1
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Mohanty V, Greenbury SF, Sarkany T, Narayanan S, Dingle K, Ahnert SE, Louis AA. Maximum mutational robustness in genotype-phenotype maps follows a self-similar blancmange-like curve. J R Soc Interface 2023; 20:20230169. [PMID: 37491910 PMCID: PMC10369032 DOI: 10.1098/rsif.2023.0169] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2023] [Accepted: 06/27/2023] [Indexed: 07/27/2023] Open
Abstract
Phenotype robustness, defined as the average mutational robustness of all the genotypes that map to a given phenotype, plays a key role in facilitating neutral exploration of novel phenotypic variation by an evolving population. By applying results from coding theory, we prove that the maximum phenotype robustness occurs when genotypes are organized as bricklayer's graphs, so-called because they resemble the way in which a bricklayer would fill in a Hamming graph. The value of the maximal robustness is given by a fractal continuous everywhere but differentiable nowhere sums-of-digits function from number theory. Interestingly, genotype-phenotype maps for RNA secondary structure and the hydrophobic-polar (HP) model for protein folding can exhibit phenotype robustness that exactly attains this upper bound. By exploiting properties of the sums-of-digits function, we prove a lower bound on the deviation of the maximum robustness of phenotypes with multiple neutral components from the bricklayer's graph bound, and show that RNA secondary structure phenotypes obey this bound. Finally, we show how robustness changes when phenotypes are coarse-grained and derive a formula and associated bounds for the transition probabilities between such phenotypes.
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Affiliation(s)
- Vaibhav Mohanty
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, UK
- Program in Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, MA, USA
- MD-PhD Program, Harvard Medical School, Boston, MA, USA and Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Sam F. Greenbury
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, Cambridge, UK
- The Alan Turing Institute, British Library, London, UK
| | - Tasmin Sarkany
- Wellcome-MRC Cambridge Stem Cell Institute, University of Cambridge, Cambridge, UK
| | - Shyam Narayanan
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Kamaludin Dingle
- Department of Mathematics and Natural Sciences, Centre for Applied Mathematics and Bioinformatics (CAMB), Gulf University of Science and Technology, Kuwait
- Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA
| | - Sebastian E. Ahnert
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, Cambridge, UK
- Department of Chemical Engineering and Biotechnology, Cavendish Laboratory, University of Cambridge, Cambridge, UK
- The Alan Turing Institute, British Library, London, UK
| | - Ard A. Louis
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, UK
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2
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Mohanty V, Louis AA. Robustness and stability of spin-glass ground states to perturbed interactions. Phys Rev E 2023; 107:014126. [PMID: 36797942 DOI: 10.1103/physreve.107.014126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2020] [Accepted: 12/16/2022] [Indexed: 06/18/2023]
Abstract
Across many problems in science and engineering, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we investigate the glassy phase of ±J spin glasses at zero temperature by calculating the robustness of the ground states to flips in the sign of single interactions. For random graphs and the Sherrington-Kirkpatrick model, we find relatively large sets of bond configurations that generate the same ground state. These sets can themselves be analyzed as subgraphs of the interaction domain, and we compute many of their topological properties. In particular, we find that the robustness, equivalent to the average degree, of these subgraphs is much higher than one would expect from a random model. Most notably, it scales in the same logarithmic way with the size of the subgraph as has been found in genotype-phenotype maps for RNA secondary structure folding, protein quaternary structure, gene regulatory networks, as well as for models for genetic programming. The similarity between these disparate systems suggests that this scaling may have a more universal origin.
