André Franz¹, Hyun-Seob Song², Doraiswami Ramkrishna², Achim Kienle^1,3

¹Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany
²Purdue University, Forney Hall of Chemical Engineering, 480 Stadium Mall Drive, West Lafayette, IN 47907, USA
³Otto-von-Guericke University, Chair of Automation/Modeling, 30106 Magdeburg, Germany

The organism used throughout this study, Cupriavidus necator¹⁾ (DSM 428, ATCC 17699, NCIB 10442) was obtained from DSMZ GmbH Braunschweig, Germany, as vacuum dried culture. The strain was cultivated with complex Luria-Bertani (LB) medium (tryptone 10g/L, yeast extract 5 g/L, NaCl 5 g/L) or with the M81 medium as recommended by the DSMZ. The composition is given in Table 1. For solid media 1.5 % (w/v) agar was added. Permanent cultures were prepared in a mixture of glycerol:M81 medium (1:4) and stored at -80 °C. 0.2 ml of these glycerol stocks were employed as inocula for liquid cultures. All chemicals were from Carl Roth GmbH (Karlsruhe, Germany).

Table 1: Composition of Medium M81

Cells inoculated on agar plates were cultured at 30 °C in an incubator-oven (Memmert, Schwabach, Germany) for different time periods. Shake-flask cultivations were carried out at 27 °C in a rack-shaker system (Kühner AG, Birsfelden, Switzerland) at 150 rpm in baffled 1000 ml shake-flasks containing 200 ml of the medium.
Cultivation in the bioreactor: C. necator was grown heterotrophically in a 7 liter fermenter (Biostat C, Sartorius, BBI Systems, Melsungen, Germany) with a 5 liter working volume. The temperature was kept constant at 30 °C and the pH was automatically maintained at pH 6.8 by adding 2 M NaOH as corrective agent. The culture broth was agitated at 400 rpm and dissolved oxygen was maintained above 50 % air saturation by changing the oxygen and nitrogen flow rate mixed with an air stream. Total flow rate was 1.5 L/min.

Cell growth was monitored by measuring the optical density at 600 nm using a Ultrospec 500 spectrophotometer (GE Healthcare, Buckinghamshire, UK). For dilution, NaCl (0.98 % (w/v)) was used when necessary. For the determination of the cell dry weight, 3 x 10ml of the culture broth were centrifuged in pre-weighed glass tubes for 15 minutes at 3000 x g. The pellets were washed in 0.98 % NaCl and subsequently dried in a freeze-dryer (Christ, Osterode am Harz, Germany). Enzymatic activities of glucose-6-phosphate dehydrogenase were determined as described in Bergmeyer (1995) in lysates obtained by disruption with a high-pressure homogenizer Emulsiflex-C5 (Avestin, Ottawa, Canada). PHB content was measured as crotonic acid, formed by acid depolymerization of PHB according to Law and Slepecky (1961). Cell pellets, harvested by centrifugation, were dissolved in methylene chloride by rapid mixing and afterwards boiled for 10 min. After the samples were cooled down, they were centrifuged at 3000 × g for 15 min and the supernatants were carefully removed and collected in glas tubes. This procedure was repeated three times. The supernatants were then evaporated and the remaining PHB-containing samples were digested in 2 ml H2SO4 (96 %) at 100 °C for 30 min and subsequently diluted with concentrated H2SO4. UV absorbance spectra were measured with an UV/VIS spectrophotometer V-560 (Jasco, Gross-Umstadt, Germany). The concentration of crotonic acid was calculated from a set of reference standards. Ammonium chloride concentration in culture supernatants broth was measured by determining NH3 with a VITROS DT60 II Chemistry System and VITROS NH3 MicroSlide from Ortho-Clinical Diagnostics (Neckargemünd, Germany) using the manufacturers instructions. Concentrations of glucose and fructose in supernantants were determined with a D-Glucose/D-Fructose test kit from R-Biopharm (Darmstadt, Germany) using the manufacturers recommended procedure.

In this study the metabolic network of Katoh et. al. [cite] was used and extended with a fructose uptake pathway, a more detailled penthose phosphate pathway and a PHB degradation pathway, see figure (x). ATP, ADP, CO2 and O2 are not drawn in the figure, but included in the network. All network reactions can be found in appendix xx.

From this network elementary modes were calculated by using METATOOL 5.1 [cite] and the number of these modes were reduced by metabolic yield analysis [cite].

The state $\bf y$ of a metabolic system can be described by the vector of external species concentration $\bf x$, the vector of specific internal species concentration $\bf m$, the vector of enzyme levels $\bf e$ and the biomass concentration $c$: ` y=[[x],[m],[e],[c]] `

In hybrid cybernetic model (HCM) approach[1] the substrate uptake in microorganisms is assumed as being distributed in a regulated way among EMs based on a steady-state assumption on intracellular metabolite concentrations. But this steady-state assumption is only true for internal metabolites with fast dynamics. Storage materials (e.g. PHB) or certain other cell compartments can have slow dynamics. Therefore it is necessary to split m into the vector mf of nm;f intracellular metabolites with fast dynamics and the vector ms of nm;s intracellular metabolites with slow dynamics. Similary, Sm is splitted into Sm;f and Sm;s:

Thus, the total biomasse concentration (e.g., c) consists of metabolites with fast and with slow dynamics. Since the steady-state assumption is not true for metabolites with slow dynamics and all internal metabolite concentration are based on total biomass concentration, the steady-state assumption do not hold even for metabolites with fast dynamics. To circumvent this problem it is convenient to divide the total biomass into two components, e.g. one component which includes the metabolites with slow dynamics and one component which includes the metabolites with fast dynamics. Usually the later one includes all the proteins and nucleic acids and one can therefore postulate that this component is the catalytically active component. Then the internal metabolite concentration can be based on the catalytically active biomass component. Since the catalytically active component is responsible for cell growth, c denotes now the concentration of this catalytically active component and no longer the concentration of total biomass. Thus, the the steady-state assumption for metabolites with fast dynamics holds (e.g.,