From: bivalve (bivalve@mail.davidson.alumlink.com)
Date: Mon Nov 17 2003 - 17:02:50 EST
>It will help me if I can use html text in my emails. Will this be a problem for anyone? <
DC: It seems unpredictable to me; some email programs generate things that do not come out well in other email programs. Of course, with this free email I am gettign what I pay for...
>functional information can be defined, in units of bits, as:
If = -log2(Nf/N) (1)<
>'Functional' can be taken generally or specifically. Generally, 'functional' means that the state/sequence/configuration has some positive/meaningful/useful effect within a larger system. Within the large category of 'functional' will be any number of specific functions. Within genetics we are usually concerned with the specific function(s) of a given protein or regulatory sequence.<
>Eqn. (1) also assumes that each possible state/sequence/configuration is approximately as probable as any other.<
>Are we okay with using Eqn. (1) as my method to quantify functional information? If not, what might be your objection. <
DC: Although Eqn. 1 seems OK (not having a particular background in information theory, I would not put too much weight in my evaluation), I'm not real sure about calculating N and Nf. For the specific application to genetics, the starting point and the goal both strongly impact their calculation. Starting from abiogenesis of simple organic compounds, the probability of generating a specific DNA sequence is quite small. However, that is an inappropriate goal. Rather, the goal from that starting point would be generation of some coherent system capable of self-replication (a basic definition of life). Determining Nf for this goal requires knowing both the entire range of possible ways to make life and the probability of each forming, which in turn requires information about appropriate environments of formation and their abundance in the universe.
On the other hand, if the goal in view is a specific gene function, it is also necessary to restrict N to reflect the range of situations in which evolution of that function is beneficial. Modeling the historical event of evolution of a particular gene may further affect N by providing a particular starting point. This is a violation of the caveat in the original post that options within N are assumed to be equally likely. Such violations would be true of all biochemical evolution beyond the initial appearance of functionality, because once a sequence is at hand, the probability of creating a similar sequence is much higher than the probability of generating that sequence randomly.
_Perspectives on an Evolving Creation_ has a couple of essays addressing these sorts of issues. One computer simulation mentioned in it violates the claim that random processes are limited in the amount of functional information that they can generate. A computer program to solve a maze can proceed by generating a short random string of bits, interpreting pairs of bits as which direction to go next, mutating the string randomly until it gets through the string without problems in the maze, and then adding another short random string and repeating the process. This can generate a functional string as large as one wants. It is true that there is functional information encoded in the maze; howeve, by analogy with genetics this would mean that the actual "Intelligent Design" intervention event would not necessarily occur in the formation of complex biochemical systems but rather in the design of the appropriate environment. This would no longer be a challenge to biological !
evolution. Also, the maze itself could be generated by a random process.
Dr. David Campbell
Old Seashells
University of Alabama
Biodiversity & Systematics
Dept. Biological Sciences
Box 870345
Tuscaloosa, AL 35487-0345 USA
bivalve@mail.davidson.alumlink.com
That is Uncle Joe, taken in the masonic regalia of a Grand Exalted Periwinkle of the Mystic Order of Whelks-P.G. Wodehouse, Romance at Droitgate Spa
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