Rugged Fitness Landscapes Research Articles

Challenges and Solutions for Leave-One-Out Biosensor Design in the Context of a Rugged Fitness Landscape

The leave-one-out (LOO) green fluorescent protein (GFP) approach to biosensor design combines computational protein design with split protein reconstitution. LOO-GFPs reversibly fold and gain fluorescence upon encountering the target peptide, which can be redefined by computational design of the LOO site. Such an approach can be used to create reusable biosensors for the early detection of emerging biological threats. Enlightening biophysical inferences for nine LOO-GFP biosensor libraries are presented, with target sequences from dengue, influenza, or HIV, replacing beta strands 7, 8, or 11. An initially low hit rate was traced to components of the energy function, manifesting in the over-rewarding of over-tight side chain packing. Also, screening by colony picking required a low library complexity, but designing a biosensor against a peptide of at least 12 residues requires a high-complexity library. This double-bind was solved using a “piecemeal” iterative design strategy. Also, designed LOO-GFPs fluoresced in the unbound state due to unwanted dimerization, but this was solved by fusing a fully functional prototype LOO-GFP to a fiber-forming protein, Drosophila ultrabithorax, creating a biosensor fiber. One influenza hemagglutinin biosensor is characterized here in detail, showing a shifted excitation/emission spectrum, a micromolar affinity for the target peptide, and an unexpected photo-switching ability.

Promoters Constrain Evolution of Expression Levels of Essential Genes in Escherichia coli.

Variability in expression levels in response to random genomic mutations varies among genes, influencing both the facilitation and constraint of phenotypic evolution in organisms. Despite its importance, both the underlying mechanisms and evolutionary origins of this variability remain largely unknown due to the mixed contributions of cis- and trans-acting elements. To address this issue, we focused on the mutational variability of cis-acting elements, that is, promoter regions, in Escherichia coli. Random mutations were introduced into the natural and synthetic promoters to generate mutant promoter libraries. By comparing the variance in promoter activity of these mutant libraries, we found no significant difference in mutational variability in promoter activity between promoter groups, suggesting the absence of a signature of natural selection for mutational robustness. In contrast, the promoters controlling essential genes exhibited a remarkable bias in mutational variability, with mutants displaying higher activities than the wild types being relatively rare compared to those with lower activities. Our evolutionary simulation on a rugged fitness landscape provided a rationale for this vulnerability. These findings suggest that past selection created nonuniform mutational variability in promoters biased toward lower activities of random mutants, which now constrains the future evolution of downstream essential genes toward higher expression levels.

The Untapped Potential of Comparative Biology in Aging Research: Insights From the Extraordinary-Long-Lived Naked Mole-Rat.

The search for solutions to the vagaries of aging has, historically, been akin to searching at night in the bright light under street lamps by utilizing the few preexisting and well-established animal model systems. Throughout my career as a comparative biologist, I have ventured into the darkness across 4 continents and studied over 150 different animal species, many of which have evolved remarkable adaptations to survive on the harsh and rugged fitness landscape that exists outside of the laboratory setting. In this Fellows Forum, I will discuss the main focus of my research for the last 25 years and dig deeply into the biology of the preternaturally long-lived naked mole-rat that makes it an ideal model system for the characterization of successful strategies to combat aging.

Evolutionary adaptation is facilitated by the presence of lethal genotypes

The rate of adaptation in theoretical models of biological evolution generally increases with the mutation rate. However, there is a threshold beyond which mutations into lethal states lead to extinction. It would be logical to assume that eliminating such lethal states could be advantageous for evolution. Here, we demonstrate that lethal mutations actually accelerate adaptation on rugged fitness landscapes with multiple peaks and valleys in the presence of competition for resources. We investigate a modified stochastic version of the quasispecies model, incorporating two types of genotypes—viable and lethal—and show that higher rates of lethal mutations result in shorter evolution times towards the best-fit genotype. This phenomenon can be attributed to an increased frequency of traversing fitness valleys, facilitated by reduced selection pressure against less-fit variants. Published by the American Physical Society 2024

Competition-driven eco-evolutionary feedback reshapes bacteriophage lambda’s fitness landscape and enables speciation