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Affiliation(s)
- Vaibhav Mohanty
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3NP, United Kingdom
- MD-PhD Program and Program in Health Sciences and Technology, Harvard Medical School, Boston, Massachusetts 02125, USA and Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Ard A Louis
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3NP, United Kingdom
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3
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The structure of genotype-phenotype maps makes fitness landscapes navigable. Nat Ecol Evol 2022; 6:1742-1752. [PMID: 36175543 DOI: 10.1038/s41559-022-01867-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Accepted: 08/01/2022] [Indexed: 11/09/2022]
Abstract
Fitness landscapes are often described in terms of 'peaks' and 'valleys', indicating an intuitive low-dimensional landscape of the kind encountered in everyday experience. The space of genotypes, however, is extremely high dimensional, which results in counter-intuitive structural properties of genotype-phenotype maps. Here we show that these properties, such as the presence of pervasive neutral networks, make fitness landscapes navigable. For three biologically realistic genotype-phenotype map models-RNA secondary structure, protein tertiary structure and protein complexes-we find that, even under random fitness assignment, fitness maxima can be reached from almost any other phenotype without passing through fitness valleys. This in turn indicates that true fitness valleys are very rare. By considering evolutionary simulations between pairs of real examples of functional RNA sequences, we show that accessible paths are also likely to be used under evolutionary dynamics. Our findings have broad implications for the prediction of natural evolutionary outcomes and for directed evolution.
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4
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Manrubia S. The simple emergence of complex molecular function. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20200422. [PMID: 35599566 DOI: 10.1098/rsta.2020.0422] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
At odds with a traditional view of molecular evolution that seeks a descent-with-modification relationship between functional sequences, new functions can emerge de novo with relative ease. At early times of molecular evolution, random polymers could have sufficed for the appearance of incipient chemical activity, while the cellular environment harbours a myriad of proto-functional molecules. The emergence of function is facilitated by several mechanisms intrinsic to molecular organization, such as redundant mapping of sequences into structures, phenotypic plasticity, modularity or cooperative associations between genomic sequences. It is the availability of niches in the molecular ecology that filters new potentially functional proposals. New phenotypes and subsequent levels of molecular complexity could be attained through combinatorial explorations of currently available molecular variants. Natural selection does the rest. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.
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Affiliation(s)
- Susanna Manrubia
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain
- Systems Biology Department, National Biotechnology Centre (CSIC), c/Darwin 3, 28049 Madrid, Spain
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5
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Martin NS, Ahnert SE. Fast free-energy-based neutral set size estimates for the RNA genotype-phenotype map. J R Soc Interface 2022; 19:20220072. [PMID: 35702868 PMCID: PMC9198509 DOI: 10.1098/rsif.2022.0072] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
The genotype–phenotype (GP) map of RNA secondary structure links each RNA sequence to its corresponding secondary structure. Previous research has shown that the large-scale structural properties of GP maps, such as the size of neutral sets in genotype space, can influence evolutionary outcomes. In order to use neutral set sizes, efficient and accurate computational methods are needed to compute them. Here, we propose a new method, which is based on free energy estimates and is much faster than existing sample-based methods. Moreover, this approach can give insight into the reasons behind neutral set size variations, for example, why structures with fewer stacks tend to have larger neutral set sizes. In addition, we generalize neutral set size calculations from the previously studied many-to-one framework, where each sequence folds into a single energetically preferred structure, to a fuller many-to-many framework, where several low-energy structures are included. We find that structures with high neutral sets in one framework also tend to have large neutral sets in the other framework for a range of parameters and thus the choice of GP map does not fundamentally affect which structures have the largest neutral set sizes.
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Affiliation(s)
- Nora S Martin
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK.,Sainsbury Laboratory, University of Cambridge, Bateman Street, Cambridge CB2 1LR, UK.,Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - Sebastian E Ahnert
- Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge CB3 0AS, UK.,The Alan Turing Institute, British Library, Euston Road, London NW1 2DB, UK
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6
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Martin NS, Ahnert SE. Insertions and deletions in the RNA sequence-structure map. J R Soc Interface 2021; 18:20210380. [PMID: 34610259 PMCID: PMC8492174 DOI: 10.1098/rsif.2021.0380] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2021] [Accepted: 09/13/2021] [Indexed: 12/21/2022] Open
Abstract
Genotype-phenotype maps link genetic changes to their fitness effect and are thus an essential component of evolutionary models. The map between RNA sequences and their secondary structures is a key example and has applications in functional RNA evolution. For this map, the structural effect of substitutions is well understood, but models usually assume a constant sequence length and do not consider insertions or deletions. Here, we expand the sequence-structure map to include single nucleotide insertions and deletions by using the RNAshapes concept. To quantify the structural effect of insertions and deletions, we generalize existing definitions for robustness and non-neutral mutation probabilities. We find striking similarities between substitutions, deletions and insertions: robustness to substitutions is correlated with robustness to insertions and, for most structures, to deletions. In addition, frequent structural changes after substitutions also tend to be common for insertions and deletions. This is consistent with the connection between energetically suboptimal folds and possible structural transitions. The similarities observed hold both for genotypic and phenotypic robustness and mutation probabilities, i.e. for individual sequences and for averages over sequences with the same structure. Our results could have implications for the rate of neutral and non-neutral evolution.
