Computational protein design quantifies structural constraints on amino acid covariation

Heterogeneity in winged helix-turn-helix and substrate DNA interactions: Insights from theory and experiments

Specific interactions between transcription factors (TFs) and substrate DNA constitute the fundamental basis of gene expression. Unlike in TFs like basic helix-loop-helix or basic leucine zippers, prediction of substrate DNA is extremely challenging for helix-turn-helix (HTH). Experimental techniques like chromatin immunoprecipitation combined with massively parallel DNA sequencing remains a viable option. We characterize the molecular basis of heterogeneity in HTH-DNA interaction using in silico tools and thence validate them experimentally. Given the profound functional diversity in HTH, we focus primarily on winged-HTH (wHTH). We consider 180 wHTH TFs, whose experimental three-dimensional structures are available in DNA bound/unbound conformations. Starting with PDB-wide scanning and curation of data, we construct a phylogenetic tree, which distributes 180 wHTH sequences under multiple sub-groups. Structure-sequence alignment followed by detailed intra/intergroup analysis, covariation studies and extensive network theory analysis help us to gain deep insight into heterogeneous wHTH-substrate DNA interactions. A central aim of this study is to find a consensus to predict the substrate DNA sequence for wHTH, amidst heterogeneity. The strength of our exhaustive theoretical investigations including molecular docking are successfully tested through experimental characterization of wHTH TF from Sulfurimonas denitrificans.

PDBench: evaluating computational methods for protein-sequence design

SUMMARY

Ever increasing amounts of protein structure data, combined with advances in machine learning, have led to the rapid proliferation of methods available for protein-sequence design. In order to utilize a design method effectively, it is important to understand the nuances of its performance and how it varies by design target. Here, we present PDBench, a set of proteins and a number of standard tests for assessing the performance of sequence-design methods. PDBench aims to maximize the structural diversity of the benchmark, compared with previous benchmarking sets, in order to provide useful biological insight into the behaviour of sequence-design methods, which is essential for evaluating their performance and practical utility. We believe that these tools are useful for guiding the development of novel sequence design algorithms and will enable users to choose a method that best suits their design target.

AVAILABILITY AND IMPLEMENTATION

https://github.com/wells-wood-research/PDBench.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

State-of-the-Art Estimation of Protein Model Accuracy Using AlphaFold

The problem of predicting a protein's 3D structure from its primary amino acid sequence is a longstanding challenge in structural biology. Recently, approaches like alphafold have achieved remarkable performance on this task by combining deep learning techniques with coevolutionary data from multiple sequence alignments of related protein sequences. The use of coevolutionary information is critical to these models' accuracy, and without it their predictive performance drops considerably. In living cells, however, the 3D structure of a protein is fully determined by its primary sequence and the biophysical laws that cause it to fold into a low-energy configuration. Thus, it should be possible to predict a protein's structure from only its primary sequence by learning an approximate biophysical energy function. We provide evidence that alphafold has learned such an energy function, and uses coevolution data to solve the global search problem of finding a low-energy conformation. We demonstrate that alphafold'slearned energy function can be used to rank the quality of candidate protein structures with state-of-the-art accuracy, without using any coevolution data. Finally, we explore several applications of this energy function, including the prediction of protein structures without multiple sequence alignments.

Key aspects of the past 30 years of protein design

Proteins are the workhorse of life. They are the building infrastructure of living systems; they are the most efficient molecular machines known, and their enzymatic activity is still unmatched in versatility by any artificial system. Perhaps proteins' most remarkable feature is their modularity. The large amount of information required to specify each protein's function is analogically encoded with an alphabet of just ∼20 letters. The protein folding problem is how to encode all such information in a sequence of 20 letters. In this review, we go through the last 30 years of research to summarize the state of the art and highlight some applications related to fundamental problems of protein evolution.

Guaranteed Diversity and Optimality in Cost Function Network Based Computational Protein Design Methods

Proteins are the main active molecules of life. Although natural proteins play many roles, as enzymes or antibodies for example, there is a need to go beyond the repertoire of natural proteins to produce engineered proteins that precisely meet application requirements, in terms of function, stability, activity or other protein capacities. Computational Protein Design aims at designing new proteins from first principles, using full-atom molecular models. However, the size and complexity of proteins require approximations to make them amenable to energetic optimization queries. These approximations make the design process less reliable, and a provable optimal solution may fail. In practice, expensive libraries of solutions are therefore generated and tested. In this paper, we explore the idea of generating libraries of provably diverse low-energy solutions by extending cost function network algorithms with dedicated automaton-based diversity constraints on a large set of realistic full protein redesign problems. We observe that it is possible to generate provably diverse libraries in reasonable time and that the produced libraries do enhance the Native Sequence Recovery, a traditional measure of design methods reliability.

