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

The organization of metabolic genotype space facilitates adaptive evolution in nitrogen metabolism

A metabolism is a complex chemical reaction system, whose metabolic genotype – the DNA encoding the enzymes catalyzing these reactions – can be compactly represented by its complement of metabolic reactions. Here, we analyze a space of such metabolic genotypes. Specifically, we study nitrogen metabolism and focus on nitrogen utilization phenotypes that are defined through the viability of a metabolism – its ability to synthesize all essential small biomass precursors – on a given combination of sole nitrogen sources. We randomly sample metabolisms with known phenotypes from metabolic genotype space with the aid of a method based on Markov Chain Monte Carlo sampling. We find that metabolisms viable on a given nitrogen source or a combination of nitrogen sources can differ in as much as 80 percent of their reactions, but can form networks of genotypes that are connected to one another through sequences of single reaction changes. The reactions that cannot vary in any one metabolism differ among metabolisms, and include a small core of “absolutely superessential” reactions that are required in all metabolisms we study. Only a small number of reaction changes are needed to reach the genotype network of one metabolic phenotype from the genotype network of another metabolic phenotype. Our observations indicate deep similarities between the genotype spaces of macromolecules, regulatory circuits, and metabolism that can facilitate the origin of novel phenotypes in evolution.  

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

Historical contingency and the gradual evolution of metabolic properties in central carbon and genome-scale metabolisms

BACKGROUND A metabolism can evolve through changes in its biochemical reactions that are caused by processes such as horizontal gene transfer and gene deletion. While such changes need to preserve an organism's viability in its environment, they can modify other important properties, such as a metabolism's maximal biomass synthesis rate and its robustness to genetic and environmental change. Whether such properties can be modulated in evolution depends on whether all or most viable metabolisms - those that can synthesize all essential biomass precursors - are connected in a space of all possible metabolisms. Connectedness means that any two viable metabolisms can be converted into one another through a sequence of single reaction changes that leave viability intact. If the set of viable metabolisms is disconnected and highly fragmented, then historical contingency becomes important and restricts the alteration of metabolic properties, as well as the number of novel metabolic phenotypes accessible in evolution. RESULTS We here computationally explore two vast spaces of possible metabolisms to ask whether viable metabolisms are connected. We find that for all but the simplest metabolisms, most viable metabolisms can be transformed into one another by single viability-preserving reaction changes. Where this is not the case, alternative essential metabolic pathways consisting of multiple reactions are responsible, but such pathways are not common. CONCLUSIONS Metabolism is thus highly evolvable, in the sense that its properties could be fine-tuned by successively altering individual reactions. Historical contingency does not strongly restrict the origin of novel metabolic phenotypes

Systems Biology Approaches to Evaluate Disease Modularity

Biological systems are in a constant process of innovation as an essential precondition to evolve. For this reason, the emergence of phenotypic variation is an inherent property of complex adaptive systems. Even though living systems acquire robustness to internal and external disturbances during the evolutionary process, pathological conditions entail impairments to their functionality. This is the rationale for studying biomedical issues according to the organizational properties of biological systems, with the aim of understanding the mechanisms of diseases. I first discuss the theoretical background that is suitable for the research included in this Thesis, such as my own interpretation of systems biology, the current theories about the origin of the biological modularity and some evolutionary considerations that concern in the genotype-phenotype relationships. In this section, I also argue the use and the development of integrative systems biology methods that should be addressed to evaluate disease modules: computational models (i.e. mathematical and network-based models) and other standardized efforts (ontologies and different databases with biological and biomedical data). Then, I enunciate the hypothesis and declare the objectives that motivated this research: i) mathematical modelling based on kinetic law formalism for studying the functional modularity of the metabolism; ii) the development of a workflow to integrate metabolic and kinetic data from different databases for metabolic modelling; iii) the evaluation of the functional coherence in phenotypic relationships between disease-causing genes by using network-based analysis; iv) the development of an integrative framework of biomedical information; v) the use of network medicine approaches to study the phenotypic and genotypic relationships in a heterogeneous group of patients with genetic syndromes. Finally, the results derived from the research carried out in this Thesis are included in the form of already published articles and manuscripts (either submitted or in preparation)

Adaptive multiscapes: an up-to-date metaphor to visualize molecular adaptation

Wright's metaphor of the fitness landscape has shaped and conditioned our view of the adaptation of populations for almost a century. Since its inception, and including criticism raised by Wright himself, the concept has been surrounded by controversy. Among others, the debate stems from the intrinsic difficulty to capture important features of the space of genotypes, such as its high dimensionality or the existence of abundant ridges, in a visually appealing two-dimensional picture. Two additional currently widespread observations come to further constrain the applicability of the original metaphor: the very skewed distribution of phenotype sizes (which may actively prevent, due to entropic effects, the achievement of fitness maxima), and functional promiscuity (i.e. the existence of secondary functions which entail partial adaptation to environments never encountered before by the population). Results: Here we revise some of the shortcomings of the fitness landscape metaphor and propose a new "scape" formed by interconnected layers, each layer containing the phenotypes viable in a given environment. Different phenotypes within a layer are accessible through mutations with selective value, while neutral mutations cause displacements of populations within a phenotype. A different environment is represented as a separated layer, where phenotypes may have new fitness values, other phenotypes may be viable, and the same genotype may yield a different phenotype, representing genotypic promiscuity. This scenario explicitly includes the many-to-many structure of the genotype-to-phenotype map. A number of empirical observations regarding the adaptation of populations in the light of adaptive multiscapes are reviewed. Conclusions: Several shortcomings of Wright's visualization of fitness landscapes can be overcome through adaptive multiscapes.This work was supported by the Spanish projects ViralESS (FIS2014-57686-P, MINECO) and FIS2015-64349-P (MINECO/FEDER, UE). The funding body did not have any role in the design of the study and collection, analysis, and interpretation of data, and did not contribute to writing the manuscript

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