Adaptation in protein fitness landscapes is facilitated by indirect paths

Multistate and functional protein design using RoseTTAFold sequence space diffusion

Protein denoising diffusion probabilistic models are used for the de novo generation of protein backbones but are limited in their ability to guide generation of proteins with sequence-specific attributes and functional properties. To overcome this limitation, we developed ProteinGenerator (PG), a sequence space diffusion model based on RoseTTAFold that simultaneously generates protein sequences and structures. Beginning from a noised sequence representation, PG generates sequence and structure pairs by iterative denoising, guided by desired sequence and structural protein attributes. We designed thermostable proteins with varying amino acid compositions and internal sequence repeats and cage bioactive peptides, such as melittin. By averaging sequence logits between diffusion trajectories with distinct structural constraints, we designed multistate parent-child protein triples in which the same sequence folds to different supersecondary structures when intact in the parent versus split into two child domains. PG design trajectories can be guided by experimental sequence-activity data, providing a general approach for integrated computational and experimental optimization of protein function.

Computational Synthetic Biology Enabled through JAX: A Showcase

Mathematical modeling is indispensable in synthetic biology but remains underutilized. Tackling problems, from optimizing gene networks to simulating intracellular dynamics, can be facilitated by the ever-growing body of modeling approaches, be they mechanistic, stochastic, data-driven, or AI-enabled. Thanks to progress in the AI community, robust frameworks have emerged to enable researchers to access complex computational hardware and compilation. Previously, these frameworks focused solely on deep learning, but they have been developed to the point where running different forms of computation is relatively simple, as made possible, notably, by the JAX library. Running simulations at scale on GPUs speeds up research, which compounds enable larger-scale experiments and greater usability of code. As JAX remains underexplored in computational biology, we demonstrate its utility in three example projects ranging from synthetic biology to directed evolution, each with an accompanying demonstrative Jupyter notebook. We hope that these tutorials serve to democratize the flexible scaling, faster run-times, easy GPU portability, and mathematical enhancements (such as automatic differentiation) that JAX brings, all with only minor restructuring of code.

The simplicity of protein sequence-function relationships

How complex are the rules by which a protein's sequence determines its function? High-order epistatic interactions among residues are thought to be pervasive, suggesting an idiosyncratic and unpredictable sequence-function relationship. But many prior studies may have overestimated epistasis, because they analyzed sequence-function relationships relative to a single reference sequence-which causes measurement noise and local idiosyncrasies to snowball into high-order epistasis-or they did not fully account for global nonlinearities. Here we present a reference-free method that jointly infers specific epistatic interactions and global nonlinearity using a bird's-eye view of sequence space. This technique yields the simplest explanation of sequence-function relationships and is more robust than existing methods to measurement noise, missing data, and model misspecification. We reanalyze 20 experimental datasets and find that context-independent amino acid effects and pairwise interactions, along with a simple nonlinearity to account for limited dynamic range, explain a median of 96% of phenotypic variance and over 92% in every case. Only a tiny fraction of genotypes are strongly affected by higher-order epistasis. Sequence-function relationships are also sparse: a miniscule fraction of amino acids and interactions account for 90% of phenotypic variance. Sequence-function causality across these datasets is therefore simple, opening the way for tractable approaches to characterize proteins' genetic architecture.

Rapid synthesis and screening of natively paired antibodies against influenza hemagglutinin stem via oPool+ display

Antibody discovery is crucial for developing therapeutics and vaccines as well as understanding adaptive immunity. However, the lack of approaches to synthesize antibodies with defined sequences in a high-throughput manner represents a major bottleneck in antibody discovery. Here, we presented oPool+ display, which combines oligo pool synthesis and mRNA display to construct and characterize many natively paired antibodies in parallel. As a proof-of-concept, we applied oPool+ display to rapidly screen the binding activity of >300 natively paired influenza hemagglutinin (HA) antibodies against the conserved HA stem domain. Structural analysis of 16.ND.92, one of the identified HA stem antibodies, revealed a unique binding mode distinct from other known broadly neutralizing HA stem antibodies with convergent sequence features. Yet, despite such differences, 16.ND.92 remained broadly reactive and conferred in vivo protection. Overall, this study not only established an experimental platform that can be applied in both research and therapeutics to accelerate antibody discovery, but also provides molecular insights into antibody responses to the influenza HA stem, which is a major target for universal influenza vaccine development.

Fine-tuning protein language models boosts predictions across diverse tasks

Prediction methods inputting embeddings from protein language models have reached or even surpassed state-of-the-art performance on many protein prediction tasks. In natural language processing fine-tuning large language models has become the de facto standard. In contrast, most protein language model-based protein predictions do not back-propagate to the language model. Here, we compare the fine-tuning of three state-of-the-art models (ESM2, ProtT5, Ankh) on eight different tasks. Two results stand out. Firstly, task-specific supervised fine-tuning almost always improves downstream predictions. Secondly, parameter-efficient fine-tuning can reach similar improvements consuming substantially fewer resources at up to 4.5-fold acceleration of training over fine-tuning full models. Our results suggest to always try fine-tuning, in particular for problems with small datasets, such as for fitness landscape predictions of a single protein. For ease of adaptability, we provide easy-to-use notebooks to fine-tune all models used during this work for per-protein (pooling) and per-residue prediction tasks.

Integrating Computational Design and Experimental Approaches for Next-Generation Biologics

Therapeutic protein engineering has revolutionized medicine by enabling the development of highly specific and potent treatments for a wide range of diseases. This review examines recent advances in computational and experimental approaches for engineering improved protein therapeutics. Key areas of focus include antibody engineering, enzyme replacement therapies, and cytokine-based drugs. Computational methods like structure-based design, machine learning integration, and protein language models have dramatically enhanced our ability to predict protein properties and guide engineering efforts. Experimental techniques such as directed evolution and rational design approaches continue to evolve, with high-throughput methods accelerating the discovery process. Applications of these methods have led to breakthroughs in affinity maturation, bispecific antibodies, enzyme stability enhancement, and the development of conditionally active cytokines. Emerging approaches like intracellular protein delivery, stimulus-responsive proteins, and de novo designed therapeutic proteins offer exciting new possibilities. However, challenges remain in predicting in vivo behavior, scalable manufacturing, immunogenicity mitigation, and targeted delivery. Addressing these challenges will require continued integration of computational and experimental methods, as well as a deeper understanding of protein behavior in complex physiological environments. As the field advances, we can anticipate increasingly sophisticated and effective protein therapeutics for treating human diseases.

Deciphering GB1's Single Mutational Landscape: Insights from MuMi Analysis

Mutational changes that affect the binding of the C2 fragment of Streptococcal protein G (GB1) to the Fc domain of human IgG (IgG-Fc) have been extensively studied using deep mutational scanning (DMS), and the binding affinity of all single mutations has been measured experimentally in the literature. To investigate the underlying molecular basis, we perform in silico mutational scanning for all possible single mutations, along with 2 μs-long molecular dynamics (WT-MD) of the wild-type (WT) GB1 in both unbound and IgG-Fc bound forms. We compute the hydrogen bonds between GB1 and IgG-Fc in WT-MD to identify the dominant hydrogen bonds for binding, which we then assess in conformations produced by Mutation and Minimization (MuMi) to explain the fitness landscape of GB1 and IgG-Fc binding. Furthermore, we analyze MuMi and WT-MD to investigate the dynamics of binding, focusing on the relative solvent accessibility of residues and the probability of residues being located at the binding interface. With these analyses, we explain the interactions between GB1 and IgG-Fc and display the structural features of binding. In sum, our findings highlight the potential of MuMi as a reliable and computationally efficient tool for predicting protein fitness landscapes, offering significant advantages over traditional methods. The methodologies and results presented in this study pave the way for improved predictive accuracy in protein stability and interaction studies, which are crucial for advancements in drug design and synthetic biology.

A combinatorially complete epistatic fitness landscape in an enzyme active site

Protein engineering often targets binding pockets or active sites which are enriched in epistasis-nonadditive interactions between amino acid substitutions-and where the combined effects of multiple single substitutions are difficult to predict. Few existing sequence-fitness datasets capture epistasis at large scale, especially for enzyme catalysis, limiting the development and assessment of model-guided enzyme engineering approaches. We present here a combinatorially complete, 160,000-variant fitness landscape across four residues in the active site of an enzyme. Assaying the native reaction of a thermostable β-subunit of tryptophan synthase (TrpB) in a nonnative environment yielded a landscape characterized by significant epistasis and many local optima. These effects prevent simulated directed evolution approaches from efficiently reaching the global optimum. There is nonetheless wide variability in the effectiveness of different directed evolution approaches, which together provide experimental benchmarks for computational and machine learning workflows. The most-fit TrpB variants contain a substitution that is nearly absent in natural TrpB sequences-a result that conservation-based predictions would not capture. Thus, although fitness prediction using evolutionary data can enrich in more-active variants, these approaches struggle to identify and differentiate among the most-active variants, even for this near-native function. Overall, this work presents a large-scale testing ground for model-guided enzyme engineering and suggests that efficient navigation of epistatic fitness landscapes can be improved by advances in both machine learning and physical modeling.

PETA: evaluating the impact of protein transfer learning with sub-word tokenization on downstream applications

Protein language models (PLMs) play a dominant role in protein representation learning. Most existing PLMs regard proteins as sequences of 20 natural amino acids. The problem with this representation method is that it simply divides the protein sequence into sequences of individual amino acids, ignoring the fact that certain residues often occur together. Therefore, it is inappropriate to view amino acids as isolated tokens. Instead, the PLMs should recognize the frequently occurring combinations of amino acids as a single token. In this study, we use the byte-pair-encoding algorithm and unigram to construct advanced residue vocabularies for protein sequence tokenization, and we have shown that PLMs pre-trained using these advanced vocabularies exhibit superior performance on downstream tasks when compared to those trained with simple vocabularies. Furthermore, we introduce PETA, a comprehensive benchmark for systematically evaluating PLMs. We find that vocabularies comprising 50 and 200 elements achieve optimal performance. Our code, model weights, and datasets are available at https://github.com/ginnm/ProteinPretraining . SCIENTIFIC CONTRIBUTION: This study introduces advanced protein sequence tokenization analysis, leveraging the byte-pair-encoding algorithm and unigram. By recognizing frequently occurring combinations of amino acids as single tokens, our proposed method enhances the performance of PLMs on downstream tasks. Additionally, we present PETA, a new comprehensive benchmark for the systematic evaluation of PLMs, demonstrating that vocabularies of 50 and 200 elements offer optimal performance.

Neural network extrapolation to distant regions of the protein fitness landscape

Machine learning (ML) has transformed protein engineering by constructing models of the underlying sequence-function landscape to accelerate the discovery of new biomolecules. ML-guided protein design requires models, trained on local sequence-function information, to accurately predict distant fitness peaks. In this work, we evaluate neural networks' capacity to extrapolate beyond their training data. We perform model-guided design using a panel of neural network architectures trained on protein G (GB1)-Immunoglobulin G (IgG) binding data and experimentally test thousands of GB1 designs to systematically evaluate the models' extrapolation. We find each model architecture infers markedly different landscapes from the same data, which give rise to unique design preferences. We find simpler models excel in local extrapolation to design high fitness proteins, while more sophisticated convolutional models can venture deep into sequence space to design proteins that fold but are no longer functional. We also find that implementing a simple ensemble of convolutional neural networks enables robust design of high-performing variants in the local landscape. Our findings highlight how each architecture's inductive biases prime them to learn different aspects of the protein fitness landscape and how a simple ensembling approach makes protein engineering more robust.

Machine learning-guided co-optimization of fitness and diversity facilitates combinatorial library design in enzyme engineering

The effective design of combinatorial libraries to balance fitness and diversity facilitates the engineering of useful enzyme functions, particularly those that are poorly characterized or unknown in biology. We introduce MODIFY, a machine learning (ML) algorithm that learns from natural protein sequences to infer evolutionarily plausible mutations and predict enzyme fitness. MODIFY co-optimizes predicted fitness and sequence diversity of starting libraries, prioritizing high-fitness variants while ensuring broad sequence coverage. In silico evaluation shows that MODIFY outperforms state-of-the-art unsupervised methods in zero-shot fitness prediction and enables ML-guided directed evolution with enhanced efficiency. Using MODIFY, we engineer generalist biocatalysts derived from a thermostable cytochrome c to achieve enantioselective C-B and C-Si bond formation via a new-to-nature carbene transfer mechanism, leading to biocatalysts six mutations away from previously developed enzymes while exhibiting superior or comparable activities. These results demonstrate MODIFY's potential in solving challenging enzyme engineering problems beyond the reach of classic directed evolution.

