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BIOMD0000000669 - Zhu2015 - Combined gemcitabine and birinapant in pancreatic cancer cells - mechanistic PD model

 

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Reference Publication
Publication ID: 26252969
Zhu X, Straubinger RM, Jusko WJ.
Mechanism-based mathematical modeling of combined gemcitabine and birinapant in pancreatic cancer cells.
J Pharmacokinet Pharmacodyn 2015 Oct; 42(5): 477-496
Department of Pharmaceutical Sciences, School of Pharmacy and Pharmaceutical Sciences, State University of New York at Buffalo, Buffalo, NY, 14214, USA.  [more]
Model
Original Model: BIOMD0000000669.origin
Submitter: Vijayalakshmi Chelliah
Submission ID: MODEL1604270001
Submission Date: 27 Apr 2016 14:54:18 UTC
Last Modification Date: 07 Feb 2018 14:20:31 UTC
Creation Date: 06 Feb 2018 10:23:00 UTC
Encoders:  Matthew Grant Roberts
set #1
null BioModels Database BIOMD0000000669
null BioModels Database Zhu2015 - combined gemcitabine and birinapant in pancreatic cancer cells - mechanistic PD model
bqbiol:hasPart KEGG Drug D02368
bqbiol:occursIn Brenda Tissue Ontology BTO:0000988
bqbiol:isDescribedBy PubMed 26252969
NCIt C49662
set #2
null NCIt C191
bqbiol:hasPart KEGG Drug D10417
Notes
Zhu2015 - combined gemcitabine and birinapant in pancreatic cancer cells - mechanistic PD model
Mechanistic mathematical model to illustrate the effectiveness of combination chemotherapy involving gemcitabine and birinapant against pancreatic cancer.

This model is described in the article:

Zhu X, Straubinger RM, Jusko WJ.
J Pharmacokinet Pharmacodyn 2015 Oct; 42(5): 477-496

Abstract:

Combination chemotherapy is standard treatment for pancreatic cancer. However, current drugs lack efficacy for most patients, and selection and evaluation of new combination regimens is empirical and time-consuming. The efficacy of gemcitabine, a standard-of-care agent, combined with birinapant, a pro-apoptotic antagonist of Inhibitor of Apoptosis Proteins (IAPs), was investigated in pancreatic cancer cells. PANC-1 cells were treated with vehicle, gemcitabine (6, 10, 20 nM), birinapant (50, 200, 500 nM), and combinations of the two drugs. Temporal changes in cell numbers, cell cycle distribution, and apoptosis were measured. A basic pharmacodynamic (PD) model based on cell numbers, and a mechanism-based PD model integrating all measurements, were developed. The basic PD model indicated that synergistic effects occurred in both cell proliferation and death processes. The mechanism-based model captured key features of drug action: temporary cell cycle arrest in S phase induced by gemcitabine alone, apoptosis induced by birinapant alone, and prolonged cell cycle arrest and enhanced apoptosis induced by the combination. A drug interaction term Ψ was employed in the models to signify interactions of the combination when data were limited. When more experimental information was utilized, Ψ values approaching 1 indicated that specific mechanisms of interactions were captured better. PD modeling identified the potential benefit of combining gemcitabine and birinapant, and characterized the key interaction pathways. An optimal treatment schedule of pretreatment with gemcitabine for 24-48 h was suggested based on model predictions and was verified experimentally. This approach provides a generalizable modeling platform for exploring combinations of cytostatic and cytotoxic agents in cancer cell culture studies.

This model is hosted on BioModels Database and identified by: BIOMD0000000669.

To cite BioModels Database, please use: Chelliah V et al. BioModels: ten-year anniversary. Nucl. Acids Res. 2015, 43(Database issue):D542-8.

