#TAR12, check the fudge factor preT, time allowed between 2 mitoses
# Only when time from previous division is larger than 30 min to avoid successive 
# mass divisions
# Introduced Target protein activated by Cdc14 and required for exit of mitosis.
# Adding Cdc14 (besides Tem1) activates Cdc15

BB(Va,Vi,Ja,Ji)= Vi-Va+Ja*Vi+Ji*Va
GK(Va,Vi,Ja,Ji)= 2*Ji*Va/(BB(Va,Vi,Ja,Ji)+sqrt(BB(Va,Vi,Ja,Ji)^2-4*(Vi-Va)*Ji*Va))

BCK2  = BCK0*MASS
CLN3  = CLN3MAX*Dn3*MASS/(Jn3+Dn3*MASS)
SIC1T = SIC1+C2+C5+SIC1P+C2P+C5P
CDC6T = CDC6+F2+F5+CDC6P+F2P+F5P
RENTP = CDC14T-RENT-CDC14
NET1P  =NET1T-NET1-CDC14T+CDC14 
PE    = ESP1T-ESP1

Vasbf= kasbf*(esbfn2*CLN2+esbfn3*(CLN3+BCK2)+esbfb5*CLB5)

Vdb2 = kdb2'+kdb2"*CDH1+kdb2p*CDC20

Vdb5 = kdb5'+kdb5"*Cdc20

Vkpc1= kd1c1+kd2c1*(ec1n3*CLN3+ec1k2*BCK2+ec1n2*CLN2+ec1b2*CLB2+ec1b5*CLB5)/(Jd2c1+SIC1T)

Vppc1= kppc1*CDC14

Vkpf6= kd1f6+kd2f6*(ef6n3*CLN3+ef6k2*BCK2+ef6n2*CLN2+ef6b2*CLB2+ef6b5*CLB5)/(Jd2f6+CDC6T)

Vppf6= kppf6*CDC14

Vaiep= kaiep*CLB2

Vacdh= kacdh'+kacdh"*CDC14

Vicdh= kicdh'+kicdh"*(eicdhn3*CLN3+eicdhn2*CLN2+eicdhb5*CLB5+eicdhb2*CLB2)

Vppnet= kppnet'+kppnet"*PPX

Vkpnet=(kkpnet'+kkpnet"*CDC15)*MASS

Vdpds= kd1pds'+kd2pds"*Cdc20+kd3pds"*CDH1

Vdppx= kdppx'+kdppx"*(eps20ppx+Cdc20)*Kmpds/(Kmpds+PDS1)

SBF  = GK(Vasbf, kisbf'+kisbf"*CLB2, Jasbf, Jisbf)

MCM1 = GK(kamcm*CLB2, kimcm, Jamcm, Jimcm)


dMASS/dt = mu*MASS

dCLN2/dt  = (ksn2'+ksn2"*SBF)*MASS-kdn2*CLN2


dCLB2/dt  =(ksb2'+ksb2"*MCM1)*MASS+(kd3c1*C2P+kd3f6*F2P)+(kdib2*C2+kdif2*F2) \
           -(Vdb2+kasb2*Sic1+kasf2*CDC6)*CLB2


dCLB5/dt  = (ksb5'+ksb5"*SBF)*MASS+(kd3c1*C5P+kd3f6*F5P)+(kdib5*C5+kdif5*F5) \
           -(Vdb5+kasb5*Sic1+kasf5*CDC6)*CLB5


dSIC1/dt =(ksc1'+ksc1"*SWI5)+(Vdb2*C2+Vdb5*C5)+(kdib2*C2+kdib5*C5)+Vppc1*SIC1P \
          -(kasb2*CLB2+kasb5*CLB5+Vkpc1)*SIC1


dCDC6/dt =(ksf6'+ksf6"*SWI5+ksf6"'*SBF)+(Vdb2*F2+Vdb5*F5)+(kdif2*F2+kdif5*F5)+Vppf6*CDC6P \
          -(kasf2*CLB2+kasf5*CLB5+Vkpf6)*CDC6


