@;$%2+)!./(3*,$/.!+)'-(3#*+!'$2%4!8)!2*)12%!#*!5-)3!.(/&).!,/$.)#3*!8#34!

./(3*,$/.!,/$.)#3*!(34!.-)!/)*2%.#3&!'$+,%)>!#*!'$+,('.!)3$2&-!.$!,)3)./(.)!.-)!,$/)*!$3!.-)!32'%)(/!

+)+8/(3)9!"#+$%)'2%(/!+)'-(3#*+*!(/)!2*)12%!.$!+$4)%!(!*#.2(.#$3!5-)/)!.-)!/(.)!$1!./(3*,$/.!

4),)34*!$3!32+8)/!$1!,$/)*!$/!'-(33)%*!,/)*)3.9!

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Knowledge Base: The binding of EGF ligand to EGFR receptor is cooperative with the homo-dimerization of

EGFR. Ligand binding enhances dimerization, but ligand-binding sites on the dimer are negatively

cooperative.

?-)!+$4)%#3&!$1!.-#*!#31$/+(.#$3!#*!./)(.)4!#3!.-)!"):06+5!O9!

Knowledge Base: Dimerized EGFR autophosphorylates on several tyrosines in its amino acid sequence,

including Y998, Y1016, Y1092, Y1110, Y1138, Y1172, Y1197 (58).

I)!+$4)%!.-)!,-$*,-$/0%(.#$3!5#.-!#4)3.#'(%!6#3).#'*7!(%.-$2&-!5)!'$2%4!,$.)3.#(%%0!2*)!(!4#11)/)3.!/(.)!

'$3*.(3.!1$/!)('-!,-$*,-$/0%(.#$39!

R(dim!+,Y998~0) -> R(dim!+,Y998~p) k_ph

R(dim!+,Y1016~0) -> R(dim!+,Y1016~p) k_ph

R(dim!+,Y1092~0) -> R(dim!+,Y1092~p) k_ph

R(dim!+,Y1110~0) -> R(dim!+,Y1110~p) k_ph

! a[!

R(dim!+,Y1138~0) -> R(dim!+,Y1138~p) k_ph

R(dim!+,Y1172~0) -> R(dim!+,Y1172~p) k_ph

R(dim!+,Y1197~0) -> R(dim!+,Y1197~p) k_ph

Knowledge Base: Dimerized EGFR kinases are also responsible for activation of phosphorylation sites on

Gab1 and Shc1 if they are present in the same complex. These include Y627 on Gab1 (59), tandem YXXP and

YXXM motifs on Gab1 (59) and Y317 on Shc1 (60).

I)!'(3!2*)!(!4$.!$,)/(.$/!.$!*-$5!.-(.!.-)*)!+$%)'2%)*!(/)!#3!.-)!*(+)!'$+,%)>!5-)3!.-)0!(/)!

+$4#1#)47!);)3!.-$2&-!.-)/)!'(3!8)!*);)/(%!5(0*!#3!5-#'-!.-)!+$%)'2%)*!'$2%4!8)!/)'/2#.)49!

R(dim!+).Gab1(YXXP~0) -> R(dim!+).Gab1(YXXP~p) k_ph

R(dim!+).Gab1(YXXM~0) -> R(dim!+).Gab1(YXXM~p) k_ph

R(dim!+).Gab1(Y627~0) -> R(dim!+).Gab1(Y627~p) k_ph

R(dim!+).Shc1(Y317~0) -> R(dim!+).Shc1(Y317~p) k_ph

Knowledge Base: If the molecule Shp2 is recruited to the complex, it opposes the phosphorylation activity of

the receptor tyrosine kinases (61).

G3!.-)!(8*)3')!$1!(!4),-$*,-$/0%(.#$3!);)3.7!.-)!,-$*,-$/0%(.#$3!*#.)*!5#%%!8)!*(.2/(.)4!.$!

,-$*,-$/0%(.#$3!);)3!5#.-!(!.#30!(+$23.!$1!4#+)/#=(.#$37!(*!)>,%(#3)4!#3!"):06+5!PDN9!L-,J!/)'/2#.)4!.$!

.-)!'$+,%)>!'(3!4),-$*,-$/0%(.)!(30!$1!.-)!6#3(*)!*28*./(.)*T!

Shp2().R(Y998~p) -> Shp2().R(Y998~0) k_deph






Shp2().Gab1(YXXP~p) -> Shp2().Gab1(YXXP~0) k_deph

Shp2().Gab1(YXXM~p) -> Shp2().Gab1(YXXM~0) k_deph

! a\!

Shp2().Gab1(Y627~p) -> Shp2().Gab1(Y627~0) k_deph

Shp2().Shc1(Y317~p) -> Shp2().Shc1(Y317~0) k_deph

Knowledge Base: The receptor phosphotyrosines recruit proteins in the following manner: Y1110, Y1138,

Y1172 and Y1197 bind both Grb2 and Shc1.Y1092 binds only Grb2. Y1016 binds only Shp2. Y998 binds both

Shp2 and Shc1 (58). All binding interactions are reversible.

?-)!#3.)/('.#$3!5#.-!.-)!/)'),.$/!#*!%$'(%#=)4!.$!.-)!L<J!4$+(#3!$3!B/8J9!?-)!A@.)/+#3(%!/)&#$3*!$1!

L-'g7!L-,J!(34!W(*(g!(%%!'$3.(#3!L<J]L<R]P?"!4$+(#3*!#3!*$+)!'$+8#3(.#$3!.-(.!)3(8%)*!8#34#3&!.$!

*,)'#1#'!,-$*,-$.0/$*#3)*9!?-)0!(/)!+$4)%)4!(*!&)3)/#'!d3e!4$+(#3*7!/)1)//#3&!.$!.-)#/!A@.)/+#3(%!

,$*#.#$39!

# Binding of Y1110, Y1138, Y1172 and Y1197

R(Y1110~p) + Grb2(sh2) <-> R(Y1110~p!1).Grb2(sh2!1) kf_pY_grb2,kr_pY_grb2




R(Y1110~p) + Shc1(n) <-> R(Y1110~p!1).Shc1(n!1) kf_pY_shc1,kr_pY_shc1




# Binding of Y1092


# Binding of Y1016

R(Y1016~p) + Shp2(n) <-> R(Y1016~p!1).Shp2(n!1) kf_pY_shp2,kr_pY_shp2

# Binding of Y998


R(Y998~p) + Shp2(n) <-> R(Y998~p!1).Shp2(n!1) kf_pY_shp2,kr_pY_shp2

! aa!

K!'$3.('.!+(,!5#.-!4)1#3)4!*0+8$%*!1$/!'$+,$3)3.*7!#3.)/('.#$3*!(34!#31%2)3')*!#*!2*)12%!#3!

*2++(/#=#3&!.-)*)!/)('.#$3!/2%)*9!?-)!'$3;)3.#$3*!1$%%$5)4!1$/!.-)!'$3.('.!+(,*!#3!.-#*!.2.$/#(%!(/)!

*-$53!#3!F68#&)!]9!K!'$3.('.!+(,!$1!.-)!6#3(*)!(34!,-$*,-(.(*)!('.#;#.#)*!#3!.-)!*#&3(%#3&!'$+,%)>!(34!

.-)!,/#+(/0!8#34#3&!#3.)/('.#$3*!5#.-!.-)!/)'),.$/!(/)!*-$53!#3!F68#&)!E^D!

?-)!+$%)'2%)*!/)'/2#.)4!.$!.-)!,/#+(/0!,-$*,-$.0/$*#3)*!$3!.-)!/)'),.$/!-(;)!'$+,%)>!#3.)/('.#$3*!

(+$3&!.-)+*)%;)*9!B/8J!(34!L-'g!(/)!(4(,.$/!,/$.)#3*!.-(.!8#34!)('-!$.-)/!(*!5)%%!(*!$.-)/!,/$.)#3*9!

B(8g7!(!,/$.)#3!/)'/2#.)4!;#(!B/8J7!#*!(!*'(11$%4!,/$.)#3!5#.-!+2%.#,%)!8#34#3&!*#.)*9!

Knowledge Base: Grb2 has three domains SH2, SH3N and SH3C. In addition to receptor phosphotyrosines

binding, the SH2 domain is capable of binding phosphorylated Y317 of Shc1 (60). The SH3N domain recruits

Sos1 through the N-terminal domain of Sos1 (62). The SH3C domain recruits Gab1 through a proline-rich

region on Gab1 (59). Certain serines on Sos1 (63) and certain serines and threonines on Gab1 (59) need to be

unphosphorylated for the Grb2 binding to be effective.

Grb2(sh2) + Shc1(Y317~p) <-> Grb2(sh2!1).Shc1(Y317~p!1) kf_grb2shc1,kr_grb2shc1

Grb2(sh3n) + Sos1(S~0,n) <-> Grb2(sh3n!1).Sos1(S~0,n!1) kf_grb2sos1,kr_grb2sos1

Grb2(sh3c) + Gab1(ST~0,pro)<->Grb2(sh3c!1).Gab1(ST~0,pro!1) kf_grb2gab1,kr_grb2gab1

Knowledge Base: The Gab1 scaffold protein contains tandem YXXP motifs that bind the N-terminal domain

of Rasa1 on phosphorylation. Similarly, a phosphorylated tandem YXXM motif binds the regulatory subunit

p85 of PI3K. Phosphorylated Y627 recruits the Shp2 phosphatase. All of these binding events require that

certain serines and threonines on Gab1 remain unphosphorylated (59).

