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<div class="moz-forward-container">From Louis H Kauffman
<<a class="moz-txt-link-abbreviated" href="mailto:loukau@gmail.com">loukau@gmail.com</a><br>
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<br>
Dear Pedro,<br>
<br>
<div class="">I think that we should assess the role of formal
tools that are already in place.</div>
<div class=""><br class="">
</div>
<div class="">1. We use the accepted (graph-theoretical +
geometry) models of molecules. These models are very powerful
and fundamentally simple, but the complexities of their
application in molecular biology is very great, requiring
computational handling of the data and geometry. Some molecular
biologists add features related to physics such as
electromagnetic fields and quantum mechanics to these models,
and it should be expected that the quantum level will eventually
be very important to the structure of molecular biology. </div>
<div class=""><br class="">
</div>
<div class="">1(a). This is a further comment on 1. In
protein-folding we use the basics of model 1, plus elementary
modeling of energy and probability of bonding. These models are
insufficient to do what Nature does naturally.</div>
<div class="">The models are combinatorial and graph theoretic in
nature but they do not address the right issues (what are they?)
to impinge on the actualities of protein folding as it happens.
The same is probably true about the topological side of protein
folding — one can easily construct topological invariants at the
combinatorial level (I have written about this) but their use by
biologists has not happened yet. At least one researcher (Anti
Niemi) suggests a different and more field theoretic approach to
protein folding. See </div>
<div class=""><a moz-do-not-send="true"
href="https://www.researchgate.net/profile/Antti_Niemi/publications"
class="">https://www.researchgate.net/profile/Antti_Niemi/publications</a></div>
<div class=""><br class="">
</div>
<div class="">1(b). There has been a nice success in applying
topology via the embedded-graph paradigm for molecules. See</div>
<div class=""><a moz-do-not-send="true"
href="https://www.google.com/search?client=safari&rls=en&q=DNA+Topology&ie=UTF-8&oe=UTF-8"
class="">DNA Topology</a></div>
<div class=""><a moz-do-not-send="true"
href="https://www.google.com/search?client=safari&rls=en&q=DNA+Topology&ie=UTF-8&oe=UTF-8#q=DNA+Topology+Kauffman+and+Lambropoulou%5D"
class="">DNA Topology Kauffman and Lambropoulou]</a></div>
<div class="">It is in this domain, that I became interested in
looking at the self-reproduction of DNA as an instance of an
abstract self-replication schema. There is much more to be done
here in linking this abstraction back</div>
<div class="">to the topology and to the actualities of the
biology. The investigation led to a number of analogies with
structure of quantum mechanics and this will in turn related to
quantum topology. This is in development.</div>
<div class=""><br class="">
</div>
<div class="">2. Further topological/geometric work is very
possible. The sort of thing seen in Pivar could be examined for
mathematical problems to be articulated. We are aware that
biological forms must arise via self-assembly and this is in
itself a possibly new field of geometry! The simplest example of
self-assembly as a model is the model of autopoesis of Maturana,
Uribe and Varela from long ago. Their model shows how a two
dimensional cell boundary can arise naturally from an abstract
‘chemical soup’.</div>
<div class=""><br class="">
</div>
<div class="">3. While I do not agree with Max Tegmark that
Mathematics is identical to Reality, I do believe that the key
to actuality is in the essence of relationships. The essence of
relationships is often accompanied by a mathematical essence or
simple fundamental pattern. This is so striking in the case of
DNA reproduction (e.g.) that I cannot help but feel that some
real progress can occur in looking at that whole story from the
abstract and recursive self-replication to how it is
instantiated in the biology. The question in general is: What
can we see about the way mathematical models are instantiated in
actuality?!</div>
<div class=""><br class="">
</div>
<div class="">I will stop here in the interest of brevity.</div>
<div class=""><br>
Best,</div>
<div class=""><br>
Lou</div>
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