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. Proteins are the molecular drivers for many of the processes necessary for life, performing functions such as binding small molecules, stabilizing other proteins, or catalyzing vital reactions. They are synthesized as linear sequences of individual building blocks called amino acids, of which there are twenty canonical types; these sequences fold into complex and dynamic three-dimensional structures to accomplish their functions. These sequences undergo mutation and selection based on the hosts’ abilities to reproduce.Protein engineers often optimize proteins through a process known as directed evolution. Directed evolution adapts nature’s evolutionary process to enable the rapid improvement of proteins for human-desired functions , 2. SpecFundamentally, directed evolution is an optimization process for protein sequences. As such, many recent advances in machine learning have been successful in improving directed evolution’s ability to identify better proteins. In this chapter, we review the core concepts that have enabled successful integration of machine learning in protein engineering by interpreting the process through the directed evolution cycle. We begin with a brief background on directed evolution, outlining the steps involved and casting them in the context of navigating protein fitness landscapes. We then highlight recent developments in machine learning’s contribution to each of these steps as well as the experimental constraints it must operate within, before ending on an outlook for the field.1Directed evolution is an adaption of natural  selection to the modern laboratory. First, consider a simplified view of how a new protein or function may arise naturally. In nature, evolution occurs within populations and is largely driven by competition to survive, grow, and reproduce. Therefore, an attribute which confers an advantage for any of these processes is selected for, enabling an organism to out-compete the organisms around it. The advantage could come from a mutation in a protein sequence that imparts a low level of activity for a new, beneficial function, making the organism and its offspring more successful. Thus, this protein sequence becomes more common as well. Through many iterations of this process, that protein sequence and its function could be further optimized. This process is similar to many engineering strategies, but contains notable distinctions for proteins, discussed in the following 1.1300 (10390) possible sequences, which is around 10300 times more than the total number of atoms in the universe. There will never be enough resources to synthesize all of these sequences let alone screen them.The number of possible protein sequences is immense, presenting a significant challenge to any protein engineering strategy. A typical protein is several hundred amino acids long, and at each position there are twenty canonical amino acids possible. This results in 20Interestingly, this does not mean that finding functional proteins or improving protein fitness is a hopeless endeavor. Maynard Smith made the critical observation that for natural selection to be possible, functional protein sequences must neighbor other functional sequences in protein space, implying that functional proteins exist clustered together within a vast sea of non-functional ones . Therefo1.1.1protein fitness landscape towards a fitness peak [Due to the iterative nature of the optimization cycle that is directed evolution, it is commonly conceptualized as a greedy, uphill walk on a ess peak . Each roFitness landscapes are often visualized as smooth, easy-to-navigate surfaces, but in reality they are discrete, high-dimensional spaces, with many of the dimensions being quite rugged. This ruggedness is due to a phenomenon in biology called epistasis, where mutational effects are dependent on higher order interactions rather than their individual contributions . EpistasIt is also important to consider the prerequisite protein properties that must be satisfied to take fitness measurements, such as expression, stability, and substrate binding. This means that fitness landscapes are a result of some combination of these factors, and changes in any of them can modulate fitness or cause epistasis. For example, Romero & Arnold outline how epistasis can arise from a protein stability threshold, where beneficial, but destabilizing mutations combine to completely ablate activity . The pro1.2In this chapter, we focus on methods employing machine learning for the directed evolution of proteins. However, there are many other aspects of protein modeling that can be explored in biology  and chemAnother view of understanding proteins is through their three-dimensional structures . Protein1.3In this chapter, we view the protein engineering process through the directed evolution cycle, which adapts natural and artificial selection to the modern laboratory. In this process, the desired properties of engineered proteins are directly queried (assayed) by man-made techniques, instead of interpreted through survival and reproduction . This allows the engineer to rapidly evolve proteins for desired properties (such as thermostability or expression) and functions (such as binding or enzymatic activity).The directed evolution cycle  or to slibrary. In nature, this process typically occurs through random mutagenesis, where random mutations in DNA correspond to random changes in the protein sequence, or recombination of existing protein fragments. In the laboratory setting, current experimental techniques give protein engineers more freedom in selecting which sequences to test. One option lies in biasing the randomness of these mutations, but rapidly decreasing DNA synthesis costs also enable the generation of any specific sequence the engineer designs, such as chimeras (recombined fragments of existing proteins) [Second, the protein sequence is randomized to generate a pool of variants, often called a roteins) , 19 or sroteins) , 21. Whiamount of data labels the machine learning modeler can expect to obtain.Third, the library is tested for the desired property. This step captures a wide range of assays that have been developed to probe biomolecules. Some examples of approaches capable of generating the largest amounts of data (high-throughput assays), are based on protein fluorescence or binding, and reach hundreds of thousands of labels per month. However, other properties such as enzymatic activity for generating small molecule substrates are measured in much lower throughput, typically on the scale of hundreds per month. This step often limits the k variants (often k = 1) are fed back into the second step for further improvement. For methods where directed evolution is further enabled by machine learning, two other steps may follow.In traditional directed evolution, the top homologs) can be obtained and aligned in Multiple Sequence Alignments (MSAs), which can be used as priors on viable sequences. However, while this history represents sequences retained in nature, it does not necessarily represent the distribution of allowed sequences for a specific protein on an engineered task.In these machine-learning-assisted approaches, the next step is to fit models to the relationship between proteins and their fitness labels. A wide variety of approaches are available to the machine learning practitioner here, and there are multiple sources of prior knowledge that can be leveraged for proteins. One example is the rich historical record of protein sequences, which can be obtained from sequence databases such as UniRef , 23. FroFinally, these models are used to select optimal proteins for experimental validation. Again, a variety of approaches have been employed in this step such as gradient-based, RL-inspired, and active learning methods . The samThe process of directed evolution with machine learning is depicted in 1.4Evolution is the core optimization process in biology. Naturally, it has inspired other optimization algorithms, particularly in the gradient-free or black box optimization settings. Here, we briefly discuss the key similarities and distinctions between natural evolution, directed evolution, and evolutionary algorithms.Natural evolution occurs on the level of organisms interacting with their environment. Mutations fixed on the individual protein level may not have a noticeable effect on fitness at the organism level, defined as its ability to survive and propagate its genes. Additionally, the objective function of natural evolution is a competition for scarce resources in constantly changing environments. Diverse solutions are often implicitly rewarded for their ability to access new ecosystems. However, for the protein engineer with the goal of optimizing individual molecules, there is not a clear mapping from the evolutionary history of similar sequences to fitness on the protein level, defined as how well a protein achieves its target function.Evolution strategies at the protein level are the subject of this review. Two key differences distinguish directed evolution of proteins from natural evolution. In traditional directed evolution campaigns, only a single parent protein sequence is used to start each round of subsequent evolution, in contrast to nature which evolves with populations. Recently, approaches where directed evolution is further guided by machine learning captures information from all explored variants in trained, surrogate models of the protein fitness landscape , which cAdditionally, fitness is more well-defined in directed evolution than in natural evolution, where fitness is influenced by a complex set of factors and can change based on environment. For example, the fluorescence of green fluorescence protein may be directly measured, and variants may be evolved for brighter fluorescence or alternative emission wavelengths. While this is largely an advantage, it is important to remember that the process of sample preparation can also affect the measurement and therefore unintentionally modify the definition of “fitness” being optimized. For example, the measured binding efficiency of a protein can also depend on the purification and expression method used to obtain it. In other words, a protein must pass both purification and expression to bind effectively to a target to be considered “fit” in this case. This concept is captured in the directed evolution adage: ”You get what you screen for” .Evolutionary algorithms are a class of optimization algorithms that are directly inspired by natural evolution, and a subset of these methods have direct analogs in directed evolution methods , 27. For2The directed evolution cycle powered by machine learning methods can be segmented into five steps, as described previously. In this section, we summarize important contributions machine learning has made, and promises to make, to improve over the directed evolution baseline over each of its steps.2.1The first consideration in a directed evolution experiment is selecting the protein variant to evolve, which can be a nontrivial task. In the most extreme setting, there may be no known proteins that perform the desired function; a more common but related setting is when the desired output of the directed evolution experiment needs to be substantially different from all known proteins due to considerations of scientific novelty or intellectual property.In such settings, machine learning can be a useful tool to help identify a sufficiently novel starting variant, typically with weak or suboptimal fitness, that can subsequently be given to a traditional or machine-learning-guided directed evolution pipeline. The two main approaches for doing so are (1) to screen a large and diverse collection of proteins for any that have a nonzero fitness value , 21, 30 et al. use an autoregressive language model, trained on approximately 1.2 million natural llama nanobody sequences, to generate a nanobody library that is screened to potentially identify novel binders to a target protein [5 generated sequences, which is 1000-fold smaller than other libraries.As an example of the first approach, Shin  protein . The genet al. de-novo design miniproteins that bind to a known, target structure [As an example of the second approach, Cao tructure . They uslocal optimum of the fitness landscape such that the evolutionary path to the unknown global optimum (or the highest-fitness variant) requires crossing a fitness valley .While we have mostly considered cases in which the starting variant is unknown or must be substantially different from existing proteins, this is not a constraint in many other settings where a good, functional variant exists and the goal is simply to improve fitness. Even in such settings, however, directly evolving the best-known variant may not be the most effective strategy. A known, high-fitness variant may be in a evolvable starting variant, even at some fitness cost, is currently an open question [Therefore, it may be desirable to begin evolution at a lower-fitness variant from which multiple fitness peaks  are accessible via a greedy uphill walk strategy typical in protein engineering. Engineering a more question  for whicquestion , and manquestion –39. More2.2The data used to train a machine learning model determines what it learns and, by extension, in what situations it can be used to make effective predictions. For protein engineering, this means that the design of the library that will provide training data is critical to the eventual effectiveness of the trained model in finding improved sequences.design space of allowed proteins, this translates to collecting maximally diverse training data that best covers that space. For proteins, this means that training data with maximal sequence diversity will be most informative for modeling an underlying true fitness landscape: 1 the more diverse the training sequences are, the more of the design space that is covered by the training data and the less a model must extrapolate to previously unseen regions of sequence space. For example, Romero et al., Bedbrook et al., and Greenhalgh et al. maximize the information entropy of the initial set of sequences when engineering P450s, channelrhodopsins, and acyl-ACP reductase, respectively [Machine learning models tend to be more effective at interpolation than extrapolation and so will typically perform best when used to make predictions in the same domain as the data used to train them. In general, for a given ectively –42.Randomly collecting sequences from a fixed design space  can thus be a valuable strategy for training data collection, as this will on average result in the collection of highly diverse sequences. Random collection of training data is also an attractive approach from an applications point of view, as fully random libraries can be easily constructed in a multiplexed fashion using degenerate oligomers or strategies like error-prone Polymerase Chain Reaction (epPCR)   higher-fitness regions of the protein fitness landscape at higher resolution and lower-fitness regions of the protein fitness landscape at lower resolution.While building a perfect map of a fitness landscape would be ideal for model-guided engineering, it is not always feasible given our limited ability to collect experimental data. More complex fitness landscapes considering larger sections of sequence space require more data to model and a small amount of randomly selected training data may be spread too thinly across the design space to build a comprehensive map . The goacombinatorial landscapes) tend to be dominated by proteins with zero or extremely low fitness. These variants are commonly referred to as holes in the fitness landscape as they only provide information on which mutations destroy protein fitness. These variants are conceptually distinct from fitness valleys mentioned previously, as they do not provide information about the extent to which a mutation impacts protein fitness, which is valuable information for training the regression models typically employed for ML-assisted protein engineering. Wittmann et al. demonstrated that by using so-called zero-shot predictor—models or strategies that can predict protein fitness prior to collection of new experimental data—focused training sets can be constructed that minimize inclusion of holes in training data [Focused libraries can be particularly helpful when navigating hole-filled protein fitness landscapes . As moreing data . ThroughThe prior information needed to construct focused libraries can come from many sources. For instance, prediction of protein thermal stability , use of Ultimately, the decision between random library design and focused library design will depend on a number of factors. If the fitness landscape to be explored is expected to be minimally complex with few holes and large amounts of training data can be easily collected for it, then random library design is a reasonable approach, as the library itself will be simple to construct, and training data gathered from it will be sufficient to build a comprehensive map of the fitness landscape. If the fitness landscape to be explored is complex, full of holes, and it is challenging to gather training data for it, then focused libraries may be a viable option, particularly if high-confidence zero-shot predictions can be made for the fitness landscape. Such libraries may be more challenging to construct in the laboratory, but they will likely result in more efficient machine learning-guided engineering.2.3The process of directed evolution is relatively simple in theory and can also be so in practice. However, the process must operate within current experimental constraints imposed by a variety of factors, including available technology, cost, and time. Current laboratory methods for directed evolution have been reviewed extensively , 57, so Notably, both the input protein sequences and the output experimental labels both depend on physical constraints. In the first section, we discuss different approaches to generating protein libraries. In the second section, we discuss varying experimental methods (assays) for obtaining protein labels. Finally, in the third section we discuss methods for pairing protein sequence and function information.2.3.1Random mutagenesis is one of the most straightforward methods for creating initial sequence diversity. Errors are introduced throughout an initial DNA sequence by either randomly damaging DNA or by introducing errors during replication such as via epPCR, a process that introduces mutations randomly by increasing the error rate of the copying enzyme, the polymerase. However, it is important to note that errors introduced via “random” mutagenesis are not perfectly random in two major ways. First, mutations from one nucleotide to another do not occur at identical frequencies, so the original base can dictate what mutations are most likely at a given position . Second,Targeted mutagenesis, of which the focused mutagenesis discussed in the previous section is a subset, is an alternative to random mutagenesis that affords more control over the final library. Unlike random mutagenesis, targeted mutagenesis typically assumes that either (1) specific sites in the protein sequence are important to mutate or (2) it is important to be able to access all amino acids at a given position. Site selection usually requires structural knowledge or other biochemical insights into the protein system. To perform targeted mutagenesis, degenerate oligos—mixtures of individual primers that together encode a distribution of mutations—are used to induce randomness at a specific codon/amino acid position or positions. Unlike random mutagenesis, multiple mutations can now be made within a single codon, allowing access to any amino acid if desired. The pool of degenerate oligos can also be modified to achieve a relatively even distribution across all twenty canonical amino acids  or to achomologous proteins, the top variants from a random mutagenesis library, or the top variants from a targeted mutagenesis library. One recombinatorial approach of note is the use of SCHEMA libraries [A final strategy for library generation is recombination, which pieces together, or “recombines”, initial diversity into different arrangements to create new diversity. Recombination is a very broad category of diversity generation, and due to the array of recombination strategies available, we do not explain them here, but they are well reviewed by Packer & Liu . The choibraries , where fibraries , 63. ImpThere is promise to disrupt these traditional paradigms of library generation with the advent of cheap gene synthesis technologies . Rather 2.3.25 to 106) can be rapidly created. Many assays for fitness, however, are limited to comparatively low-throughput chromatographic methods , which rely on physical separation of a mixture through a column, producing smaller datasets (101 to 104). The amount of data available for training a model will dictate how much of sequence space can be explored and how accurate the predictions of fitness for new sequences will be. At the same time, however, the goal of ML in protein engineering is to reduce the burden of experimental screening and expedite the process, so a balance must be found between the amount of data collected and the accuracy of predictions of models trained on that data.With proteins performing such a wide variety of different functions, the protein engineering community has had to devise countless different assays to measure them all. As such, assays for protein function vary widely in both accuracy and throughput, with ranges from tens to millions of protein variants. This amount is typically dependent on the project definition of fitness. For instance, if the measurement of fitness can be directly coupled to a sequencing assay , then large datasets   and fluo2.3.3Uncommon in the broader ML discipline, datasets that result from typical protein engineering campaigns are label-rich and feature-poor, with many assayed fitnesses and relatively few variant sequences. Because only function is being optimized in directed evolution, this process does not technically require sequencing. Indeed, only the top few variants from each round are sequenced for validation in practice, and sequencing all of the variants is considered an unnecessary, unjustifiable expense. Thus, the remainder of the unimproved variants are discarded without sequencing, resulting in fitness labels that are rendered useless. Notably, this is not true for deep mutational scanning libraries, where fitness is directly coupled to sequencing, which is why many ML approaches are currently developed on these types of datasets , 73–75.Variant sequencing, especially for low-throughput assays, has traditionally been done via Sanger sequencing, but this method scales linearly with the number of variants, costing a few dollars per sequence. Depending on the assay used for evaluating protein fitness, sequencing could easily become the most expensive part of a protein engineering campaign.Fortunately, next generation sequencing (NGS) technologies  have beg2.4Fitness datasets obtained as described above and can be used to fit models of the sequence-fitness relationship. Here, we first describe the methods for representing a protein sequence before diving into the model classes used to predict fitness from sequence.2.4.1Proteins are variable-length sequences of twenty canonical amino acids. Due to both the variability in sequence length and the categorical nature of amino acids, an important and long-standing problem has been how to best represent a protein sequence to facilitate machine learning. Roughly speaking, there are two general approaches for doing this: (1) hand-crafting features based on, for example, statistical summaries or biophysical properties of a sequence or its constituent amino acids, and (2) using evolutionarily related sequences to learn likelihoods or embeddings as representations.Statistical summaries of a sequence: higher-order terms and k-mers.One of the simplest ways to represent a protein sequence is to concatenate one-hot encodings of the amino acid at each position in the sequence. Despite its simplicity, even a linear model with this representation can be a surprisingly effective baseline in some settings—for example, when we focus on predictive performance on sequences near a wild type , 73. Amihigher-order terms—for example, the identities of the amino acids at three positions for a third-order term—have been shown to be both theoretically principled and empirically useful representations for learning protein fitness functions [Generalizing this idea further, one-hot encodings of groups of amino acids, which we call unctions , 81–86. unctions , 87, 88;unctions , 84, 86.k-mers—contiguous subsequences of k amino acids—are another kind statistical summary that has been used to represent sequences and learn fitness functions [Beyond higher-order terms, the frequencies of different unctions , 90.Beyond one-hot encodings of a sequence’s residues, or the higher-order terms between them, features based on physicochemical properties of a sequence have been used to learn fitness functions. For example, each amino acid can be featurized as a vector of various physicochemical properties , 92 or blearning relevant features by fitting low-dimensional representations of evolutionarily related sequences.However, it not generally clear which physicochemical properties will be relevant for any particular fitness function. Consequently, in recent years considerable attention has turned to wild-type protein (or multiple such wild types) that exists naturally in the genome of some organism and exhibits the function of interest to an appreciable degree. In many cases, that function of interest is needed by more than one organism, and natural selection has yielded multiple homologs residing in a variety of organisms. Though the precise fitness value differs across homologs, due to evolutionary constraints homologs are generally functional as opposed to non-functional. Based on the premise that homologs are mostly functional, a great body of work in recent years has focused on learning the distribution of homologous sequences, as a proxy for the distribution of functional sequences. The density, or approximations thereof, of the resulting learned sequence distribution has been shown to correlate with fitness in many cases, whether modeling the homologs with a hidden Markov model [In directed evolution, one generally starts by identifying a ov model , 99, 100ov model , 101, vaov model , 103, orov model , leadingCurrently, variational autoencoders such as  appear tBeyond homologs, which, by virtue of natural selection, contain sequence patterns necessary for the function of interest, the set of all proteins sequenced so far may similarly reveal patterns necessary for basic properties of all functional proteins, such as the ability to fold into a stable structure. Based on this hypothesis, a growing body of work has trained various deep learning models on massive databases of known proteins, such as UniProt , UniRef Estimates of the density from transformers have also been shown to correlate with a variety of fitness functions , 115, prDespite promising results on capturing phylogenetic relationships and various clustering tasks, these deep embeddings have shown limited success in learning fitness functions. For example, when used with ridge regression or Gaussian process regression, they do not appear to systematically outperform simpler baselines , 73, 1092.4.2Given a representation of protein sequences, a variety of model classes have been used to learn the sequence-fitness relationship. In general, however, note that models that excel under more traditional evaluation metrics—for example, prediction error on held-out sequences from the same distribution as the training data—may or may not be appropriate for use with directed evolution, since in the latter we focus on sequences the model predicts to have high fitness. That is, a model that facilitates directed evolution needs to be reliable even in regions of sequence space far from the training data, particularly in regions on which it predicts high fitness.With that in mind, a few domain-specific models have been designed with the particular goal of jointly learning (1) a density model over homologs and (2) the fitness function from experimentally labeled sequences , 118, unIn the more common setting of using only experimentally labeled sequences, two models have been shown to be very strong baselines across a variety of fitness data sets, particularly in the regime of limited training data : linear regression, for example on one-hot encodings , 73, 119Other kernel methods have been used as well, such as support vector machines for modeling enzyme enantioselectivity , membranWhen labeled sequences are abundant , deep learning models can also be effective for learning the fitness function. Models range from simple feedforward networks, which have been used to predict fluorescence , 133, hiet al. [Our understanding of what representations and models are most effective is limited by the constraints of the molecular biology techniques available to generate fitness data sets. For example, the vast majority of currently available fitness data sets only assess the fitnesses of mutants one or two mutations away from a wild type, excluding insertions and deletions , 54, 65.et al.  have colet al. , 139, whCurrent evidence suggests that, when focusing on relatively small regions of sequence space—for example, clustered around a wild type—simple models such as ridge regression on one-hot encodings can be much more effective than more complex models , 73, but2.5acquisition function (in the Bayesian optimization sense) to decide which sequences from the theoretical library to characterize next.After obtaining a trained sequence-fitness model, the goal is to use it as part of an 2.5.1design space of proteins. Example design spaces include traditional library designs for protein engineering such as all single- or double-mutants, all the possible mutations at a small number of sites [Although evaluating the sequence-fitness model is faster and cheaper than actually obtaining laboratory measurements, it is frequently impossible to evaluate it on all possible protein sequences. One approach is to explicitly define a more limited of sites , 67, 139of sites , 40, 62,of sites . If a diof sites .generative model to implicitly define the design space by learning a probability distribution over sequences. A generative model performs one or both of two fundamental tasks: (1) assigning every possible sequence a likelihood of being in the desired distribution, and (2) generating examples of sequences from a desired distribution. The simplest models assume this distribution can be modeled by considering sites independently or by relationships between pairs of sites [Another approach is to use a of sites , 104. Moof sites ; relevanof sites , 142, geof sites –145, andof sites , 146.2.5.2An acquisition function uses sequence information and the surrogate model to prioritize sequences from the theoretical library for experimental measurements. A simple example of an acquisition function is greedy selection of the top prediction (or the top few predictions) according to the sequence-function model. Greedy acquisition is common in practice and can work well , 67, 147de novo protein design Anishchenko et al. use adaptive sampling with a mutation-based generative model to identify sequences with valid folds.Given a theoretical library and an acquisition function, the simplest method for choosing sequences is to compute the surrogate score on as many members of the library as is computationally feasible, and then to use those scores to select sequences. However, when the library is defined by a generative model, the sequence-fitness model can be used to shift the generated distribution toward more optimal sequences. For example, in adaptive sampling, sequences are sampled from a generative model, the outputs of a surrogate model are used to re-estimate the parameters of the generative model, and the process iterates until convergence . BrookesBy default, adaptive sampling assumes a trustworthy sequence-fitness model; however, in practice, these models are imperfect and can be prone to poor predictions in many regions of the protein space. To address this problem, adaptive sampling can avoid these degeneracies in the surrogate model by constraining sampling to be close to the training distribution for the surrogate model , 155. InA closely-related approach uses genetic algorithms to heuristically balance both mutation and recombination to produce new sequences  by adaptWhile it is computationally convenient to exactly specify the sequences to measure next, specifying a new library and sampling from that library may allow many more sequences to be measured for the same cost as directly synthesizing a small number of sequences. This library may be optimized for expected improvement , to bala2.5.3So far, we have discussed methods for using an acquisition function based on a sequence-fitness model to choose sequences from a theoretical library that are optimized for a desired function. However, in some cases it may be possible to sequentially update the sequence-fitness model with new measurements.exploitation  and exploration [Greedy acquisition across experimental rounds (uphill climbing the fitness landscape) is the simplest implementation of sequential optimization and is used widely in practice . Going bloration –164, in Bayesian optimization is a popular framework for sequential optimization  that levGaussian process models  are a poProbabilistic surrogate models can also be implemented by model ensembles , which tcoverage, a frequentist guarantee on how often the confidence sets contain the true label of test inputs. Beyond exchangeable data, CP has been generalized to handle various forms of distribution shift, including label shift [et al. generalized CP for the setting of protein design, in which any of the aforementioned optimization procedures induces a distribution shift wherein the distribution of test  sequences is dependent on the training data [Finally, conformal prediction (CP) is an approach for rigorous uncertainty quantification that can be used with any predictive model in a black-box manner, including the aforementioned Gaussian process models or any deep learning model –176. Theel shift , covariael shift , 179, diel shift , and tesel shift . Notablying data . This me3In this chapter, we have discussed current efforts to improve protein engineering with machine learning. The field has grown rapidly over the past five years, as the development of deep learning methods and methods to obtain and organize biomolecular data have reached inflection points. We anticipate continued growth in this area of research from both directions, particularly in the following directions.3.111 [77 [The space of possible amino acid combinations is vast, but the space of functional proteins is much smaller, with estimates ranging from one in 1011  to as lo11 [77 . This ma11 [77 . TherefoFor protein engineering, it is clear that there is a balance to maintain between exploring new protein sequences and staying within predictive models’ confident regions. In the directed evolution context, where rounds of experimental data are used to train predictive oracles (or used directly), various methods encode these trust regions heuristically or probabilistically , 185, anWhile model confidence represents one challenge in protein engineering, noisy labels present another. The sample preparation methods used often introduce noise, may have limited linear range of measurement, and can be difficult to reproduce, particularly for newly developed assays designed for to probe more complex biological phenomena. While robust training under noisy labels has gained some traction in deep learning, especially for more subjective and error-prone tasks, , 187, ha3.2Much of this chapter is focused on the guided acquisition of data for a particular protein function, which is being collected and curated by ProtaBank . HoweverUniProt contains a large amount of information about proteins beyond their sequence, including cross-references to functional labels, disease-association and Protein family (Pfam) classifications at the per-residue level , Gene OnThe PDB is the primary source of protein structure data, and it largely consists of static protein structures obtained through protein crystallography, although the number of structures obtained through cryo-EM and NMR are also increasing. Protein structures are invaluable to biologists in providing much-needed context for molecules that are otherwise difficult to probe. However, mutations may have effects that are not captured by static structures. For example, they may bias the protein’s Boltzmann distribution toward different conformational states in the ensemble without perturbing the ground state crystal structure, or the crystal structure may simply have too low resolution to capture small changes. Nonetheless, structure can be a useful prior in directed evolution , 111.While protein data continues to grow, methods with inductive biases tailored for biology are comparatively underdeveloped, particular for protein engineering applications. A few notable exceptions have been developed in application to protein structure modeling. For example, the MSA Transformer  develops3.3Protein engineering is an optimization strategy, and many recent advances in machine learning have been successfully applied or developed to the directed evolution of proteins. In this chapter, we have highlighted studies where machine learning contributes to each step of the optimization process. As we continue to gather more protein information and develop methods to bootstrap and guide engineering from these data, machine learning will play an increasingly important role in protein engineering.


Biological research is generating high volumes of data distributed across various sources. The inconsistent naming of proteins and their encoding genes brings great challenges to protein data integration: proteins and their coding genes usually have multiple related names and notations, which are difficult to match absolutely; the nomenclature of genes and proteins is complex and varies from species to species; some less studied species have no nomenclature of genes and proteins; The annotation of the same protein/gene varies greatly in different databases. In summary, a comprehensive set of protein/gene synonyms is necessary for relevant studies.In this study, we propose an approach for protein and its encoding gene synonym integration based on protein ontology. The workflow of protein and gene synonym integration is composed of three modules: data acquisition, entity and attribute alignment, attribute integration and deduplication. Finally, the integrated synonym set of proteins and their coding genes contains over 128.59 million terminologies covering 560,275 proteins/genes and 13,781 species. As the semantic basis, the comprehensive synonym set was used to develop a data platform to provide one-stop data retrieval without considering the diversity of protein nomenclature and species.The synonym set constructed here can serve as an important resource for biological named entity identification, text mining and information retrieval without name ambiguity, especially synonyms associated with well-defined species categories can help to study the evolutionary relationships between species at the molecular level. More importantly, the comprehensive synonyms set is the semantic basis for our subsequent studies on Protein–protein Interaction (PPI) knowledge graph.The online version contains supplementary material available at 10.1186/s12859-023-05464-0. Most protein databases have provided rich data and free access. However, each individual database has its own specific scope and can only shed light on a limited set of scientific questions. Linking protein information from multiple data sources can thus inspire new insights and offer studies over a bigger picture. However, massive data sources often have complex interrelationships and heterogeneous syntax, semantics, and schema. There are some obstacles for integration of proteins and their encoding genes information as follows.The processes of discovery of proteins, coding genes, and these proteins being understood physiologically do not always occur simultaneously, so they do not always match each other. Scientists tend to favor one notation or name system for proteins and another for genes. Therefore, the names of genes and proteins may have their own terminologies that are always unrelated.For example, synonyms of the gene PPP2R3B_HUMAN are as many as six synonyms in different databases Table. NomenclAt present, guidelines for nomenclature of proteins and genes in mice, rats, chickens, humans, nonhuman primates, domestic animals, flies (fruit flies) and fish have been published and subsequently revised since 1940 [To distinguish species with the same proteins and genes in different organisms, nomenclatural systems provide human-versus-nonhuman specificity by using different capitalization, such as the name "PURH" in species of HUMAN and "purH" in species of JANSC. However, scientists often ignore the specification. As a result, there are various synonyms for identical proteins and genes among different species.Protein databases have recorded a huge number of protein synonyms. SwissProt records 1,098,808 synonyms, NCBI Gene has accumulated 218,622 synonyms and BioGRID has 139,587 synonyms  is a public database for protein sequence and function, covering the tree of life and over 220 million protein entries. UniProtKB is a set of expert-verified data that consists of two parts: UniProtKB/Swiss-Prot and UniProtKB/TrEMBL. While UniProtKB/TrEMBL main contains unreviewed automatic annotation and classification, calculated data, UniProtKB/Swiss-Prot is now the reviewed section, containing a high quality manually annotated and non-redundant protein sequence data, which brings together experimental results, computed features and scientific conclusions. Therefore, we chose UniProtKB/Swiss-Prot for this experiment. In the version released in June 2019, UniProtKB/SwissProt contained 560,275 protein entities and is a high-quality annotated and nonredundant protein sequence database . BioGRIDAs shown in Table We proposed an ontology-based method to integrate species-dependent synonyms. First, we created links for protein data based on external links from BioGRID to UniProt. Second, we created links for protein-encoding genes based on external links from NCBI Gene to UniProt according to “GeneID”. Third, protein ontology was built as a data schema and semantic specification. Finally, the synonyms of proteins and their encoding genes were integrated based on protein ontology and species information. The workflow is shown in Fig. Tags of CrossReference, Synonyms and Taxonomy were recorded in different labels as shown in Table The schema of the UniProt Knowledge Base was extracted as basis of the protein ontology schema, as shown in Fig. First, we converted all the names to lowercase. Second, semantic mappings were created as follows:As shown in Fig. As shown in Fig. As shown in Fig. Names of proteins and their encoding genes were obtained based on semantic mappings as related in above section. As shown in Fig. In this study, we proposed an approach for proteins and their encoding genes synonym integration based on protein ontology. The Protein ontology was developed based on Uniprot Knowledge Base. Rely on protein ontology, 560,275 proteins and coding genes from BioGrid, Uniprot and NCBI Gene databases were linked together. As a result, there were 128.59 million proteins and their coding genes’ terminologies in the integrated synonym set, which was much higher than the number of synonyms in each database  knowledge graph and a data platform  to proviOn the protein query page , users cBy identifying the species information recorded in the organism tags in the three data sources, we in turn assigned species classification information to these term sets, which statistically cover 13,781 species. As a result, each protein and its coding gene terminology is greatly integrated on the basis of species information with attribute information such as sequence, scientific name, accession, related gene, organism and data origin. When user searches for P53 in the data platform , the proIn brief, this synonyms set with species taxonomic information can not only map different protein names to the same protein scientific name, but also cluster the protein names of the same species according to the species taxonomic information. This work is fundamental to the alignment of proteins and their coding gene entities in the development of the PPI knowledge graph, and is an indispensable backbone for the subsequent semantic and species-based retrieval of proteins and their interaction information.In summary, the data integration approach based on protein ontology can provide more comprehensive synonyms for proteins and their coding genes. Through a three-level workflow of data collection, entity and attribute alignment, attribute integration and duplicate data removal, each protein and its coding gene term was greatly integrated with attribute information such as sequence, scientific name, accession, related gene, organism and data source on the basis of species information. 1. The final constructed synonym set can be used as an important resource for biological named entity identification, text mining and information retrieval without name ambiguity, especially synonyms associated with well-defined species categories can help to study the evolutionary relationships among species at the molecular level. It is of great significance for comprehensive acquisition of species taxonomic information and study of organism’s evolutionary history by means of inheritance and homology of common lineages, as well as the conserved nature of sequence and sequence structure that determine function.2. More importantly, the comprehensive synonyms set is the semantic basis for our subsequent studies on PPI knowledge graph. It offers a retrieval tool which can easily get protein information based on PPI knowledge graph without consideration protein arbitrary naming and lacking species membership information.In the future, we will provide Application Programming Interfaces (APIs) for free to allow more terminologies to be integrated to sustainably enhance the size and scalability of proteins and their encoding gene synonyms.Additional file 1: Protein Query Website Instructions.