Gab1(ST~0,YXXP~p)+Rasa1(n)<->Gab1(ST~0,YXXP~p!1).Rasa1(n!1) kf_gab1rasa1,kr_gab1rasa1

Gab1(ST~0,YXXM~p)+PI3K(p85)<->Gab1(ST~0,YXXP~p!1).PI3K(p85!1) kf_gab1pi3k,kr_gab1pi3k

Gab1(ST~0,Y627~p)+Shp2(n)<->Gab1(ST~0,YXXP~p!1).Shp2(n!1) kf_gab1shp2,kr_gab1shp2

! ac!

?-)!*)'$34(/0!8#34#3&!#3.)/('.#$3*!8).5))3!.-)!+$%)'2%)*!/)'/2#.)4!.$!.-)!/)'),.$/!(/)!*2++(/#=)4!#3!

F68#&)!EE9!?-)!'$3.('.!+(,!#3!F68#&)!EE!#*!.$!8)!'$3*#4)/)4!'$+,%)+)3.(/0!.$!.-)!'$3.('.!+(,!#3!F68#&)!

E^!(34!3$.!)>'%2*#;)9!

]@< 1$4,.)'3J*+$(($./$3*745-G'5-,.**K*!+)3.#$3)4!)(/%#)/7!')/.(#3!'(.(%0.#'!('.#;#.#)*!(/)!('.#;(.)4!$3!/)'/2#.+)3.!.$!.-)!*#&3(%#3&!'$+,%)>9!

?-)*)!'(.(%0.#'!('.#;#.#)*!/(,#4%0!'-(3&)!.-)!4#*./#82.#$3*!$1!')/.(#3!)11)'.$/!+$%)'2%)*!#3!.-)!,%(*+(!

+)+8/(3)!(34!'0.$*$%9!?-#*!+(3#1)*.*!(*!(!%(/&)!,-)3$.0,#'!*5#.'-!'(2*#3&!5-$%)*(%)!('.#;(.#$3!$1!

'$//)*,$34#3&!'0.$*$%#'!*#&3(%#3&!,(.-5(0*9!G3!.-#*!*)'.#$37!5)!'$3*#4)/!('.#;(.#$3!$1!W(*7!(!B?P(*)!

*5#.'-!(34!PGPR7!(!,-$*,-$#3$*#.#4)!+)**)3&)/9!

]@<@: 8;8>*745-G'5-,.*

P-$*,-$#3$*#.#4)*!(/)!*+(%%!%#,#4!+$%)'2%)*!.-(.!123'.#$3!(*!*)'$34(/0!+)**)3&)/*!#3!*);)/(%!)26(/0$.#'!

,(.-5(0*9!P-$*,-$#3$*#.#4)*!'(3!8)!#3.)/'$3;)/.)4!80!(44#3&!(34!/)+$;#3&!,-$*,-(.)*!$3.$!.-)!Re7Ue!

(34![e!,$*#.#$3*!$3!.-)!#3$*#.$%!+$#).09!?-)!/(.#$!(34!*,(.#(%!4#*./#82.#$3!$1!.-)!4#11)/)3.!

,-$*,-$#3$*#.#4)*!#*!)>,%$#.)4!1$/!*#&3(%#3&!,2/,$*)*9!G3!&/$5.-@1('.$/!/)'),.$/!('.#;(.#$37!.-)!

#3.)/'$3;)/*#$3!$1!,-$*,-(.#40%#3$*#.$%!CU7[D@8#*,-$*,-(.)7!(%*$!63$53!(*!PGPJ!(34!,-$*,-(.#40%#3$*#.$%!

CR7U7[D@./#*,-$*,-(.)!#*!)*,)'#(%%0!'/#.#'(%9!PGPR!#*!+(#3.(#3)4!(.!;)/0!%$5!%);)%*!80!.-)!('.#;#.0!$1!'0.$*$%#'!

P?SA!,-$*,-(.(*)9!PGPR!%);)%*!(/)!4/(*.#'(%%0!#3'/)(*)4!80!/)'/2#.+)3.!$1!PGRE!.$!.-)!+)+8/(3)9!!PGPR!

.-2*!*)/;)*!(*!(!*)'$34(/0!+)**)3&)/!1$/!('.#;(.#3&!*);)/(%!P<@4$+(#3!'$3.(#3#3&!,/$.)#3*7!(3!

#+,$/.(3.!$3)!8)#3&!K6.7!5-#'-!./#&&)/*!.-)!K6.]+?$/!,(.-5(0!'/#.#'(%!1$/!')%%!,/$%#1)/(.#$3!(34!

4#11)/)3.#(.#$39!?-)!#31$/+(.#$3!-)/)!'(3!8)!1$234!#3!!)'&9!?-)!/2%)*!4)*'/#8#3&!'-(3&)!$1!*.(.)!-(;)!.-)!

(,,/$,/#(.)!'$+,$3)3.!234)/%#3)4!1$/!)+,-(*#*9!

Knowledge Base: PIP3 is maintained at low levels by conversion to PIP2 by PTEN phosphatase.

<)/)7!5)!+$4)%!PGPR!(*!(!,-$*,-$#3$*#.#4)!5#.-!(!Re!*#.)!.(/&).)4!80!.-)!,-$*,-(.(*)9!

! af!

PTEN(c2) + PI(3p~p) <-> PTEN(c2!1).PI(3p~0!1) kf_pip3_pten,kr_pip3_pten

PTEN(c2!1).PI(3p~0!1) -> PTEN(c2) + PI(3p~p) kcat_pten

Knowledege Base: The p110 domain of PI3K catalyzes conversion of PIP2 to PIP3 when recruited to the

membrane.

R().PI3K(p110) + PI(3p~0) <-> R().PI3K(p110!1).PI(3p~0!1) kf_pip2_pi3k,kr_pip2_pi3k

PI3K(p110!1).PI(3p~0!1) -> PI3K(p110) + PI(3p~p) kcat_pi3k

Knowledege Base: PIP3 recruits PH-domain containing proteins like Gab1 (59) and Akt to the membrane.

Gab1(ph) + PI(3p~p) <-> Gab1(ph!1).PI(3p~p!1) kf_pip3_gab1,kr_pip3_gab1

Akt(ph) + PI(3p~p) <-> Akt(ph!1).PI(3p~p!1) kf_pip3_akt, kr_pip3_akt

Knowledge Base: PIP3-recruited Gab1 is at the membrane can be recruited to the signaling complex easily.

Gab1(ph!1,pro).PI(3p~p!1) + R().Grb2(sh3c)-> Gab1(ph,pro!2).Grb2(sh3c!2) + PI(3p~p) \

k_gab1grb2_mem

Knowledge Base: PIP3-recruited Akt is an active kinase with downstream substrates such as mTOR.

Akt(ph!+,kin) + mTor(S2448~0) <-> Akt(ph!+,kin!1).mTor(S2448~0!1) \

kf_akt_mtor,kr_akt_mtor

Akt(ph!+,kin!1).mTor(S2448~0!1) -> Akt(ph!+,kin) + mTor(S2448~p) kcat_akt

?-)!PGPR!('.#;(.#$3!(34!4$53*./)(+!#3.)/('.#$3*!+$4)%)4!-)/)!(/)!#%%2*./(.)4!#3!F68#&)!END!!

]@<@< !'(*745-G'5-,.*

W(*!#*!(!*+(%%!B?P(*)!,/$.)#3!.-(.!#*!.).-)/)4!.$!.-)!+)+8/(3)!(34!8#34*!5#.-!-#&-!(11#3#.0!.$!1/))!

&2(3#4#3)!32'%)$.#4)*!CB?P!(34!B`PD!#3!.-)!'0.$*$%9!W(*7!#3!#.*!8(*(%!*.(.)7!*%$5%0!'(.(%0=)*!.-)!

4),-$*,-$/0%(.#$3!$1!B?P!#3.$!B`P9!G3!.-)!(8*)3')!$1!%#&(34@#342')4!*#&3(%7!.-)!+(V$/#.0!$1!W(*!

+$%)'2%)*!(/)!8$234!.$!B`P9!I-)3!8$234!80!(!&2(3#4#3)!32'%)$.#4)!)>'-(3&)!1('.$/!CBSMD7!W(*!

/)%)(*)*!.-)!B`P!32'%)$.#4)!(34!8#34*!(!1/))!B?P!32'%)$.#4)9!L#3')!1/))!B?P!#*!#3!)>')**!$;)/!1/))!B`P!

! ch!

234)/!3$/+(%!'$34#.#$3*7!5)!'(3!(**2+)!.-(.!.-)!8#34#3&!);)3.!(1.)/!B`P!/)%)(*)!#*!(%5(0*!5#.-!(!B?P9!

?-)!W(*!,$,2%(.#$3!*5#.'-)*!1/$+!(!B`P@8$234!+(V$/#.0!.$!(!B?P@8$234!+(V$/#.09!!

W(*@B?P7!80!8#34#3&!.$!$.-)/!+$%)'2%)*7!#3#.#(.)*!+(30!*#&3(%#3&!'(*'(4)*!#3'%24#3&!.-)!:KPE!'(*'(4)9!

?-)!#3./#3*#'!B?P(*)!('.#;#.0!'(3!8)!)3-(3')4!80!(!B?P(*)!('.#;(.#3&!,/$.)#3!CBKPD!.$!,/$;#4)!.-)!

$,,$*#.)!)11)'.7!#9)9!.$!O2#'6%0!/);)/.!(!W(*@B?P!,$,2%(.#$3!.$!W(*@B`P9!SBMW!/)'/2#.*!8$.-!L$*g!C(!BSMD!

(34!W(*(g!C(!BKPD!.$!.-)!+)+8/(3)!.-/$2&-!(4(,.$/*!(34!*'(11$%4*9!!

