A computational exploration of resilience and evolvability of protein-protein interaction networks.

Protein-protein interaction (PPI) networks represent complex intra-cellular protein interactions, and the presence or absence of such interactions can lead to biological changes in an organism. Recent network-based approaches have shown that a phenotype's PPI network's resilience to environmental perturbations is related to its placement in the tree of life; though we still do not know how or why certain intra-cellular factors can bring about this resilience. Here, we explore the influence of gene expression and network properties on PPI networks' resilience. We use publicly available data of PPIs for E. coli, S. cerevisiae, and H. sapiens, where we compute changes in network resilience as new nodes (proteins) are added to the networks under three node addition mechanisms-random, degree-based, and gene-expression-based attachments. By calculating the resilience of the resulting networks, we estimate the effectiveness of these node addition mechanisms. We demonstrate that adding nodes with gene-expression-based preferential attachment (as opposed to random or degree-based) preserves and can increase the original resilience of PPI network in all three species, regardless of gene expression distribution or network structure. These findings introduce a general notion of prospective resilience, which highlights the key role of network structures in understanding the evolvability of phenotypic traits.

Modeling poliovirus replication dynamics from live time-lapse single-cell imaging data.

Viruses experience selective pressure on the timing and order of events during infection to maximize the number of viable offspring they produce. Additionally, they may experience variability in cellular environments encountered, as individual eukaryotic cells can display variation in gene expression among cells. This leads to a dynamic phenotypic landscape that viruses must face to replicate. To examine replication dynamics displayed by viruses faced with this variable landscape, we have developed a method for fitting a stochastic mechanistic model of viral infection to time-lapse imaging data from high-throughput single-cell poliovirus infection experiments. The model's mechanistic parameters provide estimates of several aspects associated with the virus's intracellular dynamics. We examine distributions of parameter estimates and assess their variability to gain insight into the root causes of variability in viral growth dynamics. We also fit our model to experiments performed under various drug treatments and examine which parameters differ under these conditions. We find that parameters associated with translation and early stage viral replication processes are essential for the model to capture experimentally observed dynamics. In aggregate, our results suggest that differences in viral growth data generated under different treatments can largely be captured by steps that occur early in the replication process.

A Phylogenetic Rate Parameter Indicates Different Sequence Divergence Patterns in Orthologs and Paralogs.

Heterotachy-the change in sequence evolutionary rate over time-is a common feature of protein molecular evolution. Decades of studies have shed light on the conditions under which heterotachy occurs, and there is evidence that site-specific evolutionary rate shifts are correlated with changes in protein function. Here, we present a large-scale, computational analysis using thousands of protein sequence alignments from animal and plant proteomes, representing genes related either by orthology (speciation events) or paralogy (gene duplication), to compare sequence divergence patterns in orthologous vs. paralogous sequence alignments. We use sequence-based phylogenetic analyses to infer overall sequence divergence (tree length/number of sequences) and to fit site-specific rates to a discrete gamma distribution with a shape parameter α. This inference method is applied to real protein sequence alignments, as well as alignments simulated under various models of protein sequence evolution. Our simulations indicate that sequence divergence and the α parameter are positively correlated when sequences evolve with heterotachy, meaning that inferred site rate distributions appear more uniform as sequences diverge. Divergence and α are also positively correlated in both orthologous and paralogous genes, but the average increase in α (as a function of divergence) is significantly higher in paralogous protein alignments than in orthologous alignments. This result is consistent with the widely held view that recently duplicated proteins initially evolve under relaxed selective pressure, promoting functional divergence by accumulation of amino acid replacements, and hence experience more evolutionary rate fluctuations than orthologous proteins. We discuss these findings in the context of the ortholog conjecture, a long-standing assumption in molecular evolution, which posits that protein sequences related by orthology tend to be more functionally conserved than paralogous proteins.

Humanization of yeast genes with multiple human orthologs reveals functional divergence between paralogs.