How to Sample Dozens of Substitutions per Site with λ Dynamics

Alchemical free energy methods are useful in computer-aided drug design and computational protein design because they provide rigorous statistical mechanics-based estimates of free energy differences from molecular dynamics simulations. λ dynamics is a free energy method with the ability to characterize combinatorial chemical spaces spanning thousands of related systems within a single simulation, which gives it a distinct advantage over other alchemical free energy methods that are mostly limited to pairwise comparisons. Recently developed methods have improved the scalability of λ dynamics to perturbations at many sites; however, the size of chemical space that can be explored at each individual site has previously been limited to fewer than ten substituents. As the number of substituents increases, the volume of alchemical space corresponding to nonphysical alchemical intermediates grows exponentially relative to the size corresponding to the physical states of interest. Beyond nine substituents, λ dynamics simulations become lost in an alchemical morass of intermediate states. In this work, we introduce new biasing potentials that circumvent excessive sampling of intermediate states by favoring sampling of physical end points relative to alchemical intermediates. Additionally, we present a more scalable adaptive landscape flattening algorithm for these larger alchemical spaces. Finally, we show that this potential enables more efficient sampling in both protein and drug design test systems with up to 24 substituents per site, enabling, for the first time, simultaneous simulation of all 20 amino acids.

Specialization restricts the evolutionary paths available to yeast sugar transporters

Functional innovation at the protein level is a key source of evolutionary novelties. The constraints on functional innovations are likely to be highly specific in different proteins, which are shaped by their unique histories and the extent of global epistasis that arises from their structures and biochemistries. These contextual nuances in the sequence-function relationship have implications both for a basic understanding of the evolutionary process and for engineering proteins with desirable properties. Here, we have investigated the molecular basis of novel function in a model member of an ancient, conserved, and biotechnologically relevant protein family. These Major Facilitator Superfamily sugar porters are a functionally diverse group of proteins that are thought to be highly plastic and evolvable. By dissecting a recent evolutionary innovation in an α-glucoside transporter from the yeast Saccharomyces eubayanus, we show that the ability to transport a novel substrate requires high-order interactions between many protein regions and numerous specific residues proximal to the transport channel. To reconcile the functional diversity of this family with the constrained evolution of this model protein, we generated new, state-of-the-art genome annotations for 332 Saccharomycotina yeast species spanning approximately 400 million years of evolution. By integrating phylogenetic and phenotypic analyses across these species, we show that the model yeast α-glucoside transporters likely evolved from a multifunctional ancestor and became subfunctionalized. The accumulation of additive and epistatic substitutions likely entrenched this subfunction, which made the simultaneous acquisition of multiple interacting substitutions the only reasonably accessible path to novelty.

Quantifying higher-order epistasis: beware the chimera

Epistasis, or interactions in which alleles at one locus modify the fitness effects of alleles at other loci, plays a fundamental role in genetics, protein evolution, and many other areas of biology. Epistasis is typically quantified by computing the deviation from the expected fitness under an additive or multiplicative model using one of several formulae. However, these formulae are not all equivalent. Importantly, one widely used formula - which we call the chimeric formula - measures deviations from a multiplicative fitness model on an additive scale, thus mixing two measurement scales. We show that for pairwise interactions, the chimeric formula yields a different magnitude, but the same sign (synergistic vs. antagonistic) of epistasis compared to the multiplicative formula that measures both fitness and deviations on a multiplicative scale. However, for higher-order interactions, we show that the chimeric formula can have both different magnitude and sign compared to the multiplicative formula - thus confusing negative epistatic interactions with positive interactions, and vice versa. We resolve these inconsistencies by deriving fundamental connections between the different epistasis formulae and the parameters of the multivariate Bernoulli distribution . Our results demonstrate that the additive and multiplicative epistasis formulae are more mathematically sound than the chimeric formula. Moreover, we demonstrate that the mathematical issues with the chimeric epistasis formula lead to markedly different biological interpretations of real data. Analyzing multi-gene knockout data in yeast, multi-way drug interactions in E. coli , and deep mutational scanning (DMS) of several proteins, we find that 10 - 60% of higher-order interactions have a change in sign with the multiplicative or additive epistasis formula. These sign changes result in qualitatively different findings on functional divergence in the yeast genome, synergistic vs. antagonistic drug interactions, and and epistasis between protein mutations. In particular, in the yeast data, the more appropriate multiplicative formula identifies nearly 500 additional negative three-way interactions, thus extending the trigenic interaction network by 25%.