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Affiliation(s)
- Nora S. Martin
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK
- Sainsbury Laboratory, University of Cambridge, Bateman Street, Cambridge CB2 1LR, UK
| | - Sebastian E. Ahnert
- Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge CB3 0AS, UK
- The Alan Turing Institute, British Library, Euston Road, London NW1 2DB, UK
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7
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McCandlish DM. System-specificity of genotype-phenotype map structure: Comment on "From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics" by Susanna Manrubia et al. Phys Life Rev 2021; 39:73-75. [PMID: 34538592 DOI: 10.1016/j.plrev.2021.08.005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2021] [Accepted: 08/29/2021] [Indexed: 11/18/2022]
Affiliation(s)
- David M McCandlish
- Simons Center for Quantitative Biology, Cold Spring Harbor Laboratory, 1 Bungtown Road, Cold Spring Harbor, NY, USA.
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8
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The search for universality in evolutionary landscapes: Comment on "From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics" by Susanna Manrubia, José A. Cuesta, et al. Phys Life Rev 2021; 39:76-78. [PMID: 34507904 DOI: 10.1016/j.plrev.2021.08.004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2021] [Accepted: 08/19/2021] [Indexed: 11/21/2022]
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9
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Camacho Mateu J, Sireci M, Muñoz MA. Phenotypic-dependent variability and the emergence of tolerance in bacterial populations. PLoS Comput Biol 2021; 17:e1009417. [PMID: 34555011 PMCID: PMC8492070 DOI: 10.1371/journal.pcbi.1009417] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Revised: 10/05/2021] [Accepted: 09/03/2021] [Indexed: 11/19/2022] Open
Abstract
Ecological and evolutionary dynamics have been historically regarded as unfolding at broadly separated timescales. However, these two types of processes are nowadays well-documented to intersperse much more tightly than traditionally assumed, especially in communities of microorganisms. Advancing the development of mathematical and computational approaches to shed novel light onto eco-evolutionary problems is a challenge of utmost relevance. With this motivation in mind, here we scrutinize recent experimental results showing evidence of rapid evolution of tolerance by lag in bacterial populations that are periodically exposed to antibiotic stress in laboratory conditions. In particular, the distribution of single-cell lag times-i.e., the times that individual bacteria from the community remain in a dormant state to cope with stress-evolves its average value to approximately fit the antibiotic-exposure time. Moreover, the distribution develops right-skewed heavy tails, revealing the presence of individuals with anomalously large lag times. Here, we develop a parsimonious individual-based model mimicking the actual demographic processes of the experimental setup. Individuals are characterized by a single phenotypic trait: their intrinsic lag time, which is transmitted with variation to the progeny. The model-in a version in which the amplitude of phenotypic variations grows with the parent's lag time-is able to reproduce quite well the key empirical observations. Furthermore, we develop a general mathematical framework allowing us to describe with good accuracy the properties of the stochastic model by means of a macroscopic equation, which generalizes the Crow-Kimura equation in population genetics. Even if the model does not account for all the biological mechanisms (e.g., genetic changes) in a detailed way-i.e., it is a phenomenological one-it sheds light onto the eco-evolutionary dynamics of the problem and can be helpful to design strategies to hinder the emergence of tolerance in bacterial communities. From a broader perspective, this work represents a benchmark for the mathematical framework designed to tackle much more general eco-evolutionary problems, thus paving the road to further research avenues.
