Local fitness landscape of the green fluorescent protein

Sampling Strategies for Experimentally Mapping Molecular Fitness Landscapes Using High-Throughput Methods

Empirical studies of genotype-phenotype-fitness maps of proteins are fundamental to understanding the evolutionary process, in elucidating the space of possible genotypes accessible through mutations in a landscape of phenotypes and fitness effects. Yet, comprehensively mapping molecular fitness landscapes remains challenging since all possible combinations of amino acid substitutions for even a few protein sites are encoded by an enormous genotype space. High-throughput mapping of genotype space can be achieved using large-scale screening experiments known as multiplexed assays of variant effect (MAVEs). However, to accommodate such multi-mutational studies, the size of MAVEs has grown to the point where a priori determination of sampling requirements is needed. To address this problem, we propose calculations and simulation methods to approximate minimum sampling requirements for multi-mutational MAVEs, which we combine with a new library construction protocol to experimentally validate our approximation approaches. Analysis of our simulated data reveals how sampling trajectories differ between simulations of nucleotide versus amino acid variants and among mutagenesis schemes. For this, we show quantitatively that marginal gains in sampling efficiency demand increasingly greater sampling effort when sampling for nucleotide sequences over their encoded amino acid equivalents. We present a new library construction protocol that efficiently maximizes sequence variation, and demonstrate using ultradeep sequencing that the library encodes virtually all possible combinations of mutations within the experimental design. Insights learned from our analyses together with the methodological advances reported herein are immediately applicable toward pooled experimental screens of arbitrary design, enabling further assay upscaling and expanded testing of genotype space.

A parameterized two-domain thermodynamic model explains diverse mutational effects on protein allostery

New experimental findings continue to challenge our understanding of protein allostery. Recent deep mutational scanning study showed that allosteric hotspots in the tetracycline repressor (TetR) and its homologous transcriptional factors are broadly distributed rather than spanning well-defined structural pathways as often assumed. Moreover, hotspot mutation-induced allostery loss was rescued by distributed additional mutations in a degenerate fashion. Here, we develop a two-domain thermodynamic model for TetR, which readily rationalizes these intriguing observations. The model accurately captures the in vivo activities of various mutants with changes in physically transparent parameters, allowing the data-based quantification of mutational effects using statistical inference. Our analysis reveals the intrinsic connection of intra- and inter-domain properties for allosteric regulation and illustrate epistatic interactions that are consistent with structural features of the protein. The insights gained from this study into the nature of two-domain allostery are expected to have broader implications for other multi-domain allosteric proteins.

GMMA Can Stabilize Proteins Across Different Functional Constraints

Stabilizing proteins without otherwise hampering their function is a central task in protein engineering and design. PYR1 is a plant hormone receptor that has been engineered to bind diverse small molecule ligands. We sought a set of generalized mutations that would provide stability without affecting functionality for PYR1 variants with diverse ligand-binding capabilities. To do this we used a global multi-mutant analysis (GMMA) approach, which can identify substitutions that have stabilizing effects and do not lower function. GMMA has the added benefit of finding substitutions that are stabilizing in different sequence contexts and we hypothesized that applying GMMA to PYR1 with different functionalities would identify this set of generalized mutations. Indeed, conducting FACS and deep sequencing of libraries for PYR1 variants with two different functionalities and applying a GMMA analysis identified 5 substitutions that, when inserted into four PYR1 variants that each bind a unique ligand, provided an increase of 2-6 °C in thermal inactivation temperature and no decrease in functionality.

Epistasis facilitates functional evolution in an ancient transcription factor

A protein's genetic architecture - the set of causal rules by which its sequence produces its functions - also determines its possible evolutionary trajectories. Prior research has proposed that the genetic architecture of proteins is very complex, with pervasive epistatic interactions that constrain evolution and make function difficult to predict from sequence. Most of this work has analyzed only the direct paths between two proteins of interest - excluding the vast majority of possible genotypes and evolutionary trajectories - and has considered only a single protein function, leaving unaddressed the genetic architecture of functional specificity and its impact on the evolution of new functions. Here, we develop a new method based on ordinal logistic regression to directly characterize the global genetic determinants of multiple protein functions from 20-state combinatorial deep mutational scanning (DMS) experiments. We use it to dissect the genetic architecture and evolution of a transcription factor's specificity for DNA, using data from a combinatorial DMS of an ancient steroid hormone receptor's capacity to activate transcription from two biologically relevant DNA elements. We show that the genetic architecture of DNA recognition consists of a dense set of main and pairwise effects that involve virtually every possible amino acid state in the protein-DNA interface, but higher-order epistasis plays only a tiny role. Pairwise interactions enlarge the set of functional sequences and are the primary determinants of specificity for different DNA elements. They also massively expand the number of opportunities for single-residue mutations to switch specificity from one DNA target to another. By bringing variants with different functions close together in sequence space, pairwise epistasis therefore facilitates rather than constrains the evolution of new functions.

Protein Engineering with Lightweight Graph Denoising Neural Networks

Protein engineering faces challenges in finding optimal mutants from a massive pool of candidate mutants. In this study, we introduce a deep-learning-based data-efficient fitness prediction tool to steer protein engineering. Our methodology establishes a lightweight graph neural network scheme for protein structures, which efficiently analyzes the microenvironment of amino acids in wild-type proteins and reconstructs the distribution of the amino acid sequences that are more likely to pass natural selection. This distribution serves as a general guidance for scoring proteins toward arbitrary properties on any order of mutations. Our proposed solution undergoes extensive wet-lab experimental validation spanning diverse physicochemical properties of various proteins, including fluorescence intensity, antigen-antibody affinity, thermostability, and DNA cleavage activity. More than 40% of ProtLGN-designed single-site mutants outperform their wild-type counterparts across all studied proteins and targeted properties. More importantly, our model can bypass the negative epistatic effect to combine single mutation sites and form deep mutants with up to seven mutation sites in a single round, whose physicochemical properties are significantly improved. This observation provides compelling evidence of the structure-based model's potential to guide deep mutations in protein engineering. Overall, our approach emerges as a versatile tool for protein engineering, benefiting both the computational and bioengineering communities.