A major challenge in evolutionary biology is explaining how populations navigate rugged fitness landscapes without getting trapped on local optima. One idea illustrated by adaptive dynamics theory is that as populations adapt, their newly enhanced capacities to exploit resources alter fitness payoffs and restructure the landscape in ways that promote speciation by opening new adaptive pathways. While there have been indirect tests of this theory, to our knowledge none have measured how fitness landscapes deform during adaptation, or test whether these shifts promote diversification. Here, we achieve this by studying bacteriophage λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}, a virus that readily speciates into co-existing receptor specialists under controlled laboratory conditions. We use a high-throughput gene editing-phenotyping technology to measure λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}’s fitness landscape in the presence of different evolved-λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document} competitors and find that the fitness effects of individual mutations, and their epistatic interactions, depend on the competitor. Using these empirical data, we simulate λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}’s evolution on an unchanging landscape and one that recapitulates how the landscape deforms during evolution. λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document} heterogeneity only evolves in the shifting landscape regime. This study provides a test of adaptive dynamics, and, more broadly, shows how fitness landscapes dynamically change during adaptation, potentiating phenomena like speciation by opening new adaptive pathways.

Evolving Multi-valued Regulatory Networks on Tunable Fitness Landscapes

Random Boolean networks have been used widely to explore aspects of gene regulatory networks. As the name implies, traditionally the model has used a binary representation scheme. This paper uses a modified form of the model to systematically explore the effects of increasing the number of gene states. These random multi-valued networks are evolved within rugged fitness landscapes to explore their behavior. Results suggest the basic properties of the original model remain, regardless of the update scheme or fitness sampling method. Changes are seen in sensitivity to high levels of connectivity, the mutation rate and the ability to vary network size.

Fluctuating selection maintains distinct species phenotypes in an ecological community in the wild

Species' phenotypic characteristics often remain unchanged over long stretches of geological time. Stabilizing selection-in which fitness is highest for intermediate phenotypes and lowest for the extremes-has been widely invoked as responsible for this pattern. At the community level, such stabilizing selection acting individually on co-occurring species is expected to produce a rugged fitness landscape on which different species occupy distinct fitness peaks. However, even with an explosion of microevolutionary field studies over the past four decades, evidence for persistent stabilizing selection driving long-term stasis is lacking. Nonetheless, biologists continue to invoke stabilizing selection as a major factor explaining macroevolutionary patterns. Here, by directly measuring natural selection in the wild, we identified a complex community-wide fitness surface in which four Anolis lizard species each occupy a distinct fitness peak close to their mean phenotype. The presence of local fitness optima within species, and fitness valleys between species, presents a barrier to adaptive evolutionary change and acts to maintain species differences through time. However, instead of continuously operating stabilizing selection, we found that species were maintained on these peaks by the combination of many independent periods among which selection fluctuated in form, strength, direction, or existence and in which stabilizing selection rarely occurred. Our results suggest that lack of substantial phenotypic evolutionary change through time may be the result of selection, but not persistent stabilizing selection as classically envisioned.

Differential Evolution Algorithm with Dual Information Guidance

As an effective tool to solve continuous optimization problems, differential evolution (DE) algorithm has been widely used in numerous fields. To enhance the performance, in recent years, many DE variants have been developed based on the idea of multiple strategies. However, there still exists an issue for them that the strategy selection method relies on the historical search experience. The experience may be suitable for the problems with smooth fitness landscapes, but not for the problems with rugged fitness landscapes. To alleviate this issue, in this work, a new multiple strategies-based DE variant with dual information guidance is proposed, called DIGDE. In the DIGDE, to avoid the unreliable historical search experience, the fitness information and spatial information are utilized simultaneously as a guidance to estimate the evolutionary states for each individual, and then the most appropriate strategy can be chosen correspondingly. To verify the effectiveness of the DIGDE, 52 test functions are included in the experiments, and three well-established DE variants and four other evolutionary algorithms are involved in the performance comparison. The results show that the DIGDE achieves competitive performance on not only the result accuracy but also the convergence rate.

