The network of sequence flow between protein structures

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.

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.

Identification and characterization of metamorphic proteins: Current and future perspectives

Proteins that can reversibly alternate between distinctly different folds under native conditions are described as being metamorphic. The "metamorphome" is the collection of all metamorphic proteins in the proteome, but it remains unknown the extent to which the proteome is populated by this class of proteins. We propose that uncovering the metamorphome will require a synergy of computational screening of protein sequences to identify potential metamorphic behavior and validation through experimental techniques. This perspective discusses computational and experimental approaches that are currently used to predict and characterize metamorphic proteins as well as the need for developing improved methodologies. Since metamorphic proteins act as molecular switches, understanding their properties and behavior could lead to novel applications of these proteins as sensors in biological or environmental contexts.

Conformational Dynamics from Ambiguous Zinc Coordination in the RanBP2-Type Zinc Finger of RBM5

The multi-domain RNA binding protein RBM5 is a molecular signature of metastasis. RBM5 regulates alternative splicing of apoptotic genes including the cell death receptor Fas and the initiator Caspase-2. The RBM5 RanBP2-type zinc finger (Zf1) is known to specifically recognize single-stranded RNAs with high affinity. Here, we study the structure and conformational dynamics of the Zf1 zinc finger of human RBM5 using NMR. We show that the presence of a non-canonical cysteine in Zf1 kinetically destabilizes the protein. Metal-exchange kinetics show that mutation of the cysteine establishes high-affinity coordination of the zinc. Our data indicate that selection of such a structurally destabilizing mutation during the course of evolution could present an opportunity for functional adaptation of the protein.

The VES KM: a pathway for protein folding in vivo

While according to the thermodynamic hypothesis, protein folding reproducibility is ensured by the assumption that the native state corresponds to the minimum of the free energy in normal cellular conditions, here, the VES kinetic mechanism for folding in vivo is described according to which the nascent chain of all proteins is helical and the first and structure defining step in the folding pathway is the bending of that initial helix around a particular amino acid site. Molecular dynamics simulations are presented which indicate both the viability of this mechanism for folding and its limitations in the presence of a Markovian thermal bath. An analysis of a set of protein structures formed only of helices and loops suggests that bending sites are correlated with regions bounded, on the N-side, by positively charged amino acids like Lysine and Histidine and on the C-side by negatively charged amino acids like Aspartic acid.

Structural metamorphism and polymorphism in proteins on the brink of thermodynamic stability

The classical view of the structure-function paradigm advanced by Anfinsen in the 1960s is that a protein's function is inextricably linked to its three-dimensional structure and is encrypted in its amino acid sequence. However, it is now known that a significant fraction of the proteome consists of intrinsically disordered proteins (IDPs). These proteins populate a polymorphic ensemble of conformations rather than a unique structure but are still capable of performing biological functions. At the boundary, between well-ordered and inherently disordered states are proteins that are on the brink of stability, either weakly stable ordered systems or disordered but on the verge of being stable. In such marginal states, even relatively minor changes can significantly alter the energy landscape, leading to large-scale conformational remodeling. Some proteins on the edge of stability are metamorphic, with the capacity to switch from one fold topology to another in response to an environmental trigger (e.g., pH, temperature/salt, redox). Many IDPs, on the other hand, are marginally unstable such that small perturbations (e.g., phosphorylation, ligands) tip the balance over to a range of ordered, partially ordered, or even more disordered states. In general, the structural transitions described by metamorphic fold switches and polymorphic IDPs possess a number of common features including low or diminished stability, large-scale conformational changes, critical disordered regions, latent or attenuated binding sites, and expansion of function. We suggest that these transitions are, therefore, conceptually and mechanistically analogous, representing adjacent regions in the continuum of order/disorder transitions.