Gauge fixing for sequence-function relationships

Quantitative models of sequence-function relationships are ubiquitous in computational biology, e.g., for modeling the DNA binding of transcription factors or the fitness landscapes of proteins. Interpreting these models, however, is complicated by the fact that the values of model parameters can often be changed without affecting model predictions. Before the values of model parameters can be meaningfully interpreted, one must remove these degrees of freedom (called "gauge freedoms" in physics) by imposing additional constraints (a process called "fixing the gauge"). However, strategies for fixing the gauge of sequence-function relationships have received little attention. Here we derive an analytically tractable family of gauges for a large class of sequence-function relationships. These gauges are derived in the context of models with all-order interactions, but an important subset of these gauges can be applied to diverse types of models, including additive models, pairwise-interaction models, and models with higher-order interactions. Many commonly used gauges are special cases of gauges within this family. We demonstrate the utility of this family of gauges by showing how different choices of gauge can be used both to explore complex activity landscapes and to reveal simplified models that are approximately correct within localized regions of sequence space. The results provide practical gauge-fixing strategies and demonstrate the utility of gauge-fixing for model exploration and interpretation.

Genotype sampling for deep-learning assisted experimental mapping of a combinatorially complete fitness landscape

MOTIVATION

Experimental characterization of fitness landscapes, which map genotypes onto fitness, is important for both evolutionary biology and protein engineering. It faces a fundamental obstacle in the astronomical number of genotypes whose fitness needs to be measured for any one protein. Deep learning may help to predict the fitness of many genotypes from a smaller neural network training sample of genotypes with experimentally measured fitness. Here I use a recently published experimentally mapped fitness landscape of more than 260 000 protein genotypes to ask how such sampling is best performed.

RESULTS

I show that multilayer perceptrons, recurrent neural networks, convolutional networks, and transformers, can explain more than 90% of fitness variance in the data. In addition, 90% of this performance is reached with a training sample comprising merely ≈103 sequences. Generalization to unseen test data is best when training data is sampled randomly and uniformly, or sampled to minimize the number of synonymous sequences. In contrast, sampling to maximize sequence diversity or codon usage bias reduces performance substantially. These observations hold for more than one network architecture. Simple sampling strategies may perform best when training deep learning neural networks to map fitness landscapes from experimental data.

AVAILABILITY AND IMPLEMENTATION

The fitness landscape data analyzed here is publicly available as described previously (Papkou et al. 2023). All code used to analyze this landscape is publicly available at https://github.com/andreas-wagner-uzh/fitness_landscape_sampling.

Computational scoring and experimental evaluation of enzymes generated by neural networks

In recent years, generative protein sequence models have been developed to sample novel sequences. However, predicting whether generated proteins will fold and function remains challenging. We evaluate a set of 20 diverse computational metrics to assess the quality of enzyme sequences produced by three contrasting generative models: ancestral sequence reconstruction, a generative adversarial network and a protein language model. Focusing on two enzyme families, we expressed and purified over 500 natural and generated sequences with 70-90% identity to the most similar natural sequences to benchmark computational metrics for predicting in vitro enzyme activity. Over three rounds of experiments, we developed a computational filter that improved the rate of experimental success by 50-150%. The proposed metrics and models will drive protein engineering research by serving as a benchmark for generative protein sequence models and helping to select active variants for experimental testing.

Rugged fitness landscapes minimize promiscuity in the evolution of transcriptional repressors

How a protein's function influences the shape of its fitness landscape, smooth or rugged, is a fundamental question in evolutionary biochemistry. Smooth landscapes arise when incremental mutational steps lead to a progressive change in function, as commonly seen in enzymes and binding proteins. On the other hand, rugged landscapes are poorly understood because of the inherent unpredictability of how sequence changes affect function. Here, we experimentally characterize the entire sequence phylogeny, comprising 1,158 extant and ancestral sequences, of the DNA-binding domain (DBD) of the LacI/GalR transcriptional repressor family. Our analysis revealed an extremely rugged landscape with rapid switching of specificity, even between adjacent nodes. Further, the ruggedness arises due to the necessity of the repressor to simultaneously evolve specificity for asymmetric operators and disfavors potentially adverse regulatory crosstalk. Our study provides fundamental insight into evolutionary, molecular, and biophysical rules of genetic regulation through the lens of fitness landscapes.

A map of the rubisco biochemical landscape

Rubisco is the primary CO2 fixing enzyme of the biosphere yet has slow kinetics. The roles of evolution and chemical mechanism in constraining the sequence landscape of rubisco remain debated. In order to map sequence to function, we developed a massively parallel assay for rubisco using an engineered E. coli where enzyme function is coupled to growth. By assaying >99% of single amino acid mutants across CO2 concentrations, we inferred enzyme velocity and CO2 affinity for thousands of substitutions. We identified many highly conserved positions that tolerate mutation and rare mutations that improve CO2 affinity. These data suggest that non-trivial kinetic improvements are readily accessible and provide a comprehensive sequence-to-function mapping for enzyme engineering efforts.

Effect of tokenization on transformers for biological sequences

MOTIVATION

Deep-learning models are transforming biological research, including many bioinformatics and comparative genomics algorithms, such as sequence alignments, phylogenetic tree inference, and automatic classification of protein functions. Among these deep-learning algorithms, models for processing natural languages, developed in the natural language processing (NLP) community, were recently applied to biological sequences. However, biological sequences are different from natural languages, such as English, and French, in which segmentation of the text to separate words is relatively straightforward. Moreover, biological sequences are characterized by extremely long sentences, which hamper their processing by current machine-learning models, notably the transformer architecture. In NLP, one of the first processing steps is to transform the raw text to a list of tokens. Deep-learning applications to biological sequence data mostly segment proteins and DNA to single characters. In this work, we study the effect of alternative tokenization algorithms on eight different tasks in biology, from predicting the function of proteins and their stability, through nucleotide sequence alignment, to classifying proteins to specific families.

RESULTS

We demonstrate that applying alternative tokenization algorithms can increase accuracy and at the same time, substantially reduce the input length compared to the trivial tokenizer in which each character is a token. Furthermore, applying these tokenization algorithms allows interpreting trained models, taking into account dependencies among positions. Finally, we trained these tokenizers on a large dataset of protein sequences containing more than 400 billion amino acids, which resulted in over a 3-fold decrease in the number of tokens. We then tested these tokenizers trained on large-scale data on the above specific tasks and showed that for some tasks it is highly beneficial to train database-specific tokenizers. Our study suggests that tokenizers are likely to be a critical component in future deep-network analysis of biological sequence data.

AVAILABILITY AND IMPLEMENTATION

Code, data, and trained tokenizers are available on https://github.com/technion-cs-nlp/BiologicalTokenizers.

