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Rat Model.R
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#author: Joris Jean van der Lugt
#date: 28-10-2021
#Human cinnamaldehyde pbk Model adapted from: "Dose-dependent DNA adduct formation by cinnamaldehyde and other food-borne α,β-unsaturated aldehydes predicted by physiologically based in silico modelling"
PBK_Cinnamaldehyde <- RxODE({
#--Defining the compartments of the model--#
Rin <- -Ka * A_GI; #Rate of change in Cinnamaldehyde concentration in the GI cavity in μmol/h
#-------------------Blood------------------------#
#Cinnamaldehyde#
C_V <- A_V / V_V ; #Concentration of Cinnamaldehyde in Venous blood in μmol/l
C_A <- A_A / V_A #Concentration of Cinnamaldehyde in Arterial blood
#Cinnamyl alcohol#
#C_OH_V <- A_OH_V / V_V; #Concentration of Cinnamyl alcOHol in venous Blood in μmol/l
#C_OH_A <- A_OH_A / V_A; #Concentration of Cinnamyl alcOHol in Arterial Blood in μmol/l
#-----------FAT---------------#
#Cinnamaldehyde#
C_F <- A_F / V_F; #Concentration in Fat in umol/kg
C_V_F <- C_F / P_F; #Concentration of cinnamaldehyde in venous blood leaving Fat in umol/l
R_F <- Q_F * (C_A - C_V_F); #rate of change in cinnamaldehyde concentration in the Fat in umol/h
#Cinnamyl alcohol#
#C_OH_F <- A_OH_F / V_F; #Concentration of Cinnamyl alcOHol in Fat in umol/kg
#C_OH_V_F <- C_OH_F / P_OH_F; #Concentration of Cinnamyl alcOHol in venous blood leaving Fat in umol/l
#R_OH_F <- Q_F * (C_OH_A - C_OH_V_F); #Rate of change in Cinnamyl alcOHol concentration in the Fat in umol/h
#-----------------------Richly perfused tissue-----------------#
#Cinnamaldehyde#
C_RP <- A_RP / V_RP; #Concentration of Cinnamaldehyde in RP tissue in umol/kg
C_V_RP <- C_RP / P_RP; #concentration of Cinnamaldehyde in RP venous blood leaving the tissue in umol/L
R_RP <- Q_RP * (C_A - C_V_RP); #rate of change in cinnamaldehyde concentration in the RP in umol/h
#Cinnamyl alcohol#
#C_OH_RP <- A_OH_RP / V_RP; #Concentration of Cinnamyl alcOHol in the RP tissue in umol/kg
#C_OH_V_RP <- C_OH_RP / P_OH_RP; #Concentration of Cinnamyl alcOHol in venous blood leaving the RP tissue in umol/l
#R_OH_RP <- Q_RP * (C_OH_A - C_OH_V_RP); #Rate of change in the Cinnamyl alcohol concentration in richly perfused tissue in umol/h
#-------------------Slowly perfused tissue--------------------#
#Cinnamaldehyde#
C_SP <- A_SP / V_SP; #Concentration in SP tissue in umol/kg
C_V_SP <- C_SP / P_SP; #Concentration of Cinnamaldehyde in venous blood leaving the SP in umol/l
R_SP <- Q_SP * (C_A - C_V_SP); #rate of change in cinnamaldehyde concentration in the SP tissue in umol/h
#Cinnamyl alcohol
#C_OH_SP <- A_OH_SP / V_SP; #Concentration of Cinnamyl alcOHol in the SP tissue in umol/kg
