Molecular Evolution and Information

The Accurate Trapped Scientist
(with Information Theory)

The previous trapped scientist models are oversimplified because they model changes to amino acid sequences without considering DNA. Since mutations alter DNA, the trapped scientist really should change DNA.
    When considering DNA, another factor will surface. Six codons specify the amino acid, arginine. Only one codon specifies methionine. Three codons specify isoleucine. From table 3.2, each amino acid may have 1,2,3,4 or 6 corresponding codons. If the bases, A, T, G and C are changed at random, the probability of creating a codon that specifies arginine is much higher than the probability of creating a codon that calls for methionine. Information theory must take this effect into account when computing the information content of a protein. For simplicity, only mutations that change A, T, C or G will be considered (no insertions or deletions allowed), and all mutations will be considered random.

Figure 3.16: Trapped Scientist Using Genetic Code

    The scientist now requires two baskets. In one he has four blocks labeled A, G, C and T. In the other, he has 18 blocks numbered 1 through 18. He is told to pull a lettered block and enter it into the computer. He is to put the block back and repeat this procedure. After he enters 18 letters, he is to press enter to see if the door opens. If the door does not open, he is to draw one lettered block and one numbered block. He is to use the number to find a corresponding letter on the computer screen (the letters on the computer screen are numbered sequentially 1 through 18). After he finds the letter corresponding to the number, he is to replace this letter with the new letter. For example, in figure 3.14, the last letter on the computer screen is T. If the scientist draws the number 18 and the letter A, then he should change the letter T to an A. He should repeat this procedure until he opens the door.
    The probability that he will open the door is now a little more complex to calculate. The door will open if the scientist enters any sequence of letters that specifies the combination of the door, methionine-alanine- valine-histidine-cysteine -lysine. Using table 3.2 for reference, there are 64 possible codons that can be typed into the computer. One of these codons specifies methionine. Four of these codons specify alanine and valine. Two codons specify histidine, cysteine and lysine.
    Methionine has a 1 in 64 chance of arising by chance. The information it contributes is 2^{(information)} = 64. Since 2⁶ = 64, methionine contributes 6 bits. Alanine and valine each have a 1 in 16 chance of arising by chance. The information they contribute is thus 2^{(information)} =16. Because 2⁴ =16, each contributes 4 bits. Histidine, cysteine, and lysine each have a 1 in 32 chance of arising by chance. Because 2⁵= 32, each contributes 5 bits. Thus, the total information required to open the door is 6 + 4 +4 +5 + 5 +5 = 29 bits. The odds that the scientist will open the door on the first try are 1 in 2²⁹ or 1 in 537 million.

home: Intelligent Design and the Origin of Life