SupplementaryfileS7.bngl.txt

begin model

# A simplified signal transduction model including the following processes:
# 1) ligand-receptor binding
# 2) receptor autophosphorylation and constitutive dephosphorylation
# 3) internalization of phosphorylated receptors and recycling of endosomes
# 4) phosphorylation of a diffusible transcription factor (TF)
# 5) phosphorylation dependent cytoplasmic <-> nuclear transport of TF
# 6) TF-dependent transcription of gene p
# 7) Transport and degradation of p mRNA
# 8) Translation of protein P
# 9) P-mediated dephosphorylation of R
# 
# The action of P on the phosphorylated receptor constitutes a negative feedback 
# loop and the system can be made to oscillate by setting a sharp threshold 
# for the level of transcriptional activity as a function of the nuclear concentration
# of TF. This is achieved in the model by using a functional rate law that uses the 
# Hill function. This model is a modified version of a model that was originally published  
# in the Proceedings of the 2009 Winter Simulation Conference 
# (doi: 10.1109/WSC.2009.5429719).                              
#
# cBNGL code: l.harris@vanderbilt.edu faeder@pitt.edu                                        
# 21 February 2015                                                                                                                                         

begin parameters

  # mean number of endosomes
  nEndo           5      

  # volumes
  vol_EC         20.0   
  vol_CP          4.0
  vol_NU          1.0
  vol_EN          0.1*nEndo
  
  # membrane surface areas
  sa_PM           0.4    
  sa_NM           0.1
  sa_EM           0.01*nEndo
  
  # effective surface width
  eff_width       1.0    

  # initial species counts (extensive units: quantity, not concentration)
  L0              100   
  R0              200     
  TF0             200
  DNA0            2

  # kinetic parameters (2nd order reaction params in vol/time units)
  kp_LR           0.1    # vol/time
  km_LR           1.0    # /time
  
  k_R_endo        1.0    # /time
  k_recycle       0.1    # /time
  k_R_phos        1.0    # /time
  k_R_dephos      0.1    # /time
  
  kp_R_TF         0.1    # vol/time
  km_R_TF         0.1    # /time
  k_TF_phos       1.0    # /time
  k_TF_dephos     10.0    # /time
  
  k_transcribe    1.0    # /time
  KM_TF_dna_trans 5.0    # number
  n_P             50.0    # Hill coefficient for transcription - exhibits strong oscillations for 
                          #   values 15 and above
  
  k_mRNA_to_CP    1.0    # /time (volume-to-volume species transport)
  k_translate     100.0    # /time
  k_mRNA_deg      1.0    # /time
  k_P_deg         0.1    # /time
  
  k_TF_import     10     # /time
  k_TF_export     10     # /time
end parameters

begin compartments
  EC  3  vol_EC 
  PM  2  sa_PM * eff_width       EC
  CP  3  vol_CP                  PM
  NM  2  sa_NM * eff_width       CP
  NU  3  vol_NU                  NM
  EM  2  sa_EM * eff_width       CP
  EN  3  vol_EN                  EM
end compartments

begin molecule types
  L(r)                 # Ligand w/ receptor binding site.
  R(l,tf~Y~pY)         # Receptor with ligand and TF binding sites.
  TF(d~Y~pY)           # Transcription factor with phosphorylation domain.
  DNA()                # DNA molecule. 
  mRNA()               # mRNA transcript.
  P(r)                 # Protein under control of TF - negative regulator of R
end molecule types

begin species
  L(r)@EC              L0
  R(l,tf~Y)@PM         R0
  TF(d~Y)@CP           TF0
  DNA()@NU             DNA0
  P(r)@CP              0
end species

begin observables
  Molecules  L_Bound_PM    @PM:L
  Molecules  L_Bound_EM    @EM:L
  Molecules  Rp_tot        R(tf~pY!?)
  Molecules  Rp_PM        @PM:R(tf~pY!?)
  Molecules  Rp_EM        @EM:R(tf~pY!?)
  Molecules  TF_nuc        @NU:TF()
  Molecules  Tot_mRNA      mRNA
  Molecules  Tot_P         P
  Molecules  P_R           P.R
end observables

begin functions
  rate_transcribe() = k_transcribe*TF_nuc^n_P/( KM_TF_dna_trans^n_P + TF_nuc^n_P) # volume/time
end functions

begin reaction rules

  # receptor-ligand binding.
  L_R_bind:  L(r) + R(l)  <->  L(r!1).R(l!1)            kp_LR, km_LR

  # phosphorylated receptor internalization.
  L_R_int:  @PM:R(tf~pY!?) ->  @EM:R(tf~pY)              k_R_endo

  # receptor recycling.
  R_recyc:  @EM:R  ->  @PM:R                           k_recycle
  
  # ligand recycling
  L_recyc:  @EN:L  ->  @EC:L                           k_recycle

  # receptor phosphorylation
  R_phos:  R(l!+,tf~Y)  ->  R(l!+,tf~pY)              k_R_phos
  
  # receptor dephosphorylation
  R_dephos:  R(tf~pY)   ->  R(tf~Y)                     k_R_dephos
  
  # receptor-mediated transcription factor phosphorylation
  R_TF_bind: R(tf~pY) + TF(d~Y) <-> R(tf~pY!1).TF(d~Y!1)   kp_R_TF, km_R_TF
  R_TF_phos: R(tf~pY!1).TF(d~Y!1) -> R(tf~pY) + TF(d~pY) k_TF_phos

  # Inhibition of receptor kinase activity by P
  P_R_bind: P(r) + R(tf~pY) <-> P(r!1).R(tf~pY!1) 10*kp_R_TF, km_R_TF
  P_R_dephos: P(r!1).R(tf~pY!1) -> P(r) + R(tf~Y) k_R_phos

  # transcription factor dephosphorylation
  TFdephos:  @CP:TF(d~pY)      ->  @CP:TF(d~Y)           k_TF_dephos
  
  # TF transport cytoplasm <-> nucleus
  TFtransp:  @CP:TF(d~pY) <-> @NU:TF(d~pY) k_TF_import, k_TF_export

  # TF-mediated transcription
  Ptransc: DNA() -> DNA() + mRNA()@NU  rate_transcribe()
    
  # mRNA transport to cytoplasm.
  mRNAtransp:  mRNA@NU  ->  mRNA@CP             k_mRNA_to_CP
  
  # mRNA translation to protein.
  Ptransl:  mRNA@CP  ->  mRNA@CP  +  P(r)@CP    k_translate
  
  # mRNA degradation.
  mRNAdeg:  mRNA     ->  0                   k_mRNA_deg  
  
  # protein degradation.
  Pdeg:  P        ->  0                   k_P_deg  DeleteMolecules
  
end reaction rules  
end model

# actions #
generate_network({overwrite=>1})
simulate({method=>"ode",t_end=>500,n_steps=>500,verbose=>1})