Rodents subjected to calorie restriction (CR), a regimen of calorie reduction without malnutrition, displayed an increased numbers of newly produced neural cells in the SGZ, coupled to increased expression of the brain-derived neurotrophic factor (BDNF) (Lee et al., 2000); while in models of diet-induced obesity and diabetes, adult neurogenesis results to be impaired (Pani, 2015). This evidence concerns the gene BDNF and obesity due to melanocortin 4 receptor deficiency.