The energy landscapes of repeat-containing proteins: topology, cooperativity, and the folding funnels of one-dimensional architectures

Reassessing the exon-foldon correspondence using frustration analysis

Protein folding and evolution are intimately linked phenomena. Here, we revisit the concept of exons as potential protein folding modules across a set of 38 abundant and conserved protein families. Taking advantage of genomic exon-intron organization and extensive protein sequence data, we explore exon boundary conservation and assess the foldon-like behavior of exons using energy landscape theoretic measurements. We found deviations in the exon size distribution from exponential decay indicating selection in evolution. We show that when taken together there is a pronounced tendency to independent foldability for segments corresponding to the more conserved exons, supporting the idea of exon-foldon correspondence. While 45% of the families follow this general trend when analyzed individually, there are some families for which other stronger functional determinants, such as preserving frustrated active sites, may be acting. We further develop a systematic partitioning of protein domains using exon boundary hotspots, showing that minimal common exons correspond with uninterrupted alpha and/or beta elements for the majority of the families but not for all of them.

Cooperative mechanics of PR65 scaffold underlies the allosteric regulation of the phosphatase PP2A

PR65, a horseshoe-shaped scaffold composed of 15 HEAT (observed in Huntingtin, elongation factor 3, protein phosphatase 2A, and the yeast kinase TOR1) repeats, forms, together with catalytic and regulatory subunits, the heterotrimeric protein phosphatase PP2A. We examined the role of PR65 in enabling PP2A enzymatic activity with computations at various levels of complexity, including hybrid approaches that combine full-atomic and elastic network models. Our study points to the high flexibility of this scaffold allowing for end-to-end distance fluctuations of 40-50 Å between compact and extended conformations. Notably, the intrinsic dynamics of PR65 facilitates complexation with the catalytic subunit and is retained in the PP2A complex enabling PR65 to engage the two domains of the catalytic subunit and provide the mechanical framework for enzymatic activity, with support from the regulatory subunit. In particular, the intra-repeat coils at the C-terminal arm play an important role in allosterically mediating the collective dynamics of PP2A, pointing to target sites for modulating PR65 function.

Evolution and folding of repeat proteins

Repeat proteins are made with tandem copies of similar amino acid stretches that fold into elongated architectures. These proteins constitute excellent model systems to investigate how evolution relates to structure, folding, and function. Here, we propose a scheme to map evolutionary information at the sequence level to a coarse-grained model for repeat-protein folding and use it to investigate the folding of thousands of repeat proteins. We model the energetics by a combination of an inverse Potts-model scheme with an explicit mechanistic model of duplications and deletions of repeats to calculate the evolutionary parameters of the system at the single-residue level. These parameters are used to inform an Ising-like model that allows for the generation of folding curves, apparent domain emergence, and occupation of intermediate states that are highly compatible with experimental data in specific case studies. We analyzed the folding of thousands of natural Ankyrin repeat proteins and found that a multiplicity of folding mechanisms are possible. Fully cooperative all-or-none transitions are obtained for arrays with enough sequence-similar elements and strong interactions between them, while noncooperative element-by-element intermittent folding arose if the elements are dissimilar and the interactions between them are energetically weak. Additionally, we characterized nucleation-propagation and multidomain folding mechanisms. We show that the global stability and cooperativity of the repeating arrays can be predicted from simple sequence scores.

Emerging accessibility patterns in long telomeric overhangs

We present single-molecule experimental and computational modeling studies investigating the accessibility of human telomeric overhangs of physiologically relevant lengths. We studied 25 different overhangs that contain 4-28 repeats of GGGTTA (G-Tract) sequence and accommodate one to seven tandem G-quadruplex (GQ) structures. Using the FRET-PAINT method, we probed the distribution of accessible sites via a short imager strand, which is complementary to a G-Tract and transiently binds to available sites. We report accessibility patterns that periodically change with overhang length and interpret these patterns in terms of the underlying folding landscape and folding frustration. Overhangs that have [4n]G-Tracts, (12, 16, 20…) demonstrate the broadest accessibility patterns where the peptide nucleic acid probe accesses G-Tracts throughout the overhang. On the other hand, constructs with [4n+2]G-Tracts, (14, 18, 22…) have narrower patterns where the neighborhood of the junction between single- and double-stranded telomeres is most accessible. We interpret these results as the folding frustration being higher in [4n]G-Tract constructs compared to [4n+2]G-Tract constructs. We also developed a computational model that tests the consistency of different folding stabilities and cooperativities between neighboring GQs with the observed accessibility patterns. Our experimental and computational studies suggest the neighborhood of the junction between single- and double-stranded telomeres is least stable and most accessible, which is significant as this is a potential site where the connection between POT1/TPP1 (bound to single-stranded telomere) and other shelterin proteins (localized on double-stranded telomere) is established.

Stochastic fluctuations promote ordered pattern formation of cells in the Notch-Delta signaling pathway

The Notch-Delta signaling pathway mediates cell differentiation implicated in many regulatory processes including spatiotemporal patterning in tissues by promoting alternate cell fates between neighboring cells. At the multicellular level, this "lateral inhibition” principle leads to checkerboard patterns with alternation of Sender and Receiver cells. While it is well known that stochasticity modulates cell fate specification, little is known about how stochastic fluctuations at the cellular level propagate during multicell pattern formation. Here, we model stochastic fluctuations in the Notch-Delta pathway in the presence of two different noise types–shot and white–for a multicell system. Our results show that intermediate fluctuations reduce disorder and guide the multicell lattice toward checkerboard-like patterns. By further analyzing cell fate transition events, we demonstrate that intermediate noise amplitudes provide enough perturbation to facilitate “proofreading” of disordered patterns and cause cells to switch to the correct ordered state (Sender surrounded by Receivers, and vice versa). Conversely, high noise can override environmental signals coming from neighboring cells and lead to switching between ordered and disordered patterns. Therefore, in analogy with spin glass systems, intermediate noise levels allow the multicell Notch system to escape frustrated patterns and relax towards the lower energy checkerboard pattern while at large noise levels the system is unable to find this ordered base of attraction.