A Genetic Programming Based Heuristic to Simplify Rugged Landscapes Exploration

Some optimization problems are difficult to solve due to a considerable number of local optima, which may result in premature convergence of the optimization process. To address this problem, we propose a novel heuristic method for constructing a smooth surrogate model of the original function. The surrogate function is easier to optimize but maintains a fundamental property of the original rugged fitness landscape: the location of the global optimum. To create such a surrogate model, we consider a linear genetic programming approach coupled with a self-tuning fitness function. More specifically, to evaluate the fitness of the produced surrogate functions, we employ Fuzzy Self-Tuning Particle Swarm Optimization, a setting-free version of particle swarm optimization. To assess the performance of the proposed method, we considered a set of benchmark functions characterized by high noise and ruggedness. Moreover, the method is evaluated over different problems’ dimensionalities. The proposed approach reveals its suitability for performing the proposed task. In particular, experimental results confirm its capability to find the global argminimum for all the considered benchmark problems and all the domain dimensions taken into account, thus providing an innovative and promising strategy for dealing with challenging optimization problems. Doi: 10.28991/ESJ-2023-07-04-01 Full Text: PDF

Protein Fitness Prediction Is Impacted by the Interplay of Language Models, Ensemble Learning, and Sampling Methods.

Advances in machine learning (ML) and the availability of protein sequences via high-throughput sequencing techniques have transformed the ability to design novel diagnostic and therapeutic proteins. ML allows protein engineers to capture complex trends hidden within protein sequences that would otherwise be difficult to identify in the context of the immense and rugged protein fitness landscape. Despite this potential, there persists a need for guidance during the training and evaluation of ML methods over sequencing data. Two key challenges for training discriminative models and evaluating their performance include handling severely imbalanced datasets (e.g., few high-fitness proteins among an abundance of non-functional proteins) and selecting appropriate protein sequence representations (numerical encodings). Here, we present a framework for applying ML over assay-labeled datasets to elucidate the capacity of sampling techniques and protein encoding methods to improve binding affinity and thermal stability prediction tasks. For protein sequence representations, we incorporate two widely used methods (One-Hot encoding and physiochemical encoding) and two language-based methods (next-token prediction, UniRep; masked-token prediction, ESM). Elaboration on performance is provided over protein fitness, protein size, and sampling techniques. In addition, an ensemble of protein representation methods is generated to discover the contribution of distinct representations and improve the final prediction score. We then implement multiple criteria decision analysis (MCDA; TOPSIS with entropy weighting), using multiple metrics well-suited for imbalanced data, to ensure statistical rigor in ranking our methods. Within the context of these datasets, the synthetic minority oversampling technique (SMOTE) outperformed undersampling while encoding sequences with One-Hot, UniRep, and ESM representations. Moreover, ensemble learning increased the predictive performance of the affinity-based dataset by 4% compared to the best single-encoding candidate (F1-score = 97%), while ESM alone was rigorous enough in stability prediction (F1-score = 92%).

Impact of population size on early adaptation in rugged fitness landscapes.

Owing to stochastic fluctuations arising from finite population size, known as genetic drift, the ability of a population to explore a rugged fitness landscape depends on its size. In the weak mutation regime, while the mean steady-state fitness increases with population size, we find that the height of the first fitness peak encountered when starting from a random genotype displays various behaviours versus population size, even among small and simple rugged landscapes. We show that the accessibility of the different fitness peaks is key to determining whether this height overall increases or decreases with population size. Furthermore, there is often a finite population size that maximizes the height of the first fitness peak encountered when starting from a random genotype. This holds across various classes of model rugged landscapes with sparse peaks, and in some experimental and experimentally inspired ones. Thus, early adaptation in rugged fitness landscapes can be more efficient and predictable for relatively small population sizes than in the large-size limit. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

Interdisciplinary approaches to predicting evolutionary biology.

Interdisciplinary approaches to predicting evolutionary biology.

Epistasis decreases with increasing antibiotic pressure but not temperature.