To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

Model
Publication ID: 26252969 Submission Date: 27 Apr 2016 14:54:18 UTC Last Modification Date: 07 Feb 2018 14:20:31 UTC Creation Date: 06 Feb 2018 10:23:00 UTC
Mathematical expressions
Rules
Assignment Rule (variable: R_total) Assignment Rule (variable: R_live) Assignment Rule (variable: Inh_1) Assignment Rule (variable: Inh_3)
Assignment Rule (variable: k_other) Assignment Rule (variable: Tlag_r) Assignment Rule (variable: Tlag_re) Assignment Rule (variable: Inh_g)
Assignment Rule (variable: Inh_b) Assignment Rule (variable: Sti_g) Assignment Rule (variable: Sti_other_g) Assignment Rule (variable: Sti_other_b)
Assignment Rule (variable: Sti_b) Assignment Rule (variable: CURVE_G1) Assignment Rule (variable: CURVE_S) Assignment Rule (variable: CURVE_G2)
Assignment Rule (variable: CURVE_FIGURE_7a/d/g) Assignment Rule (variable: CURVE_FIGURE_7b/r/h) Rate Rule (variable: G1) Rate Rule (variable: S)
Rate Rule (variable: G2) Rate Rule (variable: R_apo) Rate Rule (variable: R_other)  
Physical entities
Compartments Species
Pancreas G1 S G2
R_apo R_other R_total
R_live    
Global parameters
Inh_1 IR50 Inh_3 Imax_3
k3 k1 k_apo k2
Imax_g C_g C_b Hi_g
Hs_b Hi_b Hs_g Tlag_re
Tlag_sg k_other Hother_g Smax_b
Psi_i Psi_s Smax_g SC50_g
SC50_b k_comb2 k_comb1 k_repair
Tlag_r k_delay R_0 f(G1)_0
f(S)_0 f(apo)_0 f(other)_0 f1
Imax_b IC50_g IC50_b k_tau
Kother_g Kother_b Hother_b Inh_g
Inh_b Sti_g Sti_other_g Sti_other_b
Sti_b Sti_apo_g Sti_apo_b f(G2)_0
CURVE_G1 CURVE_S CURVE_G2 CURVE_FIGURE_7a/d/g
CURVE_FIGURE_7b/r/h CURVE_FIGURE_7c/f/i    
Reactions (0)
Rules (23)
 
 Assignment Rule (name: R_total) R_total = G1+S+G2+R_apo+R_other
 
 Assignment Rule (name: R_live) R_live = G1+S+G2
 
 Assignment Rule (name: Inh_1) Inh_1 = R_live/(IR50+R_live)
 
 Assignment Rule (name: Inh_3) Inh_3 = Imax_3*R_live/(IR50+R_live)
 
 Assignment Rule (name: k_other) k_other = piecewise(0.000297, (C_b != 0) && (C_g != 0), 0)
 
 Assignment Rule (name: Tlag_r) Tlag_r = piecewise(0, C_g == 0, k_delay*ln(C_g))
 
 Assignment Rule (name: Tlag_re) Tlag_re = (1+k_comb1*C_b)*Tlag_r
 
 Assignment Rule (name: Inh_g) Inh_g = piecewise(Imax_g*C_g^Hi_g/(IC50_g^Hi_g+C_g^Hi_g), (C_b == 0) && (time <= Tlag_r), piecewise(Imax_g*C_g^Hi_g/(IC50_g^Hi_g+C_g^Hi_g)*exp((-1)*k_repair*(time-Tlag_r)), (C_b == 0) && (time > Tlag_r), piecewise(Imax_g*C_g^Hi_g/((Psi_i*IC50_g)^Hi_g+C_g^Hi_g), (C_b != 0) && (time <= Tlag_re), piecewise(Imax_g*C_g^Hi_g/((Psi_i*IC50_g)^Hi_g+C_g^Hi_g)*exp((-1)*(1-k_comb2*C_b)*k_repair*(time-Tlag_re)), (C_b != 0) && (time > Tlag_re), 0))))
 
 Assignment Rule (name: Inh_b) Inh_b = Imax_b*C_b^Hi_b/(IC50_b^Hi_b+C_b^Hi_b)
 
 Assignment Rule (name: Sti_g) Sti_g = piecewise(0, time <= Tlag_sg, Smax_g*C_g^Hs_g/(SC50_g^Hs_g+C_g^Hs_g))
 