The Notch pathway is involved in many biological processes and is known to form precise spatial patterns alternating Sender and Receiver cell states. Quantifying the implications of stochastic fluctuations provided insight that patterns formed in Notch-mediated pathways must follow a predetermined path towards checkerboard or exist in a noisy environment which promotes order through error correction.

We model Notch pattern formation stochastically and analyze the spatiotemporal dynamics. Our results show multicellular systems equilibrate towards ordered systems, but mistakes in the initial lattice propagate causing the systems to relax into frustrated systems. Only through existing in a noisy environment are the systems able to relax into the checkerboard pattern. Analyzing the temporal dynamics confirms, in environments with intermediate noise, the “incorrect” cells (Sender in a Sender environment, and vice versa) can be flipped to the correct state (Sender in a Receiver environment, and vice versa). Comparing with the spin glass energy landscape, we suggest the multicellular model follows a rugged landscape to form patterns with stochastic fluctuations required to enforce order throughout the system.

Unraveling the Mechanics of a Repeat-Protein Nanospring: From Folding of Individual Repeats to Fluctuations of the Superhelix

Tandem-repeat proteins comprise small secondary structure motifs that stack to form one-dimensional arrays with distinctive mechanical properties that are proposed to direct their cellular functions. Here, we use single-molecule optical tweezers to study the folding of consensus-designed tetratricopeptide repeats (CTPRs), superhelical arrays of short helix-turn-helix motifs. We find that CTPRs display a spring-like mechanical response in which individual repeats undergo rapid equilibrium fluctuations between partially folded and unfolded conformations. We rationalize the force response using Ising models and dissect the folding pathway of CTPRs under mechanical load, revealing how the repeat arrays form from the center toward both termini simultaneously. Most strikingly, we also directly observe the protein's superhelical tertiary structure in the force signal. Using protein engineering, crystallography, and single-molecule experiments, we show that the superhelical geometry can be altered by carefully placed amino acid substitutions, and we examine how these sequence changes affect intrinsic repeat stability and inter-repeat coupling. Our findings provide the means to dissect and modulate repeat-protein stability and dynamics, which will be essential for researchers to understand the function of natural repeat proteins and to exploit artificial repeats proteins in nanotechnology and biomedical applications.

Unraveling the Mechanics of a Repeat-Protein Nanospring: From Folding of Individual Repeats to Fluctuations of the Superhelix

Tandem-repeat proteins comprise small secondary structure motifs that stack to form one-dimensional arrays with distinctive mechanical properties that are proposed to direct their cellular functions. Here, we use single-molecule optical tweezers to study the folding of consensus-designed tetratricopeptide repeats (CTPRs), superhelical arrays of short helix-turn-helix motifs. We find that CTPRs display a spring-like mechanical response in which individual repeats undergo rapid equilibrium fluctuations between partially folded and unfolded conformations. We rationalize the force response using Ising models and dissect the folding pathway of CTPRs under mechanical load, revealing how the repeat arrays form from the center toward both termini simultaneously. Most strikingly, we also directly observe the protein's superhelical tertiary structure in the force signal. Using protein engineering, crystallography, and single-molecule experiments, we show that the superhelical geometry can be altered by carefully placed amino acid substitutions, and we examine how these sequence changes affect intrinsic repeat stability and inter-repeat coupling. Our findings provide the means to dissect and modulate repeat-protein stability and dynamics, which will be essential for researchers to understand the function of natural repeat proteins and to exploit artificial repeats proteins in nanotechnology and biomedical applications.

Resolving the fine structure in the energy landscapes of repeat proteins

Ankyrin (ANK) repeat proteins are coded by tandem occurrences of patterns with around 33 amino acids. They often mediate protein–protein interactions in a diversity of biological systems. These proteins have an elongated non-globular shape and often display complex folding mechanisms. This work investigates the energy landscape of representative proteins of this class made up of 3, 4 and 6 ANK repeats using the energy-landscape visualisation method (ELViM). By combining biased and unbiased coarse-grained molecular dynamics AWSEM simulations that sample conformations along the folding trajectories with the ELViM structure-based phase space, one finds a three-dimensional representation of the globally funnelled energy surface. In this representation, it is possible to delineate distinct folding pathways. We show that ELViMs can project, in a natural way, the intricacies of the highly dimensional energy landscapes encoded by the highly symmetric ankyrin repeat proteins into useful low-dimensional representations. These projections can discriminate between multiplicities of specific parallel folding mechanisms that otherwise can be hidden in oversimplified depictions.

Folding and Stability of Ankyrin Repeats Control Biological Protein Function

Ankyrin repeat proteins are found in all three kingdoms of life. Fundamentally, these proteins are involved in protein-protein interaction in order to activate or suppress biological processes. The basic architecture of these proteins comprises repeating modules forming elongated structures. Due to the lack of long-range interactions, a graded stability among the repeats is the generic properties of this protein family determining both protein folding and biological function. Protein folding intermediates were frequently found to be key for the biological functions of repeat proteins. In this review, we discuss most recent findings addressing this close relation for ankyrin repeat proteins including DARPins, Notch receptor ankyrin repeat domain, IκBα inhibitor of NFκB, and CDK inhibitor p19^INK4d. The role of local folding and unfolding and gradual stability of individual repeats will be discussed during protein folding, protein-protein interactions, and post-translational modifications. The conformational changes of these repeats function as molecular switches for biological regulation, a versatile property for modern drug discovery.