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Affiliation(s)
- José Camacho Mateu
- Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés, Spain
| | - Matteo Sireci
- Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada, Spain
| | - Miguel A. Muñoz
- Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada, Spain
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10
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Manrubia S, Cuesta JA, Aguirre J, Ahnert SE, Altenberg L, Cano AV, Catalán P, Diaz-Uriarte R, Elena SF, García-Martín JA, Hogeweg P, Khatri BS, Krug J, Louis AA, Martin NS, Payne JL, Tarnowski MJ, Weiß M. From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics. Phys Life Rev 2021; 38:55-106. [PMID: 34088608 DOI: 10.1016/j.plrev.2021.03.004] [Citation(s) in RCA: 32] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2020] [Accepted: 03/01/2021] [Indexed: 12/21/2022]
Abstract
Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.
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Affiliation(s)
- Susanna Manrubia
- Department of Systems Biology, Centro Nacional de Biotecnología (CSIC), Madrid, Spain; Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain.
| | - José A Cuesta
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain; Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés, Spain; Instituto de Biocomputación y Física de Sistemas Complejos (BiFi), Universidad de Zaragoza, Spain; UC3M-Santander Big Data Institute (IBiDat), Getafe, Madrid, Spain
| | - Jacobo Aguirre
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain; Centro de Astrobiología, CSIC-INTA, ctra. de Ajalvir km 4, 28850 Torrejón de Ardoz, Madrid, Spain
| | - Sebastian E Ahnert
- Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge CB3 0AS, UK; The Alan Turing Institute, British Library, 96 Euston Road, London NW1 2DB, UK
| | | | - Alejandro V Cano
- Institute of Integrative Biology, ETH Zurich, Zurich, Switzerland; Swiss Institute of Bioinformatics, Lausanne, Switzerland
| | - Pablo Catalán
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain; Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés, Spain
| | - Ramon Diaz-Uriarte
- Department of Biochemistry, Universidad Autónoma de Madrid, Madrid, Spain; Instituto de Investigaciones Biomédicas "Alberto Sols" (UAM-CSIC), Madrid, Spain
| | - Santiago F Elena
- Instituto de Biología Integrativa de Sistemas, I(2)SysBio (CSIC-UV), València, Spain; The Santa Fe Institute, Santa Fe, NM, USA
| | | | - Paulien Hogeweg
- Theoretical Biology and Bioinformatics Group, Utrecht University, the Netherlands
| | - Bhavin S Khatri
- The Francis Crick Institute, London, UK; Department of Life Sciences, Imperial College London, London, UK
| | - Joachim Krug
- Institute for Biological Physics, University of Cologne, Köln, Germany
| | - Ard A Louis
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, UK
| | - Nora S Martin
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, Cambridge, UK; Sainsbury Laboratory, University of Cambridge, Cambridge, UK
| | - Joshua L Payne
- Institute of Integrative Biology, ETH Zurich, Zurich, Switzerland; Swiss Institute of Bioinformatics, Lausanne, Switzerland
| | | | - Marcel Weiß
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, Cambridge, UK; Sainsbury Laboratory, University of Cambridge, Cambridge, UK
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11
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Catalán P, Manrubia S, Cuesta JA. Populations of genetic circuits are unable to find the fittest solution in a multilevel genotype-phenotype map. J R Soc Interface 2020; 17:20190843. [PMID: 32486956 PMCID: PMC7328398 DOI: 10.1098/rsif.2019.0843] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2019] [Accepted: 05/12/2020] [Indexed: 01/13/2023] Open
Abstract
The evolution of gene regulatory networks (GRNs) is of great relevance for both evolutionary and synthetic biology. Understanding the relationship between GRN structure and its function can allow us to understand the selective pressures that have shaped a given circuit. This is especially relevant when considering spatio-temporal expression patterns, where GRN models have been shown to be extremely robust and evolvable. However, previous models that studied GRN evolution did not include the evolution of protein and genetic elements that underlie GRN architecture. Here we use toyLIFE, a multilevel genotype-phenotype map, to show that not all GRNs are equally likely in genotype space and that evolution is biased to find the most common GRNs. toyLIFE rules create Boolean GRNs that, embedded in a one-dimensional tissue, develop a variety of spatio-temporal gene expression patterns. Populations of toyLIFE organisms choose the most common GRN out of a set of equally fit alternatives and, most importantly, fail to find a target pattern when it is very rare in genotype space. Indeed, we show that the probability of finding the fittest phenotype increases dramatically with its abundance in genotype space. This phenotypic bias represents a mechanism that can prevent the fixation in the population of the fittest phenotype, one that is inherent to the structure of genotype space and the genotype-phenotype map.