DE-STRESS: a user-friendly web application for the evaluation of protein designs

De novo protein design is a rapidly growing field, and there are now many interesting and useful examples of designed proteins in the literature. However, most designs could be classed as failures when characterised in the lab, usually as a result of low expression, misfolding, aggregation or lack of function. This high attrition rate makes protein design unreliable and costly. It is possible that some of these failures could be caught earlier in the design process if it were quick and easy to generate information and a set of high-quality metrics regarding designs, which could be used to make reproducible and data-driven decisions about which designs to characterise experimentally. We present DE-STRESS (DEsigned STRucture Evaluation ServiceS), a web application for evaluating structural models of designed and engineered proteins. DE-STRESS has been designed to be simple, intuitive to use and responsive. It provides a wealth of information regarding designs, as well as tools to help contextualise the results and formally describe the properties that a design requires to be fit for purpose.

Structural Basis of Design and Engineering for Advanced Plant Optogenetics

In optogenetics, light-sensitive proteins are specifically expressed in target cells and light is used to precisely control the activity of these proteins at high spatiotemporal resolution. Optogenetics initially used naturally occurring photoreceptors to control neural circuits, but has expanded to include carefully designed and engineered photoreceptors. Several optogenetic constructs are based on plant photoreceptors, but their application to plant systems has been limited. Here, we present perspectives on the development of plant optogenetics, considering different levels of design complexity. We discuss how general principles of light-driven signal transduction can be coupled with approaches for engineering protein folding to develop novel optogenetic tools. Finally, we explore how the use of computation, networks, circular permutation, and directed evolution could enrich optogenetics.

Comparison of Rosetta flexible-backbone computational protein design methods on binding interactions

Computational design of binding sites in proteins remains difficult, in part due to limitations in our current ability to sample backbone conformations that enable precise and accurate geometric positioning of side chains during sequence design. Here we present a benchmark framework for comparison between flexible-backbone design methods applied to binding interactions. We quantify the ability of different flexible backbone design methods in the widely used protein design software Rosetta to recapitulate observed protein sequence profiles assumed to represent functional protein/protein and protein/small molecule binding interactions. The CoupledMoves method, which combines backbone flexibility and sequence exploration into a single acceptance step during the sampling trajectory, better recapitulates observed sequence profiles than the BackrubEnsemble and FastDesign methods, which separate backbone flexibility and sequence design into separate acceptance steps during the sampling trajectory. Flexible-backbone design with the CoupledMoves method is a powerful strategy for reducing sequence space to generate targeted libraries for experimental screening and selection.

Combining Rosetta with molecular dynamics (MD): A benchmark of the MD-based ensemble protein design

Computational protein design is a set of procedures for computing amino acid sequences that will fold into a specified structure. Rosetta Design, a commonly used software for protein design, allows for the effective identification of sequences compatible with a given backbone structure, while molecular dynamics (MD) simulations can thoroughly sample near-native conformations. We benchmarked a procedure in which Rosetta design is started on MD-derived structural ensembles and showed that such a combined approach generates 20-30% more diverse sequences than currently available methods with only a slight increase in computation time. Importantly, the increase in diversity is achieved without a loss in the quality of the designed sequences assessed by their resemblance to natural sequences. We demonstrate that the MD-based procedure is also applicable to de novo design tasks started from backbone structures without any sequence information. In addition, we implemented a protocol that can be used to assess the stability of designed models and to select the best candidates for experimental validation. In sum our results demonstrate that the MD ensemble-based flexible backbone design can be a viable method for protein design, especially for tasks that require a large pool of diverse sequences.

