In lecture 5 on the different types of weak bonds that contribute to 3 degree structure of proteins. I don't understand why the asp - - - asn interaction is called a "H-bond to ionic."

True, it is not really an H-bond, but rather an electrical attraction between the fully charged asp side group and the partially positively charged (delta plus) parts of the polar asn amide group (the H's on the N).

The Purves book says that "the beta pleated sheet is formed from two or more polypetide chains that are...lying next to each other"(39). We learned in class a beta sheet can only pertain to one chain since it is secondary structure and not quaternary. Can you explain this?  Further in the paragraph Purves points out that the participants in a beta sheet structure can bee on the same polypeptide folded back on itself (the usual case, and the one depicted by Purves in Fig. 3.5d) or, (more exceptionally) between two separate polypeptide chains, thus contributing to quaternary structure. I see no contradiction here, do not get too concerned about pigeonholing terms. Secondary structure certainly contributes to tertiary structure (th overall 3-D folding) so why not quaternary structure. There is a hierarchy here, where primary leads to secondary and tertiary, secondary to tertiary, secondary and tertiary to quaternary. My definition of secondary was just "regular, repeated interactions between (solely) backbone atoms".