Design of Pathway-Level Bioprocess Monitoring and Control Strategies Supported by Metabolic Networks - Measurement, Monitoring, Modelling, and Control of Bioprocesses - page 206

Table 2 Elementary mode reduction results for three distinct culture time points
t = 30.7 h t = 71 h t = 119 h

#EM k #EM k #EM k

EM228 a EM228 a

EM29 0.5324 0.9691 0.0745

EM193 a EM193 a EM153 0.2148 0.4303 0.0370

EM128 0.1480 EM219 0.1038 EM144 0.0110

EM189 a EM185 a EM189 a 0.1259 0.0773 0.0075

EM189 a EM18 a EM159 0.0021 0.0554 0.0067

EM290 a

EM51 0.0002 EM290 0.0449 0.0052

EM185 a EM206 0.0028 0.0010

EM18 a

0.0002 EM45 0.0007

EM120 0.0006

EM177 0.0003

a

Elementary modes that are selected at least twice

5 Pathway-Level Process Control

Upon the identification of the most significant elementary modes, macroscopic
dynamic models can be derived with implicit intracellular structure, which can
then be used for process monitoring and control. For a stirred tank bioreactor, such
material balance equations take the following general form:

dc
dt ¼ bX D ð c c in Þþ Q :

ð 11 Þ

In Eq. ( 11 ), the state space vector, c, is formed by the concentrations of
extracellular compounds, X is the biomass concentration, D is the dilution rate, c in
is the concentration of extracellular compounds in the inlet stream, and Q is the
vector of gas-liquid transfer rates of volatile extracellular compounds. Note that
Eq. ( 11 ) is analogous to the state-space equation proposed by Dochain and Bastin
to design adaptive state estimation and control algorithms [ 1 ]. The main difference
lies in the fact that the extracellular fluxes, b, and the intracellular fluxes, v, are
functions of the elementary flux mode weighting factors instead of the traditional
reaction kinetics:

¼ k

v
b

EM
A 0 EM

ð 12 Þ

An important implication is that any state-space solution of Eqs. ( 11 , 12 ) obeys
the steady-state stoichiometric constraints imposed by the metabolic network.
The main difficulty in deriving these models is the definition of the elementary
mode weighting factors as functions of environmental properties. Provost and
Bastin [ 9 ] employed Michaelis-Menten kinetic laws, resulting in very complex
nonlinear systems, which are very difficult to identify. Teixeira et al. [ 11 ] have
developed hybrid macroscopic models structured by elementary modes using
neural networks to model the respective weighting factors. In any case, the