bartholome1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000197) Biomodels notes: The values for parameters and the inital concentrations of this model where directly provided by the main author: Parameter values parameter value unit p1 0.0025 1/min p2 0.0784 1/min p3 0.0013 1/min p4 0.0827 1/min p5 0.0091 1/min p6 0.000064 1/(nmole*min) p7 0.0397 1/min p8 1000 nmole p9 0.0098 1/(nmole*min) p10 1.6 1/min p11 1000 nmole p12 0.0003 ml/min The basal chamber volume was taken as 1 ml, the apical as 1.5. As starting values x1 was set to 88 nmole, all other species to 0. Reproduction of the time courses in figure 3 of the original publication. The simulation was run using SBML odeSolver and plotted using xmgrace. JWS Online curation: Curves x5 and x3 + x4 OATP1B3-ABCC2 of Figure 3 were recreated.

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Data-based mathematical modeling of vectorial transport across double-transfected polarized cells.

  • Kilian Bartholomé
  • Maria Rius
  • Katrin Letschert
  • Daniela Keller
  • Jens Timmer
  • Dietrich Keppler
Drug Metab. Dispos. 2007; 35 (9): 1476-1481
Abstract
Vectorial transport of endogenous small molecules, toxins, and drugs across polarized epithelial cells contributes to their half-life in the organism and to detoxification. To study vectorial transport in a quantitative manner, an in vitro model was used that includes polarized MDCKII cells stably expressing the recombinant human uptake transporter OATP1B3 in their basolateral membrane and the recombinant ATP-driven efflux pump ABCC2 in their apical membrane. These double-transfected cells enabled mathematical modeling of the vectorial transport of the anionic prototype substance bromosulfophthalein (BSP) that has frequently been used to examine hepatobiliary transport. Time-dependent analyses of (3)H-labeled BSP in the basolateral, intracellular, and apical compartments of cells cultured on filter membranes and efflux experiments in cells preloaded with BSP were performed. A mathematical model was fitted to the experimental data. Data-based modeling was optimized by including endogenous transport processes in addition to the recombinant transport proteins. The predominant contributions to the overall vectorial transport of BSP were mediated by OATP1B3 (44%) and ABCC2 (28%). Model comparison predicted a previously unrecognized endogenous basolateral efflux process as a negative contribution to total vectorial transport, amounting to 19%, which is in line with the detection of the basolateral efflux pump Abcc4 in MDCKII cells. Rate-determining steps in the vectorial transport were identified by calculating control coefficients. Data-based mathematical modeling of vectorial transport of BSP as a model substance resulted in a quantitative description of this process and its components. The same systems biology approach may be applied to other cellular systems and to different substances.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
1e-09 mole
0.001 litre
60.0 second
0.016666666666666666 second^(-1.0)
1.6666666666666667e-05 litre second^(-1.0)
16666666.666666666 mole^(-1.0) second^(-1.0)
Id Name Spatial dimensions Size
apical apical extracellular space 3.0 1.5
basolat basolateral extrocellular space 3.0 1.0
cell intracellular 3.0 1.0
Id Name Initial quantity Compartment Fixed
BSP_cell intracellular BSP 0.0 cell (intracellular)
BSP_tot total BSP 0.0 apical (apical extracellular space)
x1 free basolateral BSP 88.0 basolat (basolateral extrocellular space)
x2 basolateral bound BSP 0.0 basolat (basolateral extrocellular space)
x3 free intracellular BSP 0.0 cell (intracellular)
x4 bound intracellular BSP 0.0 cell (intracellular)
x5 apical BSP 0.0 apical (apical extracellular space)

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
ABCC2 ABCC2 mediated export x3 > x5

p2 * x3
OATP1B3 OATP1B3 mediated import x1 > x3

p1 * x1
bl_BSP_binding basolateral BSP binding x1 > x2

p6 * x1 * (p8 - x2)
bl_BSP_dissoc basolateral BSP dissoc x2 > x1

p7 * x2
cellular_BSP_binding cellular BSP binding x3 > x4

p9 * x3 * (p11 - x4)
cellular_BSP_dissoc cellular BSP dissoc x4 > x3

p10 * x4
endo_ex_ap endogenous apical export x3 > x5

p5 * x3
endo_ex_bl endogenous basolateral export x3 > x1

p4 * x3
endo_in_bl endogenous basolateral import x1 > x3

p3 * x1
paracell_transp paracellular transport x1 = x5

p12 * (x1 / basolat - x5 / apical)

Global parameters

Id Value
p1 0.0025 permin
p10 1.6 permin
p11 1000.0
p12 0.0003 ml_per_min
p2 0.0784 permin
p3 0.0013 permin
p4 0.0827 permin
p5 0.0091 permin
p6 6.4e-05 per_nmole_per_ml
p7 0.0397 permin
p8 1000.0
p9 0.0098 per_nmole_per_ml

Local parameters

Id Value Reaction

Assignment rules

Definition
BSP_cell = x3 + x4
BSP_tot = x1 + x2 + x3 + x4 + x5

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments