Machine learning (ML) has been an important arsenal in computational biology used to elucidate protein function for decades. With the recent burgeoning of novel ML methods and applications, new ML approaches have been incorporated into many areas of computational biology dealing with protein function. We examine how ML has been integrated into a wide range of computational models to improve prediction accuracy and gain a better understanding of protein function. The applications discussed are protein structure prediction, protein engineering using sequence modifications to achieve stability and druggability characteristics, molecular docking in terms of protein–ligand binding, including allosteric effects, protein–protein interactions and protein-centric drug discovery. To quantify the mechanisms underlying protein function, a holistic approach that takes structure, flexibility, stability, and dynamics into account is required, as these aspects become inseparable through their interdependence. Another key component of protein function is conformational dynamics, which often manifest as protein kinetics. Computational methods that use ML to generate representative conformational ensembles and quantify differences in conformational ensembles important for function are included in this review. Future opportunities are highlighted for each of these topics. Our review presents important questions about proteins and their functions that have been around for several decades in terms of molecular biology, biochemistry, and biophysics. This scientific knowledge is where practiced researchers have an advantage; however, there is a major difference in how machine learning (ML) is used in computational biology today compared to how it was used 20 years ago . There iIn this review, we make no distinction between old or new ML methods, or whether the ML method is based on clustering, decision trees, support vectors, projection pursuit or deep/shallow neural networks. If any form of ML has been used to help elucidate protein function, we mention the method if we found it in our literature searches. For those ML methods that escaped our attention, this was not intentional, and we regret our oversight. We also discuss experimental data when they are a critical component of a method in computational biology, such as the prediction of protein structure. We discuss limited aspects of experimental methodology only if this process is part of a method within computational biology. Not all aspects of computational biology are covered in equal depth, either because of our bias toward what we believe is the most interesting aspects of protein function, or because of what is available in the computational biology literature. The biases we have towards the topics covered in this review are unabashedly applied to help researchers fuse structural bioinformatics and computational biology with ML.The rapid introduction of novel ML methods has already transformed the field of computational biology . ExpertsGiven the emergence of a new playing field that crosses ML with computational biology, we have set out to answer this two-part question: what is the current state of the art, and how does it further our knowledge on protein function? By reading the literature, we have answered this question fairly robustly. We hope that this review will help others as much as it has helped us understand the changing landscape in computational biology in terms of protein function analysis using ML. The biochemical activity of life is orchestrated by proteins, polymer chains of amino acid molecules called residues. Their function can be autonomous or in concert, as multiple-chain complexes. They play a critical biological role by conducting interactions and controlling a myriad of processes in the crowded molecular environment of cells. The in vivo environment consists of a large and diverse population of proteins mixed with other molecules that include osmolytes, ions, fatty hydrocarbons, and other macro- and meso-molecules. This large mixture of molecules within cells and at other locations of a living organism, such as the extracellular matrix, continuously undergoes chemical reactions driven by thermodynamic and kinetic considerations. To maintain reliability in the dynamically changing network of chemical reactions, proteins evolved to maintain a functionally relevant conformational ensemble that satisfies thermodynamic and kinetic stability conditions . ProteinChristian Anfinsen and co-workers showed that the 3D structure of proteins is due to thermodynamics . ThermodThe common characteristic responsible for protein function is how it interacts with partners ,13,14. TIn general, proteins that are members of the same functional family lose their function when they are placed in conditions too different from their native environment. When comparing proteins in their respective native environments, we find that they tend to have similar intrinsic properties ,17,18. AAs illustrated in In the early days of computational biology, upon the advent of the digital computer, the main interest was using computers to help with taxonomy, where similar traits classify organisms. Many experimental comparative studies at the molecular level of proteins were also conducted, which helped establish the idea of molecular evolution . The empIn the 1970s, structural considerations of proteins began to be of interest. As it became easier to solve the inverse problem for structure determination using X-ray crystallography, protein structures became more readily available. In 1971, the protein data bank (PDB) was initiated with seven protein structures . The forComputationally addressing how proteins dynamically fold also started in the 1970s , althougAs attention began to shift to native state dynamics of globular proteins, the mechanisms of action underlying protein function were able to be studied computationally. This included mutation studies and monitoring changes in dynamics of proteins as certain residues mutated  .These days, a systems biology approach is popular for tracking protein–protein interactions, which is critically important for biological regulation and maintaining homeostasis. However, predicting protein–protein interactions involves a docking problem that is particularly difficult because of the innate flexibility and size of binding regions on proteins, as well as the accuracy of scoring functions. This topic represents a current challenge in computational biology.Along with computational biology, ML has its own interesting historical development. Initially, methods for discriminant analysis were developed in statistics that are now considered ML ,47. HoweAt present, many ML methods are linked to statistical analysis, with optimization through automated procedures to draw statistical conclusions. The domain of ML is often divided into three main categories: unsupervised, supervised and reinforcement learning. Unsupervised and supervised learning uses data to train a model to perform a particular task. Unsupervised learning methods aim to learn patterns within a dataset without additional categorical information on how the data are structured. Supervised learning uses additional information during the training, such as class labels. Reinforcement learning takes the approach of self-learning, in which an agent learns to perform a particular action through trial and error, guided by a reward system, to perform a particular task when triggered by certain environmental conditions.Other frameworks of ML have emerged, such as semi-supervised learning, which uses both labeled and unlabeled data to learn a particular task. The goal of ML is to train a model to perform a useful action or task. Some common functions of ML algorithms include: clustering, binary and multi-class classification, regression, generative modeling, natural language processing (NLP) and dimensionality reduction (DR). Natural language processing (NLP) is popular in ML research, where the goal is to analyze and generate sequence data such as text analysis/speech recognition or AI-powered chatbot models. Traditionally, recurrent models such as LSTM  have beeAnother model gaining significant traction in both the ML and computational biology communities is graph neural networks (GNN) . These mAlthough ML addresses some of the limitations of traditional methods in computational biology, it also has its own caveats. Many methods require large amounts of data to train the model. When the data are high dimensional, a preprocessing step of DR is often required. As the amount of data and variables analyzed increases, algorithm performance typically wanes due to the curse of dimensionality . AnotherIn this section, we will focus on four pillars of computational biology, as shown in The vast number of functions performed by proteins are facilitated by their 3D structure. Accurate protein structure prediction (PSP) opens the door to engineering novel protein functions in medicine, furthering our understanding of mechanisms through simulation and experimentation. Historically, the two most important computational approaches to PSP are template-based and template-free modeling. Template-based modeling is based on the principle that similar amino acid sequences share the same folds ,62,63. AThe research community religiously deposits experimentally resolved protein structures (and other non-protein macro molecular structures) into the PDB, where these data are used to improve the accuracy of template-based modeling. Template-free modeling generates protein structures without the use of homologs in the PDB . This meThe critical assessment of methods of protein structure prediction (CASP) is a biennial competition where the amino acid sequences of experimentally determined structures are provided to participants through double-blind assignment. The experimental structures used in CASP competitions are initially not deposited into the PDB until after the competition. Participants are expected to submit predicted models using their unique method of determination. Models are evaluated using the Z-scores of backbone conformational similarity using various measures for accuracy. The most successful methods over the last few rounds of CASP are given in It is important to use ML whenever it enhances computational efficiency, but ML need not dominate an approach, nor turn everything into a black box model. However, having said this, we see ML methods such as AlphaFold and AlphaFold2 have produced substantially better results. Researchers should be aware that this new paradigm does not make other methods for PSP obsolete. CASP is a competition, but more importantly, CASP provides a conduit for PSP experts worldwide to share ideas. In our view, ML is a powerful multifaceted tool, but ML will not always be the best tool that solves a problem. Ideally, ML should be used to enhance models rooted in basic physics and chemistry principles.Debuting at CASP-Round XIV, AlphaFold2 by Google Deep Mind has raised the bar in PSP by achieving prediction accuracy near the experimental limits, and scoring in the competition far higher than their competitors . AlphaFoIt cannot be overemphasized that once structures are determined, mechanisms of action can be better understood by other computational methods. With a model structure in hand, new therapeutics can be developed much more rapidly, often enhanced by computer-aided structure-based drug discovery (SBDD) methods ,97. The The native state of a protein usually refers to a folded structure, which is a functionally relevant conformation of the molecule within the global minimum of the free-energy surface (FES). From the perspective of the free-energy landscape, the native state of a protein corresponds to a native free-energy basin associated with a native conformational ensemble. Zooming into the native free-energy basin at high resolution generally reveals multiple functionally relevant basins separated by low free-energy barriers. MD simulations provide a means to explore the conformational ensemble of a native basin, and possibly transition into metastable basins at longer time scales due to larger free-energy barriers that separate basins for metastable states. Thermal fluctuations typically govern dynamic processes on millisecond or longer timescales where many functional processes take place, as shown in The practical goal of performing MD simulations