The oral glucose tolerance test and meal tolerance test are common clinical tests of the glucose-insulin system. Several mathematical models have been suggested as means to extract information about beta-cell function from data from oral tolerance tests. Any such model needs to be fairly simple but should at the same time be linked to the underlying biology of the insulin-secreting beta-cells. The scope of the present work is to present a way to make such a connection using a recent model describing intracellular mechanisms. We show how the three main components of oral minimal secretion models, derivative control, proportional control, and delay, are related to subcellular events, thus providing mechanistic underpinning of the assumptions of the minimal models.