Dear Louis and colleagues,
Thanks for the bio-logic exercise. From my view, closer to the bio, but
rather distant from the logic, it is a challenging essay quite demanding
for a cogent response.
That the living cell is an excellent theater for knot theory and
topology becomes manifest in the amazing capabilities of the enzymes in
charge of DNA processing: helicases, gyrases, topoisomerases,
resolvases, integrases, inteases, etc.etc. Some new drugs are precisely
targeting the topo-knotty capabilities of those agents. In the
intracellular / extracellular traffic of membranes ("endocytic matrix"
dynamics), topology is strongly involved too--functionally, it means
energy, digestion, transportation, recycling, etc. Actually, the formal
field known as membrane computing has exploited some of those basic
membrane topological processes in order build an interesting new
computational tool (but not much close to biological dynamics, I think).
More in general, the problem of most bioinspired formal systems is their
factual distance from biomolecular application. In your proposal, the
reliance on cybernetic epistemology about the interlacement of selves
and organisms may be taken as a safeguard. And your subsequent comments
on hierarchies and reductionism... "useful only as partial forms of
explanation" are also well put. But when you deal with recursive
processes in organisms, although the wording is quite suggestive, too
many fundamentals are left invisible, with too weak a reality anchor
onto the biostuff. For instance, the separation of entity and blueprint
is in itself questionable--where is the "blueprint" for the membrane,
and for the inner environment, and for water itself? If considered as
addressed only to RNAs, enzymes, and proteins--where do come from the
necessary folding events? Now it is becoming clear that in the origins
of complex cells and multicell organisms, viruses are strongly
involved--an unsuspected "fourth branch" for Margulis' symbiotic theory.
I mean, DNA-centrism is not enough... even for the simplest cells.
About self-production, as you say "in living systems there is an
essential circularity that is the living structure. Living systems
produce themselves from themselves and the materials and energy of the
environment." It is fine, but I would like to emphasize that cellular
self-production is intertwined with communication. People working in
prokaryotic signaling (eg, Ulrich, 2005) have emphasized the centrality
of "one component systems" (OTCs) for the most basic productive
interrelationship with the environment. It is not easy to explain, but
it means somehow that before "eating" any environment portion the
bacteria "tastes" it via those OTCs. They tell what parts of the
"edible" world are there, and what the bacterium should do concerning
its gene expression in order to grab them, process them, digest them,
etc.. From this basic communication tools, further communicative tools
for relating with other living agents, conspecifics and microbial
ecosystems, were developed (two component systems, three component
systems, etc.) The eukariotic inner cell ecosystem became possible too.
To sum up these bio comments, I think that a more interesting approach
to biological self-production and communication, to genuinely "being in
the word" could be build... (at least I attempted that in my part of the
recent phenomenology special issue). And it may admit formal
developments, and perhaps "recombine" with other existing ones...
I hope you don't mind that actually I have deserted from the formal realm!
A final note, in your biblio, I am curious about the "calculus of
distinctions" (1987). Could it apply to receptors' work as well?
Best regards--Pedro
El 07/03/2016 a las 18:06, Louis H Kauffman escribió:
A Pattern of Self-Replication
by Louis H. Kauffman
A longer introduction is enclosed. Here I will just discuss the gist of my
considerations.
I am interested in the pattern of DNA self-replication and how that pattern is
related to other aspects of self-replication that occur in logic and recursion
and in the
study of self-reference. We can describe the abstract form of DNA replication by writing
DNA = <W|C> indicating that the DNA molecule is a binding of a Watson strand
<W| and a
Crick strand |C>. Enzymes break the bonds between the strands resulting in <W| E
|C> where E denotes the cellular environment now available to both Watson and Crick.
The environment facilitates the formation of complementary base-pairing,
resulting in a new Crick strand for Watson and a new Watson strand for Crick.
DNA = <W|C> ————> <W| E |C> ———————> <W|C> <C|W> = DNA DNA.
All this happens in a complex environment where there are topological and
geometric considerations that we have not indicated in this schema.
Nevertheless this schema is the backbone of the DNA self-replication and it can
itself be summarized even more abstractly by the following description.
Let there be an algebraic entity O and a dual entity O* such that OO* is a
stable entity, but O*O arises from unity: We write this as 1 = O*O.
Then OO* = O1O* = OO*OO* and we see that OO* will reproduce itself.
--
-------------------------------------------------
Pedro C. Marijuán
Grupo de Bioinformación / Bioinformation Group
Instituto Aragonés de Ciencias de la Salud
Centro de Investigación Biomédica de Aragón (CIBA)
Avda. San Juan Bosco, 13, planta X
50009 Zaragoza, Spain
Tfno. +34 976 71 3526 (& 6818)
pcmarijuan.i...@aragon.es
http://sites.google.com/site/pedrocmarijuan/
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