#numerical parameters
@ MAXSTOR=500000
@ BOUNDS=1e+20
@ DT=0.001
@ TOTAL=1000
@ NJMP=100

# (nmol/ml*min) = uM/min
# minute=60 seconds
 minute=60
# uMmM converts uM to mM
 uMmM=1000

####################################################
# compartmentalization parameters and calculations #
####################################################

# total volume (in ml)
param V=1.0

# proportion of V occupied my cytosol
param pcytosol=0.5

# density of cystosolic protein mg/ml
param dcytosol=75

# proportion of V occupied my mitochondria
param pmito=0.05

# density of mitochondrial protein mg/ml
param dmito=1000

# proportion of V occupied my ER
param per=0.10

# density of ER protein mg/ml
param der=1000

# cmito in nmol/(mV*mg)
param cmito=0.0725

# calculation of protein amounts

M=V*Pmito*Dmito

C=V*pcytosol*Dcytosol

E=V*Per*Der

# calculation of compartment volumes

Vc=(V*pcytosol)

Vm=(V*pmito)

Ve=(V*per)

#################################################
# Nucleotide conversion/conservation relations  #
# from Magnus and Keizer 1997, 1998a)           #
#################################################

# conservation conditions (nmol/mg converted to mM)

ATPm=(12*dmito/uMmM)-ADPm

NAD=(8*dmito/uMmM)-NADHM

# ATPi already in mM
ATPi=2-ADPi

# proportion of free nucleotides
# (Magnus and Keizer 1998a) table 2

ADPmf=0.8*ADPm

ADPif=0.3*ADPi

# charged, free nucleotides

ADP3Mm=0.45*ADPmf

ADP3Mi= 0.45*ADPif

MgADPMi = 0.55*ADPif

ATP4Mi=0.05*ATPi
 
ATP4Mm=0.05*ATPm

###############################
#   Mitochondrial Components  #
###############################

#### mitochondria - CA2+ handling

# mitochondrial uniporter (nmol/(mg*min))
# modified from equation (19) (Magnus and Keizer 1997)

  param rhouni=300
  # MWC refers to Monod-Wyman-Changeux (MWC) model for concerted allosteric transitions
  MWCnum=(CAC/6)*((1+(CAC/6))^3)
  MWCdenom=((1+(CAC/6))^4)+(50/((1+(CAC/0.38))^2.8))
  MWC=MWCnum/MWCdenom
  VDuni=(PSI-91)/13.35 
  # RT/2F = 13.35 for T = 310 K, dPSI* = 91 mV 

  Juni=(rhouni*VDuni*(MWC-CAM*exp(-VDuni))/(1-exp(-VDuni)))*(1-PTPh)
  # Includes contribution due to PTP opening in high conductance state 

# Na/Ca exchanger (nmol/(mg*min))
# equation (21) (Magnus and Keizer 1997)

  param rhonc=3

  VDnaca=exp((PSI-91)/53.4)

  Jnc=(rhonc*VDnaca*(1/(1+(9.4/30)**2))*(1/(1+(0.003*Dmito/CAM))))*(1-PTPh)  


#### Mitochondria - respiration

  param rhores=0.4 

# Ares=affinity bracketed expression
# based on equation (4) (Magnus and Keizer 1997)
  
  Ares = (1.35e18)*nadhm^0.5/(nad)^0.5

# VDres=exp(6*0.85*F*PSI/RT)
  VDres=exp(0.191*PSI)

# proton pump (nmol/(mg*min))
# equation (6) (Magnus and Keizer 1997)

  r1=7e-7
  r2=(2.54e-3)*Ares
  r3=0.639*VDres
  r4=7.58e13+(1.57e-4)*Ares
  r5=(1.73 + Ares*1.06e-17)*VDres

  Jhres= 360*rhores*((r1+r2-r3)/(r4+r5))