Parallel and Sequential Pathways of Molecular Recognition of a Tandem-Repeat Protein and Its Intrinsically Disordered Binding Partner

The Wnt signalling pathway plays an important role in cell proliferation, differentiation, and fate decisions in embryonic development and the maintenance of adult tissues. The twelve armadillo (ARM) repeat-containing protein β-catenin acts as the signal transducer in this pathway. Here, we investigated the interaction between β-catenin and the intrinsically disordered transcription factor TCF7L2, comprising a very long nanomolar-affinity interface of approximately 4800 Å2 that spans ten of the twelve ARM repeats of β-catenin. First, a fluorescence reporter system for the interaction was engineered and used to determine the kinetic rate constants for the association and dissociation. The association kinetics of TCF7L2 and β-catenin were monophasic and rapid (7.3 ± 0.1 × 107 M-1·s-1), whereas dissociation was biphasic and slow (5.7 ± 0.4 × 10-4 s-1, 15.2 ± 2.8 × 10-4 s-1). This reporter system was then combined with site-directed mutagenesis to investigate the striking variability in the conformation adopted by TCF7L2 in the three different crystal structures of the TCF7L2-β-catenin complex. We found that the mutation had very little effect on the association kinetics, indicating that most interactions form after the rate-limiting barrier for association. Mutations of the N- and C-terminal subdomains of TCF7L2 that adopt relatively fixed conformations in the crystal structures had large effects on the dissociation kinetics, whereas the mutation of the labile sub-domain connecting them had negligible effect. These results point to a two-site avidity mechanism of binding with the linker region forming a "fuzzy" complex involving transient contacts that are not site-specific. Strikingly, the two mutations in the N-terminal subdomain that had the largest effects on the dissociation kinetics showed two additional phases, indicating partial flux through an alternative dissociation pathway that is inaccessible to the wild type. The results presented here provide insights into the kinetics of the molecular recognition of a long intrinsically disordered region with an elongated repeat-protein surface, a process found to involve parallel routes with sequential steps in each.

Large Ankyrin repeat proteins are formed with similar and energetically favorable units

Ankyrin containing proteins are one of the most abundant repeat protein families present in all extant organisms. They are made with tandem copies of similar amino acid stretches that fold into elongated architectures. Here, we built and curated a dataset of 200 thousand proteins that contain 1.2 million Ankyrin regions and characterize the abundance, structure and energetics of the repetitive regions in natural proteins. We found that there is a continuous roughly exponential variety of array lengths with an exceptional frequency at 24 repeats. We described that individual repeats are seldom interrupted with long insertions and accept few deletions, in line with the known tertiary structures. We found that longer arrays are made up of repeats that are more similar to each other than shorter arrays, and display more favourable folding energy, hinting at their evolutionary origin. The array distributions show that there is a physical upper limit to the size of an array of repeats of about 120 copies, consistent with the limit found in nature. The identity patterns within the arrays suggest that they may have originated by sequential copies of more than one Ankyrin unit.

Decoupling a tandem-repeat protein: Impact of multiple loop insertions on a modular scaffold

The simple topology and modular architecture of tandem-repeat proteins such as tetratricopeptide repeats (TPRs) and ankyrin repeats makes them straightforward to dissect and redesign. Repeat-protein stability can be manipulated in a predictable way using site-specific mutations. Here we explore a different type of modification - loop insertion - that will enable a simple route to functionalisation of this versatile scaffold. We previously showed that a single loop insertion has a dramatically different effect on stability depending on its location in the repeat array. Here we dissect this effect by a combination of multiple and alternated loop insertions to understand the origins of the context-dependent loss in stability. We find that the scaffold is remarkably robust in that its overall structure is maintained. However, adjacent repeats are now only weakly coupled, and consequently the increase in solvent protection, and thus stability, with increasing repeat number that defines the tandem-repeat protein class is lost. Our results also provide us with a rulebook with which we can apply these principles to the design of artificial repeat proteins with precisely tuned folding landscapes and functional capabilities, thereby paving the way for their exploitation as a versatile and truly modular platform in synthetic biology.

Inferring repeat-protein energetics from evolutionary information

Natural protein sequences contain a record of their history. A common constraint in a given protein family is the ability to fold to specific structures, and it has been shown possible to infer the main native ensemble by analyzing covariations in extant sequences. Still, many natural proteins that fold into the same structural topology show different stabilization energies, and these are often related to their physiological behavior. We propose a description for the energetic variation given by sequence modifications in repeat proteins, systems for which the overall problem is simplified by their inherent symmetry. We explicitly account for single amino acid and pair-wise interactions and treat higher order correlations with a single term. We show that the resulting evolutionary field can be interpreted with structural detail. We trace the variations in the energetic scores of natural proteins and relate them to their experimental characterization. The resulting energetic evolutionary field allows the prediction of the folding free energy change for several mutants, and can be used to generate synthetic sequences that are statistically indistinguishable from the natural counterparts.

Toward a quantitative description of microscopic pathway heterogeneity in protein folding

Experimentally consistent statistical modeling of protein folding thermodynamics reveals unprecedented complexity with numerous parallel folding routes in five different proteins.

Binding of NFκB Appears to Twist the Ankyrin Repeat Domain of IκBα

Total internal reflection fluorescence-based single-molecule Förster resonance energy transfer (FRET) measurements were previously carried out on the ankyrin repeat domain (ARD) of IκBα, the temporally regulated inhibitor of canonical NFκB signaling. Under native conditions, most of the IκBα molecules showed stable, high FRET signals consistent with distances between the fluorophores estimated from the crystal structures of the NFκB(RelA/p50)-IκBα complex. Similar high FRET efficiencies were found when the IκBα molecules were either free or in complex with NFκB(RelA/p50), and were interpreted as being consistent with the crystallographically observed ARD structure. An exception to this was observed when the donor and acceptor fluorophores were attached in AR3 (residue 166) and AR6 (residue 262). Surprisingly, the FRET efficiency was lower for the bound IκBα molecules (0.67) than for the free IκBα molecules (0.74), apparently indicating that binding of NFκB(RelA/p50) stretches the ARD of IκBα. Here, we conducted confocal-based single-molecule FRET studies to investigate this phenomenon in greater detail. The results not only recapitulated the apparent stretching of the ARD but also showed that the effect was more pronounced when the N-terminal domains (NTDs) of both RelA and p50 were present, even though the interface between NFκB(RelA/p50) and IκBα encompasses only the dimerization domains. We also performed mass spectrometry-detected amide hydrogen/deuterium exchange (HDXMS) experiments on IκBα as well as IκBα bound to dimerization-domain-only constructs or full-length NFκB(RelA/p50). Although we expected the stretched IκBα to have regions with increased exchange, instead the HDXMS experiments showed decreases in exchange in AR3 and AR6 that were more pronounced when the NFκB NTDs were present. Simulations of the interaction recapitulated the increased distance between residues 166 and 262, and also provide a plausible mechanism for a twisting of the IκBα ARD induced by interactions of the IκBα proline-glutamate-serine-threonine-rich sequence with positively charged residues in the RelA NTD.

