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Cardiac Physiome Society workshop: November 6-9, 2017 , Toronto

# Comp1Reaction

Models single compartment with reversible reaction C becoming D and D becoming C with rate constants Gc2d and Gd2c. Uses non-physiological units.

Model number: 0243

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## Description

In a single compartment, C is converted to D with rate constant Gc2d, and D is converted back to C with rate constant Gd2c. This is an "in vitro" beaker experiment. Numeric and analytic solutions are given. The concentrations at long time are calculated.

## Equations

#### Ordinary Differential Equations

$\large {\frac {d}{dt}}C \left( t \right) =-{\frac {{\it G_{c2d}}\ \cdot C \left( t \right) }{V}}+{\frac {{\it G_{d2c}}\cdot {D} \left( t \right) }{V}}$
$\large {\frac {d}{dt}} {D} \left( t \right) =+{\frac {{\it G_{c2d}}\cdot C \left( t \right) }{V}}-{\frac {{\it G_{d2c}}\cdot {D} \left( t \right) }{V}}$

#### Initial Conditions

$\large {\it C} \left( 0 \right) ={\it C_0}$ ,   $\large {\it D} \left( 0 \right) ={\it D_0}$ .

#### Analytic Solutions

$\large {\it C_{analytic}}= \frac {\left( {\it G_{d2c}}\, \left( {\it D_0}+{\it C_0} \right) + \left( {\it G_{c2d}}\,{\it C_0}-{\it D_0}\,{\it G_{d2c}} \right) {e^{-{ \frac { \left( {\it G_{c2d}}+{\it G_{d2c}} \right) t}{V}}}} \right) } { \left( {\it G_{c2d}}+{\it G_{d2c}} \right) }$
$\large {\it D_{analytic}}= \frac {\left( {\it G_{c2d}}\, \left( {\it D_0}+{\it C_0} \right) + \left( {\it G_{c2d}}\,{\it C_0}-{\it D_0}\,{\it G_{d2c}} \right) {e^{-{ \frac { \left( {\it G_{c2d}}+{\it G_{d2c}} \right) t}{V}}}} \right) } { \left( {\it G_{c2d}}+{\it G_{d2c}} \right) }$

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.

## References

 None.



## Related Models

Single Compartment Models:

Two Compartment Models:

N>2 Compartment Models:

Osmotic Exchange:

Pharmacology:

## Key Terms

Course, compartment, compartmental, tutorial, conversion, reaction, flux