Direct observation of parallel folding pathways revealed using a symmetric repeat protein system

A STRP-ed definition of Structured Tandem Repeats in Proteins

Tandem Repeat Proteins (TRPs) are a class of proteins with repetitive amino acid sequences that have been studied extensively for over two decades. Different features at the level of sequence, structure, function and evolution have been attributed to them by various authors. And yet many of its salient features appear only when looking at specific subclasses of protein tandem repeats. Here, we attempt to rationalize the existing knowledge on Tandem Repeat Proteins (TRPs) by pointing out several dichotomies. The emerging picture is more nuanced than generally assumed and allows us to draw some boundaries of what is not a "proper" TRP. We conclude with an operational definition of a specific subset, which we have denominated STRPs (Structural Tandem Repeat Proteins), which separates a subclass of tandem repeats with distinctive features from several other less well-defined types of repeats. We believe that this definition will help researchers in the field to better characterize the biological meaning of this large yet largely understudied group of proteins.

Replacement of the native cis prolines by alanine leads to simplification of the complex folding mechanism of a small globular protein

The folding mechanism of MNEI, a single-chain variant of naturally occurring double-chain monellin, is complex, with multiple parallel refolding channels. To determine whether its folding energy landscape could be simplified, the two native cis-prolines, Pro41 and Pro93, were mutated, singly and together, to Ala. The stability of P93A was the same as that of the wild-type protein, pWT; however, P41A and P41AP93A were destabilized by ∼0.9 kcal mol-1. The effects of the mutations on the very fast, fast, slow, and very slow phases of folding were studied. They showed that heterogeneity in the unfolded state arises due to cis to trans isomerization of the Gly92-Pro93 peptide bond. The Pro41 to Ala mutation abolished the very slow phase of folding, whereas surprisingly, the Pro93 to Ala mutation abolished the very fast phase of folding. Double-jump, interrupted folding experiments indicated that two sequential trans to cis proline isomerization steps, of the Gly92-Pro93 peptide bond followed by the Arg40-Pro41 peptide bond, lead to the formation of the native state. They also revealed the accumulation of a late native-like intermediate, N∗, which differs from the native state in the isomeric status of the Arg40-Pro41 bond, as well as in a few tertiary contacts as monitored by near-UV CD measurements. The Pro to Ala mutations not only eliminated the cis to trans Pro isomerization reaction in the unfolded state, but also the two trans to cis Pro isomerization reactions during folding. By doing so, and by differentially affecting the relative stabilities of folding intermediates, the mutations resulted in a simplification of the folding mechanism. The two Pro to Ala mutations together accelerate folding to such an extent that the native state forms more than 1000-fold faster than in the case of pWT.

Stability Islands and the Folding Cooperativity of a Seven-Repeat Array from Topoisomerase V

Cooperativity is a central feature of protein folding, but the thermodynamic and structural origins of cooperativity remain poorly understood. To quantify cooperativity, we measured guanidine-induced unfolding transitions of single helix-hairpin-helix (HhH)2 repeats and tandem pairs from a seven-repeat segment of Methanopyrus kandleri Topoisomerase V (Topo V) to determine intrinsic repeat stability and interfacial free energies between repeats. Most single-repeat constructs are folded and stable; moreover, several pairs have unfolding midpoints that exceed midpoints of the single repeats they comprise, demonstrating favorable coupling between repeats. Analyzing unfolding transitions with a modified Ising model, we find a broad range of intrinsic and interfacial free energies. Surprisingly, the G repeat, which lacks density in the crystal structure of Topo V without DNA, is the most stable repeat in the array. Using nuclear magnetic resonance spectroscopy, we demonstrate that the isolated G repeat adopts a canonical (HhH)2 fold and forms an ordered interface with the F-repeat but not with the H repeat. Using parameters from our paired Ising fit, we built a partition function for the seven-repeat array. The multistate unfolding transition predicted from this partition function is in excellent agreement with the experimental unfolding transition, providing strong justification for the nearest-neighbor model. The seven-repeat partition function predicts a native state in which three independent segments ("stability islands") of interacting repeats are separated by two unstable interfaces. We confirm this segmented architecture by measuring the unfolding transition of an equimolar mixture of these three separate polypeptides. This segmented structural organization may facilitate wrapping around DNA.

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.