A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach this problem by constructing coarse-grained molecular potentials based on artificial neural networks and grounded in statistical mechanics. For training, we build a unique dataset of unbiased all-atom molecular dynamics simulations of approximately 9 ms for twelve different proteins with multiple secondary structure arrangements. The coarse-grained models are capable of accelerating the dynamics by more than three orders of magnitude while preserving the thermodynamics of the systems. Coarse-grained simulations identify relevant structural states in the ensemble with comparable energetics to the all-atom systems. Furthermore, we show that a single coarse-grained potential can integrate all twelve proteins and can capture experimental structural features of mutated proteins. These results indicate that machine learning coarse-grained potentials could provide a feasible approach to simulate and understand protein dynamics. Understanding protein dynamics is a complex scientific challenge. Here, authors construct coarse-grained molecular potentials using artificial neural networks, significantly accelerating protein dynamics simulations while preserving their thermodynamics. A complete description of the dynamics of a protein requires the determination of (1) its stable and metastable conformational states, (2) the relative probabilities of these states, and (3) the rates of interconversion among them. Here, we focus on addressing the first two problems by demonstrating how to learn coarse-grained potentials that preserve protein thermodynamics.Proteins are complex dynamical systems that exist in an equilibrium of distinct conformational states, and their multi-state behavior is critical for their biological functions6. As remarked by Karplus & McCammon7, these simulations were pivotal towards the realization that proteins are dynamic systems and that those dynamics play a fundamental role in their biological function2. When compared with experimental methods such as X-ray crystallography, MD simulations may obtain a complete description of the dynamics in atomic resolution. This information can explain slow events at the millisecond or microsecond timescale, typically with a femtosecond time resolution.Due to the structural heterogeneity of proteins and the ranges of time and length scales over which their dynamics occur, there is no single technique that is able to successfully model protein behavior across the whole spatiotemporal scale. Computationally, the main method to study protein dynamics has traditionally been molecular dynamics (MD). The first MD simulation ever made was carried out in 1977 on the BPTI protein in vacuum, and only accounted for 9.2 picoseconds of simulation time8 and Piana et al.9 simulated several proteins that undergo multiple folding events over the course of micro- to millisecond trajectories, yielding crucial insights into the hierarchy and timescales of the various structural rearrangements. With current technological limitations, unbiased MD is not capable of describing longer-timescale events, such as the dynamics of large proteins or the formation of multi-protein complexes. Due to the computational cost and timescales involved, there are just a few examples of modeling of such events, including folding of a dimeric protein Top7-CFr10 and all-atom computational reconstruction of protein-protein (Barnase-Barstar) recognition11. Many methods have been developed to alleviate these sampling limitations, for instance, umbrella sampling12, biased Monte Carlo methods13, and biased molecular dynamics like replica-exchange15, steered MD17, and metadynamics18. More recently, a new generative method based on normalizing flows has been proposed to sample structures from the Boltzmann distribution in one-shot, thereby avoiding the many steps needed in MD to sample different metastable states20.In the last several decades, there have been many attempts to better understand protein dynamics by long unbiased MD. For example, Lindorff-Larsen et al.22 and since the pioneering work of Levitt and Warshel23, many different approaches to CG have been proposed29. Notably, the work by Hills et al.30 has made significant strides towards creating a transferable bottom-up coarse-grained potential for the simulation of proteins, contributing valuable insights to the field. Popular CG approaches include structure-based models31, MARTINI33, CABS34, AWSEM35, and Rosetta36. In general, a CG model consists of two parts: the selection of the CG resolution (or mapping) and the design of an effective energy function for the model once the mapping has been assigned. Although recent work has attempted to combine these two points37, they are in general kept distinct. The choice of an optimal mapping strategy is still an open research problem40 and we will assume in the following that the mapping is given, focusing instead on the second point, which is the choice of an energy function for the CG model that can reproduce relevant properties of the fine-grained system. Recently, our groups and others have used machine learning methods to extend the theoretical ideas of coarse-graining to systems of practical interest, which provides a systematic and general solution to reduce the degrees of freedom of a molecular system by building a potential of mean force over the coarse-grained system47.Another way to access the timescales of slow biological processes is through the use of coarse-graining (CG) approaches. Coarse-graining has a long history in the modeling of protein dynamics51. One particularly interesting feature of machine learning potentials is that they can learn many-body atomic interactions52. A steady level of improvement of the methodology over the years has led to dozens of novel and better modeling architectures for predicting the energy of small molecules. The first important contributions are rooted in the seminal works by Behler and Parrinello53 and Rupp et al.54. One of the earliest transferable machine learning potentials for biomolecules, ANI-155, is based on Behler-Parrinello (BP) representation, while other models use more modern graph convolutions57.Machine learning models, in particular neural network potentials (NNPs), can learn fast, yet accurate, potential energy functions for use in MD simulations by training on large-scale databases obtained from more expensive approachesIn this work, we investigate twelve non-trivial protein systems with a variety of secondary structural elements. We build a unique multi-millisecond dataset of unbiased all-atom MD simulations of studied proteins. We show the recovery of experimental conformations starting from disordered configurations through the classical Langevin simulations of a machine-learned CG force field. We demonstrate transferability across macromolecular systems by using a single multi-protein machine learning potential for all the targets. Finally, we investigate the predictive capabilities of the NNP through simulation and analysis of selected mutants .58 and Lindorff-Larsen et al.8 Supplementary Table α-helices and β-strands, as well as unique tertiary structures and various lengths from 10 to 80 amino acids. In the case of the shortest proteins, Chignolin and Trp-Cage (up to 20 amino acids), the secondary structure is quite simple. In general, the dataset contains a higher proportion of α-helical proteins. The exceptions are the β-turn present in Chignolin, the mostly β-sheet structure of WW-Domain, and the mixed αβ structures of BBA, NTL9, and Protein G 62. This ds 69 scores above 60 (Table A Markov state model (MSM)8. It is worth noting that, with current software, coarse-grained molecular dynamics with neural network potentials is 1–2 orders of magnitude slower than equivalent simulation with explicit solvent using classical force fields63. However, we expect that this difference is going to reduce fast. In addition, individual trajectories were able to explore the conformational landscape and transition between different metastable states observed in the original all-atom trajectories. For each protein, a representative trajectory is shown in a video included in α3D, and λ-repressor, failed to sample direct transitions from ordered to disordered conformations n B Fig.  and 4. Tα-helix and the first hairpin. Next, the native structure is completed by the formation of the second hairpin. Alternatively, a second pathway is possible where the structure goes through a misfolded state with an almost complete native structure except for the first hairpin, which shows increased flexibility. This replicates the results of all-atomistic MD simulations performed by Lindorff-Larsen et al.8. The variant simulated both there and in this study is intermediate in sequence between the wild type and redesigned NuG2 variant. Despite high similarities in the sequence, experiments show that these variants exhibit distinct folding pathways. The difference is in the order of formation of the elements of β-sheet; in the wild-type variant of Protein G, the second hairpin folds before the first hairpin73 while in the NuG2 variant the order is reversed74. The CG simulation using NNP shows the majority of flow going into the NuG2 variant folding, which agrees with one of the possible folding pathways. In addition, the simulation correctly recovered the minima around the native conformation of Protein G, however, the position of the other minima on the free energy surface are less similar. In general, the