Beyond Thermodynamic Constraints: Evolutionary Sampling Generates Realistic Protein Sequence Variation

Biological evolution generates a surprising amount of site-specific variability in protein sequences. Yet, attempts at modeling this process have been only moderately successful, and current models based on protein structural metrics explain, at best, 60% of the observed variation. Surprisingly, simple measures of protein structure, such as solvent accessibility, are often better predictors of site-specific variability than more complex models employing all-atom energy functions and detailed structural modeling. We suggest here that these more complex models perform poorly because they lack consideration of the evolutionary process, which is, in part, captured by the simpler metrics. We compare protein sequences that are computationally designed to sequences that are computationally evolved using the same protein-design energy function and to homologous natural sequences. We find that, by a wide variety of metrics, evolved sequences are much more similar to natural sequences than are designed sequences. In particular, designed sequences are too conserved on the protein surface relative to natural sequences, whereas evolved sequences are not. Our results suggest that evolutionary simulation produces a realistic sampling of sequence space. By contrast, protein design-at least as currently implemented-does not. Existing energy functions seem to be sufficiently accurate to correctly describe the key thermodynamic constraints acting on protein sequences, but they need to be paired with realistic sampling schemes to generate realistic sequence alignments.

Biophysical Models of Protein Evolution: Understanding the Patterns of Evolutionary Sequence Divergence

For decades, rates of protein evolution have been interpreted in terms of the vague concept of functional importance. Slowly evolving proteins or sites within proteins were assumed to be more functionally important and thus subject to stronger selection pressure. More recently, biophysical models of protein evolution, which combine evolutionary theory with protein biophysics, have completely revolutionized our view of the forces that shape sequence divergence. Slowly evolving proteins have been found to evolve slowly because of selection against toxic misfolding and misinteractions, linking their rate of evolution primarily to their abundance. Similarly, most slowly evolving sites in proteins are not directly involved in function, but mutating these sites has a large impact on protein structure and stability. In this article, we review the studies in the emerging field of biophysical protein evolution that have shaped our current understanding of sequence divergence patterns. We also propose future research directions to develop this nascent field.

An Evolution-Based Approach to De Novo Protein Design

EvoDesign is a computational algorithm that allows the rapid creation of new protein sequences that are compatible with specific protein structures. As such, it can be used to optimize protein stability, to resculpt the protein surface to eliminate undesired protein-protein interactions, and to optimize protein-protein binding. A major distinguishing feature of EvoDesign in comparison to other protein design programs is the use of evolutionary information in the design process to guide the sequence search toward native-like sequences known to adopt structurally similar folds as the target. The observed frequencies of amino acids in specific positions in the structure in the form of structural profiles collected from proteins with similar folds and complexes with similar interfaces can implicitly capture many subtle effects that are essential for correct folding and protein-binding interactions. As a result of the inclusion of evolutionary information, the sequences designed by EvoDesign have native-like folding and binding properties not seen by other physics-based design methods. In this chapter, we describe how EvoDesign can be used to redesign proteins with a focus on the computational and experimental procedures that can be used to validate the designs.

Flexible Backbone Methods for Predicting and Designing Peptide Specificity

Protein-protein interactions play critical roles in essentially every cellular process. These interactions are often mediated by protein interaction domains that enable proteins to recognize their interaction partners, often by binding to short peptide motifs. For example, PDZ domains, which are among the most common protein interaction domains in the human proteome, recognize specific linear peptide sequences that are often at the C-terminus of other proteins. Determining the set of peptide sequences that a protein interaction domain binds, or it's "peptide specificity," is crucial for understanding its cellular function, and predicting how mutations impact peptide specificity is important for elucidating the mechanisms underlying human diseases. Moreover, engineering novel cellular functions for synthetic biology applications, such as the biosynthesis of biofuels or drugs, requires the design of protein interaction specificity to avoid crosstalk with native metabolic and signaling pathways. The ability to accurately predict and design protein-peptide interaction specificity is therefore critical for understanding and engineering biological function. One approach that has recently been employed toward accomplishing this goal is computational protein design. This chapter provides an overview of recent methodological advances in computational protein design and highlights examples of how these advances can enable increased accuracy in predicting and designing peptide specificity.

Computational Redesign of Thioredoxin Is Hypersensitive toward Minor Conformational Changes in the Backbone Template

Despite the development of powerful computational tools, the full-sequence design of proteins still remains a challenging task. To investigate the limits and capabilities of computational tools, we conducted a study of the ability of the program Rosetta to predict sequences that recreate the authentic fold of thioredoxin. Focusing on the influence of conformational details in the template structures, we based our study on 8 experimentally determined template structures and generated 120 designs from each. For experimental evaluation, we chose six sequences from each of the eight templates by objective criteria. The 48 selected sequences were evaluated based on their progressive ability to (1) produce soluble protein in Escherichia coli and (2) yield stable monomeric protein, and (3) on the ability of the stable, soluble proteins to adopt the target fold. Of the 48 designs, we were able to synthesize 32, 20 of which resulted in soluble protein. Of these, only two were sufficiently stable to be purified. An X-ray crystal structure was solved for one of the designs, revealing a close resemblance to the target structure. We found a significant difference among the eight template structures to realize the above three criteria despite their high structural similarity. Thus, in order to improve the success rate of computational full-sequence design methods, we recommend that multiple template structures are used. Furthermore, this study shows that special care should be taken when optimizing the geometry of a structure prior to computational design when using a method that is based on rigid conformations.

