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Strong Selection Significantly Increases Epistatic Interactions in the Long-Term Evolution of a Protein.

Gupta A, Adami C - PLoS Genet. (2016)

Bottom Line: While epistasis is thought to enhance evolvability via valley-crossing early-on in adaptation, it can hinder adaptation later when the landscape has turned rugged.However, we find no evidence that the HIV-1 protease has reached its potential for evolution after 9 years of adapting to a drug environment that itself is constantly changing.We suggest that the mechanism of encoding new information into pairwise interactions is central to protein evolution not just in HIV-1 protease, but for any protein adapting to a changing environment.

View Article: PubMed Central - PubMed

Affiliation: Department of Microbiology and Molecular Genetics, Michigan State University, East Lansing, Michigan, United States of America.

ABSTRACT
Epistatic interactions between residues determine a protein's adaptability and shape its evolutionary trajectory. When a protein experiences a changed environment, it is under strong selection to find a peak in the new fitness landscape. It has been shown that strong selection increases epistatic interactions as well as the ruggedness of the fitness landscape, but little is known about how the epistatic interactions change under selection in the long-term evolution of a protein. Here we analyze the evolution of epistasis in the protease of the human immunodeficiency virus type 1 (HIV-1) using protease sequences collected for almost a decade from both treated and untreated patients, to understand how epistasis changes and how those changes impact the long-term evolvability of a protein. We use an information-theoretic proxy for epistasis that quantifies the co-variation between sites, and show that positive information is a necessary (but not sufficient) condition that detects epistasis in most cases. We analyze the "fossils" of the evolutionary trajectories of the protein contained in the sequence data, and show that epistasis continues to enrich under strong selection, but not for proteins whose environment is unchanged. The increase in epistasis compensates for the information loss due to sequence variability brought about by treatment, and facilitates adaptation in the increasingly rugged fitness landscape of treatment. While epistasis is thought to enhance evolvability via valley-crossing early-on in adaptation, it can hinder adaptation later when the landscape has turned rugged. However, we find no evidence that the HIV-1 protease has reached its potential for evolution after 9 years of adapting to a drug environment that itself is constantly changing. We suggest that the mechanism of encoding new information into pairwise interactions is central to protein evolution not just in HIV-1 protease, but for any protein adapting to a changing environment.

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Two-loci two-allele model.The left panel shows the fitness landscapes and epistasis given by Eq (9) in the first and second half of the simulation (updates 0–499: w0 = 1 and w1 = w2 = w3 = 10−5 ≈ 0; updates 500–1000: w0 = w3 = 1 and w1 = w2 = 10−5 ≈ 0). The xy-plane shows the four genotypes while the z-axis shows genotype fitness. The middle panel shows the genotype probabilities while the right panel shows the mutual information during the course of the simulation. Note that the increase in epistasis at the 500th update is reflected in the increase in mutual information. The mutation rate was 0.1 and starting population frequencies were p0 = 1 and p1 = p2 = p3 = 0.
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pgen.1005960.g008: Two-loci two-allele model.The left panel shows the fitness landscapes and epistasis given by Eq (9) in the first and second half of the simulation (updates 0–499: w0 = 1 and w1 = w2 = w3 = 10−5 ≈ 0; updates 500–1000: w0 = w3 = 1 and w1 = w2 = 10−5 ≈ 0). The xy-plane shows the four genotypes while the z-axis shows genotype fitness. The middle panel shows the genotype probabilities while the right panel shows the mutual information during the course of the simulation. Note that the increase in epistasis at the 500th update is reflected in the increase in mutual information. The mutation rate was 0.1 and starting population frequencies were p0 = 1 and p1 = p2 = p3 = 0.

Mentions: An extreme example occurs when w0 = w3 = 1 and w1 = w2 = 0, that is, when the double mutant has the same fitness as the wild type, but the intermediate genotypes have no fitness. In that case, it is necessary to cross a valley in the fitness landscape to reach the double mutant aa. In this case of reciprocal sign epistasis [63], E = ∞, andI(1:2)=-(1-p0)log(1-p0)-(1-p3)log(1-p3).(10)If p0 = p3 = 0.5 (full equilibration) this extreme level of epistasis correspond to 1 bit of information (the maximum possible). Fig 8 shows the changes in genotype probabilities and mutual information as the population adapts from a single-peak landscape (w0 = 1 and w1 = w2 = w3 ≈ 0) to a two-peak fitness landscape landscape (w0 = w3 = 1 and w1 = w2 ≈ 0). Pairwise mutual information increases as the landscape becomes more rugged. See S7 Text for simulations for a three-loci two-allele model that show that an increase in the sum of mutual information coincides with the increase in the ruggedness of the fitness landscape.


