Re: [Fis] Group-theoretic biology

From: Scott Muller <[email protected]>
Date: Sat 14 Jun 2003 - 06:49:14 CEST

Firstly. Thank you for inviting me to join the list. I have been
reviewing the list's archives and discovered many exciting discussions.
 
To the point at hand. I have a number of concerns regarding the
feasibility of using of labeled bipartite graphs to describe molecules
(or molecular information depending on how I read Jerry) - it may be
simple but it is inaccurate even for small molecules. First,
constraining graphs to be bipartite is too restrictive since many
molecular structures are unrepresentable as graphs under this schema
(e.g. cyclopentane). This is probably true for any k-partite (layered)
schema. So we might merely require labeled undirected graphs be used.
But this also has shortcomings. It ignores, as John Collier as already
pointed out, the importance of bond strength and type. The water
molecule, for instance, is not a permanent structure. It is subject to
protonation/deprotonation processes with a residence time of the order
of milliseconds. Further the interaction of water molecules (hydrogen
bonding) gives rise to the interesting the macro properties of water
which would not occur due to sigma bonds alone. Perhaps, then we might
introduce bond representation in the form of weighted edges and move
from labeled graphs to labeled networks. But major problem still exists
and it is in the use of labels. Labels here are made to do a lot of work
All the properties that distinguish an atom from other atoms are bundled
into labels. Consider Carbon Tetrachloride and Silicon Tetrachloride
which are both tetrahedral in structure (in this case capable of being
represented by a labeled bipartite graph) with the distinguishing atom
at the centre. SiCl4 is soluble in water whereas CCl4 isn't (because the
C atom is smaller than Si, the Cl atoms effectively shield the C atom
from the hydrolysis reaction). One may say that the intrinsic
information in each molecule is the same however if we limit ourselves
solely to this level of information in isolation we will never construct
a robust information theory of chemistry or biology. A general account
of information is required which incorporates notions such as
distinguishability and interaction. I am confident group theory can
provide this. The structure of a mathematical object need CAN represent
the relations among or correspond to the structure of a natural object
but not using graphs alone.
S.
>John:
>See interlaced comments.
>>> "jlrchand@erols.com
<mailto:jlrchand@erols.com?Subject=Re:%20%5bFis%5d%20Group-theoretic%20b
iology&In-Reply-To=%3cv04210103bb04108c1818@%5b66.44.65.54%5d%3e> "
<jlrchand@pop.mail.rcn.net
<mailto:jlrchand@pop.mail.rcn.net?Subject=Re:%20%5bFis%5d%20Group-theore
tic%20biology&In-Reply-To=%3cv04210103bb04108c1818@%5b66.44.65.54%5d%3e>
> 06/03/03 01:37 AM >>>
An Open Comment:
You ask "why"?
Because the simplest possible mathematical representation of a
chemical molecule is a labeled bipartite graph.
JDC: It seems to me that there is a lot that leaves out with respect
to relative energy levels, structure of non-ioniv bonds, and other
things. Scott's a physical chemist by original training, and is not
insensitive to the importance of these things.
JLRC: Yes. Chemical attributes are either deduced from the
structure or measured. If you re-read my post carefully you may wish
to reflect on the relation to denotation.
And, because the structure of a mathematical object need not
represent the relations among or correspond to the structure of
natural object.
JDC: Part of the subtlety of Scott's treatment is that he has
developed a way to test whether or not this is true for specific
mathematical objects and specific physical states for which we can
have evidence. Jaynes argues for the ambiguity of information content
because of multiple accurate descriptions. Scott shows that Jaynes'
argument is flawed beecase there is a general way to overcome the
ambiguity problem. We still need evidence of the structure, of
course, and we may well not be clever enough to come up with an
accurate description of this evidence.
JLRC: My original post consisted of comments about chemistry and
mathematics. At issue are the relations between chemical objects,
physical objects and mathematical objects. A labelled bipartite
graph is not ambiguous as a chemical structure. If life itself were
simply a trivial extension of well known physical and mathematical
principles, these positions and statements would be superfluous,
nicht wahr?
I conclude that the languages and structures of natural systems are
vastly richer than I was able to state or imagine.
Cheers
Jerry LR Chandler
 
Received on Sat Jun 14 06:50:36 2003

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