W(*!-(*!.-/))!*28.0,)*T!<W(*7!AW(*!(34!EW(*!5#.-!+(30!'$++$3!#3.)/('.#$3*!(+$3&!.-)+9!<)/)7!5)!

+$4)%!<W(*!(*!(3!)>(+,%)9!G3*.)(4!$1!+$4)%#3&!.-)!32'%)$.#4)!(*!(!*),(/(.)!+$%)'2%)7!5)!+$4)%!#.!(*!

*#+,%0!(!*.(.)!$3!(!<W(*!'$+,$3)3.9!?-#*!#*!8)'(2*)!.-)!8#34#3&!$1!B`P]B?P!.$!<W(*!#*!;)/0!*./$3&!(34!

4$)*!3$.!/);)/*)!*,$3.(3)$2*%09!K30!1/))!<W(*!O2#'6%0!8#34*!.$!)>')**!1/))!32'%)$.#4)9!?-)!32'%)$.#4)!

8#34#3&!*#.)!#*!234)/%#3)4!1$/!)+,-(*#*!5-)3);)/!(!B?P@B`P!$/!B`P@B?P!./(3*#.#$3!$''2/*9!!

?-)!1$%%$5#3&!#31$/+(.#$3!#*!.(6)3!1/$+!!)$&9!?-)!/2%)*!4)*'/#8#3&!'-(3&)!$1!*.(.)!-(;)!.-)!(,,/$,/#(.)!

'$+,$3)3.!234)/%#3)4!1$/!)+,-(*#*9!

Knowledge Base: HRas has a protein binding site and a nucleotide binding site. The nucleotide binding site

can be assumed to bind GTP or GDP strongly. HRas has innate GTPase activity.

HRas(pbs,nbs~gtp) -> HRas(pbs,nbs~gdp) k_hras_gtpase

Knowledge Base: Receptor bound Rasa1 is a GAP, i.e. it enhances the GTPase activity of HRas.

R().Rasa1(gap)+HRas(pbs,nbs~gtp) -> R().Rasa1(gap!1).HRas(pbs!1,nbs~gtp) kf_rasa1_hras

Rasa1(gap!1).HRas(pbs!1,nbs~gtp) -> Rasa1(gap) + HRas(pbs,nbs~gtp) kr_rasa1_hras

Rasa1(gap!1).HRas(pbs!1,nbs~gtp) -> Rasa1(gap) + HRas(pbs,nbs~gdp) kcat_rasa1

Knowledge Base: Sos1 recruited to the membrane can bind HRas at two places, an allosteric site and a

catalytic site. Sos1 possesses GEF activity, i.e. it catalyzes the release of GDP from the HRas bound at the

! cg!

catalytic site. The GEF activity is enhanced by the presence of another HRas bound at the allosteric site.

When GDP is released, GTP is assumed to bind immediately since it is in excess over GDP.

# HRas-GDP binding at GEF site

R().Sos1(gef)+HRas(pbs,nbs~gdp)->R().Sos1(gef!1).HRas(pbs!1,nbs~gdp) kf_sos1gef_hras

Sos1(gef!1).HRas(pbs!1,nbs~gdp)-> Sos1(gef) + HRas(pbs,nbs~gdp) kr_sos1gef_hras

# HRas (both GTP and GDP) binding at allosteric site

R().Sos1(allo) + HRas(pbs) -> R().Sos1(allo!1).HRas(pbs!1) kf_sos1allo_hras

Sos1(allo!1).HRas(pbs!1) -> Sos1(allo) + HRas(pbs) kr_sos1allo_hras

# GEF activity in presence/absence of GTP at allo-site

HRas(pbs!1,nbs~gdp).Sos1(gef!1,allo)-> HRas(pbs,nbs~gtp)+Sos1(gef,allo) kcat_sos1_1

HRas(pbs!1,nbs~gdp).Sos1(gef!1,allo!+)->HRas(pbs,nbs~gtp)+Sos1(gef,allo!+) kcat_sos1_2

?-)!+$4)%)4!<W(*!('.#;(.#$3!#*!#%%2*./(.)4!#3!F68#&)!ECD!!

]@> AJ5,(,#-4*1-/.'#-./*%*+78R*A'(4')$*?-)!W(*!,/$.)#3*7!$3!('.#;(.#$3!80!B?P!8#34#3&7!&$!$3!.$!('.#;(.)!*);)/(%!,(.-5(0*9!N3)!$1!.-)!+$*.!

5#4)%0@*.24#)4!W(*@('.#;(.)4!,(.-5(0*!#*!.-)!'%(**#'(%!+#.$&)3!('.#;(.)4!,/$.)#3!6#3(*)!C:KPED!'(*'(4)9!

:KPE*!(/)!6#3(*)*!.-(.!(/)!-)(;#%0!#3;$%;)4!#3!&/$5.-@/)%(.)4!./(3*'/#,.#$3!1('.$/!/)&2%(.#$39!

P/);#$2*%07!.-)!,(/(4#&+!$1!('.#;(.#$3!5(*!.-(.!:KPE*!5)/)!,-$*,-$/0%(.)4!80!:KPJE*!(34!:KPJE*!

5)/)!,-$*,-$/0%(.)4!80!:KPRE*7!5-#'-!#3!.2/3!5)/)!('.#;(.)4!80!8#34#3&!$1!W(*@B?P9!<$5);)/7!(*!

);#4)3')!(''2+2%(.)47!#.!8)'(+)!1(#/%0!$8;#$2*!.-(.!.-)!*#.2(.#$3!#*!3$.!*$!*#+,%)9!?-)!,/)*)3')!$1!

+2%.#,%)!*28.0,)*7!$%#&$+)/#=(.#$37!*'(11$%4*7!1))48('6@+)'-(3#*+*!(34!')%%@*,)'#1#'!'$34#.#$3*!

'$31$234!.-)!*.240!$1!.-#*!'$+,%)>!,(.-5(09!!

K*!+)3.#$3)4!)(/%#)/7!.-)/)!(/)!.-/))!*28.0,)*!$1!W(*!,/$.)#3*T!<W(*7!EW(*!(34!:W(*9!:KPRE*!(/)!$1!

.-/))!.0,)*!.$$T!W(1g7!W(1J!(34!W(1R9?-)0!(/)!*28V)'.!.$!'$+,%)>!/)&2%(.#$3!1/$+!$.-)/!*#&3(%#3&!

,(.-5(0*!(*!5)%%!(*!/)&2%(.#$3!80!)('-!$.-)/9!:)6g!(34!:)6J!(/)!:KPJE!*28.0,)*9!:KPE*!.-)+*)%;)*!

! cJ!

-(;)!+2%.#,%)!1(+#%#)*!*2'-!(*!.-)!S/6!CS/6g!(34!S/6JD!(34!^369!S/6J!'(3!'(2*)!3)&(.#;)!1))48('6!80!

4)('.#;(.#3&!B(8g!(34!L$*g7!)(/%0!,(/.#'#,(3.*!#3!W(*@('.#;(.#$39!?-)!,/#+(/0!123'.#$3!$1!.-)!:KPE*!

*))+*!.$!8)!#3!.-)!32'%)2*!.-$2&-7!'(2*#3&!('.#;(.#$3!$1!&/$5.-@/)%(.)4!./(3*'/#,.#$3!1('.$/*!*2'-!(*!

.-$*)!$1!.-)!KPg!1(+#%09!

I#.-!.-)*)!'(;)(.*7!.-)!+$4)%!,/)*)3.)4!-)/)!$+#.*!+(30!$1!.-)!63$53!4).(#%*!$1!.-)!:KPE!'(*'(4)!

(34!#*!,/$;#4)4!.$!#%%2*./(.)!-$5!.-)!8(*#'!8#$'-)+#*./0!'(3!8)!)3'$4)49!?-)!/2%)*!4)*'/#8#3&!'-(3&)!$1!

*.(.)!-(;)!.-)!(,,/$,/#(.)!'$+,$3)3.!234)/%#3)4!1$/!)+,-(*#*9!

_'4+0I)-6-.!_3%-KA<>!B65,-!3%/E!%5,!:%#-)-!%!:+5/+&$%06+5%2!:I%58)!!"#$D!3%/E!6-!5+*!%5!%:06H)!

;65%-)!0I%0!:%5!4I+-4I+&'2%0)!1);E!!""$!+5!"NEY!%5,!"NNND!<I)!4I+-4I+&'2%06+5!6-!%50%8+56?),!B'!

0I)!4I+-4I%0%-)!>>NG!!"%$D!

# HRas-GTP binds Raf1

HRas(nbs~gtp,pbs) + Raf1(rbd) -> HRas(nbs~gtp,pbs!1).Raf1(rbd!1) kf_hras_raf1

HRas(pbs!1).Raf1(rbd!1) -> HRas(pbs!1) + Raf1(rbd!1) kr_hras_raf1

# Ras-bound Raf1 is a kinase of Mek1

Raf1(rbd!+,kin) + Mek1(S218~0) -> Raf1(rbd!+,kin!1).Mek1(S218~0!1) kf_raf1_mek1

Raf1(rbd!+,kin) + Mek1(S222~0) -> Raf1(rbd!+,kin!1).Mek1(S222~0!1) kf_raf1_mek1

Raf1(kin!1).Mek1(S218~0!1) -> Raf1(kin!1) + Mek1(S218~0) kr_raf1_mek1

Raf1(kin!1).Mek1(S222~0!1) -> Raf1(kin!1) + Mek1(S222~0) kr_raf1_mek1

Raf1(kin!1).Mek1(S218~0!1) -> Raf1(kin) + Mek1(S218~p) kcat_raf1

Raf1(kin!1).Mek1(S222~0!1) -> Raf1(kin) + Mek1(S222~p) kcat_raf1

# PP2A is a phosphatase of Mek1

PP2A(pptase) + Mek1(S218~p) -> PP2A(pptase!1).Mek1(S218~p!1) kf_pp2a_mek1

PP2A(pptase) + Mek1(S222~p) -> PP2A(pptase!1).Mek1(S222~p!1) kf_pp2a_mek1

PP2A(pptase!1).Mek1(S218~p!1) -> PP2A(pptase) + Mek1(S218~p) kr_pp2a_mek1

PP2A(pptase!1).Mek1(S222~p!1) -> PP2A(pptase) + Mek1(S222~p) kr_pp2a_mek1

! cR!