How Many Protein Sequences Fold to a Given Structure? A Coevolutionary Analysis

Quantifying the relationship between protein sequence and structure is key to understanding the protein universe. A fundamental measure of this relationship is the total number of amino acid sequences that can fold to a target protein structure, known as the "sequence capacity," which has been suggested as a proxy for how designable a given protein fold is. Although sequence capacity has been extensively studied using lattice models and theory, numerical estimates for real protein structures are currently lacking. In this work, we have quantitatively estimated the sequence capacity of 10 proteins with a variety of different structures using a statistical model based on residue-residue co-evolution to capture the variation of sequences from the same protein family. Remarkably, we find that even for the smallest protein folds, such as the WW domain, the number of foldable sequences is extremely large, exceeding the Avogadro constant. In agreement with earlier theoretical work, the calculated sequence capacity is positively correlated with the size of the protein, or better, the density of contacts. This allows the absolute sequence capacity of a given protein to be approximately predicted from its structure. On the other hand, the relative sequence capacity, i.e., normalized by the total number of possible sequences, is an extremely tiny number and is strongly anti-correlated with the protein length. Thus, although there may be more foldable sequences for larger proteins, it will be much harder to find them. Lastly, we have correlated the evolutionary age of proteins in the CATH database with their sequence capacity as predicted by our model. The results suggest a trade-off between the opposing requirements of high designability and the likelihood of a novel fold emerging by chance.

The Role of Evolutionary Selection in the Dynamics of Protein Structure Evolution

Homology modeling is a powerful tool for predicting a protein's structure. This approach is successful because proteins whose sequences are only 30% identical still adopt the same structure, while structure similarity rapidly deteriorates beyond the 30% threshold. By studying the divergence of protein structure as sequence evolves in real proteins and in evolutionary simulations, we show that this nonlinear sequence-structure relationship emerges as a result of selection for protein folding stability in divergent evolution. Fitness constraints prevent the emergence of unstable protein evolutionary intermediates, thereby enforcing evolutionary paths that preserve protein structure despite broad sequence divergence. However, on longer timescales, evolution is punctuated by rare events where the fitness barriers obstructing structure evolution are overcome and discovery of new structures occurs. We outline biophysical and evolutionary rationale for broad variation in protein family sizes, prevalence of compact structures among ancient proteins, and more rapid structure evolution of proteins with lower packing density.

Predicting Designability of Small Proteins from Graph Features of Contact Maps

Highly designable structures can be distinguished based on certain geometric graphical features of the interactions, confirming the fact that the topology of a protein structure and its residue-residue interaction network are important determinants of its designability. The most designable structures and least designable structures obtained for sets of proteins having the same number of residues are compared. It is shown that the most designable structures predicted by the graph features of the contact diagrams are more densely packed, whereas the poorly designable structures are more open structures or structures that are loosely packed. Interestingly enough, it can also be seen that the highly designable identified are also common structural motifs found in nature.

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.

Comprehensive analysis of sequences of a protein switch

Switches form a special class of proteins that dramatically change their three-dimensional structures upon a small perturbation. One possible perturbation that we explore is that of a single point mutation. Building on the pioneering experimental work of Alexander et al. (Alexander et al. PNAS, 2007; 104,11963-11968) that determines switch sequences between α and α+β folds we conduct a comprehensive sequence sampling by a Markov Chain with multiple fitness criteria to identify new switches given the experimental folds. We screen for switch sequences using a combination of contact potential, secondary structure prediction, and finally molecular dynamics simulations. Statistical properties of switch sequences are discussed and illustrated to be most sensitive to mutation at the N- and C- termini of the switch protein. Based on this analysis, a particularly stable putative switch pair is identified and proposed for further experimental analysis.