Despite over a billion years of evolutionary divergence, several thousand human genes possess clearly identifiable orthologs in yeast, and many have undergone lineage-specific duplications in one or both lineages. These duplicated genes may have been free to diverge in function since their expansion, and it is unclear how or at what rate ancestral functions are retained or partitioned among co-orthologs between species and within gene families. Thus, in order to investigate how ancestral functions are retained or lost post-duplication, we systematically replaced hundreds of essential yeast genes with their human orthologs from gene families that have undergone lineage-specific duplications, including those with single duplications (1 yeast gene to 2 human genes, 1:2) or higher-order expansions (1:>2) in the human lineage. We observe a variable pattern of replaceability across different ortholog classes, with an obvious trend toward differential replaceability inside gene families, and rarely observe replaceability by all members of a family. We quantify the ability of various properties of the orthologs to predict replaceability, showing that in the case of 1:2 orthologs, replaceability is predicted largely by the divergence and tissue-specific expression of the human co-orthologs, i.e., the human proteins that are less diverged from their yeast counterpart and more ubiquitously expressed across human tissues more often replace their single yeast ortholog. These trends were consistent with in silico simulations demonstrating that when only one ortholog can replace its corresponding yeast equivalent, it tends to be the least diverged of the pair. Replaceability of yeast genes having more than 2 human co-orthologs was marked by retention of orthologous interactions in functional or protein networks as well as by more ancestral subcellular localization. Overall, we performed >400 human gene replaceability assays, revealing 50 new human-yeast complementation pairs, thus opening up avenues to further functionally characterize these human genes in a simplified organismal context.

Quantifying the relative importance of variation in predation and the environment for species coexistence.

Coexistence and food web theory are two cornerstones of the long-standing effort to understand how species coexist. Although competition and predation are known to act simultaneously in communities, theory and empirical study of these processes continue to be developed largely independently. Here, we integrate modern coexistence theory and food web theory to simultaneously quantify the relative importance of predation and environmental fluctuations for species coexistence. We first examine coexistence in a theoretical, multitrophic model, adding complexity to the food web using machine learning approaches. We then apply our framework to a stochastic model of the rocky intertidal food web, partitioning empirical coexistence dynamics. We find the main effects of both environmental fluctuations and variation in predator abundances contribute substantially to species coexistence. Unexpectedly, their interaction tends to destabilise coexistence, leading to new insights about the role of bottom-up vs. top-down forces in both theory and the rocky intertidal ecosystem.

The Many Nuanced Evolutionary Consequences of Duplicated Genes.

Gene duplication is seen as a major source of structural and functional divergence in genome evolution. Under the conventional models of sub or neofunctionalization, functional changes arise in one of the duplicates after duplication. However, we suggest here that the presence of a duplicated gene can result in functional changes to its interacting partners. We explore this hypothesis by in silico evolution of a heterodimer when one member of the interacting pair is duplicated. We examine how a range of selection pressures and protein structures leads to differential patterns of evolutionary divergence. We find that a surprising number of distinct evolutionary trajectories can be observed even in a simple three member system. Further, we observe that selection to correct dosage imbalance can affect the evolution of the initial function in several unexpected ways. For example, if a duplicate is under selective pressure to avoid binding its original binding partner, this can lead to changes in the binding interface of a nonduplicated interacting partner to exclude the duplicate. Hence, independent of the fate of the duplicate, its presence can impact how the original function operates. Additionally, we introduce a conceptual framework to describe how interacting partners cope with dosage imbalance after duplication. Contextualizing our results within this framework reveals that the evolutionary path taken by a duplicate's interacting partners is highly stochastic in nature. Consequently, the fate of duplicate genes may not only be controlled by their own ability to accumulate mutations but also by how interacting partners cope with them.

Evolution and Structure of Proteins and Proteomes.

This themed issue centered on the evolution and structure of proteins and proteomes is comprised of seven published manuscripts. [...].

