Super folds,networks, and barriers

Exhaustive enumeration of sequences and folds is conducted for a simple lattice model of conformations, sequences, and energies. Examination of all foldable sequences and their nearest connected neighbors (sequences that differ by no more than a point mutation) illustrates the following: (i) There exist unusually large number of sequences that fold into a few structures (super‐folds). The same observation was made experimentally and computationally using stochastic sampling and exhaustive enumeration of related models. (ii) There exist only a few large networks of connected sequences that are not restricted to one fold. These networks cover a significant fraction of fold spaces (super‐networks). (iii) There exist barriers in sequence space that prevent foldable sequences of the same structure to “connect” through a series of single point mutations (super‐barrier), even in the presence of the sequence connection between folds. While there is ample experimental evidence for the existence of super‐folds, evidence for a super‐network is just starting to emerge. The prediction of a sequence barrier is an intriguing characteristic of sequence space, suggesting that the overall sequence space may be disconnected. The implications and limitations of these observations for evolution of protein structures are discussed. Proteins 2012. © 2011 Wiley Periodicals, Inc.     

Relationship between energy distribution and fold stability: Insights from molecular dynamics simulations of native and mutant proteins

Most proteins must fold to a well-defined structure with a minimal stability to perform their function. Here we use a simple, molecular dynamics-based, energy decomposition approach to map the principal energetic interactions in a set of proteins representative of different folds. This work involves the all-atom simulation and analysis of the native structures and mutants of five different proteins representative of an all-alpha (yACPB, Protein A), all-beta (SH3), and a mixed alpha/beta fold (Proteins G and L). Given a certain structure, a native sequence and a set of mutants, we show that our model discriminates the ability of a mutation to yield a more or less stable protein, in agreement with experimental data, catching the principal energetic determinants of protein stabilization. Our approach identifies the interaction determinants responsible to define a fold and shows that mutations can either modulate the strength of pair-wise coupling between residues important for folding, or modify the profile of the principal interactions. Furthermore, we address the question of how to evaluate the fitness of a sequence to a given structure by comparing the information contained in the energy map, which recapitulates the chemistry of the sequence, to that contained in the contact map, which recapitulates the fold topology. The results show that the better fit between the energetic properties of the sequence and the fold topology corresponds to a higher stabilization of the protein. We discuss the relevance of these observations to the analysis of protein designability and to the rational evolution of new sequences.     

Folding mechanisms of proteins with high sequence identity but different folds

The problem of how a protein folds from a linear chain of amino acids to the three-dimensional structure necessary for function is often investigated using proteins with a low degree of sequence identity that adopt different folds. The design of pairs of proteins with a high degree of sequence identity but different folds offers the opportunity for a complementary study; in two highly similar sequences, which residues are the most important in directing folding to a particular structure? Here we use molecular dynamics simulations to characterize the folding-unfolding pathways of a pair of proteins designed by Bryan and co-workers [Alexander, P. A., et al. (2005) Biochemistry 44, 14045-14054; He, Y. N., et al. (2005) Biochemistry 44, 14055-14061]. Despite being 59% identical, the two protein sequences fold to two different structures. The first sequence folds to the alpha+beta protein G structure and the second to the all-alpha-helical protein A structure. We show that the final protein structure is determined early along the folding pathway. In folding to the protein G structure, the single alpha-helix (alpha1) and the beta3-beta4 turn fold early. Formation of the hairpin turn essentially prevents folding to helical structure in this region of the protein. This early structure is then consolidated by formation of long-range hydrophobic interactions between alpha1 and the beta3-beta4 turn. The protein A sequence differs both in the residues that form the beta3-beta4 turn and also in many of the residues that form the early hydrophobic interactions in the protein G structure. Instead, in the protein A sequence, a more hierarchical mechanism is observed, with helices folding before many of the tertiary interactions are formed. We find that small, but critical, sequence differences determine the topology of the protein early along the folding pathway, which help to explain the process by which one fold can evolve into another.     

