View source for Quasi-steady-state analysis example

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Description of the quasy-steady-state approximation method is done in the section "[[Quasi-Steady-State Analysis]]". Below we use the notation given there.

==Reproducing a test case in BioUML==

To reproduce a test case below in the [[BioUML]] workbench, go to the <b>Analyses</b> tab in the navigation pane and follow to ''analyses'' > ''Methods'' > ''Differential algebraic equations''.

After double click on ''Quasi-Steady-State Analysis'', a new tab with analysis opens.

Set the following analysis settings:

*'''Input diagram''' = ''data/Examples/DAE models/Data/Diagrams/Simplest_enzyme_reaction''
*'''Result table''' = ''data/Collaboration/Demo/Data/Temp/Quasi-Steady-State Analysis results''
*'''Initial time''' = 0.0
*'''Completion time''' = 0.01
*'''Time increment''' = 0.001

<br>[[File:qssa_figure_1.png]]<br><br>

After you click the <b>Run</b> button and the calculations are finished, you can see the result table, including ranges of fast dynamics of diagram entities.

Ready analysis results can be found in the table:

''data/Examples/DAE models/Data/Quasi-Steady-State Analysis results''

==Description of the test case==

As an example we consider the simplest enzyme reaction

[[File:qssa_formula_1.png]]

which involves an enzyme ''E'' binding to a substrate ''S'' to form a complex ''ES'' and its dissociation into a product ''P'' and the enzyme ''E''.

Let us find the conditions under which the concentration of the complex ''ES'' is quasi-stationary in time ''t'' = 0. To do this, we consider the expressions

[[File:qssa_formula_2.png]]

which result in the following derivatives

[[File:qssa_formula_3.png]]

Next, we find the formulas for ''δt<sub>ES</sub>'' and ''r<sub>ES</sub>'':

[[File:qssa_formula_4.png]]

Thus, the complex ''ES'' is in quasi-steady state at ''t'' = 0 only when ''δt<sub>ES</sub>'' << 1, i.e.

[[File:qssa_formula_5.png]]

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