Functional effects of mutations in proteins can be predicted and interpreted by guided selection of sequence covariation information

Predicting the effects of one or more mutations to the in vivo or in vitro properties of a wild-type protein is a major computational challenge, due to the presence of epistasis, that is, of interactions between amino acids in the sequence. We introduce a computationally efficient procedure to build minimal epistatic models to predict mutational effects by combining evolutionary (homologous sequence) and few mutational-scan data. Mutagenesis measurements guide the selection of links in a sparse graphical model, while the parameters on the nodes and the edges are inferred from sequence data. We show, on 10 mutational scans, that our pipeline exhibits performances comparable to state-of-the-art deep networks trained on many more data, while requiring much less parameters and being hence more interpretable. In particular, the identified interactions adapt to the wild-type protein and to the fitness or biochemical property experimentally measured, mostly focus on key functional sites, and are not necessarily related to structural contacts. Therefore, our method is able to extract information relevant for one mutational experiment from homologous sequence data reflecting the multitude of structural and functional constraints acting on proteins throughout evolution.

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.

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.

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.

Robust genetic codes enhance protein evolvability

The standard genetic code defines the rules of translation for nearly every life form on Earth. It also determines the amino acid changes accessible via single-nucleotide mutations, thus influencing protein evolvability-the ability of mutation to bring forth adaptive variation in protein function. One of the most striking features of the standard genetic code is its robustness to mutation, yet it remains an open question whether such robustness facilitates or frustrates protein evolvability. To answer this question, we use data from massively parallel sequence-to-function assays to construct and analyze 6 empirical adaptive landscapes under hundreds of thousands of rewired genetic codes, including those of codon compression schemes relevant to protein engineering and synthetic biology. We find that robust genetic codes tend to enhance protein evolvability by rendering smooth adaptive landscapes with few peaks, which are readily accessible from throughout sequence space. However, the standard genetic code is rarely exceptional in this regard, because many alternative codes render smoother landscapes than the standard code. By constructing low-dimensional visualizations of these landscapes, which each comprise more than 16 million mRNA sequences, we show that such alternative codes radically alter the topological features of the network of high-fitness genotypes. Whereas the genetic codes that optimize evolvability depend to some extent on the detailed relationship between amino acid sequence and protein function, we also uncover general design principles for engineering nonstandard genetic codes for enhanced and diminished evolvability, which may facilitate directed protein evolution experiments and the bio-containment of synthetic organisms, respectively.

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.

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.

Opportunities and Challenges for Machine Learning-Assisted Enzyme Engineering

Enzymes can be engineered at the level of their amino acid sequences to optimize key properties such as expression, stability, substrate range, and catalytic efficiency-or even to unlock new catalytic activities not found in nature. Because the search space of possible proteins is vast, enzyme engineering usually involves discovering an enzyme starting point that has some level of the desired activity followed by directed evolution to improve its "fitness" for a desired application. Recently, machine learning (ML) has emerged as a powerful tool to complement this empirical process. ML models can contribute to (1) starting point discovery by functional annotation of known protein sequences or generating novel protein sequences with desired functions and (2) navigating protein fitness landscapes for fitness optimization by learning mappings between protein sequences and their associated fitness values. In this Outlook, we explain how ML complements enzyme engineering and discuss its future potential to unlock improved engineering outcomes.

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.

Inference of annealed protein fitness landscapes with AnnealDCA

The design of proteins with specific tasks is a major challenge in molecular biology with important diagnostic and therapeutic applications. High-throughput screening methods have been developed to systematically evaluate protein activity, but only a small fraction of possible protein variants can be tested using these techniques. Computational models that explore the sequence space in-silico to identify the fittest molecules for a given function are needed to overcome this limitation. In this article, we propose AnnealDCA, a machine-learning framework to learn the protein fitness landscape from sequencing data derived from a broad range of experiments that use selection and sequencing to quantify protein activity. We demonstrate the effectiveness of our method by applying it to antibody Rep-Seq data of immunized mice and screening experiments, assessing the quality of the fitness landscape reconstructions. Our method can be applied to several experimental cases where a population of protein variants undergoes various rounds of selection and sequencing, without relying on the computation of variants enrichment ratios, and thus can be used even in cases of disjoint sequence samples.

Protein language models meet reduced amino acid alphabets

MOTIVATION

Protein language models (PLMs), which borrowed ideas for modelling and inference from natural language processing, have demonstrated the ability to extract meaningful representations in an unsupervised way. This led to significant performance improvement in several downstream tasks. Clustering amino acids based on their physical-chemical properties to achieve reduced alphabets has been of interest in past research, but their application to PLMs or folding models is unexplored.