dC2/dt   = kasb2*CLB2*SIC1+Vppc1*C2P-(kdib2+Vdb2+Vkpc1)*C2

dC5/dt   = kasb5*CLB5*SIC1+Vppc1*C5P-(kdib5+Vdb5+Vkpc1)*C5

dF2/dt   = kasf2*CLB2*CDC6+Vppf6*F2P-(kdif2+Vdb2+Vkpf6)*F2

dF5/dt   = kasf5*CLB5*CDC6+Vppf6*F5P-(kdif5+Vdb5+Vkpf6)*F5

dSIC1P/dt=Vkpc1*SIC1-(Vppc1+kd3c1)*SIC1P+Vdb2*C2P+Vdb5*C5P

dC2P/dt  =Vkpc1*C2-(Vppc1+kd3c1+Vdb2)*C2P

dC5P/dt  =Vkpc1*C5-(Vppc1+kd3c1+Vdb5)*C5P


dCDC6P/dt=Vkpf6*CDC6-(Vppf6+kd3f6)*CDC6P+Vdb2*F2P+Vdb5*F5P

dF2P/dt  =Vkpf6*F2-(Vppf6+kd3f6+Vdb2)*F2P

dF5P/dt  =Vkpf6*F5-(Vppf6+kd3f6+Vdb5)*F5P


dSWI5T/dt = ksswi'+ksswi"*MCM1-kdswi*SWI5T

dSWI5/dt  = ksswi'+ksswi"*MCM1+kaswi*CDC14*(SWI5T-SWI5)-(kiswi*CLB2+kdswi)*SWI5

dIEP/dt   = Vaiep*(1-IEP)/(Jaiep+1-IEP)-kiiep*IEP/(Jiiep+IEP)

dCDC20T/dt= (ks20'+ks20"*MCM1)-kd20*CDC20T 

dCDC20/dt = (ka20'+ka20"*IEP)*(CDC20T-CDC20)-(Vi20+kd20)*CDC20


dCDH1T/dt = kscdh - kdcdh*CDH1T

dCDH1/dt  =kscdh-kdcdh*CDH1+Vacdh*(CDH1T-CDH1)/(Jacdh+CDH1T-CDH1) \
           -Vicdh*CDH1/(Jicdh+CDH1)

dCDC14T/dt =ks14 -  kd14*CDC14T

dCDC14/dt =(kdirent*RENT+kdirentp*RENTP) \
          -(kasrent*NET1+kasrentp*NET1P)*CDC14 \
          +ks14-kd14*CDC14+kdnet*(RENT+RENTP)

dNET1T/dt = ksnet - kdnet*NET1T

dNET1/dt  = kdirent*RENT-kasrent*NET1*CDC14+Vppnet*NET1P-Vkpnet*NET1 \
            +ksnet-kdnet*NET1+kd14*RENT

dRENT/dt  =-kdirent*RENT+kasrent*NET1*CDC14+Vppnet*RENTP-Vkpnet*RENT \
            -(kd14+kdnet)*RENT

dTEM1/dt  = lte1*(TEM1T-TEM1)/(Jatem+TEM1T-TEM1)-BUB2*TEM1/(Jitem+TEM1)

dCdc15/dt= (ka15'*(Tem1T-Tem1)+ka15"*Tem1+ka15p*Cdc14)*(Cdc15T-Cdc15)-ki15*Cdc15

dPPX/dt   = ksppx-Vdppx*PPX

dPDS1/dt  = (kspds'+ks1pds"*SBF+ks2pds"*MCM1)+kdiesp*PE-(Vdpds+kasesp*ESP1)*PDS1

dESP1/dt  = -kasesp*PDS1*ESP1+(kdiesp+Vdpds)*PE

dORI/dt   = ksori*(eorib5*CLB5+eorib2*CLB2)-kdori*ORI  

dBUD/dt   = ksbud*(ebudn2*CLN2+ebudn3*CLN3+ebudb5*CLB5)-kdbud*BUD

dSPN/dt   = ksspn*CLB2/(Jspn+CLB2)-kdspn*SPN

dTarget/dt=(katar'+katar"*Cdc14)*(1-Target)/(Jatar+1-Target) \
           -(kitar'+kitar"*Clb2)*Target/(Jitar+Target)