is to observe molecular processes in more detail than can be obtained from experiments by sampling conformations in the form of a time series. A theoretical goal that is difficult to achieve in practice is to compute thermodynamic properties through the partition function of statistical mechanics. How much information can be extracted from time series data greatly depends on whether the process is stationary, and the sampling adequacy. The partition function requires a sum over all accessible states of a system with appropriate statistical weights. Fortunately, almost all accessible states have negligible probability. Only the most probable states need to be explored in practice. Furthermore, by obtaining probability distributions based on counting from sampling, it is possible to obtain free energy without directly calculating a partition function. While these simplifications tremendously help mitigate the problem of under-sampling, barriers in the FES greatly hinder MD from exploring the functionally relevant conformational space. In general, accuracy increases as more conformations are sampled from different free-energy basins. To increase the ability for MD to sample a wider range of conformations, it is necessary to consider enhanced sampling methods.A few approaches are available to increase sampling to capture the relevant conformations for protein function. The oldest approach is to use coarse-grained models to simulate the motions of proteins on longer time scales ,102,103.Replica exchange ,115 is aSimulated annealing  can be uLastly, non-equilibrium MD combined with Monte-Carlo methods are used to enhance conformational sampling. This approach can be classified into two schemes: introducing biases based on collective variables that are predefined, or biases placed on the Hamiltonian of the system with a potential energy that fills in the FES the longer the system spends time in a basin. Both methods increase in bias to push the system out of a basin the longer it resides there. In this way, more basins can be explored much faster than in physical reality. The objective is to capture a diverse set of conformations, not to provide real-time dynamics. These methods are often referred to as metadynamics ,120.In the first class of methods, a biasing force estimates the free energy along a particular reaction coordinate by computing the average force, and computing the FES by thermodynamic integration. In the second class, one way to fill up free energy basins is to add positive potentials in the form of Gaussian functions. Another method called Adaptive Biasing Force (ABF) ,122 usesThese methods have been widely applied to MD simulation, and combinations of these classic methods with ML algorithms to further improve FES sampling have been explored extensively. In the following subsections, applications of ML to various aspects of these enhancement algorithms are reviewed.a priori defined collective variable (CV), defined using expert knowledge by hand-selecting a set of residues to track coordinates, distance pairs or dihedral angles. Recent work has incorporated empirical data for CV selection, such as using co-evolutionary residue couplings [Many enhanced sampling algorithms rely on an ouplings  or the N entropy . More geN atoms in the molecule. However, the The natural description of protein dynamics is the 3D coordinates of each of the  sampled ,127. Theh as PCA . Normallh as PCA , MDAnalyh as PCA  or ModeTh as PCA . These mLarge-scale motions are effectively represented in a low-dimensional space and are used to accelerate MD simulation  and idenV is a matrix whose columns represent the collective independent components, V, that maximize autocorrelation are found. The eigenvalues, A popular method for CV determination as well as analysis of MD simulation data is time-lagged Independent Component Analysis (tICA) . ICA is compared . The timt0ln(λi) . Usuallyt0ln(λi)  and is wt0ln(λi) . The soft0ln(λi)  and MSMBt0ln(λi)  construcNeural networks have also been used to parameterize CVs because they are able to be computed on the fly during the MD simulation. Moreover, neural networks are differentiable, which lends to computing biasing forces . AutoencThe low-dimensional representations learned by autoencoder models have been used in several applications to construct a Markov state model (MSM) to characterize long-timescale motions ,150. Simt0 later . An enset0 later .z. This distribution is sampled to produce a point x during training, and subsequently generates a new sample during test time. The model is trained to minimize both reconstruction error, so that the decoder can generate new points of x given a latent point z, and the Kullback–Leibler divergence between the learned distribution in the latent space of z and a normal distribution. This second training term constrains the learned distribution on z so that it may be efficiently sampled without the need for the encoder after training. VAEs have been used in combination with other methods to find reaction coordinates [The variation autoencoder, VAE, is used for probabilistic generative modeling. VAEs work similarly to autoencoders in that they learn an encoder and decoder model. However, rather than learning discrete points in the latent space, the model learns the parameters rdinates . As an erdinates  to trainrdinates  for a stA related method which blends ideas from VAEs and tICA has recently been described for finding slow reaction coordinates by characterizing a MSM for protein dynamics, called the Variational Approach to Markov Processes (VAMP) . In VAMPius norm . This apius norm ,161.Methods such as metadynamics  and adapHere, we highlight three examples of how neural networks can be used to compute adaptive bias potentials. The first method, called NN2B , is simiClustering data is a task that is ubiquitously used in data science and within ML methods. This section will describe many clustering methods, but the main application of interest is to quantify the similarity between conformations. Clustering conformations is an essential element of constructing a MSM. Often, a trajectory can be clustered into hundreds to thousands of microstates to describe the kinetics of biophysical processes.Clustering is an unsupervised ML task in which a space or set of inputs is divided into groups based on how similar or different inputs are from each other . At the Clustering algorithms are sensitive to the type of distance metrics used to quantify similarity between two conformations. A common approach is to use the RMSD and TM score . The RMSAn ongoing issue in comparing molecular structures is the requirement of a consensus set of residues to facilitate the comparison. After the residues are selected, the conformations to be compared must first be structurally aligned into the same frame of reference. In general, as the consensus set of residues becomes large, distance comparisons become less useful because of the curse of dimensionality. This is why the coordinate space is often transformed into low-dimensional, informative representations prior to clustering. Linear distance metrics such as euclidean distance t scales . To remorelation .k cluster centriods it is closest to. The centriod locations are recomputed, and this process is iterated until convergence is reached. Geometric clustering is easy to implement and has been effective with MD data, and thus has been included in analysis packages such as MSMBuilder [As applied to molecular simulation, the major classes of clustering that are popular are: geometric or partitioning methods, hierarchical methods, and model-based methods including spectral clustering . GeometrMBuilder .Hierarchical clustering constructs a dendrogram of the data points by iteratively grouping data points or clusters of data points one at a time until either the root is reached, or a specified number of distinct clusters is found. Hierarchical clustering can be employed using a top-down approach which starts at the root and works its way to the leaves, or a bottom-up approach that starts with the leaves and works its way to the root. The bottom-up approach can be referred to as agglomerative clustering. An example of hierarchical methods used in clustering protein conformations is the Bayesian Agglomerative Clustering Engine (BACE) method.BACE  is an agW, converted to similarities by a transformation of the users choice, and diagonalized. The resulting matrix of the first k-means. According to spectral clustering theory, the number of clusters within a dataset corresponds to the number of eigenvalues of the Laplacian matrix that are equal to 1, or practically, within a tolerance. The most commonly used spectral clustering approach is Perron-Cluster Cluster Analysis (PCCA) and Robust PCCA (PCCA+).It is worth noting that model-based clustering assumes an underlying model for the data, which is exploited to cluster data points. To analyze MD trajectories, spectral clustering methods are used, which decompose a particular matrix using eigen-vector/value  decomposition . In partP, to construct the Laplacian matrix, where in the above equation for L, P will become block diagonal under appropriate permutations, indicating that data points within a cluster only form edges with other data points in the same cluster within the graph representation of the dataset. The eigenvalue spectrum will have a Perron Cluster of eigenvalues at 1, allowing for the spectral clustering. This method has been used to construct Markov models and analyze rare dynamic processes in MD simulation [PCCA and PCCA+ ,177 is amulation . A weaknk-means and then hierarchically ordered based on the density of the state, which is proportional to the number of conformations within the state. The microstates are then divided into n clusters, such that the number of conformations (not microstates) are about equal between them, so that the resulting set with less microstates is more dense in conformation space. Density sets are accumulated into a super density set, such that the i-th super density level contains all of the density sets 0 to i. Spectral clustering is performed at each super density level to reveal kinetic clusters, which form successively more connected graph representations with increasing set level. This allows clustering to be performed hierarchically and reveals structured information about the underlying FES. Further extensions of this algorithm, called the Hierarchical Nyström Extension Graph, have been published by the same authors [Methods of clustering are not restricted to an established clustering method in ML. As an example, Super-Level-Set Hierarchical Clustering  blends m authors  to accoun microstates and converts them into more coarse-grained macrostates. The trajectory is first reduced into a low-dimensional form by PCA, then the free energy is computed and microstate transition probabilities are approximated via the assumption that i, i. The transition path is followed by jumping to the nearest neighbor state with the highest probability . An IDP has disordered regions, which can mix with ordered domains or small well-defined structural motifs. Often IDPs undergo induced conformation change upon binding . DisordeWorking with conformational ensembles provides a direct route to elucidate protein stability, dynamics and function. However, there remain open questions about the best way to generate, represent and quantify conformational ensembles. Early work includes taking a statistical approach , knowledPredicting stable conformations using ML has been achieved using neural networks  by operaTypically, for initial descriptors, these models use a combination of structural features, sequence information using singleton or multiple sequence alignment, and structural topology representations such as contact or distance matrices. Feature crafting is a key element of well-designed learning algorithms. In addition to sequence propensity scores, structural features include atomic packing , electroThere is a resurgent interest in predicting protein stability, mainly from sequence information, and possibly from static structures. For example, emergent sequence features from transformer processes with alternating self-attention with feed-forward neural network connections  have bee created . Further created . To obta created . Possibl created .In our view, a purely sequential approach will fail to give robust protein stability