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Affiliation(s)
- Pablo Catalán
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain
- Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés, Madrid, Spain
| | - Susanna Manrubia
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain
- Departamento de Biología de Sistemas, Centro Nacional de Biotecnología (CSIC), Madrid, Spain
| | - José A. Cuesta
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain
- Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés, Madrid, Spain
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Zaragoza, Spain
- UC3M-Santander Big Data Institute (IBiDat), Universidad Carlos III de Madrid, Getafe, Madrid, Spain
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12
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Weiß M, Ahnert SE. Using small samples to estimate neutral component size and robustness in the genotype-phenotype map of RNA secondary structure. J R Soc Interface 2020; 17:20190784. [PMID: 32429824 DOI: 10.1098/rsif.2019.0784] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
In genotype-phenotype (GP) maps, the genotypes that map to the same phenotype are usually not randomly distributed across the space of genotypes, but instead are predominantly connected through one-point mutations, forming network components that are commonly referred to as neutral components (NCs). Because of their impact on evolutionary processes, the characteristics of these NCs, like their size or robustness, have been studied extensively. Here, we introduce a framework that allows the estimation of NC size and robustness in the GP map of RNA secondary structure. The advantage of this framework is that it only requires small samples of genotypes and their local environment, which also allows experimental realizations. We verify our framework by applying it to the exhaustively analysable GP map of RNA sequence length L = 15, and benchmark it against an existing method by applying it to longer, naturally occurring functional non-coding RNA sequences. Although it is specific to the RNA secondary structure GP map in the first place, our framework can probably be transferred and adapted to other sequence-to-structure GP maps.
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Affiliation(s)
- Marcel Weiß
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK.,Sainsbury Laboratory, University of Cambridge, Bateman Street, Cambridge CB2 1LR, UK
| | - Sebastian E Ahnert
- Theory of Condensed Matter Group, 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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13
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Oliver CG, Reinharz V, Waldispühl J. On the emergence of structural complexity in RNA replicators. RNA (NEW YORK, N.Y.) 2019; 25:1579-1591. [PMID: 31467146 PMCID: PMC6859851 DOI: 10.1261/rna.070391.119] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/15/2019] [Accepted: 08/19/2019] [Indexed: 06/10/2023]
Abstract
The RNA world hypothesis relies on the ability of ribonucleic acids to spontaneously acquire complex structures capable of supporting essential biological functions. Multiple sophisticated evolutionary models have been proposed for their emergence, but they often assume specific conditions. In this work, we explore a simple and parsimonious scenario describing the emergence of complex molecular structures at the early stages of life. We show that at specific GC content regimes, an undirected replication model is sufficient to explain the apparition of multibranched RNA secondary structures-a structural signature of many essential ribozymes. We ran a large-scale computational study to map energetically stable structures on complete mutational networks of 50-nt-long RNA sequences. Our results reveal that the sequence landscape with stable structures is enriched with multibranched structures at a length scale coinciding with the appearance of complex structures in RNA databases. A random replication mechanism preserving a 50% GC content may suffice to explain a natural enrichment of stable complex structures in populations of functional RNAs. In contrast, an evolutionary mechanism eliciting the most stable folds at each generation appears to help reaching multibranched structures at highest GC content.