High temperature delays and low temperature accelerates evolution of a new protein phenotype

Since the origin of life, temperatures on earth have fluctuated both on short and long time scales. How such changes affect the rate at which Darwinian evolution can bring forth new phenotypes remains unclear. On the one hand, high temperature may accelerate phenotypic evolution because it accelerates most biological processes. On the other hand, it may slow phenotypic evolution, because proteins are usually less stable at high temperatures and therefore less evolvable. Here, to test these hypotheses experimentally, we evolved a green fluorescent protein in E. coli towards the new phenotype of yellow fluorescence at different temperatures. Yellow fluorescence evolved most slowly at high temperature and most rapidly at low temperature, in contradiction to the first hypothesis. Using high-throughput population sequencing, protein engineering, and biochemical assays, we determined that this is due to the protein-destabilizing effect of neofunctionalizing mutations. Destabilization is highly detrimental at high temperature, where neofunctionalizing mutations cannot be tolerated. Their detrimental effects can be mitigated through excess stability at low temperature, leading to accelerated adaptive evolution. By modifying protein folding stability, temperature alters the accessibility of mutational paths towards high-fitness genotypes. Our observations have broad implications for our understanding of how temperature changes affect evolutionary adaptations and innovations.

Convolutions are competitive with transformers for protein sequence pretraining

Pretrained protein sequence language models have been shown to improve the performance of many prediction tasks and are now routinely integrated into bioinformatics tools. However, these models largely rely on the transformer architecture, which scales quadratically with sequence length in both run-time and memory. Therefore, state-of-the-art models have limitations on sequence length. To address this limitation, we investigated whether convolutional neural network (CNN) architectures, which scale linearly with sequence length, could be as effective as transformers in protein language models. With masked language model pretraining, CNNs are competitive with, and occasionally superior to, transformers across downstream applications while maintaining strong performance on sequences longer than those allowed in the current state-of-the-art transformer models. Our work suggests that computational efficiency can be improved without sacrificing performance, simply by using a CNN architecture instead of a transformer, and emphasizes the importance of disentangling pretraining task and model architecture. A record of this paper's transparent peer review process is included in the supplemental information.

Biophysics-based protein language models for protein engineering

Protein language models trained on evolutionary data have emerged as powerful tools for predictive problems involving protein sequence, structure, and function. However, these models overlook decades of research into biophysical factors governing protein function. We propose Mutational Effect Transfer Learning (METL), a protein language model framework that unites advanced machine learning and biophysical modeling. Using the METL framework, we pretrain transformer-based neural networks on biophysical simulation data to capture fundamental relationships between protein sequence, structure, and energetics. We finetune METL on experimental sequence-function data to harness these biophysical signals and apply them when predicting protein properties like thermostability, catalytic activity, and fluorescence. METL excels in challenging protein engineering tasks like generalizing from small training sets and position extrapolation, although existing methods that train on evolutionary signals remain powerful for many types of experimental assays. We demonstrate METL's ability to design functional green fluorescent protein variants when trained on only 64 examples, showcasing the potential of biophysics-based protein language models for protein engineering.

Machine learning to predict continuous protein properties from binary cell sorting data and map unseen sequence space

Proteins are a diverse class of biomolecules responsible for wide-ranging cellular functions, from catalyzing reactions to recognizing pathogens. The ability to evolve proteins rapidly and inexpensively toward improved properties is a common objective for protein engineers. Powerful high-throughput methods like fluorescent activated cell sorting and next-generation sequencing have dramatically improved directed evolution experiments. However, it is unclear how to best leverage these data to characterize protein fitness landscapes more completely and identify lead candidates. In this work, we develop a simple yet powerful framework to improve protein optimization by predicting continuous protein properties from simple directed evolution experiments using interpretable, linear machine learning models. Importantly, we find that these models, which use data from simple but imprecise experimental estimates of protein fitness, have predictive capabilities that approach more precise but expensive data. Evaluated across five diverse protein engineering tasks, continuous properties are consistently predicted from readily available deep sequencing data, demonstrating that protein fitness space can be reasonably well modeled by linear relationships among sequence mutations. To prospectively test the utility of this approach, we generated a library of stapled peptides and applied the framework to predict affinity and specificity from simple cell sorting data. We then coupled integer linear programming, a method to optimize protein fitness from linear weights, with mutation scores from machine learning to identify variants in unseen sequence space that have improved and co-optimal properties. This approach represents a versatile tool for improved analysis and identification of protein variants across many domains of protein engineering.

Evaluating generalizability of artificial intelligence models for molecular datasets

Deep learning has made rapid advances in modeling molecular sequencing data. Despite achieving high performance on benchmarks, it remains unclear to what extent deep learning models learn general principles and generalize to previously unseen sequences. Benchmarks traditionally interrogate model generalizability by generating metadata based (MB) or sequence-similarity based (SB) train and test splits of input data before assessing model performance. Here, we show that this approach mischaracterizes model generalizability by failing to consider the full spectrum of cross-split overlap, i.e., similarity between train and test splits. We introduce Spectra, a spectral framework for comprehensive model evaluation. For a given model and input data, Spectra plots model performance as a function of decreasing cross-split overlap and reports the area under this curve as a measure of generalizability. We apply Spectra to 18 sequencing datasets with associated phenotypes ranging from antibiotic resistance in tuberculosis to protein-ligand binding to evaluate the generalizability of 19 state-of-the-art deep learning models, including large language models, graph neural networks, diffusion models, and convolutional neural networks. We show that SB and MB splits provide an incomplete assessment of model generalizability. With Spectra, we find as cross-split overlap decreases, deep learning models consistently exhibit a reduction in performance in a task- and model-dependent manner. Although no model consistently achieved the highest performance across all tasks, we show that deep learning models can generalize to previously unseen sequences on specific tasks. Spectra paves the way toward a better understanding of how foundation models generalize in biology.

EvoAI enables extreme compression and reconstruction of the protein sequence space

Designing proteins with improved functions requires a deep understanding of how sequence and function are related, a vast space that is hard to explore. The ability to efficiently compress this space by identifying functionally important features is extremely valuable. Here, we first establish a method called EvoScan to comprehensively segment and scan the high-fitness sequence space to obtain anchor points that capture its essential features, especially in high dimensions. Our approach is compatible with any biomolecular function that can be coupled to a transcriptional output. We then develop deep learning and large language models to accurately reconstruct the space from these anchors, allowing computational prediction of novel, highly fit sequences without prior homology-derived or structural information. We apply this hybrid experimental-computational method, which we call EvoAI, to a repressor protein and find that only 82 anchors are sufficient to compress the high-fitness sequence space with a compression ratio of 1048. The extreme compressibility of the space informs both applied biomolecular design and understanding of natural evolution.

