# 
# Shift from stochastic to spatially-ordered patterns of expression for metabolic enzymes in 3D microtumors
# Manjulata Singha, Tomoko Warita, Katsuhiko Warita, James R. Faeder, Robin E.C. Lee, Shilpa Santa and Zoltán N. Oltvai
# 
# 3D microtumor model
# M1 and M2 can be switched via the rule "NUc->INHIBc" 
begin parameters
    NA 6.02e23 # Avogadros number
    Rcore = 300 # Radius to outer edge of Core
    Rinner =450 # Radius to outer edge of Inner Layer
    Rspheroid =600 #Model Spheroids are 600 microns
    Vcore = 4/3*3.14*(Rcore)^3 # V = 113094000 for 600u spheroid
    Vinner = 4/3*3.14*(Rinner)^3-4/3*3.14*(Rcore)^3 # V = 268598250 for 600u spheroid
    Vouter = 4/3*3.14*(Rspheroid)^3-4/3*3.14*(Rinner)^3 #V = 523059750
    NUe 10^6 #Diffusible nutrient (amino acid) from liquid environment
    diff 1 #Diffusion rate between outer-inner compartments; all rates are normalized to diffusion
    f_diff 1/2.25 # Change in diffusion rate between outer-inner and inner-core is the ratio of the surface areas = (Rcore)^2/(Rinner)^2 = 1/2.25
   end parameters
   
begin seed species
NUo 0
NUi 0
NUc 0
PHGDHo 0 #Cellular enzyme for amino acid biosynthesis (default 15)
PHGDHi 0
PHGDHc 0
Ki67o 0 #Cellular marker for proliferation (default 5000)
Ki67i 0 #(default 2500)
Ki67c 0 #(default 1000)
INHIBc 0 #Inhibitor of PHGDH expression in M2
INHIBi 0
INHIBo 0
INHIBe 0
end seed species

begin observables
Molecules NU_o NUo
Molecules NU_i NUi 
Molecules NU_c NUc
Molecules Ki67_o Ki67o
Molecules Ki67_i Ki67i 
Molecules Ki67_c Ki67c
Molecules PHGDH_o PHGDHo
Molecules PHGDH_i PHGDHi
Molecules PHGDH_c PHGDHc
Molecules INHIB_c INHIBc
Molecules INHIB_i INHIBi
Molecules INHIB_o INHIBo

end observables

begin functions
  NUp_i()= if(NU_o()>0,NU_i()/NU_o(),0)
  NUp_c()= if(NU_o()>0,NU_c()/NU_o(),0)
  Ki67p_i()= if(Ki67_o()>0,Ki67_i()/Ki67_o(),1)
  Ki67p_c()= if(Ki67_o()>0,Ki67_c()/Ki67_o(),1)
  PHGDHp_i()= if(PHGDH_o()>0,PHGDH_i()/PHGDH_o(),1)
  PHGDHp_c()= if(PHGDH_o()>0,PHGDH_c()/PHGDH_o(),1)
end functions

begin reaction rules
#compartments extracellular (e), outer layer (o), inner layer (i), and core (c)

# Nutrient transport between (o) and (e)
# NUe is extracellular pool; NUo is the nutrient pool within outer surface layer; model assumes extracellular nutrients are in excess and not depleted so that a steady state can be achieved
0->NUo 0.00001*NUe  
NUo-> 0 0.0001 

#PHGDH production consumes nutrients, rate of production is reduced in the presence of Inhibitor 
NUo->PHGDHo 0.001/(1+5*INHIB_o) 
NUi->PHGDHi 0.001/(1+5*INHIB_i)
NUc->PHGDHc 0.001/(1+5*INHIB_c)

#Production of factors that contribute to Ki-67 positive status consume nutrients
NUo->Ki67o 0.1 
NUi->Ki67i 0.1
NUc->Ki67c 0.1

#Select rule for Model 1 (M1) or Model 2 (M2)
#NUc->INHIBc 0 #M1: No Inhibitor; comment out this rule for model 2
NUc->INHIBc 0.05 #M2: Inhibitor is expressed; comment out this rule for model 1

# Transport of inhibitor 
INHIBc<->INHIBi 0.001,0.001
INHIBi<->INHIBo 0.001,0.001 
INHIBo<->INHIBe 0.001,0.001 

#Transport of nutrients within the microtumor
NUo<->NUi diff,diff #default value of 0.5,0.5
NUi<->NUc f_diff*diff,f_diff*diff #Modified diffusion relates to flux through compartment surfaces

#de novo serine biosynthesis
PHGDHo->NUo+PHGDHo 1  
PHGDHi->NUi+PHGDHi 1
PHGDHc->NUc+PHGDHc 1

#decay of species
Ki67o->0 0.01  
Ki67i->0 0.01
Ki67c->0 0.01
PHGDHo->0 0.05
PHGDHi->0 0.05
PHGDHc->0 0.05
INHIBc->0 0.005
INHIBi->0 0.005
INHIBo->0 0.005
end reaction rules

generate_network({overwrite=>1});
simulate_ode({t_end=>6e5, n_steps=>10,print_functions=>1});
#EOF