Multivalent Interaction of Beta-Catenin With its Intrinsically Disordered Binding Partner Adenomatous Polyposis Coli

The Wnt signalling pathway plays key roles in cell proliferation, differentiation and fate decisions in embryonic development and maintenance of adult tissues, and the twelve Armadillo (ARM) repeat-containing protein β-catenin acts as the signal transducer in this pathway. Here we investigate the interaction between β-catenin's ARM repeat domain and the intrinsically disordered protein adenomatous polyposis coli (APC). APC is a giant multivalent scaffold that brings together the different components of the so-called "β-catenin destruction complex", which drives β-catenin degradation via the ubiquitin-proteasome pathway. Mutations and truncations in APC, resulting in loss of APC function and hence elevated β-catenin levels and upregulation of Wnt signalling, are associated with numerous cancers including colorectal carcinomas. APC has a long intrinsically disordered region (IDR) that contains a series of 15-residue and 20-residue binding regions for β-catenin. Here we explore the multivalent nature of the interaction of β-catenin with the highest affinity APC repeat, both at equilibrium and under kinetic conditions. We use a combination of single-site substitutions, deletions and insertions to dissect the mechanism of molecular recognition and the roles of the three β-catenin-binding subdomains of APC.

Functionalization of a symmetric protein scaffold: Redundant folding nuclei and alternative oligomeric folding pathways

Successful de novo protein design ideally targets specific folding kinetics, stability thermodynamics, and biochemical functionality, and the simultaneous achievement of all these criteria in a single step design is challenging. Protein design is potentially simplified by separating the problem into two steps: (a) an initial design of a protein "scaffold" having appropriate folding kinetics and stability thermodynamics, followed by (b) appropriate functional mutation-possibly involving insertion of a peptide functional "cassette." This stepwise approach can also separate the orthogonal effects of the "stability/function" and "foldability/function" tradeoffs commonly observed in protein design. If the scaffold is a protein architecture having an exact rotational symmetry, then there is the potential for redundant folding nuclei and multiple equivalent sites of functionalization; thereby enabling broader functional adaptation. We describe such a "scaffold" and functional "cassette" design strategy applied to a β-trefoil threefold symmetric architecture and a heparin ligand functionality. The results support the availability of redundant folding nuclei within this symmetric architecture, and also identify a minimal peptide cassette conferring heparin affinity. The results also identify an energy barrier of destabilization that switches the protein folding pathway from monomeric to trimeric, thereby identifying another potential advantage of symmetric protein architecture in de novo design.

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.

Heterogeneity in Protein Folding and Unfolding Reactions

Proteins have dynamic structures that undergo chain motions on time scales spanning from picoseconds to seconds. Resolving the resultant conformational heterogeneity is essential for gaining accurate insight into fundamental mechanistic aspects of the protein folding reaction. The use of high-resolution structural probes, sensitive to population distributions, has begun to enable the resolution of site-specific conformational heterogeneity at different stages of the folding reaction. Different states populated during protein folding, including the unfolded state, collapsed intermediate states, and even the native state, are found to possess significant conformational heterogeneity. Heterogeneity in protein folding and unfolding reactions originates from the reduced cooperativity of various kinds of physicochemical interactions between various structural elements of a protein, and between a protein and solvent. Heterogeneity may arise because of functional or evolutionary constraints. Conformational substates within the unfolded state and the collapsed intermediates that exchange at rates slower than the subsequent folding steps give rise to heterogeneity on the protein folding pathways. Multiple folding pathways are likely to represent distinct sequences of structure formation. Insight into the nature of the energy barriers separating different conformational states populated during (un)folding can also be obtained by resolving heterogeneity.

Engineering and exploiting synthetic allostery of NanoLuc luciferase

Allostery enables proteins to interconvert different biochemical signals and form complex metabolic and signaling networks. We hypothesize that circular permutation of proteins increases the probability of functional coupling of new N- and C- termini with the protein's active center through increased local structural disorder. To test this we construct a synthetically allosteric version of circular permutated NanoLuc luciferase that can be activated through ligand-induced intramolecular non-covalent cyclisation. This switch module is tolerant of the structure of binding domains and their ligands, and can be used to create biosensors of proteins and small molecules. The developed biosensors covers a range of emission wavelengths and displays sensitivity as low as 50pM and dynamic range as high as 16-fold and could quantify their cognate ligand in human fluids. We apply hydrogen exchange kinetic mass spectroscopy to analyze time resolved structural changes in the developed biosensors and observe ligand-mediated folding of newly created termini.

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.

