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Compensatory mutations cause excess of antagonistic epistasis in RNA secondary structure folding.

Wilke CO, Lenski RE, Adami C - BMC Evol. Biol. (2003)

Bottom Line: However, in a number of recent studies, a prevalence of antagonistic epistasis (the tendency of multiple mutations to have a mitigating rather than reinforcing effect) has been observed.We found a clear prevalence of antagonistic epistasis in RNA secondary structure folding.Our findings imply that the average direction of epistasis in simple fitness landscapes is directly related to the density with which fitness peaks are distributed in these landscapes.

View Article: PubMed Central - HTML - PubMed

Affiliation: Digital Life Laboratory 136-93, California Institute of Technology, Pasadena, CA 91125, USA. wilke@caltech.edu

ABSTRACT

Background: The rate at which fitness declines as an organism's genome accumulates random mutations is an important variable in several evolutionary theories. At an intuitive level, it might seem natural that random mutations should tend to interact synergistically, such that the rate of mean fitness decline accelerates as the number of random mutations is increased. However, in a number of recent studies, a prevalence of antagonistic epistasis (the tendency of multiple mutations to have a mitigating rather than reinforcing effect) has been observed.

Results: We studied in silico the net amount and form of epistatic interactions in RNA secondary structure folding by measuring the fraction of neutral mutants as a function of mutational distance d. We found a clear prevalence of antagonistic epistasis in RNA secondary structure folding. By relating the fraction of neutral mutants at distance d to the average neutrality at distance d, we showed that this prevalence derives from the existence of many compensatory mutations at larger mutational distances.

Conclusions: Our findings imply that the average direction of epistasis in simple fitness landscapes is directly related to the density with which fitness peaks are distributed in these landscapes.

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Related in: MedlinePlus

Relationship between the distribution of high-fitness sequences and directional epistasis, according to Wilke and Adami [11]. The drawing on the left visualizes genotype space, with the small filled circles representing high-fitness genotypes. A and B are two particular reference sequences, and the concentric rings around A and B indicate the mutants that are a fixed Hamming distance away from either A or B. In the case of A, the average fitness w(d) of the sequences at Hamming distance d from A decays faster at higher d than at lower d, and therefore A shows synergistic epistasis. In the case of B, the decay of w(d) slows down as d increases, and hence B shows antagonistic epistasis.
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Figure 1: Relationship between the distribution of high-fitness sequences and directional epistasis, according to Wilke and Adami [11]. The drawing on the left visualizes genotype space, with the small filled circles representing high-fitness genotypes. A and B are two particular reference sequences, and the concentric rings around A and B indicate the mutants that are a fixed Hamming distance away from either A or B. In the case of A, the average fitness w(d) of the sequences at Hamming distance d from A decays faster at higher d than at lower d, and therefore A shows synergistic epistasis. In the case of B, the decay of w(d) slows down as d increases, and hence B shows antagonistic epistasis.

Mentions: The argument relating directional epistasis to the distribution of high-fitness sequences within a cluster of fit sequences goes as follows (Figure 1). Consider a sequence that lies near the center of a dense cluster of high-fitness sequences. Such a sequence is surrounded by many other high-fitness genotypes, and the average harm done by a single mutation is therefore relatively low. But as more random mutations are added, high-fitness genotypes become less common, and the average harm of multiple mutations is stronger than what the effect of single mutations indicated. This increasingly harmful effect of mutations at greater distances away from the original sequence corresponds to synergistic epistasis. By contrast, if a sequence is located at the periphery of a high-fitness cluster, or in a region of low density of high-fitness sequences, then this synergistic tendency is lessened, and we might even observe antagonistic epistasis for this sequence. One prediction of this hypothesis of density inhomogeneities is that the average fitness effect of single mutations must be correlated with the strength and direction of epistatic interactions at larger mutational distances. This prediction was confirmed in RNA secondary structure folding and in digital organisms [11]. A similar effect was observed for quantitative trait loci in mice [19].


