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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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Schematic illustration of the Boolean model of gene regulatory circuits.(A) A Boolean circuit with  genes (a,b,c), which are represented as open circles. Two genes are connected by a directed edge  if the expression of gene b is regulated by the product of gene a. Gene expression is binary, such that genes are either expressed (1) or not (0). The signal-integration logic of each gene is shown as a lookup table that explicitly maps all  possible input expression states to an output expression state, implicitly determining the circuit's topology. In the hypothetical circuit shown, the expression state of gene a is independent of the expression state of gene b, so  is a non-existing regulatory interaction (gray arrow), whereas  and  are both existing regulatory interactions (black arrows). (B) The wiring diagram and signal-integration logic of the entire circuit can be represented by a single vector G that is constructed by concatenating the rightmost columns of the lookup tables of the individual genes in panel (A). The vector G corresponds to the circuit's genotype. (C) The circuit in (A) maps all of the  possible initial states  (gray brackets) onto two distinct stable equilibrium expression states  (black brackets). This circuit therefore can have up to  functions, and can express such a “bifunction” in  different ways, since 6 initial states map to one equilibrium expression state and the other 2 initial states map to another equilibrium expression state. (D) In a genotype network, vertices represent circuits and two vertices share an edge if the genotypes G differ by a single element, yet have the same functions. Here, the genotype network corresponds to circuits with the bifunction , . For visual clarity, each circle only shows the first 8 binary digits of G, which represent the signal-integration logic of gene a. Note how changes in G may implicitly translate to changes in circuit topology.
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pcbi-1003071-g001: Schematic illustration of the Boolean model of gene regulatory circuits.(A) A Boolean circuit with genes (a,b,c), which are represented as open circles. Two genes are connected by a directed edge if the expression of gene b is regulated by the product of gene a. Gene expression is binary, such that genes are either expressed (1) or not (0). The signal-integration logic of each gene is shown as a lookup table that explicitly maps all possible input expression states to an output expression state, implicitly determining the circuit's topology. In the hypothetical circuit shown, the expression state of gene a is independent of the expression state of gene b, so is a non-existing regulatory interaction (gray arrow), whereas and are both existing regulatory interactions (black arrows). (B) The wiring diagram and signal-integration logic of the entire circuit can be represented by a single vector G that is constructed by concatenating the rightmost columns of the lookup tables of the individual genes in panel (A). The vector G corresponds to the circuit's genotype. (C) The circuit in (A) maps all of the possible initial states (gray brackets) onto two distinct stable equilibrium expression states (black brackets). This circuit therefore can have up to functions, and can express such a “bifunction” in different ways, since 6 initial states map to one equilibrium expression state and the other 2 initial states map to another equilibrium expression state. (D) In a genotype network, vertices represent circuits and two vertices share an edge if the genotypes G differ by a single element, yet have the same functions. Here, the genotype network corresponds to circuits with the bifunction , . For visual clarity, each circle only shows the first 8 binary digits of G, which represent the signal-integration logic of gene a. Note how changes in G may implicitly translate to changes in circuit topology.

Mentions: We consider circuits of genes (Fig. 1A). We choose a compact representation of a circuit's genotype G that allows us to represent both a circuit's signal-integration logic and its architecture by a single binary vector of length (Fig. 1B). Changes to this vector can be caused by mutations in the cis-regulatory regions of DNA. Such mutations may alter the binding affinity of a transcription factor to its binding site, thereby creating or removing a regulatory interaction [34]. Alternatively, they may affect the distance of a transcription factor binding site from the transcription start site, changing its rotational position on the DNA helix. In turn, this may alter the regulatory effect of the transcription factor [54], and change the downstream gene's signal-integration logic. Lastly, such mutations may change the distance between adjacent transcription factor binding sites, enabling or disabling a functional interaction between proximally bound transcription factors [35]. We note that mutations in G could also be conceptualized as changes in the DNA binding domain of a transcription factor. However, evolutionary evidence from microbes suggest that alterations in the structure and logic of regulatory circuits occurs preferentially via changes in cis-regulatory regions, rather than via changes in the transcription factors that bind these regions [55].