 Assignment Rule (name: Sti_other_g) Sti_other_g = Kother_g*C_g^Hother_g
 
 Assignment Rule (name: Sti_other_b) Sti_other_b = Kother_b*C_b^Hother_b
 
 Assignment Rule (name: Sti_b) Sti_b = Smax_b*C_b^Hs_b/((Psi_s*SC50_b)^Hs_b+C_b^Hs_b)
 
 Assignment Rule (name: CURVE_G1) CURVE_G1 = G1/R_total
 
 Assignment Rule (name: CURVE_S) CURVE_S = S/R_total
 
 Assignment Rule (name: CURVE_G2) CURVE_G2 = G2/R_total
 
 Assignment Rule (name: CURVE_FIGURE_7a_d_g) CURVE_FIGURE_7a/d/g = R_live/R_total
 
 Assignment Rule (name: CURVE_FIGURE_7b_r_h) CURVE_FIGURE_7b/r/h = R_apo/R_total
 
 Rate Rule (name: G1) d [ G1] / d t= ((2*(1-Inh_3)*(1-Inh_b)*k3*G2-(1-Inh_1)*(1-Inh_b)*k1*G1)-(1+Sti_apo_g)*(1+Sti_apo_b)*k_apo*G1)-(1+Sti_other_g)*(1+Sti_other_b)*k_other*G1
 
 Rate Rule (name: S) d [ S] / d t= (((1-Inh_1)*(1-Inh_b)*k1*G1-(1-Inh_g)*k2*S)-(1+Sti_apo_g)*(1+Sti_apo_b)*k_apo*S)-(1+Sti_other_g)*(1+Sti_other_b)*k_other*S
 
 Rate Rule (name: G2) d [ G2] / d t= (((1-Inh_g)*k2*S-(1-Inh_3)*(1-Inh_b)*k3*G2)-(1+Sti_apo_g)*(1+Sti_apo_b)*k_apo*G2)-(1+Sti_other_g)*(1+Sti_other_b)*k_other*G2
 
 Rate Rule (name: R_apo) d [ R_apo] / d t= (1+Sti_apo_g)*(1+Sti_apo_b)*k_apo*(G1+S+G2)-(1+Sti_apo_g)*(1+Sti_apo_b)*f1*k_apo*R_apo
 
 Rate Rule (name: R_other) d [ R_other] / d t= (1+Sti_other_g)*(1+Sti_other_b)*k_other*(G1+S+G2)-k_other*R_other
 
 Pancreas Spatial dimensions: 3.0  Compartment size: 1.0
 
 G1
Compartment: Pancreas
Initial concentration: 113516.0
 
 S
Compartment: Pancreas
Initial concentration: 25488.0
 
 G2
Compartment: Pancreas
Initial concentration: 81656.0
 
 R_apo
Compartment: Pancreas
Initial concentration: 11800.0
 
 R_other
Compartment: Pancreas
Initial concentration: 3540.0
 
  R_total
Compartment: Pancreas
Initial concentration: 236000.0
 
  R_live
Compartment: Pancreas
Initial concentration: 220660.0
 
Global Parameters (58)
 