force-matching method does not preserve kinetics60, so the height of the energy barriers is not expected to be accurately captured, as shown in the free energy plot , which required simulations at lower temperatures to recover the native state.The results obtained with the multi-protein model are in line with protein-specific models, which indicates that our approach could scale to create a general-use CG force field. This model was able to simulate the transition from random coil to the correct native conformation for almost all target proteins, with the exception of To further test the multi-protein NNP and assess its predictive power we simulated mutants of the originally targeted proteins. All mutants were sourced from PDB and the mutations did not affect the native structure of the target. Supplementary Table The results show that the multi-protein CG model is able to recover the native conformation for all cases that succeeded in the initial validation, except one (Protein B mutant 2N35), with reasonably low RMSD values , the NNP failed to obtain the native structure. Its sequence contains 10 mutated residues, which may exceed the capacity of the model to generalize outside of the training set. As shown in Supplementary Table β-sheets, the NNP recovered native macrostates of α-helical proteins with minor changes in the sequence. This shows some capacity of the model to generalize.Overall, the mutagenesis tests have shown limited but encouraging results for the predictive capabilities of the multi-protein model. Despite its failure to keep the native conformation stable for the sequences that are substantially altered or for proteins that contain 44. Then, in the following publication, we replicated the task using a model architecture that is in principle transferable43. In this work, we apply a revised model architecture and show that we can effectively learn thermodynamics for twelve structurally diverse proteins at once, in a single model. This demonstrates for the first time that the model architecture is truly transferable and might generalize providing enough data. To achieve that, we generated a multi-millisecond dataset of MD simulations sampling the dynamical landscape of the proteins and used it to obtain machine-learned CG potentials for studying the protein dynamics. Results show that we were able to model protein dynamics in computationally accessible timescales, and recover the native structure of all twelve proteins through coarse-grained MD simulations using NNPs and an α-carbon CG representation, with a unique bead type corresponding to each amino-acid type. From the model-generated CG simulation data, we were able to reconstruct multiple metastable states, capturing the folding pathways and the formation of different types of secondary and tertiary structures. In contrast to novel deep-learning structure prediction methods76, our method offers a substantial improvement and models protein dynamics, which is essential for understanding protein function.In the previous work, we have shown that an NNP with a non-transferable coarse-grained model architecture can learn the thermodynamics of a single proteinThe multi-protein model, trained over all proteins in the MD dataset, demonstrates that we were able to model multiple proteins with a single NNP. The following tests on mutants of the 12 proteins have shown the robustness of the multi-protein NNP to small differences in sequence. We highlight, however, that the current training set, while being one of the largest ever produced, only contains data for 12 small proteins. With such a small number of training examples, it is unrealistic to expect that the NNP will model sequences different from the training set. Therefore we do not provide a hold-out test set. While it is not a physical model, this work is a fundamental step in that direction.44. The network also relies on large datasets of all-atom molecular dynamics trajectories which are expensive to produce. Furthermore, the current accuracy of coarse-grained MD is limited by the accuracy of the underlying all-atom simulations. While all-atom force fields are reasonably good for proteins, improved approaches are required for coarse-grained small molecules77. Ultimately, the ability to create a truly general model that is transferable from smaller to larger proteins would revolutionize the field78. Some works suggest that transferability can be achieved by a sufficient sampling of various configurations and state variables79. We think that, in order to learn transferable potentials, some key improvements need to be made, mainly: much larger molecular simulation datasets, alternative training strategies, improved coarse-grained mapping strategies, and more robust architectures that can deal with non-physical states. Current results indicate that this might be achievable.There are a few limitations to the current approach. In general, machine learning potentials do not extrapolate well outside of the training set for atom positions that are never sampled in the training set. Therefore, unseen positions are assigned unrealistically low energies and often produce spikes in forces. This has been solved by limiting the physical sampled space with the use of basic prior energy terms8. MD simulations were performed with ACEMD80 on the GPUGRID.net distributed computing network81. The systems were simulated using the CHARMM22*82 force field and TIP3P water model83 at the temperature of 350 K. All the simulations were performed following a previously used adaptive sampling strategy84, in order to explore efficiently as many conformations as possible. Homeodomain dataset also contains simulations that started from the native conformation, as low RMSD values (≤2 Å) with respect to the native structure are difficult to sample when starting from random coil conformations. A Langevin integrator was used with a damping constant of 0.1 ps−1. Integration time step was set to 4 fs, with heavy hydrogen atoms  and holonomic constraints on all hydrogen-heavy atom bond terms85. Electrostatics were computed using Particle Mesh Ewald with a cutoff distance of 9 Å and grid spacing of 1 Å. Ten NVT simulations of 1 to 10 ns length were carried out for each protein, with a dielectric constant of 80 and temperature of 500 K to generate ten different starting random coil conformations for the production runs. Production simulations consisted of thousands of short trajectories of 20, 50, or 100 ns, distributed across different epochs using the adaptive sampling86 protocols implemented in HTMD87. In adaptive sampling, multiple rounds of simulations are performed, and in each round the available trajectories are analyzed to select the initial coordinates for the next round of simulations. The MSM constructed during the analysis was done using atom distances, using TICA for dimensionality reduction and k-centers for clustering. From the trajectories, we extracted forces and coordinates with an interval of 100 ps. Total aggregate times used for training for all the proteins are summarized in Table All initial structures were solvated in a cubic box and ionized as described by Lindorff-Larsen et al.Based on the MD dataset we built MSMs for each protein. The models were able to describe the conformational dynamics of each protein, sample the native conformation and identify intermediate and metastable states for some of them, such as Villin, NTL9, WW-Domain, or Protein G  makes the free energy surface smooth, while shifted softplus (ssp) caused the trajectories to collapse into many local minima, making the surface grainy. Other parameters that have a significant influence on the quality of the models are the number of interaction layers and the range of radial base functions. It is important to mention that in some cases even the random seed has an influence on the quality of the models, especially on the coverage of the free energy landscape. For that reason, to ensure reproducibility of the results we trained 2–4 replicas of each model, as mentioned in the main text. Based on the results for protein-specific models as well as the multi-protein model, we selected the following combination: 4 interaction layers, 128 filters used in continuous-filter convolution, 128 features to describe atomic environments, and 18 expnorm as radial base functions (RBF) span in the range from 3.0 to 12.0 Å. In general, we found that the models with hyperparameters similar to these tend to be good quality in terms of the metrics mentioned before.The hyperparameters were selected based on the quality of the simulation produced using protein-specific models. An example of a training input file is presented in Supplementary Listing N interaction blocks. Note that for clarity, we have omitted learnable additive biases in all linear operations above, though they are easily incorporated. The first step of the message-passing update involves expanding the pairwise distances into a set of radial basis functions, ϕ. ϕ then comprises a filter generating network used to produce a set of continuous filters, WC:W1, W2 are learnable linear weights and σ is an element-wise non-linearity. These filters are used in a continuous filter convolution through an element-wise multiplication with the current node features for The series of full network operations can be written as:α-carbon atoms (CA). To speed up the training of protein-specific modes, trajectories were further reduced by selecting every 10th frame. However, for smaller proteins , the training data was not