PP2A(pptase!1).Mek1(S218~p!1) -> PP2A(pptase) + Mek1(S218~0) kcat_pp2a

PP2A(pptase!1).Mek1(S222~p!1) -> PP2A(pptase) + Mek1(S222~0) kcat_pp2a

_'4+0I)-6-.!964I+-4I+&'2%0),!1);!E!6-!%5!%:06H)!;65%-)!0I%0!:%5!4I+-4I+&'2%0)!T&;N!!""$!+5!<EYP!%5,!

`EYMD!<I)!4I+-4I+&'2%06+5!6-!%50%8+56?),!B'!0I)!4I+-4I%0%-)!@#-4E!!"&$D!

# Biphosphorylated Mek1 is a kinase of Erk2

Mek1(S218~p,S222~p,kin) + Erk2(T185~0)-> Mek1(S218~p,S222~p,kin!1).Er2(T185~0!1) \

kf_mek1_erk2

Mek1(S218~p,S222~p,kin) + Erk2(Y187~0)-> Mek1(S218~p,S222~p,kin!1).Er2(Y187~0!1) \

kf_mek1_erk2

Mek1(kin!1).Erk2(T185~0!1) -> Mek1(kin!1) + Erk2(T185~0) kr_mek1_erk2

Mek1(kin!1).Erk2(Y187~0!1) -> Mek1(kin!1) + Erk2(Y187~0) kr_mek1_erk2

Mek1(kin!1).Erk2(T185~0!1) -> Mek1(kin) + Erk2(T185~p) kcat_mek1

Mek1(kin!1).Erk2(Y187~0!1) -> Mek1(kin) + Erk2(Y187~p) kcat_mek1

# Dusp1 is a phosphatase of Erk2

Dusp1(pptase) + Erk2(T185~p) -> Dusp1(pptase!1).Erk2(T185~p!1) kf_dusp1_erk2

Dusp1(pptase) + Erk2(Y187~p) -> Dusp1(pptase!1).Erk2(Y187~p!1) kf_dusp1_erk2

Dusp1(pptase!1).Erk2(T185~p!1) -> Dusp1(pptase) + Erk2(T185~p) kr_dusp1_erk2

Dusp1(pptase!1).Erk2(Y187~p!1) -> Dusp1(pptase) + Erk2(Y187~p) kr_dusp1_erk2

Dusp1(pptase!1).Erk2(T185~p!1) -> Dusp1(pptase) + Erk2(T185~0) kcat_dusp1

Dusp1(pptase!1).Erk2(Y187~p!1) -> Dusp1(pptase) + Erk2(Y187~0) kcat_dusp1

L#&3(%!./(3*42'.#$3!3).5$/6*!)>-#8#.!*#&3#1#'(3.!4+-606H)!%5,!5)8%06H)!/)),B%:;7!#9)9!4$53*./)(+!

)11)'.$/*!4$28%#3&!8('6!(34!+$4#10#3&!C)3-(3'#3&!$/!(..)32(.#3&D!.-)!,/$,)/.#)*!$1!2,*./)(+!*#&3(%!

,/$.)#3*9!?-#*!)3(8%)*!2%./(@*)3*#.#;#.0!#3!/)&2%(.#$3!(34!(4(,.#;)!/)*,$3*)*!.$!#3'$+#3&!*#&3(%*9!

G3.)/)*.#3&!403(+#'!,-)3$+)3(!*2'-!(*!$*'#%%(.#$3*!(34!./(;)%%#3&!5(;)*!(/)!(%*$!$8*)/;)4!#3!*$+)!

'(*)*!42)!.$!*2'-!1))48('6!!)2&9!

! cU!

Knowledge Base: Biphosphorylated Erk2 can dimerize with other Erk2 (phosphorylated or

unphosphorylated). The dimer is catalytically active on many substrates [54], including negative regulatory

sites on Gab1 (59) and Sos1 (68).

Erk2(T185~p,Y187~p,dim)+ Erk(dim) -> Erk2(T185~p,Y187~p,dim!1)+ Erk2(dim!1) kf_erk2_dim

Erk2(dim!1).Erk(dim!1) -> Erk2(dim) + Erk(dim) kr_erk2_dim

Erk2(dim!+,kin) + Gab1(ST~0) -> Erk2(dim!+,kin!1).Gab1(ST~0!1) kf_erk2_gab1

Erk2(kin!1).Gab1(ST~0!1) -> Erk2(kin) + Gab1(ST~0) kr_erk2_gab1

Erk2(kin!1).Gab1(ST~0!1) -> Erk2(kin) + Gab1(ST~p) kcat_erk2_gab1

Erk2(dim!+,kin) + Sos1(S~0) -> Erk2(dim!+,kin!1).Sos1(S~0!1) kf_erk_sos1

Erk2(kin!1).Sos1(S~0!1) -> Erk2(kin) + Sos1(S~0) kr_erk_sos1

Erk2(kin!1).Sos1(S~0!1) -> Erk2(kin) + Sos1(S~p) kcat_erk2_sos1

?-)!+$4)%)4!/2%)*!(/)!#%%2*./(.)4!#3!F68#&)!EQD!!

]@B S$.$*!$/"#'5-,.*S>./(')%%2%(/!*#&3(%*!-(;)!.-)#/!12/.-)*.@/)('-#3&!)11)'.*!5-)3!.-)!./(3*42')4!*#&3(%*!'2%+#3(.)!#3!.-)!

32'%)2*9!?-#*!#*!2*2(%%0!(''$+,%#*-)4!80!'-(3&#3&!.-)!4#*./#82.#$3!$1!./(3*'/#,.#$3!1('.$/*!#3!.-)!32'%)2*!

'(2*#3&!/),/)**#$3!$/!)3-(3')+)3.!$1!+WAK!./(3*'/#,.!,/$42'.#$3!1/$+!+2%.#,%)!&)3)*9!

?-)!')3./(%!4$&+(!$1!8#$%$&07!#9)9!./(3*'/#,.#$3!1$%%$5)4!80!./(3*%(.#$3!'(3!8)!)>,%#'#.%0!#+,%)+)3.)4!

2*#3&!/2%)*9!"$.-!#3;$%;)!'/)(.#$3!$1!3)5!+$%)'2%)*!C+WAK!./(3*'/#,.*!(34!,/$.)#3*D9!

Gene(a) -> Gene(a) + Transcript(a) k_transcription

Transcript(a) -> Transcript(a) + Protein(a) k_translation

G1!*.$'-(*.#'!1%2'.2(.#$3*!C42)!.$!&)3)*!.2/3#3&!$3!(34!$11!(/)!#+,$/.(3.!.$!.-)!*0*.)+D7!.-)3!#.!#*!

#+,$/.(3.!.$!/)*./#'.!.-)!32+8)/!$1!+$%)'2%)*!$1!.-)!Gene!.$!.-)!('.2(%!'$,0!32+8)/!.$!/),%#'(.)!/)(%!

8)-(;#$/9!

! c[!

K!*#+,%#10#3&!(**2+,.#$3!'(3!8)!+(4)!5-)/)!(%%!.-)!./(3*'/#,.#$37!./(3*%(.#$3!(34!,$*.@*03.-).#'!

+$4#1#'(.#$3!*.),*!'(3!8)!'$+,/)**)4!#3.$!(!*#3&%)!*.),9!?-#*!(+$23.*!.$!(**2+#3&!.-(.!.-)!4)%(0!

'(2*)4!80!*)O2)3')!$1!*.),*!#3!'/)(.#3&!.-)!,/$42'.!#*!3)&%#&#8%)!5-)3!'$+,(/)4!.$!.-)!/(.)*!(.!5-#'-!

.-)!,/$.)#3!#*!,/$42')4!C*))!!'2&,*2,,%)+)3.(/0!+(.)/#(%D9!?-)!)11)'.#;)!/)('.#$3!5$2%4!8)T!

Gene(a) -> Gene(a) + Protein(a) k_syn

P/$.)#3!*03.-)*#*!'(3!(%*$!8)!+(4)!4),)34)3.!$3!./(3*'/#,.#$3@1('.$/!8#34#3&9

Gene(tf)+ TF(gene) <-> Gene(tf!0).TF(gene!0) kf_gene_tf,kr_gene_tf

Gene(tf!+) -> Gene(tf!+) + Protein(a) k_syn

N1.)3!.-)!8#34#3&!'(3!8)!(**2+)4!.$!8)!#3!O2(*#@)O2#%#8/#2+!$3!.-)!.#+)!*'(%)!$3!5-#'-!&)3)*!(/)!

)>,/)**)47!*$!.-(.!.-)!)>,/)**#$3!/(.)!8)'$+)*!(!123'.#$3!$1!.-)!./(3*'/#,.#$3!1('.$/!'$3')3./(.#$39!K3!

)>(+,%)!#*!*-$53!-)/)!2*#3&!(!<#%%!/(.)!%(5!C*))!"):06+5!PDCDN!1$/!4).(#%*D9!

