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Jouffrey V, Leonard AS, Ahnert SE. Gene duplication and subsequent diversification strongly affect phenotypic evolvability and robustness. R Soc Open Sci 2021; 8:201636. [PMID: 34168886 PMCID: PMC8220273 DOI: 10.1098/rsos.201636] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/12/2020] [Accepted: 03/17/2021] [Indexed: 06/13/2023]
Abstract
We study the effects of non-determinism and gene duplication on the structure of genotype-phenotype (GP) maps by introducing a non-deterministic version of the Polyomino self-assembly model. This model has previously been used in a variety of contexts to model the assembly and evolution of protein quaternary structure. Firstly, we show the limit of the current deterministic paradigm which leads to built-in anti-correlation between evolvability and robustness at the genotypic level. We develop a set of metrics to measure structural properties of GP maps in a non-deterministic setting and use them to evaluate the effects of gene duplication and subsequent diversification. Our generalized versions of evolvability and robustness exhibit positive correlation for a subset of genotypes. This positive correlation is only possible because non-deterministic phenotypes can contribute to both robustness and evolvability. Secondly, we show that duplication increases robustness and reduces evolvability initially, but that the subsequent diversification that duplication enables has a stronger, inverse effect, greatly increasing evolvability and reducing robustness relative to their original values.
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Affiliation(s)
- V. Jouffrey
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK
- Sainsbury Laboratory, University of Cambridge, Bateman Street, Cambridge CB2 1LR, UK
| | - A. S. Leonard
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK
- Sainsbury Laboratory, University of Cambridge, Bateman Street, Cambridge CB2 1LR, UK
| | - S. E. Ahnert
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK
- Sainsbury Laboratory, University of Cambridge, Bateman Street, Cambridge CB2 1LR, UK
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Abstract
Self-assembly processes are widespread in nature and lie at the heart of many biological and physical phenomena. The characteristics of self-assembly building blocks determine the structures that they form. Two crucial properties are the determinism and boundedness of the self-assembly. The former tells us whether the same set of building blocks always generates the same structure, and the latter whether it grows indefinitely. These properties are highly relevant in the context of protein structures, as the difference between deterministic protein self-assembly and nondeterministic protein aggregation is central to a number of diseases. Here we introduce a graph theoretical approach that can determine the determinism and boundedness for several geometries and dimensionalities of self-assembly more accurately and quickly than conventional methods. We apply this methodology to a previously studied lattice self-assembly model and discuss generalizations to a wide range of other self-assembling systems.
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Affiliation(s)
- S Tesoro
- Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, CB3 0HE Cambridge, United Kingdom
| | - S E Ahnert
- Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, CB3 0HE Cambridge, United Kingdom
- Sainsbury Laboratory, University of Cambridge, CB2 1LR Cambridge, United Kingdom
| | - A S Leonard
- Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, CB3 0HE Cambridge, United Kingdom
- Sainsbury Laboratory, University of Cambridge, CB2 1LR Cambridge, United Kingdom
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Ahnert SE, Fink TMA. Form and function in gene regulatory networks: the structure of network motifs determines fundamental properties of their dynamical state space. J R Soc Interface 2017; 13:rsif.2016.0179. [PMID: 27440255 PMCID: PMC4971217 DOI: 10.1098/rsif.2016.0179] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2016] [Accepted: 06/23/2016] [Indexed: 01/18/2023] Open
Abstract
Network motifs have been studied extensively over the past decade, and certain motifs, such as the feed-forward loop, play an important role in regulatory networks. Recent studies have used Boolean network motifs to explore the link between form and function in gene regulatory networks and have found that the structure of a motif does not strongly determine its function, if this is defined in terms of the gene expression patterns the motif can produce. Here, we offer a different, higher-level definition of the ‘function’ of a motif, in terms of two fundamental properties of its dynamical state space as a Boolean network. One is the basin entropy, which is a complexity measure of the dynamics of Boolean networks. The other is the diversity of cyclic attractor lengths that a given motif can produce. Using these two measures, we examine all 104 topologically distinct three-node motifs and show that the structural properties of a motif, such as the presence of feedback loops and feed-forward loops, predict fundamental characteristics of its dynamical state space, which in turn determine aspects of its functional versatility. We also show that these higher-level properties have a direct bearing on real regulatory networks, as both basin entropy and cycle length diversity show a close correspondence with the prevalence, in neural and genetic regulatory networks, of the 13 connected motifs without self-interactions that have been studied extensively in the literature.