Direct prediction of profiles of sequences compatible with a protein structure by neural networks with fragment‐based local and energy‐based nonlocal profiles

Locating sequences compatible with a protein structural fold is the well‐known inverse protein‐folding problem. While significant progress has been made, the success rate of protein design remains low. As a result, a library of designed sequences or profile of sequences is currently employed for guiding experimental screening or directed evolution. Sequence profiles can be computationally predicted by iterative mutations of a random sequence to produce energy‐optimized sequences, or by combining sequences of structurally similar fragments in a template library. The latter approach is computationally more efficient but yields less accurate profiles than the former because of lacking tertiary structural information. Here we present a method called SPIN that predicts Sequence Profiles by Integrated Neural network based on fragment‐derived sequence profiles and structure‐derived energy profiles. SPIN improves over the fragment‐derived profile by 6.7% (from 23.6 to 30.3%) in sequence identity between predicted and wild‐type sequences. The method also reduces the number of residues in low complex regions by 15.7% and has a significantly better balance of hydrophilic and hydrophobic residues at protein surface. The accuracy of sequence profiles obtained is comparable to those generated from the protein design program RosettaDesign 3.5. This highly efficient method for predicting sequence profiles from structures will be useful as a single‐body scoring term for improving scoring functions used in protein design and fold recognition. It also complements protein design programs in guiding experimental design of the sequence library for screening and directed evolution of designed sequences. The SPIN server is available at http://sparks‐lab.org . Proteins 2014; 82:2565–2573. © 2014 Wiley Periodicals, Inc.     

The role of negative selection in protein evolution revealed through the energetics of the native state ensemble

Knowing the determinants of conformational specificity is essential for understanding protein structure, stability, and fold evolution. To address this issue, a novel statistical measure of energetic compatibility between sequence and structure was developed using an experimentally validated model of the energetics of the native state ensemble. This approach successfully matched sequences from a diverse subset of the human proteome to their respective folds. Unexpectedly, significant energetic compatibility between ostensibly unrelated sequences and structures was also observed. Interrogation of these matches revealed a general framework for understanding the origins of conformational specificity within a proteome: specificity is a complex function of both the ability of a sequence to adopt folds other than the native, and ability of a fold to accommodate sequences other than the native. The regional variation in energetic compatibility indicates that the compatibility is dominated by incompatibility of sequence for alternative fold segments, suggesting that evolution of protein sequences has involved substantial negative selection, with certain segments serving as “gatekeepers” that presumably prevent alternative structures. Beyond these global trends, a size dependence exists in the degree to which the energetic compatibility is determined from negative selection, with smaller proteins displaying more negative selection. This partially explains how short sequences can adopt unique folds, despite the higher probability in shorter proteins for small numbers of mutations to increase compatibility with other folds. In providing evolutionary ground rules for the thermodynamic relationship between sequence and fold, this framework imparts valuable insight for rational design of unique folds or fold switches. Proteins 2016; 84:435–447. © 2016 Wiley Periodicals, Inc.     

Sequence and structure classification of kinases

Kinases are a ubiquitous group of enzymes that catalyze the phosphoryl transfer reaction from a phosphate donor (usually ATP) to a receptor substrate. Although all kinases catalyze essentially the same phosphoryl transfer reaction, they display remarkable diversity in their substrate specificity, structure, and the pathways in which they participate. In order to learn the relationship between structural fold and functional specificities in kinases, we have done a comprehensive survey of all available kinase sequences (>17,000) and classified them into 30 distinct families based on sequence similarities. Of these families, 19, covering nearly 98% of all sequences, fall into seven general structural folds for which three-dimensional structures are known. These fold groups include some of the most widespread protein folds, such as Rossmann fold, ferredoxin fold, ribonuclease H fold, and TIM beta/alpha-barrel. On the basis of this classification system, we examined the shared substrate binding and catalytic mechanisms as well as variations of these mechanisms in the same fold groups. Cases of convergent evolution of identical kinase activities occurring in different folds are discussed.     

