Table 5.
Rate laws and their reaction categories. This table gives an overview of all rate laws that are currently implemented in the software SBMLsqueeezer 2. All rate laws are described in detail in [67, p. 17–38]. The key idea of the algorithm in this paper is to separate the list of available rate laws from more general reaction categories to which these rate laws can be applied. With this separation, extending this list and to add more specific rate laws becomes very straightforward to do as long as each such rate law specifies to which categories it can be assigned. Table 4 provides a detailed overview of all categories. Example reactions for all categories can be seen in Fig. 2. The rate laws mentioned in this table are again families of equations. The precise structure of the equation that is generated for a specific reaction can vary, depending on several reaction properties, e.g., how many and which kind of modifiers participate in this reaction, if it is reversible, etc. The creation of the specific equation including its parameters and required units is therefore the next step of the algorithm
| Rate laws | Categories | Citation |
|---|---|---|
| Additive Model Linear | B, H, I, J, K, L | [45] |
| Additive Model Non Linear | B, H, I, J, K, L | [46] |
| Common Modular Rate Law (CM) | C, D, E, F, I, J | [35] |
| Convenience Kinetics | C, D, E, F, H, I, J | [16] |
| Direct Binding Modular Rate Law (DM) | C, D, E, F, I, J | [35] |
| Enzymatic Rate Law for Competitive Inhibition of Irreversible Uni-reactant Enzymes by Non-Exclusive Non-Cooperative Inhibitors | C, H, I | SBO |
| Enzymatic Rate Law for Irreversible Non-modulated Non-interacting Reactant Enzymes | C, D, E, F, G, H | SBO |
| Force Dependent Modular Rate Law (FM) | C, D, E, F, I, J | [35] |
| Generalized Mass Action | A, H, I, J | [29], [30, p. 14–17] |
| Hill Equation | B, C, G, H, I, J | [14], [70, p. 314] |
| Hill-Hinze Equation | B, H, I, J, K, L | [42] |
| Hill-Radde Equation | B, H, I, J, K, L | [43, 44] |
| H-System | B, H, I, J, K, L | [51] |
| Michaelis-Menten | C, H, I, J | [71] |
| NetGenerator Linear | B, H, I, J, K, L | [46] |
| NetGenerator Non-Linear | B, H, I, J, K, L | [46] |
| Ordered Mechanism (compulsory-order ternary-complex mechanism) | D, E, H, I, J | [72, 73], [70, p. 167] |
| Ping-Pong Mechanism (substituted enzyme mechanism) | E, H, I, J | [72, 73], [70, p. 169] |
| Power Law Modular Rate Law (PM) | C, D, E, F, I, J | [35] |
| Random Order Ternary-Complex Mechanism | D, E, H, I, J | [72, 73], [70, p. 169] |
| Simultaneous Binding Modular Rate Law (SM) | C, D, E, F, I, J | [35] |
| S-System | B, H, I, J, K, L | [50, 51, 74–76] |
| Vohradský’s equation | B, H, I, J, K, L | [47, 48] |
| Weaver’s equation | B, H, I, J, K, L | [49] |
| Zeroth Order Forward Generalized Mass-Action | A, H, I, J, K, L | [70, p. 6] |
| Zeroth Order Reverse Generalized Mass-Action | A, H, I, J, K, L | [70, p. 6] |