Re: Second law of Thermodynamics

Glenn Morton (
Thu, 20 Nov 1997 17:57:37 -0600

At 05:26 AM 11/20/97 EST, David Bowman wrote:

>It seems to me that having, on average, one functional cytochrome c molecule
>for every 10^43 (= 10^(137-94) possible sequences *is* quite limiting, unless
>most of these excess permutations are forbidden by some dynamical
>constraints. One in 10^43 is quite a needle in a haystack.

For those who are unfamiliar with sequence space, I need to define the term.
If you have 4 nucleotides and want to make a 2-unit long DNA there are 4 x
4 or 16 different possibilities. One can place these 16 possibilities on a
2d plane which looks like


This is a 2 dimensional sequence space. Each point on that plane represents
one permutation of the DNA. A 3 unit long DNA has a 3d volume for its
sequence space. A 4 unit long DNA has a 4 dimensional euclidean space as
its sequence space. For humans with a 3.5 billion long DNA, we have a 3.5
billion dimensional sequence space. Scattered throughout the volume are the
10^93 different permutations of fine and dandy cytochrome c. Surrounding
each of the points are regions of points in which the functionality is
harmed but the function still takes place, albeit inefficiently. This can
be illustrated by the following example. Consider the sequence:

My cat is very stupid

This is a 21 unit long sequence (including spaces) and has a 21 dimensional
sequence space. Other 21 unit long sequences perform the same function i.e.
convey information on the intelligence of my cat. These can be statements like

My feline is retarded
My mouser is retarded
My tomcat is retarded
That cat was an idiot
My cat is awful dense
She is one stupid cat
The tomcat is a moron

etc etc.

Now, surrounding each of these reagions in the sequence space are other
sequences which work but work less effectively. To illustrate these by
taking one of the above sentence and writing it (or miswriting it):

Thet cat is an idiot
thet cat is an idyot
That kat is an idiut

While these don't work as well, if you stumble on to one of these sequences
and apply a selection which rewards efficient communication, you will end up
with a sequence that is correctly spelled.

I would direct anyone who wants experimental evidence of this type of
behavior in biological molecules to

Gerald F. Joyce, "Directed Evolution," Scientific America,Dec. 1992,

Peter Radetsky, "Speeding Through Evolution", Discover, May, 1994, p. 87

Amber A. Beaudry and Gerald F. Joyce, "Directed Evolution of an RNA Enzyme,"
Science, 257, July 31, 1992, p. 637-638


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