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Constraint and contingency in multifunctional gene regulatory circuits.

Payne JL, Wagner A - PLoS Comput. Biol. (2013)

Bottom Line: Multifunctionality presumably constrains this number, but we do not know to what extent.As a result, historical contingency becomes widespread in circuits with many functions.Circuits with many functions also become increasingly brittle and sensitive to mutation.

View Article: PubMed Central - PubMed

Affiliation: University of Zurich, Institute of Evolutionary Biology and Environmental Studies, Zurich, Switzerland.

ABSTRACT
Gene regulatory circuits drive the development, physiology, and behavior of organisms from bacteria to humans. The phenotypes or functions of such circuits are embodied in the gene expression patterns they form. Regulatory circuits are typically multifunctional, forming distinct gene expression patterns in different embryonic stages, tissues, or physiological states. Any one circuit with a single function can be realized by many different regulatory genotypes. Multifunctionality presumably constrains this number, but we do not know to what extent. We here exhaustively characterize a genotype space harboring millions of model regulatory circuits and all their possible functions. As a circuit's number of functions increases, the number of genotypes with a given number of functions decreases exponentially but can remain very large for a modest number of functions. However, the sets of circuits that can form any one set of functions becomes increasingly fragmented. As a result, historical contingency becomes widespread in circuits with many functions. Whether a circuit can acquire an additional function in the course of its evolution becomes increasingly dependent on the function it already has. Circuits with many functions also become increasingly brittle and sensitive to mutation. These observations are generic properties of a broad class of circuits and independent of any one circuit genotype or phenotype.

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Robustness and multifunctionality.(A) The robustness of a k-function is shown in relation to the number of functions k. Each data point corresponds to the genotype set of a specific combination of k functions. The data include all k-functions. The solid line depicts the average robustness of a k-function. The inset shows the proportion and number of genotypes in the genotype set of a k-function, as a function of k. Note the logarithmic scale of the y-axes. (B–D) Distributions of genotypic robustness for (B) , (C) , and (D) . For each k, we show data for a single genotype network.
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pcbi-1003071-g003: Robustness and multifunctionality.(A) The robustness of a k-function is shown in relation to the number of functions k. Each data point corresponds to the genotype set of a specific combination of k functions. The data include all k-functions. The solid line depicts the average robustness of a k-function. The inset shows the proportion and number of genotypes in the genotype set of a k-function, as a function of k. Note the logarithmic scale of the y-axes. (B–D) Distributions of genotypic robustness for (B) , (C) , and (D) . For each k, we show data for a single genotype network.

Mentions: Fig. 3A shows that the robustness of a k-function decreases approximately linearly as k increases, indicating a trade-off between multifunctionality and robustness. However, some degree of robustness is maintained so long as . For larger k, some functions exist that have zero robustness (Text S1), that is, none of the circuits with these functions can tolerate a change in their regulatory genotype. The inset of Fig. 3A reveals a similar inverse relationship between the size of a genotype set and the number of functions k, implying that multifunctions become increasingly less “designable” [64] — fewer circuits have them — as k increases (Text S1). For example, for as few as functions, the genotype set may comprise a single genotype, reducing the corresponding robustness of the k-function to zero. For each value of k, the maximum proportion of genotypes with a given k-function is equal to the square of the maximum proportion of genotypes with a function, explaining the triangular shape of the data in the inset. This triangular shape indicates that the genotype set of a given k-function is always smaller than the union of the k constituent genotypes sets. Additionally, we find that the robustness of a k-function and the size of its genotype set are strongly correlated (Fig. S1), indicating that the genotypes of larger genotype sets are, on average, more robust than those of smaller genotype sets. This result is not trivial because the structure of a genotype set may change with its size. For example, large genotype sets may comprise many isolated genotypes, or their genotype networks might be structured as long linear chains. In either case, the robustness of a k-function would decrease as the size of its genotype set increased.