Using the Mutation-Selection Framework to Characterize Selection on Protein Sequences.

When mutational pressure is weak, the generative process of protein evolution involves explicit probabilities of mutations of different types coupled to their conditional probabilities of fixation dependent on selection. Establishing this mechanistic modeling framework for the detection of selection has been a goal in the field of molecular evolution. Building on a mathematical framework proposed more than a decade ago, numerous methods have been introduced in an attempt to detect and measure selection on protein sequences. In this review, we discuss the structure of the original model, subsequent advances, and the series of assumptions that these models operate under.

Beyond Thermodynamic Constraints: Evolutionary Sampling Generates Realistic Protein Sequence Variation.

Biological evolution generates a surprising amount of site-specific variability in protein sequences. Yet, attempts at modeling this process have been only moderately successful, and current models based on protein structural metrics explain, at best, 60% of the observed variation. Surprisingly, simple measures of protein structure, such as solvent accessibility, are often better predictors of site-specific variability than more complex models employing all-atom energy functions and detailed structural modeling. We suggest here that these more complex models perform poorly because they lack consideration of the evolutionary process, which is, in part, captured by the simpler metrics. We compare protein sequences that are computationally designed to sequences that are computationally evolved using the same protein-design energy function and to homologous natural sequences. We find that, by a wide variety of metrics, evolved sequences are much more similar to natural sequences than are designed sequences. In particular, designed sequences are too conserved on the protein surface relative to natural sequences, whereas evolved sequences are not. Our results suggest that evolutionary simulation produces a realistic sampling of sequence space. By contrast, protein design-at least as currently implemented-does not. Existing energy functions seem to be sufficiently accurate to correctly describe the key thermodynamic constraints acting on protein sequences, but they need to be paired with realistic sampling schemes to generate realistic sequence alignments.

Sicegar: R package for sigmoidal and double-sigmoidal curve fitting.

Sigmoidal and double-sigmoidal dynamics are commonly observed in many areas of biology. Here we present sicegar, an R package for the automated fitting and classification of sigmoidal and double-sigmoidal data. The package categorizes data into one of three categories, "no signal," "sigmoidal," or "double-sigmoidal," by rigorously fitting a series of mathematical models to the data. The data is labeled as "ambiguous" if neither the sigmoidal nor double-sigmoidal model fit the data well. In addition to performing the classification, the package also reports a wealth of metrics as well as biologically meaningful parameters describing the sigmoidal or double-sigmoidal curves. In extensive simulations, we find that the package performs well, can recover the original dynamics even under fairly high noise levels, and will typically classify curves as "ambiguous" rather than misclassifying them. The package is available on CRAN and comes with extensive documentation and usage examples.

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.

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

BACKGROUND: While commonly assumed in the biochemistry community that the control of metabolic pathways is thought to be critical to cellular function, it is unclear if metabolic pathways generally have evolutionarily stable rate limiting (flux controlling) steps. RESULTS: A set of evolutionary simulations using a kinetic model of a metabolic pathway was performed under different conditions to evaluate the evolutionary stability of rate limiting steps. Simulations used combinations of selection for steady state flux, selection against the cost of molecular biosynthesis, and selection against the accumulation of high concentrations of a deleterious intermediate. Two mutational regimes were used, one with mutations that on average were neutral to molecular phenotype and a second with a preponderance of activity-destroying mutations. The evolutionary stability of rate limiting steps was low in all simulations with non-neutral mutational processes. Clustering of parameter co-evolution showed divergent inter-molecular evolutionary patterns under different evolutionary regimes. CONCLUSIONS: This study provides a null model for pathway evolution when compensatory processes dominate with potential applications to predicting pathway functional change. This result also suggests a possible mechanism in which studies in statistical genetics that aim to associate a genotype to a phenotype assuming independent action of variants may be mis-specified through a mis-characterization of the link between individual gene function and pathway function. A better understanding of the genotype-phenotype map has potential applications in differentiating between compensatory changes and directional selection on pathways as well as detecting SNPs and fixed differences that might have phenotypic effects. REVIEWERS: This article was reviewed by Arne Elofsson, David Ardell, and Shamil Sunyaev.