Repeat proteins challenge the concept of structural domains

Structural domains are believed to be modules within proteins that can fold and function independently. Some proteins show tandem repetitions of apparent modular structure that do not fold independently, but rather co-operate in stabilizing structural forms that comprise several repeat-units. For many natural repeat-proteins, it has been shown that weak energetic links between repeats lead to the breakdown of co-operativity and the appearance of folding sub-domains within an apparently regular repeat array. The quasi-1D architecture of repeat-proteins is crucial in detailing how the local energetic balances can modulate the folding dynamics of these proteins, which can be related to the physiological behaviour of these ubiquitous biological systems.

Comparison of protein repeat classifications based on structure and sequence families

Tandem repeats (TR) in proteins are common in nature and have several unique functions. They come in various forms that are frequently difficult to recognize from a sequence. A previously proposed structural classification has been recently implemented in the RepeatsDB database. This defines five main classes, mainly based on repeat unit length, with subclasses representing specific folds. Sequence-based classifications, such as Pfam, provide an alternative classification based on evolutionarily conserved repeat families. Here, we discuss a detailed comparison between the structural classes in RepeatsDB and the corresponding Pfam repeat families and clans. Most instances are found to map one-to-one between structure and sequence. Some notable exceptions such as leucine-rich repeats (LRRs) and α-solenoids are discussed.

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.

Structural and Energetic Characterization of the Ankyrin Repeat Protein Family

Ankyrin repeat containing proteins are one of the most abundant solenoid folds. Usually implicated in specific protein-protein interactions, these proteins are readily amenable for design, with promising biotechnological and biomedical applications. Studying repeat protein families presents technical challenges due to the high sequence divergence among the repeating units. We developed and applied a systematic method to consistently identify and annotate the structural repetitions over the members of the complete Ankyrin Repeat Protein Family, with increased sensitivity over previous studies. We statistically characterized the number of repeats, the folding of the repeat-arrays, their structural variations, insertions and deletions. An energetic analysis of the local frustration patterns reveal the basic features underlying fold stability and its relation to the functional binding regions. We found a strong linear correlation between the conservation of the energetic features in the repeat arrays and their sequence variations, and discuss new insights into the organization and function of these ubiquitous proteins.

Some natural proteins are formed with repetitions of similar amino acid stretches. Ankyrin-repeat proteins constitute one of the most abundant families of this class of proteins that serve as model systems to analyze how variations in sequences exert effects in structures and biological functions. We present an in-depth analysis of the ankyrin repeat protein family, characterizing the variations in the repeating arrays both at the structural and energetic level. We introduce a consistent annotation for the repeat characteristics and describe how the structural differences are related to the sequences by their underlying energetic signatures.

Mapping the Topography of a Protein Energy Landscape

Protein energy landscapes are highly complex, yet the vast majority of states within them tend to be invisible to experimentalists. Here, using site-directed mutagenesis and exploiting the simplicity of tandem-repeat protein structures, we delineate a network of these states and the routes between them. We show that our target, gankyrin, a 226-residue 7-ankyrin-repeat protein, can access two alternative (un)folding pathways. We resolve intermediates as well as transition states, constituting a comprehensive series of snapshots that map early and late stages of the two pathways and show both to be polarized such that the repeat array progressively unravels from one end of the molecule or the other. Strikingly, we find that the protein folds via one pathway but unfolds via a different one. The origins of this behavior can be rationalized using the numerical results of a simple statistical mechanics model that allows us to visualize the equilibrium behavior as well as single-molecule folding/unfolding trajectories, thereby filling in the gaps that are not accessible to direct experimental observation. Our study highlights the complexity of repeat-protein folding arising from their symmetrical structures; at the same time, however, this structural simplicity enables us to dissect the complexity and thereby map the precise topography of the energy landscape in full breadth and remarkable detail. That we can recapitulate the key features of the folding mechanism by computational analysis of the native structure alone will help toward the ultimate goal of designed amino-acid sequences with made-to-measure folding mechanisms-the Holy Grail of protein folding.

Capturing coevolutionary signals inrepeat proteins

BACKGROUND

The analysis of correlations of amino acid occurrences in globular domains has led to the development of statistical tools that can identify native contacts - portions of the chains that come to close distance in folded structural ensembles. Here we introduce a direct coupling analysis for repeat proteins - natural systems for which the identification of folding domains remains challenging.

RESULTS

We show that the inherent translational symmetry of repeat protein sequences introduces a strong bias in the pair correlations at precisely the length scale of the repeat-unit. Equalizing for this bias in an objective way reveals true co-evolutionary signals from which local native contacts can be identified. Importantly, parameter values obtained for all other interactions are not significantly affected by the equalization. We quantify the robustness of the procedure and assign confidence levels to the interactions, identifying the minimum number of sequences needed to extract evolutionary information in several repeat protein families.

CONCLUSIONS

The overall procedure can be used to reconstruct the interactions at distances larger than repeat-pairs, identifying the characteristics of the strongest couplings in each family, and can be applied to any system that appears translationally symmetric.