predictions. The environment dictates the nature of the conformational ensemble in conjunction with the constraints placed by a sequence. Without context, stability is undetermined. Specifically, solvent and conformational entropy effects cannot be neglected when quantifying protein stability. Therefore, the ML methods that incorporate environmental and conformational ensemble information will likely perform well in the long run. In the short term, good results may be obtained by working with small datasets that have systematic trends; however, experimental evidence in the late 1980s and early 1990s ,36 suggeProtein stability highly depends on environmental factors. Most work takes into account how protein stability can be altered with different formulations or how stability can be shifted by small molecular ligands. While numerous factors are present in the crowded cell, we limit our review to the description of protein stability as a function of the chemical composition of small solute molecules. This simpler situation is already a rich and important problem, germane to synthesis and purification of proteins in practice.2 of 0.48 and AUC above 0.8 [Practical computational approaches employ datasets that characterize protein sequence/structure characteristics and correlate this information to solubility using ML models. A graph-convolutional network trained on soluble protein datasets, such as eSOL, treats solubility prediction as a regression problem. By including contact maps along with a variety of sequence and structural information about the protein, predicted accuracy benchmarks had an Rbove 0.8 .In another line of research, improving solubility by modifying moieties through solubility tags is of great interest. An algorithm that creates these for peptides was found to increase solubility in empirical studies by over 100%. This work also trained on the eSOL database using support vector regression to inform a genetic algorithm to optimize the tag additions for the given sequence . SimilarThe ability to increase protein stability without loss in protein function efficacy is the objective of designing protein formulations. A key lacking aspect seems to be understanding this for a specified aqueous co-solutes, whether ionic or aliphatic in nature. One cannot separate the conformational ensemble of a protein in an aqueous solution without taking into account the exchange of protons from the protein to the medium. From explicit MD simulations of constant pH, training a convolutional neural network in tandem with dense layers for pKa prediction was shown to be fairly robust for soluble proteins by using MD simulations to train ML models . A modelThe environment of a protein need not be of aqueous nature. There has been recent work with ML to predict membrane interfaces of proteins using reinforcement learning on structural data generated from MD, after determining appropriate CVs. Utilizing an ensemble of predictors tied together with a meta classifier, exhaustively tested and optimized, yielded state-of-the-art accuracy under limited conditions . In a siIn each of the cases discussed above, a key dataset is used to train a model for inferring relationships between sequence/structural information and how the protein will react to the environment. In each of these applications, extrinsic information is being inferred on data from a secondary source. A key opportunity is to look for transferability in the ML model to account for changes in the environment.Mutating residues to modify protein function or achieve a specific molecular property is the earliest examples of protein design, also known as re-design and protein engineering. We are interested in the computational biology underpinnings of in silico structural based platforms that proceed along these lines ,235,236.To help quantify the shifting of stability in a protein, ProTherm was created as an empirical mutational database that includes the attributes of d an ANN ,243. A dignments . When thignments , which cignments .Most recent advancements in predicting stability changes of a protein due to mutation include hallucinations via diffusion models applied to protein structures to generate novel composite single and multi-domain globular proteins . ImproviIn most works to date, the process of prediction followed by refinement using known features is applied. Prediction of stability shifts due to mutagenesis requires structural and thermodynamic considerations, which makes it challenging to achieve reliability.Understanding molecular function extends past the intrinsic characteristics of individual structures/sequences and involves the dynamics of protein–protein interactions (PPIs). These interactions can occur in many ways, such as permanent  or transient relationships  . PredictSequence-based PPI prediction methods generally begin with two protein sequences and result in a score which ranks the probability that an interaction occurs. Encoding the complex information required for robust PPI predictions is of vital importance while performing feature engineering . FurtherThe majority of ML methods for PPI prediction are sequence based (static structures), and do not account for conformational ensembles or the role played in PPIs by local environment. Despite the use of high-throughput techniques in discovering PPIs, the coverage of experimentally determined PPI data remains poor . This trBeyond the classical structure–function paradigm, which is grounded in a general lock-and-key model driven by the assumption of unique structures, is a continued interest in the role of IDPs and protein hybrids. Protein hybrids are comprised of intrinsically disordered protein regions (IDPRs) and ordered domains. Disorder-based functionality complements the known function of these ordered proteins and domains . The proOf particular interest are the IDPRs known as molecular recognition features (MoRFs), which execute their function through a phenomenon known as disorder-to-order transitions (induced folding) . While trd dataset contained 414/646 target IDPs that were absent of any positive labels that were derived from the experiment. Two overarching challenges were set; the first of these assessed performance of the predictors when the objective was the identification/prediction of fully disordered proteins (IDPs) using datasets 1 and 2. The second challenge evaluated the performance of the predictors when the objective focused on the prediction of disordered protein binding regions (DPBRs), benchmarked using dataset 3.The gold standard for IDP/IDPR predictor evaluation is the critical assessment of protein intrinsic disorder prediction (CAID). This is a community-based blind experiment aimed at identifying state-of-the-art IDP/IDPR predictors. In the 2021 CAID benchamrk , 43 methHere, we provide a brief summary for the performance of the participants and discuss general trends. The primary metric for performance during CAID is the maximum Given the recent non-incremental increase in the structure prediction field by AlphaFold2, it is pertinent to address recent concerns relating to AlphaFold2 and intrinsic disorder prediction. It has been noted that the disorder predictor one constructs from a predicted AlphaFold2 structure determines accuracy . This isProtein motion, of which there are many types, as schematically shown in This is because XRC only provides static structures. Crystal packing biases the B-factors during the process of solving the inverse problem for structure from the raw X-ray diffraction data, as resolution errors are folded into the B-factors . In the arameter . There aIn addition to these incompleteness and indirect measurement problems, directly resolving dynamical correlations among flexible regions in a protein remains an experimental challenge. Therefore, MD simulations are typically used to identify flexible regions within a protein and monitor time correlations. However, MD simulations cannot reach long time scales, and there are insufficient statistics at the longest timescales that can be reached. Furthermore, it is a challenge to identify functionally relevant dynamics both experimentally and computationally. This is because the observation of atomic motions does not answer how important these motions are for a mechanism of action. In general, non-functional motions will hide functionally relevant small-amplitude motions, especially when non-functional motions have large amplitude. Therefore, functional dynamics are likely to be missed by methods that intrinsically extract large structural fluctuations in a protein, such as PCA. Since PCA is used as a dimension reduction method, it is possible to lose important information about functional dynamics before more sophisticated ML methods are applied whenever PCA is indiscriminately applied.For brevity, we only discuss globular proteins and IDP as two classes of proteins. Globular proteins tend to hold a well-conserved 3D shape, although parts of the structure can flex. The most flexible parts of a globular protein are located in its loop regions. In general, large-scale motions and localized flexible regions are important for protein function. Flexibility in a particular macrostate  exists as a hierarchy in the size of certain structural elements and in terms of local minimums in the free-energy funnel. As an example of this, a full domain of a protein may undergo a concerted, global conformational change, while regions of secondary structure remain more rigid due to stabilizing hydrogen bonding. Loops, particularly those protruding into the solvent can be quite flexible in contrast with the the stable core of a molecule ,307 FinaOne approach for ML to directly predict flexibility in proteins is to use the structure data collected in the PDB to predict the experimental flexibility metrics, such as the B-factor and el (ENM)  allow RMrameters . Anotherrameters ,311 whicrameters  has pittnetworks  to predinetworks  has beenn masses is M is a diagonal matrix containing the mass of each mass point, and the elements of matrix K, i and j. K is called the Hessian matrix for the model, where harmonic potentials connect to mass points. The eigenvectors represent the normal modes of motion for the system, and their eigenvalues are the corresponding frequency of that motion. The mass of each mass point will in general be different because the constituent atoms associated with each mass point are heterogeneous. However, often the masses of all mass points are set equal. These spring connections are heuristic, and the ENM is not the same as a true normal mode analysis since the ENM is set at a coarse grained level description.In the literature, there are many types of ENMs . In geneIn principle, equilibrium MD simulation provides the best way to investigate flexibility by directly sampling the conformational space. However, as discussed above, in practice there is usually an unobtainable computational cost, and to make matters worse, one faces massive amounts of data, which must be analyzed to quantify flexibility through dimension reduction. Nevertheless, the most popular method for extracting flexible motions from equilibrium simulations is Essential Dynamics (ED). Essential Dynamics  applies A link was found between ED and ENM, where the Hessian matrix can be approximated for a sampling of conformations by the inverse of their covariance matrix, which is the matrix used in PCA. Thus, within the qausi-Harmonic approximation, the most variant PCA mode  is equivalent to the lowest-frequency ENM mode  . It is iSome ML methods have been used to predict flexible and dynamic regions in proteins. Much of this research is driven by better docking algorithms that can accommodate flexibility in the receptor and ligand. For example, SVMs have been used as binary classification algorithms to determine whether loops have high mobility or not. Early classification algorithms often use curated features such as solvent-accessible surface areas, B-factors, and other structural quantities, which improve but likely bias predictions. Informative features for describing protein flexibility are required to elucidate which atomic motions correlate with functional characteristics. Random forest is commonly used for classification and regression tasks, but metrics such as Gini impurity  allow thSPLOC) algorithm [Connecting conformational dynamics to function can be built into models that directly work with