Models for gene duplication when dosage balance works as a transition state to subsequent neo-or sub-functionalization.

BACKGROUND: Dosage balance has been described as an important process for the retention of duplicate genes after whole genome duplication events. However, dosage balance is only a temporary mechanism for duplicate gene retention, as it ceases to function following the stochastic loss of interacting partners, as dosage balance itself is lost with this event. With the prolonged period of retention, on the other hand, there is the potential for the accumulation of substitutions which upon release from dosage balance constraints, can lead to either subsequent neo-functionalization or sub-functionalization. Mechanistic models developed to date for duplicate gene retention treat these processes independently, but do not describe dosage balance as a transition state to eventual functional change. RESULTS: Here a model for these processes (dosage plus neofunctionalization and dosage plus subfunctionalization) has been built within an existing framework. Because of the computational complexity of these models, a simpler modeling framework that captures the same information is also proposed. This model is integrated into a phylogenetic birth-death model, expanding the range of available models. CONCLUSIONS: Including further levels of biological reality in methods for gene tree/species tree reconciliation should not only increase the accuracy of estimates of the timing and evolutionary history of genes but can also offer insight into how genes and genomes evolve. These new models add to the tool box for characterizing mechanisms of duplicate gene retention probabilistically.

A generalized birth and death process for modeling the fates of gene duplication.

BACKGROUND: Accurately estimating the timing and mode of gene duplications along the evolutionary history of species can provide invaluable information about underlying mechanisms by which the genomes of organisms evolved and the genes with novel functions arose. Mechanistic models have previously been introduced that allow for probabilistic inference of the evolutionary mechanism for duplicate gene retention based upon the average rate of loss over time of the duplicate. However, there is currently no probabilistic model embedded in a birth-death modeling framework that can take into account the effects of different evolutionary mechanisms of gene retention when analyzing gene family data. RESULTS: In this study, we describe a generalized birth-death process for modeling the fates of gene duplication. Use of mechanistic models in a phylogenetic framework requires an age-dependent birth-death process. Starting with a single population corresponding to the lineage of a phylogenetic tree and with an assumption of a clock that starts ticking for each duplicate at its birth, an age-dependent birth-death process is developed by extending the results from the time-dependent birth-death process. The implementation of such models in a full phylogenetic framework is expected to enable large scale probabilistic analysis of duplicates in comparative genomic studies. CONCLUSIONS: We develop an age-dependent birth-death model for understanding the mechanisms of gene retention, which allows a gene loss rate dependent on each duplication event. Simulation results indicate that different mechanisms of gene retentions produce distinct likelihood functions, which can be used with genomic data to quantitatively distinguish those mechanisms.

What Fraction of Duplicates Observed in Recently Sequenced Genomes Is Segregating and Destined to Fail to Fix?

Most sequenced eukaryotic genomes show a large excess of recent duplicates. As duplicates age, both the population genetic process of failed fixation and the mutation-driven process of nonfunctionalization act to reduce the observed number of duplicates. Understanding the processes generating the age distributions of recent duplicates is important to also understand the role of duplicate genes in the functional divergence of genomes. To date, mechanistic models for duplicate gene retention only account for the mutation-driven nonfunctionalization process. Here, a neutral model for the distribution of synonymous substitutions in duplicated genes which are segregating and expected to never fix in a population is introduced. This model enables differentiation of neutral loss due to failed fixation from loss due to mutation-driven nonfunctionalization. The model has been validated on simulated data and subsequent analysis with the model on genomic data from human and mouse shows that conclusions about the underlying mechanisms for duplicate gene retention can be sensitive to consideration of population genetic processes.

Integrating landscape genomics and spatially explicit approaches to detect loci under selection in clinal populations.