Intermediate divergence levels maximize the strength of structure-sequence correlations in enzymes and viral proteins

Structural properties such as solvent accessibility and contact number predict site-specific sequence variability in many proteins. However, the strength and significance of these structure-sequence relationships vary widely among different proteins, with absolute correlation strengths ranging from 0 to 0.8. In particular, two recent works have made contradictory observations. Yeh et al. (Mol. Biol. Evol. 31:135-139, 2014) found that both relative solvent accessibility (RSA) and weighted contact number (WCN) are good predictors of sitewise evolutionary rate in enzymes, with WCN clearly out-performing RSA. Shahmoradi et al. (J. Mol. Evol. 79:130-142, 2014) considered these same predictors (as well as others) in viral proteins and found much weaker correlations and no clear advantage of WCN over RSA. Because these two studies had substantial methodological differences, however, a direct comparison of their results is not possible. Here, we reanalyze the datasets of the two studies with one uniform analysis pipeline, and we find that many apparent discrepancies between the two analyses can be attributed to the extent of sequence divergence in individual alignments. Specifically, the alignments of the enzyme dataset are much more diverged than those of the virus dataset, and proteins with higher divergence exhibit, on average, stronger structure-sequence correlations. However, the highest structure-sequence correlations are observed at intermediate divergence levels, where both highly conserved and highly variable sites are present in the same alignment.

The Gearbox of the Bacterial Flagellar Motor Switch

Switching of flagellar motor rotation sense dictates bacterial chemotaxis. Multi-subunit FliM-FliG rotor rings couple signal protein binding in FliM with reversal of a distant FliG C-terminal (FliG_C) helix involved in stator contacts. Subunit dynamics were examined in conformer ensembles generated by molecular simulations from the X-ray structures. Principal component analysis extracted collective motions. Interfacial loop immobilization by complex formation coupled elastic fluctuations of the FliM middle (FliM_M) and FliG middle (FliG_M) domains. Coevolved mutations captured interfacial dynamics as well as contacts. FliG_M rotation was amplified via two central hinges to the FliG_C helix. Intrinsic flexibility, reported by the FliG_MC ensembles, reconciled conformers with opposite FliG_C helix orientations. FliG domain stacking deformed the inter-domain linker and reduced flexibility; but conformational changes were not triggered by engineered linker deletions that cause a rotation-locked phenotype. These facts suggest that binary rotation states arise from conformational selection by stacking interactions.

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Switch complex exploits differential subunit stiffness for mechanical amplification

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Distinct rotor protein X-ray structures generate overlapping conformer ensembles

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Stacking constraints on a flexible helix linker could select diverse rotation states

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Non-contact elastic couplings at the subunit interface in the complex have coevolved

Using natural sequences and modularity to design common and novel protein topologies

Protein design is still a challenging undertaking, often requiring multiple attempts or iterations for success. Typically, the source of failure is unclear, and scoring metrics appear similar between successful and failed cases. Nevertheless, the use of sequence statistics, modularity and symmetry from natural proteins, combined with computational design both at the coarse-grained and atomistic levels is propelling a new wave of design efforts to success. Here we highlight recent examples of design, showing how the wealth of natural protein sequence and topology data may be leveraged to reduce the search space and increase the likelihood of achieving desired outcomes.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

Causes of evolutionary rate variation among protein sites

It has long been recognized that certain sites within a protein, such as sites in the protein core or catalytic residues in enzymes, are evolutionarily more conserved than other sites. However, our understanding of rate variation among sites remains surprisingly limited. Recent progress to address this includes the development of a wide array of reliable methods to estimate site-specific substitution rates from sequence alignments. In addition, several molecular traits have been identified that correlate with site-specific mutation rates, and novel mechanistic biophysical models have been proposed to explain the observed correlations. Nonetheless, current models explain, at best, approximately 60% of the observed variance, highlighting the limitations of current methods and models and the need for new research directions.

