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

# Progress3.React

Sequence of three uncatalyzed 1st order irreversible reactions.

Model number: 0269

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## Description

In a single compartment A is converted to B in an irreversible reaction and B is converted to C in an irreversible reaction. The system conserves mass. At any time, A(t)+B(t)+C(t) = A(0)+B(0)+C(0).

## Equations

#### Ordinary Differential Equations

$\large {\frac {d}{dt}}A \left( t \right) =-{\it k_a}\cdot A \left( t \right)$

$\large {\frac {d}{dt}}B \left( t \right) ={\it k_a}\cdot A \left( t \right) -{\it k_b}\cdot B \left( t \right)$

$\large {\frac {d}{dt}}C \left( t \right) ={\it k_b}\cdot B \left( t \right)$

#### Initial Conditions

$\large {\it A} \left( 0 \right) ={\it A_0}$ ,   $\large {\it B} \left( 0 \right) ={\it B_0}$ ,   and   $\large {\it C} \left( 0 \right) ={\it C_0}$ .

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.

## References

  None



## Related Models

Single Compartment Models:

Two Compartment Models:

N>2 Compartment Models:

Osmotic Exchange:

Pharmacology:

## Key Terms

Progress curves, irreversible reactions, first order kinetics, tutorial, progress3.react