Strong Selection Significantly Increases Epistatic Interactions in the Long-Term Evolution of a Protein.

Gupta A, Adami C - PLoS Genet. (2016)

Two-loci two-allele model.The left panel shows the fitness landscapes and epistasis given by Eq (9) in the first and second half of the simulation (updates 0–499: w0 = 1 and w1 = w2 = w3 = 10−5 ≈ 0; updates 500–1000: w0 = w3 = 1 and w1 = w2 = 10−5 ≈ 0). The xy-plane shows the four genotypes while the z-axis shows genotype fitness. The middle panel shows the genotype probabilities while the right panel shows the mutual information during the course of the simulation. Note that the increase in epistasis at the 500th update is reflected in the increase in mutual information. The mutation rate was 0.1 and starting population frequencies were p0 = 1 and p1 = p2 = p3 = 0.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4814079&req=5

pgen.1005960.g008: Two-loci two-allele model.The left panel shows the fitness landscapes and epistasis given by Eq (9) in the first and second half of the simulation (updates 0–499: w0 = 1 and w1 = w2 = w3 = 10−5 ≈ 0; updates 500–1000: w0 = w3 = 1 and w1 = w2 = 10−5 ≈ 0). The xy-plane shows the four genotypes while the z-axis shows genotype fitness. The middle panel shows the genotype probabilities while the right panel shows the mutual information during the course of the simulation. Note that the increase in epistasis at the 500th update is reflected in the increase in mutual information. The mutation rate was 0.1 and starting population frequencies were p0 = 1 and p1 = p2 = p3 = 0.
Mentions: An extreme example occurs when w0 = w3 = 1 and w1 = w2 = 0, that is, when the double mutant has the same fitness as the wild type, but the intermediate genotypes have no fitness. In that case, it is necessary to cross a valley in the fitness landscape to reach the double mutant aa. In this case of reciprocal sign epistasis [63], E = ∞, andI(1:2)=-(1-p0)log(1-p0)-(1-p3)log(1-p3).(10)If p0 = p3 = 0.5 (full equilibration) this extreme level of epistasis correspond to 1 bit of information (the maximum possible). Fig 8 shows the changes in genotype probabilities and mutual information as the population adapts from a single-peak landscape (w0 = 1 and w1 = w2 = w3 ≈ 0) to a two-peak fitness landscape landscape (w0 = w3 = 1 and w1 = w2 ≈ 0). Pairwise mutual information increases as the landscape becomes more rugged. See S7 Text for simulations for a three-loci two-allele model that show that an increase in the sum of mutual information coincides with the increase in the ruggedness of the fitness landscape.

Bottom Line: While epistasis is thought to enhance evolvability via valley-crossing early-on in adaptation, it can hinder adaptation later when the landscape has turned rugged.However, we find no evidence that the HIV-1 protease has reached its potential for evolution after 9 years of adapting to a drug environment that itself is constantly changing.We suggest that the mechanism of encoding new information into pairwise interactions is central to protein evolution not just in HIV-1 protease, but for any protein adapting to a changing environment.

View Article: PubMed Central - PubMed

Affiliation: Department of Microbiology and Molecular Genetics, Michigan State University, East Lansing, Michigan, United States of America.

ABSTRACT
Epistatic interactions between residues determine a protein's adaptability and shape its evolutionary trajectory. When a protein experiences a changed environment, it is under strong selection to find a peak in the new fitness landscape. It has been shown that strong selection increases epistatic interactions as well as the ruggedness of the fitness landscape, but little is known about how the epistatic interactions change under selection in the long-term evolution of a protein. Here we analyze the evolution of epistasis in the protease of the human immunodeficiency virus type 1 (HIV-1) using protease sequences collected for almost a decade from both treated and untreated patients, to understand how epistasis changes and how those changes impact the long-term evolvability of a protein. We use an information-theoretic proxy for epistasis that quantifies the co-variation between sites, and show that positive information is a necessary (but not sufficient) condition that detects epistasis in most cases. We analyze the "fossils" of the evolutionary trajectories of the protein contained in the sequence data, and show that epistasis continues to enrich under strong selection, but not for proteins whose environment is unchanged. The increase in epistasis compensates for the information loss due to sequence variability brought about by treatment, and facilitates adaptation in the increasingly rugged fitness landscape of treatment. While epistasis is thought to enhance evolvability via valley-crossing early-on in adaptation, it can hinder adaptation later when the landscape has turned rugged. However, we find no evidence that the HIV-1 protease has reached its potential for evolution after 9 years of adapting to a drug environment that itself is constantly changing. We suggest that the mechanism of encoding new information into pairwise interactions is central to protein evolution not just in HIV-1 protease, but for any protein adapting to a changing environment.

Show MeSH
Related in: MedlinePlus