We studied the energetics of finite and infinite polyalanine chains in the alpha-helical and extended structure by employing density-functional theory. On the basis of these results we extracted the energy of hydrogen bonds (hb's) and their interactions by taking the full peptide-peptide connectivity (backbone) of proteins into account. We focus on two limiting cases: an isolated hb and one within an infinite alpha-helical chain. In the infinite chain the cooperativity within an infinite network of hb's strengthens each individual bond by more than a factor of 2. This effect has important consequences for the stability of alpha-helices.