Enumerating alcohols and other classes of chemical molecules

Richard Mathar mathar at strw.leidenuniv.nl
Tue Feb 12 10:44:30 CET 2008

If they mean that AT LEAST ONE hydrogen in the initial hydrocarbon
(alkane) has been replaced by an -OH, then n-propane CH3-CH2-CH3 has
two distinct (nonisomorphic) alcohols derived from it by substitution
of exactly one -H by an OH, namely : OH-CH2-CH2-CH3 and
CH3-(HO-CH)-CH3 which correspond to rooting the tree x-x-x at either
an end or the center node.

Next, 3 alcohols derived from propane by substitution of exactly two
-H by an OH, i.e.propanediols, namely
(OH)2-CH-CH2-CH3 and HO-CH2-(HO-CH)-CH3 and HO-CH2-(CH2)-CH2-OH

and so forth, until one has the unique n-propylocta-ol (HO)3-C(OH)2-C(OH)3
and do the same sort of thing to iso-propane... and to one of the
single bonds between two carbons being replaced with a double bond...

if I've slightly abused the "quaint" Geneva Convention for organic
chemical nomenclature...

Note that "alcohol" is arbitrary, the OH can replaced by any -R
radical. The rootedness is not to a surface, but as to where the -R is
stuck, where the -R might just as well be a thiol or a benzyl or an

I think.

In which case why is this NOT in OEIS?

Jonathan Vos Post

p.s. [don't read this postscript if you don't want applied
biomathematics and icky stuff]
Thank you for the biochem review, Richard, because there are
biochemistry submodels among some of the submodels in the
model-composed-of-submodels in Systems Biology Markup Language that
I'm building at Caltech for the paper I'm coauthoring with the surgeon
who did my emergency bowel resection (a kind of manifold surgery, in
the math sense, where 4 inches of gangrenous approximately cylindrical
small intestine was removed before the gangrene would have spread
through the abdominal cavity and killed me,  4 weeks ago, and the
freshly cut ends stitched together to make a small intestine 59/60 as
long as the original); and then the rest of the 9 days in hospital
inventing a novel way to diagnose and treat the postoperative
paralysis of the the intestine ("ileus" not to be confused with the
part of the small intestine called "ileum") when my gut wouldn't
spontaneously "reboot" to normal function with its properly modulated
low amplitude axisymmetric waves known as peristalsis that are
classically described by ordinary differential equations coupled to
the mechanics of lumps of food "bolus" being transported where the
lumps are in general 3rdor 4th order non-Newtonian viscoelastic as
described by a tensor) and coupled by myoelectrical equations of the
modified Fitzhugh-Nagamo kind adapted from cardiological models, and
coupled to feedback loops of regulation by several categories of gut
hormones that can be interfered with in various ways by various
pharmacological inputs (i.e. the opioid painkillers such as dialudid
eliminate agony, but inhibit peristalsis and should be discontinued as
soon as the patient can stand being switched to a non-narcotic
To me, one amazing thing is that the human gastrointestinal system
has, mostly as a distributed network of neurons such as the ICC
(Interstitial Cells of Cajal) in between the two layers of smooth
muscle (circular and longitudinal) roughly 10^9 neurons.  That means
that we have mini-brains in our guts which have 1% as many neurons as
the primary brains in our skulls.  And the various feedback loops from
neural, hormonal, and other regulatory types are poorly understood. My
literature search showed 28 different kinds of models of the
gastrointestinal system, and nobody ever had the interdisciplinary
chutzpah to combine the 28 views of the elephant (as oppsed to 13 ways
of looking at a blackbird, for you fans of poet-insurance executive
Wallace Stevens), starting with the 2300 year old (correct!)
qualitative description by Aristotle (later tweaked by Galen), other
models being Boolean, cellular automaton, bifurcation, homotopy,
spatiotemporal map, finite element, and on and on... So I joke that
I'm creating (with my coauthor, and as supported by simulation, and
then to be clinically tested as a surgical advice system at USC Med
School), in part by applying the lovely theory by Ian Stewart and
Martin Golubitsky, namely Groupoid formalism for the nonlinear
dynamics of biological networks (see Bull. Am. Math. Soc July 2006) to
synthesize a Grand Unified Theory of the gastrointestinal system, or
G.U.T. of GUT.

On Feb 12, 2008 1:44 AM, Richard Mathar <mathar at strw.leidenuniv.nl> wrote:
> ma> From seqfan-owner at ext.jussieu.fr  Tue Feb 12 06:36:41 2008
> ma> Date: Mon, 11 Feb 2008 21:36:01 -0800
> ma> From: "Max Alekseyev" <maxale at gmail.com>
> ma> To: SeqFan <seqfan at ext.jussieu.fr>
> ma> Subject: Enumerating alcohols and other classes of chemical molecules
> ma>
> ma> SeqFans,
> ma>
> ma> I've just found a page
> ma> http://algo.inria.fr/libraries/autocomb/Polya-html/Polya.html
> ma> where a number of sequences related to enumeration of classes of
> ma> chemical molecules are derived and references to the EIS book are
> ma> given.
> ma> But one of the sequences is described as
> ma>
> ma> "This series does not appear in the book by N. J. A. Sloane and S.
> ma> Plouffe [ The Encyclopedia of Integer Sequences , (1995), Academic
> ma> Press]"
> ma>
> ma> I've checked a few first terms in OEIS, and it is still not there.
> ma> Could somebody with chemical background submit this sequence to OEIS
> ma> with an appropriate description (a reference to this page and a maple
> ma> code from there will be also useful)?
> ma>
> ma> Also, it makes sense to find the other mentioned sequences (that are
> ma> present in OEIS) and give a reference to this page in OEIS entries.
> ma>
> ma> Thanks,
> ma> Max
> The problem starts when the author says that these chemical substances
> are equivalent to rooted trees. I just cannot see why the simple
> example of CH3-CH2-CH3 ought be called rooted on any of the three
> carbons (unless you are able to stick it onto a specific solid surface,
> which is an entirely different thing). So discussion and enumeration
> of some forms of colored rooted trees is fine, but we must be able
> to eliminate the structural duplicates that show up in the rooted versions
> to end up with some standard gas-phase chemistry (which is different to
> the sub-Kelvin surface chemistry). I guess this business
> becomes fuzzy very quickly; we have to worry about definitions like
> "di-ethyl-ester-full" , "not di-ethyl-ester-free" and the like. Enumerations
> related to the real chemical structures would probably not be anymore similar
> to the sequences found in the web page. A mine-field for anyone with some reputation
> to loose as a mathematician or a chemist.
> Richard

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