trajectories that describe protein dynamics. The tICA method, which we discussed in lgorithm . This melgorithm  such as lgorithm .Generative models provide an interesting approach to studying the flexibility of proteins, which requires training on known conformational ensembles. This data can be obtained from MD simulation trajectories. The MD data provides the model with a baseline for how the atoms move. Then the model learns low dimensional distributions that are used to generate more conformations to help fill out the low sampled regions. This provides a means for studying molecular motions in the native state. A simple, but effective method for doing this is to determine the normal modes of a protein with an ENM, and then use the modes themselves as displacement vectors for perturbing the structure . This stAutoencoders have also been used to generate realistic conformational ensembles . A disadIn the early days of structural bioinformatics and computational biology applied to understanding the structure and dynamics of proteins, methods were developed to predict the most flexible regions in a protein. As reviewed above, this is not a difficult task, as there are many methods (based on ML and/or physics-based models) available to identify flexibility or mobility. It is seen that a wide range of methods yield results that are consistent with experiments that measure mobility. The more interesting question that goes to the heart of protein function is how flexible regions and their motions are correlated. The construction of conformational ensembles using MD simulation can, in principle, uncover this correlation, but to reach the timescale of functional dynamics could require calculation times that are not feasible. Our view is that physics-based modeling will be the rate-limiting step in characterizing functional dynamics, and successful models must include the effects of thermodynamic and mechanical stability and their interrelationships.Allosteric signaling is a long-range communication present in proteins that affects function, conformation stability, or interaction propensities between partner molecules . Note thSeveral normal-mode-based allosteric site prediction software exist ,336,337.Attempts at classifying allosteric signaling using local features generated from MD have been attempted. Results using naive Baysian inference and SVM yielded poor allosteric predictions . RecentlSome limited work involving engineering allosteric sites into existing proteins has been carried out previously . These eTo perform MD simulations, there must be a molecular forcefield, which must be parameterized. The most accurate method is using ab initio quantum calculations to determine the exact Hamiltonian of the system. Unfortunately, this direct approach becomes intractable for systems larger than several hundred atoms. In addition, the calculations are difficult in principle because environmental effects (from more atoms) are difficult to model implicitly, leading to a non-local parameterization that does not generalize to all systems. Alternatively, a functional form can be approximated based on modeling physical interactions at a local level  plus non-local electrostatics. These models can be parameterized based on fitting the functions to known experimental data. While this is more practical, it is limited by the experimental data available, which often does not generalize to systems and environments much beyond the realm described by the fitting data. Limitations from systematic experimental data availability will be present in all ML methods too, but ML may help the procedures to obtain better models for the data that are available.In recent reviews of the subject ,348, reqIdeally a molecular representation models an atom with its local environment, which influences the forces acting on the atom. To achieve this, as well as the other requirements for representations, Atom Centered Symmetry Functions (ACSFs)  were intSeveral methods of transforming molecular representations for predicting forces with ML have been reviewed . One of The Born–Oppenheimer approximation allows the nuclear and electronic wave functions to be treated independently, where the nuclear degrees of freedom are treated classically. Because classical MD simulation does not simulate electron dynamics, a forcefield need not account for this detail. One approach developed in 2010  is the GEarly work using ML to parameterize forcefields to simulate the dynamics of molecules involved using neural nets to predict parameterization for potential energy surfaces. Refs. ,356,357 l, More recent ML models have used the many advanced architectures and methods developed in the past few decades. PhysNet  is an exW transforms the pairwise distances to the feature space dimensions. The model was implemented in a new network structure called SchNet [d-dimensional feature space which is updated with each sequential cf-convolution layer added to the model. The difference is that convolutions, rather than message passing, are performed to update the feature representation. Recent trends have seen use of GNNs for molecular fingerprinting extensively explored for predicting molecular properties such as energy and force. Some examples of method that use GNNs for predicting energies and forces include DimeNet [The matrix d SchNet  which had SchNet . Forces  DimeNet , GNNFF [ DimeNet , and New DimeNet . These mThere are several implementations of deep ML potentials that can be used in MD simulation software instead of classical potentials. TorchMD is an MD engine (downloadable via github) writen in pytorch that uses combined classical and deep learning potentials . For TorOne of the strongest drivers of ML method development for computational biology and protein design is drug discovery. The drug discovery process takes an average of 12 years from start to commercialization, with an average cost of USD 1.8 billion ; consequMolecular docking is a vital step in the drug design process, and acts as a filter to identify candidate molecules for the purpose of reducing costs by streamlining experimental work. Virtual screening often refers to a high-throughput candidate selection procedure . The paiClassical docking scoring functions assume an additive functional form in order to model a linear relationship between the binding affinity and features characterizing protein–ligand complexes . UnfortuWe identify three considerations that should be taken into account which ground many of the remaining challenges in molecular docking. First, not all the complexes in the PDB are functional, and this consideration should be reflected when determining protein sets for training ML models . FurtherBinding affinities are important for evaluating novel drug molecules and their targets. Within computational biology, this falls under applications of virtual screening and docking. The dissociation constant, In principle, ML can be trained on experimental data to directly predict binding affinities. Therefore, datasets are important for this approach. A few examples of databases which contain binding affinity information are BioLiP , BindingWith deep learning and large datasets becoming increasingly accessible, various neural network architectures have been exploited, particularly the CNN architecture. Early work on applying CNNs to predict binding affinity was carried out in 2009 , where iOther deep-learning approaches have been used to predict binding affinities. For example, Zhao et al.  replacedAnother random forest model called iSEE predicts changes to binding affinity, utations . Again, training . The iSEng FoldX , CC-PBSAng FoldX , BeAtMuSng FoldX , BindProng FoldX , which ung FoldX ,432. To Although molecular docking and prediction of binding affinity is a mature area of computational biology that has been impactful in drug design for more than two decades, there remain open challenges. Better methods are needed to robustly identify binding sites on protein structure. This proved to be a difficult task, as binding models must consider environmental and preferential binding effects due to thermodynamic linkage ,435,436.Our review cited over 300 papers on ML methods used in applications of computational biology, and over 100 papers on protein function and computational methods that have historically been successful in protein function analysis. We tied together the ML methods used to elucidate protein function, along with practical applications involving proteins with drug discovery. The context of the underlying biophysics, biochemistry and molecular biology puts into perspective the domain knowledge required to successfully integrate ML into computational biology applications. The convergence of computational biology with ML has already shown many fruitful directions. Due to the complexity of the subject, we believe that the recent gains in model predictions for protein function or functional attributes will continue to increase in the foreseeable future. We have emphasized the conformational ensemble perspective, because there is a natural continuum that bridges proteins with various degrees of conserved structural motifs and disorder. We believe that modeling conformational ensembles and protein dynamics under different environmental conditions is necessary to make the most progress in protein science through computational biology. It is the modeling of these general concepts that also pushes ML to its current state-of-the-art limits. The convergence of computational biology with ML is clearly beneficial for both areas of study, as challenges in protein function analysis are addressed.Despite recent work over the last two decades in terms of accurately describing conformational ensembles of proteins, more work is needed to represent these ensembles in a computationally tractable and mathematically complete way. ML is a tool that can help achieve controllable approximation. We stressed that protein function is linked to specificity, because proteins function in the crowded cellular environment. Understanding how proteins function under environmental changes requires finding representations for environmental effects. It appears ML can improve protein engineering through in silico mutation studies. Changes in the environment and the primary structure of a protein together have significant effects on stability and function, both of which are related to the conformational ensemble.Another necessary step is to find ways to simulate protein dynamics over long time scales. Due to the intrinsic limitation of the MD methodology of integrating differential equations on the femtosecond time scale, coupled with the problem that biologically important timescales routinely exceed one second, and the desire to simulate ever larger systems, there will always be a major problem with sampling on classical computers in the foreseeable future. Although this sampling problem presents a bleak picture, there are already many ways to address this problem by using coarse-grained models, metadynamics, and other bias techniques to explore functionally relevant dynamics, with ML greatly improving the effectiveness of these methods. There is also the challenge of identifying functional dynamics, for which ML can be used for discriminant analysis and dimensionality reduction of MD simulation data. On these fronts, ML provides a means to solve—or at least mitigate—sampling problems and identify the functionally relevant part of the generated conformational ensemble. To obtain accurate thermodynamic properties, such as binding affinity, it is imperative that the appropriate conformational ensemble is sufficiently sampled. Although more sampling allows flexibility in docking to be accounted for, the docking application remains a challenging problem.The sampling challenge also motivates the ongoing development of better forcefields for MD simulations and thermodynamic models that take into account non-additivity in conformational entropy. We also reviewed progress on forcefield development using ML methods that have already made progress on these challenges and promise many more advances in the near future. In this time of convergence between ML and computational biology, decades of nurtured ideas have begun to bear fruit. The protein folding problem, while remaining a major challenge in protein science, is on the cusp of being solved, as are many other grand challenges in protein science.


