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Heterologous gene expression draws resources from host cells. These resources include vital components to sustain growth and replication, and the resulting cellular burden is a widely recognized bottleneck in the design of robust circuits. In this tutorial we discuss the use of computational models that integrate gene circuits and the physiology of host cells. Through various use cases, we illustrate the power of host-circuit models to predict the impact of design parameters on both burden and circuit functionality. Our approach relies on