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From: lew@ihlpa.UUCP
Newsgroups: sci.bio
Subject: Re: question
Message-ID: <3451@ihlpa.ATT.COM>
Date: Mon, 30-Mar-87 21:37:00 EST
Article-I.D.: ihlpa.3451
Posted: Mon Mar 30 21:37:00 1987
Date-Received: Wed, 1-Apr-87 05:37:54 EST
References: <11189@teknowledge-vaxc.ARPA> <978@aecom.UUCP> <3310@udenva.UUCP>
Organization: AT&T Bell Laboratories - Naperville, Illinois
Lines: 40
Summary: genetic information capacity

In article <3310@udenva.UUCP>, agranok@udenva.UUCP (Alexander Granok) writes:
> The whole arguement gets caught up in definitions, here.  I would consider a
> bit to be a base pair, and a byte to be the set of three that encodes for one
> amino acid.  Instead of eight bits to a byte, there are three.  After all, one
> base pair by itself doesn't do much good.  But, if a base pair is a bit, then
> what is a nucleotide?  I guess it all depends on what you mean by "informa-
> tion." 

Indeed! But this question has been well considered and has a conventional
answer.  A channel consisting of a series of uncorrelated symbols carries
x bits per symbol where:

	 x = sum ( i = 1 ; i<N ; i++ ) { P(i) * log2 ( 1 / P(i) ) }

N is the number of symbol values.  P(i) is the probability of
occurrence of the ith symbol value. Note that the information carried
depends on the usage.

If we assume each value occurs with probability 1/N then the expression
simplifies to:

	x = log2 N

With this simplification, DNA has a capacity of 2 bits per base pair
since there are 4 different base pairs.  However, each triplet only
codes for 20 amino acids plus a stop and start symbol so each triplet
carries log2 ( 22 ) = 4.5 bits or 1.5 bits per base pair.

If one goes on to consider the correlations among sequential codons
the bits per base pair are further reduced.  Lila Gatlin ( I think that's
the name ) wrote a book in which she (?) tries to build up a big
theory of genetic information content.  I tried to read it some time
ago and decided she didn't understand information theory. She kept talking
about the information content of a single genome, which is meaningless.

The above definition defines the information carrying capacity of a
channel in terms of the statistics of the messages it carries. The
information content of a given message is not defined.

	Lew Mammel, Jr.