# Amino acid relations - alt representations

Gaston Gonnet gonnet at inf.ethz.ch
Mon Dec 7 10:24:45 EST 1992

```In article <9212012010.AA22705 at net.bio.net> mangalam at SALK-SC2.SDSC.EDU writes:
>Saludos,
>   Does anyone have refs for alternative representations of the
>relationships among amino acids?  ie - is there a more graphical (but still
>accurate) way of showing the information in a substitution matrix other
>than the usual tabular form?
>  Star or ellipsoid diagrams, especially 3-D, come to mind, but I haven't
>come up with anything within easy reach. I'll summarize if I get anything.
>Or maybe I'll write a grant ....8).
>
>
>Harry
=========================================================
We have been looking at representation of amino acids such that
distance between them relates to likelihood of inter-mutation.

Let me explain this in a bit more of detail.  From a sufficiently
large set of alignments (or from a Dayhoff matrix) you can compute
the probability of amino acid i mutating into amino acid j for
every i and j.  This is known as a mutation matrix in the
standard jargon.  Now you make the analogy that distance between
amino acids is inversely proportional to the probability of
mutation.  I.e.  double the distance means half likely to mutate
into each other.

Hence, "close" amino acids will likely mutate into each other,
"distant" amino acids are unlikely to mutate into each other.
Close amino acids must have similar properties for protein function.

To represent this information we have two alternatives.  The
first is to represent them as an unrooted tree.  The amino
acids are at the leaves and the distance between amino acids
is measured by the length of all the branches that link the
two together.  This is very much like phylogenetic tree
construction, except that it is done for similarities, not for
common ancestry.

The second method is to use euclidean distances and represent
the 20 points in space.  Two dimension placements give a rather
primitive approximation, but is much easier to see than 3D (not
to mention 4D, 5D, etc.).

In both cases, for the unrooted tree and for the 2D placement,
the constructions are approximations.  It is generally impossible
to find a tree or points in 2D which satisfy all 20*(20-1)/2=190
distance constraints.

This message includes the postscript for the tree and for the 2D
placement.  This can be displayed in most bitmapped terminals
and on postscript printers.  The postscript files are separated
by dashed lines.  Enjoy it!

Gaston H. Gonnet, Informatik, ETH Zurich.

-------------------unrooted tree of amino acids-------------------
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% END of Darwin plot
-----------------------------end of unrooted tree---------------
--------------------2D placement of amino acids-----------------
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-------------------------------end of 2D placement-------------

```