#C_OH_V_SP <- C_OH_SP / P_OH_SP; #Concentration of Cinnamyl alcOHol in venous blood leaving the SP tissue in umol/l
#R_OH_SP <- Q_SP * (C_OH_A - C_OH_V_SP); #Rate of change in the Cinnamyl alcohol concentration in slowly perfused tissue in umol/h
#-----------------------Small intestine-----------------------#
#Cinnamaldehyde#
C_SI <- A_SI / V_SI; #Concentration Cinnamaldehyde in the Small intestine in umol/kg
C_V_SI <- C_SI / P_SI; #Concentration of cinnamaldehyde in venous blood leaving the Small intestine in umol/l
#RM_SI_CA <- k_SI_CA * C_SI; #Rate of Cinnamaldehyde enzymatically oxidized to cabroxylic acid in the small intestine in μmol/h
#RM_SI_AP <- k_GSH * C_SI * C_PRO_SI * V_SI; #Rate of Cinnamaldehyde protein adducts in the small intestine in umol/h
#GSH#
#C_SIc_GSH <- AM_SIc_GSH / V_SI; #Concentration of GSH in the Small Intestine in umol/l
#RM_SI_AG_GST <- Vsmax_SI_GST * C_SI * C_SIc_GSH / (Km_SI_GST_G * C_SI + Km_SI_GST * C_SIc_GSH + C_SIc_GSH * C_SI); #-amount of cinnamaldehyde metabolized in the small intestine to GSH conjugate by GST in μmol
#RM_SI_AG_CHEM <- k_GSH * C_SI * C_SIc_GSH * V_SI; #Rate of Cinnamaldehyde binding in the small intestine to GSH in umol/h
#RM_SIc_GSH <- G_SYN_SI * V_SI * 0.9 #- (RM_SI_AG_GST + RM_SI_AG_CHEM + k_SI_GLOS * C_SIc_GSH); #Rate of GSH concentration in the Smal intestine cytosol umol/h
#Cinnamyl alchol#
#C_OH_SI <- A_OH_SI / V_SI; #Concentration of Cinnamyl alcOHol in the Small intestine in umol/l
#C_OH_V_SI <- C_OH_SI / P_OH_SI; #Concentration of Cinnamyl alcOHol in venous blood leaving the Small intestine in umol/l
#RM_SI_AO <- Vsmax_SI_AO * C_SI / (Km_SI_AO + C_SI); #Amount of Cinnamaldehyde reduced to cinnamyl alcOHol in the small intestine in umol
#R_OH_M_SI_C_A <- Vsmax_SI_OH * C_OH_SI/(Km_SI_OH + C_OH_SI); #Rate of Cinnamyl alcOHol enzymaticly oxidized to cinnamaldehyde in the small intestine in umol
#R_OH_SI <- Q_SI * (C_OH_A - C_OH_SI) + RM_SI_AO# - R_OH_M_SI_C_A;#Rate of Cinnamyl alcohol concentration change in the small intestine in umol/h
#Over all output small intestine#
R_SI <- Q_SI * (C_A - C_V_SI) + R_OH_M_SI_C_A -Rin - (RM_SI_CA + RM_SI_AO);# + RM_SI_AP + RM_SI_AG_GST + RM_SI_AG_CHEM )# ) #Rate of change in cinnamaldehyde concentration in the SI in umol/h
#---------------Liver-----------------------------------#
#-Cinnamaldehyde-#
C_L <- A_L / V_L; #Concentration Cinnamaldehyde in the Liver in umol/kg
C_V_L <- C_L / P_L; #Concentration of cinnamaldehyde in venous blood leaving the Liver in umol/l
#RM_L_CA <- k_L_CA * C_L; #Rate of Cinnamaldehyde oxidation to carboxylic acid in the liver in μmol/h
#RM_L_AP <- k_GSH * C_L * C_PRO_L * V_L; #Rate of Cinnamaldehyde proteins adducts formation in the liver in umol/h
#GSH#
#C_Lc_GSH <- AM_Lc_GSH / V_L; #Concentration of GSH in the liver cytosol in umol/l