Predicting mutational effects is essential for the control of antibiotic resistance (ABR). Predictions are difficult when there are strong genotype-by-environment (G × E), gene-by-gene (G × G or epistatic) or gene-by-gene-by-environment (G × G × E) interactions. We quantified G × G × E effects in Escherichia coli across environmental gradients. We created intergenic fitness landscapes using gene knock-outs and single-nucleotide ABR mutations previously identified to vary in the extent of G × E effects in our environments of interest. Then, we measured competitive fitness across a complete combinatorial set of temperature and antibiotic dosage gradients. In this way, we assessed the predictability of 15 fitness landscapes across 12 different but related environments. We found G × G interactions and rugged fitness landscapes in the absence of antibiotic, but as antibiotic concentration increased, the fitness effects of ABR genotypes quickly overshadowed those of gene knock-outs, and the landscapes became smoother. Our work reiterates that some single mutants, like those conferring resistance or susceptibility to antibiotics, have consistent effects across genetic backgrounds in stressful environments. Thus, although epistasis may reduce the predictability of evolution in benign environments, evolution may be more predictable in adverse environments. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

Rapid adaptation of recombining populations on tunable fitness landscapes.

How does standing genetic variation affect polygenic adaptation in recombining populations? Despite a large body of work in quantitative genetics, epistatic and weak additive fitness effects among simultaneously segregating genetic variants are difficult to capture experimentally or to predict theoretically. In this study, we simulated adaptation on fitness landscapes with tunable ruggedness driven by standing genetic variation in recombining populations. We confirmed that recombination hinders the movement of a population through a rugged fitness landscape. When surveying the effect of epistasis on the fixation of alleles, we found that the combined effects of high ruggedness and high recombination probabilities lead to preferential fixation of alleles that had a high initial frequency. This indicates that positive epistatic alleles escape from being broken down by recombination when they start at high frequency. We further extract direct selection coefficients and pairwise epistasis along the adaptive path. When taking the final fixed genotype as the reference genetic background, we observe that, along the adaptive path, beneficial direct selection appears stronger and pairwise epistasis weaker than in the underlying fitness landscape. Quantitatively, the ratio of epistasis and direct selection is smaller along the adaptive path ( ) than expected. Thus, adaptation on a rugged fitness landscape may lead to spurious signals of direct selection generated through epistasis. Our study highlights how the interplay of epistasis and recombination constrains the adaptation of a diverse population to a new environment.

Adaptive diversification and niche packing on rugged fitness landscapes

Explaining the emergence of diversity and the coexistence of competing types has long been one of the main goals of ecological theory. Rugged fitness landscapes have often been used to explain diversity through the presence of local peaks, or adaptive zones, in the fitness landscape acting as available niches for different species. Alternatively, niche-packing and theories based on limiting similarity describe frequency-dependent selection leading to the organic differentiation of a continuous phenotype space into multiple coexisting types. By combining rugged carrying capacity landscapes with frequency-dependent selection, here we investigate the effects of ruggedness on adaptive diversification and stably maintained diversity. We show that while increased ruggedness often leads to a decreased opportunity for adaptive diversification, it is the shape of the global carrying capacity function, not the local ruggedness, that determines the diversity of the ESS and the total diversity a system can stably maintain.

Genetic complementation fosters evolvability in complex fitness landscapes

The ability of natural selection to optimize traits depends on the topology of the genotype-fitness map (fitness landscape). Epistatic interactions produce rugged fitness landscapes, where adaptation is constrained by the presence of low-fitness intermediates. Here, we used simulations to explore how evolvability in rugged fitness landscapes is influenced by genetic complementation, a process whereby different sequence variants mutually compensate for their deleterious mutations. We designed our model inspired by viral populations, in which genetic variants are known to interact frequently through coinfection. Our simulations indicate that genetic complementation enables a more efficient exploration of rugged fitness landscapes. Although this benefit may be undermined by genetic parasites, its overall effect on evolvability remains positive in populations that exhibit strong relatedness between interacting sequences. Similar processes could operate in contexts other than viral coinfection, such as in the evolution of ploidy.