TF()+Gene() -> TF()+Gene()+Protein() Hill(k,K,n)

G3!.-)!/)*.!$1!.-#*!*)'.#$3!5)!5#%%!#+,%)+)3.!/)('.#$3!/2%)*!,)/.(#3#3&!.$!&)3)!/)&2%(.#$3!80!(!'0.$*$%#'!

*#&3(%9!?-)!/2%)*!5#%%!8)!+$4)%)4!#3!.-)!'$+,(/.+)3.(%!'$3.)>.7!/).(#3#3&!.-)!*(+)!'$+,(/.+)3.(%!

-#)/(/'-0!#3!"):06+5!MDQ!(34!F68#&)!P9!L,)'#1#'(%%0!5)!5#%%!+$4)%!.-)!./(3*42'.#$3!$1!*#&3(%!1/$+!.5$!

,(/(%%)%!:KPE!,(.-5(0*!#3!.-)!1$/+!$1!S/6J!(34!^36g!#3.$!.-)!32'%)2*!(34!('.#;(.#$3!$1!.-)!KPg!

./(3*'/#,.#$3!1('.$/9!?-)!#31$/+(.#$3!,/)*)3.)4!-)/)!#*!/);#)5)4!#3!!0"#0$#0%&9!

Knowledge Base: Biphosphorylated Erk2 and Jnk1 can reversibly homodimerize in both cytosolic and

nuclear compartments. It is sufficient that one partner is phosphorylated.

Erk2(T185~p,Y187~p,dim)+ Erk(dim) -> Erk2(S218~p,S222~p,dim!1)+ Erk2(dim!1) kf_erk2_dim

Erk2(dim!1).Erk(dim!1) -> Erk2(dim) + Erk(dim) kr_erk2_dim

Jnk1(T183~p,Y185~p,dim)+ Jnk(dim) -> Jnk1(T183~p,Y185~p,dim!1)+ Jnk1(dim!1) kf_jnk1_dim

Jnk1(dim!1).Jnk(dim!1) -> Jnk1(dim) + Jnk(dim) kr_jnk1_dim

! c\!

L#3')!-$+$@4#+)/#=(.#$3!$''2/*!#3!8$.-!'0.$*$%#'!(34!32'%)(/!'$+,(/.+)3.*7!#.!#*!*211#'#)3.!.$!+$4)%!

.-)+!5#.-!23#;)/*(%!/)('.#$3!/2%)*9!

Knowledge Base: Both Erk2 and Jnk1 monomers passively diffuse into the nucleus. Erk2 and Jnk1 dimers

also translocate to the nucleus at a faster rates.

L#3')!.-)!32'%)2*!(34!'0.$*$%!(/)!8/#4&)4!80!.-)!32'%)(/!+)+8/(3)7!5)!2*)!8/#4&)4@;$%2+)!+$%)'2%)!

./(3*,$/.!/2%)*9!I)!(%*$!3))4!.$!(%%$'(.)!*),(/(.)!+#'/$*'$,#'!/(.)*!1$/!+$3$+)/*!(34!4#+)/*9!

# Erk2 and Jnk1 monomer transport

Erk2(T185,Y187,dim,kin)@Cyt <-> Erk2(T185,Y187,dim,kin)@Nuc k_tr_erk2_m,k_tr_erk2_m

Jnk1(T183,Y185,dim,kin)@Cyt <-> Jnk1(T183,Y185,dim,kin)@Nuc k_tr_jnk1_m,k_tr_jnk1_m

# Erk2 and Jnk1 dimer transport

Erk2(T185,Y187,dim!1,kin)@Cyt.Erk2(T185,Y187,dim!1,kin)@Cyt <-> \

Erk2(T185,Y187,dim!1,kin)@Nuc.Erk2(T185,Y187,dim!1,kin)@Nuc k_tr_erk2_d,k_tr_erk2_d

Jnk1(T183,Y185,dim!1,kin)@Cyt.Jnk1(T183,Y185,dim!1,kin)@Cyt <-> \

Jnk1(T183,Y185,dim!1,kin)@Nuc.Jnk1(T183,Y185,dim!1,kin)@Nuc k_tr_jnk1_d,k_tr_jnk1_d

A$.)!.-(.!.-)!$.-)/!'$+,$3)3.*!$3!S/6J!(34!^36g!3))4!.$!8)!#3!238$234!*.(.)!.$!(%%$5!./(3*,$/.9!

Knowledge Base: Fos and Jun are transcription factors synthesized and maintained at a certain level in the

nucleus.

FosGene()@Nuc -> FosGene()@Nuc + Fos(y~0)@Nuc k_syn_fos

JunGene()@Nuc -> JunGene()@Nuc + Jun(y~0)@Nuc k_syn_jun

Fos()@Nuc -> 0 k_del_fos

Jun()@Nuc -> 0 k_del_jun

G3*.)(4!$1!*#+,%0!'/)(.#3&!(!,/))>#*.#3&!32+8)/!$1!M$*!(34!^23!+$%)'2%)*7!5)!3$5!-(;)!(!403(+#'!

)O2#%#8/#2+!$1!*03.-)*#*]4)&/(4(.#$3!);)3.*!.-(.!%)(4*!.$!(!*.)(40!*.(.)!32+8)/!$1!M$*!(34!^239!

! ca!

Knowledge Base: Activated Erk2 and Jnk1 dimers can phosphorylate Fos and Jun respectively.

Erk(dim!+,fos) + Fos(y~0)<-> Erk(dim!+,fos!0).Fos(y~0!0) kf_erk_fos,kr_erk_fos

Erk(dim!+,fos!0).Fos(y~0!0)-> Erk(dim!+,fos) + Fos(y~p) k_ph_erk

Jnk(dim!+,kin) + Jun(y~0)<-> Jnk(dim!+,kin!0).Jun(y~0!0) kf_jnk_kin,kr_jnk_kin

Jnk(dim!+,kin!0).Jun(y~0!0)-> Jnk(dim!+,kin) + Jun(y~p) k_ph_jnk

L#3')!.-)/)!(/)!3$!4#/)'.!$/!#34#/)'.!./(3*,$/.!+)'-(3#*+*!1$/!M$*!(34!^237!23#;)/*(%!/2%)*!(/)!*211#'#)3.!

.$!+$4)%!.-)*)!#3.)/('.#$3*9!K'.#;(.)4!M$*!(34!^23!'(3!4#+)/#=)!.$!1$/+!.-)!./(3*'/#,.#$3!1('.$/!KPg!

5-#'-!*-$5*!8#34#3&!(11#3#.0!1$/!$.-)/!./(3*'/#,.#$3!1('.$/*!(34!')/.(#3!,/$+$.)/!`AK!*)O2)3')*9!?-)!

8#34#3&!*#.)*!(/)!*-(/)4!('/$**!8$.-!M$*!(34!^23!*2823#.*9!L#3')!.-)!M$*@^23!4#+)/!*))+*!.$!8)-(;)!(*!

(3!#34),)34)3.!+$%)'2%)!.0,)!5#.-!8#34#3&!*#.)*7!5)!'/)(.)!(!3)5!+$%)'2%)!.0,)!'(%%)4!KPg9!

Knowledge Base: Activated Fos and Jun can hetero-dimerize to form AP1 (Fos-Jun). AP1 can be degraded.

Fos(y~p) + Jun(y~p) <-> AP1(g,nfat) kf_kin_kin,kr_kin_kin

AP1()@Nuc -> 0 k_del_ap1

Knowledge Base: AP1 can bind to promoter sequences and activate target genes on its own or in

combination with other transcription factors (NFAT). AP1 bound genes enable synthesis of target proteins in

the cytosol.

AP1(nfat) + NFAT(ap1) <-> AP1(nfat!0).NFAT(ap1!0) kf_ap1_nfat,kr_ap1_nfat

AP1(g) + TargetGene(prm) <-> AP1(g!0).TargetGene(prm!0) kf_ap1_gene,kr_ap1_gene

TargetGene(prm!+)@Nuc -> TargetGene(prm!+)@Nuc + TargetProtein@Cyt k_syn_ap1

?-)!&)3)!/)&2%(.#$3!+$4)%!#*!#%%2*./(.)4!#3!F68#&)!EP9!

:^ S,,)*+,)$#-./*83'45-4$*

?-#*!*)'.#$3!#*!#3.)34)4!(*!(!*2++(/0!$1!.-)!'/#.#'(%!,$#3.*!1/$+!.-)!,/);#$2*!*)'.#$3*9!

• A(+)!+$%)'2%)*!(1.)/!#+,$/.(3.!#34#;#*#8%)!)3.#.#)*!#3!.-)!+$4)%9!

! cc!

• A(+)!'$+,$3)3.*!(1.)/!8#$%$&#'(%!*28*./2'.2/)*!C4$+(#3*7!+$.#1*7!(+#3$!('#4!*)O2)3')!,$*#.#$37!

).'9D!$/!.-)#/!8#34#3&!,(/.3)/!$/!.-)#/!4)*#&3(.)4!123'.#$39!

• ?-)!1)5)/!.-)!./(3*1$/+(.#$3*!#3!(!/)('.#$3!/2%)7!.-)!+$/)!/)(%#*.#'!#.!#*9!

• Z3#+$%)'2%(/!(34!8#+$%)'2%(/!/)('.#$3!$/4)/*!(/)!/)(%#*.#'9!<#&-)/!$/4)/*!(/)!%)**!*$9!

• ?-)!/(.)!'$3*.(3.!2*)4!*-$2%4!8)!.-)!(*0++)./#'7!,)/@*#.)!/(.)@'$3*.(3.7!5-#'-!5$2%4!/)O2#/)!