Protein design using structure-based residue preferences

Recent developments in protein design rely on large neural networks with up to 100s of millions of parameters, yet it is unclear which residue dependencies are critical for determining protein function. Here, we show that amino acid preferences at individual residues-without accounting for mutation interactions-explain much and sometimes virtually all of the combinatorial mutation effects across 8 datasets (R2 ~ 78-98%). Hence, few observations (~100 times the number of mutated residues) enable accurate prediction of held-out variant effects (Pearson r > 0.80). We hypothesized that the local structural contexts around a residue could be sufficient to predict mutation preferences, and develop an unsupervised approach termed CoVES (Combinatorial Variant Effects from Structure). Our results suggest that CoVES outperforms not just model-free methods but also similarly to complex models for creating functional and diverse protein variants. CoVES offers an effective alternative to complicated models for identifying functional protein mutations.

Accurate top protein variant discovery via low-N pick-and-validate machine learning

A strategy to obtain the greatest number of best-performing variants with least amount of experimental effort over the vast combinatorial mutational landscape would have enormous utility in boosting resource producibility for protein engineering. Toward this goal, we present a simple and effective machine learning-based strategy that outperforms other state-of-the-art methods. Our strategy integrates zero-shot prediction and multi-round sampling to direct active learning via experimenting with only a few predicted top variants. We find that four rounds of low-N pick-and-validate sampling of 12 variants for machine learning yielded the best accuracy of up to 92.6% in selecting the true top 1% variants in combinatorial mutant libraries, whereas two rounds of 24 variants can also be used. We demonstrate our strategy in successfully discovering high-performance protein variants from diverse families including the CRISPR-based genome editors, supporting its generalizable application for solving protein engineering tasks. A record of this paper's transparent peer review process is included in the supplemental information.

A parametrized two-domain thermodynamic model explains diverse mutational effects on protein allostery

New experimental findings continue to challenge our understanding of protein allostery. Recent deep mutational scanning study showed that allosteric hotspots in the tetracycline repressor (TetR) and its homologous transcriptional factors are broadly distributed rather than spanning well-defined structural pathways as often assumed. Moreover, hotspot mutation-induced allostery loss was rescued by distributed additional mutations in a degenerate fashion. Here, we develop a two-domain thermodynamic model for TetR, which readily rationalizes these intriguing observations. The model accurately captures the in vivo activities of various mutants with changes in physically transparent parameters, allowing the data-based quantification of mutational effects using statistical inference. Our analysis reveals the intrinsic connection of intra- and inter-domain properties for allosteric regulation and illustrate epistatic interactions that are consistent with structural features of the protein. The insights gained from this study into the nature of two-domain allostery are expected to have broader implications for other multidomain allosteric proteins.

The simplicity of protein sequence-function relationships

How complicated is the genetic architecture of proteins - the set of causal effects by which sequence determines function? High-order epistatic interactions among residues are thought to be pervasive, making a protein's function difficult to predict or understand from its sequence. Most studies, however, used methods that overestimate epistasis, because they analyze genetic architecture relative to a designated reference sequence - causing measurement noise and small local idiosyncrasies to propagate into pervasive high-order interactions - or have not effectively accounted for global nonlinearity in the sequence-function relationship. Here we present a new reference-free method that jointly estimates global nonlinearity and specific epistatic interactions across a protein's entire genotype-phenotype map. This method yields a maximally efficient explanation of a protein's genetic architecture and is more robust than existing methods to measurement noise, partial sampling, and model misspecification. We reanalyze 20 combinatorial mutagenesis experiments from a diverse set of proteins and find that additive and pairwise effects, along with a simple nonlinearity to account for limited dynamic range, explain a median of 96% of total variance in measured phenotypes (and >92% in every case). Only a tiny fraction of genotypes are strongly affected by third- or higher-order epistasis. Genetic architecture is also sparse: the number of terms required to explain the vast majority of variance is smaller than the number of genotypes by many orders of magnitude. The sequence-function relationship in most proteins is therefore far simpler than previously thought, opening the way for new and tractable approaches to characterize it.

Protein sequence landscapes are not so simple: on reference-free versus reference-based inference

In a recent preprint, Park, Metzger, and Thornton reanalyze 20 empirical protein sequence-function landscapes using a "reference-free analysis" (RFA) method they recently developed. They argue that these empirical landscapes are simpler and less epistatic than earlier work suggested, and attribute the difference to limitations of the methods used in the original analyses of these landscapes, which they claim are more sensitive to measurement noise, missing data, and other artifacts. Here, we show that these claims are incorrect. Instead, we find that the RFA method introduced by Park et al. is exactly equivalent to the reference-based least-squares methods used in the original analysis of many of these empirical landscapes (and also equivalent to a Hadamard-based approach they implement). Because the reanalyzed and original landscapes are in fact identical, the different conclusions drawn by Park et al. instead reflect different interpretations of the parameters describing the inferred landscapes; we argue that these do not support the conclusion that epistasis plays only a small role in protein sequence-function landscapes.

Molecular mechanisms and evolutionary robustness of a color switch in proteorhodopsins

Proteorhodopsins are widely distributed photoreceptors from marine bacteria. Their discovery revealed a high degree of evolutionary adaptation to ambient light, resulting in blue- and green-absorbing variants that correlate with a conserved glutamine/leucine at position 105. On the basis of an integrated approach combining sensitivity-enhanced solid-state nuclear magnetic resonance (ssNMR) spectroscopy and linear-scaling quantum mechanics/molecular mechanics (QM/MM) methods, this single residue is shown to be responsible for a variety of synergistically coupled structural and electrostatic changes along the retinal polyene chain, ionone ring, and within the binding pocket. They collectively explain the observed color shift. Furthermore, analysis of the differences in chemical shift between nuclei within the same residues in green and blue proteorhodopsins also reveals a correlation with the respective degree of conservation. Our data show that the highly conserved color change mainly affects other highly conserved residues, illustrating a high degree of robustness of the color phenotype to sequence variation.

Empirical validation of ProteinMPNN's efficiency in enhancing protein fitness

Introduction: Protein engineering, which aims to improve the properties and functions of proteins, holds great research significance and application value. However, current models that predict the effects of amino acid substitutions often perform poorly when evaluated for precision. Recent research has shown that ProteinMPNN, a large-scale pre-training sequence design model based on protein structure, performs exceptionally well. It is capable of designing mutants with structures similar to the original protein. When applied to the field of protein engineering, the diverse designs for mutation positions generated by this model can be viewed as a more precise mutation range. Methods: We collected three biological experimental datasets and compared the design results of ProteinMPNN for wild-type proteins with the experimental datasets to verify the ability of ProteinMPNN in improving protein fitness. Results: The validation on biological experimental datasets shows that ProteinMPNN has the ability to design mutation types with higher fitness in single and multi-point mutations. We have verified the high accuracy of ProteinMPNN in protein engineering tasks from both positive and negative perspectives. Discussion: Our research indicates that using large-scale pre trained models to design protein mutants provides a new approach for protein engineering, providing strong support for guiding biological experiments and applications in biotechnology.

