Functional information and the emergence of biocomplexity
- *Geophysical Laboratory, Carnegie Institution, 5251 Broad Branch Road NW, Washington, DC 20015-1305;
- ‡California Institute for Quantitative Biomedical Research and Berkeley Center for Synthetic Biology, University of California, 717 Potter Street MC 3224, Berkeley, CA 94720-3224; and
- §Howard Hughes Medical Institute, Department of Molecular Biology and Center for Computational and Integrative Biology, 7215 Simches Research Center, Massachusetts General Hospital, Boston, MA 02114-2696
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Fig. 1.Distribution of the not/and (NAND) function in 300-line Avida genomes in a randomly generated sample of 107 genomes. The degree of function, E, is the number of times NAND is executed by the genome, whereas functional information, I (in bits), is −log2 of the fraction of all sequences that achieves at least that degree of function, F(E). Note the discontinuities, which are a recurrent feature in these experiments.
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Fig. 2.The frequency of the ADD function in 100-, 200-, 300-, and 500-line linear Avida genomes in randomly generated samples of 106 genomes. Degree of function, E, is the number of times the ADD function is executed by the genome, whereas functional information, I (in bits), is −log2 of the fraction of all sequences that achieves at least that degree of function, F(E). Note that maximum E increases with genome length.
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Fig. 3.Schematic representation of four discrete functional classes, or “islands,” of solutions that display function. The vertical axis is degree of function, E, whereas the horizontal plane represents a two-dimensional projection in sequence space. The number of sequences with degree of function ≥E corresponds to the area intersected by the horizontal plane at that height along the E axis. Increasing E above the heights of the flat-topped islands A and B will result in discontinuities in the function E versus I, as illustrated in Figs. 1 and 2. Island C is a cone-shaped distribution, and island D represents a discrete solution of the type that might not be discovered in random sampling experiments.
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Fig. 4.I(E) versus E for the statistically random system, where E is the number of times the digit 1 appears at least that many times in a sequence of 100 digits. This statistically random case is not stepped, in contrast to the topology of Avida genomes.
Footnotes
- †To whom correspondence should be addressed. E-mail: rhazen{at}gl.ciw.edu
- © 2007 by The National Academy of Sciences of the USA
