Mathematical Biology Seminar - Sabina Altus
Sabina Altus, Department of Applied Mathematics, University of Colorado Boulder
Asymptotic Behavior of a Highly-Structured Population as a Semigroup Perturbation
Cyanobacteria are photosynthetic microorganisms with promising applications in renewable energy and agriculture as they are able to convert light energy into more stable forms of chemical energy, such as biomass, as well as kinetic energy. This process occurs within microcompartments, called carboxysomes, which are passed discretely, and persist through many cell cycles before they ultimately disintegrate. Carboxysome productivity is a key factor driving cell growth, and is thought to decrease over time.
To investigate this claim, we have developed a multi-structured model for the evolution of a cyanobacteria population. The model is formulated as a partial differential equation wherein demographic parameters describing birth, death, and growth processes are all age-, size-, and carboxysome-age-dependent. The evolutionary system is analyzed along with its associated linear operator and the strongly-continuous semigroup it is shown to generate. The reproductive process in this highly structured population is expressed as a perturbation to the semigroup by a step response leading to a Stieltjes-type renewal equation, and ultimately allows us to characterize the perturbed semigroup and its asymptotic behavior.
Monday, August 31, 2020 at 4:00pm to 5:00pmVirtual Event