Pervasive epistasis exposes intramolecular networks in adaptive enzyme evolution

Enzyme evolution is characterized by constant alterations of the intramolecular residue networks supporting their functions. The rewiring of these network interactions can give rise to epistasis. As mutations accumulate, the epistasis observed across diverse genotypes may appear idiosyncratic, that is, exhibit unique effects in different genetic backgrounds. Here, we unveil a quantitative picture of the prevalence and patterns of epistasis in enzyme evolution by analyzing 41 fitness landscapes generated from seven enzymes. We show that >94% of all mutational and epistatic effects appear highly idiosyncratic, which greatly distorted the functional prediction of the evolved enzymes. By examining seemingly idiosyncratic changes in epistasis along adaptive trajectories, we expose several instances of higher-order, intramolecular rewiring. Using complementary structural data, we outline putative molecular mechanisms explaining higher-order epistasis along two enzyme trajectories. Our work emphasizes the prevalence of epistasis and provides an approach to exploring this phenomenon through a molecular lens.

ProtWave-VAE: Integrating Autoregressive Sampling with Latent-Based Inference for Data-Driven Protein Design

Deep generative models (DGMs) have shown great success in the understanding and data-driven design of proteins. Variational autoencoders (VAEs) are a popular DGM approach that can learn the correlated patterns of amino acid mutations within a multiple sequence alignment (MSA) of protein sequences and distill this information into a low-dimensional latent space to expose phylogenetic and functional relationships and guide generative protein design. Autoregressive (AR) models are another popular DGM approach that typically lacks a low-dimensional latent embedding but does not require training sequences to be aligned into an MSA and enable the design of variable length proteins. In this work, we propose ProtWave-VAE as a novel and lightweight DGM, employing an information maximizing VAE with a dilated convolution encoder and an autoregressive WaveNet decoder. This architecture blends the strengths of the VAE and AR paradigms in enabling training over unaligned sequence data and the conditional generative design of variable length sequences from an interpretable, low-dimensional learned latent space. We evaluated the model's ability to infer patterns and design rules within alignment-free homologous protein family sequences and to design novel synthetic proteins in four diverse protein families. We show that our model can infer meaningful functional and phylogenetic embeddings within latent spaces and make highly accurate predictions within semisupervised downstream fitness prediction tasks. In an application to the C-terminal SH3 domain in the Sho1 transmembrane osmosensing receptor in baker's yeast, we subject ProtWave-VAE-designed sequences to experimental gene synthesis and select-seq assays for the osmosensing function to show that the model enables synthetic protein design, conditional C-terminus diversification, and engineering of the osmosensing function into SH3 paralogues.

Evolutionary paths that link orthogonal pairs of binding proteins

Some protein binding pairs exhibit extreme specificities that functionally insulate them from homologs. Such pairs evolve mostly by accumulating single-point mutations, and mutants are selected if their affinity exceeds the threshold required for function1-4. Thus, homologous and high-specificity binding pairs bring to light an evolutionary conundrum: how does a new specificity evolve while maintaining the required affinity in each intermediate5,6? Until now, a fully functional single-mutation path that connects two orthogonal pairs has only been described where the pairs were mutationally close thus enabling experimental enumeration of all intermediates2. We present an atomistic and graph-theoretical framework for discovering low molecular strain single-mutation paths that connect two extant pairs, enabling enumeration beyond experimental capability. We apply it to two orthogonal bacterial colicin endonuclease-immunity pairs separated by 17 interface mutations7. We were not able to find a strain-free and functional path in the sequence space defined by the two extant pairs. But including mutations that bridge amino acids that cannot be exchanged through single-nucleotide mutations led us to a strain-free 19-mutation trajectory that is completely viable in vivo. Our experiments show that the specificity switch is remarkably abrupt, resulting from only one radical mutation on each partner. Furthermore, each of the critical specificity-switch mutations increases fitness, demonstrating that functional divergence could be driven by positive Darwinian selection. These results reveal how even radical functional changes in an epistatic fitness landscape may evolve.

ProteinGym: Large-Scale Benchmarks for Protein Design and Fitness Prediction

Predicting the effects of mutations in proteins is critical to many applications, from understanding genetic disease to designing novel proteins that can address our most pressing challenges in climate, agriculture and healthcare. Despite a surge in machine learning-based protein models to tackle these questions, an assessment of their respective benefits is challenging due to the use of distinct, often contrived, experimental datasets, and the variable performance of models across different protein families. Addressing these challenges requires scale. To that end we introduce ProteinGym, a large-scale and holistic set of benchmarks specifically designed for protein fitness prediction and design. It encompasses both a broad collection of over 250 standardized deep mutational scanning assays, spanning millions of mutated sequences, as well as curated clinical datasets providing high-quality expert annotations about mutation effects. We devise a robust evaluation framework that combines metrics for both fitness prediction and design, factors in known limitations of the underlying experimental methods, and covers both zero-shot and supervised settings. We report the performance of a diverse set of over 70 high-performing models from various subfields (eg., alignment-based, inverse folding) into a unified benchmark suite. We open source the corresponding codebase, datasets, MSAs, structures, model predictions and develop a user-friendly website that facilitates data access and analysis.

Proteins Need Extra Attention: Improving the Predictive Power of Protein Language Models on Mutational Datasets with Hint Tokens

In this computational study, we introduce "hint token learning," a novel machine learning approach designed to enhance protein language modeling. This method effectively addresses the unique challenges of protein mutational datasets, characterized by highly similar inputs that may differ by only a single token. Our research highlights the superiority of hint token learning over traditional fine-tuning methods through three distinct case studies. We first developed a highly accurate free energy of folding model using the largest protein stability dataset to date. Then, we applied hint token learning to predict a biophysical attribute, the brightness of green fluorescent protein mutants. In our third case, hint token learning was utilized to assess the impact of mutations on RecA bioactivity. These diverse applications collectively demonstrate the potential of hint token learning for improving protein language modeling across general and specific mutational datasets. To facilitate broader use, we have integrated our protein language models into the HuggingFace ecosystem for downstream, mutational fine-tuning tasks.

