Selection on metabolic pathway function in the presence of mutation-selection-drift balance leads to rate-limiting steps that are not evolutionarily stable

PEMPS: a phylogenetic software tool to model the evolution of metabolic pathways

BACKGROUND

Metabolic pathways support the enzyme flux that converts input chemicals into energy and cellular building blocks. With a constant rate of input, steady-state flux is achieved when metabolite concentrations and reaction rates remain constant over time. Individual genes undergo mutation, while selection acts on higher level functions of the pathway, such as steady-state flux where applicable. Modeling the evolution of metabolic pathways through mechanistic sets of ordinary differential equations is a piece of the genotype-phenotype map model for interpreting genetic variation and inter-specific differences. Such models can generate distinct compensatory changes and adaptive changes from directional selection, indicating single nucleotide polymorphisms and fixed differences that could affect phenotype. If used for inference, this would ultimately enable detection of selection on metabolic pathways as well as inference of ancestral states for metabolic pathway function.

RESULTS

A software tool for simulating the evolution of metabolic pathways based upon underlying biochemistry, phylogenetics, and evolutionary considerations is presented. The Python program, Phylogenetic Evolution of Metabolic Pathway Simulator (PEMPS), implements a mutation-selection framework to simulate the evolution of the pathway over a phylogeny by interfacing with COPASI to calculate the steady-state flux of the metabolic network, introducing mutations as alterations in parameter values according to a model, and calculating a fitness score and corresponding probability of fixation based on the change in steady-state flux value(s). Results from simulations are consistent with a priori expectations of fixation probabilities and systematic change in model parameters.

CONCLUSIONS

The PEMPS program simulates the evolution of a metabolic pathway with a mutation-selection modeling framework based on criteria like steady-state flux that is designed to work with SBML-formatted kinetic models, and Newick-formatted phylogenetic trees. The Python software is run on the Linux command line and is available at https://github.com/nmccloskey/PEMPS .

A review of visualisations of protein fold networks and their relationship with sequence and function

Proteins form arguably the most significant link between genotype and phenotype. Understanding the relationship between protein sequence and structure, and applying this knowledge to predict function, is difficult. One way to investigate these relationships is by considering the space of protein folds and how one might move from fold to fold through similarity, or potential evolutionary relationships. The many individual characterisations of fold space presented in the literature can tell us a lot about how well the current Protein Data Bank represents protein fold space, how convergence and divergence may affect protein evolution, how proteins affect the whole of which they are part, and how proteins themselves function. A synthesis of these different approaches and viewpoints seems the most likely way to further our knowledge of protein structure evolution and thus, facilitate improved protein structure design and prediction.

The Memory Problem for Neutral Mutational Models of Evolution

Models for the evolution of various phenotypes are sometimes constructed with an assumption that mutational effects will be symmetrically distributed about a static mean. This model produces a memory effect that over long evolutionary times results in an expectation that randomized sequences underlying the genetic architecture of the trait will on average retain the ancestral phenotype. This expectation is unrealistic and also inconsistent with our current understanding of processes of molecular evolution.

Decoding 'Unnecessary Complexity': A Law of Complexity and a Concept of Hidden Variation Behind "Missing Heritability" in Precision Medicine

The high hopes for the Human Genome Project and personalized medicine were not met because the relationship between genotypes and phenotypes turned out to be more complex than expected. In a previous study we laid the foundation of a theory of complexity and showed that because of the blind nature of evolution, and molecular and historical contingency, cells have accumulated unnecessary complexity, complexity beyond what is necessary and sufficient to describe an organism. Here we provide empirical evidence and show that unnecessary complexity has become integrated into the genome in the form of redundancy and is relevant to molecular evolution of phenotypic complexity. Unnecessary complexity creates uncertainty between molecular and phenotypic complexity, such that phenotypic complexity (CP) is higher than molecular complexity (CM), which is higher than DNA complexity (CD). The qualitative inequality in complexity is based on the following hierarchy: CP > CM > CD. This law-like relationship holds true for all complex traits, including complex diseases. We present a hypothesis of two types of variation, namely open and closed (hidden) systems, show that hidden variation provides a hitherto undiscovered "third source" of phenotypic variation, beside genotype and environment, and argue that "missing heritability" for some complex diseases is likely to be a case of "diluted heritability". There is a need for radically new ways of thinking about the principles of genotype-phenotype relationship. Understanding how cells use hidden, pathway variation to respond to stress can shed light on why two individuals who share the same risk factors may not develop the same disease, or how cancer cells escape death.

