Genotype networks, innovation, and robustness in sulfur metabolism

Background: A metabolism is a complex network of chemical reactions. This network synthesizes multiple small precursor molecules of biomass from chemicals that occur in the environment. The metabolic network of any one organism is encoded by a metabolic genotype, defined as the set of enzyme-coding genes whose products catalyze the network's reactions. Each metabolic genotype has a metabolic phenotype. We define this metabolic phenotype as the spectrum of different sources of a chemical element that a metabolism can use to synthesize biomass. We here focus on the element sulfur. We study properties of the space of all possible metabolic genotypes in sulfur metabolism by analyzing random metabolic genotypes that are viable on different numbers of sulfur sources. Results: We show that metabolic genotypes with the same phenotype form large connected genotype networks - networks of metabolic networks - that extend far through metabolic genotype space. How far they reach through this space depends linearly on the number of super-essential reactions. A super-essential reaction is an essential reaction that occurs in all networks viable in a given environment. Metabolic networks can differ in how robust their phenotype is to the removal of individual reactions. We find that this robustness depends on metabolic network size, and on other variables, such as the size of minimal metabolic networks whose reactions are all essential in a specific environment. We show that different neighborhoods of any genotype network harbor very different novel phenotypes, metabolic innovations that can sustain life on novel sulfur sources. We also analyze the ability of evolving populations of metabolic networks to explore novel metabolic phenotypes. This ability is facilitated by the existence of genotype networks, because different neighborhoods of these networks contain very different novel phenotypes. Conclusions: We show that the space of metabolic genotypes involved in sulfur metabolism is organized similarly to that of carbon metabolism. We demonstrate that the maximum genotype distance and robustness of metabolic networks can be explained by the number of superessential reactions and by the sizes of minimal metabolic networks viable in an environment. In contrast to the genotype space of macromolecules, where phenotypic robustness may facilitate phenotypic innovation, we show that here the ability to access novel phenotypes does not monotonically increase with robustness

Adding levels of complexity enhances robustness and evolvability in a multilevel genotype-phenotype map

This paper has been presented at: 6th Meeting of the Spanish Society for Evolutionary Biology (SESBE): Palma,17th – 19th January 2018Robustness and evolvability are the main properties that account for the stability andaccessibility of phenotypes. They have been studied in a number of computationalgenotype- phenotype maps. In this contribution we study a metabolic genotypephenotypemap defined in toyLIFE, a multi-level computational model that representsa simplified cellular biology. toyLIFE includes several levels of phenotypic expression,from proteins to regulatory networks to metabolism. Our results show that toyLIFEshares many similarities with other seemingly unrelated computational genotypephenotypemaps. Thus, toyLIFE shows a high degeneracy in the mapping fromgenotypes to phenotypes, as well as a highly skewed distribution of phenotypicabundances. The neutral networks associated with abundant phenotypes are highlynavigable, and common phenotypes are close to each other in genotype space. Allof these properties are remarkable, as toyLIFE is built on a version of the HP proteinfolding model that is neither robust nor evolvable: phenotypes cannot be mutuallyaccessed through point mutations. In addition, both robustness and evolvabilityincrease with the number of genes in a genotype. Therefore, our results suggest thatadding levels of complexity to the mapping of genotypes to phenotypes and increasinggenome size enhances both these properties

Tradeoff between robustness and elaboration in carotenoid networks produces cycles of avian color diversification