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Affiliation(s)
- Carlos G Oliver
- School of Computer Science, McGill University, Montreal, QC H3A 2B3, Canada
| | - Vladimir Reinharz
- Center for Soft and Living Matter, Institute for Basic Science, Ulsan 34126, South Korea
| | - Jérôme Waldispühl
- School of Computer Science, McGill University, Montreal, QC H3A 2B3, Canada
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14
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Grabow WW, Andrews GE. On the nature and origin of biological information: The curious case of RNA. Biosystems 2019; 185:104031. [PMID: 31525398 DOI: 10.1016/j.biosystems.2019.104031] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2019] [Revised: 09/11/2019] [Accepted: 09/12/2019] [Indexed: 11/18/2022]
Abstract
Biological information is most commonly thought of in terms of biology's Central Dogma where DNA is viewed as a linearized code used to synthesize proteins. Using DNA's chemical cousin, RNA, as a case study we consider how biological information operates outside the linear arrangement of its polymeric subunits. Much like individual pieces of a jigsaw puzzle, particular structures enable biomolecules to undergo precise molecular interactions with one another based on their respective shapes. By exploring the relationship between sequence and structure in RNA we argue that biological information finds its ultimate functional fulfillment in the three-dimensional structural arrangement of its atoms. We show how recurrent structural RNA motifs-operating at the tertiary level of a molecule-provide robust building blocks for the formation of new structural configurations and thereby convey the information required for emergent biological functions. We posit that these same RNA structures, guided by their respective thermodynamic stabilities, experience selective pressure to maintain particular three-dimensional architectures over and above pressures to maintain a particular sequence of nucleotides. Ultimately, this framework for understanding the nature of biological information provides a useful paradigm for understanding its origins and how biological information can result from chaotic prebiotic conditions.
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Affiliation(s)
- Wade W Grabow
- Department of Chemistry and Biochemistry, Seattle Pacific University, Seattle, WA, 918119-1997, USA.
| | - Grace E Andrews
- Department of Chemistry and Biochemistry, Seattle Pacific University, Seattle, WA, 918119-1997, USA
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15
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Weiß M, Ahnert SE. Phenotypes can be robust and evolvable if mutations have non-local effects on sequence constraints. J R Soc Interface 2019; 15:rsif.2017.0618. [PMID: 29321270 DOI: 10.1098/rsif.2017.0618] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2017] [Accepted: 12/07/2017] [Indexed: 11/12/2022] Open
Abstract
The mapping between biological genotypes and phenotypes plays an important role in evolution, and understanding the properties of this mapping is crucial to determine the outcome of evolutionary processes. One of the most striking properties observed in several genotype-phenotype (GP) maps is the positive correlation between the robustness and evolvability of phenotypes. This implies that a phenotype can be strongly robust against mutations and at the same time evolvable to a diverse range of alternative phenotypes. Here, we examine the causes for this positive correlation by introducing two analytically tractable GP map models that follow the principles of real biological GP maps. The first model is based on gene-like GP maps, reflecting the way in which genetic sequences are organized into protein-coding genes, and the second one is based on the GP map of RNA secondary structure. For both models, we find that a positive correlation between phenotype robustness and evolvability only emerges if mutations at one sequence position can have non-local effects on the sequence constraints at another position. This highlights that non-local effects of mutations are closely related to the coexistence of robustness and evolvability in phenotypes, and are likely to be an important feature of many biological GP maps.
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Affiliation(s)
- Marcel Weiß
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK .,Sainsbury Laboratory, University of Cambridge, Bateman Street, Cambridge CB2 1LR, UK
| | - Sebastian E Ahnert
- Theory of Condensed Matter Group, 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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16
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Catalán P, Wagner A, Manrubia S, Cuesta JA. Adding levels of complexity enhances robustness and evolvability in a multilevel genotype-phenotype map. J R Soc Interface 2019; 15:rsif.2017.0516. [PMID: 29321269 DOI: 10.1098/rsif.2017.0516] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2017] [Accepted: 12/01/2017] [Indexed: 01/24/2023] Open
Abstract
Robustness and evolvability are the main properties that account for the stability and accessibility of phenotypes. They have been studied in a number of computational genotype-phenotype maps. In this paper, we study a metabolic genotype-phenotype map defined in toyLIFE, a multilevel computational model that represents a simplified cellular biology. toyLIFE includes several levels of phenotypic expression, from proteins to regulatory networks to metabolism. Our results show that toyLIFE shares many similarities with other seemingly unrelated computational genotype-phenotype maps. Thus, toyLIFE shows a high degeneracy in the mapping from genotypes to phenotypes, as well as a highly skewed distribution of phenotypic abundances. The neutral networks associated with abundant phenotypes are highly navigable, and common phenotypes are close to each other in genotype space. All of these properties are remarkable, as toyLIFE is built on a version of the HP protein-folding model that is neither robust nor evolvable: phenotypes cannot be mutually accessed through point mutations. In addition, both robustness and evolvability increase with the number of genes in a genotype. Therefore, our results suggest that adding levels of complexity to the mapping of genotypes to phenotypes and increasing genome size enhances both these properties.
