Oriol Basallo ^1,2,3 Abel Lucido ^1,2,3 Albert Sorribas ^1,2,3 Alberto Marin-Sanguino ^1,2,3 Ester Vilaprinyo ^1,2,3 Emilce Martinez ^1,2,3,4 Abderrahmane Eleiwa ^1,2,3 Rui Alves ^1,2,3*

• ¹ Grup de Recerca Consolidat de la Generalitat de Catalunya 2021 SGR 1353 MathSy2Bio, Lleida, Spain
• ² Lleida Institute for Biomedical Research (IRBLleida), Lleida, Catalonia, Spain
• ³ Ciències Mèdiques Bàsiques, Universitat de Lleida, Lleida, Catalonya, Spain
• ⁴ National Institute of Agricultural Technology (INTA), Cordoba, Cordoba, Argentina

Terpenoids are valued chemicals in the pharmaceutical, biotechnological, cosmetic, and biomedical industries. Biosynthesis of these chemicals relies on polymerization of Isopentenyl di-phosphate (IPP) and/or dimethylallyl diphosphate (DMAPP) monomers, which plants synthesize using a cytosolic mevalonic acid (MVA) pathway and a plastidic methyleritritol-4-phosphate (MEP) pathway. Circadian regulation affects MVA and MEP pathway activity at three levels: substrate availability, gene expression of pathway enzymes, and utilization of IPP and DMAPP for synthesizing complex terpenoids. There is a gap in understanding the interplay between the circadian rhythm and the dynamics and regulation of the two pathways. In this paper we create a mathematical model of the MVA and MEP pathways in plants that incorporates the effects of circadian rhythms.We then used the model to investigate how annual and latitudinal variations in circadian rhythm affect IPP and DMAPP biosynthesis. We found that, despite significant fluctuations in daylight hours, the amplitude of oscillations in IPP and DMAPP concentrations remains stable, highlighting the robustness of the system. We also examined the impact of removing circadian regulation from different parts of the model on its dynamic behavior. We found that regulation of pathway substrate availability alone results in higher sensitivity to daylight changes, while gene expression regulation alone leads to less robust IPP/DMAPP concentration oscillations. Our results suggest that the combined circadian regulation of substrate availability, gene expression, and product utilization, along with MVA-and MEP-specific regulatory loops, create an optimal operating regime. This regime maintains pathway flux closely coupled to demand and stable across a wide range of daylight hours, balancing the dynamic behavior of the pathways and ensuring robustness in response to cellular demand for IPP/DMAPP. Table 6. List of models and the regulation modules they contain. Circadian regulation of… Pathway substrate availability MVA and MEP pathway gene expression IPP and DMAPP consumption Model A No No No Model B Yes No No Model C No Yes