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BIOMD0000000327 - Whitcomb2004_Bicarbonate_Pancreas

 

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Reference Publication
Publication ID: 15257112
Whitcomb DC, Ermentrout GB.
A mathematical model of the pancreatic duct cell generating high bicarbonate concentrations in pancreatic juice.
Pancreas 2004 Aug; 29(2): e30-40
Department of Medicine, University of Pittsburgh, UPMC Presbyterian, Pittsburgh, Pennsylvania 15213, USA. whitcomb@pitt.edu  [more]
Model
Original Model: BIOMD0000000327.origin
Submitter: Kieran Smallbone
Submission ID: MODEL1104180000
Submission Date: 18 Apr 2011 20:04:04 UTC
Last Modification Date: 08 Apr 2016 16:59:34 UTC
Creation Date: 14 Apr 2011 00:00:00 UTC
Encoders:  Lukas Endler
   Kieran Smallbone
set #1
bqbiol:isVersionOf Gene Ontology pancreatic juice secretion
set #2
bqbiol:occursIn Taxonomy Homo sapiens
Brenda Tissue Ontology pancreatic duct
Notes

A mathematical model of the pancreatic duct cell generating high bicarbonate concentrations in pancreatic juice
David C Whitcomb, G Bard Ermentrout, Pancreas 2004 29:e30-40; PubMedID:15257112

Abstract:
OBJECTIVE: To develop a simple, physiologically based mathematical model of pancreatic duct cell secretion using experimentally derived parameters that generates pancreatic fluid bicarbonate concentrations of >140 mM after CFTR activation.
METHODS: A new mathematical model was developed simulating a duct cell within a proximal pancreatic duct and included a sodium-2-bicarbonate cotransporter (NBC) and sodium-potassium pump (NaK pump) on a chloride-impermeable basolateral membrane, CFTR on the luminal membrane with 0.2 to 1 bicarbonate to chloride permeability ratio. Chloride-bicarbonate antiporters (Cl/HCO3 AP) were added or subtracted from the basolateral (APb) and luminal (APl) membranes. The model was integrated over time using XPPAUT.
RESULTS: This model predicts robust, NaK pump-dependent bicarbonate secretion with opening of the CFTR, generates and maintains pancreatic fluid secretion with bicarbonate concentrations >140 mM, and returns to basal levels with CFTR closure. Limiting CFTR permeability to bicarbonate, as seen in some CFTR mutations, markedly inhibited pancreatic bicarbonate and fluid secretion.
CONCLUSIONS: A simple CFTR-dependent duct cell model can explain active, high-volume, high-concentration bicarbonate secretion in pancreatic juice that reproduces the experimental findings. This model may also provide insight into why CFTR mutations that predominantly affect bicarbonate permeability predispose to pancreatic dysfunction in humans.

This SBML version of the model was created directly from the XPPAUT code found in the appendix with the exception of the parameter vr, the ratio between the duct cell volume and the duct lumen, which is defined inversely to the main text in the XPPAUT code. vr was defined as the ratio of the duct cell volume to the duct lumen volume as in the main text. The model reproduces the figures found in the article. The model uses initial assignments for the lumen volume and events to trigger CFTR opening, so only tools supporting these features can be used to simulate it (eg. Copasi and SBW/Roadrunner).

Model
Publication ID: 15257112 Submission Date: 18 Apr 2011 20:04:04 UTC Last Modification Date: 08 Apr 2016 16:59:34 UTC Creation Date: 14 Apr 2011 00:00:00 UTC
Mathematical expressions
Reactions
nbc bcftr ccftr apl
apbl nak naleak buffering
bac cac outflow  
Rules
Assignment Rule (variable: CL-) Assignment Rule (variable: eb) Assignment Rule (variable: enbc) Assignment Rule (variable: ec)
Assignment Rule (variable: ena) Assignment Rule (variable: kccf) Assignment Rule (variable: kbcf) Assignment Rule (variable: knbc)
Assignment Rule (variable: v) Assignment Rule (variable: jnbc) Assignment Rule (variable: jbcftr) Assignment Rule (variable: jccftr)
Assignment Rule (variable: japl) Assignment Rule (variable: japbl) Assignment Rule (variable: jlum) Assignment Rule (variable: jnak)
Assignment Rule (variable: jnaleak)      
Events
       