Liquid-theory analogy of direct-coupling analysis of multiple-sequence alignment and its implications for protein structure prediction

The direct-coupling analysis is a powerful method for protein contact prediction, and enables us to extract “direct” correlations between distant sites that are latent in “indirect” correlations observed in a protein multiple-sequence alignment. I show that the direct correlation can be obtained by using a formulation analogous to the Ornstein-Zernike integral equation in liquid theory. This formulation intuitively illustrates how the indirect or apparent correlation arises from an infinite series of direct correlations, and provides interesting insights into protein structure prediction.

Coupling Protein Side-Chain and Backbone Flexibility Improves the Re-design of Protein-Ligand Specificity

Interactions between small molecules and proteins play critical roles in regulating and facilitating diverse biological functions, yet our ability to accurately re-engineer the specificity of these interactions using computational approaches has been limited. One main difficulty, in addition to inaccuracies in energy functions, is the exquisite sensitivity of protein–ligand interactions to subtle conformational changes, coupled with the computational problem of sampling the large conformational search space of degrees of freedom of ligands, amino acid side chains, and the protein backbone. Here, we describe two benchmarks for evaluating the accuracy of computational approaches for re-engineering protein-ligand interactions: (i) prediction of enzyme specificity altering mutations and (ii) prediction of sequence tolerance in ligand binding sites. After finding that current state-of-the-art “fixed backbone” design methods perform poorly on these tests, we develop a new “coupled moves” design method in the program Rosetta that couples changes to protein sequence with alterations in both protein side-chain and protein backbone conformations, and allows for changes in ligand rigid-body and torsion degrees of freedom. We show significantly increased accuracy in both predicting ligand specificity altering mutations and binding site sequences. These methodological improvements should be useful for many applications of protein – ligand design. The approach also provides insights into the role of subtle conformational adjustments that enable functional changes not only in engineering applications but also in natural protein evolution.

Designing new protein–ligand interactions has tremendous potential for engineering sensitive biosensors for diagnostics or new enzymes useful in biotechnology, but these applications are extremely challenging, both because of inaccuracies of the energy functions used in modeling and design, and because protein active and binding sites are highly sensitive to subtle changes in structure. Here we describe a new method that addresses the second problem and couples changes in the structure of the protein backbone and of the amino acid side chains, the amino acid sequence, and the conformation of the ligand and its orientation in the binding site. We show that our method improvements significantly increase the accuracy of designing protein–ligand interactions compared to current state-of-the-art design methods. We assess these improvements in two important tests: the first predicts mutations that change ligand-binding preferences in enzymes, and the second predicts protein sequences that bind a given ligand. In these tests, subtle conformational changes made in our model are essential to recapitulate both the results from engineering experiments and the sequence diversity occurring in natural protein families. These results therefore shed light on the mechanisms of how new protein functions might have emerged and can be engineered in the laboratory.

A Web Resource for Standardized Benchmark Datasets, Metrics, and Rosetta Protocols for Macromolecular Modeling and Design

The development and validation of computational macromolecular modeling and design methods depend on suitable benchmark datasets and informative metrics for comparing protocols. In addition, if a method is intended to be adopted broadly in diverse biological applications, there needs to be information on appropriate parameters for each protocol, as well as metrics describing the expected accuracy compared to experimental data. In certain disciplines, there exist established benchmarks and public resources where experts in a particular methodology are encouraged to supply their most efficient implementation of each particular benchmark. We aim to provide such a resource for protocols in macromolecular modeling and design. We present a freely accessible web resource (https://kortemmelab.ucsf.edu/benchmarks) to guide the development of protocols for protein modeling and design. The site provides benchmark datasets and metrics to compare the performance of a variety of modeling protocols using different computational sampling methods and energy functions, providing a "best practice" set of parameters for each method. Each benchmark has an associated downloadable benchmark capture archive containing the input files, analysis scripts, and tutorials for running the benchmark. The captures may be run with any suitable modeling method; we supply command lines for running the benchmarks using the Rosetta software suite. We have compiled initial benchmarks for the resource spanning three key areas: prediction of energetic effects of mutations, protein design, and protein structure prediction, each with associated state-of-the-art modeling protocols. With the help of the wider macromolecular modeling community, we hope to expand the variety of benchmarks included on the website and continue to evaluate new iterations of current methods as they become available.