Constructive Neutral Evolution 20 Years Later

Evolution has led to a great diversity that ranges from elegant simplicity to ornate complexity. Many complex features are often assumed to be more functional or adaptive than their simpler alternatives. However, in 1999, Arlin Stolzfus published a paper in the Journal of Molecular Evolution that outlined a framework in which complexity can arise through a series of non-adaptive steps. He called this framework Constructive Neutral Evolution (CNE). Despite its two-decade-old roots, many evolutionary biologists still appear to be unaware of this explanatory framework for the origins of complexity. In this perspective piece, we explain the theory of CNE and how it changes the order of events in narratives that describe the evolution of complexity. We also provide an extensive list of cellular features that may have become more complex through CNE. We end by discussing strategies to determine whether complexity arose through neutral or adaptive processes.

Ancestral Sequence Reconstruction: From Chemical Paleogenetics to Maximum Likelihood Algorithms and Beyond

As both a computational and an experimental endeavor, ancestral sequence reconstruction remains a timely and important technique. Modern approaches to conduct ancestral sequence reconstruction for proteins are built upon a conceptual framework from journal founder Emile Zuckerkandl. On top of this, work on maximum likelihood phylogenetics published in Journal of Molecular Evolution in 1996 was one of the first approaches for generating maximum likelihood ancestral sequences of proteins. From its computational history, future model development needs as well as potential applications in areas as diverse as computational systems biology, molecular community ecology, infectious disease therapeutics and other biomedical applications, and biotechnology are discussed. From its past in this journal, there is a bright future for ancestral sequence reconstruction in the field of evolutionary biology.

Characterizing lineage-specific evolution and the processes driving genomic diversification in chordates

Background

Understanding the origins of genome content has long been a goal of molecular evolution and comparative genomics. By examining genome evolution through the guise of lineage-specific evolution, it is possible to make inferences about the evolutionary events that have given rise to species-specific diversification. Here we characterize the evolutionary trends found in chordate species using The Adaptive Evolution Database (TAED). TAED is a database of phylogenetically indexed gene families designed to detect episodes of directional or diversifying selection across chordates. Gene families within the database have been assessed for lineage-specific estimates of dN/dS and have been reconciled to the chordate species to identify retained duplicates. Gene families have also been mapped to the functional pathways and amino acid changes which occurred on high dN/dS lineages have been mapped to protein structures.

Results

An analysis of this exhaustive database has enabled a characterization of the processes of lineage-specific diversification in chordates. A pathway level enrichment analysis of TAED determined that pathways most commonly found to have elevated rates of evolution included those involved in metabolism, immunity, and cell signaling. An analysis of protein fold presence on proteins, after normalizing for frequency in the database, found common folds such as Rossmann folds, Jelly Roll folds, and TIM barrels were overrepresented on proteins most likely to undergo directional selection. A set of gene families which experience increased numbers of duplications within short evolutionary times are associated with pathways involved in metabolism, olfactory reception, and signaling. An analysis of protein secondary structure indicated more relaxed constraint in β-sheets and stronger constraint on alpha Helices, amidst a general preference for substitutions at exposed sites. Lastly a detailed analysis of the ornithine decarboxylase gene family, a key enzyme in the pathway for polyamine synthesis, revealed lineage-specific evolution along the lineage leading to Cetacea through rapid sequence evolution in a duplicate gene with amino acid substitutions causing active site rearrangement.

Conclusion

Episodes of lineage-specific evolution are frequent throughout chordate species. Both duplication and directional selection have played large roles in the evolution of the phylum. TAED is a powerful tool for facilitating this understanding of lineage-specific evolution.