Subdomain interactions foster the design of two protein pairs with ∼80% sequence identity but different folds

Metamorphic proteins, including proteins with high levels of sequence identity but different folds, are exceptions to the long-standing rule-of-thumb that proteins with as little as 30% sequence identity adopt the same fold. Which topologies can be bridged by these highly identical sequences remains an open question. Here we bridge two 3-α-helix bundle proteins with two radically different folds. Using a straightforward approach, we engineered the sequences of one subdomain within maltose binding protein (MBP, α/β/α-sandwich) and another within outer surface protein A (OspA, β-sheet) to have high sequence identity (80 and 77%, respectively) with engineered variants of protein G (GA, 3-α-helix bundle). Circular dichroism and nuclear magnetic resonance spectra of all engineered variants demonstrate that they maintain their native conformations despite substantial sequence modification. Furthermore, the MBP variant (80% identical to GA) remained active. Thermodynamic analysis of numerous GA and MBP variants suggests that the key to our approach involved stabilizing the modified MBP and OspA subdomains via external interactions with neighboring substructures, indicating that subdomain interactions can stabilize alternative folds over a broad range of sequence variation. These findings suggest that it is possible to bridge one fold with many other topologies, which has implications for protein folding, evolution, and misfolding diseases.

The energy landscape of a protein switch

Protein switches are made of highly similar sequences that fold to dramatically different structures. A structural switching system with 31 sequence variants for α and α+β folds has been illustrated experimentally by He et al., Structure, 2012, 20, 283 and is investigated computationally in the present study. Methods to assign a sequence to one of the two folds are reported and analyzed. A fast and accurate protocol to identify the correct fold of the 31 sequences is based on enriching modeled structures using short molecular dynamics (MD) trajectories and scoring these structures with coarse-grained energy functions. We examine five coarse-grained energy functions and illustrate that the Hinds-Levitt potential works the best for this task. We show that enrichment by MD significantly enhances prediction accuracy. Finally, we find that melting temperature correlates well with the energy difference between the two folds (correlation coefficient ∼-0.7). The correlation reduces dramatically (∼0.4) if the absolute energy of the correct fold is considered. Moreover, prediction of melting temperature is sensitive to the structural templates. We emphasize in our analyses the use of native structures as templates since these folds are more readily available from structural biology experiments.

A polymetamorphic protein

Arc repressor is a homodimeric protein with a ribbon-helix-helix fold. A single polar-to-hydrophobic substitution (N11L) at a solvent-exposed position leads to population of an alternate dimeric fold in which 3₁₀ helices replace a β-sheet. Here we find that the variant Q9V/N11L/R13V (S-VLV), with two additional polar-to-hydrophobic surface mutations in the same β-sheet, forms a highly stable, reversibly folded octamer with approximately half the α-helical content of wild-type Arc. At low protein concentration and low ionic strength, S-VLV also populates both dimeric topologies previously observed for N11L, as judged by NMR chemical shift comparisons. Thus, accumulation of simple hydrophobic mutations in Arc progressively reduces fold specificity, leading first to a sequence with two folds and then to a manifold bridge sequence with at least three different topologies. Residues 9-14 of S-VLV form a highly hydrophobic stretch that is predicted to be amyloidogenic, but we do not observe aggregates of higher order than octamer. Increases in sequence hydrophobicity can promote amyloid aggregation but also exert broader and more complex effects on fold specificity. Altered native folds, changes in fold coupled to oligomerization, toxic pre-amyloid oligomers, and amyloid fibrils may represent a near continuum of accessible alternatives in protein structure space.

Comparing proteins by their internal dynamics: exploring structure-function relationships beyond static structural alignments

The growing interest for comparing protein internal dynamics owes much to the realisation that protein function can be accompanied or assisted by structural fluctuations and conformational changes. Analogously to the case of functional structural elements, those aspects of protein flexibility and dynamics that are functionally oriented should be subject to evolutionary conservation. Accordingly, dynamics-based protein comparisons or alignments could be used to detect protein relationships that are more elusive to sequence and structural alignments. Here we provide an account of the progress that has been made in recent years towards developing and applying general methods for comparing proteins in terms of their internal dynamics and advance the understanding of the structure-function relationship.

