Thoroughly sampling sequence space: large-scale protein design of structural ensembles

Modeling the inherent flexibility of the protein backbone as part of computational protein design is necessary to capture the behavior of real proteins and is a prerequisite for the accurate exploration of protein sequence space. We present the results of a broad exploration of sequence space, with backbone flexibility, through a novel approach: large-scale protein design to structural ensembles. A distributed computing architecture has allowed us to generate hundreds of thousands of diverse sequences for a set of 253 naturally occurring proteins, allowing exciting insights into the nature of protein sequence space. Designing to a structural ensemble produces a much greater diversity of sequences than previous studies have reported, and homology searches using profiles derived from the designed sequences against the Protein Data Bank show that the relevance and quality of the sequences is not diminished. The designed sequences have greater overall diversity than corresponding natural sequence alignments, and no direct correlations are seen between the diversity of natural sequence alignments and the diversity of the corresponding designed sequences. For structures in the same fold, the sequence entropies of the designed sequences cluster together tightly. This tight clustering of sequence entropies within a fold and the separation of sequence entropy distributions for different folds suggest that the diversity of designed sequences is primarily determined by a structure's overall fold, and that the designability principle postulated from studies of simple models holds in real proteins. This has important implications for experimental protein design and engineering, as well as providing insight into protein evolution.     

Combinations of Ancestral Modules in Proteins

Twenty-seven protein sequence elements, six to nine amino acids long, were extracted from 15 phylogenetically diverse complete prokaryotic proteomes. The elements are present in all of these proteomes, with at least one copy each (omnipresent elements), and have presumably been conserved since the last universal common ancestor (LUCA). All these omnipresent elements are identified in crystallized protein structures as parts of highly conserved closed loops, 25–30 residues long, thus representing the closed-loop modules discovered in 2000 by Berezovsky et al. The omnipresent peptides make up seven distinct groups, of which the largest groups, Aleph and Beth, contain 18 and four elements, respectively, which are related but different, while five other groups are represented by only one element each. The LUCA modules appear with one or several copies per protein molecule in a variety of combinations depending on the functional identity of the corresponding protein. The functional involvement of individual LUCA modules is outlined on the basis of known protein annotations. Analyses of all the related sequences in a large, formatted protein sequence space suggest that many, if not all, of the 27 omnipresent elements have a common sequence origin. This sequence space network analysis may lead to elucidation of the earliest stages of protein evolution.     

Evolution of an Arbitrary Sequence in Solubility

We have investigated the evolvability of an insoluble random polypeptide, RP3-34, to a soluble form through iterative mutation and selection with the aid of the green fluorescent protein (GFP) folding reporter. To assess the solubility of the polypeptides in the selected clones of each generation, the polypeptide genes were detached from the GFP fusions and expressed with a His₆ tag. The solubility of the variant random polypeptides increased in each generation within the scope of the evolutionary process, and the polypeptides assumed a soluble form from the fourth generation. Analysis of the synonymous and nonsynonymous mutations found in the deduced amino acid sequence of the selected polypeptides revealed that selection had accelerated the evolutionary rate. The solubility and hydrophobicity of the polypeptides and the 25 arbitrarily chosen random polypeptides found in a previously prepared library were determined, analyzed, and interpreted from the landscape on the protein sequence space. This study showed the evolvability of an insoluble arbitrary sequence toward a soluble one, hence, it provides a new perspective on the field of artificial evolution.     

What limits the primary sequence space of natural proteins?

Abstract

Number of naturally occurring primary sequences of proteins is an infinitesimally small subset of the possible number of primary sequences that can be synthesized using 20 amino acids. Prevailing views ascribe this to slow and incremental mutational/selection evolutionary mechanisms. However, considering the large number of avenues available in form of diversity of emerging/evolving and/or disappearing living systems for exploring the primary sequence space over the evolutionary time scale of ～3.5 billion years, this remains a conjecture. Therefore, to investigate primary sequence space limitations, we carried out a systematic study for finding primary sequences absent in nature. We report the discovery of the smallest peptide sequence “Cysteine-Glutamine-Tryptophan-Tryptophan” that is not found in over half-a-million curated protein sequences in the Uniprot (Swiss-Prot) database. Additionally, we report a library of 83605 pentapeptides that are not found in any of the known protein sequences. Compositional analyses of these absent primary sequences yield a remarkably strong power relationship between the percentage occurrence of individual amino acids in all known protein sequences and their respective frequency of occurrence in the absent peptides, regardless of their specific position in the sequences. If random evolutionary mechanisms were responsible for limitations to the primary sequence space, then one would not expect any relationship between compositions of available and absent primary sequences. Thus, we conclusively show that stoichiometric constraints on amino acids limit the primary sequence space of proteins in nature. We discuss the possibly profound implications of our findings in both evolutionary and synthetic biology.