Physical entities
Compartments Species
plasma HCO3- CL- Na+
     
cell HCO3- CL- Na+
     
lumen HCO3- CL-  
Global parameters
g_bi g_cl zeta kbi
kcl gnbc gapl gapbl
vr bi0 buf gcftron
gcftrbase ek gk gas constant
Faraday constant temp ionstr gnak
np0 epump gnaleak jac
rat ton toff gcftr
eb enbc ec ena
kccf kbcf knbc v
jnbc jbcftr jccftr japl
japbl jlum jnak jnaleak
Reactions (11)
 
 nbc 2.0 × [HCO3-] + [Na+] ↔ 2.0 × [HCO3-] + [Na+];  
 
 bcftr [HCO3-] ↔ [HCO3-];  
 
 ccftr [CL-] ↔ [CL-];  
 
 apl [HCO3-] + [CL-] ↔ [HCO3-] + [CL-];  
 
 apbl [HCO3-] + [CL-] ↔ [HCO3-] + [CL-];  
 
 nak [Na+] ↔ [Na+];  
 
 naleak [Na+] ↔ [Na+];  
 
 buffering  ↔ [HCO3-];  
 
 bac  ↔ [HCO3-];  
 
 cac  ↔ [CL-];  
 
 outflow [HCO3-] ↔ ;  
 
Rules (17)
 
 Assignment Rule (name: cl) CL- = 160-bl
 
 Assignment Rule (name: eb) eb = r*temp/f*log(bi/bl)
 
 Assignment Rule (name: enbc) enbc = r*temp/f*log(bi^2*ni/(bb^2*nb))
 
 Assignment Rule (name: ec) ec = r*temp/f*log(ci/cl)
 
 Assignment Rule (name: ena) ena = r*temp/f*log(nb/ni)
 
 Assignment Rule (name: kccf) kccf = g(ci, cl)*gcftr*g_cl
 
 Assignment Rule (name: kbcf) kbcf = g(bi, bl)*gcftr*g_bi
 
 Assignment Rule (name: knbc) knbc = gnbc
 
 Assignment Rule (name: v) v = (knbc*enbc+kbcf*eb+kccf*ec+gk*ek+gnaleak*ena)/(knbc+kbcf+kccf+gk)
 
 Assignment Rule (name: jnbc) jnbc = knbc*(v-enbc)
 
 Assignment Rule (name: jbcftr) jbcftr = kbcf*(v-eb)
 
 Assignment Rule (name: jccftr) jccftr = kccf*(v-ec)
 
 Assignment Rule (name: japl) japl = ap(bl, bi, cl, ci, kbi, kcl)*gapl
 
 Assignment Rule (name: japbl) japbl = ap(bb, bi, cb, ci, kbi, kcl)*gapbl
 
 Assignment Rule (name: jlum) jlum = ((-(jccftr+jbcftr))*vr+jac*(1+rat))/ionstr
 
 Assignment Rule (name: jnak) jnak = gnak*(v-epump)*(ni/np0)^3
 
 Assignment Rule (name: jnaleak) jnaleak = gnaleak*(v-ena)
 
Events (2)
 
  
gcftr = gcftron
 
  
gcftr = gcftrbase
 
Functions (2)
 
 ap lambda(ao, ai, bo, bi, ka, kb, (ao*bi-bo*ai)/(ka*kb*((1+ai/ka+bi/kb)*(ao/ka+bo/kb)+(1+ao/ka+bo/kb)*(ai/ka+bi/kb))))
 
 g lambda(xi, xo, xi*xo*log(xi/xo)/(xi-xo))
 
