  The closure of cooperative chains of Hydrogen Bonding, HB, to form cycles can
enhance cooperativity. Cycles of charge transfer can balance charge into and
out of every site, eliminating the charge build-up that limits the
cooperativity of open unidirectional cooperative chains. If cycles of
cooperative HB exist in proteins, these could be expected to be significant in
protein structure and function in ways described below. We find no mention of
an example of this kind of cycle in the literature. We investigate whether
cooperative HB cycles not traversing solvent, ligand or modified residues occur
in proteins by means including search of Nuclear Magnetic Resonance
spectroscopy entries of the Protein Data Bank.
  For the direct interactions of inter-amide HB, when the energy associated
with Natural Bond Orbital, NBO, steric exchange is deducted from that of NBO
donor-acceptor interactions, the result is close to zero, so that HB is not
primarily due to the sum of direct inter-amide NBO interactions. The NBO
binding energy is primarily associated with the increase in resonance of the
amides, a consequence of which is that the majority of the NBO binding energy
is susceptible to variation by electrostatic field with component parallel or
antiparallel to an amide C-N bond.
  The question of what geometry most favours HB in amides is revisited with
emphasis on the inequivalence of amide/carbonyl oxygen lone pairs.
  A possible avenue for the design of HB-chaining polymers with improved
stability is discussed.
