init HH=0.02473521
init HSF1S=0.04999897
init HSF12S=0.01666647
init HSF13S=5.211987E-7
init HHp=0.02892615
init HHpp=0.0002070167
init HHppp=0.0002182003
init HHpppp=0.0003742879
init HHMK3=0.4999243
init HHpMK3=0.03578938
init HHppMK3=1.219185e-6
init HHpppMK3=1.921212E-6
init HHppppPP5=0.003804995
init HHpppPP5=0.008330155
init HHpppPP5S=0.00905032
init HHppPP5=0.007913356
init HHppPP5S=0.005366535
init HHpPP5=0.1673194
init HHpPP5S=0.9998112
init HHPP5=0.1056238
init mRNA90=3.742879E-5
init HSP90op=6.074816E-6
init HSP90ATPBN=2.765055E-5
init HSP90I1=5.751563E-6
init HSP90I2=4.148362E-6
init HSP90CL=1.871447E-5
init HHSP90CL=0.0009017037	

 
############## PARAMETERS###################
par kstress=0.001



############ These parameters gives rise to Mushroom ### ## ################# transition ############################


# par HSF1TOT=288.742
# par HSETOT=1323.216
# par PP5TOT=92.000
# par MK3TOT=39.07797
# par kh2=0.00013,kh22=0.00006
# par kh3=0.00807,kh33=0.00645
# par kh4=0.00040,kh44=0.00001
# par kd=0.0650
# par k1=1.6,k11=1.05061,par k2=0.0800
# par k3=5.28762,k33=1.06534,k4=0.12916
# par h1=0.36241,h11=0.25773,h2=0.94724
# par h3=0.06404,h33=0.00099
# par h4=0.02342,h44=0.01300,h5=0.06271
# par h6=0.53447,h66=0.00128
# par k5=0.02391,k55=0.00084,k6=2.88988
# par h7=0.00829,h77=0.00640,h8=0.01778,h9=0.05795,h99=0.01300
# par k7=0.01644,k77=0.00088,k8=2.39472	
# par h10=0.06349,h101=0.01089,h111=0.06264
# par h12=0.06391,h121=0.00844
# par kl1=8.73649,kl11=1.2000
# par kl2=0.00109,kl21=0.05428

# par kd1=0.0065,kd2=0.35868

#######################################################################################
########## These parameters gives rise to S-Shaped bistability ############and ##  ultrasensitivity ############################

# par HSF1TOT=322.4585
# par HSETOT=1950.00
# par PP5TOT=92.00
# par MK3TOT=46.4411
# par kh2=0.0001,kh22=0.0001
# par kh3=0.0080,kh33=0.0065
# par kh4=0.0004,kh44=0.00001
# par kd=0.0644
# par k1=2.5931,k11=1.300,par k2=0.0838
# par k3=4.48,k33=1.17,k4=0.1089
# par h1=0.5200,h11=0.2966,h2=0.7714
# par h3=0.0634,h33=0.0008
# par h4=0.0248,h44=0.01300,h5=0.0540
# par h6=0.6500,h66=0.0014
# par k5=0.0232,k55=0.0011,k6=3.7659
# par h7=0.0130,h77=0.0040,h8=0.0246,h9=0.0578,h99=0.0109
# par k7=0.0260,k77=0.0013,k8=2.5625	
# par h10=0.0425,h101=0.013,h111=0.0650
# par h12=0.0499,h121=0.0080
# par kl1=10.4000,kl11=1.9500
# par kl2=0.0013,kl21=0.0401
# par kd1=0.00650,kd2=0.3710

######## These are the parameters that gives rise to irreversible ####################

 
######## These are the parameters that gives rise to irreversible ####################

 
 par HSF1TOT=296
 par HSETOT=1421.6
 par PP5TOT=94.8
 par MK3TOT=65
 par kh2=0.0001,kh22=0.00004
 par kh3=0.01,kh33=0.005
 par kh4=0.00065,kh44=0.00001
 par kd=0.065
 par k1=2.3,k11=0.8
 par k2=0.08
 par k3=6.3,k33=0.819,k4=0.0804
 par h1=0.3251,h11=0.24,h2=0.9339
 par h3=0.065,h33=0.00013
 par h4=0.0259,h44=0.010,h5=0.042
 par h6=0.4025,h66=0.0014
 par k5=0.0163,k55=0.0013,k6=2.4019
 par h7=0.0101,h77=0.0040,h8=0.0257
 par h9=0.063,h99=0.013
 par k7=0.0232,k77=0.001,k8=1.73
 par h10=0.06349,h101=0.0089,h111=0.066
 par h12=0.06,h121=0.0126
 par kl1=8.51,kl11=1.9
 par kl2=0.0083,kl21=0.0541
 par kd1=0.002,kd2=0.355


################################################################################################