Ordered supramolecular assemblies have recently beencreated usingelectrostatic interactions between oppositely charged proteins. Despiterecent progress, the fundamental mechanisms governing the assemblyof oppositely supercharged proteins are not fully understood. Here,we use a combination of experiments and computational modeling tosystematically study the supramolecular assembly process for a seriesof oppositely supercharged green fluorescent protein variants. Weshow that net charge is a sufficient molecular descriptor to predictthe interaction fate of oppositely charged proteins under a givenset of solution conditions , but the assembledsupramolecular structures critically depend on surface charge distributions.Interestingly, our results show that a large excess of charge is necessaryto nucleate assembly and that charged residues not directly involvedin interprotein interactions contribute to a substantial fraction(∼30%) of the interaction energy between oppositely chargedproteins via long-range electrostatic interactions. Dynamic subunitexchange experiments further show that relatively small, 16-subunitassemblies of oppositely charged proteins have kinetic lifetimes onthe order of ∼10–40 min, which is governed by proteincomposition and solution conditions. Broadly, our results inform howprotein supercharging can be used to create different ordered supramolecularassemblies from a single parent protein building block. The supramolecular assembly process is studied for a seriesof oppositely charged proteins using experiments and simulations tounderstand the fundamental mechanisms governing assembly of superchargedproteins. Overall, the development of newfunctional biomaterials would greatly benefit by achieving a detailed,fundamental understanding of the protein assembly process.The assembly of biologically encoded moleculesinto ordered supramolecularstructures gives rise to unique properties in natural biological systems,such as increased stability and complex functionality of macromolecularassemblies in cells.11 Using de novo engineering of synthetic proteins,different assembled protein architectures have been created,12 including one-dimensional (1D) nanowires,15 nanorings and nanotubes,19 and 2D and 3D protein crystals.24 However, protein engineering strategies for supramolecular assemblygenerally require precise and targeted design of complex molecularinterfaces due to the highly specific nature of the governing intermolecularinteractions. Given the complexity of biomolecular interfaces andinteractions, many supramolecular assembly strategies are not easilygeneralizable across different classes of proteins, which limits theirpotential use in developing new functional biological materials.Supramolecularassembly of proteins can be driven by several differentstrategies including receptor–ligand, metal–ligand,electrostatic, and hydrophobic interactions.25 Electrostatic interactionsbetween folded proteins have been used to create binary protein crystalsfrom highly symmetric cage proteins30 as well as to localize charged proteins in Matryoshka-likecages31 and protein capsules.35 Supramolecular assembly of proteins via electrostatic interactionscan be extended to initially uncharged proteins by supercharging proteinsurfaces to include charged residues.37 Recent workhas shown that oppositely supercharged green fluorescent protein (GFP)variants readily assemble into an organized 16-subunit protomer, suggestingthat highly symmetrical building blocks may not be necessary to drivehierarchical assembly into ordered structures.38 Although electrostatic interactions provide a promisingmethod of protein supramolecular assembly that could yield syntheticbiological assemblies and materials with functional properties, welack a complete understanding of the underlying assembly process andthe molecular design rules governing electrostatic-mediated protein–proteininteractions.Electrostatic interactions between oppositely charged proteinsare known to drive hierarchical assembly of both folded and unfoldedproteins.39 as well as patchy attractive interactions41 give rise to symmetric hierarchical assembly. By changing the distributionof attractive patches on the surface of a protein, it is thought thatproteins can assemble into a variety of different quaternary structures.For example, ferritin cage proteins are known to assemble into differenthierarchical structures by changing the location of the attractivepatches or the assembly conditions.42 In addition, it was reported that changing the distribution of chargeson protein surfaces affects their ability to form complex coacervateswith strong polyelectrolytes.44 We therefore hypothesizedthat different hierarchical assembled structures can be obtained froma single parent protein building block by changing the net chargeand surface charge distributions on oppositely supercharged proteinpartner pairs.Complexities in supercharged protein assemblyarise due to thenature of multicharge and multibody interactions, which includes therole of surface charge distributions. In general, protein superchargingdoes not yield a uniform surface charge distribution, but rather incorporateslocalized charged regions dispersed over the entire protein surface.Prior computational and experimental studies on spherical and polyhedralcolloidal particles have shown that both shape complementarityIn this work, we use a combination of experimentsand computationalmodeling to understand the assembly mechanisms of supercharged proteins.Using a series of oppositely supercharged proteins 1, we exp38 At this spatialresolution, 176 specific interprotein interactions  were identified as stabilizing the structure.Although 126 (72%) of the interactions involved a mutated chargedamino acid, only 29% of the mutated charged amino acids were involvedin stabilizing interprotein interactions in the ordered assembly.38 A natural question then arises: what is therole of noninteracting, outward-facing mutated charged residues inpromoting supercharged assembly?We began by studying the role of noninteractingcharged residues in supramolecular protein assemblies. Prior workreported the structure of an assembled 16-mer protein (two stackedoctamers) composed of oppositely supercharged GFPs (denoted as GFP-17and Ceru+32o in this work) solved at 3.47 Å resolution usingcryo-electron microscopy.38 The minimally mutated variant of GFP-17 (named GFP-min) has 4 ofthe original 11 mutations and a nominal net charge of −8 atpH 7.4. The minimally mutated variant of Ceru+32o (named Ceru-min)has 6 of the original 24 mutations and a nominal net charge of +3at pH 7.4. Clearly, the minimally mutated variants have significantlysmaller net charges than the fully supercharged variants, but theyretain the requisite set of mutated amino acids involved in stabilizingthe interprotein interfaces in the 16-mer assembled structure.To understand the role of noninteractingcharged residues in supramolecular assembly of supercharged proteins,we designed and expressed two minimally mutated GFP and Cerulean variantsthat contain only the mutations participating in interprotein interactionsand do not contain any of the externally facing, noninteracting chargedamino acids identified by Simon et al.45 and superfolderGFP,46 the Förster distance Ro for the protein pair is calculated to be 5.5nm.47 Thus, for FRET efficiency >0.5,theaverage spacing between Ceru+32o and GFP-17 is expected to be lessthan approximately 5.5 nm. Our results show that the FRET efficienciesbetween Ceru-min and GFP-min are significantly lower than those betweenthe fully supercharged variants at all NaCl concentrations and are<0.5 at all salt concentrations, indicating weakly associatingproteins. Ultimately, these results suggest that minimally mutatedvariants do not associate as strongly as the supercharged proteinpairs.We began by determining the Förster resonance energy transfer(FRET) efficiency between the fully supercharged-proteins (Ceru+32o/GFP-17)and minimally mutated protein pairs (Ceru-min/GFP-min) as a functionof ionic strength 2a. As io38 large aggregates (>1000 nm in diameter) form at low salt concentration.As salt concentration increases, intermediate particle sizes (∼12nm) are observed, indicating that the proteins assemble into a protomerstructure. Compared to the fully supercharged variants, assembliesformed from the minimally mutated variants (Ceru-min/GFP-min) haveaverage sizes matching the monomeric species even at low salt concentrations.For example, the average diameter of particles at 0 M NaCl is 7.5nm, which is not significantly different than the monomeric species(approximately 5–7 nm in diameter). These results are consistentwith FRET measurements and suggest that Ceru-min and GFP-min do notstrongly associate at the range of salt concentrations consideredhere.Dynamic light scattering (DLS) was used to determinethe averagesize (hydrodynamic radius) of assembled protein structures as a functionof ionic strength 2b. As pr38 However, only unassembled proteinsare observed between Ceru-min and GFP-min even with no added salt(Transmission electron microscopy (TEM) was further usedto directlyimage protein assemblies formed from oppositely charged GFP variants. ded salt2d. Thus,G0bind) between supercharged protein dimers and minimallymutated protein dimers. The assembled 16-mer is composed of four distinctprotein–protein interfaces:38 twointraplanar interfaces  the noninteractingsurface charges contribute stabilizing long-range electrostatic interactionswithin the assembled structure, or (2) the noninteracting surfacecharges are required to nucleate protomer formation. To test the validityof these hypotheses, atomistic MD simulations were performed to determinethe standard free energy of binding  has movedby at least 25 Å and the separation potential of mean force (PMF)has plateaued, indicating that the proteins are unbound and noninteracting, and the force required to pull the proteinsapart decreases. At separation distances larger than r*, the PMF is observed to remain nearly constant. Separation simulationswere performed under various conformational, orientational, and positionalconstraints using steered MD, and the contributions of the constraintsto ΔG0bind were exploredusing umbrella sampling and adaptive biasing force (ABF) methods (Supporting Information). In all cases, the separationPMF is found to be the largest contributor to ΔG0bind.MD simulations were performed using a previouslyreported methodto determine the absolute binding free energies using biased simulations1.48−53 Teracting3g–j.TheG0bind and separation PMFs for eight different protein dimersystems showseveral interesting trends. First, interfaces with more contacts inthe bound state have larger values of ΔG0bind and separation PMF . For example, “Ceru+32 Clockwise”, an intraplanarinterface with 8+ interprotein contacts, has the highest PMF at r* and the largest ΔG0bind . This