Understanding and identifying amino acid repeats

Amino acid repeats (AARs) are abundant in protein sequences. They have particular roles in protein function and evolution. Simple repeat patterns generated by DNA slippage tend to introduce length variations and point mutations in repeat regions. Loss of normal and gain of abnormal function owing to their variable length are potential risks leading to diseases. Repeats with complex patterns mostly refer to the functional domain repeats, such as the well-known leucine-rich repeat and WD repeat, which are frequently involved in protein–protein interaction. They are mainly derived from internal gene duplication events and stabilized by ‘gate-keeper’ residues, which play crucial roles in preventing inter-domain aggregation. AARs are widely distributed in different proteomes across a variety of taxonomic ranges, and especially abundant in eukaryotic proteins. However, their specific evolutionary and functional scenarios are still poorly understood. Identifying AARs in protein sequences is the first step for the further investigation of their biological function and evolutionary mechanism. In principle, this is an NP-hard problem, as most of the repeat fragments are shaped by a series of sophisticated evolutionary events and become latent periodical patterns. It is not possible to define a uniform criterion for detecting and verifying various repeat patterns. Instead, different algorithms based on different strategies have been developed to cope with different repeat patterns. In this review, we attempt to describe the amino acid repeat-detection algorithms currently available and compare their strategies based on an in-depth analysis of the biological significance of protein repeats.

Folding pathway of a multidomain protein depends on its topology of domain connectivity

How do the folding mechanisms of multidomain proteins depend on protein topology? We addressed this question by developing an Ising-like structure-based model and applying it for the analysis of free-energy landscapes and folding kinetics of an example protein, Escherichia coli dihydrofolate reductase (DHFR). DHFR has two domains, one comprising discontinuous N- and C-terminal parts and the other comprising a continuous middle part of the chain. The simulated folding pathway of DHFR is a sequential process during which the continuous domain folds first, followed by the discontinuous domain, thereby avoiding the rapid decrease in conformation entropy caused by the association of the N- and C-terminal parts during the early phase of folding. Our simulated results consistently explain the observed experimental data on folding kinetics and predict an off-pathway structural fluctuation at equilibrium. For a circular permutant for which the topological complexity of wild-type DHFR is resolved, the balance between energy and entropy is modulated, resulting in the coexistence of the two folding pathways. This coexistence of pathways should account for the experimentally observed complex folding behavior of the circular permutant.

Frustration in biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their own structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of frustration in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and especially how biomolecular structure connects to function by means of localized frustration. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding mechanisms. We review here how the biological functions of proteins are related to subtle local physical frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. In this review, we also emphasize that frustration, far from being always a bad thing, is an essential feature of biomolecules that allows dynamics to be harnessed for function. In this way, we hope to illustrate how Frustration is a fundamental concept in molecular biology.

A disorder-induced domino-like destabilization mechanism governs the folding and functional dynamics of the repeat protein IκBα

The stability of the repeat protein IκBα, a transcriptional inhibitor in mammalian cells, is critical in the functioning of the NF-κB signaling module implicated in an array of cellular processes, including cell growth, disease, immunity and apoptosis. Structurally, IκBα is complex, with both ordered and disordered regions, thus posing a challenge to the available computational protocols to model its conformational behavior. Here, we introduce a simple procedure to model disorder in systems that undergo binding-induced folding that involves modulation of the contact map guided by equilibrium experimental observables in combination with an Ising-like Wako-Saitô-Muñoz-Eaton model. This one-step procedure alone is able to reproduce a variety of experimental observables, including ensemble thermodynamics (scanning calorimetry, pre-transitions, m-values) and kinetics (roll-over in chevron plot, intermediates and their identity), and is consistent with hydrogen-deuterium exchange measurements. We further capture the intricate distance-dynamics between the domains as measured by single-molecule FRET by combining the model predictions with simple polymer physics arguments. Our results reveal a unique mechanism at work in IκBα folding, wherein disorder in one domain initiates a domino-like effect partially destabilizing neighboring domains, thus highlighting the effect of symmetry-breaking at the level of primary sequences. The offshoot is a multi-state and a dynamic conformational landscape that is populated by increasingly partially folded ensembles upon destabilization. Our results provide, in a straightforward fashion, a rationale to the promiscuous binding and short intracellular half-life of IκBα evolutionarily engineered into it through repeats with variable stabilities and expand the functional repertoire of disordered regions in proteins.

Complex energy landscape of a giant repeat protein

Here, we reveal a remarkable complexity in the unfolding of giant HEAT-repeat protein PR65/A, a molecular adaptor for the heterotrimeric PP2A phosphatases. The repeat array ruptures at multiple sites, leading to intermediate states with noncontiguous folded subdomains. There is a dominant sequence of unfolding, which reflects a nonuniform stability distribution across the repeat array and can be rationalized by theoretical models accounting for heterogeneous contact density in the folded structure. Unfolding of certain intermediates is, however, competitive, leading to parallel unfolding pathways. The low-stability, central repeats sample unfolded conformations under physiological conditions, suggesting how folding directs function: certain regions present rigid motifs for molecular recognition, whereas others have the flexibility with which to broaden the search area, as in the fly-casting mechanism. Partial unfolding of PR65/A also impacts catalysis by altering the proximity of bound catalytic subunit and substrate. Thus, the repeat array orchestrates the assembly and activity of PP2A.

Crystal structure of c5321: a protective antigen present in uropathogenic Escherichia coli strains displaying an SLR fold

Background

Increasing rates of antimicrobial resistance among uropathogens led, among other efforts, to the application of subtractive reverse vaccinology for the identification of antigens present in extraintestinal pathogenic E. coli (ExPEC) strains but absent or variable in non-pathogenic strains, in a quest for a broadly protective Escherichia coli vaccine. The protein coded by locus c5321 from CFT073 E. coli was identified as one of nine potential vaccine candidates against ExPEC and was able to confer protection with an efficacy of 33% in a mouse model of sepsis. c5321 (known also as EsiB) lacks functional annotation and structurally belongs to the Sel1-like repeat (SLR) family. Herein, as part of the general characterization of this potential antigen, we have focused on its structural properties.

