| S |
Substrate concentration (g/L) |
| P |
Product concentration (g/L) |
| E |
Enzyme concentration (g/L) |
| ES |
Enzyme substrate complex concentration (g/L) |
|
k1, k−1, k2
|
Reaction rates [h−1] |
| ẋ(t) |
Ordinary differential equations (ODE) |
|
x(t) |
Internal model states |
|
u(t) |
External stimuli |
| rmax |
Maximum specific reaction rate [h−1] |
| Ks |
Half saturation constant [g*L−1] |
| θ |
Best currently available estimations of the set of parameters which must be determined (rmax, KS) |
| ŷ(t) |
Measured response variables |
|
y(t) |
Simulated response variables (substrate and product) |
|
g(x(t)) |
Set of relations between the measured response variables ŷ(t) and the internal model states x(t) |
| η(t) |
Measurement errors |
| COV |
Parameter variance-covariance matrix |
| Σθ
|
Covariance of the measuring noise |
|
nmes
|
Number of measuring points |
|
nresp
|
Number of responses |
|
nexp
|
Number of experiments |
| J |
Sum of squares of residuals |
|
y0
|
Initial conditions for (t = t0 = 0) |
|
tsp
|
Sampling times (n = 2) |
|
Sensitivity of the responses to parameter values |
| FIM |
Fisher information matrix |
| φ |
Experiment design vector, including sampling times, initial values and other experimental inputs for the future experiment |
| Ω |
Measure of the FIM, i.e. optimal experimental design criterium |