Fig. 1

A model of the light-limited chemostat. a Schematic representation. The light source irradiates a culture vessel of depth \(z_m\). The culture is aerated with \(\text {CO}_{2}\)-enriched air and nutrients are well mixed. Different from other nutrients, the photon flux is inhomogeneous and decays exponentially with depth. b A coarse-grained single-cell model. The model describes carbon assimilation and metabolism, light harvesting, photosynthesis, and protein translation by ribosomes. External inorganic carbon \(c_i^x\) is transported into the cell (\(v_t\)), assimilated (\(v_c\)) into organic carbon precursors \(c_3\) from which amino acids aa are synthesized (\(v_m\)). Amino acids serve as precursors for protein synthesis (\(\gamma _j\)). The model consists of seven coarse-grained protein complexes, including ribosomes R, transport proteins \(E_T\), metabolic enzymes \(E_C\), \(E_M\), \(E_Q\), photosynthetic units PSU, and quota proteins \(P_Q\). All catalyzed reactions are fueled by energy units e that are produced by activated photosynthetic units \(PSU^{*}\) (\(v_2\)). Activation of resting photosynthetic units \(PSU^0\) is facilitated by light. High light intensities cause photodamage (\(v_i\)), i.e., the degradation of PSU into its constituent amino acids. The model also incorporates a general protein degradation term (\(d_p\)), as well as an energy maintenance reaction (\(v_{me}\)). c The optimized specific growth rate as a function of light intensity, shown together with experimental values for Synechocystis sp. PCC 6803 obtained from quantitative growth experiments in an optically thin turbidostat [15, 54]. d Proteome allocation within the system is formulated as an optimization problem (parsimonious allocation) such that the ribosome fractions \(\beta _j\) translating the different proteins give rise to a maximal specific growth rate \(\mu\)