Table 2.

Best parameter estimates for batch culture data (initial model: value I) and additionally optimized fed-batch culture data (refined model: value II)

Symbol	Description	Value I	Value II	Units
${\mathit{\alpha }}_0$	Offset parameter $\mathrm{\beta }$-carotene synthesis	4.2 $\times {10}^{-2}$	6.5 $\times {10}^{-2}$	–
${\mathit{\alpha }}_1$	Gain parameter $\mathrm{\beta }$-carotene synthesis	3.47 $\times {10}^{-5}$	7 $\times {10}^{-5}$	m${}^2$ s $\mathrm{\mu }$mol${}^{-1}$ photons
${\mathit{\gamma }}_{\max }$	Max. intracell. chlorophyll to nitrate ratio	0.69	0.75	g Chl g${}^{-1}$ N
${\mathit{\eta }}_0$	Offset parameter for chlorophyll specific eff.	8 $\times {10}^{-4}$	0	–
${\mathit{\eta }}_1$	Gain parameter for chlorophyll specific eff.	3.2	3.2	–
$\mathit{\lambda }$	Duration of the lag phase	1.37	1.37	d
${\mathit{\omega }}_{\mathrm{N},\min }$	Min. nitrogen cell quota	0.021	0.021	g N g${}^{-1}$dw
${\mathit{\omega }}_{\mathrm{N},\max }$	Max. nitrogen cell quota	0.101	0.101	g N g${}^{-1}$dw
${\overline{E}}_{\mathrm{x},\mathrm{A}}$	Crit. light int. for $\mathrm{\beta }$-carotene synthesis	32	420	$\mathrm{\mu }$mol photons g${}^{-1}$ dw h${}^{-1}$
${\overline{E}}_{\mathrm{sat}}$	Saturation light int. for chlorophyll to nitrate ratio	75.5	75.5	$\mathrm{\mu }$mol photons m${}^{-2}$s${}^{-1}$
$K_{\mathrm{E}}$	Inhibition coeff. for chlorophyll to nitrate ratio	12.5	12.5	$\mathrm{\mu }$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 $\mathrm{\beta }$-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. $\mathrm{\beta }$-carotene synthesis rate rate	0.0309	0.0309	g NO${}_3$ g${}^{-1}$dw h${}^{-1}$ L${}^{-1}$
$v_{{\mathrm{NO}}_3,\mathrm{met},\max }$	Max. nitrogen assimilation flux	0.19	0.19	mmol g${}^{-1}$ dw h${}^{-1}$
$x_{\mathrm{eff}}$	Photon efficiency	0.0375	0.0375	–
$x_{\dim }$	Unit conversion factor	3.6	3.6	L g${}^{-1}$
${\mathit{\eta }}_{\mathrm{s}}$	Smoothing factor	4000	40	–