Artificial bee colony algorithm based on online fitness landscape analysis

As an effective optimization tool, artificial bee colony (ABC) algorithm has attracted increasing attention in recent years. However, ABC still shows unsatisfactory performance in solving complex optimization problems. Although many ABC variants have been developed, the structural features of problems have been rarely considered, which have a significant effect on algorithm performance. Therefore, a novel ABC variant, called FLABC, is proposed by designing an online fitness landscape analysis technique. In this technique, the population is considered as a sample of the fitness landscape, and the idea of dispersion metric is used to identify the landscape features. According to the identified features, the solution search equations with distinct characteristics can be adaptively used, which helps adapt the search to the fitness landscape. In addition, FLABC has another two modifications, i.e., the dynamic multiple subpopulations and modified scout bee phase. In the experiments, FLABC is verified on two well-known test suites (CEC2013 and CEC2015) and two real-world optimization problems. Seven well-established ABC variants and five non-ABC variants are included in the performance comparison, and the results verify that FLABC has very competitive performance, especially on the functions with rugged fitness landscapes.

Getting higher on rugged landscapes: Inversion mutations open access to fitter adaptive peaks in NK fitness landscapes.

Molecular evolution is often conceptualised as adaptive walks on rugged fitness landscapes, driven by mutations and constrained by incremental fitness selection. It is well known that epistasis shapes the ruggedness of the landscape's surface, outlining their topography (with high-fitness peaks separated by valleys of lower fitness genotypes). However, within the strong selection weak mutation (SSWM) limit, once an adaptive walk reaches a local peak, natural selection restricts passage through downstream paths and hampers any possibility of reaching higher fitness values. Here, in addition to the widely used point mutations, we introduce a minimal model of sequence inversions to simulate adaptive walks. We use the well known NK model to instantiate rugged landscapes. We show that adaptive walks can reach higher fitness values through inversion mutations, which, compared to point mutations, allows the evolutionary process to escape local fitness peaks. To elucidate the effects of this chromosomal rearrangement, we use a graph-theoretical representation of accessible mutants and show how new evolutionary paths are uncovered. The present model suggests a simple mechanistic rationale to analyse escapes from local fitness peaks in molecular evolution driven by (intragenic) structural inversions and reveals some consequences of the limits of point mutations for simulations of molecular evolution.

Nonbinary Representations in the NK and NKCS Models

The NK model has been used widely to explore aspects of natural evolution and complex systems. Traditionally, the model has used a binary representation scheme. This paper introduces a modified form of the NK model through which to systematically explore the effects of discrete, nonbinary representations on evolution over rugged fitness landscapes. Results suggest the basic properties of the original model remain but changes are seen in walk lengths to optima and the sensitivity to mutation rates, in particular. The variation to the case of coupled fitness landscapes, the NKCS model, is also extended in the same way. Again, similarities and differences to the binary case are found.

Evolution of Amino Acid Propensities under Stability-Mediated Epistasis.

Site-specific amino acid preferences are influenced by the genetic background of the protein. The preferences for resident amino acids are expected to, on average, increase over time because of replacements at other sites—a nonadaptive phenomenon referred to as the “evolutionary Stokes shift.” Alternatively, decreases in resident amino acid propensity have recently been viewed as evidence of adaptations to external environmental changes. Using population genetics theory and thermodynamic stability constraints, we show that nonadaptive evolution can lead to both positive and negative shifts in propensities following the fixation of an amino acid, emphasizing that the detection of negative shifts is not conclusive evidence of adaptation. By examining propensity shifts from when an amino acid is first accepted at a site until it is subsequently replaced, we find that 50% of sites show a decrease in the propensity for the newly resident amino acid while the remaining sites show an increase. Furthermore, the distributions of the magnitudes of positive and negative shifts were comparable. Preferences were often conserved via a significant negative autocorrelation in propensity changes—increases in propensities often followed by decreases, and vice versa. Lastly, we explore the underlying mechanisms that lead propensities to fluctuate. We observe that stabilizing replacements increase the mutational tolerance at a site and in doing so decrease the propensity for the resident amino acid. In contrast, destabilizing substitutions result in more rugged fitness landscapes that tend to favor the resident amino acid. In summary, our results characterize propensity trajectories under nonadaptive stability-constrained evolution against which evidence of adaptations should be calibrated.