Table 2 Best parameter estimates for batch culture data (initial model: value I) and additionally optimized fed-batch culture data (refined model: value II)
From: Dynamic flux balance modeling to increase the production of high-value compounds in green microalgae
Symbol | Description | Value I | Value II | Units |
|---|---|---|---|---|
\(\alpha _{\mathrm {0}}\) | Offset parameter \(\upbeta\)-carotene synthesis | 4.2 \(\times 10^{-2}\) | 6.5 \(\times 10^{-2}\) | – |
\(\alpha _{\mathrm {1}}\) | Gain parameter \(\upbeta\)-carotene synthesis | 3.47 \(\times 10^{-5}\) | 7 \(\times 10^{-5}\) | m\(^2\) s \(\upmu\)mol\(^{-1}\) photons |
\(\gamma _{{\mathrm {max}}}\) | Max. intracell. chlorophyll to nitrate ratio | 0.69 | 0.75 | g Chl g\(^{-1}\) N |
\(\eta _{\mathrm {0}}\) | Offset parameter for chlorophyll specific eff. | 8 \(\times 10^{-4}\) | 0 | – |
\(\eta _{\mathrm {1}}\) | Gain parameter for chlorophyll specific eff. | 3.2 | 3.2 | – |
\(\lambda\) | Duration of the lag phase | 1.37 | 1.37 | d |
\(\omega _{\mathrm {N,min}}\) | Min. nitrogen cell quota | 0.021 | 0.021 | g N g\(^{-1}\,\)dw |
\(\omega _{\mathrm {N,max}}\) | Max. nitrogen cell quota | 0.101 | 0.101 | g N g\(^{-1}\,\)dw |
\(\bar{E}_{\mathrm {x,A}}\) | Crit. light int. for \(\upbeta\)-carotene synthesis | 32 | 420 | \(\upmu\)mol photons g\(^{-1}\) dw h\(^{-1}\) |
\(\bar{E}_{\mathrm {sat}}\) | Saturation light int. for chlorophyll to nitrate ratio | 75.5 | 75.5 | \(\upmu\)mol photons m\(^{-2}\)s\(^{-1}\) |
\(K_{\mathrm {E}}\) | Inhibition coeff. for chlorophyll to nitrate ratio | 12.5 | 12.5 | \(\upmu\)mol photons m\(^{-2}\)s\(^{-1}\) |
\(K_{\mathrm {m}}\) | Michaelis–Menten coeff. for NO\(_{3}\) uptake | 0.0013 | 0.0013 | g NO\(_{3}\) L\(^{-1}\) |
\(n_{\mathrm {Car}}\) | Hill coefficient for \(\upbeta\)-carotene synthesis | 4 | 2 | – |
ngam | Non-growth associated maintenance | 0.183 | 0.183 | mmol g\(^{-1}\) dw h\(^{-1}\) |
\(v_{\mathrm {Car,max}}\) | 3 \(\times 10^{-3}\) | 18 \(\times 10^{-3}\) | mmol g\(^{-1}\) dw h\(^{-1}\) | |
\({v}_{\mathrm {NO_3,max}}\) | Max. nitrogen uptake Max. \(\upbeta\)-carotene synthesis rate rate | 0.0309 | 0.0309 | g NO\(_{3}\) g\(^{-1}\)dw h\(^{-1}\) L\(^{-1}\) |
\(v_{\mathrm {NO_3,met,max}}\) | Max. nitrogen assimilation flux | 0.19 | 0.19 | mmol g\(^{-1}\) dw h\(^{-1}\) |
\(x_{\mathrm {eff}}\) | Photon efficiency | 0.0375 | 0.0375 | – |
\(x_{\mathrm {dim}}\) | Unit conversion factor | 3.6 | 3.6 | L g\(^{-1}\) |
\(\eta _{\mathrm {s}}\) | Smoothing factor | 4000 | 40 | – |