dVi20/dt = 0

dlte1/dt = 0

dBub2/dt = 0

dPRET/dt = 1

# if PRET>mintval, which is 30 min, the time from the previous division is more than 30 min,
# mitosis is allowed, Mallow=1, else Mallow=0


Mallow=heav(PRET-mintval)

global +1 {ORI-1} {Vi20=ki20"; Bub2=Bub2h}

global +1 {SPN-1} {Vi20=ki20'; lte1=lte1h; Bub2=Bub2l}

global +1 {TARGET-KEZtar} {MASS=Mallow*abs(MorD+f-1)*MASS+(1-Mallow)*MASS; \
lte1=Mallow*lte1l+(1-Mallow)*lte1;BUD=(1-Mallow)*BUD;SPN=(1-Mallow)*SPN; \
PRET=(1-Mallow)*PRET}

global -1 {CLB2+CLB5-KEZ2} {ORI=0}

aux CLB2T=CLB2+C2+F2+C2P+F2P
aux CLB5T=CLB5+C5+F5+C5P+F5P
aux CKIT=SIC1T+CDC6T
aux SIC1T=SIC1T
aux CDC6T=CDC6T
aux SBF=SBF
aux Mallow=Mallow

param  BCK0=0.054,   CLN3MAX=0.4,  Dn3=1,        Jn3=6

param  ksn2'=0,      ksn2"=0.15,    kdn2=0.12

param  esbfn2=2,     esbfn3=10,    esbfb5=2

param  kasbf=0.38,   kisbf'=0.6,   kisbf"=8

param  Jasbf=0.01,   Jisbf=0.01

param  ksb2'=0.001,  ksb2"=0.04,   kdb2'=0.003   

param  kdb2"=0.4,    kdb2p=0.15    

param  kamcm=1,      kimcm=0.15,   Jamcm=0.1,    Jimcm=0.1

param  ksb5'=0.0008,  ksb5"=0.005

param  kdb5'=0.01,   kdb5"=0.16

param  ksc1'=0.012,  ksc1"=0.12  

param  kd1c1=0.01,   kd2c1=1,      Jd2c1=0.05

param  ec1k2=0.03,   ec1n2=0.06,   ec1b5=0.1,   ec1b2=0.45,    ec1n3=0.3

param  kasb2=50,     kdib2=0.05,   kasb5=50,     kdib5=0.06

param  kd3c1=1,      kppc1=4              

param  ksf6'=0.024,  ksf6"=0.12,   ksf6"'=0.004

param  kd1f6=0.01,   kd2f6=1,      Jd2f6=0.05

param  ef6k2=0.03,   ef6n2=0.06,   ef6b5=0.1,    ef6b2=0.55,   ef6n3=0.3

param  kasf2=15,     kdif2=0.5,    kasf5=0.01,   kdif5=0.01

param  kd3f6=1,      kppf6=4

param  ksswi'=0.005, ksswi"=0.08,   kdswi=0.08,    kaswi=2,    kiswi=0.05

param  kaiep=0.1,    kiiep=0.15,   Jaiep=0.1,    Jiiep=0.1

param  ks20'=0.006,  ks20"=0.6,    kd20=0.3    

param  ka20'=0.05,   ka20"=0.2,    ki20'=0.01,   ki20"=8 

param  kscdh=0.01,   kdcdh=0.01

param  kacdh'=0.01,  kacdh"=0.8,   Jicdh=0.03,   Jacdh=0.03

param  kicdh'=0.001, kicdh"=0.08

param  eicdhn2=0.4,  eicdhn3=0.25, eicdhb5=8,   eicdhb2=1.2 

param  ks14=0.2,    kd14=0.1

param  ksnet=0.084,  kdnet=0.03

param  kasrent=160,  kasrentp=1,   kdirent=1,    kdirentp=2

param  kppnet'=0.05, kppnet"=3,    kkpnet'=0.01, kkpnet"=0.6

param  kspds'=0,     ks1pds"=0.03, ks2pds"=0.055  

param  kd1pds'=0.01, kd2pds"=0.2, kd3pds"=0.04

