If we identify the Self with autopoetic entities, we find a way to ground Piercean Semiotics. The components of the autopoetic model are directly connected to the three elements of the sign. The operational closure of the entity is what generates the self and the ego, not as concrete entities but instead as emergent aspects of the interaction of the entity with its environment (structural coupling). The three aspects of signs are related directly to this structural coupling where the operationally closed self is altering its internal state in response to interactions with the environment (atomic components of the structured coupling). In terms of the signs, we say that the internal state change represents the interpretant, and the self or ego is the site or space in which interpretants and further information processing (semiosis) takes place.
Internally to the entity, the occurance of a sign generates a sequence of interpretation where the sign referring and the thing referred to are identified such that an interaction can occur. When the fish responds to a lure as if it were a fly, it finds out too late that it is mistaken; when the hook bites, in the interaction, the internal state of the fish is identical whether striking a fly or a lure. The sign of the lure/fly is taken to be a fly for the purposes of the interaction (striking at a meal).
Note that if we use this same model on physical entities like atoms and molecules we find another basis for the deep interpretation of the doctrine of signs suggested by J. Deely. If the entity is a free hydrogen radical (i.e. on proto), the presense of an electron generates a field (the interpretant from the standpoint of a particular atom or molecule, in this case a free proton), and the possibilities of interaction (structural coupling). It can resonate with that electron and create a new entity representing the bound state. The math of QED is all about how this particular structural coupling works in nearly complete detail. This is one of science's most complete and accurate theories.
My claim is that if we take Pierce's program to make the doctrine of signs into a complete theory that can connect math, science and philosophy into a unified whole, that many paradoxes of the current paradigms can be much more directly addressed. It will do a lot for the foundational clarity of the harder sciences with more complete theories, but I think it has even more to offer to workers in the cognitive sciences, and understanding living systems and in particular the emergence of mental qualities of intelligence, wisdom and consciousness.