Compensatory mutations cause excess of antagonistic epistasis in RNA secondary structure folding.

Wilke CO, Lenski RE, Adami C - BMC Evol. Biol. (2003)

Relationship between the distribution of high-fitness sequences and directional epistasis, according to Wilke and Adami [11]. The drawing on the left visualizes genotype space, with the small filled circles representing high-fitness genotypes. A and B are two particular reference sequences, and the concentric rings around A and B indicate the mutants that are a fixed Hamming distance away from either A or B. In the case of A, the average fitness w(d) of the sequences at Hamming distance d from A decays faster at higher d than at lower d, and therefore A shows synergistic epistasis. In the case of B, the decay of w(d) slows down as d increases, and hence B shows antagonistic epistasis.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC149451&req=5

Figure 1: Relationship between the distribution of high-fitness sequences and directional epistasis, according to Wilke and Adami [11]. The drawing on the left visualizes genotype space, with the small filled circles representing high-fitness genotypes. A and B are two particular reference sequences, and the concentric rings around A and B indicate the mutants that are a fixed Hamming distance away from either A or B. In the case of A, the average fitness w(d) of the sequences at Hamming distance d from A decays faster at higher d than at lower d, and therefore A shows synergistic epistasis. In the case of B, the decay of w(d) slows down as d increases, and hence B shows antagonistic epistasis.
Mentions: The argument relating directional epistasis to the distribution of high-fitness sequences within a cluster of fit sequences goes as follows (Figure 1). Consider a sequence that lies near the center of a dense cluster of high-fitness sequences. Such a sequence is surrounded by many other high-fitness genotypes, and the average harm done by a single mutation is therefore relatively low. But as more random mutations are added, high-fitness genotypes become less common, and the average harm of multiple mutations is stronger than what the effect of single mutations indicated. This increasingly harmful effect of mutations at greater distances away from the original sequence corresponds to synergistic epistasis. By contrast, if a sequence is located at the periphery of a high-fitness cluster, or in a region of low density of high-fitness sequences, then this synergistic tendency is lessened, and we might even observe antagonistic epistasis for this sequence. One prediction of this hypothesis of density inhomogeneities is that the average fitness effect of single mutations must be correlated with the strength and direction of epistatic interactions at larger mutational distances. This prediction was confirmed in RNA secondary structure folding and in digital organisms [11]. A similar effect was observed for quantitative trait loci in mice [19].

Bottom Line: However, in a number of recent studies, a prevalence of antagonistic epistasis (the tendency of multiple mutations to have a mitigating rather than reinforcing effect) has been observed.We found a clear prevalence of antagonistic epistasis in RNA secondary structure folding.Our findings imply that the average direction of epistasis in simple fitness landscapes is directly related to the density with which fitness peaks are distributed in these landscapes.

View Article: PubMed Central - HTML - PubMed

Affiliation: Digital Life Laboratory 136-93, California Institute of Technology, Pasadena, CA 91125, USA. wilke@caltech.edu

ABSTRACT

Background: The rate at which fitness declines as an organism's genome accumulates random mutations is an important variable in several evolutionary theories. At an intuitive level, it might seem natural that random mutations should tend to interact synergistically, such that the rate of mean fitness decline accelerates as the number of random mutations is increased. However, in a number of recent studies, a prevalence of antagonistic epistasis (the tendency of multiple mutations to have a mitigating rather than reinforcing effect) has been observed.

Results: We studied in silico the net amount and form of epistatic interactions in RNA secondary structure folding by measuring the fraction of neutral mutants as a function of mutational distance d. We found a clear prevalence of antagonistic epistasis in RNA secondary structure folding. By relating the fraction of neutral mutants at distance d to the average neutrality at distance d, we showed that this prevalence derives from the existence of many compensatory mutations at larger mutational distances.

Conclusions: Our findings imply that the average direction of epistasis in simple fitness landscapes is directly related to the density with which fitness peaks are distributed in these landscapes.

Show MeSH
Related in: MedlinePlus