is followed by the intraplanar interface “GFP-17 Clockwise”, interplanarInter-GFP-17 , and finally interplanar Inter-Ring . These results suggest that the intraplanarinterfaces dominate the free-energy of binding in the assembled 16-merstructure, and mutations that disrupt these interactions are expectedto inhibit supramolecular assembly.The values of ΔG0bind forthe intraplanar interfaces are significantlylarger than previously reported values for protein–proteininterfaces .54 This is consistent with the notionthat interactions between supercharged protein mutants arise due tostrong electrostatic interactions that are absent in parent proteins.However, ΔG0bind is alsoa function of the size of the interface,56 so equivalently large values of ΔG0bind are expected for larger endogenous protein–proteininterfaces. Nevertheless, the ΔG0bind values for interactions between minimally chargedproteins are consistently 20–30% smaller than those betweenthe fully charged proteins. MD simulations were further used to understandthe contribution of each constraint imposed on the proteins duringseparation to the calculated ΔG0bind values. Interestingly, we find that the equilibriumvalues for the conformational, positional, and orientational constraintsare similar  for the fully charged and minimallymutated systems . Therefore, these results suggest that the fullycharged and minimally charged protein variants preferentially adoptsimilar equilibrium bound configurations. Thus, the difference inΔG0bind between the fullycharged and minimally charged proteins is attributed to the absenceof long-range electrostatic interactions in the minimally mutatedvariants. Due to the logarithmic nature of free energy calculations(ΔGbind = −kbTlnKbind), small changes in ΔG0bind can have dramatic effects on the equilibrium binding constant Kbind. For example, the Kbind values for the fully charged “Ceru+32 Clockwise”interface is a factor of ∼1012 larger than thatof the minimally mutated protein interface, which suggests that long-rangeelectrostatic interactions significantly increase the probabilityof forming an interface and promoting assembly. Overall, these resultssuggest that identification of specific protein–protein contactsfrom high-resolution protein structures alone is insufficient to fullyunderstand the interactions between supercharged proteins.Our results show that thevalues of Δ57 At pH 7.4, the negatively charged GFP variants had nominal net chargesof −11, −17 (two variants: GFP-17 and GFP-17b), and−32, and the positively charged Ceru variants had nominal netcharges of +15 (two variants: Ceru+15r and Ceru+15a) and +32 (twovariants: Ceru+32o and Ceru+32b). For variants with the same net charge,different sets of mutations were used to generate different surfacecharge distributions. By varying the solution pH, the net chargeson the proteins (and surface charge distributions) were varied toproduce more negatively charged (lower pH) or positively charged (higherpH) monomeric proteins ,and proteins are expected to exist in monomeric, noninteracting states.For more highly negatively charged protein variants, larger ionicstrengths are required to induce disassembly. For example, the assemblybetween Ceru+32o and GFP-11 had a FRET efficiency = 0.5 at 110 mMNaCl, whereas the assembly between Ceru+32o and GFP-32 had a FRETefficiency = 0.5 at 350 mM NaCl. The FRET efficiencies between Ceru+15r,Ceru+15a, and Ceru+32b and each of the negatively charged GFP variantsat different NaCl concentrations and pH values are shown in Figures S6–S8, and the effect of pH onthe assembled structures for Ceru+32o/GFP-17 is shown in Figures S9 and S10.Z1Z2) between oppositely chargedproteins. To understand the role of net protein charge on assembly,we determined the critical salt concentration at which FRET efficiency= 0.5 (Table S5). The critical salt concentrationwas used to determine a corresponding Debye screening length κ–1:0 is vacuum permittivity,εw is the dielectric constant of water, kb is Boltzmann’s constant, T isabsolute temperature, e is the elementary charge,and ci and zi are the number densities and valencies of the electrolyte ions (hereNaCl). As shown in crit–1 isinversely related to the product of net charge on each protein (Z1Z2). Upon increasingCoulombic attraction between oppositely charged proteins, a highersalt concentration (and shorter Debye screening length) is requiredto disrupt assembly. A similar trend is also observed at pH 6 and9 for slightly different net charges  , suggesting the observed trend isgeneralizable to different solution compositions.Our results generally show that more highly chargedproteins robustlyassemble into supramolecular structures at higher ionic strengths,which is attributed to the larger Coulombic attraction . GST-40is a supercharged dimeric protein with a nominal net charge of −39at pH 7.4.36 The critical Debye screeninglengths for GFP-GST-40 and each positively charged Ceru variant areshown in Table S5. Although an inverse relationship between Debye lengthand Coulombic attraction is observed, the critical Debye lengths forthe fusion proteins are slightly larger than those predicted by thesimple electrostatic model, which suggests that electrostatic attractionsare more readily screened, possibly arising from electrostatic shieldingdue to the neutrally charged GFP.To assess the generality of the electricaldouble-layer relationship,FRET efficiencies were determined for mixtures of the positively chargedCeru variants and a fusion protein consisting of negatively superchargedglutathione S-transferase (GST-40) fused with neutrally charged GFP, and assembly is expected. Conversely, if the Debyelength is shorter than κcrit–1, then supercharged proteins are expectedto exist in noninteracting states. Overall, net charge provides asimple metric to predict whether supercharged GFP variants will interactand assemble in solution, but the precise phase diagram will changedepending on protein concentrations or ratio of positively to-negativelycharged protein.26We further used the electricaldouble-layer analysis to developan approximate phase diagram for supercharged assembly 4b. If thWe further explored how changing surface charge distribution (ata constant net charge) affects the assembly of proteins. Figure S13).38 Upon increasing salt concentration, the average diameter of thedominant assembled structures between GFP-17 and either Ceru+32o orCeru+32b was 10–12 nm, which is consistent with the aggregatesize previously observed between Ceru+32o and GFP-17, suggesting astable protomeric structure.38 On the otherhand, the dominant assembled structures between GFP-17b and eitherCeru+32o or Ceru+32b consisted of large aggregates (>1000 nm) forNaCl concentrations <400 mM. Interestingly, no intermediate-sizedprotomeric structures were observed for protein pairs involving GFP-17b,which only differs from GFP-17 in the distribution of surface charges.At high NaCl concentrations (>600 mM), the dominant structure insolutionfrom DLS matched the monomeric protein size for all protein combinations,indicating electrostatic-driven assembly was effectively screened.To understand the role of surface charge distributions,we studiedsupramolecular assembly of charged protein variants with differentsurface charge distributions using DLS, confocal microscopy, and negativestain TEM. n ≈ 2000) were consistent with prior reports  did not yield evidence of an ordered structure. We note that these dilution experimentswere only used to identify potential candidates for dynamic subunitexchange experiments, as described below. If proteins rapidly exchangewith nearby protein partners in solution ,64 then the dominant assembled structure is expected to depend on solutioncomposition and protein concentration. For assemblies between proteinswith relatively small net charges ,our results show that the FRET ratio decreased upon dilution, suggestingrapid dynamic subunit exchange in solution. However, for supramolecularassemblies consisting of proteins with larger net charges, the FRETratio did not significantly change upon dilution, suggesting slowdynamic exchange in solution.We next assessed the stabilityof supramolecular complexes by performing a series of dynamic subunitexchange measurements. First, the concentration dependence of supramolecularassemblies was assessed using dilution experiments to qualitativelyassess the kinetic stability protein assemblies. In these experiments,the assembled protein structures were diluted with buffered solution,and equilibrium FRET ratios were measured after ∼15 min  were observed to assemble withpositively charged Ceru variants with identical average sizes andshapes as determined by DLS and TEM imaging . Dynamic exchange experiments were then performed by addingnonfluorescent proteins to a solution containing preassembled structuresfrom oppositely supercharged fluorescent proteins, and changes inFRET were measured as the nonfluorescent analogues dynamically exchangedwith GFP in the supramolecular assembled structures (t = 0 min). The FRET ratio was notobserved to change over the time scale of the measurement when bufferwas added instead of GFP-17nf , suggesting that exchange of nonfluorescent GFP-17nf into the assembledstructure (rather than photobleaching) is responsible for observedchanges in fluorescence. In addition, the final FRET ratio at eachsalt concentration was measured by premixing GFP-17 and GFP-17nf beforetriggering assembly with Ceru+32o .To understand the kinetic stabilityof assembled protein structures that are relatively insensitive todilution, we performed a series of dynamic subunit exchange measurementsusing nonfluorescent analogues of the supercharged fluorescent proteins.Nonfluorescent analogues of the negatively charged GFP variants (containinga Gly-Gly-Gly construct in place of the chromophore) imaging S15. Dyna imaging S15. Dyna imaging S15. DynaFigure S18). Based on these results, wehypothesize that the initial rapid decrease in FRET ratio arises fromdisplacement of weakly associating proteins from the protomers, andthe slower decrease in FRET ratio arises from dynamic subunit exchangewithin the protomer. On the other hand, large aggregate forming assemblies showmuch slower change in normalized FRET ratio at all salt concentrationsmeasured .68 In this model, monomers dissociatefrom the protomer sequentially according to a unimolecular rate constant kd, which is assumed to be constant for all proteinsin the protomer. The probability of a protomer dissociating to yielda free fluorescent monomer of GFP-17 (G) or free nonfluorescent analogue(A) is determined by the composition of the assembled protein structure.In terms of association, monomeric GFP-17 (G) or nonfluorescent analogue(A) proteins form protomers with a bimolecular rate constant ka. Because of the strong binding energy betweenoppositely charged proteins, association reactions are assumed tobe fast, and