In this work, a novel insulin-glucagon-glucose model is proposed, where the glucagon effect on the endogenous glucose production (EGP) is described by the dynamics of the glucagon receptors. In order to assess the quality of the model, its parameters are fitted in such a way that the influence of glucagon on EGP is isolated. Experimental data is used to validate the model structure and show that the receptor dynamics allow to explain some of the glucagon-related phenomena observed in the clinical data. This physiology-focused model will be useful in the development of artificial pancreas algorithms both for more realistic in silico validations and in the development of model-based control strategies.