To see a World in a Grain of Cells: Statistical Auguries of Nonequilibrium

Precisely what new mathematical and biological behaviors are unlocked as cells---and their collectives---operate out of equilibrium? In this thesis, we take simple steps towards accounting for the characteristic scales of biological energy expenditures and tracing their functional destinies. After embarking on an initial Census of lively dissipation (Chapter 1) to set the stage, Part I explores cells on the bioenergetic brink of survival and death. In Chapter 2 we explore the sweep of the smallest measured cellular metabolic rates; reflect on their empirical and philosophical underpinnings; and endeavor an initial order of magnitude accounting of the biophysical processes that could most plausibly dominate the energy budgets of starving cells. Followed by this tour, Chapter 3 hones in on fresh, provocative experiments probing anaerobic maintenance metabolism of Pseudomonas, proposing simple math to predict how microbes die in balance with their energetic resources and interpreting measured reactions to salt. Part II travels to intracellular gene regulation. Among other regulatory settings, in Chapter 4 we investigate the most common regulated architecture of gene regulation in prokaryotes and ask how its behaviors categorically change under different investments in biochemical drive. Chapter 5 narrates how graph theory gives powerful tools for humanly thinking about even large regulatory state graphs. In Part III, we work closely with inspiring new experimental collaborations and data on patterns of microtubules made by molecular motors. Chapter 6 reports on measuring biochemical energy profiles, and their rates of change, over time and space. Using this phenomenology, in Chapter 7 we develop theory to ask about the fundamental costs required to build or maintain biochemical gradients. Last, in Chapter 8 (Part IV) we ask how a common mathematics might unify a large class of biological dynamics with disperse initial conditions but coherent final conditions, a setting we refer to as exploratory dynamics. Collectively, we hope these case studies give quantitative glimpses of precisely how energy so exquisitely animates biology.