Communicated by Ramaswamy H. Sarma     

A database of unique protein sequence identifiers for proteome studies

In proteome studies, identification of proteins requires searching protein sequence databases. The public protein sequence databases (e.g., NCBInr, UniProt) each contain millions of entries, and private databases add thousands more. Although much of the sequence information in these databases is redundant, each database uses distinct identifiers for the identical protein sequence and often contains unique annotation information. Users of one database obtain a database-specific sequence identifier that is often difficult to reconcile with the identifiers from a different database. When multiple databases are used for searches or the databases being searched are updated frequently, interpreting the protein identifications and associated annotations can be problematic. We have developed a database of unique protein sequence identifiers called Sequence Globally Unique Identifiers (SEGUID) derived from primary protein sequences. These identifiers serve as a common link between multiple sequence databases and are resilient to annotation changes in either public or private databases throughout the lifetime of a given protein sequence. The SEGUID Database can be downloaded (http://bioinformatics.anl.gov/SEGUID/) or easily generated at any site with access to primary protein sequence databases. Since SEGUIDs are stable, predictions based on the primary sequence information (e.g., pI, Mr) can be calculated just once; we have generated approximately 500 different calculations for more than 2.5 million sequences. SEGUIDs are used to integrate MS and 2-DE data with bioinformatics information and provide the opportunity to search multiple protein sequence databases, thereby providing a higher probability of finding the most valid protein identifications.     

蛋白质序列的聚类结构分析

基于模糊邻近关系的粒度空间,对蛋白质序列进行聚类结构分析。利用MEGA软件计算选取的木聚糖酶序列间的比对距离,引入内积将其转化为模糊邻近关系(或矩阵),再应用算法求解其粒度空间,进行序列的聚类结构分析和最佳聚类确定研究。这些研究为蛋白质序列提供了定量分析的工具。     

BRCA1蛋白的序列及空间结构的分析

查询人的BRCA1蛋白的氨基酸序列,利用生物信息学的方法进行相似性搜索,获得一系列BRCA1蛋白的氨基酸序列。选择了其中的11条序列,对BRCA1蛋白进行了多重序列分析和进化分析,对BRCA1蛋白的BRCT结构域进行三维同源模型的构建与比较分析。分析结果表明:BRCA1中某些特定部位的氨基酸序列高度保守;确定氨基酸的保守位点并联合进化分析可对基因错义突变的致病性做初步地猜测;相近物种来源的BRCA1具有较近的亲缘关系,而且具有极其相似的三维空间结构。这些为研究BRCA1蛋白的结构与功能关系提供指导意义。     

Funnel-like organization in sequence space determines the distributions of protein stability and folding rate preferred by evolution

To understand the physical and evolutionary determinants of protein folding, we map out the complete organization of thermodynamic and kinetic properties for protein sequences that share the same fold. The exhaustive nature of our study necessitates using simplified models of protein folding. We obtain a stability map and a folding rate map in sequence space. Comparison of the two maps reveals a common organizational principle: optimality decreases more or less uniformly with distance from the optimal sequence in the sequence space. This gives a funnel-shaped optimality surface. Evolutionary dynamics of a sequence population on these two maps reveal how the simple organization of sequence space affects the distributions of stability and folding rate preferred by evolution.     

Principal eigenvector of contact matrices and hydrophobicity profiles in proteins