*'(%#3&!80!;$%2+)!(34!K;$&(4/$!32+8)/!#3!"AB!(34!$3%0!80!K;$&(4/$!32+8)/!#3!'"AB9!

• I-)3!5/#.#3&!/)('.#$3!/2%)*7!$+#.!'$+,$3)3.*!.-(.!4$!3$.!#31%2)3')!.-)!/(.)!$1!.-)!/)('.#$39!

• ?5$!/)('.#$3*!-(;#3&!.-)!*(+)!/)('.#$3!')3.)/!'(3!-(;)!4#11)/)3.!6#3).#'*9!G1!.-#*!#*!.-)!'(*)7!2*)!

.5$!4#11)/)3.!/2%)*!.$!+$4)%!.-)+7!23%)**!.-)!4#11)/)3')!#*!42)!.$!*0++)./0!(34!+2%.#,%#'#.0!

)11)'.*7!5-#'-!"#$A).B)3!4).)/+#3)*!(2.$+(.#'(%%09!

• F$$,)/(.#;)!#3.)/('.#$3*!+2*.!$8)0!4).(#%)4!8(%(3')9!

• Z*)!5#%4'(/4*!#3!/)('.#$3!/2%)*!(34!$8*)/;(8%)*!.$!1#3)%0!.(#%$/!+(.'-#3&!'$34#.#$3*!#3!,(..)/3*9!

• I-)3!*03.-)*#=#3&!(!3)5!*,)'#)*!#3!(!/)('.#$3!/2%)7!,/$;#4)!.-)!12%%!*,)'#)*!*,)'#1#'(.#$39!

• :$*.!./(3*1$/+(.#$3*!(/)!/);)/*#8%)!#3!(!/)(%#*.#'!+$4)%9!Z3%)**!.-)/)!#*!*,)'#1#'!#31$/+(.#$3!$3!

#//);)/*#8#%#.07!.-)/)!*-$2%4!)>#*.!/2%)*!.-(.T!

o `),-$*,-$/0%(.)!(%%!,-$*,-$/0%(.#$3!*#.)*9!

o "/)(6!(%%!8$34*!.-(.!'(3!8)!1$/+)49!

o `)&/(4)!(%%!+$%)'2%)*!.-(.!'(3!8)!*03.-)*#=)49!

• `)%).#$3!/2%)*!4)%).)!.-)!5-$%)!*,)'#)*!80!4)1(2%.9!Z*)!DeleteMolecules!6)05$/4!.$!4)%).)!$3%0!

.-)!/)*,)'.#;)!+$%)'2%)*!3$.!.-)!5-$%)!*,)'#)*9!

• I-)3!./(3*,$/.#3&!+$%)'2%)*!#3!'"AB7!'-)'6!.$!*))!#1!0$2!(/)!./(3*,$/.#3&!+$%)'2%)*!$/!*,)'#)*9!!

• K;$#4!/(.)@%(5!(,,/$>#+(.#$3*9!P/)1)/!)>,%#'#.!+)'-(3#*+*9!

• K**2+)!.5$!#3.)/('.#$3*!(/)!#34),)34)3.!C4#*./#82.#;)D7!23%)**!.-)/)!#*!*,)'#1#'!/)(*$3!.$!+$4)%!

.-)+!*)O2)3.#(%%0!C,/$')**#;)D9!?-)!%#.)/(.2/)!'(3!8)!+#*%)(4#3&!(8$2.!.-)!*)O2)3.#(%!3(.2/)9!

! cf!

• Z*)!*./2'.2/(%!63$5%)4&)!.$!#31)/!-$5!#3.)/('.#$3*!(11)'.!)('-!$.-)/9!G3!.-)!(8*)3')!$1!

#31$/+(.#$37!(**2+)!#34),)34)3')!$1!#3.)/('.#$3*9!

• G1!*+(%%!'-(3&)*!'(3!'(2*)!4/(*.#'!)11)'.*7!2*)!(!*.$'-(*.#'!*#+2%(.$/9!

• G1!.-)!3).5$/6!#*!.$$!8#&7!2*)!(!3).5$/6@1/))!*#+2%(.$/9!

• ?$!*#+2%(.)!(!.0,#'(%!8#$%$&#'(%!)>,)/#+)3.7!(%5(0*!)O2#%#8/(.)!8)1$/)!,)/.2/8#3&9!

• K;$#4!-(;#3&!.$!&)3)/(.)!.-)!*(+)!3).5$/6!/),)(.)4%07!)*,)'#(%%0!5#.-!%(/&)!3).5$/6*9!

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!$0$3$.4$(*

g9 Kholodenko, B. N., Hancock, J. F. and Kolch, W. (2010), Signalling ballet in space and time, Nat Rev Mol Cell

Biol 11, 414-26.

J9 Kholodenko, B. N. (2006), Cell-signalling dynamics in time and space, Nat Rev Mol Cell Biol 7, 165-76.

R9 Scott, J. D. and Pawson, T. (2009), Cell signaling in space and time: where proteins come together and when

they're apart, Science (New York, NY) 326, 1220-4.

U9 Natarajan, M., Lin, K.-M., Hsueh, R. C., Sternweis, P. C. and Ranganathan, R. (2006), A global analysis of cross-

talk in a mammalian cellular signalling network, Nat Cell Biol 8, 571-80.

[9 Hecker, M., Lambeck, S., Toepfer, S., van Someren, E. and Guthke, R. (2009), Gene regulatory network

inference: data integration in dynamic models-a review, BioSystems 96, 86-103.

\9 Hlavacek, W. S. and Faeder, J. R. (2009), The complexity of cell signaling and the need for a new mechanics,

Science Signaling 2, 46.

! fh!

a9 Hlavacek, W., Faeder, J. and Blinov, M. (2006), Rules for modeling signal-transduction systems, Science's STKE

344, 6.

c9 Bachman, J. A. and Sorger, P. (2011), New approaches to modeling complex biochemistry, Nat Methods 8, 130-

1.

f9 Faeder, J., Blinov, M. and Hlavacek, W. (2009), Rule-based modeling of biochemical systems with BioNetGen,

Methods Mol. Biol 500, 113-167.

gh9 Blinov, M. L., Faeder, J. R., Goldstein, B. and Hlavacek, W. S. (2004), BioNetGen: software for rule-based

modeling of signal transduction based on the interactions of molecular domains, Bioinformatics 20, 3289-91.

gg9 Danos, V. and Laneve, C. (2004), Formal molecular biology, Theoretical Computer Science 325, 69-110.

gJ9 Feret, J., Danos, V., Krivine, J., Harmer, R. and Fontana, W. (2009), Internal coarse-graining of molecular

systems, Proc Natl Acad Sci USA 106, 6453-8.

gR9 Haugh, J. M. and Lauffenburger, D. A. (1997), Physical modulation of intracellular signaling processes by

locational regulation, Biophys J 72, 2014-31.

gU9 Michaelis, L. and Menten, M. (1913), Die kinetik der invertinwirkung, Biochem. Z 49, 333-369.

g[9 Briggs, G. and Haldane, J. (1925), A note on the kinetics of enzyme action, Biochem J 19, 338.

g\9 Weiss, J. (1997), The Hill equation revisited: uses and misuses, FASEB J 11, 835-841.

ga9 Cornish-Bowden, A. (2004), Fundamentals of Enzyme Kinetics, Ed. 3, Portland Press.

gc9 Chen, W. W., Niepel, M. and Sorger, P. K. (2010), Classic and contemporary approaches to modeling

biochemical reactions, Gene Dev 24, 1861-75.

gf9 Tracy, T. S. and Hummel, M. A. (2004), Modeling kinetic data from in vitro drug metabolism enzyme experiments,

Drug Metab Rev 36, 231-42.

Jh9 Sabouri-Ghomi, M., Ciliberto, A., Kar, S., Novak, B. and Tyson, J. J. (2008), Antagonism and bistability in protein

interaction networks, J Theor Biol 250, 209-18.

Jg9 Sneddon, M. W., Faeder, J. R. and Emonet, T. (2011), Efficient modeling, simulation and coarse-graining of

biological complexity with NFsim, Nat Methods 8, 177-83.

JJ9 Chen, W. W., Schoeberl, B., Jasper, P. J., Niepel, M., Nielsen, U. B., Lauffenburger, D. A. and Sorger, P. K.

! fg!

(2009), Input-output behavior of ErbB signaling pathways as revealed by a mass action model trained against

dynamic data, Mol Syst Biol 5, 239.

JR9 Barik, D., Baumann, W. T., Paul, M. R., Novak, B. and Tyson, J. J. (2010), A model of yeast cell-cycle regulation

based on multisite phosphorylation, Mol Syst Biol 6, 405.

JU9 Hänggi, P. (2002), Stochastic resonance in biology how noise can enhance detection of weak signals and help

improve biological information processing, ChemPhysChem 3, 285-290.

J[9 Gillespie, D. (1976), A general method for numerically simulating the stochastic time evolution of coupled

chemical reactions, J Comput Phys 22, 403-434.

J\9 Yang, J., Monine, M. I., Faeder, J. R. and Hlavacek, W. S. (2008), Phys Rev E 78, 031910.

Ja9 Borisov, N., Chistopolsky, A., Faeder, J. and Kholodenko, B. (2008), Domain-oriented reduction of rule-based

network models, IET systems biology 2, 342-351.

Jc9 Conzelmann, H., Saez-Rodriguez, J., Sauter, T., Kholodenko, B. N. and Gilles, E. D. (2006), A domain-oriented

approach to the reduction of combinatorial complexity in signal transduction networks, BMC Bioinformatics 7, 34.