# Oxygen Consumption rate (nmol/(mg*min))
# equation (5) (Magnus and Keizer 1997)

  o1=Ares*2.55e-3
  o2=Ares*2.00e-5
  o3=0.639*(VDres)
  o4=(VDres)*Ares*8.63e-18
  o5=(1+Ares*2.08e-18)*7.54e13
  o6=(1.73+1.06e-17*Ares)*VDres

  Jo=30*rhores*(o1+o2-o3+o4)/(o5+o6)


#### Mitochondria - Fo/F1 ATPase equations:

  param rhof1=0.7

# AF1=affinity bracketed expression
# based on equation (12) (Magnus and Keizer 1997)

  param pim=20
  Af1 = (1.71e9)*(ATPm)/(ADPmf*pim)

# VDf1=exp(3*F*PSI/RT)
  VDf1=exp(0.112*PSI)

## Fo/F1 ATPase phosphorylation of ADPm (nmol/(mg*min))
# equation (13) (Magnus and keizer 1997)

  f1= 10.5*Af1
  f2= 166*VDf1
  f3= (4.85e-12)*Af1*VDf1
  f4= (1e7+0.135*Af1)*275
  f5= (7.74 + (6.65e-8)*Af1)*VDf1

  Jpf1=-60*rhof1*((f1-f2+f3)/(f4+f5))

# proton flux due to ATPase (nmol/(mg*min))
# equation (14) (Magnus and Keizer, 1997)

  Jhf1=-180*rhof1*(0.213+f1-169*VDf1)/(f4+f5)


#  mitochondrial membrane proton leak (nmol/(min*mV*mg))
#  equation (7) (Magnus and Keizer, 1997)

  param rholeak=0.2

  Jhl=rholeak*(PSI+24.6)

#fraction of activated pyruvate (dimless)
# equation (18) (Magnus and Keizer, 1998a)

  fpdh = 1/(1+(1.1*(1+(15/(1+(cam/0.05))^2))))

# NADH reduction rate (nmol/(mg*min))
# equation (21) (Magnus and Keizer, 1998a)

  param Jredbasal=20

  Jred = Jredbasal + 6.3944*fpdh*Jglytotal

#ATP/ADP antiport flux (nmol/(mg*min))
# equation (16) (Magnus and Keizer 1997)

  param JmaxANT=900

  ant1=(ATP4Mi/ADP3Mi)*(ADP3Mm/ATP4Mm)*exp(-PSI/26.7)
  ant2=1+(ATP4Mi/ADP3Mi)*exp(-PSI/53.4)
  ant3=1+(ADP3Mm/ATP4Mm) 

  Jant=JmaxANT*((1-ant1)/(ant2*ant3))

## phosphorylation of ADPm from TCA cycle (nmol/(mg*min))

  Jptca = (Jredbasal/3)+0.84*fpdh*Jglytotal

#########################
# Cytosolic Components  #
#########################

# glucose concentration in mM
  param glc=1

### glycolytic rate based on hexokinase (nmol/(mg*min)
# equation (10) (Magnus and Keizer 1998a)

  glynum=(123.3*(1+1.66*glc)*(glc*ATPi))*0.0249
  glydenom=1+(4*ATPi)+((1+2.83*ATPi)*1.3*glc)+((1+2.66*ATPi)*0.16*glc^2)

  Jglytotal=glynum/glydenom

# phosphorylation of ADPi from glycolysis (nmol/(mg*min))
# (Magnus and Keizer, 1998a)

  Jpgly=2*Jglytotal

# Cytosolic hydrolysis of ATP
# equations (35) and (37) (Magnus and Keizer, 1998a)
  param Jhydmax=30.1

  Jhyd =41*(ATPi)+Jhydmax/(1+(8.7/glc)^2.7)

##############################
# ER Ca2+ handling modified  #
# from Li and Rinzel         #
##############################

# IP3 receptor and leak

  param vIP3=3000
  param vLEAK=0.1

  param dip3=0.25
  param dinh=1.4
  param dact=1
  param tau=4

  jerout=(vIP3*((ip3/(ip3+dip3))^3)*((CAC/(CAC+dact))^3)*(h^3)+vLEAK)*(CAER-CAC)

