Scale-up is a major challenge in bioprocess engineering. Because physically achievable mixing times in large-scale bioreactors are limited, gradients of dissolved oxygen are likely to occur. Since the impact on performance of production strains in this environment is poorly understood, we address this question by developing a distributed parameter model. This approach makes it possible to model the adaptive behavior of Escherichia coli during reoccurring switches between oxygen free and oxygen rich environments. We use a set of first-order hyperbolic partial differential equations actuated by spatially varying activation dynamics. The design of the distributed parameter model is based on a scale-down bioreactor, which is used for an experimental validation of the simulation results.