Mutational tipping points for switching protein folds and functions

While disordered to ordered rearrangements are relatively common, the ability of proteins to switch from one ordered fold to a completely different fold is generally regarded as rare, and few fold switches have been characterized. Here, in a designed system, we examine the mutational requirements for transitioning between folds and functions. We show that switching between monomeric 3α and 4β+α folds can occur in multiple ways with successive single amino acid changes at diverse residue positions, raising the likelihood that such transitions occur in the evolution of new folds. Even mutations on the periphery of the core can tip the balance between alternatively folded states. Ligand-binding studies illustrate that a new immunoglobulin G-binding function can be gained well before the relevant 4β+α fold is appreciably populated in the unbound protein. The results provide new insights into the evolution of fold and function.

The porous borders of the protein world

Fold switching may play a role in the evolution of new protein folds and functions. He et al., in this issue of Structure, use protein design to illustrate that the same drastic change in a protein fold can occur via multiple different mutational pathways.

Analytic markovian rates for generalized protein structure evolution

A general understanding of the complex phenomenon of protein evolution requires the accurate description of the constraints that define the sub-space of proteins with mutations that do not appreciably reduce the fitness of the organism. Such constraints can have multiple origins, in this work we present a model for constrained evolutionary trajectories represented by a Markovian process throughout a set of protein-like structures artificially constructed to be topological intermediates between the structure of two natural occurring proteins. The number and type of intermediate steps defines how constrained the total evolutionary process is. By using a coarse-grained representation for the protein structures, we derive an analytic formulation of the transition rates between each of the intermediate structures. The results indicate that compact structures with a high number of hydrogen bonds are more probable and have a higher likelihood to arise during evolution. Knowledge of the transition rates allows for the study of complex evolutionary pathways represented by trajectories through a set of intermediate structures.

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.

Protein folding absent selection

Biological proteins are known to fold into specific 3D conformations. However, the fundamental question has remained: Do they fold because they are biological, and evolution has selected sequences which fold? Or is folding a common trait, widespread throughout sequence space? To address this question arbitrary, unevolved, random-sequence proteins were examined for structural features found in folded, biological proteins. Libraries of long (71 residue), random-sequence polypeptides, with ensemble amino acid composition near the mean for natural globular proteins, were expressed as cleavable fusions with ubiquitin. The structural properties of both the purified pools and individual isolates were then probed using circular dichroism, fluorescence emission, and fluorescence quenching techniques. Despite this necessarily sparse "sampling" of sequence space, structural properties that define globular biological proteins, namely collapsed conformations, secondary structure, and cooperative unfolding, were found to be prevalent among unevolved sequences. Thus, for polypeptides the size of small proteins, natural selection is not necessary to account for the compact and cooperative folded states observed in nature.

Complexity Arrangements for Sustained Innovation: Lessons from 3M Corporation

Innovation processes are complex. It is through local interactions among people and technologies that diverse and novel outcomes emerge. Even when governed by simple rules, such interactions can generate nonlinear temporal dynamics. Given such complexities, how might an organization sustain innovation for continued growth and vitality? Drawing on an in-depth study of innovation practices and journeys at 3M Corporation, we identify how combinations of practices — which we conceptualize as complexity arrangements — afford multiple agentic orientations simultaneously for the actors involved and thereby facilitate sustained innovation.

Evolutionary bridges to new protein folds: design of C-terminal Cro protein chameleon sequences

