Statistical properties and dynamics of phenotype components in individual bacteria
Cellular phenotype is characterized by different components such as cell size, protein content and cell cycle time. These are global variables that are the outcome of multiple internal microscopic processes. Accordingly, they display some universal statistical properties and scaling relations, such as distribution collapse and relation between moments. Cell size statistics and its relation to growth and division has been mostly studied separately from proteins and other cellular variables. Here we present experimental and theoretical analyses of these phenotype components in a unified framework that reveals their correlations and interactions inside the cell. We measure these components simultaneously in single cells over dozens of generations, quantify their correlations, and compare population to temporal statistics. We find that cell size and highly expressed proteins have very similar dynamics over growth and division cycles, which result in parallel statistical properties, both universal and individual. In particular, while distribution shapes of fluctuations along time are common to all cells and components, other properties are variable and remain distinct in individual cells for a surprisingly large number of generations. These include temporal averages of cell size and protein content, and the structure of their auto-correlation functions. We explore possible roles of the different components in controlling cell growth and division. We find that in order to stabilize exponential accumulation and division of all components across generations, coupled dynamics among them is required. Finally, we incorporate effective coupling within the cell cycle with a phenomenological mapping across consecutive cycles, and show that this model reproduces the entire array of experimental observations.