| There are many different levels at which one can model biological phenomena, and the choice depends on one's objectives. First, one can address questions at the single-cell or subcellular level, including those concerning cellular responses to environmental signals, proliferation, motility etc. Alternatively one can ask more macroscopic questions about the behavior of cellular populations, which may involve the temporal evolution of cellular density, spatial pattern formation and so on. In this thesis we develop and apply mathematical and computational methods aimed at connecting these different levels of description. The goal is to answer population level questions from the models of individual behavior.; The first model system that we use is bacterial chemotaxis. Much is known in this system about signal transduction and motor control at the single cell level, and the individual behavior can be described as a biased random walk. Depending on the complexity of the model for individual cells, we address the population-level behavior using either analytical methods that involve deriving and analyzing macroscopic partial differential equations, or computational methods based on a newly developed computer-assisted equation-free approach.; Other methods and other biological test systems are also discussed. The connections with existing, primarily phenomenological macroscopic models are presented. The result of our work is a better understanding of how individual behavior determines the collective properties of cellular populations. |
