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. 2019 May 24;7:122. doi: 10.3389/fbioe.2019.00122
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)
S¯ 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