Regions of amino-acid sequence that are compatible with multiple folds may facilitate evolutionary transitions in protein structure. In a previous study, we described a heuristically designed chameleon sequence (SASF1, structurally ambivalent sequence fragment 1) that could adopt either of two naturally occurring conformations (α-helical or β-sheet) when incorporated as part of the C-terminal dimerization subdomain of two structurally divergent transcription factors, P22 Cro and λ Cro. Here we describe longer chameleon designs (SASF2 and SASF3) that in the case of SASF3 correspond to the full C-terminal half of the ordered region of a P22 Cro/λ Cro sequence alignment (residues 34-57). P22-SASF2 and λ(WDD)-SASF2 show moderate thermal stability in denaturation curves monitored by circular dichroism (T(m) values of 46 and 55°C, respectively), while P22-SASF3 and λ(WDD)-SASF3 have somewhat reduced stability (T(m) values of 33 and 49°C, respectively). (13)C and (1)H NMR secondary chemical shift analysis confirms two C-terminal α-helices for P22-SASF2 (residues 36-45 and 54-57) and two C-terminal β-strands for λ(WDD)-SASF2 (residues 40-45 and 50-52), corresponding to secondary structure locations in the two parent sequences. Backbone relaxation data show that both chameleon sequences have a relatively well-ordered structure. Comparisons of (15)N-(1)H correlation spectra for SASF2 and SASF3-containing proteins strongly suggest that SASF3 retains the chameleonism of SASF2. Both Cro C-terminal conformations can be encoded in a single sequence, showing the plausibility of linking different Cro folds by smooth evolutionary transitions. The N-terminal subdomain, though largely conserved in structure, also exerts an important contextual influence on the structure of the C-terminal region.

Thermodynamics of protein folding: a random matrix formulation

The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters, e.g. the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon molecules. Our study, based on random matrix modeling of the interactions, shows, however, that the evolution of the statistical measures, e.g. Gibbs free energy, heat capacity, and entropy, is single parametric. The information can explain the selection of specific folding pathways from an infinite number of possible ways as well as other folding characteristics observed in computer simulation studies.

Proteins that switch folds

An increasing number of proteins demonstrate the ability to switch between very different fold topologies, expanding their functional utility through new binding interactions. Recent examples of fold switching from naturally occurring and designed systems have a number of common features: (i) The structural transitions require states with diminished stability; (ii) Switching involves flexible regions in one conformer or the other; (iii) A new binding surface is revealed in the alternate fold that can lead to both stabilization of the alternative state and expansion of biological function. Fold switching not only provides insight into how new folds evolve, but also indicates that an amino acid sequence has more information content than previously thought. A polypeptide chain can encode a stable fold while simultaneously hiding latent propensities for alternative states with novel functions.

Metamorphic proteins mediate evolutionary transitions of structure

The primary sequence of proteins usually dictates a single tertiary and quaternary structure. However, certain proteins undergo reversible backbone rearrangements. Such metamorphic proteins provide a means of facilitating the evolution of new folds and architectures. However, because natural folds emerged at the early stages of evolution, the potential role of metamorphic intermediates in mediating evolutionary transitions of structure remains largely unexplored. We evolved a set of new proteins based on approximately 100 amino acid fragments derived from tachylectin-2--a monomeric, 236 amino acids, five-bladed beta-propeller. Their structures reveal a unique pentameric assembly and novel beta-propeller structures. Although identical in sequence, the oligomeric subunits adopt two, or even three, different structures that together enable the pentameric assembly of two propellers connected via a small linker. Most of the subunits adopt a wild-type-like structure within individual five-bladed propellers. However, the bridging subunits exhibit domain swaps and asymmetric strand exchanges that allow them to complete the two propellers and connect them. Thus, the modular and metamorphic nature of these subunits enabled dramatic changes in tertiary and quaternary structure, while maintaining the lectin function. These oligomers therefore comprise putative intermediates via which beta-propellers can evolve from smaller elements. Our data also suggest that the ability of one sequence to equilibrate between different structures can be evolutionary optimized, thus facilitating the emergence of new structures.

