I will briefly review classic structured population models (based mainly on the classical deterministic age-structured McKendrick model) and show how these PDEs can be used to describe problems in physical biology. Two applications are evolving populations of cells stratified by size, added size, and/or age, and waiting times in kinetic proofreading reactions. These applications not only highlight the utility of classical PDE models, but also motivate the development of new theoretical extensions. Here, I will present a stochastic framework of structured population models that can developed using ideas from gas kinetic theory. The high-dimensional kinetic equations can be marginalized in different ways to define PDEs for different moments and correlations, which can be closed under certain conditions on individual parameters such as birth and death rates. The kinetic theory is shown to unify Markovian birth-death type master equations with deterministic age-dependent birth/death rate models. The new kinetic theory can be further extended to track multiple attributes (such as a whole panel of gene expression levels) and generational subpopulations.
The Ser/Thr protein kinase Akt is a key signaling enzyme that participates in the regulation of cell growth and other physiologic processes, and its dysregulation contributes to many cancers. Notably, mTORC2-mediated Akt C-tail phosphorylation on Ser473 acts as a major, well-defined regulatory site and is commonly measured as a proliferative mark in cancer. It has been poorly understood how mTORC2 recognizes and phosphorylates Akt1 on Ser473. Here, we have provided a detailed portrait of how mTORC2 but not mTORC1 can selectively recognize and phosphorylate Akt Ser473 to activate this key signaling kinase.
Last update: 10/17/2024, Ralf Bundschuh