#RM_L_AG_GST <- k_L_GST * C_L * C_Lc_GSH/(Km_L_GST_G + C_Lc_GSH); #Amount of cinnamaldehyde metabolized with GSH in the liver to conjugate GST #KM_L_GST_G is stil unknown
#RM_L_AG_CHEM <- k_GSH * C_L * C_Lc_GSH * V_L; #Amount of Cinnamaldehyde chemically bound in liver to GSH in umol
#RM_Lc_GSH <- G_SYN_L * V_L * 0.9 #- (RM_L_AG_GST + RM_L_AG_CHEM + k_L_GLOS * C_Lc_GSH);#Rate of change in GSH concentration in the liver cytosol umol/h
#RM_L_DA_FORM <- k_DNA * C_L * C_L_dG * V_L; #Rate of DNA adduct formation in the liver
#RM_L_DA <- RM_L_DA_FORM - AM_L_DA * (log(2)/T_0.5); #Rate of DNA adduct removal in the liver
#Cinnamyl alcohol
#C_OH_L <- A_OH_L / V_L; #Concentration of Cinnamyl alcOHol in the Liver in umol/kg
#C_OH_V_L <- C_OH_L / P_OH_L; #Concentration of Cinnamyl alcOHol in venous blood leaving the Liver in umol/l
#RM_L_AO <- (Vsmax_L_AO * C_L) / (Km_L_AO + C_L ); #Rate of Cinnamaldehyde reduced to cinnamyl alcOHol in the liver in umol/h
#R_OH_M_L_C_A <- (Vsmax_L_OH *C_OH_L) /(Km_L_OH + C_OH_L); #Rate of Cinnamyl alcOHol oxidized to cinnamaldehyde in the liver in umol/h
#R_OH_L <- Q_L * C_OH_A + Q_SI * C_OH_V_SI - (Q_L + Q_SI) * C_OH_V_L + RM_L_AO - R_OH_M_L_C_A;#Rate of in Cinnamyl alcOHol concentration in the liver in umol
#Over al output Liver#
R_L <- Q_L * C_A + Q_SI * C_V_SI - (Q_L + Q_SI) * C_V_L# + R_OH_M_L_C_A - (RM_L_CA + RM_L_AO);# + RM_L_AP + RM_L_AG_GST + RM_L_AG_CHEM + RM_L_DA_FORM ); #Rate of change in Cinnamaldehyde concentration in the liver in umol/h
#----------------Blood------------------------#
#Cinnamaldehyde#
R_V <- Q_F * C_V_F + (Q_L + Q_SI) * C_V_L + Q_RP * C_V_RP + Q_SP * C_V_SP - Q_C * C_V; #Rate of change in Cinnamaldehyde concentration in the venous blood in μmol
R_A <- Q_C * C_V - (Q_F * C_A + Q_L * C_A + Q_SI * C_A + Q_RP * C_A + Q_SP * C_A ); #Rate of change in Cinnamaldehyde concentration in the arterial blood in μmol
#Cinnamyl alcohol
#R_OH_V <- Q_F * C_OH_V_F + (Q_L + Q_SI) * C_OH_V_L + Q_RP * C_OH_V_RP + Q_SP * C_OH_V_SP - Q_C * C_OH_V;
#R_OH_A <- Q_C * C_OH_V - (Q_F * C_OH_A + Q_L * C_OH_A + Q_SI * C_OH_A + Q_RP * C_OH_A + Q_SP * C_OH_A);
#----------------------------------------------Differential equations-------------------------------------------------------------------------------#
#-GI tract-#
d/dt(A_GI) <- Rin; #Amount of Cinnamaldehyde in GI cavity in μmol
#--------Blood----------#
#-Venous-#
d/dt(A_V) <- R_V; #Amount of Cinnamaldehyde in Venous blood in μmol
d/dt(A_OH_V) <- R_OH_V; #Amount of Cinnamyl alcohol in Venous blood in μmol
#-Arterial-#
d/dt(A_A) <- R_A; #Amount of Cinnamaldehyde in Arterial blood in μmol
d/dt(A_OH_A) <- R_OH_A; #Amount of Cinnamyl alcohol in Arterial blood in μmol
#-Fat calculations-#
d/dt(A_F) <- R_F; #Amount of Cinnamaldehyde in the Fat in μmol