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Affiliation(s)
- Pablo Catalán
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain .,Departamento de Matematicas, Universidad Carlos III de Madrid, Madrid, Spain
| | - Andreas Wagner
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland.,Santa Fe Institute, Santa Fe, NM, USA.,Swiss Institute of Bioinformatics, Zurich, Switzerland
| | - Susanna Manrubia
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain.,Programa de Biología de Sistemas, Centro Nacional de Biotecnologia, Madrid, Spain
| | - José A Cuesta
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain.,Departamento de Matematicas, Universidad Carlos III de Madrid, Madrid, Spain.,Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Zaragoza, Spain.,Institute of Financial Big Data (IFiBiD), Universidad Carlos III de Madrid, UC3M-BS, Madrid, Spain
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17
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Catalán P, Elena SF, Cuesta JA, Manrubia S. Parsimonious Scenario for the Emergence of Viroid-Like Replicons De Novo. Viruses 2019; 11:v11050425. [PMID: 31075860 PMCID: PMC6563258 DOI: 10.3390/v11050425] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2019] [Revised: 04/30/2019] [Accepted: 05/02/2019] [Indexed: 01/12/2023] Open
Abstract
Viroids are small, non-coding, circular RNA molecules that infect plants. Different hypotheses for their evolutionary origin have been put forward, such as an early emergence in a precellular RNA World or several de novo independent evolutionary origins in plants. Here, we discuss the plausibility of de novo emergence of viroid-like replicons by giving theoretical support to the likelihood of different steps along a parsimonious evolutionary pathway. While Avsunviroidae-like structures are relatively easy to obtain through evolution of a population of random RNA sequences of fixed length, rod-like structures typical of Pospiviroidae are difficult to fix. Using different quantitative approaches, we evaluated the likelihood that RNA sequences fold into a rod-like structure and bear specific sequence motifs facilitating interactions with other molecules, e.g., RNA polymerases, RNases, and ligases. By means of numerical simulations, we show that circular RNA replicons analogous to Pospiviroidae emerge if evolution is seeded with minimal circular RNAs that grow through the gradual addition of nucleotides. Further, these rod-like replicons often maintain their structure if independent functional modules are acquired that impose selective constraints. The evolutionary scenario we propose here is consistent with the structural and biochemical properties of viroids described to date.
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Affiliation(s)
- Pablo Catalán
- Biosciences, College of Life and Environmental Sciences, University of Exeter, Exeter EX4 4QD, UK.
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain.
| | - Santiago F Elena
- Instituto de Biología Integrativa de Sistemas (I2SysBio), CSIC-Universitat de València, Paterna, 46980 València, Spain.
- The Santa Fe Institute, Santa Fe, NM 87501, USA.
| | - José A Cuesta
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain.
- Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain.
- Instituto de Biocomputación y Física de Sistemas Complejos (BiFi), Universidad de Zaragoza, 50018 Zaragoza, Spain.
- Institute of Financial Big Data (IFiBiD), Universidad Carlos III de Madrid⁻Banco de Santander, 28903 Getafe, Spain.
| | - Susanna Manrubia
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain.
- National Biotechnology Centre (CSIC), 28049 Madrid, Spain.
