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. 2006 May;2(5):e58.
doi: 10.1371/journal.pcbi.0020058. Epub 2006 May 26.

Evolutionary potential of a duplicated repressor-operator pair: simulating pathways using mutation data

Frank J Poelwijk  1 , Daniel J Kiviet, Sander J Tans
Affiliations

Evolutionary potential of a duplicated repressor-operator pair: simulating pathways using mutation data

Frank J Poelwijk et al. PLoS Comput Biol. 2006 May.

Abstract

Ample evidence has accumulated for the evolutionary importance of duplication events. However, little is known about the ensuing step-by-step divergence process and the selective conditions that allow it to progress. Here we present a computational study on the divergence of two repressors after duplication. A central feature of our approach is that intermediate phenotypes can be quantified through the use of in vivo measured repression strengths of Escherichia coli lac mutants. Evolutionary pathways are constructed by multiple rounds of single base pair substitutions and selection for tight and independent binding. Our analysis indicates that when a duplicated repressor co-diverges together with its binding site, the fitness landscape allows funneling to a new regulatory interaction with early increases in fitness. We find that neutral mutations do not play an essential role, which is important for substantial divergence probabilities. By varying the selective pressure we can pinpoint the necessary ingredients for the observed divergence. Our findings underscore the importance of coevolutionary mechanisms in regulatory networks, and should be relevant for the evolution of protein-DNA as well as protein-protein interactions.

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Conflict of interest statement

Competing interests. The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Divergence Process, Fitness Criterion, and Mutational Dataset of Repression Values
(A) Diagram of the studied divergence process: after a duplication event, a new regulatory interaction can be formed by mutating the two operators, O1 and O2, and two repressors, R1 and R2. (B) Duplication and divergence yields heterodimers, which can all bind to the operator. The (initially symmetric) operators and repressors are based on the lac sequence, as indicated. Base pairs that are key to altering specificity (colored red and blue) can be mutated to arbitrary sequence. (C) The selective pressure for independent regulation follows from four input conditions that contribute to the total fitness. When, e.g., R1 is high and R2 low, this implies that X should be low and Y high. Out of all interaction parameters of the network, in this case only F O1R1 and (F O2R1)−1 are relevant and need to be optimized. When R1 and R2 are high, both X and Y should be low, regardless of which repressor-dimer causes repression. Therefore max(F O1) (the strongest interaction with O1 by either homodimers of R1 or R2 or by the heterodimer of R1 and R2) and max(F O2) need to be be optimized. When both R1 and R2 are low, no parameters need to be optimized. (D) Resulting repression value landscape, showing repression values based on actual measurements of mutants.
Figure 2
Figure 2. Divergence Success Ratio and Path Length Distributions
(A) Fraction of starting sequences (numbering 132 in total) that successfully diverge, as a function of the number of networks carried to the next round (L). Dashed line, idem, but with the additional requirement of continued tight binding (F ≥ 100) for both repressors. (B) Distribution of path lengths until divergence. Red color map, optimal co-divergence pathways. Blue color map, pathways with the additional requirement of F ≥ 100 for both repressors. Note that a vertical summation of the color maps yields the lines in (A).
Figure 3
Figure 3. Analysis of Pathway Detours and Local Environment of Fitness Optima
(A) Histogram showing the number of detour mutations of the divergence pathways. The Hamming distance dH of two sequences is defined as the number of positions at which they have different base pairs. Paths that are longer than dH arrive at an optimum after a detour. (B) Histogram of the Hamming distance between the optimum that is found and the closest optimum. If this measure is zero, a path leads to the closest optimum. (C) Median fitness value as a function of the Hamming distance from a global optimum (solid line). Gray levels indicate the spread of the fitness values.
Figure 4
Figure 4. Typical Divergence Pathway: Network Changes, Fitness, and Sequence
(A) Evolving interaction network, where line thickness denotes binding strength between repressor monomer and operator-half. Dotted lines denote negligible repression. Yellow crosses indicate repressor and operator mutations, which are positioned at the top and bottom of the interaction lines respectively. (B) Fitness trajectory (black) and corresponding repression of each repressor on its operator (red and blue). Fitness is normalized to the maximum value (~1 ×1010). (C) Sequences for each round. Mutated positions are colored white.
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References

    1. Stephens SG. Possible significance of duplication in evolution. Adv Genet. 1951;4:247–265. - PubMed
    1. Ohno S. Evolution by gene duplication. New York: Springer-Verlag; 1970. 160. p.
    1. Lynch M, Conery JS. The evolutionary fate and consequences of duplicate genes. Science. 2000;290:1151–1155. - PubMed
    1. Teichmann SA, Madan Babu M. Gene regulatory network growth by duplication. Nat Genet. 2004;36:492–496. - PubMed
    1. Madan Babu M, Teichmann SA. Evolution of transcription factors and the gene regulatory network in Escherichia coli . Nucleic Acids Res. 2003;31:1234–1244. - PMC - PubMed

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