Figure 5

Calculation of the derivatives at a specific point in time. First, the vector for saving the derivatives of all quantities$\dot{\overrightarrow{Q}}$ is set to the null vector$\overrightarrow{0}$. Then the rate rules of the model are processed by solving the function$\overrightarrow{g}(\overrightarrow{Q},t)$, which can change$\dot{\overrightarrow{Q}}$ in some dimensions. After that for every reaction channel R _j its velocity J _j is computed. The derivatives of each species (with index i) participating in the currently processed reaction channel R _j are updated in each step adding the product of the stoichiometry n _{i j} and the reaction’s velocity J _j . In this figure, the stoichiometric values n _{i j} in the matrix N are assumed to be constant for the sake of simplicity. These values can be variable. Before Level 3, SBML provided StoichiometryMath elements that could be used for a direct computation of the stoichiometry. In Level 3, the StoichiometryMath element has been removed and these values can be changed by treating them as the subject of assignment rules. In both cases, the values for n _{i j} have to be updated in each simulation step.