ProteinNPT: Improving Protein Property Prediction and Design with Non-Parametric Transformers

Protein design holds immense potential for optimizing naturally occurring proteins, with broad applications in drug discovery, material design, and sustainability. However, computational methods for protein engineering are confronted with significant challenges, such as an expansive design space, sparse functional regions, and a scarcity of available labels. These issues are further exacerbated in practice by the fact most real-life design scenarios necessitate the simultaneous optimization of multiple properties. In this work, we introduce ProteinNPT, a non-parametric transformer variant tailored to protein sequences and particularly suited to label-scarce and multi-task learning settings. We first focus on the supervised fitness prediction setting and develop several cross-validation schemes which support robust performance assessment. We subsequently reimplement prior top-performing baselines, introduce several extensions of these baselines by integrating diverse branches of the protein engineering literature, and demonstrate that ProteinNPT consistently outperforms all of them across a diverse set of protein property prediction tasks. Finally, we demonstrate the value of our approach for iterative protein design across extensive in silico Bayesian optimization and conditional sampling experiments.

A rugged yet easily navigable fitness landscape

Fitness landscape theory predicts that rugged landscapes with multiple peaks impair Darwinian evolution, but experimental evidence is limited. In this study, we used genome editing to map the fitness of >260,000 genotypes of the key metabolic enzyme dihydrofolate reductase in the presence of the antibiotic trimethoprim, which targets this enzyme. The resulting landscape is highly rugged and harbors 514 fitness peaks. However, its highest peaks are accessible to evolving populations via abundant fitness-increasing paths. Different peaks share large basins of attraction that render the outcome of adaptive evolution highly contingent on chance events. Our work shows that ruggedness need not be an obstacle to Darwinian evolution but can reduce its predictability. If true in general, the complexity of optimization problems on realistic landscapes may require reappraisal.

AlphaFold2 Can Predict Single-Mutation Effects

AlphaFold2 (AF) is a promising tool, but is it accurate enough to predict single mutation effects? Here, we report that the localized structural deformation between protein pairs differing by only 1-3 mutations-as measured by the effective strain-is correlated across 3901 experimental and AF-predicted structures. Furthermore, analysis of ∼11 000 proteins shows that the local structural change correlates with various phenotypic changes. These findings suggest that AF can predict the range and magnitude of single-mutation effects on average, and we propose a method to improve precision of AF predictions and to indicate when predictions are unreliable.

Deep mutational scanning of proteins in mammalian cells

Protein mutagenesis is essential for unveiling the molecular mechanisms underlying protein function in health, disease, and evolution. In the past decade, deep mutational scanning methods have evolved to support the functional analysis of nearly all possible single-amino acid changes in a protein of interest. While historically these methods were developed in lower organisms such as E. coli and yeast, recent technological advancements have resulted in the increased use of mammalian cells, particularly for studying proteins involved in human disease. These advancements will aid significantly in the classification and interpretation of variants of unknown significance, which are being discovered at large scale due to the current surge in the use of whole-genome sequencing in clinical contexts. Here, we explore the experimental aspects of deep mutational scanning studies in mammalian cells and report the different methods used in each step of the workflow, ultimately providing a useful guide toward the design of such studies.

Coherent Blending of Biophysics-Based Knowledge with Bayesian Neural Networks for Robust Protein Property Prediction

Predicting properties of proteins is of interest for basic biological understanding and protein engineering alike. Increasingly, machine learning (ML) approaches are being used for this task. However, the accuracy of such ML models typically degrades as test proteins stray further from the training data distribution. On the other hand, models that are more data-free, such as biophysics-based models, are typically uniformly accurate over all of the protein space, even if inferior for test points close to the training distribution. Consequently, being able to cohesively blend these two types of information within one model, as appropriate in different parts of the protein space, will improve overall importance. Herein, we tackle just this problem to yield a simple, practical, and scalable approach that can be easily implemented. In particular, we use a Bayesian formulation to integrate biophysical knowledge into neural networks. However, in doing so, a technical challenge arises: Bayesian neural networks (BNNs) enable the user to specify prior information only on the neural network weight parameters, rather than on the function values given to us from a typical biophysics-based model. Consequently, we devise a principled probabilistic method to overcome this challenge. Our approach yields intuitively pleasing results: predictions rely more heavily on the biophysical prior information when the BNN epistemic uncertainty─uncertainty arising from a lack of training data rather than sensor noise─is large and more heavily on the neural network when the epistemic uncertainty is small. We demonstrate this approach on an illustrative synthetic example, on two examples of protein property prediction (fluorescence and binding), and for generality on one small molecule property prediction problem.

Discovering pathways through ribozyme fitness landscapes using information theoretic quantification of epistasis

The identification of catalytic RNAs is typically achieved through primarily experimental means. However, only a small fraction of sequence space can be analyzed even with high-throughput techniques. Methods to extrapolate from a limited data set to predict additional ribozyme sequences, particularly in a human-interpretable fashion, could be useful both for designing new functional RNAs and for generating greater understanding about a ribozyme fitness landscape. Using information theory, we express the effects of epistasis (i.e., deviations from additivity) on a ribozyme. This representation was incorporated into a simple model of the epistatic fitness landscape, which identified potentially exploitable combinations of mutations. We used this model to theoretically predict mutants of high activity for a self-aminoacylating ribozyme, identifying potentially active triple and quadruple mutants beyond the experimental data set of single and double mutants. The predictions were validated experimentally, with nine out of nine sequences being accurately predicted to have high activity. This set of sequences included mutants that form a previously unknown evolutionary "bridge" between two ribozyme families that share a common motif. Individual steps in the method could be examined, understood, and guided by a human, combining interpretability and performance in a simple model to predict ribozyme sequences by extrapolation.

Large-scale pathway reconstruction and colorimetric screening accelerate cellular metabolism engineering

The capability to manipulate and analyze hard-wired metabolic pathways sets the pace at which we can engineer cellular metabolism. Here, we present a framework to extensively rewrite the central metabolic pathway for malonyl-CoA biosynthesis in yeast and readily assess malonyl-CoA output based on pathway-scale DNA reconstruction in combination with colorimetric screening (Pracs). We applied Pracs to generate and test millions of enzyme variants by introducing genetic mutations into the whole set of genes encoding the malonyl-CoA biosynthetic pathway and identified hundreds of beneficial enzyme mutants with increased malonyl-CoA output. Furthermore, the synthetic pathways reconstructed by randomly integrating these beneficial enzyme variants generated vast phenotypic diversity, with some displaying higher production of malonyl-CoA as well as other metabolites, such as carotenoids and betaxanthin, thus demonstrating the generic utility of Pracs to efficiently orchestrate central metabolism to optimize the production of different chemicals in various metabolic pathways. Pracs will be broadly useful to advance our ability to understand and engineer cellular metabolism.