Results

We report the 1.74 Å-resolution crystal structure of c5321 from CFT073 E. coli determined by Se-Met SAD phasing. The structure is composed of 11 SLR units in a topological organisation that highly resembles that found in HcpC from Helicobacter pylori, with the main difference residing in how the super-helical fold is stabilised. The stabilising effect of disulfide bridges in HcpC is replaced in c5321 by a strengthening of the inter-repeat hydrophobic core. A metal-ion binding site, uncharacteristic of SLR proteins, is detected between SLR units 3 and 4 in the region of the inter-repeat hydrophobic core. Crystal contacts are observed between the C-terminal tail of one molecule and the C-terminal amphipathic groove of a neighbouring one, resembling interactions between ligand and proteins containing tetratricopeptide-like repeats.

Conclusions

The structure of antigen c5321 presents a mode of stabilization of the SLR fold different from that observed in close homologs of known structure. The location of the metal-ion binding site and the observed crystal contacts suggest a potential role in regulation of conformational flexibility and interaction with yet unidentified target proteins, respectively. These findings open new perspectives in both antigen design and for the identification of a functional role for this protective antigen.

The diminishing role of hubs in dynamical processes on complex networks

It is notoriously difficult to predict the behaviour of a complex self-organizing system, where the interactions among dynamical units form a heterogeneous topology. Even if the dynamics of each microscopic unit is known, a real understanding of their contributions to the macroscopic system behaviour is still lacking. Here, we develop information-theoretical methods to distinguish the contribution of each individual unit to the collective out-of-equilibrium dynamics. We show that for a system of units connected by a network of interaction potentials with an arbitrary degree distribution, highly connected units have less impact on the system dynamics when compared with intermediately connected units. In an equilibrium setting, the hubs are often found to dictate the long-term behaviour. However, we find both analytically and experimentally that the instantaneous states of these units have a short-lasting effect on the state trajectory of the entire system. We present qualitative evidence of this phenomenon from empirical findings about a social network of product recommendations, a protein–protein interaction network and a neural network, suggesting that it might indeed be a widespread property in nature.

Detecting repetitions and periodicities in proteins by tiling the structural space

The notion of energy landscapes provides conceptual tools for understanding the complexities of protein folding and function. Energy landscape theory indicates that it is much easier to find sequences that satisfy the “Principle of Minimal Frustration” when the folded structure is symmetric (Wolynes, P. G. Symmetry and the Energy Landscapes of Biomolecules. Proc. Natl. Acad. Sci. U.S.A.1996, 93, 14249–14255). Similarly, repeats and structural mosaics may be fundamentally related to landscapes with multiple embedded funnels. Here we present analytical tools to detect and compare structural repetitions in protein molecules. By an exhaustive analysis of the distribution of structural repeats using a robust metric, we define those portions of a protein molecule that best describe the overall structure as a tessellation of basic units. The patterns produced by such tessellations provide intuitive representations of the repeating regions and their association toward higher order arrangements. We find that some protein architectures can be described as nearly periodic, while in others clear separations between repetitions exist. Since the method is independent of amino acid sequence information, we can identify structural units that can be encoded by a variety of distinct amino acid sequences.

Tandem-repeat proteins: regularity plus modularity equals design-ability

Researchers in the field of rational protein design face a significant challenge, which arises from the two defining and inter-related features of typical globular protein structures, namely topological complexity and cooperativity. In striking contrast to globular proteins, tandem repeat proteins, such as ankyrin, tetratricopeptide and leucine-rich repeats, have regular, modular, linearly arrayed structures which makes it especially straightforward to dissect and redesign their properties. Here we review what we have learnt about the biophysics of natural repeat proteins and recent progress in applying that knowledge to engineer the thermodynamics, folding pathways and molecular recognition properties of tandem repeat proteins, and we discuss the wealth of possibilities presented for the extension of this modular construction process to build new molecules for use in medicine and biotechnology.

Structure and mechanism of maximum stability of isolated alpha-helical protein domains at a critical length scale

The stability of alpha helices is important in protein folding, bioinspired materials design, and controls many biological properties under physiological and disease conditions. Here we show that a naturally favored alpha helix length of 9 to 17 amino acids exists at which the propensity towards the formation of this secondary structure is maximized. We use a combination of thermodynamical analysis, well-tempered metadynamics molecular simulation and statistical analyses of experimental alpha helix length distributions and find that the favored alpha helix length is caused by a competition between alpha helix folding, unfolding into a random coil and formation of higher-order tertiary structures. The theoretical result is suggested to be used to explain the statistical distribution of the length of alpha helices observed in natural protein structures. Our study provides mechanistic insight into fundamental controlling parameters in alpha helix structure formation and potentially other biopolymers or synthetic materials. The result advances our fundamental understanding of size effects in the stability of protein structures and may enable the design of de novo alpha-helical protein materials.

Discrete kinetic models from funneled energy landscape simulations

A general method for facilitating the interpretation of computer simulations of protein folding with minimally frustrated energy landscapes is detailed and applied to a designed ankyrin repeat protein (4ANK). In the method, groups of residues are assigned to foldons and these foldons are used to map the conformational space of the protein onto a set of discrete macrobasins. The free energies of the individual macrobasins are then calculated, informing practical kinetic analysis. Two simple assumptions about the universality of the rate for downhill transitions between macrobasins and the natural local connectivity between macrobasins lead to a scheme for predicting overall folding and unfolding rates, generating chevron plots under varying thermodynamic conditions, and inferring dominant kinetic folding pathways. To illustrate the approach, free energies of macrobasins were calculated from biased simulations of a non-additive structure-based model using two structurally motivated foldon definitions at the full and half ankyrin repeat resolutions. The calculated chevrons have features consistent with those measured in stopped flow chemical denaturation experiments. The dominant inferred folding pathway has an “inside-out”, nucleation-propagation like character.

