Most cellular proteins retain a stable concentration as cells grow and divide, but there are exceptions. Some cell cycle regulators change in concentration with cell size. In fission yeast, Cdc13 (cyclin B), an important activator of the core cell cycle kinase Cdc2 (CDK1), increases in concentration as cells grow. It has been proposed that the concentration of such cell cycle regulators serves as a proxy for cell size and makes cell cycle progression dependent on cell size, thereby contributing to cell size homeostasis. The underlying mechanisms for the size-dependent scaling of these cell cycle regulators are poorly understood. Here, I show that Cdc13 protein concentration, but not mRNA concentration, increases with cell size. Furthermore, only the nuclear, but not the cytoplasmic, fraction of Cdc13 increases in concentration as cell size increases. Computational modeling along with half-life measurements suggests that stabilization of Cdc13 in the nucleus plays an important role in establishing this pattern. Taken together, my results suggest that Cdc13 scales with time, and therefore only indirectly—not directly—with cell size. This leaves open the possibility that Cdc13 contributes to cell size homeostasis, but in a different way than originally proposed. / Master of Science / Cells maintain their size very efficiently, but how they manage to do so is not well characterized. It has been suggested that cells sense their size by the size-dependent concentration changes of cell cycle proteins. I have investigated how cyclin B may serve as such a proxy for cell size in fission yeast. My data suggest that fission yeast cyclin B indirectly scales with cell size through an unknown time-based mechanism.

<p dir="ltr">In this dissertation, I use methods of theoretical physics to study principles governing the stochastic dynamics of living timekeepers in a few different contexts. First, focusing on the phenomenon of stochastic growth and division processes in the simplest living organism (the bacterial cell), I present a procedure for analyzing high-throughput, high-precision dynamic datasets to identify emergent simplicities, in particular scaling laws, that provide new insights into a long-standing problem (that of cell size homeostasis). Recasting the question from a stochastic, intergenerational viewpoint (i.e., one that considers the entire life histories of individual cells without recourse to a priori mechanistic assumptions), and taking advantage of identified emergent simplicities to achieve dimensional reduction of the problem, permits a reformulation that captures the inherent stochasticity of individual cells. Identification of discrete modes by which homeostasis is maintained---in particular, via reflexive (elastic) adaptation of cell size and reflective (plastic) adaptation of growth rate---provides important insights into key system constraints that govern living bacterial cells, with additional implications for the design of functional adaptive synthetic homeostats. The observation of non-Markovian dynamics in single-cell growth rates implies the existence of intergenerational memory and plastic adaptation in these simple organisms. I also present my work on the process of early endosomal maturation in human cell lines, multi- fork DNA replication in Escherichia coli cells, and a physics principle and theory predictions for emergent periodicity in a decentralized follow-the-leader dynamic in a collective of randomly signaling agents. This body of work provides mechanistic insights into how temporal organization in outcomes emerges despite the inherently stochastic nature of the constituent dynamics, with each system adopting its own mechanism to achieve this universal goal.</p>