Insulin secretion from pancreatic beta cells is a fundamental physiological process, and its impairment plays a pivotal role in the development of diabetes. Mathematical modeling of insulin secretion has a long history, both on the level of the entire body and on the cellular and subcellular scale. However, little direct communication between these disparate scales has been included in mathematical models so far. Recently, we have proposed a minimal model for the incretin effect by which the gut hormone glucagon-like peptide 1 (GLP-1) enhances insulin secretion. To understand how this model couples to cellular events, we use a previously published mechanistic model of insulin secretion, and show mathematically that induction of glucose competence in beta cells by GLP-1 can underlie derivative control by GLP-1.