Uncovering the genetic basis of adaptation hinges on the ability to detect loci under selection. However, population genomics outlier approaches to detect selected loci may be inappropriate for clinal populations or those with unclear population structure because they require that individuals be clustered into populations. An alternate approach, landscape genomics, uses individual-based approaches to detect loci under selection and reveal potential environmental drivers of selection. We tested four landscape genomics methods on a simulated clinal population to determine their effectiveness at identifying a locus under varying selection strengths along an environmental gradient. We found all methods produced very low type I error rates across all selection strengths, but elevated type II error rates under "weak" selection. We then applied these methods to an AFLP genome scan of an alpine plant, Campanula barbata, and identified five highly supported candidate loci associated with precipitation variables. These loci also showed spatial autocorrelation and cline patterns indicative of selection along a precipitation gradient. Our results suggest that landscape genomics in combination with other spatial analyses provides a powerful approach for identifying loci potentially under selection and explaining spatially complex interactions between species and their environment.

On the need for mechanistic models in computational genomics and metagenomics.

Computational genomics is now generating very large volumes of data that have the potential to be used to address important questions in both basic biology and biomedicine. Addressing these important biological questions becomes possible when mechanistic models rooted in biochemistry and evolutionary/population genetic processes are developed, instead of fitting data to off-the-shelf statistical distributions that do not enable mechanistic inference. Three examples are presented, the first involving ecological processes inferred from metagenomic data, the second involving mechanisms of gene regulation rooted in protein-DNA interactions with consideration of DNA structure, and the third involving existing models for the retention of duplicate genes that enables prediction of evolutionary mechanisms. This description of mechanistic models is generalized toward future developments in computational genomics and the need for biological mechanisms and processes in biological models.

The interface of protein structure, protein biophysics, and molecular evolution.

Abstract The interface of protein structural biology, protein biophysics, molecular evolution, and molecular population genetics forms the foundations for a mechanistic understanding of many aspects of protein biochemistry. Current efforts in interdisciplinary protein modeling are in their infancy and the state-of-the art of such models is described. Beyond the relationship between amino acid substitution and static protein structure, protein function, and corresponding organismal fitness, other considerations are also discussed. More complex mutational processes such as insertion and deletion and domain rearrangements and even circular permutations should be evaluated. The role of intrinsically disordered proteins is still controversial, but may be increasingly important to consider. Protein geometry and protein dynamics as a deviation from static considerations of protein structure are also important. Protein expression level is known to be a major determinant of evolutionary rate and several considerations including selection at the mRNA level and the role of interaction specificity are discussed. Lastly, the relationship between modeling and needed high-throughput experimental data as well as experimental examination of protein evolution using ancestral sequence resurrection and in vitro biochemistry are presented, towards an aim of ultimately generating better models for biological inference and prediction.

Toward a general model for the evolutionary dynamics of gene duplicates.

Gene duplication is an important process in the functional divergence of genes and genomes. Several processes have been described that lead to duplicate gene retention over different timescales after both smaller-scale events and whole-genome duplication, including neofunctionalization, subfunctionalization, and dosage balance. Two common modes of duplicate gene loss include nonfunctionalization and loss due to population dynamics (failed fixation). Previous work has characterized expectations of duplicate gene retention under the neofunctionalization and subfunctionalization models. Here, that work is extended to dosage balance using simulations. A general model for duplicate gene loss/retention is then presented that is capable of fitting expectations under the different models, is defined at t = 0, and decays to an orthologous asymptotic rate rather than zero, based upon a modified Weibull hazard function. The model in a maximum likelihood framework shows the property of identifiability, recovering the evolutionary mechanism and parameters of simulation. This model is also capable of recovering the evolutionary mechanism of simulation from data generated using an unrelated network population genetic model. Lastly, the general model is applied as part of a mixture model to recent gene duplicates from the Oikopleura dioica genome, suggesting that neofunctionalization may be an important process leading to duplicate gene retention in that organism.