Jf9 Lok, L. and Brent, R. (2005), Automatic generation of cellular reaction networks with Moleculizer 1.0, Nat

Biotechnol 23, 131-6.

Rh9 Faeder, Blinov, M., Goldstein, B. and Hlavacek, W. (2005), Rule-based modeling of biochemical networks,

Complexity 10, 22-41.

Rg9 Danos, V., Feret, J., Fontana, W. and Krivine, J. (2007), Scalable simulation of cellular signaling networks,

Lecture Notes in Computer Science 4807, 139-157.

RJ9 Le Novére, N. and Shimizu, T. S. (2001), STOCHSIM: modelling of stochastic biomolecular processes,

Bioinformatics 17, 575-6.

RR9 Colvin, J., Monine, M. I., Faeder, J. R., Hlavacek, W. S., Hoff, D. D. V. and Posner, R. G. (2009), Simulation of

large-scale rule-based models, Bioinformatics 25, 910-7.

RU9 Colvin, J., Monine, M. I., Gutenkunst, R. N., Hlavacek, W. S., Hoff, D. D. V. and Posner, R. G. (2010),

RuleMonkey: software for stochastic simulation of rule-based models, BMC Bioinformatics 11, 404.

R[9 Walker, F., Orchard, S. G., Jorissen, R. N., Hall, N. E., Zhang, H.-H., Hoyne, P. A., Adams, T. E., Johns, T. G.,

! fJ!

Ward, C., Garrett, T. P. J., Zhu, H.-J., Nerrie, M., Scott, A. M., Nice, E. C. and Burgess, A. W. (2004), CR1/CR2

interactions modulate the functions of the cell surface epidermal growth factor receptor, J Biol Chem 279, 22387-

98.

R\9 Jorissen, R. N., Walker, F., Pouliot, N., Garrett, T. P. J., Ward, C. W. and Burgess, A. W. (2003), Epidermal

growth factor receptor: mechanisms of activation and signalling, Exp Cell Res 284, 31-53.

Ra9 Zhang, X., Gureasko, J., Shen, K., Cole, P. A. and Kuriyan, J. (2006), An allosteric mechanism for activation of

the kinase domain of epidermal growth factor receptor, Cell 125, 1137-49.

Rc9 Tao, R. and Maruyama, I. (2008), All EGF (ErbB) receptors have preformed homo-and heterodimeric structures in

living cells, J Cell Sci 121, 3207-3217.

Rf9 Kholodenko, B. N., Demin, O. V., Moehren, G. and Hoek, J. B. (1999), Quantification of short term signaling by

the epidermal growth factor receptor, J Biol Chem 274, 30169-81.

Uh9 Schoeberl, B., Eichler-Jonsson, C., Gilles, E. D. and Müller, G. (2002), Computational modeling of the dynamics

of the MAP kinase cascade activated by surface and internalized EGF receptors, Nat Biotechnol 20, 370-5.

Ug9 Wofsy, C., Goldstein, B., Lund, K. and Wiley, H. S. (1992), Implications of epidermal growth factor (EGF) induced

egf receptor aggregation, Biophys J 63, 98-110.

UJ9 Ollivier, J. F., Shahrezaei, V. and Swain, P. S. (2010), Scalable rule-based modelling of allosteric proteins and

biochemical networks, PLoS Comput Biol 6, e1000975.

UR9 Macdonald, J. L. and Pike, L. J. (2008), Heterogeneity in EGF-binding affinities arises from negative cooperativity

in an aggregating system, Proc Natl Acad Sci USA 105, 112-7.

UU9 Alvarado, D., Klein, D. E. and Lemmon, M. A. (2010), Structural Basis for Negative Cooperativity in Growth Factor

Binding to an EGF Receptor, Cell 142, 568-579.

U[9 Harris, L. A., Hogg, J. S. and Faeder, J. R. (2009), Compartmental Rule-based Modeling of Biochemical Systems,

Proceedings of the 2009 Winter Simulation Conference.

U\9 Saltelli, A., Ratto, M., Tarantola, S. and Campolongo, F. (2005), Sensitivity analysis for chemical models, Chem.

Rev 105, 2811-2827.

Ua9 Seewöster, T. and Lehmann, J. (1997), Cell size distribution as a parameter for the predetermination of

! fR!

exponential growth during repeated batch cultivation of CHO cells, Biotechnol Bioeng 55, 793-797.

Uc9 Swanson, J. A., Lee, M. and Knapp, P. E. (1991), Cellular dimensions affecting the nucleocytoplasmic volume

ratio, J Cell Biol 115, 941-8.

Uf9 Lipniacki, T., Puszynski, K., Paszek, P., Brasier, A. R. and Kimmel, M. (2007), Single TNFalpha trimers mediating

NF-kappaB activation: stochastic robustness of NF-kappaB signaling, BMC Bioinformatics 8, 376.

[h9 Ghaemmaghami, S., Huh, W.-K., Bower, K., Howson, R. W., Belle, A., Dephoure, N., O'Shea, E. K. and

Weissman, J. S. (2003), Global analysis of protein expression in yeast, Nature 425, 737-41.

[g9 Lee, B., LeDuc, P. R. and Schwartz, R. (2008), Stochastic off-lattice modeling of molecular self-assembly in

crowded environments by Green's function reaction dynamics, Phys Rev E Stat 78, 031911.

[J9 Kim, J. S. and Yethiraj, A. (2010), Crowding effects on association reactions at membranes, Biophys J 98, 951-8.

[R9 Gabdoulline, R. R. and Wade, R. C. (2002), Biomolecular diffusional association, Curr Opin Struct Biol 12, 204-

13.

[U9 Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K. and Watson, J. D. (1994), Molecular Biology of the Cell, Ed.

3, Garland Publishing.

[[9 Hlavacek, W. S., Faeder, J. R., Blinov, M. L., Perelson, A. S. and Goldstein, B. (2003), The complexity of

complexes in signal transduction, Biotechnol Bioeng 84, 783-94.

[\9 Berman, H. M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T. N., Weissig, H., Shindyalov, I. N. and Bourne, P. E.

(2000), The Protein Data Bank, Nucleic Acids Res 28, 235-42.

[a9 Consortium, U. (2010), The Universal Protein Resource (UniProt) in 2010, Nucleic Acids Res 38, D142-8.

[c9 Schulze, W. X., Deng, L. and Mann, M. (2005), Phosphotyrosine interactome of the ErbB-receptor kinase family,

Mol Syst Biol 1, 2005.0008.

[f9 Gu, H. and Neel, B. G. (2003), The "Gab" in signal transduction, Trends Cell Biol 13, 122-30.

\h9 Ravichandran, K. S. (2001), Signaling via Shc family adapter proteins, Oncogene 20, 6322-30.

\g9 Neel, B., Gu, H. and Pao, L. (2003), The 'Shp'ing news: SH2 domain-containing tyrosine phosphatases in cell

signaling, Trends Biochem Sci 28, 284-293.

\J9 Das, J., Ho, M., Zikherman, J., Govern, C., Yang, M., Weiss, A., Chakraborty, A. K. and Roose, J. P. (2009),

! fU!

Digital signaling and hysteresis characterize ras activation in lymphoid cells, Cell 136, 337-51.

\R9 Langlois, W. J., Sasaoka, T., Saltiel, A. R. and Olefsky, J. M. (1995), Negative feedback regulation and

desensitization of insulin- and epidermal growth factor-stimulated p21ras activation, J Biol Chem 270, 25320-3.

\U9 Seminario, M.-C., Precht, P., Bunnell, S. C., Warren, S. E., Morris, C. M., Taub, D. and Wange, R. L. (2004),

PTEN permits acute increases in D3-phosphoinositide levels following TCR stimulation but inhibits distal signaling

events by reducing the basal activity of Akt, Eur J Immunol 34, 3165-75.

\[9 Terai, K. and Matsuda, M. (2005), Ras binding opens c-Raf to expose the docking site for mitogen-activated

protein kinase kinase, EMBO Rep 6, 251-255.

\\9 Huang, W., Kessler, D. S. and Erikson, R. L. (1995), Biochemical and biological analysis of Mek1 phosphorylation

site mutants, Mol Biol Cell 6, 237-45.

\a9 Grethe, S. and Pцrn-Ares, M. I. (2006), p38 MAPK regulates phosphorylation of Bad via PP2A-dependent

suppression of the MEK1/2-ERK1/2 survival pathway in TNF-alpha induced endothelial apoptosis, Cell Signal 18,

531-40.

\c9 Kamioka, Y., Yasuda, S., Fujita, Y., Aoki, K. and Matsuda, M. (2010), Multiple decisive phosphorylation sites for

the negative feedback regulation of SOS1 via ERK, J Biol Chem 285, 33540-8.

\f9 Caunt, C. J., Rivers, C. A., Conway-Campbell, B. L., Norman, M. R. and McArdle, C. A. (2008), Epidermal growth

factor receptor and protein kinase C signaling to ERK2: spatiotemporal regulation of ERK2 by dual specificity

phosphatases, J Biol Chem 283, 6241-52.

ah9 Sauro, H. M. and Kholodenko, B. N. (2004), Quantitative analysis of signaling networks, Prog Biophys Mol Biol

86, 5-43.

ag9 Cobb, M. H. and Goldsmith, E. J. (2000), Dimerization in MAP-kinase signaling, Trends Biochem Sci 25, 7-9.

aJ9 Chang, L. and Karin, M. (2001), Mammalian MAP kinase signalling cascades, Nature 410, 37-40.

aR9 Shaulian, E. and Karin, M. (2002), AP-1 as a regulator of cell life and death, Nat Cell Biol 4, E131-6.

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!"