RESULTS

Here, we investigate the efficacy of PLMs trained on reduced amino acid alphabets in capturing evolutionary information, and we explore how the loss of protein sequence information impacts learned representations and downstream task performance. Our empirical work shows that PLMs trained on the full alphabet and a large number of sequences capture fine details that are lost in alphabet reduction methods. We further show the ability of a structure prediction model(ESMFold) to fold CASP14 protein sequences translated using a reduced alphabet. For 10 proteins out of the 50 targets, reduced alphabets improve structural predictions with LDDT-Cα differences of up to 19%.

AVAILABILITY AND IMPLEMENTATION

Trained models and code are available at github.com/Ieremie/reduced-alph-PLM.

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.

Selection pressures on evolution of ribonuclease H explored with rigorous free-energy-based design

Understanding natural protein evolution and designing novel proteins are motivating interest in development of high-throughput methods to explore large sequence spaces. In this work, we demonstrate the application of multisite λ dynamics (MSλD), a rigorous free energy simulation method, and chemical denaturation experiments to quantify evolutionary selection pressure from sequence-stability relationships and to address questions of design. This study examines a mesophilic phylogenetic clade of ribonuclease H (RNase H), furthering its extensive characterization in earlier studies, focusing on E. coli RNase H (ecRNH) and a more stable consensus sequence (AncCcons) differing at 15 positions. The stabilities of 32,768 chimeras between these two sequences were computed using the MSλD framework. The most stable and least stable chimeras were predicted and tested along with several other sequences, revealing a designed chimera with approximately the same stability increase as AncCcons, but requiring only half the mutations. Comparing the computed stabilities with experiment for 12 sequences reveals a Pearson correlation of 0.86 and root mean squared error of 1.18 kcal/mol, an unprecedented level of accuracy well beyond less rigorous computational design methods. We then quantified selection pressure using a simple evolutionary model in which sequences are selected according to the Boltzmann factor of their stability. Selection temperatures from 110 to 168 K are estimated in three ways by comparing experimental and computational results to evolutionary models. These estimates indicate selection pressure is high, which has implications for evolutionary dynamics and for the accuracy required for design, and suggests accurate high-throughput computational methods like MSλD may enable more effective protein design.

Master regulators of biological systems in higher dimensions

A longstanding goal of biology is to identify the key genes and species that critically impact evolution, ecology, and health. Network analysis has revealed keystone species that regulate ecosystems and master regulators that regulate cellular genetic networks. Yet these studies have focused on pairwise biological interactions, which can be affected by the context of genetic background and other species present, generating higher-order interactions. The important regulators of higher-order interactions are unstudied. To address this, we applied a high-dimensional geometry approach that quantifies epistasis in a fitness landscape to ask how individual genes and species influence the interactions in the rest of the biological network. We then generated and also reanalyzed 5-dimensional datasets (two genetic, two microbiome). We identified key genes (e.g., the rbs locus and pykF) and species (e.g., Lactobacilli) that control the interactions of many other genes and species. These higher-order master regulators can induce or suppress evolutionary and ecological diversification by controlling the topography of the fitness landscape. Thus, we provide a method and mathematical justification for exploration of biological networks in higher dimensions.

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.

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.

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.

Deep mutational scanning reveals the functional constraints and evolutionary potential of the influenza A virus PB1 protein

IMPORTANCE

The influenza virus polymerase is important for adaptation to new hosts and, as a determinant of mutation rate, for the process of adaptation itself. We performed a deep mutational scan of the polymerase basic 1 (PB1) protein to gain insights into the structural and functional constraints on the influenza RNA-dependent RNA polymerase. We find that PB1 is highly constrained at specific sites that are only moderately predicted by the global structure or larger domain. We identified a number of beneficial mutations, many of which have been shown to be functionally important or observed in influenza virus' natural evolution. Overall, our atlas of PB1 mutations and their fitness impacts serves as an important resource for future studies of influenza replication and evolution.

STAR: A Web Server for Assisting Directed Protein Evolution with Machine Learning

Protein engineering has made significant contributions to industries such as agriculture, food, and pharmaceuticals. In recent years, directed evolution combined with artificial intelligence has emerged as a cutting-edge R&D approach. However, the application of machine learning techniques can be challenging for those without relevant experience and coding skills. To address this issue, we have developed a web-based protein sequence recommendation system: STAR (Sequence recommendaTion via ARtificial intelligence). Our system utilizes Bayesian optimization as its backbone and includes a filtering step using a regression model to enhance the success rate of recommended sequences. Additionally, we have incorporated an in silico-directed evolution approach to expand the exploration of the protein space. The Web site can be accessed at https://www.FindProteinStar.com/.