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Affiliation(s)
- S E Ahnert
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK
| | - T M A Fink
- London Institute of Mathematical Sciences, 35A South Street, London W1K 2XF, UK
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Abstract
We investigate general properties of nondeterministic self-assembly with asymmetric interactions, using a computational model and DNA tile assembly experiments. By contrasting symmetric and asymmetric interactions we show that the latter can lead to self-limiting cluster growth. Furthermore, by adjusting the relative abundance of self-assembly particles in a two-particle mixture, we are able to tune the final sizes of these clusters. We show that this is a fundamental property of asymmetric interactions, which has potential applications in bioengineering, and provides insights into the study of diseases caused by protein aggregation.
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Affiliation(s)
- S Tesoro
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB3 0HE Cambridge, United Kingdom
| | - K Göpfrich
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB3 0HE Cambridge, United Kingdom
| | - T Kartanas
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB3 0HE Cambridge, United Kingdom
| | - U F Keyser
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB3 0HE Cambridge, United Kingdom
| | - S E Ahnert
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB3 0HE Cambridge, United Kingdom
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6
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Abstract
Self-assembly is ubiquitous in nature, particularly in biology, where it underlies the formation of protein quaternary structure and protein aggregation. Quaternary structure assembles deterministically and performs a wide range of important functions in the cell, whereas protein aggregation is the hallmark of a number of diseases and represents a nondeterministic self-assembly process. Here we build on previous work on a lattice model of deterministic self-assembly to investigate nondeterministic self-assembly of single lattice tiles and mixtures of two tiles at varying relative concentrations. Despite limiting the simplicity of the model to two interface types, which results in 13 topologically distinct single tiles and 106 topologically distinct sets of two tiles, we observe a wide variety of concentration-dependent behaviors. Several two-tile sets display critical behaviors in the form of a sharp transition from bound to unbound structures as the relative concentration of one tile to another increases. Other sets exhibit gradual monotonic changes in structural density, or nonmonotonic changes, while again others show no concentration dependence at all. We catalog this extensive range of behaviors and present a model that provides a reasonably good estimate of the critical concentrations for a subset of the critical transitions. In addition, we show that the structures resulting from these tile sets are fractal, with one of two different fractal dimensions.
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Affiliation(s)
- S Tesoro
- Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, CB3 0HE Cambridge, United Kingdom
| | - S E Ahnert
- Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, CB3 0HE Cambridge, United Kingdom
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Greenbury SF, Ahnert SE. The organization of biological sequences into constrained and unconstrained parts determines fundamental properties of genotype-phenotype maps. J R Soc Interface 2015; 12:20150724. [PMID: 26609063 PMCID: PMC4707848 DOI: 10.1098/rsif.2015.0724] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2015] [Accepted: 10/30/2015] [Indexed: 11/12/2022] Open
Abstract
Biological information is stored in DNA, RNA and protein sequences, which can be understood as genotypes that are translated into phenotypes. The properties of genotype-phenotype (GP) maps have been studied in great detail for RNA secondary structure. These include a highly biased distribution of genotypes per phenotype, negative correlation of genotypic robustness and evolvability, positive correlation of phenotypic robustness and evolvability, shape-space covering, and a roughly logarithmic scaling of phenotypic robustness with phenotypic frequency. More recently similar properties have been discovered in other GP maps, suggesting that they may be fundamental to biological GP maps, in general, rather than specific to the RNA secondary structure map. Here we propose that the above properties arise from the fundamental organization of biological information into 'constrained' and 'unconstrained' sequences, in the broadest possible sense. As 'constrained' we describe sequences that affect the phenotype more immediately, and are therefore more sensitive to mutations, such as, e.g. protein-coding DNA or the stems in RNA secondary structure. 'Unconstrained' sequences, on the other hand, can mutate more freely without affecting the phenotype, such as, e.g. intronic or intergenic DNA or the loops in RNA secondary structure. To test our hypothesis we consider a highly simplified GP map that has genotypes with 'coding' and 'non-coding' parts. We term this the Fibonacci GP map, as it is equivalent to the Fibonacci code in information theory. Despite its simplicity the Fibonacci GP map exhibits all the above properties of much more complex and biologically realistic GP maps. These properties are therefore likely to be fundamental to many biological GP maps.