Predicting evolutionary site variability from structure in viral proteins: buriedness, packing, flexibility, and design

Several recent works have shown that protein structure can predict site-specific evolutionary sequence variation. In particular, sites that are buried and/or have many contacts with other sites in a structure have been shown to evolve more slowly, on average, than surface sites with few contacts. Here, we present a comprehensive study of the extent to which numerous structural properties can predict sequence variation. The quantities we considered include buriedness (as measured by relative solvent accessibility), packing density (as measured by contact number), structural flexibility (as measured by B factors, root-mean-square fluctuations, and variation in dihedral angles), and variability in designed structures. We obtained structural flexibility measures both from molecular dynamics simulations performed on nine non-homologous viral protein structures and from variation in homologous variants of those proteins, where they were available. We obtained measures of variability in designed structures from flexible-backbone design in the Rosetta software. We found that most of the structural properties correlate with site variation in the majority of structures, though the correlations are generally weak (correlation coefficients of 0.1-0.4). Moreover, we found that buriedness and packing density were better predictors of evolutionary variation than structural flexibility. Finally, variability in designed structures was a weaker predictor of evolutionary variability than buriedness or packing density, but it was comparable in its predictive power to the best structural flexibility measures. We conclude that simple measures of buriedness and packing density are better predictors of evolutionary variation than the more complicated predictors obtained from dynamic simulations, ensembles of homologous structures, or computational protein design.

Coevolutionary information, protein folding landscapes, and the thermodynamics of natural selection

The energy landscape used by nature over evolutionary timescales to select protein sequences is essentially the same as the one that folds these sequences into functioning proteins, sometimes in microseconds. We show that genomic data, physical coarse-grained free energy functions, and family-specific information theoretic models can be combined to give consistent estimates of energy landscape characteristics of natural proteins. One such characteristic is the effective temperature T(sel) at which these foldable sequences have been selected in sequence space by evolution. T(sel) quantifies the importance of folded-state energetics and structural specificity for molecular evolution. Across all protein families studied, our estimates for T(sel) are well below the experimental folding temperatures, indicating that the energy landscapes of natural foldable proteins are strongly funneled toward the native state.

Multidimensional mutual information methods for the analysis of covariation in multiple sequence alignments

Background

Several methods are available for the detection of covarying positions from a multiple sequence alignment (MSA). If the MSA contains a large number of sequences, information about the proximities between residues derived from covariation maps can be sufficient to predict a protein fold. However, in many cases the structure is already known, and information on the covarying positions can be valuable to understand the protein mechanism and dynamic properties.

Results

In this study we have sought to determine whether a multivariate (multidimensional) extension of traditional mutual information (MI) can be an additional tool to study covariation. The performance of two multidimensional MI (mdMI) methods, designed to remove the effect of ternary/quaternary interdependencies, was tested with a set of 9 MSAs each containing <400 sequences, and was shown to be comparable to that of the newest methods based on maximum entropy/pseudolikelyhood statistical models of protein sequences. However, while all the methods tested detected a similar number of covarying pairs among the residues separated by < 8 Å in the reference X-ray structures, there was on average less than 65% overlap between the top scoring pairs detected by methods that are based on different principles.

Conclusions

Given the large variety of structure and evolutionary history of different proteins it is possible that a single best method to detect covariation in all proteins does not exist, and that for each protein family the best information can be derived by merging/comparing results obtained with different methods. This approach may be particularly valuable in those cases in which the size of the MSA is small or the quality of the alignment is low, leading to significant differences in the pairs detected by different methods.

Amino-acid site variability among natural and designed proteins

Computational protein design attempts to create protein sequences that fold stably into pre-specified structures. Here we compare alignments of designed proteins to alignments of natural proteins and assess how closely designed sequences recapitulate patterns of sequence variation found in natural protein sequences. We design proteins using RosettaDesign, and we evaluate both fixed-backbone designs and variable-backbone designs with different amounts of backbone flexibility. We find that proteins designed with a fixed backbone tend to underestimate the amount of site variability observed in natural proteins while proteins designed with an intermediate amount of backbone flexibility result in more realistic site variability. Further, the correlation between solvent exposure and site variability in designed proteins is lower than that in natural proteins. This finding suggests that site variability is too uniform across different solvent exposure states (i.e., buried residues are too variable or exposed residues too conserved). When comparing the amino acid frequencies in the designed proteins with those in natural proteins we find that in the designed proteins hydrophobic residues are underrepresented in the core. From these results we conclude that intermediate backbone flexibility during design results in more accurate protein design and that either scoring functions or backbone sampling methods require further improvement to accurately replicate structural constraints on site variability.