  Inh_1
Value: 0.642088110341617
 
 IR50
Value: 123000.0
Constant
 
  Inh_3
Value: 0.483492347087237
 
 Imax_3
Value: 0.753
Constant
 
 k3
Value: 0.222
Constant
 
 k1
Value: 0.357
Constant
 
 k_apo
Value: 0.00394
Constant
 
 k2
Value: 0.114
Constant
 
 Imax_g
Value: 0.878
Constant
 
 C_g
Value: 20.0
Constant
 
 C_b
Value: 500.0
Constant
 
 Hi_g
Value: 4.34
Constant
 
 Hs_b
Value: 1.24
Constant
 
 Hi_b
Value: 1.0
Constant
 
 Hs_g
Value: 3.0
Constant
 
  Tlag_re
Value: 81.3242453104881
 
 Tlag_sg
Value: 38.7
Constant
 
  k_other
Value: 2.97E-4
 
 Hother_g
Value: 0.1
Constant
 
 Smax_b
Value: 3.72
Constant
 
 Psi_i
Value: 0.949
Constant
 
 Psi_s
Value: 1.26
Constant
 
 Smax_g
Value: 2.74
Constant
 
 SC50_g
Value: 23.6
Constant
 
 SC50_b
Value: 50.1
Constant
 
 k_comb2
Value: 7.75E-4
Constant
 
 k_comb1
Value: 9.19E-4
Constant
 
 k_repair
Value: 0.0495
Constant
 
  Tlag_r
Value: 55.7206202881042
 
 k_delay
Value: 18.6
Constant
 
 R_0
Value: 236000.0
Constant
 
 f(G1)_0
Value: 48.1
Constant
 
 f(S)_0
Value: 10.8
Constant
 
 f(apo)_0
Value: 5.0
Constant
 
 f(other)_0
Value: 1.5
Constant
 
 f1
Value: 0.467
Constant
 
 Imax_b
Value: 0.177
Constant
 
 IC50_g
Value: 6.0
Constant
 
 IC50_b
Value: 154.0
Constant
 
 k_tau
Value: 0.376
Constant
 
 Kother_g
Value: 1.0E-5
Constant
 
 Kother_b
Value: 0.0055
Constant
 
 Hother_b
Value: 1.0
Constant
 
  Inh_g
Value: 0.874253042562929
 
  Inh_b
Value: 0.135321100917431
 
  Sti_g  
 
  Sti_other_g
Value: 1.34928284767356E-5
 
  Sti_other_b
Value: 2.75
 
  Sti_b
Value: 3.45458166847543
 
 Sti_apo_g
Constant
 
 Sti_apo_b
Constant
 
 f(G2)_0
Value: 34.6
Constant
 
  CURVE_G1
Value: 0.481
 
  CURVE_S
Value: 0.108
 
  CURVE_G2
Value: 0.346
 
  CURVE_FIGURE_7a/d/g
Value: 0.935
 
  CURVE_FIGURE_7b/r/h
Value: 0.05
 
 CURVE_FIGURE_7c/f/i
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000669

Curator's comment: (updated: 07 Feb 2018 14:13:17 GMT)

Similar figures of figure 5 of the reference publication have been produced with k_delay set to 18.6 as opposed to 38.6 as listed in table 2 of the reference publication. Additionally, the values of Sti_apo_g and Sti_apo_b were not found in the reference publication and were set to 0. The parameter k_tau, altough listed in table 2, was not used.

The figures illustrate the fraction of live/proliferating cells in G0/G1 (blue), S (red) and G2/M (green) phases over a period of 100 hours. The top row represents the control case where both drug concentrations are set to 0. The effects of germcitabine, birinapant and combination treatment on cell cycle phase transition are illustrated in the second, third and bottom row respectively with increasing drug concentration from left to right. 20nm germcitabine + 500 nM birinapant treatment resulted in a large quantity of cells remaining in the S phase for an extended period of time, thus preventing transition to M phase.

One discrepancy, for example, is that the red curve for figure 5J (bottom right) starts to decrease after approximately t=25 whereas in the reference publication it is monotonically increasing until approximately t=80. Despite the y-axis being labelled as 'Cell Fraction', if the raw/non-scaled values of G1, S and G2 are plotted, the curated figure will be more similar to the figure in the reference publication.

The simulations were performed in COPASI V4.22 (Build 170) and figures were generated in MATLAB R2014.

Additional file(s)
  • COPASI file:
    Curated and annotated COPASI file.
  • SED-ML file:
    SED-ML file to produce a similar figure to figure 5J of the reference publication. Concentration of germcitabine and birinapant is set to 20nM and 500nM respectively with k_delay set to 18.6 as opposed to 36.8 and Sti_apo_g and Sti_apo_b set to 0 as values for these parameters could not be found. k_tau is also not used.

    If raw/non-scaled values of G1, S and G2 are plotted (that is, the 'species' values and not the scaled 'quantity' values) the simulated figure is much more similar to the figure in the reference publication. However, the y-axis is labelled as 'Cell Fraction' and supposedly scaled between 0-1.
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