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.

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.

Neural network extrapolation to distant regions of the protein fitness landscape

Machine learning (ML) has transformed protein engineering by constructing models of the underlying sequence-function landscape to accelerate the discovery of new biomolecules. ML-guided protein design requires models, trained on local sequence-function information, to accurately predict distant fitness peaks. In this work, we evaluate neural networks' capacity to extrapolate beyond their training data. We perform model-guided design using a panel of neural network architectures trained on protein G (GB1)-Immunoglobulin G (IgG) binding data and experimentally test thousands of GB1 designs to systematically evaluate the models' extrapolation. We find each model architecture infers markedly different landscapes from the same data, which give rise to unique design preferences. We find simpler models excel in local extrapolation to design high fitness proteins, while more sophisticated convolutional models can venture deep into sequence space to design proteins that fold but are no longer functional. Our findings highlight how each architecture's inductive biases prime them to learn different aspects of the protein fitness landscape.

Statistically learning the functional landscape of microbial communities

Microbial consortia exhibit complex functional properties in contexts ranging from soils to bioreactors to human hosts. Understanding how community composition determines function is a major goal of microbial ecology. Here we address this challenge using the concept of community-function landscapes-analogues to fitness landscapes-that capture how changes in community composition alter collective function. Using datasets that represent a broad set of community functions, from production/degradation of specific compounds to biomass generation, we show that statistically inferred landscapes quantitatively predict community functions from knowledge of species presence or absence. Crucially, community-function landscapes allow prediction without explicit knowledge of abundance dynamics or interactions between species and can be accurately trained using measurements from a small subset of all possible community compositions. The success of our approach arises from the fact that empirical community-function landscapes appear to be not rugged, meaning that they largely lack high-order epistatic contributions that would be difficult to fit with limited data. Finally, we show that this observation holds across a wide class of ecological models, suggesting community-function landscapes can be efficiently inferred across a broad range of ecological regimes. Our results open the door to the rational design of consortia without detailed knowledge of abundance dynamics or interactions.

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.

DeCOIL: Optimization of Degenerate Codon Libraries for Machine Learning-Assisted Protein Engineering

With advances in machine learning (ML)-assisted protein engineering, models based on data, biophysics, and natural evolution are being used to propose informed libraries of protein variants to explore. Synthesizing these libraries for experimental screens is a major bottleneck, as the cost of obtaining large numbers of exact gene sequences is often prohibitive. Degenerate codon (DC) libraries are a cost-effective alternative for generating combinatorial mutagenesis libraries where mutations are targeted to a handful of amino acid sites. However, existing computational methods to optimize DC libraries to include desired protein variants are not well suited to design libraries for ML-assisted protein engineering. To address these drawbacks, we present DEgenerate Codon Optimization for Informed Libraries (DeCOIL), a generalized method that directly optimizes DC libraries to be useful for protein engineering: to sample protein variants that are likely to have both high fitness and high diversity in the sequence search space. Using computational simulations and wet-lab experiments, we demonstrate that DeCOIL is effective across two specific case studies, with the potential to be applied to many other use cases. DeCOIL offers several advantages over existing methods, as it is direct, easy to use, generalizable, and scalable. With accompanying software (https://github.com/jsunn-y/DeCOIL), DeCOIL can be readily implemented to generate desired informed libraries.

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.

Transition paths in Potts-like energy landscapes: General properties and application to protein sequence models

We study transition paths in energy landscapes over multicategorical Potts configurations using the mean-field approach introduced by Mauri et al. [Phys. Rev. Lett. 130, 158402 (2023)0031-900710.1103/PhysRevLett.130.158402]. Paths interpolate between two fixed configurations or are anchored at one extremity only. We characterize the properties of "good" transition paths realizing a trade-off between exploring low-energy regions in the landscape and being not too long, such as their entropy or the probability of escape from a region of the landscape. We unveil the existence of a phase transition separating a regime in which paths are stretched in between their anchors from another regime where paths can explore the energy landscape more globally to minimize the energy. This phase transition is first illustrated and studied in detail on a mathematically tractable Hopfield-Potts toy model, then studied in energy landscapes inferred from protein sequence data.

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.

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.