Metabolic Determinants of Enzyme Evolution in a Genome-Scale Bacterial Metabolic Network

Different genes and proteins evolve at very different rates. To identify the factors that explain these differences is an important aspect of research in molecular evolution. One such factor is the role a protein plays in a large molecular network. Here, we analyze the evolutionary rates of enzyme-coding genes in the genome-scale metabolic network of Escherichia coli to find the evolutionary constraints imposed by the structure and function of this complex metabolic system. Central and highly connected enzymes appear to evolve more slowly than less connected enzymes, but we find that they do so as a by-product of their high abundance, and not because of their position in the metabolic network. In contrast, enzymes catalyzing reactions with high metabolic flux-high substrate to product conversion rates-evolve slowly even after we account for their abundance. Moreover, enzymes catalyzing reactions that are difficult to by-pass through alternative pathways, such that they are essential in many different genetic backgrounds, also evolve more slowly. Our analyses show that an enzyme's role in the function of a metabolic network affects its evolution more than its place in the network's structure. They highlight the value of a system-level perspective for studies of molecular evolution.

Protein evolution depends on multiple distinct population size parameters

That population size affects the fate of new mutations arising in genomes, modulating both how frequently they arise and how efficiently natural selection is able to filter them, is well established. It is therefore clear that these distinct roles for population size that characterize different processes should affect the evolution of proteins and need to be carefully defined. Empirical evidence is consistent with a role for demography in influencing protein evolution, supporting the idea that functional constraints alone do not determine the composition of coding sequences.

Given that the relationship between population size, mutant fitness and fixation probability has been well characterized, estimating fitness from observed substitutions is well within reach with well-formulated models. Molecular evolution research has, therefore, increasingly begun to leverage concepts from population genetics to quantify the selective effects associated with different classes of mutation. However, in order for this type of analysis to provide meaningful information about the intra- and inter-specific evolution of coding sequences, a clear definition of concepts of population size, what they influence, and how they are best parameterized is essential.

Here, we present an overview of the many distinct concepts that “population size” and “effective population size” may refer to, what they represent for studying proteins, and how this knowledge can be harnessed to produce better specified models of protein evolution.

Characterizing the roles of changing population size and selection on the evolution of flux control in metabolic pathways

Background

Understanding the genotype-phenotype map is fundamental to our understanding of genomes. Genes do not function independently, but rather as part of networks or pathways. In the case of metabolic pathways, flux through the pathway is an important next layer of biological organization up from the individual gene or protein. Flux control in metabolic pathways, reflecting the importance of mutation to individual enzyme genes, may be evolutionarily variable due to the role of mutation-selection-drift balance. The evolutionary stability of rate limiting steps and the patterns of inter-molecular co-evolution were evaluated in a simulated pathway with a system out of equilibrium due to fluctuating selection, population size, or positive directional selection, to contrast with those under stabilizing selection.

Results

Depending upon the underlying population genetic regime, fluctuating population size was found to increase the evolutionary stability of rate limiting steps in some scenarios. This result was linked to patterns of local adaptation of the population. Further, during positive directional selection, as with more complex mutational scenarios, an increase in the observation of inter-molecular co-evolution was observed.

Conclusions

Differences in patterns of evolution when systems are in and out of equilibrium, including during positive directional selection may lead to predictable differences in observed patterns for divergent evolutionary scenarios. In particular, this result might be harnessed to detect differences between compensatory processes and directional processes at the pathway level based upon evolutionary observations in individual proteins. Detecting functional shifts in pathways reflects an important milestone in predicting when changes in genotypes result in changes in phenotypes.

Electronic supplementary material

The online version of this article (doi:10.1186/s12862-017-0962-7) contains supplementary material, which is available to authorized users.

Accelerated simulation of evolutionary trajectories in origin-fixation models

We present an accelerated algorithm to forward-simulate origin-fixation models. Our algorithm requires, on average, only about two fitness evaluations per fixed mutation, whereas traditional algorithms require, per one fixed mutation, a number of fitness evaluations of the order of the effective population size, Ne Our accelerated algorithm yields the exact same steady state as the original algorithm but produces a different order of fixed mutations. By comparing several relevant evolutionary metrics, such as the distribution of fixed selection coefficients and the probability of reversion, we find that the two algorithms behave equivalently in many respects. However, the accelerated algorithm yields less variance in fixed selection coefficients. Notably, we are able to recover the expected amount of variance by rescaling population size, and we find a linear relationship between the rescaled population size and the population size used by the original algorithm. Considering the widespread usage of origin-fixation simulations across many areas of evolutionary biology, we introduce our accelerated algorithm as a useful tool for increasing the computational complexity of fitness functions without sacrificing much in terms of accuracy of the evolutionary simulation.