Constraint and contingency in multifunctional gene regulatory circuits.

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

Schematic illustration of the Boolean model of gene regulatory circuits.(A) A Boolean circuit with  genes (a,b,c), which are represented as open circles. Two genes are connected by a directed edge  if the expression of gene b is regulated by the product of gene a. Gene expression is binary, such that genes are either expressed (1) or not (0). The signal-integration logic of each gene is shown as a lookup table that explicitly maps all  possible input expression states to an output expression state, implicitly determining the circuit's topology. In the hypothetical circuit shown, the expression state of gene a is independent of the expression state of gene b, so  is a non-existing regulatory interaction (gray arrow), whereas  and  are both existing regulatory interactions (black arrows). (B) The wiring diagram and signal-integration logic of the entire circuit can be represented by a single vector G that is constructed by concatenating the rightmost columns of the lookup tables of the individual genes in panel (A). The vector G corresponds to the circuit's genotype. (C) The circuit in (A) maps all of the  possible initial states  (gray brackets) onto two distinct stable equilibrium expression states  (black brackets). This circuit therefore can have up to  functions, and can express such a “bifunction” in  different ways, since 6 initial states map to one equilibrium expression state and the other 2 initial states map to another equilibrium expression state. (D) In a genotype network, vertices represent circuits and two vertices share an edge if the genotypes G differ by a single element, yet have the same functions. Here, the genotype network corresponds to circuits with the bifunction , . For visual clarity, each circle only shows the first 8 binary digits of G, which represent the signal-integration logic of gene a. Note how changes in G may implicitly translate to changes in circuit topology.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003071-g001: Schematic illustration of the Boolean model of gene regulatory circuits.(A) A Boolean circuit with genes (a,b,c), which are represented as open circles. Two genes are connected by a directed edge if the expression of gene b is regulated by the product of gene a. Gene expression is binary, such that genes are either expressed (1) or not (0). The signal-integration logic of each gene is shown as a lookup table that explicitly maps all possible input expression states to an output expression state, implicitly determining the circuit's topology. In the hypothetical circuit shown, the expression state of gene a is independent of the expression state of gene b, so is a non-existing regulatory interaction (gray arrow), whereas and are both existing regulatory interactions (black arrows). (B) The wiring diagram and signal-integration logic of the entire circuit can be represented by a single vector G that is constructed by concatenating the rightmost columns of the lookup tables of the individual genes in panel (A). The vector G corresponds to the circuit's genotype. (C) The circuit in (A) maps all of the possible initial states (gray brackets) onto two distinct stable equilibrium expression states (black brackets). This circuit therefore can have up to functions, and can express such a “bifunction” in different ways, since 6 initial states map to one equilibrium expression state and the other 2 initial states map to another equilibrium expression state. (D) In a genotype network, vertices represent circuits and two vertices share an edge if the genotypes G differ by a single element, yet have the same functions. Here, the genotype network corresponds to circuits with the bifunction , . For visual clarity, each circle only shows the first 8 binary digits of G, which represent the signal-integration logic of gene a. Note how changes in G may implicitly translate to changes in circuit topology.
Mentions: We consider circuits of genes (Fig. 1A). We choose a compact representation of a circuit's genotype G that allows us to represent both a circuit's signal-integration logic and its architecture by a single binary vector of length (Fig. 1B). Changes to this vector can be caused by mutations in the cis-regulatory regions of DNA. Such mutations may alter the binding affinity of a transcription factor to its binding site, thereby creating or removing a regulatory interaction [34]. Alternatively, they may affect the distance of a transcription factor binding site from the transcription start site, changing its rotational position on the DNA helix. In turn, this may alter the regulatory effect of the transcription factor [54], and change the downstream gene's signal-integration logic. Lastly, such mutations may change the distance between adjacent transcription factor binding sites, enabling or disabling a functional interaction between proximally bound transcription factors [35]. We note that mutations in G could also be conceptualized as changes in the DNA binding domain of a transcription factor. However, evolutionary evidence from microbes suggest that alterations in the structure and logic of regulatory circuits occurs preferentially via changes in cis-regulatory regions, rather than via changes in the transcription factors that bind these regions [55].

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