Do omnivore mammals vary food preferences based on dietary needs?
For what concerns amino acids, mice rapidly reject meals that are not balanced in essential amino acids and continue to look for other kind of foods. This behavior is called aversion response and it is an adaptive phenomena that can be observed already 20 minutes after exposure to the unbalanced food. The mechanism involves brain sensing of uncharged tRNAs. The significance of the aversion response is to minimize depletion of essential amino acids that can not be directly synthethized but are required for protein synthesis. You can find good reviews in PubMed, for instance Gietzen et al. 2007, Annual Review of Nutrition, and Gietzen and Aya 2012, Molecular Neurobiology.