MBE: model-based enrichment estimation and prediction for differential sequencing data

Characterizing differences in sequences between two conditions, such as with and without drug exposure, using high-throughput sequencing data is a prevalent problem involving quantifying changes in sequence abundances, and predicting such differences for unobserved sequences. A key shortcoming of current approaches is their extremely limited ability to share information across related but non-identical reads. Consequently, they cannot use sequencing data effectively, nor be directly applied in many settings of interest. We introduce model-based enrichment (MBE) to overcome this shortcoming. We evaluate MBE using both simulated and real data. Overall, MBE improves accuracy compared to current differential analysis methods.

Artificial intelligence-aided protein engineering: from topological data analysis to deep protein language models

Protein engineering is an emerging field in biotechnology that has the potential to revolutionize various areas, such as antibody design, drug discovery, food security, ecology, and more. However, the mutational space involved is too vast to be handled through experimental means alone. Leveraging accumulative protein databases, machine learning (ML) models, particularly those based on natural language processing (NLP), have considerably expedited protein engineering. Moreover, advances in topological data analysis (TDA) and artificial intelligence-based protein structure prediction, such as AlphaFold2, have made more powerful structure-based ML-assisted protein engineering strategies possible. This review aims to offer a comprehensive, systematic, and indispensable set of methodological components, including TDA and NLP, for protein engineering and to facilitate their future development.

Phenotype switching of the mutation rate facilitates adaptive evolution

The mutation rate plays an important role in adaptive evolution. It can be modified by mutator and anti-mutator alleles. Recent empirical evidence hints that the mutation rate may vary among genetically identical individuals: evidence from bacteria suggests that the mutation rate can be affected by expression noise of a DNA repair protein and potentially also by translation errors in various proteins. Importantly, this non-genetic variation may be heritable via a transgenerational epigenetic mode of inheritance, giving rise to a mutator phenotype that is independent from mutator alleles. Here, we investigate mathematically how the rate of adaptive evolution is affected by the rate of mutation rate phenotype switching. We model an asexual population with two mutation rate phenotypes, non-mutator and mutator. An offspring may switch from its parental phenotype to the other phenotype. We find that switching rates that correspond to so-far empirically described non-genetic systems of inheritance of the mutation rate lead to higher rates of adaptation on both artificial and natural fitness landscapes. These switching rates can maintain within the same individuals both a mutator phenotype and intermediary mutations, a combination that facilitates adaptation. Moreover, non-genetic inheritance increases the proportion of mutators in the population, which in turn increases the probability of hitchhiking of the mutator phenotype with adaptive mutations. This in turns facilitates the acquisition of additional adaptive mutations. Our results rationalize recently observed noise in the expression of proteins that affect the mutation rate and suggest that non-genetic inheritance of this phenotype may facilitate evolutionary adaptive processes.

Protein engineering via sequence-performance mapping

Discovery and evolution of new and improved proteins has empowered molecular therapeutics, diagnostics, and industrial biotechnology. Discovery and evolution both require efficient screens and effective libraries, although they differ in their challenges because of the absence or presence, respectively, of an initial protein variant with the desired function. A host of high-throughput technologies-experimental and computational-enable efficient screens to identify performant protein variants. In partnership, an informed search of sequence space is needed to overcome the immensity, sparsity, and complexity of the sequence-performance landscape. Early in the historical trajectory of protein engineering, these elements aligned with distinct approaches to identify the most performant sequence: selection from large, randomized combinatorial libraries versus rational computational design. Substantial advances have now emerged from the synergy of these perspectives. Rational design of combinatorial libraries aids the experimental search of sequence space, and high-throughput, high-integrity experimental data inform computational design. At the core of the collaborative interface, efficient protein characterization (rather than mere selection of optimal variants) maps sequence-performance landscapes. Such quantitative maps elucidate the complex relationships between protein sequence and performance-e.g., binding, catalytic efficiency, biological activity, and developability-thereby advancing fundamental protein science and facilitating protein discovery and evolution.

Learning protein fitness landscapes with deep mutational scanning data from multiple sources

One of the key points of machine learning-assisted directed evolution (MLDE) is the accurate learning of the fitness landscape, a conceptual mapping from sequence variants to the desired function. Here, we describe a multi-protein training scheme that leverages the existing deep mutational scanning data from diverse proteins to aid in understanding the fitness landscape of a new protein. Proof-of-concept trials are designed to validate this training scheme in three aspects: random and positional extrapolation for single-variant effects, zero-shot fitness predictions for new proteins, and extrapolation for higher-order variant effects from single-variant effects. Moreover, our study identified previously overlooked strong baselines, and their unexpectedly good performance brings our attention to the pitfalls of MLDE. Overall, these results may improve our understanding of the association between different protein fitness profiles and shed light on developing better machine learning-assisted approaches to the directed evolution of proteins. A record of this paper's transparent peer review process is included in the supplemental information.

Linear-Scaling Kernels for Protein Sequences and Small Molecules Outperform Deep Learning While Providing Uncertainty Quantitation and Improved Interpretability

Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their excessive computational cost and by the difficulty in adapting them for analyzing sequences (e.g., amino acid sequences) and graphs (e.g., small molecules). In this study, we introduce a group of random feature-approximated kernels for sequences and graphs that exhibit linear scaling with both the size of the training set and the size of the sequences or graphs. We incorporate these new kernels into our new Python library for GP regression, xGPR, and develop an efficient and scalable algorithm for fitting GPs equipped with these kernels to large datasets. We compare the performance of xGPR on 17 different benchmarks with both standard and state-of-the-art deep learning models and find that GP regression achieves highly competitive accuracy for these tasks while providing with well-calibrated uncertainty quantitation and improved interpretability. Finally, in a simple experiment, we illustrate how xGPR may be used as part of an active learning strategy to engineer a protein with a desired property in an automated way without human intervention.

Jointly modeling deep mutational scans identifies shifted mutational effects among SARS-CoV-2 spike homologs

Deep mutational scanning (DMS) is a high-throughput experimental technique that measures the effects of thousands of mutations to a protein. These experiments can be performed on multiple homologs of a protein or on the same protein selected under multiple conditions. It is often of biological interest to identify mutations with shifted effects across homologs or conditions. However, it is challenging to determine if observed shifts arise from biological signal or experimental noise. Here, we describe a method for jointly inferring mutational effects across multiple DMS experiments while also identifying mutations that have shifted in their effects among experiments. A key aspect of our method is to regularize the inferred shifts, so that they are nonzero only when strongly supported by the data. We apply this method to DMS experiments that measure how mutations to spike proteins from SARS-CoV-2 variants (Delta, Omicron BA.1, and Omicron BA.2) affect cell entry. Most mutational effects are conserved between these spike homologs, but a fraction have markedly shifted. We experimentally validate a subset of the mutations inferred to have shifted effects, and confirm differences of > 1,000-fold in the impact of the same mutation on spike-mediated viral infection across spikes from different SARS-CoV-2 variants. Overall, our work establishes a general approach for comparing sets of DMS experiments to identify biologically important shifts in mutational effects.