Modulation of folding kinetics of repeat proteins: interplay between intra- and interdomain interactions

Repeat proteins have unique elongated structures that, unlike globular proteins, are quite modular. Despite their simple one-dimensional structure, repeat proteins exhibit intricate folding behavior with a complexity similar to that of globular proteins. Therefore, repeat proteins allow one to quantify fundamental aspects of the biophysics of protein folding. One important feature of repeat proteins is the interfaces between the repeating units. In particular, the distribution of stabilities within and between the repeats was previously suggested to affect their folding characteristics. In this study, we explore how the interface affects folding kinetics and cooperativity by investigating two families of repeat proteins, namely, the Ankyrin and tetratricopeptide repeat proteins, which differ in the number of interfacial contacts that are formed between their units as well as in their folding behavior. By using simple topology-based models, we show that modulating the energetic strength of the interface relative to that of the repeat itself can drastically change the protein stability, folding rate, and cooperativity. By further dissecting the interfacial contacts into several subsets, we isolated the effects of each of these groups on folding kinetics. Our study highlights the importance of interface connectivity in determining the folding behavior.

From artificial antibodies to nanosprings: the biophysical properties of repeat proteins

In this chapter we review recent studies of repeat proteins, a class of proteins consisting of tandem arrays of small structural motifs that stack approximately linearly to produce elongated structures. We discuss the observation that, despite lacking the long-range tertiary interactions that are thought to be the hallmark of globular protein stability, repeat proteins can be as stable and as co-orperatively folded as their globular counterparts. The symmetry inherent in the structures of repeat arrays, however, means there can be many partly folded species (whether it be intermediates or transition states) that have similar stabilities. Consequently they do have distinct folding properties compared with globular proteins and these are manifest in their behaviour both at equilibrium and under kinetic conditions. Thus, when studying repeat proteins one appears to be probing a moving target: a relatively small perturbation, by mutation for example, can result in a shift to a different intermediate or transition state. The growing literature on these proteins illustrates how their modular architecture can be adapted to a remarkable array of biological and physical roles, both in vivo and in vitro. Further, their simple architecture makes them uniquely amenable to redesign-of their stability, folding and function-promising exciting possibilities for future research.

The contribution of entropy, enthalpy, and hydrophobic desolvation to cooperativity in repeat-protein folding

Cooperativity is a defining feature of protein folding, but its thermodynamic and structural origins are not completely understood. By constructing consensus ankyrin repeat protein arrays that have nearly identical sequences, we quantify cooperativity by resolving stability into intrinsic and interfacial components. Heteronuclear NMR and CD spectroscopy show that these constructs adopt ankyrin repeat structures. Applying a one-dimensional Ising model to a series of constructs chosen to maximize information content in unfolding transitions, we quantify stabilities of the terminal capping repeats, and resolve the effects of denaturant into intrinsic and interfacial components. Reversible thermal denaturation resolves interfacial and intrinsic free energies into enthalpic, entropic, and heat capacity terms. Intrinsic folding is entropically disfavored, whereas interfacial interaction is entropically favored and attends a decrease in heat capacity. These results suggest that helix formation and backbone ordering occurs upon intrinsic folding, whereas hydrophobic desolvation occurs upon interfacial interaction, contributing to cooperativity.

Analysis of the equilibrium and kinetics of the ankyrin repeat protein myotrophin

We apply the Wako-Saito-Muñoz-Eaton model to the study of myotrophin, a small ankyrin repeat protein, whose folding equilibrium and kinetics have been recently characterized experimentally. The model, which is a native-centric with binary variables, provides a finer microscopic detail than the Ising model that has been recently applied to some different repeat proteins, while being still amenable for an exact solution. In partial agreement with the experiments, our results reveal a weakly three-state equilibrium and a two-state-like kinetics of the wild-type protein despite the presence of a nontrivial free-energy profile. These features appear to be related to a careful "design" of the free-energy landscape, so that mutations can alter this picture, stabilizing some intermediates and changing the position of the rate-limiting step. Also, the experimental findings of two alternative pathways, an N-terminal and a C-terminal one, are qualitatively confirmed, even if the variations in the rates upon the experimental mutations cannot be quantitatively reproduced. Interestingly, the folding and unfolding pathways appear to be different, even if closely related: a property that is not generally considered in the phenomenological interpretation of the experimental data.

Modulating repeat protein stability: the effect of individual helix stability on the collective behavior of the ensemble

Repeat proteins are tandem arrays of a small structural motif, in which tertiary structure is stabilized by interactions within a repeat and between neighboring repeats. Several studies have shown that this modular structure is manifest in modular thermodynamic properties. Specifically, the global stability of a repeat protein can be described by simple linear models, considering only two parameters: the stability of the individual repeated units (H) and the coupling interaction between the units (J). If the repeat units are identical, single values of H and J, together with the number of repeated units, is sufficient to completely describe the thermodynamic behavior of any protein within a series. In this work, we demonstrate how the global stability of a repeat protein can be changed, in a predictable fashion, by modifying only the H parameter. Taking a previously characterized series of consensus tetratricopeptide repeats (TPR) (CTPRa) proteins, we introduced mutations into the basic repeating unit, such that the stability of the individual repeat unit was increased, but its interaction with neighboring units was unchanged. In other words, we increased H but kept J constant. We demonstrated that the denaturation curves for a series of such repeat proteins can be fit and additional curves can be predicted by the one-dimensional Ising model in which only H has changed from the original fit for the CTPRa series. Our results show that we can significantly increase the stability of a repeat protein by rationally increasing the stability of the units (H), whereas the interaction between repeats (J) remains unchanged.