Capturing protein sequence–structure specificity using computational sequence design

It is well known that protein fold recognition can be greatly improved if models for the underlying evolution history of the folds are taken into account. The improvement, however, exists only if such evolutionary information is available. To circumvent this limitation for protein families that only have a small number of representatives in current sequence databases, we follow an alternate approach in which the benefits of including evolutionary information can be recreated by using sequences generated by computational protein design algorithms. We explore this strategy on a large database of protein templates with 1747 members from different protein families. An automated method is used to design sequences for these templates. We use the backbones from the experimental structures as fixed templates, thread sequences on these backbones using a self‐consistent mean field approach, and score the fitness of the corresponding models using a semi‐empirical physical potential. Sequences designed for one template are translated into a hidden Markov model‐based profile. We describe the implementation of this method, the optimization of its parameters, and its performance. When the native sequences of the protein templates were tested against the library of these profiles, the class, fold, and family memberships of a large majority (>90%) of these sequences were correctly recognized for an E‐value threshold of 1. In contrast, when homologous sequences were tested against the same library, a much smaller fraction (35%) of sequences were recognized; The structural classification of protein families corresponding to these sequences, however, are correctly recognized (with an accuracy of >88%). Proteins 2013; © 2013 Wiley Periodicals, Inc.     

Representing and comparing protein folds and fold families using three‐dimensional shape‐density representations

The question of how best to compare and classify the (three‐dimensional) structures of proteins is one of the most important unsolved problems in computational biology. To help tackle this problem, we have developed a novel shape‐density superposition algorithm called 3D‐Blast which represents and superposes the shapes of protein backbone folds using the spherical polar Fourier correlation technique originally developed by us for protein docking. The utility of this approach is compared with several well‐known protein structure alignment algorithms using receiver‐operator‐characteristic plots of queries against the “gold standard” CATH database. Despite being completely independent of protein sequences and using no information about the internal geometry of proteins, our results from searching the CATH database show that 3D‐Blast is highly competitive compared to current state‐of‐the‐art protein structure alignment algorithms. A novel and potentially very useful feature of our approach is that it allows an average or “consensus” fold to be calculated easily for a given group of protein structures. We find that using consensus shapes to represent entire fold families also gives very good database query performance. We propose that using the notion of consensus fold shapes could provide a powerful new way to index existing protein structure databases, and that it offers an objective way to cluster and classify all of the currently known folds in the protein universe. Proteins 2012. © 2011 Wiley Periodicals, Inc.     

Targeting novel folds for structural genomics

The ultimate goal of structural genomics is to obtain the structure of each protein coded by each gene within a genome to determine gene function. Because of cost and time limitations, it remains impractical to solve the structure for every gene product experimentally. Up to a point, reasonably accurate three‐dimensional structures can be deduced for proteins with homologous sequences by using comparative modeling. Beyond this, fold recognition or threading methods can be used for proteins showing little homology to any known fold, although this is relatively time‐consuming and limited by the library of template folds currently available. Therefore, it is appropriate to develop methods that can increase our knowledge base, expanding our fold libraries by earmarking potentially “novel” folds for experimental structure determination. How can we sift through proteomic data rapidly and yet reliably identify novel folds as targets for structural genomics? We have analyzed a number of simple methods that discriminate between “novel” and “known” folds. We propose that simple alignments of secondary structure elements using predicted secondary structure could potentially be a more selective method than both a simple fold recognition method (GenTHREADER) and standard sequence alignment at finding novel folds when sequences show no detectable homology to proteins with known structures. Proteins 2002;48:44–52. © 2002 Wiley‐Liss, Inc.     

Search for the most stable folds of protein chains: III. Improvement in fold recognition by averaging over homologous sequences and 3D structures

Three-dimensional (3D) protein fold recognition by query sequence can be improved using information of fold recognition yielded by the sequences homologous to the query one. This idea is now used more and more widely. Our paper presents its consequent development. We suggest incorporating information both on the sequences homologous to the query protein sequence and the 3D structures homologous to the target (already deciphered) protein folds. We show that both these tricks, and especially their combination reduces errors in fold recognition by the threading method. Proteins 2000;40:494-501.     

