Applications of Positive Semigroups for Modeling a Dually-Age-Structured Population
聽Cyanobacteria take in atmospheric CO2 and use light energy to synthesize聽the necessary organic compounds to gain energy and grow biomass, releasing oxygen as a byproduct. Their biomass and metabolic capabilities have wide-ranging and valuable applications in many environmentally impactful areas such as, biofuel and bioplastic production, and wastewater treatment. Icosahedral nanostructures called carboxysomes drive photosynthesis by concentrating all of the carbon near the key carbon-fixing enzyme, RuBisCO.聽As these structures are inherited discretely through many generations, improving photosynthetic capability relies on an understanding of how carboxysome functionality changes over time. In this work, the McKendrick-von Foerster PDE is used as the base-case age-structured population model and is shown to generate a strongly continuous one-parameter semigroup. Additional candidate models are presented which seek to incorporate carboxysome age-structuring in the population as adaptations or perturbations of the McKendrick model.