Protein folding - seeing is deceiving

This Perspective is intended to raise questions about the conventional interpretation of protein folding. According to the conventional interpretation, developed over many decades, a protein population can visit a vast number of conformations under unfolding conditions, but a single dominant native population emerges under folding conditions. Accordingly, folding comes with a substantial loss of conformational entropy. How is this price paid? The conventional answer is that favorable interactions between and among the side chains can compensate for entropy loss, and moreover, these interactions are responsible for the structural particulars of the native conformation. Challenging this interpretation, the Perspective introduces a proposal that high energy (i.e., unfavorable) excluding interactions winnow the accessible population substantially under physical-chemical conditions that favor folding. Both steric clash and unsatisfied hydrogen bond donors and acceptors are classified as excluding interactions, so called because conformers with such disfavored interactions will be largely excluded from the thermodynamic population. Both excluding interactions and solvent factors that induce compactness are somewhat nonspecific, yet together they promote substantial chain organization. Moreover, proteins are built on a backbone scaffold consisting of α-helices and strands of β-sheet, where the number of hydrogen bond donors and acceptors is exactly balanced. These repetitive secondary structural elements are the only two conformers that can be both completely hydrogen-bond satisfied and extended indefinitely without encountering a steric clash. Consequently, the number of fundamental folds is limited to no more than ~10,000 for a protein domain. Once excluding interactions are taken into account, the issue of "frustration" is largely eliminated and the Levinthal paradox is resolved. Putting the "bottom line" at the top: it is likely that hydrogen-bond satisfaction represents a largely under-appreciated parameter in protein folding models.

Parallel reaction pathways accelerate folding of a guanine quadruplex

G-quadruplexes (G4s) are four-stranded, guanine-rich nucleic acid structures that can influence a variety of biological processes such as the transcription and translation of genes and DNA replication. In many cases, a single G4-forming nucleic acid sequence can adopt multiple different folded conformations that interconvert on biologically relevant timescales, entropically stabilizing the folded state. The coexistence of different folded conformations also suggests that there are multiple pathways leading from the unfolded to the folded state ensembles, potentially modulating the folding rate and biological activity. We have developed an experimental method for quantifying the contributions of individual pathways to the folding of conformationally heterogeneous G4s that is based on mutagenesis, thermal hysteresis kinetic experiments and global analysis, and validated our results using photocaged kinetic NMR experiments. We studied the regulatory Pu22 G4 from the c-myc oncogene promoter, which adopts at least four distinct folded isomers. We found that the presence of four parallel pathways leads to a 2.5-fold acceleration in folding; that is, the effective folding rate from the unfolded to folded ensembles is 2.5 times as large as the rate constant for the fastest individual pathway. Since many G4 sequences can adopt many more than four isomers, folding accelerations of more than an order of magnitude are possible via this mechanism.

Testing the length limit of loop grafting in a helical repeat protein

Alpha-helical repeat proteins such as consensus-designed tetratricopeptide repeats (CTPRs) are exceptionally stable molecules that are able to tolerate destabilizing sequence alterations and are therefore becoming increasingly valued as a modular platform for biotechnology and biotherapeutic applications. A simple approach to functionalize the CTPR scaffold that we are pioneering is the insertion of short linear motifs (SLiMs) into the loops between adjacent repeats. Here, we test the limits of the scaffold by inserting 17 highly diverse amino acid sequences of up to 58 amino acids in length into a two-repeat protein and examine the impact on protein folding, stability and solubility. The sequences include three SLiMs that bind oncoproteins and eleven naturally occurring linker sequences all predicted to be intrinsically disordered but with conformational preferences ranging from compact globules to expanded coils. We show that the loop-grafted proteins retain the native CTPR structure and are thermally stable with melting temperatures above 60 ​°C, despite the longest loop sequence being almost the same size as the CTPR scaffold itself (68 amino acids). Although the main determinant of the effect of stability was found to be loop length and was relatively insensitive to amino acid composition, the relationship between protein solubility and the loop sequences was more complex, with the presence of negatively charged amino acids enhancing the solubility. Our findings will help us to fully realize the potential of the repeat-protein scaffold, allowing a rational design approach to create artificial modular proteins with customized functional capabilities.

A collection of programs for one-dimensional Ising analysis of linear repeat proteins with point substitutions

A collection of programs is presented to analyze the thermodynamics of folding of linear repeat proteins using a 1D Ising model to determine intrinsic folding and interfacial coupling free energies. Expressions for folding transitions are generated for a series of constructs with different repeat numbers and are globally fitted to transitions for these constructs. These programs are designed to analyze Ising parameters for capped homopolymeric consensus repeat constructs as well as heteropolymeric constructs that contain point substitutions, providing a rigorous framework for analysis of the effects of mutation on intrinsic and directional (i.e., N- vs. C-terminal) interfacial coupling free-energies. A bootstrap analysis is provided to estimate parameter uncertainty as well as correlations among fitted parameters. Rigorous statistical analysis is essential for interpreting fits using the complex models required for Ising analysis of repeat proteins, especially heteropolymeric repeat proteins. Programs described here are available at https://github.com/barricklab-at-jhu/Ising_programs.