Fold usage on genomes and protein fold evolution

We review fold usage on completed genomes to explore protein structure evolution. The patterns of presence or absence of folds on genomes gives us insights into the relationships between folds, the age of different folds and how we have arrived at the set of folds we see today. We examine the relationships between different measures which describe protein fold usage, such as the number of copies of a fold per genome, the number of families per fold, and the number of genomes a fold occurs on. We obtained these measures of fold usage by searching for the structural domains on 157 completed genome sequences from all three kingdoms of life. In our comparisons of these measures we found that bacteria have relatively more distinct folds on their genomes than archaea. Eukaryotes were found to have many more copies of a fold on their genomes. If we separate out the different fold classes, the alpha/beta class has relatively fewer distinct folds on large genomes, more copies of a fold on bacteria and more folds occurring in all three kingdoms simultaneously. These results possibly indicate that most alpha/beta folds originated earlier than other folds. The expected power law distribution is observed for copies of a fold per genome and we found a similar distribution for the number of families per fold. However, a more complicated distribution appears for fold occurrence across genomes, which strongly depends on fold class and kingdom. We also show that there is not a clear relationship between the three measures of fold usage. A fold which occurs on many genomes does not necessarily have many copies on each genome. Similarly, folds with many copies do not necessarily have many families or vice versa.     

Defining the fold space of membrane proteins: the CAMPS database

Recent progress in structure determination techniques has led to a significant growth in the number of known membrane protein structures, and the first structural genomics projects focusing on membrane proteins have been initiated, warranting an investigation of appropriate bioinformatics strategies for optimal structural target selection for these molecules. What determines a membrane protein fold? How many membrane structures need to be solved to provide sufficient structural coverage of the membrane protein sequence space? We present the CAMPS database (Computational Analysis of the Membrane Protein Space) containing almost 45,000 proteins with three or more predicted transmembrane helices (TMH) from 120 bacterial species. This large set of membrane proteins was subjected to single‐linkage clustering using only sequence alignments covering at least 40% of the TMH present in a given family. This process yielded 266 sequence clusters with at least 15 members, roughly corresponding to membrane structural folds, sufficiently structurally homogeneous in terms of the variation of TMH number between individual sequences. These clusters were further subdivided into functionally homogeneous subclusters according to the COG (Clusters of Orthologous Groups) system as well as more stringently defined families sharing at least 30% identity. The CAMPS sequence clusters are thus designed to reflect three main levels of interest for structural genomics: fold, function, and modeling distance. We present a library of Hidden Markov Models (HMM) derived from sequence alignments of TMH at these three levels of sequence similarity. Given that 24 out of 266 clusters corresponding to membrane folds already have associated known structures, we estimate that 242 additional new structures, one for each remaining cluster, would provide structural coverage at the fold level of roughly 70% of prokaryotic membrane proteins belonging to the currently most populated families. Proteins 2006. © 2006 Wiley‐Liss, Inc.     

A review of visualisations of protein fold networks and their relationship with sequence and function

Proteins form arguably the most significant link between genotype and phenotype. Understanding the relationship between protein sequence and structure, and applying this knowledge to predict function, is difficult. One way to investigate these relationships is by considering the space of protein folds and how one might move from fold to fold through similarity, or potential evolutionary relationships. The many individual characterisations of fold space presented in the literature can tell us a lot about how well the current Protein Data Bank represents protein fold space, how convergence and divergence may affect protein evolution, how proteins affect the whole of which they are part, and how proteins themselves function. A synthesis of these different approaches and viewpoints seems the most likely way to further our knowledge of protein structure evolution and thus, facilitate improved protein structure design and prediction.     

An in silico exploration of the neutral network in protein sequence space

Designating amino-acid sequences that fold into a common main-chain structure as "neutral sequences" for the structure, regardless of their function or stability, we investigated the distribution of neutral sequences in protein sequence space. For four distinct target structures (alpha, beta,alpha/beta and alpha+beta types) with the same chain length of 108, we generated the respective neutral sequences by using the inverse folding technique with a knowledge-based potential function. We assumed that neutral sequences for a protein structure have Z scores higher than or equal to fixed thresholds, where thresholds are defined as the Z score for the corresponding native sequence (case 1) or much greater Z score (case 2). An exploring walk simulation suggested that the neutral sequences mapped into the sequence space were connected with each other through straight neutral paths and formed an inherent neutral network over the sequence space. Through another exploring walk simulation, we investigated contiguous regions between or among the neutral networks for the distinct protein structures and obtained the following results. The closest approach distance between the two neutral networks ranged from 5 to 29 on the Hamming distance scale, showing a linear increase against the threshold values. The sequences located at the "interchange" regions between the two neutral networks have intermediate sequence-profile-scores for both corresponding structures. Introducing a "ball" in the sequence space that contains at least one neutral sequence for each of the four structures, we found that the minimal radius of the ball that is centered at an arbitrary position ranged from 35 to 50, while the minimal radius of the ball that is centered at a certain special position ranged from 20 to 30, in the Hamming distance scale. The relatively small Hamming distances (5-30) may support an evolution mechanism by transferring from a network for a structure to another network for a more beneficial structure via the interchange regions.     