dissociation reactions are rate limiting . Similar exchange kinetics were observedwhen different concentrations of nonfluorescent analogues are addedto solution, which supports the assumption that dissociation is ratelimiting . A detailed descriptionof the kinetic model is provided in Supporting Information.To quantitativelydescribe the kinetic stability experiments, we developed a simplekinetic model to understand the dynamic exchange of protein subunitsfor complexes between Ceru+32o/GFP-17 and Ceru+32b/GFP-17 .69 Here, kd was varied to directlycompare the simulated fraction of GFP-17 remaining in the protomerto the experimentally determined normalized FRET ratio. For protomerassembly between Ceru+32o and GFP-17 , ranging from 0.0004 s–1 to 0.003 s–1 at 25 mM and 150 mM NaCl, respectively. These values of kd suggest kinetic lifetimes ranging from 7 to40 min depending on the solution composition. For protomer assemblybetween Ceru+32b and GFP-17 .Results from the kinetic model are shownas solid lines in d GFP-17 6c, kd inncreases S21, rangncreases S21, rang70 which rangefrom seconds 71 todays .72 Fromthis view, assembly between oppositely supercharged proteins providesa mechanism to drive long-lasting association between two otherwisenoninteracting proteins. However, the stability of the assembled structurestrongly depends on the precise intermolecular interactions and solutionconditions. In addition, assembly between oppositely superchargedproteins can be used to generate extremely stable biomaterials withtransport-limited exchange leading to kinetic lifetimes >1 day.In general, the kinetic lifetimes for dynamic subunit exchangemeasurements of protomers are consistent with those observed in endogenousbiological protein complexes,G0bind are relatively large for both the minimallycharged and fully charged variants compared to naturally occurringprotein–protein interfaces.54 Unexpectedly,ΔG0bind for the minimallycharged protein variants are significantly smaller (∼30%) thanthose of the fully charged variants even though the interfaces retainall specific local attractions .Such differences in binding energy are attributed to long-range electrostaticinteractions between the fully charged variants. From this view, specificinterprotein interactions contribute to the bulk of the binding energybetween oppositely supercharged proteins, but noninteracting excesscharges are required to stabilize the assembled protein complexes.In this work, we study the assembly processof oppositely superchargedproteins using a combination of experiments and computational modeling.Our results highlight the role of surface charge distributions onthe supramolecular assembly process for oppositely supercharged proteins.Using minimally mutated variants of supercharged proteins (GFP-minand Ceru-min) that retain only the mutations ostensibly involved instabilizing the assemblies, we systematically explored the role noninteractingcharges play on assembly. Minimally charged variants were not observedto assemble into ordered hierarchical structures. Results from MDsimulations show that the values of Δ77 In particular, rational design methods for supercharged proteinsshould take into consideration long-range electrostatic interactionsaway from the interface for stabilizing protein complexes, which areknown to play a role in kinetic assembly and disassembly processesinvolving supramolecular protein complexes.Furthermore, our results suggest that identification of specificinterprotein interactions from high-resolution structures alone isinsufficient to fully describe the interactions and assembly processbetween oppositely supercharged proteins. Our results show that assemblyof supercharged proteins is governed by both these local attractionsas well as long-range electrostatic interactions. Therefore, thesefindings will be useful for informing the rational design of new hierarchicalstructures based on predictions of complementary surfaces.42 Importantly,our results show that proteins with similar net charges but differentsurface charge distributions give rise to different assembled structures.Surprisingly, the kinetic stabilities of these different supramolecularstructures were found to depend on surface charge distribution, suggestingthat assembled structures with different functional properties canbe formed from a common building block. Overall, our results showthat supercharging proteins provides an efficient method to createstable, long-lived protein assemblies while further highlighting therole of surface charge distribution and precise stabilizing interproteininteractions on the structure of assembled supercharged proteins.Our results elucidatehow net charge and average Coulombic attractioncan predict whether oppositely supercharged proteins will interactas a function of ionic strength conditions. We found that the supramolecularstructure strongly depends on the precise distribution of chargeson the proteins surface. Prior work has shown that different assembledstructures can be obtained from a common parent protein building blockby changing the supramolecular assembly strategy .


A number of examples of communities are shown for diverse proteins, including GPCRs. It is a tool that can immediately simplify and clarify the most essential functional moving parts of any given protein. Proteins usually can be subdivided into groups of residues that move as communities. These are usually densely packed local sub-structures, but in some cases can be physically distant residues identified to be within the same community. The set of these communities for each protein are the moving parts. The ways in which these are organized overall can aid in understanding many aspects of functional dynamics and allostery. DCI enables a more direct understanding of functions including enzyme activity, action across membranes and changes in the community structure from mutations or ligand binding. The DCI server is freely available on a web site (Bioinformatics online.  Since the first protein structure of myoglobin was determined, there has been a struggle to interpret protein structures in terms of their functions . Recent The approach taken is to identify the most rigid parts of a structure and how they move, i.e. the groups of amino acids that move in the most coherent ways, which are naturally the most rigid parts of a structure. This coarse-graining approach for interpreting protein structures significantly simplifies the understanding of dynamics, making the most important functional motions significantly clearer, and usually leads to a view of dynamics in terms of the most essential dynamics required for function. This is clearly an approximation that overlooks some local details of dynamics but is justified by the simpler comprehension of protein function provided. Usually this provides an essential view of how dynamics relates to function. The functional motions are then the changes in the relative positions and orientations among these communities with respect to one another. In this way the identification of the most coherent groups of amino acids enables the identification of the most important characteristic motions of any given protein. This is an approach that was first demonstrated by using the Gaussian elastic network model (GNM)  has furtElastic network model (ENM) have been widely implemented to study the characteristic motions of a protein . CorrelaThe aim of this article is to further demonstrate the utility of this approach and its ability to explain many important functional aspects of dynamics, including but not limited to, both for globular proteins, as well as for membrane proteins, where the communities are found to be quite extended in shape and spanning across the membrane. Another intention of the present work is to make the approach more accessible to a broad group of users across the many different categories of protein researchers.Protein structures were collected from the Protein Databank (PDB) . Protein) within a Cα cutoff distance of 7.0 s N is the total number of residues, s Elastic network models capture the characteristic dynamics of a protein. GNM, in particular, was constructed to study the scalar fluctuations of a molecular structures and it has been used to study motions (https://scikit-learn.org/stable/modules/generated/sklearn.cluster.AgglomerativeClustering.html) (nth (connect it with the cluster number) iteration of hierarchical clustering and the matrix Agglomerative hierarchical clustering (ng.html)  using WaH) score  applied α atoms of each residue within a distance cutoff of 15 ith eigenvector, the corresponding motion of protein is calculated as,x, y and z coordinate of the protein residues displaced along the direction of the ith eigenvector, x, y and z coordinate of the protein residues at initial state and ith eigenvector.The anisotropic network model  are the most studied and most diverse group of membrane bound proteins, which are an essential component of many cell signaling cascades. It regulates diverse signaling cascades across the membrane , which mGPCR proteins are one of the most frequently studied cases of allosteric signal transduction for drug design. Here we generated community arrangements of angiotensin II type 1 receptor GPCR protein bonded to the allosteric effectors TRV026 peptide and nanobody Nb.AT110i1_le. It has been shown that the synthetic nanobody Nb.AT110i1_le stabilizes the active state of AT1R  and Nb.ADynamic communities can be used to study the allosteric property in a protein  plays anA similar trend of dynamic allostery is observed in ATP synthase , where rproteins . This ty4β2 nicotinic receptor is an acetylcholine receptor, abundantly found in human brain, which comprised Human αnd 3α:2β . Alternand 3α:2β , indicatnd 3α:2β , also inNot only can DCI detect tightly packed and dynamically connected regions of a protein (domains), but it can also enable us to identify residues involved in hinges associated with protein open-closed transitions, find communities that directly communicate allosterically within proteins, and the conformational dynamics changes resulting from ligand binding as shown for hemoglobin. Protein functions are regulated by correlated motions among the residues. Therefore, the residue motion correlations, when combined with a data-driven clustering parameter estimation, enables DCI to detect the communities which are essential for a wide range of biological functions. Representations of protein dynamics as dynamic communities derived with DCI can help in the understanding the functionally important, strongly correlated protein motions and their functional relationships. And we have shown here that we are able to identify protein functional domains, detect cryptic pockets and aid in understanding allosteric relationships for a wide range of different types of proteins.btac159_Supplementary_DataClick here for additional data file.