 plasma Spatial dimensions: 3.0  Compartment size: 1.0
 
 HCO3-
Compartment: plasma
Initial concentration: 22.0
Constant
 
 CL-
Compartment: plasma
Initial concentration: 130.0
Constant
 
 Na+
Compartment: plasma
Initial concentration: 140.0
Constant
 
 cell Spatial dimensions: 3.0  Compartment size: 1.0
 
 HCO3-
Compartment: cell
Initial concentration: 15.0
 
 CL-
Compartment: cell
Initial concentration: 60.0
 
 Na+
Compartment: cell
Initial concentration: 14.0
 
 lumen Spatial dimensions: 3.0  Compartment size: 0.1
 
 HCO3-
Compartment: lumen
Initial concentration: 32.0
 
  CL-
Compartment: lumen
 
Global Parameters (44)
 
 g_bi
Value: 0.2   (Units: dimensionless)
Constant
 
 g_cl
Value: 1.0   (Units: dimensionless)
Constant
 
 zeta
Value: 50.0   (Units: m^2 per L)
Constant
 
 kbi
Value: 1.0   (Units: mM)
Constant
 
 kcl
Value: 10.0   (Units: mM)
Constant
 
 gnbc
Value: 2.0   (Units: mmol per volt per sec per m^2)
Constant
 
 gapl
Value: 0.25   (Units: mmol per volt per sec per m^2)
Constant
 
 gapbl
Value: 0.005   (Units: mmol per volt per sec per m^2)
Constant
 
 vr
Value: 10.0   (Units: dimensionless)
Constant
 
 bi0
Value: 15.0   (Units: mM)
Constant
 
 buf
Value: 0.1   (Units: L per sec per m^2)
Constant
 
 gcftron
Value: 1.0   (Units: L per volt per sec per m^2)
Constant
 
 gcftrbase
Value: 7.0E-5   (Units: L per volt per sec per m^2)
Constant
 
 ek
Value: -0.085   (Units: volt)
Constant
 
 gk
Value: 1.0   (Units: mmol per volt per sec per m^2)
Constant
 
 gas constant
Value: 8.31451   (Units: J per mol per K)
Constant
 
 Faraday constant
Value: 96485.0   (Units: C per mol)
Constant
 
 temp
Value: 310.0   (Units: kelvin)
Constant
 
 ionstr
Value: 160.0   (Units: mM)
Constant
 
 gnak
Value: 3.125   (Units: mmol per volt per sec per m^2)
Constant
 
 np0
Value: 25.0   (Units: mM)
Constant
 
 epump
Value: -0.2   (Units: volt)
Constant
 
 gnaleak
Value: 0.4   (Units: mmol per volt per sec per m^2)
Constant
 
 jac
Value: 0.025   (Units: mmol per sec per m^2)
Constant
 
 rat
Value: 0.25   (Units: dimensionless)
Constant
 
 ton
Value: 60.0   (Units: second)
Constant
 
 toff
Value: 360.0   (Units: second)
Constant
 
 gcftr
Value: NaN   (Units: L per volt per sec per m^2)
 
   eb
Value: NaN   (Units: volt)
 
   enbc
Value: NaN   (Units: volt)
 
   ec
Value: NaN   (Units: volt)
 
   ena
Value: NaN   (Units: volt)
 
   kccf
Value: NaN   (Units: mmol per volt per sec per m^2)
 
   kbcf
Value: NaN   (Units: mmol per volt per sec per m^2)
 
   knbc
Value: NaN   (Units: mmol per volt per sec per m^2)
 
   v
Value: NaN   (Units: volt)
 
   jnbc
Value: NaN   (Units: mmol per sec per m^2)
 
   jbcftr
Value: NaN   (Units: mmol per sec per m^2)
 
   jccftr
Value: NaN   (Units: mmol per sec per m^2)
 
   japl
Value: NaN   (Units: mmol per sec per m^2)
 
   japbl
Value: NaN   (Units: mmol per sec per m^2)
 
   jlum
Value: NaN   (Units: L per sec per m^2)
 
   jnak
Value: NaN   (Units: mmol per sec per m^2)
 
   jnaleak
Value: NaN   (Units: mmol per sec per m^2)
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000327

Curator's comment: (updated: 27 Apr 2011 23:34:11 BST)

Time courses for varying ratios of duct cell to lumen volumes, vr, as in figure 6 of the original publication.
CFTR was activated (parameter ton) at 60 sec and deactivated (parameter toff) after 360 sec.
The simulations were performed using Copasi v4.6.33.

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