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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
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