Here, we carried out an The analysis was based on the structure of the spike protein from two SARS-CoV-2 variants, the original Wuhan and the Botswana (Omicron). The full-length genome sequences and protein sequences were obtained from databanks. The interaction of the spike proteins with the human Angiotensin Converting Enzyme 2 (ACE2) receptor was evaluated through the open-source software. The Immune Epitope Database was used to analyze the potential immune evasion of the viruses.Our data show that the Omicron spike protein resulted in 37 amino acid changes. The physicochemical properties of the spike had changed, and the electrostatic potentials differed between both variants. This resulted in a decrease in protein interactions, which does not establish a greater interaction with the ACE2 receptor. These changes compromise key receptor-binding motif residues in the SARS-CoV-2 spike protein that interact with neutralizing antibodies and ACE2.These mutations appear to confer enhanced properties of infectivity. The Omicron variant appears to be more effective at evading immune responses. The successive variants of SARS-CoV-2 that have appeared have posed a challenge for the scientific community, constituting a source of uncertainty for clinicians in charge of patient care and a challenge for public health preventive measures –3. The pOver recent months, the appearance of a new variant in South Africa has contributed to the further expansion of the virus worldwide, with the appearance of a new wave of cases, with obvious clinical consequences , 5. Thisin vitro neutralizing activity against Omicron -directed monoclonal antibodies lost  Omicron . The Omi Omicron , raising Omicron , 11.in-silico study analyzing the structures of the SARS-CoV-2 spike protein, the protein electrostatic potential, the rest of the mutations found in Omicron spike protein, as well as the potential immune evasion of the changes.Consequently, it seems necessary to clarify the role of the new Omicron variant in the interaction between the spike protein-ACE2 receptor and the immune evasion. Here, we hypothesize that the new conformation of the RBD in the spike of this variant does not back up what we know about its increased infectivity. To test the hypothesis, we carried out an https://www.gisaid.org/) and the protein sequence was obtained from the Research Collaboratory for Structural Bioinformatics Protein Data Bank . The translation of the peptide sequences from the nucleic acid sequences was estimated at the European Bioinformatics Institute's European Molecular Biology Laboratory using EMBOSS Transeq  here referred to as wild type (WT), and the first of the B.1.1.529 lineage detected in Botswana Omicron; . The ful Transeq . One-let Transeq .We used a multiple alignment of protein sequences software   arranginhttp://imed.med.ucm.es/Tools/SMS/ident_sim.html). From a group of aligned sequences (in FASTA or GDE format), this service calculates the identity and similarity of each sequence pair.In order to compare the similarity between proteins, we used the “Ident and Sim” service in the Sequence Manipulation Suite, provided by the Universidad Complutense de Madrid, Spain  to investigate the stability of formation of macromolecular complexes  and to give detailed analysis of the surfaces, interfaces and assemblies between proteins (2); ΔiG, which indicates the solvation free energy gain upon formation of the interface, in kcal/mol - the value is calculated as the difference in total solvation energies of isolated and interfacing structures. That is why the values of ΔiG can be so low and even 0 in the case of non-interface residues (inaccessible residues or solvent-accessible residues). Therefore, the positive solvation energy ΔiG of a residue contributes negatively to the solvation energy gain of the interface, which corresponds to the hydrophobic effect. A negative ΔiG corresponds to hydrophobic interfaces, or positive protein affinity. Solvation energy estimates in PISA do not include the effect of satisfied hydrogen bonds and salt bridges across the interface; HSD, which in the interface residues table indicates residues that contain the across-interface hydrogen bond, salt bridge or disulfide bond atoms. The corresponding table cells have a red background and contain letter H in case of hydrogen bond, S in case of salt bridge and D in case of disulfide bond or any combination of the above. A particular atom may be found from the Hydrogen Bond, Salt Bridge and Disulfide Bond Tables. The effect of hydrogen bonds , salt bridges  and disulphide bonds  is calculated separately; ASA, which in the interface residues table indicates the solvent-accessible surface area of the corresponding residue, in Å2; and finally, BSA, which in the interface residues table indicates the solvent-accessible surface area of the corresponding residue that is buried upon interface formation, in Å2. In this model, the buried area fraction is represented by a number of vertical bars that give a mnemonic representation showing bars which correspond to 10% of the total solvent-accessible surface area buried; iNat is the number of atoms of the interface; iNres is the number of residues of the interface.The interaction of the spike proteins with the human ACE2 receptor was calculated for the WT variant and the Omicron variants using the open-source software PDBePISA. This is a web based interactive tool made available by the PDBe  information on 3,337 different epitopes in the spike protein, filtering Organism equals to SARS-CoV-2 (ID: 2697049) and Antigen equals to spike glycoprotein . In the epitope table obtained from the Immune Epitope Database, we filtered those epitopes that affect the RBD of the spike, to keep the epitopes involved in the potential neutralization of the coronavirus - that is, those that really matter in immunization - from position 317–533 of the glycoprotein. After filtering these epitopes, we looked for the sequences that included any of the substitutions existing in the Omicron variant and plotted this information constructing Immunome Browser maps.In order to analyze the potential immune evasion of the viruses belonging to this lineage, we used the Immune Epitope Database (http://imed.med.ucm.es/Tools/SMS/ident_sim.html) calculates the identity and similarity of aligned sequences (in FASTA or GDE format). Identity and similarity values are used to assess whether or not two sequences share a common ancestor or function.The Idem and Sim tool  and salt bridges  across the interface, it results in B.1.1.529 RBD having 13 hydrogen bonds and 1 salt bridge making a total of −5.87 kcal/mol of solvation energy, while Wu-01 RBD has 14 hydrogen bonds and 1 salt bridge which make −6.31 kcal/mol of solvation energy. The solvation free energy gain upon formation of the interface of ACE2 and Wu-01 RBD adds a further −0.44 kcal/mol, and it therefore shows a better protein-protein affinity. and RDB , it is cin-silico study therefore show that mutations in the spike protein of the new variant of coronavirus do not establish a greater interaction with the ACE2 receptor compared to the primary lineage of the virus.In addition to the physicochemical properties detailed above, there are several crucial changes in RBD surface electrostatic potentials, with a greater polarity and relevant change of exposed charge (to positive) in the Omicron variant. These two factors confirm the decrease in protein interactions in the RBD site of the new variant, due to an electrostatic repulsive force, when facing polarities of the same sign. The results of the The distribution of hydrogen bonds and salt bridges of both variants is similar in structure and arrangement, as shown in A 3D modeling analysis can show the distributions of these new mutations between the RBD and the RBM, as shown in Applying the Ident and Sim tool to the RBDs of the SARS-CoV-2 variants under study and that of SARS-2005, we found, as expected, that if we calculate the identity between the three proteins, the proteins that share the greatest number of identical residues are higher among the variants of SARS-CoV-2. However, it was surprising to find that the homology of function measured by the similarity indicates that the RBD protein of the variant B.1.1.529 is closer to SARS-2005 than to the original Wu-01.Our study details the epitopes compromised by the substitutions in the variant under study and in the regions of interest in the interaction between these proteins. We have shown that mutations and deletions in the SARS-CoV-2 spike protein of the variant under study, offer greater structural instability of that spike and change the affinity with the ACE2 receptor downward. In addition, we suggest the existence of other key receptors in the increase of infectivity. That is, the participation of other receptors in the increase of infectivity and the loss of neutralization capacity of antibodies generated in response to other variants. Similarly, the present report informs about the SARS-CoV-2 lineage under study, which has 6 nucleotides inserted with respect to the reference sequence and a gap of 36 nucleotides with respect to the primary lineage. These substitutions do not confer to this variant a higher capacity for interaction between the spike protein of the virus and the human ACE2 receptor, suggesting that the greater infectivity confirmed in clinical data must also be supported by other receptors and by the fact that it compromises residues that change the physiochemical properties of the protein-to-protein ligands, between host cells and the lineage under study. Additionally, RBM is key in the spike protein of SARS-CoV-2 which interacts with neutralizing antibodies. These modifications confer an ability to evade already acquired immunity against the new coronavirus in this new variant under study.The first known confirmed B.1.1.529 infection was on November 9, 2021. This lineage is a clear example of the rapid molecular evolution of the new coronavirus, which has accumulated up to 60 mutations, 37 of which are located in the gene that encodes for the spike protein on the surface of the virus , Instituto de Salud Carlos III, Ministerio de Ciencia e Innovación.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.