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Affiliation(s)
- S F Greenbury
- Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
| | - S E Ahnert
- Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
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Taylor-Teeples M, Lin L, de Lucas M, Turco G, Toal TW, Gaudinier A, Young NF, Trabucco GM, Veling MT, Lamothe R, Handakumbura PP, Xiong G, Wang C, Corwin J, Tsoukalas A, Zhang L, Ware D, Pauly M, Kliebenstein DJ, Dehesh K, Tagkopoulos I, Breton G, Pruneda-Paz JL, Ahnert SE, Kay SA, Hazen SP, Brady SM. An Arabidopsis gene regulatory network for secondary cell wall synthesis. Nature 2014; 517:571-5. [PMID: 25533953 PMCID: PMC4333722 DOI: 10.1038/nature14099] [Citation(s) in RCA: 447] [Impact Index Per Article: 44.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2013] [Accepted: 11/20/2014] [Indexed: 12/15/2022]
Abstract
The plant cell wall is an important factor for determining cell shape, function and response to the environment. Secondary cell walls, such as those found in xylem, are composed of cellulose, hemicelluloses and lignin and account for the bulk of plant biomass. The coordination between transcriptional regulation of synthesis for each polymer is complex and vital to cell function. A regulatory hierarchy of developmental switches has been proposed, although the full complement of regulators remains unknown. Here, we present a protein-DNA network between Arabidopsis transcription factors and secondary cell wall metabolic genes with gene expression regulated by a series of feed-forward loops. This model allowed us to develop and validate new hypotheses about secondary wall gene regulation under abiotic stress. Distinct stresses are able to perturb targeted genes to potentially promote functional adaptation. These interactions will serve as a foundation for understanding the regulation of a complex, integral plant component.
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Affiliation(s)
- M Taylor-Teeples
- 1] Department of Plant Biology, University of California Davis, One Shields Avenue, Davis, California 95616, USA [2] Genome Center, University of California Davis, One Shields Avenue, Davis, California 95616, USA
| | - L Lin
- Biology Department, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - M de Lucas
- 1] Department of Plant Biology, University of California Davis, One Shields Avenue, Davis, California 95616, USA [2] Genome Center, University of California Davis, One Shields Avenue, Davis, California 95616, USA
| | - G Turco
- 1] Department of Plant Biology, University of California Davis, One Shields Avenue, Davis, California 95616, USA [2] Genome Center, University of California Davis, One Shields Avenue, Davis, California 95616, USA
| | - T W Toal
- 1] Department of Plant Biology, University of California Davis, One Shields Avenue, Davis, California 95616, USA [2] Genome Center, University of California Davis, One Shields Avenue, Davis, California 95616, USA
| | - A Gaudinier
- 1] Department of Plant Biology, University of California Davis, One Shields Avenue, Davis, California 95616, USA [2] Genome Center, University of California Davis, One Shields Avenue, Davis, California 95616, USA
| | - N F Young
- Biology Department, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - G M Trabucco
- Biology Department, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - M T Veling
- Biology Department, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - R Lamothe
- Biology Department, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - P P Handakumbura
- Biology Department, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - G Xiong
- Department of Plant and Microbial Biology, University of California Berkeley, Berkeley, California 94720, USA
| | - C Wang
- Department of Plant Biology, University of California Davis, One Shields Avenue, Davis, California 95616, USA
| | - J Corwin
- Department of Plant Sciences, University of California Davis, One Shields Avenue, Davis, California 95616, USA
| | - A Tsoukalas
- 1] Genome Center, University of California Davis, One Shields Avenue, Davis, California 95616, USA [2] Department of Computer Science, University of California Davis, One Shields Avenue, Davis, California 95616, USA
| | - L Zhang
- Cold Spring Harbor Laboratory, Cold Spring Harbor, New York 11724, USA
| | - D Ware
- 1] Cold Spring Harbor Laboratory, Cold Spring Harbor, New York 11724, USA [2] US Department of Agriculture, Agricultural Research Service, Ithaca, New York 14853, USA
| | - M Pauly
- Department of Plant and Microbial Biology, University of California Berkeley, Berkeley, California 94720, USA
| | - D J Kliebenstein
- Department of Plant Sciences, University of California Davis, One Shields Avenue, Davis, California 95616, USA
| | - K Dehesh
- Department of Plant Biology, University of California Davis, One Shields Avenue, Davis, California 95616, USA
| | - I Tagkopoulos
- 1] Genome Center, University of California Davis, One Shields Avenue, Davis, California 95616, USA [2] Department of Computer Science, University of California Davis, One Shields Avenue, Davis, California 95616, USA
| | - G Breton
- Section of Cell and Developmental Biology, Division of Biological Sciences, University of California San Diego, La Jolla, California 92093, USA
| | - J L Pruneda-Paz
- Section of Cell and Developmental Biology, Division of Biological Sciences, University of California San Diego, La Jolla, California 92093, USA
| | - S E Ahnert
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
| | - S A Kay
- Section of Cell and Developmental Biology, Division of Biological Sciences, University of California San Diego, La Jolla, California 92093, USA
| | - S P Hazen
- Biology Department, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - S M Brady
- 1] Department of Plant Biology, University of California Davis, One Shields Avenue, Davis, California 95616, USA [2] Genome Center, University of California Davis, One Shields Avenue, Davis, California 95616, USA
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