With the aim of studying the relationship between protein sequences and their native structures, we adopted vectorial representations for both sequence and structure. The structural representation was based on the principal eigenvector of the fold's contact matrix (PE). As has been recently shown, the latter encodes sufficient information for reconstructing the whole contact matrix. The sequence was represented through a hydrophobicity profile (HP), using a generalized hydrophobicity scale that we obtained from the principal eigenvector of a residue-residue interaction matrix, and denoted as interactivity scale. Using this novel scale, we defined the optimal HP of a protein fold, and, by means of stability arguments, predicted to be strongly correlated with the PE of the fold's contact matrix. This prediction was confirmed through an evolutionary analysis, which showed that the PE correlates with the HP of each individual sequence adopting the same fold and, even more strongly, with the average HP of this set of sequences. Thus, protein sequences evolve in such a way that their average HP is close to the optimal one, implying that neutral evolution can be viewed as a kind of motion in sequence space around the optimal HP. Our results indicate that the correlation coefficient between N-dimensional vectors constitutes a natural metric in the vectorial space in which we represent both protein sequences and protein structures, which we call vectorial protein space. In this way, we define a unified framework for sequence-to-sequence, sequence-to-structure and structure-to-structure alignments. We show that the interactivity scale is nearly optimal both for the comparison of sequences to sequences and sequences to structures.     

Nonlinearities in protein space limit the utility of informatics in protein biophysics

We examine the utility of informatic‐based methods in computational protein biophysics. To do so, we use newly developed metric functions to define completely independent sequence and structure spaces for a large database of proteins. By investigating the relationship between these spaces, we demonstrate quantitatively the limits of knowledge‐based correlation between the sequences and structures of proteins. It is shown that there are well‐defined, nonlinear regions of protein space in which dissimilar structures map onto similar sequences (the conformational switch), and dissimilar sequences map onto similar structures (remote homology). These nonlinearities are shown to be quite common—almost half the proteins in our database fall into one or the other of these two regions. They are not anomalies, but rather intrinsic properties of structural encoding in amino acid sequences. It follows that extreme care must be exercised in using bioinformatic data as a basis for computational structure prediction. The implications of these results for protein evolution are examined. Proteins 2015; 83:1923–1928. © 2015 Wiley Periodicals, Inc.     

Sequence variations within protein families are linearly related to structural variations

It is commonly believed that similarities between the sequences of two proteins infer similarities between their structures. Sequence alignments reliably recognize pairs of protein of similar structures provided that the percentage sequence identity between their two sequences is sufficiently high. This distinction, however, is statistically less reliable when the percentage sequence identity is lower than 30% and little is known then about the detailed relationship between the two measures of similarity. Here, we investigate the inverse correlation between structural similarity and sequence similarity on 12 protein structure families. We define the structure similarity between two proteins as the cRMS distance between their structures. The sequence similarity for a pair of proteins is measured as the mean distance between the sequences in the subsets of sequence space compatible with their structures. We obtain an approximation of the sequence space compatible with a protein by designing a collection of protein sequences both stable and specific to the structure of that protein. Using these measures of sequence and structure similarities, we find that structural changes within a protein family are linearly related to changes in sequence similarity.     

A robust method to detect structural and functional remote homologues

With currently available sequence data, it is feasible to conduct extensive comparisons among large sets of protein sequences. It is still a much more challenging task to partition the protein space into structurally and functionally related families solely based on sequence comparisons. The ProtoNet system automatically generates a treelike classification of the whole protein space. It stands to reason that this classification reflects evolutionary relationships, both close and remote. In this article, we examine this hypothesis. We present a semiautomatic procedure that singles out certain inner nodes in the ProtoNet tree that should ideally correspond to structurally and functionally defined protein families. We compare the performance of this method against several expert systems. Some of the competing methods incorporate additional extraneous information on protein structure or on enzymatic activities. The ProtoNet-based method performs at least as well as any of the methods with which it was compared. This article illustrates the ProtoNet-based method on several evolutionarily diverse families. Using this new method, an evolutionary divergence scheme can be proposed for a large number of structural and functional related superfamilies.     

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.     

蛋白质序列间进化距离的估计

本文考察了目前采用的估计同源蛋白质序列间进化距离的方法缺陷,并提出了几个新的计算公式,它们考虑了氨基酸位点间显然存在的替代速率的差异。另外,提出了一种考虑氨基酸间不同替代概率的最大似然估计方法。文中对这些公式进行了计算比较,并对它在实际中的运用提出了建议。     

Determination of the primary structure of homologous proteins by sequence analysis of peptide mixtures

We propose a rapid method to determine the primary structure of a protein knowing the sequence of a homologous protein. The method consists in submitting both the reduced and alkylated proteins to an enzymatic or chemical hydrolysis and performing the sequence analysis of the peptide mixtures. The assessment of the unknown sequence and the degree of identity of the two proteins are reached by comparing the two sequence analyses. The sequences of all the possible peptides present in the two mixtures are reconstructed and the differences in the two sequences are determined. If necessary, the differences can be confirmed by performing a mass spectrometric analysis of the two mixtures. We used this procedure on two homologous proteins of known sequence to furnish an application example of the method.     