Molecular mechanisms of system control of NF-kappaB signaling by IkappaBalpha

The NF-kappaB family of transcription factors responds to inflammatory cytokines with rapid transcriptional activation and subsequent signal repression. Much of the system control depends on the unique characteristics of its major inhibitor, IkappaBalpha, which appears to have folding dynamics that underlie the biophysical properties of its activity. Theoretical folding studies followed by experiments have shown that a portion of the ankyrin repeat domain of IkappaBalpha folds on binding. In resting cells, IkappaBalpha is constantly being synthesized, but most of it is rapidly degraded, leaving only a very small pool of free IkappaBalpha. Nearly all of the NF-kappaB is bound to IkappaBalpha, resulting in near-complete inhibition of nuclear localization and transcriptional activation. Combined solution biophysical measurements and quantitative protein half-life measurements inside cells have allowed us to understand how the inhibition occurs, why IkappaBalpha can be degraded quickly in the free state but remain extremely stable in the bound state, and how signal activation and repression can be tuned by IkappaB folding dynamics. This review summarizes results of in vitro and in vivo experiments that converge demonstrating the effective interplay between biophysics and cell biology in understanding transcriptional control by the NF-kappaB signaling module.

Expansion of tandem repeats in sea anemone Nematostella vectensis proteome: A source for gene novelty?

BACKGROUND

The complete proteome of the starlet sea anemone, Nematostella vectensis, provides insights into gene invention dating back to the Cnidarian-Bilaterian ancestor. With the addition of the complete proteomes of Hydra magnipapillata and Monosiga brevicollis, the investigation of proteins having unique features in early metazoan life has become practical. We focused on the properties and the evolutionary trends of tandem repeat (TR) sequences in Cnidaria proteomes.

RESULTS

We found that 11-16% of N. vectensis proteins contain tandem repeats. Most TRs cover 150 amino acid segments that are comprised of basic units of 5-20 amino acids. In total, the N. Vectensis proteome has about 3300 unique TR-units, but only a small fraction of them are shared with H. magnipapillata, M. brevicollis, or mammalian proteomes. The overall abundance of these TRs stands out relative to that of 14 proteomes representing the diversity among eukaryotes and within the metazoan world. TR-units are characterized by a unique composition of amino acids, with cysteine and histidine being over-represented. Structurally, most TR-segments are associated with coiled and disordered regions. Interestingly, 80% of the TR-segments can be read in more than one open reading frame. For over 100 of them, translation of the alternative frames would result in long proteins. Most domain families that are characterized as repeats in eukaryotes are found in the TR-proteomes from Nematostella and Hydra.

CONCLUSIONS

While most TR-proteins have originated from prediction tools and are still awaiting experimental validations, supportive evidence exists for hundreds of TR-units in Nematostella. The existence of TR-proteins in early metazoan life may have served as a robust mode for novel genes with previously overlooked structural and functional characteristics.

Exploring the folding energy landscape of a series of designed consensus tetratricopeptide repeat proteins

Repeat proteins contain short, tandem arrays of simple structural motifs (20-40 aa). These stack together to form nonglobular structures that are stabilized by short-range interactions from residues close in primary sequence. Unlike globular proteins, they have few, if any, long-range nonlocal stabilizing interactions. One ubiquitous repeat is the tetratricopeptide motif (TPR), a 34-aa helix-turn-helix motif. In this article we describe the folding kinetics of a series of 7 designed TPR proteins that are assembled from arraying identical designed consensus repeats (CTPRan). These range from the smallest 2-repeat protein to a large 10-repeat protein (approximately 350 aa). In particular, we describe how the energy landscape changes with the addition of repeat units. The data reveal that although the CTPRa proteins have low local frustration, their highly symmetric, modular native structure is reflected in their multistate kinetics of unfolding and folding. Moreover, although the initial folding of all CTPRan proteins involves a nucleus with similar solvent accessibility, their subsequent folding to the native structure depends directly on repeat number. This corresponds to an increasingly complex landscape that culminates in CTPRa10 populating a misfolded, off-pathway intermediate. These results extend our current understanding of the malleable folding pathways of repeat proteins and highlight the consequences of adding identical repeats to the energy landscape.

Intra-molecular chaperone: the role of the N-terminal in conformational selection and kinetic control

The vast majority of the proteins in nature are under thermodynamic control, consistent with the universally accepted notion that proteins exist in their thermodynamically most stable state. Yet, recently a number of examples of proteins whose fold is under kinetic control have come to light. Their functions and environments vary. The first among these are some proteases, discovered in the early 1990s. There, an N-terminal proregion is self-cleaved after the protein folded, leaving the remainder of the chain in a kinetically trapped state. A related scenario was observed for microcin J25, an antibacterial peptide. This peptide presents a trapped covalently knotted conformation. The third and the most recently discovered case is the multidrug-resistant transporter protein, P-glycoprotein. There, a synonymous 'silent' mutation leads to ribosome stalling with a consequent altered kinetically trapped state. Here we argue that in all three examples, the N-terminal plays the role of an intra-molecular chaperone, that is, the N-terminal conformation selects among all competing local conformations of a downstream segment. By providing a pattern, the N-terminal chaperone segment assists the protein folding process. If the N-terminal is subsequently cleaved, the protein can be under kinetic control, since it is trapped in a thermodynamically less-stable state.

Characterization of the unfolded state of repeat proteins

The unfolded state ensemble of proteins has been described as a structurally featureless state. While this approach is supported by the fact that many unfolded proteins follow the scaling law behavior of a random coil, there is evidence that the unfolded states of various proteins are stabilized by native or non-native interactions. Recently, the existence of extensive non-native structure was reported for a repeat protein, which resulted in a scaling law exponent that is significantly smaller than that of a random polymer [Cortajarena et al., J. Mol. Biol. 382(1), 203-212 (2008)]. It was concluded that the high compactness of this protein stems from a significant fraction of interacting PP(II) helical segments in the unfolded state. In this study, we aim at providing possible molecular understanding of this anomalous compactness of the unfolded state and to investigate its origin. Using a hierarchy of computational models, we ask whether in general the unfolded state of a repeat protein is likely to be intrinsically more compact than the unfolded state of globular proteins, or whether this phenomenon depends mostly on the occurrence of a specific sequence that promotes PP(II) conformations. Our results suggest that the formation of the PP(II) conformation is indeed essential, yet the recurring sequence of repeat proteins promotes the interactions between these PP(II) segments and the formation of non-native interactions in the unfolded state.