Aspirin

Salicylic acid (SA) clearance for three different dose ranges is modeled as an enzyme reaction.

Model number: 0280

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Description

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This is an enzyme conversion model for salicylic acid clearance simultaneously fitting three independent data sets using shared parameters. The initial concentrations of salicylic acid range over almost two orders of magnitude.

         kon1->        koff2->     Gp->
  LSA+LE<-----> LSAE <-----> LE+LP-----> (Low Dose) 
         <-koff1        <-kon2


         kon1->        koff2->     Gp->
  MSA+ME<-----> MSAE <-----> ME+MP-----> (Mid Dose)
         <-koff1        <-kon2


         kon1->        koff2->     Gp->
  HSA+HE<-----> HSAE <-----> HE+HP-----> (Hi Dose)
         <-koff1        <-kon2

    koff1=KD1*kon1   koff2=KD2*kon1

where LSA, MSA, and HSA are Salicylic Acid concentrations, HE, ME, and HE are the free enzyme concentrations, LSAE, MSAE, and HSAE are salicylic acid-enzyme complex concentrations, and LP, MP, and HP are the product concentrations. The parameters kon1, koff2, koff1, kon2, Gp, and the total amount of enzyme are the same for all three models.

Equations

Algebraic Equations

${\it k_{off_1}}={\it KD_1}\,{\it k_{on_1}}$
${\it k_{off_2}}={\it KD_2}\,{\it k_{on_2}}$

Ordinary Differential and Mass Balance Equations

${\frac {d}{dt}}{\it LSA}=-{\it k_{on_1}}\cdot {\it LSA}\cdot {\it LE}+{\it k_{off_1}} \cdot { \it LSAE}$
${\frac {d}{dt}}{\it LSAE}={\it k_{on_1}}\cdot {\it LSA}\cdot {\it LE}-{\it k_{off_1}} \cdot { \it LSAE}-{\it k_{off_2}}\cdot {\it LSAE}+{\it k_{on_2}}\cdot {\it LE}\cdot{\it LP}$
${\frac {d}{dt}}{\it LP}={\it k_{off_2}}\cdot {\it LSAE}-{\it k_{on_2}}\cdot {\it LE}\cdot{\it LP -G_p \cdot LP}$
${\it E_{tot}}={\it LE}+{\it LSAE}$

${\frac {d}{dt}}{\it MSA}=-{\it k_{on_1}}\cdot {\it MSA}\cdot {\it ME}+{\it k_{off_1}} \cdot { \it MSAE}$
${\frac {d}{dt}}{\it MSAE}={\it k_{on_1}}\cdot {\it MSA}\cdot {\it ME}-{\it k_{off_1}} \cdot { \it MSAE}-{\it k_{off_2}}\cdot {\it MSAE}+{\it k_{on_2}}\cdot {\it ME}\cdot{\it MP}$
${\frac {d}{dt}}{\it MP}={\it k_{off_2}}\cdot {\it MSAE}-{\it k_{on_2}}\cdot {\it ME}\cdot{\it MP -G_p \cdot MP}$
${\it E_{tot}}={\it ME}+{\it MSAE}$

${\frac {d}{dt}}{\it HSA}=-{\it k_{on_1}}\cdot {\it HSA}\cdot {\it HE}+{\it k_{off_1}} \cdot { \it HSAE}$
${\frac {d}{dt}}{\it HSAE}={\it k_{on_1}}\cdot {\it HSA}\cdot {\it HE}-{\it k_{off_1}} \cdot { \it HSAE}-{\it k_{off_2}}\cdot {\it HSAE}+{\it k_{on_2}}\cdot {\it HE}\cdot{\it HP}$
${\frac {d}{dt}}{\it HP}={\it k_{off_2}}\cdot {\it HSAE}-{\it k_{on_2}}\cdot {\it HE}\cdot{\it HP -G_p \cdot HP}$
${\it E_{tot}}={\it HE}+{\it HSAE}$

Initial Conditions

${\it LSA} \left( 0 \right) ={\it LSA_{tot}}$ , ${\it MSA} \left( 0 \right) ={\it MSA_{tot}}$ , ${\it HSA} \left( 0 \right) ={\it HSA_{tot}}$ .
${\it LSAE} \left( 0 \right) ={\it 0}$ , ${\it MSAE} \left( 0 \right) ={\it 0}$ , ${\it HSAE} \left( 0 \right) ={\it 0}$ .

The equations for this model may also be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

Download JSim project file

References


 IH Benedek, AS Joshi, HJ Pieniaszek, SY King and DM Kornhauser;
 Variability in the pharmacokinetics and pharmacodynamics of low
 dose aspirin in healthy male volunteers. J. Clin. Pharmacol 35:
1181-1186, 1995.

  
 L Aarons, K Hopkins, M Rowland, S Brossel, and JF Thiercelin: Route of
 administration and sex differences in the pharmacokinetics of aspirin,
 administered as its lysine salt. Pharmaceutical Res 6: 660-666, 1989.  


 LF Prescott, M Balali-Mood, JA Critchley, AF Johnstone, AT Proudfoot;
 Diuresis or urinary alkalinisation for salicylate poisoning?.
 Br Med J, 285 1383-1384, 1982.

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Key Terms

aspirin, salicylic acid, enzyme, clearance, covariance, confidence limits, optimization, Data, Tutorial

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Acknowledgements

Please cite www.physiome.org in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

[This page was last modified 09Feb10, 10:20 am.]

Model development and archiving support at physiome.org provided by the following grants: NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.