Tellurium notebooks—An environment for reproducible dynamical modeling in systems biology
Fig 3
A demo of an SBML/SED–ML encoding contained in a COMBINE archive showing two useful features of the encoding: Multiple parameter sets (A) and post–processing (B).
(A) Transient responses of M phase control [44]. This model was published with two parameter sets. One set is based on measurements from Xenopus oocyte extracts (top) whereas the other is based on measuremetns from intact embryos (bottom). (B) Phase portraits of representative state variables in the model. These variables are chosen after [44] and are as follows: total cyclin, doubly–phosphorylated MPF (PPMPF, the predominant inactive form of MPF [44]), active MPF, and time. Each pair of variables is plotted in this matrix. Y–axis variables are indicated in the rows of the plot and x–axis variables are indicated in the columns. The title of each subplot is given in terms of x vs y, e.g., the top left subplot shows total cyclin on the x–axis vs active MPF on the y–axis. Phase portraits can show transients (such as the initial response of total cyclin in the upper left corner in blue, which starts at 100 and decreases to its normal range) as well as limit cycles (exhibited by all three phase portraits in the upper part of (B)). The slope of a given region of the phase portrait is useful for showing the relative rate of change of two quantities. The green and orange curves show regions where one quantity changes rapidly with respect to another. These regions correspond to the rapid rise in active MPF due to positive feedback from MPF to its own self–activation, and the subsequent falloff of total cyclin due to cyclin degradation via a ubiquitin pathway activated by MPF. The plot in part (B) is derived from the parameter set for oocyte extract, corresponding to the top plot in part (A).