Long- and short-range interactions in native protein structures are consistent/minimally frustrated in sequence space

We show that long- and short-range interactions in almost all protein native structures are actually consistent with each other for coarse-grained energy scales; specifically we mean the long-range inter-residue contact energies and the short-range secondary structure energies based on peptide dihedral angles, which are potentials of mean force evaluated from residue distributions observed in protein native structures. This consistency is observed at equilibrium in sequence space rather than in conformational space. Statistical ensembles of sequences are generated by exchanging residues for each of 797 protein native structures with the Metropolis method. It is shown that adding the other category of interaction to either the short- or long-range interactions decreases the means and variances of those energies for essentially all protein native structures, indicating that both interactions consistently work by more-or-less restricting sequence spaces available to one of the interactions. In addition to this consistency, independence by these interaction classes is also indicated by the fact that there are almost no correlations between them when equilibrated using both interactions and significant but small, positive correlations at equilibrium using only one of the interactions. Evidence is provided that protein native sequences can be regarded approximately as samples from the statistical ensembles of sequences with these energy scales and that all proteins have the same effective conformational temperature. Designing protein structures and sequences to be consistent and minimally frustrated among the various interactions is a most effective way to increase protein stability and foldability.     

Simulating protein evolution in sequence and structure space

Naturally occurring proteins comprise a special subset of all plausible sequences and structures selected through evolution. Simulating protein evolution with simplified and all-atom models has shed light on the evolutionary dynamics of protein populations, the nature of evolved sequences and structures, and the extent to which today's proteins are shaped by selection pressures on folding, structure and function. Extensive mapping of the native structure, stability and folding rate in sequence space using lattice proteins has revealed organizational principles of the sequence/structure map important for evolutionary dynamics. Evolutionary simulations with lattice proteins have highlighted the importance of fitness landscapes, evolutionary mechanisms, population dynamics and sequence space entropy in shaping the generic properties of proteins. Finally, evolutionary-like simulations with all-atom models, in particular computational protein design, have helped identify the dominant selection pressures on naturally occurring protein sequences and structures.     

Computationally mapping sequence space to understand evolutionary protein engineering

Evolutionary protein engineering has been dramatically successful, producing a wide variety of new proteins with altered stability, binding affinity, and enzymatic activity. However, the success of such procedures is often unreliable, and the impact of the choice of protein, engineering goal, and evolutionary procedure is not well understood. We have created a framework for understanding aspects of the protein engineering process by computationally mapping regions of feasible sequence space for three small proteins using structure-based design protocols. We then tested the ability of different evolutionary search strategies to explore these sequence spaces. The results point to a non-intuitive relationship between the error-prone PCR mutation rate and the number of rounds of replication. The evolutionary relationships among feasible sequences reveal hub-like sequences that serve as particularly fruitful starting sequences for evolutionary search. Moreover, genetic recombination procedures were examined, and tradeoffs relating sequence diversity and search efficiency were identified. This framework allows us to consider the impact of protein structure on the allowed sequence space and therefore on the challenges that each protein presents to error-prone PCR and genetic recombination procedures.     

A protein sequence fitness function for identifying natural and nonnatural proteins

The infinitesimally small sequence space naturally scouted in the millions of years of evolution suggests that the natural proteins are constrained by some functional prerequisites and should differ from randomly generated sequences. We have developed a protein sequence fitness scoring function that implements sequence and corresponding secondary structural information at tripeptide levels to differentiate natural and nonnatural proteins. The proposed fitness function is extensively validated on a dataset of about 210 000 natural and nonnatural protein sequences and benchmarked with existing methods for differentiating natural and nonnatural proteins. The high sensitivity, specificity, and percentage accuracy (0.81%, 0.95%, and 91% respectively) of the fitness function demonstrates its potential application for sampling the protein sequences with higher probability of mimicking natural proteins. Moreover, the four major classes of proteins (α proteins, β proteins, α/β proteins, and α + β proteins) are separately analyzed and β proteins are found to score slightly lower as compared to other classes. Further, an analysis of about 250 designed proteins (adopted from previously reported cases) helped to define the boundaries for sampling the ideal protein sequences. The protein sequence characterization aided by the proposed fitness function could facilitate the exploration of new perspectives in the design of novel functional proteins.