sufficient to produce satisfactory models. Therefore all the frames were used in the training of these systems. To train the multi-protein model we combined the datasets for all the targets. Each CA bead was assigned a bead type based on the amino acid type. In the assignment, we ignored the protonation states and distinguished norleucine, a non-standard residue appearing in Villin, as a unique entity. The terminal residues were assigned the same embedding as the non-terminal residues, despite the charge. As a result, we obtained 21 unique bead types. To each bead type we assigned a unique integer, an embedding that will be used as an input for the network.Coarse-grained representations were created by filtering all-atom coordinates such that only certain atoms are retained. This mapping is a simple linear selection, wherein the mapping matrix that transforms the all-atom coordinates to the coarse-grained coordinates is a matrix where zero-entries filter out unwanted beads. The all-atom trajectories were filtered to retain the coordinates and forces of 63, an MD simulation code written entirely in PyTorch93. The package allows for an easy simulation with a mix of classical force terms and NNPs. The parameters for the prior energy terms were enumerated and stored in YAML files. The NNP was introduced as an external force, as described in the previous work63. We carried out CG simulations over all the proteins, both for each protein-specific model and for the multi-protein model, as well as selected mutants. Simulations were set up with a configuration file . The basic concept behind MSMs is that the dynamics of the system are modeled as a memory-less jump process, where future states are only conditioned on the current state, hence the dynamics are Markovian. MSM estimation of transition rates and probabilities requires partitioning the high-dimensional conformational space into discrete states. In order to project the high-dimensional conformational space into an optimal low-dimensional space, we use TICA, a linear transformation method that projects simulation data into its slowest components by maximizing autocorrelation of transformed coordinates at a given lag timeCα distances and applied TICA to project the featurized data into the first 4 components. Next, the components were clustered using a K-means algorithm and the discretized data was used to perform the MSM estimation. Although better reference MSM models could be obtained by using different featurizations, we are limited to only using pairwise Cα distances as it is transferable between systems and comparable with the coarse-grained simulations.For the all-atom MD simulations, we featurized the simulation data into pairwise For the coarse-grained simulations, the same procedure was used. However, when projecting the featurized data into the main TICs, we used the covariance matrices computed with the all-atom MD simulations to project the first 3 components, in order to compare how well the coarse-grained simulations reproduce the free energy surface for each protein. For each MSM, we used the PCCA algorithm to cluster microstates into macrostates for better interpretability of the model and to define a native macrostate that we can use to evaluate the performance of the coarse-grained simulations.The free energy surface plots used for comparison were obtained by binning over the first two TICA components, dividing them into an 80 × 80 grid, and averaging the weights of the equilibrium probability in each bin, obtained for each defined microstate through MSM analysis. To recover the native conformation from a set of coarse-graining simulations, we used the MSMs and sampled conformations from the native macrostate. The native macrostate was defined as the macrostate containing the frame with the minimum RMSD to the experimental structure.To ensure the reproducibility of the results, the training of each model was repeated 2 to 4 times with different random seeds. Each replica was then tested by performing a fast simulation of 4 parallel trajectories of a corresponding system, with the objective of a fast assessment of the model. The model that produced the best results was selected for the main validation.All the statistics obtained using MSMs are reported with an average and standard deviation obtained from estimating 10 different models by bootstrapping the simulation data, taking 90% of the trajectories. This was performed for both reference MD and coarse-grained simulations. In addition, for coarse-grained trajectories, we removed 10% of the initial frames of each trajectory from the analysis to avoid biasing the model with starting conformations. All structures shown were obtained by sampling 10 conformations from the corresponding macrostates.Further information on research design is available in the Supplementary InformationPeer Review FileReporting SummarySource Data


A single base changes causing a change to the amino acid sequence of the encoded protein, which is defined as non-synonymous single nucleotide polymorphisms (nsSNPs). Many of the nsSNPs can cause disease, and these nsSNPs are considered as pathogenic mutations. In the study, the high-risk nsSNPs of WFS1 and their influence on the structure and function of wolframin protein were predicted by multiple bioinformatics software. We obtained 13 high-risk nsSNPs of WFS1. All the 13 high-risk nsSNPs are highly conserved residues with a conservative score of 9 or 8 and mostly may cause a decrease in protein stability. The high-risk nsSNPs have an important effect on not only amino acid size, charge and hydrophobicity, but also protein's spatial structure. Among these, 11 nsSNPs had been previously published or cited and 2 nsSNPs (G695S and E776K) had not been reported to date. The two novel variants increased or decreased hydrogen bonds. In conclusion, through different computational tools, it is presumed that the mechanism of pathogenic WFS1 nsSNPs should include the changes of physicochemical properties, significant structural changes and abnormal binding with functional partners. We accomplished the computational-based screening and analysis for deleterious nsSNPs in WFS1, which had important reference value and could contribute to further studies of the mechanism of WFS1 related disease. The computational analysis has many advantages, but the results should be identified by further experimental studies in vivo and in vitro. SNPs include two categories: synonymous or non-synonymous SNPs. Due to amino acid substitutions, the non-synonymous coding SNPs (nsSNPs) may significantly influence the protein function and structure, thus the disease phenotype. We should deeply delve into how the nsSNPs affect the function of proteins to have a better knowledge of the genetic basis of human intricate diseases such as hearing loss.Single nucleotide polymorphisms (SNPs) are widely known to be the most common genetics variant of human genome, defined as a substitution of a single nucleotide occurring at a specific position in the genome. The frequency of each of SNPs in the general population is more than 1%. The SNPs generally have an important effect on many genetic diseases2. Mutations are mostly found to occur in exon 8, which is the largest exon, containing 2.6 kb of DNA. The wolframin protein is a 100.29-kDa protein containing 890 amino acids and encoded by WFS1 gene, predominantly localizing in endoplasmic reticulum (ER). The hypothetical structure of the wolframin protein is shown in Fig 3. The protein consists of three parts: a hydrophilic N-terminus of about 300 residues, a hydrophilic C-terminus of 240 residues, and a central hydrophobic domain of 350 residues, containing nine transmembrane regions.The Wolfram syndrome type 1 WFS1) gene maps to chromosome 4p16.1, and its 3628 bp coding sequence is arranged in eight exons, the first of which is non-coding , Deafness variation database (https://deafnessvariationdatabase.org/) and dbSNP database (http://www.ncbi.nlm.nih.gov/projects/SNP/). We used the ANNOVAR to identify the WFS1 SNPs. According to its instruction, we used the 1000 Genomes Project (2014 Oct) annotations through changing command line argument to 1000g2014oct.Three databases retrieved WFS1 SNPs for subsequent computational analysis, including the ClinVar database  and Protein variation effect analyzer (PROVEAN) (http://provean.jcvi.org) can predict the potential influence of an amino acid substitution in a protein according to the sequence homology6. Polymorphism phenotyping V2 (PolyPhen-2) (http://genetics.bwh.harvard.edu/pph2/) can calculate the potential functional effect of amino acid substitutions from its individual characteristics via Naïve Bayes classifier7. Likelihood Ratio Test (LRT) uses the statistical method of likelihood ratio test to make predictions by analyzing the conservation of amino acids8. Unlike SIFT and PloyPhen-2, LRT does not need to analyze the evolutionary distance between homologous protein sequences to predict amino acid conservation, and has a wider range of applications. Functional Analysis through Hidden Markov Models (FATHMM) (http://fathmm.biocompute.org.uk/inherited.html) can predict the impact of missense mutations on the function of protein with optional species-specific weights9. Its MKL algorithm can be used to predict both coding and non-coding variants. Mutation Taster (http://www.mutationtaster.org/ChrPos.html) is an analysis tool which have recruits several biomedical databases, and predict that the mutation is a polymorphism or