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Fragata I, Blanckaert A, Dias Louro MA, Liberles DA, Bank C. Evolution in the light of fitness landscape theory. Trends Ecol Evol 2019; 34:69-82. [DOI: 10.1016/j.tree.2018.10.009] [Citation(s) in RCA: 84] [Impact Index Per Article: 16.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2018] [Revised: 10/16/2018] [Accepted: 10/17/2018] [Indexed: 01/28/2023]
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Rezazadegan R, Reidys C. Degeneracy and genetic assimilation in RNA evolution. BMC Bioinformatics 2018; 19:543. [PMID: 30587112 PMCID: PMC6307299 DOI: 10.1186/s12859-018-2497-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2018] [Accepted: 11/16/2018] [Indexed: 12/27/2022] Open
Abstract
BACKGROUND The neutral theory of Motoo Kimura stipulates that evolution is mostly driven by neutral mutations. However adaptive pressure eventually leads to changes in phenotype that involve non-neutral mutations. The relation between neutrality and adaptation has been studied in the context of RNA before and here we further study transitional mutations in the context of degenerate (plastic) RNA sequences and genetic assimilation. We propose quasineutral mutations, i.e. mutations which preserve an element of the phenotype set, as minimal mutations and study their properties. We also propose a general probabilistic interpretation of genetic assimilation and specialize it to the Boltzmann ensemble of RNA sequences. RESULTS We show that degenerate sequences i.e. sequences with more than one structure at the MFE level have the highest evolvability among all sequences and are central to evolutionary innovation. Degenerate sequences also tend to cluster together in the sequence space. The selective pressure in an evolutionary simulation causes the population to move towards regions with more degenerate sequences, i.e. regions at the intersection of different neutral networks, and this causes the number of such sequences to increase well beyond the average percentage of degenerate sequences in the sequence space. We also observe that evolution by quasineutral mutations tends to conserve the number of base pairs in structures and thereby maintains structural integrity even in the presence of pressure to the contrary. CONCLUSIONS We conclude that degenerate RNA sequences play a major role in evolutionary adaptation.
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Affiliation(s)
- Reza Rezazadegan
- University of Virginia Biocomplexity Institute, 995 Research Park Boulevard, Charlottesville, 22911 USA
| | - Christian Reidys
- University of Virginia Biocomplexity Institute, 995 Research Park Boulevard, Charlottesville, 22911 USA
- Department of Mathematics, University of Virginia, 141 Cabell Drive, Charlottesville, 22904 USA
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García-Martín JA, Catalán P, Manrubia S, Cuesta JA. Statistical theory of phenotype abundance distributions: A test through exact enumeration of genotype spaces. ACTA ACUST UNITED AC 2018. [DOI: 10.1209/0295-5075/123/28001] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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21
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Aguirre J, Catalán P, Cuesta JA, Manrubia S. On the networked architecture of genotype spaces and its critical effects on molecular evolution. Open Biol 2018; 8:180069. [PMID: 29973397 PMCID: PMC6070719 DOI: 10.1098/rsob.180069] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2018] [Accepted: 06/12/2018] [Indexed: 12/26/2022] Open
Abstract
Evolutionary dynamics is often viewed as a subtle process of change accumulation that causes a divergence among organisms and their genomes. However, this interpretation is an inheritance of a gradualistic view that has been challenged at the macroevolutionary, ecological and molecular level. Actually, when the complex architecture of genotype spaces is taken into account, the evolutionary dynamics of molecular populations becomes intrinsically non-uniform, sharing deep qualitative and quantitative similarities with slowly driven physical systems: nonlinear responses analogous to critical transitions, sudden state changes or hysteresis, among others. Furthermore, the phenotypic plasticity inherent to genotypes transforms classical fitness landscapes into multiscapes where adaptation in response to an environmental change may be very fast. The quantitative nature of adaptive molecular processes is deeply dependent on a network-of-networks multilayered structure of the map from genotype to function that we begin to unveil.
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Affiliation(s)
- Jacobo Aguirre
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain
- Programa de Biología de Sistemas, Centro Nacional de Biotecnología (CSIC), Madrid, Spain
| | - Pablo Catalán
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain
- Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés, Madrid, Spain
| | - José A Cuesta
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain
- Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés, Madrid, Spain
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Zaragoza, Spain
- UC3M-BS Institute of Financial Big Data (IFiBiD), Universidad Carlos III de Madrid, Getafe, Madrid, Spain
| | - Susanna Manrubia
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain
- Programa de Biología de Sistemas, Centro Nacional de Biotecnología (CSIC), Madrid, Spain
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