MK3=MK3TOT-(HHMK3+HHpMK3+HHppMK3+HHpppMK3)
PP5=PP5TOT-(HHppppPP5+HHpppPP5+HHpppPP5S+HHppPP5+HHppPP5S+HHpPP5+HHpPP5S+HHPP5)
HSF1=HSF1TOT-(HSF1S+HSF12S+HSF13S+HHSP90cl+HHp+HHpp+HHppp+HHpppp+HHMK3+HHpMK3+HHppMK3+HHpppMK3+HHppppPP5+HHpppPP5+HHpppPP5S+HHppPP5+HHppPP5S+HHpPP5+HHpPP5S+HHPP5)   

######ADDING NEGATIVE FEEDBACK OF HSP90cl by binding to HSF1##############################
ul1= kl1*HSF1*HSP90cl-kl11*HHSP90cl
ul2=kl2*HHSP90cl-kl21*HSF1S*HSP90cl



HSE=HSETOT-(HH+HHp+HHpp+HHppp+HHpppp+HHMK3+HHpMK3+HHppMK3+HHpppMK3+HHppppPP5+HHpppPP5+HHpppPP5S+HHppPP5+HHppPP5S+HHpPP5+HHpPP5S+HHPP5)   


hs2=2*kh2*(HSF1S^2)-kh22*HSF12S
hs3=kh3*HSF12S*HSF1S-kh33*HSF13S
ux=kh4*HSF13S*HSE-kh44*HH


u1=k1*HH*MK3-k11*HHMK3
u2=k2*HHMK3
u3=k3*HHp*MK3-k33*HHpMK3
u4=k4*HHpMK3
w1=h1*HHpp*PP5-h11*HHppPP5S
w2=h2*HHppPP5S
w3=h3*HHpPP5-h33*HHp*PP5
w4=h4*HHp*PP5-h44*HHpPP5S
w5=h5*HHpPP5S	
w6=h6*HHPP5-h66*PP5*HH


#########ADDDING PHOSPHORYLATION-DEPHOSPHORYLATION REACTION #############

u5 = k5*HHpp*MK3-k55*HHppMK3 
u6 = k6*HHppMK3

w7 = h7*HHppp*PP5-h77*HHpppPP5S 
w8 = h8*HHpppPP5S
w9 = h9*HHppPP5-h99*HHpp*PP5

###################ADDING PHOSPHORYLATION DEPHOSPHORYLATION #################### REACTION##########
u7=k7*HHppp*MK3-k77*HHpppMK3
u8=k8*HHpppMK3

w10=h10*HHpppp*PP5-h101*HHppppPP5
w11=h111*HHppppPP5
w12=h12*HHpppPP5-h121*HHppp*PP5


HH'=ux-u1+kd*HHpppp
HSF1S'=kstress+ul2-hs2-hs3
HSF12S'=hs2-hs3
HSF13S'=hs3-ux 

HHp'=u2-u3+w3-w4 
HHpp'=u4-u5-w1+w9
HHppp'=u6-w7-u7+w12
HHpppp'=u8-w10-kd*HHpppp

HHMK3'=u1-u2 
HHpMK3'=u3-u4
HHppMK3'=u5-u6
HHpppMK3'=u7-u8

HHppppPP5'=w10-w11
HHpppPP5'=w11-w12
HHpppPP5S'=w7-w8
HHppPP5'=w8-w9
HHppPP5S'=w1-w2
HHpPP5'=w2-w3 
HHpPP5S'=w4-w5 
HHPP5'=w5-w6


#############HSP90 REGULATION###################

#par khs1=40,khs2=0.4,khs3=1.0,khs4=0.6,khs5=0.03
#par khs11=8.7,khs22=1.5,khs33=0.8,khs44=0.003

#par khs1=2400,khs2=24,khs3=60.0,khs4=36,khs5=1.8
#par khs11=522,khs22=90,khs33=48,khs44=0.18


par khs1=0.67,khs2=0.0067,khs3=0.0167,khs4=0.01,khs5=0.0005
par khs11=0.145,khs22=0.025,khs33=0.013,khs44=0.00005


#par kd1=0.005,kd2=0.05

#par kd1=0.005,kd2=0.3

mRNA90'=kd*HHpppp-kd1*mRNA90

HSP90op'=kd1*mRNA90 + khs5*HSP90CL + khs11*HSP90ATPBN - khs1*HSP90op
 
HSP90ATPBN'=khs1*HSP90op + khs22*HSP90I1 - (khs2+khs11)*HSP90ATPBN
 
HSP90I1'=khs2*HSP90ATPBN + khs33*HSP90I2 - (khs3+khs22)*HSP90I1
 
HSP90I2'=khs3*HSP90I1 + khs44*HSP90CL -(khs4+khs33)*HSP90I2
 
HSP90CL'=khs4*HSP90I2-(khs44+khs5)*HSP90CL-kd2*HSP90CL + ul2-ul1

HHSP90CL'=ul1-ul2

aux totpp=HHp+HHpp+HHppp+HHpppp

@ meth=cvode,total=180000,dt=.5,tol=1e-8,atol=1e-7
@ xlo=0,xhi=2000,ylo=0,yhi=12,yp=lz,maxstor=10000000
@ bound=1e7

@ autoxmin=0,autoxmax=1.2,autoymin=0,autoymax=150

@ autovar=HHSP90CL


d