can a protein contain both alpha helix and beta sheet?
Proteins have very complex structures. The primary structure, which is the basis of the protein, is the sequence of amino acids that form the basic polypeptide. The polypeptide then folds in a regular pattern, known as the secondary structure. The alpha helix and the beta pleat are the two major forms of secondary fold; both are created and stabilized by hydrogen bonds. The alpha helix is a right-handed coiling, while the beta pleat is a accordion-type fold. These folds help determine the texture and the function of the protein. For example, the proteins of wool fiber have many alpha helices, which helps to make wool springy and resilient. The proteins of silk consist of all beta pleats, which gives silk its smooth texture and its ability to stretch without breaking.
Additional structural modifications can include the additional of functional groups, and the bonding of two or more proteins into a larger molecule. Because proteins can be very large, and because they serve a wide variety of functions, there are indeed proteins occurring in nature which include both alpha and beta secondary folds. At this link you can see structural diagrams of examples, such as angiogenin and lysozyme.