# serca pump
  
  param vserca=110
  param kserca=0.4

  Jserca=vserca*CAC^2/(kserca^2+CAC^2)

##############################
### differential equations   #
##############################
# uMmM converts uM to mM
# minute=60 seconds

#ODE eqn for mitochondrial NADH (mM)
  dNADHm/dt= (Jred-Jo)*M/(uMmM*Vm*minute)

#ODE eqn for mitochondrial ADPm (mM) 
  dADPm/dt= (Jant-Jptca-Jpf1)*M/(uMmM*Vm*minute)

#ODE for cytosolic ADPi (mM)
  dADPi/dt=(-Jant*M + (Jhyd-Jpgly)*C)/(uMmM*Vc*minute)

#ODE eqn for mitochondrial inner membrane voltage
  dPSI/dt= -(-Jhres + Jhf1 +Jant +Jhptp +Jhl +2*Juni +2*Jcaptp)*M/(cmito*minute)

#ODE eqn for mitochondrial Ca 
# fm = mitochondrial Ca buffering
  param fm=0.0003

  dCAM/dt= (fm*(Juni-Jnc+Jcaptp)*M/(Vm*minute))

#ODE for cytosolic CA2+
# fi = cytosolic Ca2+ buffering
  param fi=0.01

param aV1=0.0065, aV2=4, Valpha=0.05, aKalpha=120, an=2, am=4, akbeta=0.2, ak1=0.01, ak2=0.1


  dCAC/dt=(fi*(M*(Jnc-Juni-Jcaptp)-E*(Jserca-Jerout))/(Vc*minute)+akbeta*a^am)

  dh/dt=(dinh-(CaC+dinh)*h)/tau

#ODE for ER ca2+

 dCaer/dt= fi*(E*(Jserca-Jerout))/(Ve*minute)

#ODE for beta-amyloid

da/dt=aV1+Valpha*CAC^an/(aKalpha^an+CAC^an)-ak1*a

########################
### INITIAL CONDITIONS 
########################

# mV
PSI(0)=164

# uM
Cam(0)=0.05
CaC(0)=0.05
CaER(0)=11

# mM
ADPm(0)=4.46
ADPi(0)=0.028
NADHm(0)=0.16

# percentage closed channels
h(0)=0.95


#####################
# IP3 step function #
#####################

param baseline=0.3
param amplitude=0.3
param init=10
param duration=100

stepupf=heav(t-init)

stepdownf=heav(t-(init+duration))

IP3=baseline+amplitude*(stepupf-stepdownf)


#####################
# PTPH Integration  #
#####################

param CAMthresh = 4
param ythresh = 0.8

tauy = 1000*((1000/cosh(CAM/0.1)) + 0.1)
tauh = tauy/8

PTPhinf = heav(y - ythresh)

yinf = heav(CAM - CAMthresh)

dy/dt = (yinf - y)/tauy

dPTPh/dt = (PTPhinf - PTPh)/tauh


#####################
# PTPL Integration  #
#####################

param fHM = 0.00000128
param p1 = 0.022
param p2 = 0.0001
param p3 = 0.0231
param p4 = 0.0001
param amptau = 26000
param p6 = 0.001
param permlh = 3.0
param permca = 0.40
param postptp = 2

Jhptp = permlh*PTPl*PSI*(HM-0.0000000398*exp(-37.434*PSI)/(1-exp(-37.434*PSI)))

Jcaptp = permca*PTPl*Juni*(1-postptp*PTPh)

dHM/dt = (fHM/tauh)*(Jhl+Jhf1-Jhres+Jhptp)

taul = p6+amptau/cosh((HM-p3)/p4)

PTPlinf = 0.5*(1+tanh((p1-HM)/p2))

dPTPl/dt = (PTPlinf - PTPl)/taul

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



END