Constraint and contingency in multifunctional gene regulatory circuits.

Payne JL, Wagner A - PLoS Comput. Biol. (2013)

Robustness and multifunctionality.(A) The robustness of a k-function is shown in relation to the number of functions k. Each data point corresponds to the genotype set of a specific combination of k functions. The data include all k-functions. The solid line depicts the average robustness of a k-function. The inset shows the proportion and number of genotypes in the genotype set of a k-function, as a function of k. Note the logarithmic scale of the y-axes. (B–D) Distributions of genotypic robustness for (B) , (C) , and (D) . For each k, we show data for a single genotype network.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC3675121&req=5

pcbi-1003071-g003: Robustness and multifunctionality.(A) The robustness of a k-function is shown in relation to the number of functions k. Each data point corresponds to the genotype set of a specific combination of k functions. The data include all k-functions. The solid line depicts the average robustness of a k-function. The inset shows the proportion and number of genotypes in the genotype set of a k-function, as a function of k. Note the logarithmic scale of the y-axes. (B–D) Distributions of genotypic robustness for (B) , (C) , and (D) . For each k, we show data for a single genotype network.
Mentions: Fig. 3A shows that the robustness of a k-function decreases approximately linearly as k increases, indicating a trade-off between multifunctionality and robustness. However, some degree of robustness is maintained so long as . For larger k, some functions exist that have zero robustness (Text S1), that is, none of the circuits with these functions can tolerate a change in their regulatory genotype. The inset of Fig. 3A reveals a similar inverse relationship between the size of a genotype set and the number of functions k, implying that multifunctions become increasingly less “designable” [64] — fewer circuits have them — as k increases (Text S1). For example, for as few as functions, the genotype set may comprise a single genotype, reducing the corresponding robustness of the k-function to zero. For each value of k, the maximum proportion of genotypes with a given k-function is equal to the square of the maximum proportion of genotypes with a function, explaining the triangular shape of the data in the inset. This triangular shape indicates that the genotype set of a given k-function is always smaller than the union of the k constituent genotypes sets. Additionally, we find that the robustness of a k-function and the size of its genotype set are strongly correlated (Fig. S1), indicating that the genotypes of larger genotype sets are, on average, more robust than those of smaller genotype sets. This result is not trivial because the structure of a genotype set may change with its size. For example, large genotype sets may comprise many isolated genotypes, or their genotype networks might be structured as long linear chains. In either case, the robustness of a k-function would decrease as the size of its genotype set increased.

Bottom Line: Multifunctionality presumably constrains this number, but we do not know to what extent.As a result, historical contingency becomes widespread in circuits with many functions.Circuits with many functions also become increasingly brittle and sensitive to mutation.

View Article: PubMed Central - PubMed

Affiliation: University of Zurich, Institute of Evolutionary Biology and Environmental Studies, Zurich, Switzerland.

ABSTRACT
Gene regulatory circuits drive the development, physiology, and behavior of organisms from bacteria to humans. The phenotypes or functions of such circuits are embodied in the gene expression patterns they form. Regulatory circuits are typically multifunctional, forming distinct gene expression patterns in different embryonic stages, tissues, or physiological states. Any one circuit with a single function can be realized by many different regulatory genotypes. Multifunctionality presumably constrains this number, but we do not know to what extent. We here exhaustively characterize a genotype space harboring millions of model regulatory circuits and all their possible functions. As a circuit's number of functions increases, the number of genotypes with a given number of functions decreases exponentially but can remain very large for a modest number of functions. However, the sets of circuits that can form any one set of functions becomes increasingly fragmented. As a result, historical contingency becomes widespread in circuits with many functions. Whether a circuit can acquire an additional function in the course of its evolution becomes increasingly dependent on the function it already has. Circuits with many functions also become increasingly brittle and sensitive to mutation. These observations are generic properties of a broad class of circuits and independent of any one circuit genotype or phenotype.

Show MeSH
Related in: MedlinePlus