param  kasesp=50,    kdiesp=0.5,   ESP1T=1

param  ksppx=0.1,    kmpds=0.04

param  kdppx'=0.17,  kdppx"=2,     eps20ppx=0.15
     
param  ksori=2,      kdori=0.06,   eorib5=0.9,   eorib2=0.45

param  ksbud=0.2,    kdbud=0.06,   ebudn2=0.25,  ebudn3=0.05,  ebudb5=1

param  ksspn=0.1,   kdspn=0.06,   Jspn=0.14

param  lte1l=0.1,    lte1h=1,      Bub2l=0.2,    Bub2h=1   

param  TEM1T=1,      jatem=0.1,    Jitem=0.1

param  Cdc15T=1,     ka15'=0.002,  ka15"=1,      ka15p=0.001, ki15=0.5   

param  KEZ=0.3,      mdt=90,       MorD=1       

param  kez2=0.2

param  katar'=0.02,  katar"=1,    kitar'=0.01,  kitar"=0.53 

param  Jatar=0.05,    Jitar=0.05

param  keztar=0.4

param  mintval=0


# derived parameter f (for division of mass between mother/daughter)
# to satisfy Hartwell & Ungar's experiment. mu is growth rate, 
# D is daughtercycle time, f is the fraction of mass given to daughter

!mu=ln(2)/mdt
!D=1.026/mu-32
!f=exp(-mu*D)

@ Maxstore=100000, bound=2000, dt=1
@ Meth=Stiff, total=1000, xplot=t, xlo=0, xhi=1000, ylo=0, yhi=3
@ NPLOT=8, yp1=MASS, yp2=CLB2T, yp3=CKIT, yp4=CDH1, yp5=CDC20, yp6=Pds1, yp7=CLN2

Init MASS=1.212595105171204  
init CLN2=0.06160590425133705  
init CLB2=0.1463514417409897  
init CLB5=0.05336679145693779  
init SIC1=0.0224220622330904  
init CDC6=0.1065565720200539  
init C2=0.2355565875768662  
INIT C5=0.07044374197721481  
INIT F2=0.2333101183176041  
INIT F5=7.30368701624684e-005  

INIT SIC1P=0.006754010915756226  
INIT C2P=0.02513346634805203  
INIT C5P=0.007269222289323807  
INIT CDC6P=0.01626908965408802  
INIT F2P=0.0287732295691967  
INIT F5P=8.398712452617474e-006 
INIT SWI5T=0.9746344089508057  
INIT SWI5=0.9530601501464844  
INIT IEP=0.1031579822301865  
INIT CDC20T=1.915212273597717  
  
INIT CDC20=0.4455196857452393  
INIT CDH1T=1    
INIT CDH1=0.9031444191932678  
INIT CDC14T=2     
INIT CDC14=0.4156905114650726  
INIT NET1T=2.799999952316284  
INIT NET1=0.02745954133570194  
INIT RENT=1.145977735519409  
INIT TEM1=0.8588392734527588  
INIT CDC15=0.649145245552063  
  
INIT PPX=0.1245575398206711  
INIT PDS1=0.02615203335881233  
INIT ESP1=0.2967464327812195  
INIT ORI=0.0002092957147397101  
INIT BUD=0.01568104699254036  
INIT SPN=0.05497833341360092  
INIT Target=0.6562694907188416  
INIT VI20=0.009999999776482582  
INIT LTE1=0.1000000014901161  
INIT BUB2=0.2000000029802322  
INIT PRET=0.8718729615211487  

done