Protein folding rate evolution upon mutations

Despite the spectacular success of cutting-edge protein fold prediction methods, many critical questions remain unanswered, including why proteins can reach their native state in a biologically reasonable time. A satisfactory answer to this simple question could shed light on the slowest folding rate of proteins as well as how mutations-amino-acid substitutions and/or post-translational modifications-might affect it. Preliminary results indicate that (i) Anfinsen's dogma validity ensures that proteins reach their native state on a reasonable timescale regardless of their sequence or length, and (ii) it is feasible to determine the evolution of protein folding rates without accounting for epistasis effects or the mutational trajectories between the starting and target sequences. These results have direct implications for evolutionary biology because they lay the groundwork for a better understanding of why, and to what extent, mutations-a crucial element of evolution and a factor influencing it-affect protein evolvability. Furthermore, they may spur significant progress in our efforts to solve crucial structural biology problems, such as how a sequence encodes its folding.

Artificial intelligence-aided protein engineering: from topological data analysis to deep protein language models

Protein engineering is an emerging field in biotechnology that has the potential to revolutionize various areas, such as antibody design, drug discovery, food security, ecology, and more. However, the mutational space involved is too vast to be handled through experimental means alone. Leveraging accumulative protein databases, machine learning (ML) models, particularly those based on natural language processing (NLP), have considerably expedited protein engineering. Moreover, advances in topological data analysis (TDA) and artificial intelligence-based protein structure prediction, such as AlphaFold2, have made more powerful structure-based ML-assisted protein engineering strategies possible. This review aims to offer a comprehensive, systematic, and indispensable set of methodological components, including TDA and NLP, for protein engineering and to facilitate their future development.

BioAutoMATED: An end-to-end automated machine learning tool for explanation and design of biological sequences

The design choices underlying machine-learning (ML) models present important barriers to entry for many biologists who aim to incorporate ML in their research. Automated machine-learning (AutoML) algorithms can address many challenges that come with applying ML to the life sciences. However, these algorithms are rarely used in systems and synthetic biology studies because they typically do not explicitly handle biological sequences (e.g., nucleotide, amino acid, or glycan sequences) and cannot be easily compared with other AutoML algorithms. Here, we present BioAutoMATED, an AutoML platform for biological sequence analysis that integrates multiple AutoML methods into a unified framework. Users are automatically provided with relevant techniques for analyzing, interpreting, and designing biological sequences. BioAutoMATED predicts gene regulation, peptide-drug interactions, and glycan annotation, and designs optimized synthetic biology components, revealing salient sequence characteristics. By automating sequence modeling, BioAutoMATED allows life scientists to incorporate ML more readily into their work.

Evolvability-enhancing mutations in the fitness landscapes of an RNA and a protein

Can evolvability-the ability to produce adaptive heritable variation-itself evolve through adaptive Darwinian evolution? If so, then Darwinian evolution may help create the conditions that enable Darwinian evolution. Here I propose a framework that is suitable to address this question with available experimental data on adaptive landscapes. I introduce the notion of an evolvability-enhancing mutation, which increases the likelihood that subsequent mutations in an evolving organism, protein, or RNA molecule are adaptive. I search for such mutations in the experimentally characterized and combinatorially complete fitness landscapes of a protein and an RNA molecule. I find that such evolvability-enhancing mutations indeed exist. They constitute a small fraction of all mutations, which shift the distribution of fitness effects of subsequent mutations towards less deleterious mutations, and increase the incidence of beneficial mutations. Evolving populations which experience such mutations can evolve significantly higher fitness. The study of evolvability-enhancing mutations opens many avenues of investigation into the evolution of evolvability.

Systematic conformation-to-phenotype mapping via limited deep sequencing of proteins

Non-native conformations drive protein-misfolding diseases, complicate bioengineering efforts, and fuel molecular evolution. No current experimental technique is well suited for elucidating them and their phenotypic effects. Especially intractable are the transient conformations populated by intrinsically disordered proteins. We describe an approach to systematically discover, stabilize, and purify native and non-native conformations, generated in vitro or in vivo, and directly link conformations to molecular, organismal, or evolutionary phenotypes. This approach involves high-throughput disulfide scanning (HTDS) of the entire protein. To reveal which disulfides trap which chromatographically resolvable conformers, we devised a deep-sequencing method for double-Cys variant libraries of proteins that precisely and simultaneously locates both Cys residues within each polypeptide. HTDS of the abundant E. coli periplasmic chaperone HdeA revealed distinct classes of disordered hydrophobic conformers with variable cytotoxicity depending on where the backbone was cross-linked. HTDS can bridge conformational and phenotypic landscapes for many proteins that function in disulfide-permissive environments.

Mutation bias and the predictability of evolution

Predicting evolutionary outcomes is an important research goal in a diversity of contexts. The focus of evolutionary forecasting is usually on adaptive processes, and efforts to improve prediction typically focus on selection. However, adaptive processes often rely on new mutations, which can be strongly influenced by predictable biases in mutation. Here, we provide an overview of existing theory and evidence for such mutation-biased adaptation and consider the implications of these results for the problem of prediction, in regard to topics such as the evolution of infectious diseases, resistance to biochemical agents, as well as cancer and other kinds of somatic evolution. We argue that empirical knowledge of mutational biases is likely to improve in the near future, and that this knowledge is readily applicable to the challenges of short-term prediction. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

Global epistasis on fitness landscapes

Epistatic interactions between mutations add substantial complexity to adaptive landscapes and are often thought of as detrimental to our ability to predict evolution. Yet, patterns of global epistasis, in which the fitness effect of a mutation is well-predicted by the fitness of its genetic background, may actually be of help in our efforts to reconstruct fitness landscapes and infer adaptive trajectories. Microscopic interactions between mutations, or inherent nonlinearities in the fitness landscape, may cause global epistasis patterns to emerge. In this brief review, we provide a succinct overview of recent work about global epistasis, with an emphasis on building intuition about why it is often observed. To this end, we reconcile simple geometric reasoning with recent mathematical analyses, using these to explain why different mutations in an empirical landscape may exhibit different global epistasis patterns—ranging from diminishing to increasing returns. Finally, we highlight open questions and research directions.

This article is part of the theme issue ‘Interdisciplinary approaches to predicting evolutionary biology’.