Machine Learning for Protein Engineering

Directed evolution of proteins has been the most effective method for protein engineering. However, a new paradigm is emerging, fusing the library generation and screening approaches of traditional directed evolution with computation through the training of machine learning models on protein sequence fitness data. This chapter highlights successful applications of machine learning to protein engineering and directed evolution, organized by the improvements that have been made with respect to each step of the directed evolution cycle. Additionally, we provide an outlook for the future based on the current direction of the field, namely in the development of calibrated models and in incorporating other modalities, such as protein structure.

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'.

Ultrahigh-Throughput Enzyme Engineering and Discovery in In Vitro Compartments

Novel and improved biocatalysts are increasingly sourced from libraries via experimental screening. The success of such campaigns is crucially dependent on the number of candidates tested. Water-in-oil emulsion droplets can replace the classical test tube, to provide in vitro compartments as an alternative screening format, containing genotype and phenotype and enabling a readout of function. The scale-down to micrometer droplet diameters and picoliter volumes brings about a >107-fold volume reduction compared to 96-well-plate screening. Droplets made in automated microfluidic devices can be integrated into modular workflows to set up multistep screening protocols involving various detection modes to sort >107 variants a day with kHz frequencies. The repertoire of assays available for droplet screening covers all seven enzyme commission (EC) number classes, setting the stage for widespread use of droplet microfluidics in everyday biochemical experiments. We review the practicalities of adapting droplet screening for enzyme discovery and for detailed kinetic characterization. These new ways of working will not just accelerate discovery experiments currently limited by screening capacity but profoundly change the paradigms we can probe. By interfacing the results of ultrahigh-throughput droplet screening with next-generation sequencing and deep learning, strategies for directed evolution can be implemented, examined, and evaluated.

The Surprising Ease of Finding Optimal Solutions for Controlling Nonlinear Phenomena in Quantum and Classical Complex Systems

This Perspective addresses the often observed surprising ease of achieving optimal control of nonlinear phenomena in quantum and classical complex systems. The circumstances involved are wide-ranging, with scenarios including manipulation of atomic scale processes, maximization of chemical and material properties or synthesis yields, Nature's optimization of species' populations by natural selection, and directed evolution. Natural evolution will mainly be discussed in terms of laboratory experiments with microorganisms, and the field is also distinct from the other domains where a scientist specifies the goal(s) and oversees the control process. We use the word "control" in reference to all of the available variables, regardless of the circumstance. The empirical observations on the ease of achieving at least good, if not excellent, control in diverse domains of science raise the question of why this occurs despite the generally inherent complexity of the systems in each scenario. The key to addressing the question lies in examining the associated control landscape, which is defined as the optimization objective as a function of the control variables that can be as diverse as the phenomena under consideration. Controls may range from laser pulses, chemical reagents, chemical processing conditions, out to nucleic acids in the genome and more. This Perspective presents a conjecture, based on present findings, that the systematics of readily finding good outcomes from controlled phenomena may be unified through consideration of control landscapes with the same common set of three underlying assumptions─the existence of an optimal solution, the ability for local movement on the landscape, and the availability of sufficient control resources─whose validity needs assessment in each scenario. In practice, many cases permit using myopic gradient-like algorithms while other circumstances utilize algorithms having some elements of stochasticity or introduced noise, depending on whether the landscape is locally smooth or rough. The overarching observation is that only relatively short searches are required despite the common high dimensionality of the available controls in typical scenarios.

Geometry of fitness landscapes: peaks, shapes and universal positive epistasis

Darwinian evolution is driven by random mutations, genetic recombination (gene shuffling) and selection that favors genotypes with high fitness. For systems where each genotype can be represented as a bitstring of length L, an overview of possible evolutionary trajectories is provided by the L-cube graph with nodes labeled by genotypes and edges directed toward the genotype with higher fitness. Peaks (sinks in the graphs) are important since a population can get stranded at a suboptimal peak. The fitness landscape is defined by the fitness values of all genotypes in the system. Some notion of curvature is necessary for a more complete analysis of the landscapes, including the effect of recombination. The shape approach uses triangulations (shapes) induced by fitness landscapes. The main topic for this work is the interplay between peak patterns and shapes. Because of constraints on the shapes for [Formula: see text] imposed by peaks, there are in total 25 possible combinations of peak patterns and shapes. Similar constraints exist for higher L. Specifically, we show that the constraints induced by the staircase triangulation can be formulated as a condition of universal positive epistasis, an order relation on the fitness effects of arbitrary sets of mutations that respects the inclusion relation between the corresponding genetic backgrounds. We apply the concept to a large protein fitness landscape for an immunoglobulin-binding protein expressed in Streptococcal bacteria.