Computational exploration of the network of sequence flow between protein structures

We investigate small sequence adjustments (of one or a few amino acids) that induce large conformational transitions between distinct and stable folds of proteins. Such transitions are intriguing from evolutionary and protein-design perspectives. They make it possible to search for ancient protein structures or to design protein switches that flip between folds and functions. A network of sequence flow between protein folds is computed for representative structures of the Protein Data Bank. The computed network is dense, on an average each structure is connected to tens of other folds. Proteins that attract sequences from a higher than expected number of neighboring folds are more likely to be enzymes and alpha/beta fold. The large number of connections between folds may reflect the need of enzymes to adjust their structures for alternative substrates. The network of the Cro family is discussed, and we speculate that capacity is an important factor (but not the only one) that determines protein evolution. The experimentally observed flip from all alpha to alpha + beta fold is examined by the network tools. A kinetic model for the transition of sequences between the folds (with only protein stability in mind) is proposed. Proteins 2010. (c) 2009 Wiley-Liss, Inc.

On the information expressed in enzyme primary structure: lessons from Ribonuclease A

The information expressed in an enzyme's primary structure is investigated. Brownian computations are directed at Ribonuclease A (RNase A) so as to quantify the information at the atom/covalent bond level. The information content and distribution are crucial because the primary structure underpins the molecule's chemical functions. Brownian computation data are illustrated for the native protein, mutants, and sequence isomers. The results identify signature features of the active protein on new information grounds. The same tools offer rapid screening of proteins and polypeptides whereby several examples are illustrated.

A minimal sequence code for switching protein structure and function

We present here a structural and mechanistic description of how a protein changes its fold and function, mutation by mutation. Our approach was to create 2 proteins that (i) are stably folded into 2 different folds, (ii) have 2 different functions, and (iii) are very similar in sequence. In this simplified sequence space we explore the mutational path from one fold to another. We show that an IgG-binding, 4beta+alpha fold can be transformed into an albumin-binding, 3-alpha fold via a mutational pathway in which neither function nor native structure is completely lost. The stabilities of all mutants along the pathway are evaluated, key high-resolution structures are determined by NMR, and an explanation of the switching mechanism is provided. We show that the conformational switch from 4beta+alpha to 3-alpha structure can occur via a single amino acid substitution. On one side of the switch point, the 4beta+alpha fold is >90% populated (pH 7.2, 20 degrees C). A single mutation switches the conformation to the 3-alpha fold, which is >90% populated (pH 7.2, 20 degrees C). We further show that a bifunctional protein exists at the switch point with affinity for both IgG and albumin.

Structural relatedness via flow networks in protein sequence space

A novel approach for evaluation of sequence relatedness via a network over the sequence space is presented. This relatedness is quantified by graph theoretical techniques. The graph is perceived as a flow network, and flow algorithms are applied. The number of independent pathways between nodes in the network is shown to reflect structural similarity of corresponding protein fragments. These results provide an appropriate parameter for quantitative estimation of such relatedness, as well as reliability of the prediction. They also demonstrate a new potential for sequence analysis and comparison by means of the flow network in the sequence space.

Evolution of protein modularity

Proteins in their evolution appear to follow several discrete stages, which is reflected in their modular organization. The sequences of the protein modules are highly variable while their functions and structures are rather conserved. The relatedness of the variable sequences is well represented by the networks in natural protein sequence space that also suggests evolutionary connections.

Contact density affects protein evolutionary rate from bacteria to animals

The density of contacts or the fraction of buried sites in a protein structure is thought to be related to a protein's designability, and genes encoding more designable proteins should evolve faster than other genes. Several recent studies have tested this hypothesis but have found conflicting results. Here, we investigate how a gene's evolutionary rate is affected by its protein's contact density, considering the four species Escherichia coli, Saccharomyces cerevisiae, Drosophila melanogaster, and Homo sapiens. We find for all four species that contact density correlates positively with evolutionary rate, and that these correlations do not seem to be confounded by gene expression level. The strength of this signal, however, varies widely among species. We also study the effect of contact density on domain evolution in multidomain proteins and find that a domain's contact density influences the domain's evolutionary rate. Within the same protein, a domain with higher contact density tends to evolve faster than a domain with lower contact density. Our study provides evidence that contact density can increase evolutionary rates, and that it acts similarly on the level of entire proteins and of individual protein domains.