Steady State AnalysisΒΆ

The dynamics of a biochemical network is described by the system equation

\frac{d}{dt}\mathbf{s}(t) = \mathbf{N} \mathbf{v}(\mathbf{s}(t),\mathbf{p},t),

where \mathbf{s} is the vector of species concentrations, \mathbf{p} is a vector of time independent parameters, and t is time. The steady state is the solution to the network equations when all the rates of change are zero. That is the concentrations of the floating species, \mathbf{s} that satisfy:

\mathbf{N} \mathbf{v}(\mathbf{s}(t),\mathbf{p},t) = 0

The steady state is easily calculated using the steady state method:

>>> rr.steadyState()

The call to steadyState returns a value that represents the sum of squares of the rates of change. Therefore the smaller this value the more likely the steady state solution has been found. Often a value less that 10E-6 indicates a steady state has been found. After a successful call all the species levels will be at their steady state values.

Steady state values can be obtained using getSteadyStateValues() and steadyStateSelections() can be used to decide what values to return. For example the following would retrieve a single value:

>>> rr.steadyStateSelections = ['S1']
>>> rr.getSteadyStateValues()
array([ 0.54314239])

The following methods deal with steady state analysis:


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