Table 5.
Error results comparing the application of empirical balanced truncation, lumping, and the combined method of model reduction to the ERK activation model
| Dimension | EBT error | Lumping error | Stiffness | Combined error |
|---|---|---|---|---|
| 75 | 0.76% | ≈0% ∗ | 42658 | − |
| 50 | # | 0.01% | 42633 | − |
| 25 | # | 0.52% | 10664 | − |
| 15 | # | 1.26% | 7934 | − |
| 14 | # | 2.21% | 7934 | − |
| 13 | # | 2.29% | 7934 | − |
| 12 | # | 1.21% | 1591 | − |
| 11 | # | 3.07% | 236 | − |
| 10 | # | 6.02% | 264 | 2.84% |
| 9 | # | 10.96% | 211 | 4.02% |
| 8 | # | 13.12% | 43 | 4.32% |
| 7 | # | 14.18% | 42 | 4.77% |
| 6 | # | 29.53% | 44 | 13.08% |
| 5 | # | 39.03% | 45 | 20.81% |
| 4 | # | 46.47% | 212 | 31.09% |
| 3 | # | 54.67% | 42 | 34.58% |
| 2 | # | 53.52% | 18 | 41.10% |
| 1 | # | 55.73% | 1 | 50.46% |
Note: ‘ #’ implies Matlab could not numerically simulate this reduction using ode15s due to issues associated with stiffness. ‘-’ implies the reduction error at this point was equal to the lumping error. The errors stated represent the maximal relative error between the original and reduced systems when simulated to steady-state under the introduction of agonist increasing the rate of EGF receptor binding by 50% at t=0. ∗ implies that the error was within the numerical tolerance of the simulator