d/dt(A_OH_F) <- R_OH_F; #Amount of Cinnamyl alcOHol in Fat in μmol
#--------------------Liver calculations-------------#
d/dt(A_L) <- R_L; #Amount of Cinnamaldehyde in the liver in μmol
d/dt(AM_L_CA) <- RM_L_CA; #Amount of Cinnamaldehyde oxidized to cinnamic acid in the liver in μmol
#d/dt(AM_L_AP) <- RM_L_AP; #Amount of Cinnamaldehyde proteins adduct in the liver in μmol
#--GSH in the Liver cytosol--#
d/dt(AM_Lc_GSH) <- RM_Lc_GSH; #Amount of GSH in the liver cytosol
#d/dt(AM_L_AG_GST) <- RM_L_AG_GST; #Amount of Cinnamaldehyde metabolized with GSH in the liver to conjugate GST
#d/dt(AM_L_AG_CHEM) <- RM_L_AG_CHEM; #Amount of Cinnamaldehyde chemically bound in liver to GSH in μmol
#--Cinnamyl alcohol--#
d/dt(A_OH_M_L_C_A) <- R_OH_M_L_C_A; #Amount of Cinnamyl alcOHol oxidized to Cinnamaldehyde in the liver in μmol
d/dt(AM_L_AO) <- RM_L_AO; #Amount of Cinnamaldehyde reduced to cinnamyl alcOHol in the liver in μmol
d/dt(A_OH_L) <- R_OH_L; #Amount of Cinnamyl alcOHol in the liver in μmol
#---DNA adduct formation--#
#d/dt(AM_L_DA_FORM) <- RM_L_DA_FORM; #Amount of DNA adduct formed in the liver
#d/dt(AM_L_DA) <- RM_L_DA; #Amount of DNA adduct removed from the liver
#-----------Si calculations--------------#
d/dt(A_SI) <- R_SI; #Amount of Cinnamaldehyde in the small intestine-#
d/dt(AM_SI_CA) <- RM_SI_CA; #Amount of Cinnamaldehyde enzymatically oxidized Cinnamic acid in the small intestine in μmol
#d/dt(AM_SI_AP) <- RM_SI_AP; #Amount of Cinnamaldehyde protein adducts in the small intestine in μmol
#-GSH in the small intestine cytosol-#
#d/dt(AM_SI_AG_GST) <- RM_SI_AG_GST; #Amount of Cinnamaldehyde metabolized in the small intestine to GSH conjugate by GST in μmol
#d/dt(AM_SI_AG_CHEM) <- RM_SI_AG_CHEM; #Amount of Cinnamaldehyde bound in the small intestine to GSH in μmol
d/dt(AM_SIc_GSH) <- RM_SIc_GSH; #Amount of GSH in the small intestine cytosol
#--Cinnamyl alcohol--#
d/dt(AM_SI_AO) <- RM_SI_AO; #Amount of Cinnamaldehyde reduced to cinnamyl alcOHol in the SI in μmol
d/dt(A_OH_M_SI_C_A) <- R_OH_M_SI_C_A; #Amount of Cinnamyl alcOHol enzymatically oxidized to Cinnamaldehyde in the small intestine in μmol
d/dt(A_OH_SI) <- R_OH_SI; #Amount of Cinnamyl alcOHol in the small intestine in μmol
#--------Richly perfused Tissue---------#
#Cinnamaldehyde#
d/dt(A_RP) <- R_RP; #Amount of Cinnamaldehyde in the RP tissue in μmol
#Cinnamyl alcohol#
d/dt(A_OH_RP) <- R_OH_RP; #Amount of Cinnamyl alcOHol in the RP tissue in μmol
#---------------Slowly perfused Tissue----------------#
#Cinnamaldehyde
d/dt(A_SP) <- R_SP; #Amount of Cinnamaldehyde in the SP tissue in μmol
#Cinnamyl alcohol
d/dt(A_OH_SP) <- R_OH_SP; #Amount of Cinnamyl alcOHol in the SP tissue in μmol
})
solve.pbk_rat <- solve(PBK_Cinnamaldehyde, parameters, events = ex, inits) #Solve the PBPK model