Modeling repetitive,non‐globular proteins

While ab initio modeling of protein structures is not routine, certain types of proteins are more straightforward to model than others. Proteins with short repetitive sequences typically exhibit repetitive structures. These repetitive sequences can be more amenable to modeling if some information is known about the predominant secondary structure or other key features of the protein sequence. We have successfully built models of a number of repetitive structures with novel folds using knowledge of the consensus sequence within the sequence repeat and an understanding of the likely secondary structures that these may adopt. Our methods for achieving this success are reviewed here.     

SPIN2: Predicting sequence profiles from protein structures using deep neural networks

Designing protein sequences that can fold into a given structure is a well‐known inverse protein‐folding problem. One important characteristic to attain for a protein design program is the ability to recover wild‐type sequences given their native backbone structures. The highest average sequence identity accuracy achieved by current protein‐design programs in this problem is around 30%, achieved by our previous system, SPIN. SPIN is a program that predicts sequences compatible with a provided structure using a neural network with fragment‐based local and energy‐based nonlocal profiles. Our new model, SPIN2, uses a deep neural network and additional structural features to improve on SPIN. SPIN2 achieves over 34% in sequence recovery in 10‐fold cross‐validation and independent tests, a 4% improvement over the previous version. The sequence profiles generated from SPIN2 are expected to be useful for improving existing fold recognition and protein design techniques. SPIN2 is available at http://sparks-lab.org .     

A novel member of the YchN-like fold: solution structure of the hypothetical protein Tm0979 from Thermotoga maritima

We report herein the NMR structure of Tm0979, a structural proteomics target from Thermotoga maritima. The Tm0979 fold consists of four beta/alpha units, which form a central parallel beta-sheet with strand order 1234. The first three helices pack toward one face of the sheet and the fourth helix packs against the other face. The protein forms a dimer by adjacent parallel packing of the fourth helices sandwiched between the two beta-sheets. This fold is very interesting from several points of view. First, it represents the first structure determination for the DsrH family of conserved hypothetical proteins, which are involved in oxidation of intracellular sulfur but have no defined molecular function. Based on structure and sequence analysis, possible functions are discussed. Second, the fold of Tm0979 most closely resembles YchN-like folds; however the proteins that adopt these folds differ in secondary structural elements and quaternary structure. Comparison of these proteins provides insight into possible mechanisms of evolution of quaternary structure through a simple mechanism of hydrophobicity-changing mutations of one or two residues. Third, the Tm0979 fold is found to be similar to flavodoxin-like folds and beta/alpha barrel proteins, and may provide a link between these very abundant folds and putative ancestral half-barrel proteins.     

Comparing folding codes for proteins and polymers

Proteins fold to unique compact native structures. Perhaps other polymers could be designed to fold in similar ways. The chemical nature of the monomer “alphabet” determines the “energy matrix” of monomer interactions—which defines the folding code, the relationship between sequence and structure. We study two properties of energy matrices using two-dimensional lattice models: uniqueness, the number of sequences that fold to only one structure, and encodability, the number of folds that are unique lowest-energy structures of certain monomer sequences. For the simplest model folding code, involving binary sequences of H (hydrophobic) and P (polar) monomers, only a small fraction of sequences fold uniquely, and not all structures can be encoded. Adding strong repulsive interactions results in a folding code with more sequences folding uniquely and more designable folds. Some theories suggest that the quality of a folding code depends only on the number of letters in the monomer alphabet, but we find that the energy matrix itself can be at least as important as the size of the alphabet. Certain multi-letter codes, including some with 20 letters, may be less physical or protein-like than codes with smaller numbers of letters because they neglect correlations among inter-residue interactions, treat only maximally compact conformations, or add arbitrary energies to the energy matrix.