| Abstract: | Cell populations exhibit broad distribution of phenotypic properties. Recent research has advanced our understanding of how stochastic properties of single cells are reflected in the statistical properties of large populations. However, many biologically relevant situations entail finite populations and finite times as well as constrained environments. These systems raise several practical and fundamental issues concerning “micro-populations”, such as inter-population variability and dependence on initial conditions. Inspired by the recent technology of microdroplet-based population growth, we study the statistical properties of micro-populations that arise from the metabolic variability of single cells and the competition for a finite amount of growth substrate. We develop a stochastic model of a discrete population and show that the statistical properties of final micro-populations can be mapped onto a generalization of Polya’s Urn, a classic problem of probability theory. Both the mean population properties and their variance between micro-populations are found to depend on initial conditions.
Cell populations exhibit broad distribution of phenotypic properties. Recent research has advanced our understanding of how stochastic properties of single cells are reflected in the statistical properties of large populations. However, many biologically relevant situations entail finite populations and finite times as well as constrained environments. These systems raise several practical and fundamental issues concerning “micro-populations”, such as inter-population variability and dependence on initial conditions. Inspired by the recent technology of microdroplet-based population growth, we study the statistical properties of micro-populations that arise from the metabolic variability of single cells and the competition for a finite amount of growth substrate. We develop a stochastic model of a discrete population and show that the statistical properties of final micro-populations can be mapped onto a generalization of Polya’s Urn, a classic problem of probability theory. Both the mean population properties and their variance between micro-populations are found to depend on initial conditions.
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