R

lig

L

rec

R

lig

L

rec

R

lig

L

rec

R

lig

L

rec

R

lig

L

rec

R

lig

L

rec

chopen

chclosed

chopen

chclosed

#"

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begin parameters

# Universal constants

N_Avo 6.023e23 # per mol

# Biophysical considerations

# Cell is a CHO cell, dimensions & quantities from ref 1

# Volume 1.2 pL, Cytoplasm 1 pL, Radius 6.6 microns, Sphere

# Surface area 5.5e-10 m^2 or 5.5e-8 dm^2, Membrane thickness 10 nm (or) 1e-7 dm

# External volume 1.6 nL (assuming 6.15e5 cells/mL)

V_ext 1.6e-9 # L

V_cell 1.2e-12 # L

V_cyt 1.0e-12 # L

V_nuc V_cell - V_cyt # L

h_mem 1e-7 # dm

S_mem 5.5e-8 # dm^2

V_mem h_mem*S_mem # L, comes to 5.5 fL

# Assumed association reaction rate constant, per M per s

k_ext 1e9 # EGF, small freely diffusing ligand, so high

k_mem 1e6 # EGFR, large bulky protein, so low. Calculated from refs 5-7

k_cyt 1e9 # Only small molecules such as Grb2, Sos

# Equilibrium Constants (Association Constants). Calculated from ref 2

Kdim_2D 5.3e9 # per (mol/dm^2)

Kdim Kdim_2D*h_mem # per (mol/dm^3) or per M

Kbind 4.6e9 # per M

alpha 120

beta 0.07

# Kinetic Rate Constants

k_f k_ext/(N_Avo*V_ext)

k_f_d k_mem/(N_Avo*V_mem)

k_r1 k_ext/Kbind

k_r2 k_r1/alpha

k_r3 k_r1/beta

k_r_d1 k_mem/Kdim

k_r_d2 k_r_d1/alpha

k_r_d3 k_r_d1/(alpha*beta)

# Kinase & Phosphatase

kcat 0.025 # per s

# Initial Concentrations

R_conc 1e5 # Receptors per cell

L_conc 1e-3 # M

P_conc 200e-9 # M

R0 R_conc

L0_new L_conc*V_ext*N_Avo

P0 P_conc*V_cyt*N_Avo

L0 0

end parameters

begin molecule types

R(lig,dim,tyr~u~p,tyr~u~p)

L(rec)

PTase(a)

end molecule types

("

begin seed species

R(lig,dim,tyr~u,tyr~u) R0

L(rec) L0

PTase(a) P0

end seed species

begin reaction rules

# Ligand binding

R(lig) + L(rec) -> R(lig!0).L(rec!0) k_f

R(dim,lig!0).L(rec!0) -> R(dim,lig) + L(rec) k_r1

R(dim!1,lig).R(dim!1,lig!0).L(rec!0) -> R(dim!1,lig).R(dim!1,lig) + L(rec) k_r2

R(dim!1,lig!+).R(dim!1,lig!0).L(rec!0) -> R(dim!1,lig!+).R(dim!1,lig) + L(rec) k_r3

# Dimerization

R(dim) + R(dim) -> R(dim!0).R(dim!0) k_f_d

R(dim!0,lig).R(dim!0,lig) -> R(dim,lig) + R(dim,lig) k_r_d1

R(dim!0,lig!+).R(dim!0,lig) -> R(dim,lig!+) + R(dim,lig) k_r_d2

R(dim!0,lig!+).R(dim!0,lig!+) -> R(dim,lig!+) + R(dim,lig!+) k_r_d3

# Phosphorylation

R(dim!+,tyr~u) -> R(dim!+,tyr~p) kcat

R(tyr~p) -> R(tyr~u) kcat

#R(tyr~p) -> R(tyr~u) Sat(vmax,KM)

end reaction rules

begin observables

Molecules BoundLig L(rec!+)

Molecules Monomers R(dim)

Molecules DimerMolec R(dim!+)

Molecules Phosph R(tyr~p)

end observables

begin actions

generate_network({overwrite=>1});

simulate_ssa({suffix=>ssa,t_start=>0,t_end=>200,n_steps=>200});

saveConcentrations();

setConcentration("L(rec)","L0_new");

simulate_ssa({suffix=>ssa,continue=>1,t_start=>200,t_end=>500,n_steps=>300});

end actions

#references

#1: Seewoster and Lehmann. Biotechnology and Bioengineering (1997) vol. 55 (5) pp. 793-797

#2: Macdonald and Pike. Proc Natl Acad Sci USA (2008) vol. 105 (1) pp. 112-7

#3: Gabdoulline and Wade.Current Opinion in Struct Biol (2002) vol. 12 (2) pp. 204-13

#4: Kholodenko. European Journal of Biochemistry (2000) vol. (267) pp. 1583-1588

#5: Mayawala et al. Biophys Chem (2006) vol. 121 (3) pp. 194-208

#6: Lauffenburger and Linderman, Oxford University Press, New York, 1993.

#7: Kusumi et al. Biophysical Journal (1993) vol. 65 (5) pp. 2021-40

)"

Ext

PlmCyt

Num

Nuc

End

Enm

*"

Volume

Surface

Volume

Surface

Volume

C

c

A

a

A

a

B

b

B

b

C

c

B

b

B

b

C

c

A

a

B

b

C

c

A

a

B

b

C

c

A

a

A

a

C

c

B

b

C

c

B

b

B

b

B

b

Topologically Consistent Topologically Inconsistent

Individual molecules in

compartments

Molecules linking adjacent compartments

Bonds traversing through a compartment

Molecules linking volumes through a

surface

Molecules linking surfaces

through a volume

B

b

+"

Volume

Surface

Volume

Surface

Volume

C

c

A

a

C

c

A

a

A

a

A

a

A

a

A

a

C

c

B

b

A

a1

A

a

C

c

B

b

C

c

A

a

B

b

a2

A

a2

a1

C

c

Adjacent compartment

molecular transport

Bridged volume

molecular transport

Bridged volume species transport

Bridged volumeconnected transport

Bridged surface species transport

,"

Transcription

Factor

Interactions

Transcription

Factor

Regulation

Gene

Regulation

Transcription

Epigenetic

Regulation

Nucleus

Signaling

Pathways &

Crosstalk

Metabolism

Translation

Folding &

Post-

Translational

Modification

Degradation

Sorting &

Trafficking

Cytosol

Receptor-

Ligand

Interactions

Ion

Transport

Small

Molecule

Transport

Receptor

Interactions

Lipid Rafts

Signaling

Complex

Assembly

Secondary

Messenger

Activation

Plasma Membrane

Cell Exterior

-"

Aa

Bb

Aa

Bb1 b2

A1a1 B

bA2a2

Cc

Aa 0 p

Aa1 0 p

a3

Bb

Aa1 0 p

a3

Bb

Aa1 0 p

a3

Bb

a2 0 p

A has component a, B has component bComponents a and b may form a bond

A1a1

Bb1

A2a2

b2

0

p

A1a1

Bb1

A2a2

b2

0

p

Component b in B may form a bond with either a1 in A1 or a2 in A2

The b2-c bond has an influence on the a-b1 bond

A has component a, with internal states 0 and p

The a3-b bond is necessary for the conversion:A(a1~0) -> A(a1~p)

The a3-b bond is necessary for the conversion:A(a1~p) -> A(a1~0)

The a3-b bond is necessary for the conversions:A(a2~p) -> A(a2~0)A(a3~p) -> A(a3~0)

b1 may form a bond with either a1 or a2b2~p has an influence on both a1-b1 and a2-b1 bonds

b1 may form a bond with either a1 or a2b2~p has an influence on the a2-b1 bond,

but not on the a1-b1 bond

MeaningContact Map

!."

R

dim

lig

Grb2sh2

sh3n

sh3c

Gab1

Shc1

Y317

n

Shp2

pptase

n

Y1016

Y998

ph

Y1092

Y1138

Y1172

Y1197

YXXP

YXXMnegST

Y627

Y1110

pro

0 p

0 p

0 p

0 p

0 p

0 p

0 p

0 p

L

rec

0 p

0 p

0 p

!!"

PI3K

reg

kin

Rasa1

gap

n

Sos1

gef

n

Grb2sh2

sh3n

sh3c

Gab1

Shc1

Y317

n

Shp2

pptase

nph

YXXP

YXXM

negST

Y627

pro

0 p

0 p

0 p

0 p

0 p

0 pnegS

allo

!#"

EGFR

Sos1

gef

n

negS

allo

HRas

pbs nbs

Rasa1

gap

n

gdp gtp

!'"

HRas

pbsnbs

Raf1

kinrbd

Mek1

S218

PP2A

pptase

kin

Erk2

T185 dim kin

Dusp1

pptase

Gab1

ph

YXXP

YXXM

negST

Y627

pro

Sos1

gef

n negS

allo

0 p

S222

T187p

0

gdp

gtp

p

0

p

0

0 p

p

0

!("

EGFR PI3K

reg

kin

PTEN

pptase

c2

PI(4,5)P2

P3

Gab1

Y627

YXXP

YXXM

negST

ph

pro

Akt

ph

kin

p

0

!)"

Erk2

dim

Y187

T185

kin

fos

0 p

0 p

Jnk1

dim

Y185

T183

kin

jnk

0 p

0 p

Erk2dim

kin

fos

Jnk1dim

kin

jnk

Y187

T185

Y185

T183

Fosy 0 p

Juny 0 p

AP1nfat

g

NFATap1

TargetGene

prm

TargetProtein

FosGene JunGene

*

Plm

Num

Nuc

Rule-Based Modeling of Signal Transduction: A Primer

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Transcript of Rule-Based Modeling of Signal Transduction: A Primer