disease causing through a naive Bayes classifier210. Based on evolutionary conservation of the mutant amino acid in protein homologs, Mutation Assessor (http://mutationassessor.org/r3/) can assess the functional influence of nsSNPs11. Protein variation effect analyzer Variant Effect Scoring Tool 3 (VEST3) (http://karchinlab.org/apps/appVest.html) can predict the functional influence of variants according to the probability of missense mutations causing disease12. There are also following six comprehensive prediction tools using machine learning and other related algorithms to score the pathogenicity of a SNP and other variants: CADD13, DANN14, Meta SVM, MetaLR15, M-CAP16 and REVEL17.Sorting intolerant from tolerant (SIFT) (http://mupro.proteomics.ics.uci.edu) can predict protein stability changes without tertiary structures with two machine learning methods: Neural Networks and Support Vector Machines18. The confidence score is between 1 and -1. The bigger the absolute value, the more confident the prediction is. I-Mutant2.0 (https://folding.biofold.org/i-mutant/i-mutant2.0.html) can evaluate the change of protein stability upon single site mutation starting from the protein sequence or structure. INPS-MD (http://inpsmd.biocomp.unibo.it), also named as Impact of Non-Synonymous Mutations on Protein Stability-Multi Dimension, is a web server devised to prediction of protein stability change upon single point mutation19. The iStable (http://predictor.nchu.edu.tw/istable/indexSeq.php) is a comprehensive predictor of protein stability change after single mutation20.MUpro (http://consurf.tau.ac.il) can calculate the conservation score to estimate the conservation of amino acids in evolution through a maximum likelihood (ML) method or an empirical Bayesian method21. The score between 7 and 9 is considered evolutionarily conservative.The ConSurf server  is an online tool, based on a hidden Markov model (HMM) approach, for prediction of transmembrane structures in proteins.SOPMA is also named as Self-Optimized Prediction Method with Alignment based on the homologue method. It can predict the secondary structure of protein through five independent algorithmshttp://robetta.bakerlab.org/) is a prediction server of protein structure, using the Robetta fragment-insertion method. It can predict a full chain protein structure automatically for ab initio and comparative modeling. The three-dimension (3D) model of the wolframin protein was built by Alphafold2, with the template performed using Robetta server. PyRAMA was used to geometrically evaluated the modeled 3D structure by calculating the Ramachandran plot. Structural presentation of wild and mutant proteins was made by using PyMOL programs. Cartoon drawings of the structures were obtained. PyMOL software was used to label native as well mutant amino acids and present the hydrogen bond between them. Modeled mutant proteins was superimposed with PyMOL on the wild protein for comparison of three-dimensional structure of wild and mutant proteins. As an online web service, HOPE (http://www.cmbi.umcn.nl/hope) can analyze the impact of a given mutation on the protein structure. The Accessible Surface Area and Accessibility Calculation for Protein (ver. 1.2) online server can calculate the solvent-accessible surface areas of 890 amino acids of wolframin protein(http://cib.cf.ocha.ac.jp/bitool/ASA/)23.The Robetta (https://cn.string-db.org/), also named as Search Tool for the Retrieval of Interacting Genes/proteins, is a web based server exploring the target gene interaction network with other proteins. The high confidence level is above 0.700.STRING  that have not been reported  and other chaperones (ERN1 and DNAJC3). Among the other interacting proteins of the WFS1, CISD2 and TMEM38A play a vital part in regulation of cytosolic Ca2+ homeostasis, and ADCY8 is essential for activating the glucose-induced signaling pathways in beta cells. WFS1 also interacts with the insulin release-related proteins (HHEX and CDKAL1), which are strongly associated with genetic risk variants for diabetes.It is shown that WFS1 interacts with ATP1A1, ATP1A2, ATP1A3 and ATP1B1, then connecting with Na/K-ATPase. It is also named as sodium/potassium adenosine triphosphatase or ATP1A protein. ATP1A consists of a α subunit and a β subunit and plays an important part in keeping the electrochemical gradient on the cell membrane. ATP1A1, ATP1A2 and ATP1A3 belong to the α subunit, and ATP1B1 belongs to the β subunit. Furthermore, WFS1 interacted with ATF6, ATF6B and XBP1, which were involved in the unfolded protein response (UPR) and endoplasmic reticulum stress (ERS), and maintained interactions with Ca27. The G494R and R732H were reported as the variants of uncertain significance. Wolfram syndrome is an autosomal recessive disorder, and its clinical features are diabetes insipidus, diabetes mellitus, optic atrophy and deafness. The mutational studies of Wolfram syndrome reported most pathogenic variants were located in transmembrane region and carboxy tail of wolframin protein, inside exon 8. However, the nsSNP  was detected in two siblings from Southern Italy with Wolfram syndrome (WS), inside exon 428.We screened out 13 high-risk nsSNPs of WFS1 gene, in which 11 nsSNPs had been reported in the literature. It is noteworthy that one nsSNP (L829P) is associated with non-syndromic hearing loss and eight nsSNPs  are associated with Wolfram syndrome (WS)We obtained two novel nsSNPs (G695S and E776K) from WFS1 high-risk nsSNPs. We speculate that they are highly likely to be pathogenic mutations, because:(1) they were all predicted to be highly harmful by all predictive tools; (2) they all had highly score 9 in conservation analysis; (3) they could all lead to decreasing protein stability; (4) they could all cause changes in amino acid properties and tertiary structure. However, clinical literature reports and other evidence are needed to verify their pathogenicity.In order to further explore the potential pathogenic mechanism of WFS1 high-risk nsSNPs, we analyzed the stability, conservation, the physical and chemical properties, tertiary structure through many software tools. The conservation analysis showed that all 13 high-risk nsSNPs were highly conserved in the WFS1, regarded as massively damaging, because the residues of the conserved domain have an important effect on biological process such as interactions among proteins. The wild-type residues of G107R, G494R, G695S, G702S, G736S and G736R are glycine, which is flexible enough to make torsion angles. Their mutant residues cause torsion angles to be unusual so that force the local backbone into an incorrect conformation and disturb the local structure. As the wild-type residues of P724L and P885L, proline has a very rigid structure, thus inducing a special backbone conformation which might be required at corresponding positions. These mutations with leucine residue maybe disturb the local structure and function of wolframin protein.29; (2) regulation of the ER stress response30;(3) regulation of the cellular calcium homeostasis31; and (4) regulation of insulin production and secretion from pancreatic β-cells32. The same conclusion can be drawn from the WFS1 protein interaction network analyzed by STRING. The C-terminal region of wolframin is located on the cytoplasmic side of the ER membrane, adopting a folded confirmation. It can interact with the C-terminal region of the ER-localized Na + /K + ATPase beta1 subunit, which is important for subunit maturation. Na + /K + ATPase deficiency is known to be responsible for apoptosis and neural degenerative disease. If a similar association exists within the inner ear, amino acid substitutions may result in hearing loss in this way. The state of accumulation of misfolded and unfolded proteins in the organelle is ER stress. The unfolded protein response (UPR), also called the ER stress signaling network, can deal with ER stress in cells. Wolframin can negatively regulate the ER stress signaling network through interaction with the master regulators of the UPR (such as ATF6). Under normal conditions, WFS1 recruited ATF6α to an E3 ligase, HRD1, and the proteasome, prevents ATF6 activation and promotes ATF6 ubiquitination and proteasomal degradation. WFS1 also can reduce the expression of ATF6α target genes, for example HPSA5/GRP78/BiP and XBP-1. In patients with Wolfram syndrome, because of the variation of WFS1, ATF6 is hyperactivated, leading to dysregulated ATF6 signaling pathway. Wolframin can modulate the filling state of the ER Ca2+ store to participate in the regulation of cellular Ca2+ homeostasis. Once a variant occurs in WFS1, ER stress is strongly induced, and endolymphatic ion composition and homeostasis are disrupted, which leads to deafness. The C-terminal segment of wolframin protein in ER lumen bind to vesicular cargo proteins including proinsulin directly. The pathogenic variants in the domain may disrupt the interaction and result in abnormal accumulation of proinsulin in endoplasmic reticulum, which impede insulin secretion and proinsulin processing.According to multiple studies, the wolframin protein have a vital function on the following aspects: (1) interaction with Na+/K + ATPase β subunitIn conclusion, the bioinformatics analysis is useful to efficiently identify high-risk nsSNPs. Pathogenicity of some high-risk WFS1 nsSNPs has been confirmed by pedigree and genetic analysis, but further vivo and vitro functional studies are required to verify the accuracy of our methods.Supplementary Information.