BACKGROUND: Resolution of the link between micro- and macroevolution calls for comparing both processes on the same deterministic landscape, such as genomic, metabolic or fitness networks. We apply this perspective to the evolution of carotenoid pigmentation that produces spectacular diversity in avian colors and show that basic structural properties of the underlying carotenoid metabolic network are reflected in global patterns of elaboration and diversification in color displays. Birds color themselves by consuming and metabolizing several dietary carotenoids from the environment. Such fundamental dependency on the most upstream external compounds should intrinsically constrain sustained evolutionary elongation of multi-step metabolic pathways needed for color elaboration unless the metabolic network gains robustness - the ability to synthesize the same carotenoid from an additional dietary starting point. RESULTS: We found that gains and losses of metabolic robustness were associated with evolutionary cycles of elaboration and stasis in expressed carotenoids in birds. Lack of metabolic robustness constrained lineage's metabolic explorations to the immediate biochemical vicinity of their ecologically distinct dietary carotenoids, whereas gains of robustness repeatedly resulted in sustained elongation of metabolic pathways on evolutionary time scales and corresponding color elaboration. CONCLUSIONS: The structural link between length and robustness in metabolic pathways may explain periodic convergence of phylogenetically distant and ecologically distinct species in expressed carotenoid pigmentation; account for stasis in carotenoid colors in some ecological lineages; and show how the connectivity of the underlying metabolic network provides a mechanistic link between microevolutionary elaboration and macroevolutionary diversification. REVIEWERS: This article was reviewed by Junhyong Kim, Eugene Koonin, and Fyodor Kondrashov. For complete reports, see the Reviewers' reports section.This item is part of the UA Faculty Publications collection. For more information this item or other items in the UA Campus Repository, contact the University of Arizona Libraries at [email protected]

Models in molecular evolution: the case of toyLIFE

Mención Internacional en el título de doctorThis thesis set out to contribute to the growing body of knowledge pertaining models of the genotype-phenotype map. In the process, we proposed and studied a new computational model, toyLIFE, and a new metaphor for molecular evolution —adaptive multiscapes. We also studied functional promiscuity and the evolutionary dynamics of shifting environments. The first result of this thesis was the definition of toyLIFE, a simplified model of cellular biology that incorporated toy versions of genes, proteins and regulation as well as metabolic laws. Molecules in toyLIFE interact between each other following the laws of the HP protein folding model, which endows toyLIFE with a simplified chemistry. From these laws, we saw how something reminiscent of cell-like behavior emerged, with complex regulatory and metabolic networks that grew in complexity as the genome increased. toyLIFE is, to our knowledge, the first multi-level model of the genotype- phenotype map, compared to previous models studied in the literature, such as RNA, proteins, gene regulatory networks (GRNs) or metabolic networks. All of these models either disregarded cellular context when assigning phenotype and function (RNA and proteins) or omitted genome dynamics, by defining their genotypes from high-level abstractions (GRNs and metabolic networks). toyLIFE shares the same features exhibited by all genotype-phenotype maps studied so far. There is strong degeneracy in the map, with many genotypes mapping into the same phenotype. This degeneracy translates into the existence of neutral networks, that span genotype space as soon as the genotype contains more than two genes. There is also a strong asymmetry in the size distribution of phenotypes: most phenotypes were rare, while a few of them covered most genotypes. Moreover, most common phenotypes are easily accessed from each other. We also studied the prevalence of functional promiscuity (the ability to perform more than one function) in computational models of the genotypephenotype map. In particular, we studied RNA, Boolean GRNs and toy- LIFE. Our results suggest that promiscuity is the norm, rather than the exception. These results prompt us to rethink our understanding of biology as a neatly functioning machine. One of the most interesting results of this thesis came from studying the evolutionary dynamics of shifting environments in populations showing functional promiscuity: our results show that there is an optimal frequency of change that minimizes the time to extinction of the population. Finally, we presented a new metaphor for molecular evolution: adaptive multiscapes. This framework intends to update the fitness landscape metaphor proposed by Sewall Wright in the 1930s. Adaptive multiscapes include many features that we have learned from computational studies of the genotype-phenotype map, and that have been discussed throughout the thesis. The existence of neutral networks, the asymmetry in phenotype sizes -and the concomitant asymmetry in phenotype accessibility- and the presence of functional promiscuity all alter the original fitness landscape picture.Programa Oficial de Doctorado en Ingeniería MatemáticaPresidente: Joshua Levy Payne.- Secretario: Saúl Arés García.- Vocal: Jacobo Aguirre Arauj