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.

Competition of individual domain folding with inter-domain interaction in WW domain engineered repeat proteins

Engineered repeat proteins have proven to be a fertile ground for studying the competition between folding, misfolding and transient aggregation of tethered protein domains. We examine the interplay between folding and inter-domain interactions of engineered FiP35 WW domain repeat proteins with n = 1 through 5 repeats. We characterize protein expression, thermal and guanidium melts, as well as laser T-jump kinetics. All experimental data is fitted by a global fitting model with two states per domain (U, N), plus a third state M to account for non-native states due to domain interactions present in all but the monomer. A detailed structural model is provided by coarse-grained simulated annealing using the AWSEM Hamiltonian. Tethered FiP35 WW domains with n = 2 and 3 domains are just slightly less stable than the monomer. The n = 4 oligomer is yet less stable, its expression yield is much lower than the monomer's, and depends on the purification tag used. The n = 5 plasmid did not express at all, indicating the sudden onset of aggregation past n = 4. Thus, tethered FiP35 has a critical nucleus size for inter-domain aggregation of n ≈ 4. According to our simulations, misfolded structures become increasingly prevalent as one proceeds from monomer to pentamer, with extended inter-domain beta sheets appearing first, then multi-sheet 'intramolecular amyloid' structures, and finally novel motifs containing alpha helices. We discuss the implications of our results for oligomeric aggregate formation and structure, transient aggregation of proteins whilst folding, as well as for protein evolution that starts with repeat proteins.

Ambidextrous helical nanotubes from self-assembly of designed helical hairpin motifs

Tandem repeat proteins exhibit native designability and represent potentially useful scaffolds for the construction of synthetic biomimetic assemblies. We have designed 2 synthetic peptides, HEAT_R1 and LRV_M3Δ1, based on the consensus sequences of single repeats of thermophilic HEAT (PBS_HEAT) and Leucine-Rich Variant (LRV) structural motifs, respectively. Self-assembly of the peptides afforded high-aspect ratio helical nanotubes. Cryo-electron microscopy with direct electron detection was employed to analyze the structures of the solvated filaments. The 3D reconstructions from the cryo-EM maps led to atomic models for the HEAT_R1 and LRV_M3Δ1 filaments at resolutions of 6.0 and 4.4 Å, respectively. Surprisingly, despite sequence similarity at the lateral packing interface, HEAT_R1 and LRV_M3Δ1 filaments adopt the opposite helical hand and differ significantly in helical geometry, while retaining a local conformation similar to previously characterized repeat proteins of the same class. The differences in the 2 filaments could be rationalized on the basis of differences in cohesive interactions at the lateral and axial interfaces. These structural data reinforce previous observations regarding the structural plasticity of helical protein assemblies and the need for high-resolution structural analysis. Despite these observations, the native designability of tandem repeat proteins offers the opportunity to engineer novel helical nanotubes. Moreover, the resultant nanotubes have independently addressable and chemically distinguishable interior and exterior surfaces that would facilitate applications in selective recognition, transport, and release.

Context-Dependent Energetics of Loop Extensions in a Family of Tandem-Repeat Proteins

Consensus-designed tetratricopeptide repeat proteins are highly stable, modular proteins that are strikingly amenable to rational engineering. They therefore have tremendous potential as building blocks for biomaterials and biomedicine. Here, we explore the possibility of extending the loops between repeats to enable further diversification, and we investigate how this modification affects stability and folding cooperativity. We find that extending a single loop by up to 25 residues does not disrupt the overall protein structure, but, strikingly, the effect on stability is highly context-dependent: in a two-repeat array, destabilization is relatively small and can be accounted for purely in entropic terms, whereas extending a loop in the middle of a large array is much more costly because of weakening of the interaction between the repeats. Our findings provide important and, to our knowledge, new insights that increase our understanding of the structure, folding, and function of natural repeat proteins and the design of artificial repeat proteins in biotechnology.

Folding cooperativity and allosteric function in the tandem-repeat protein class

The term allostery was originally developed to describe structural changes in one binding site induced by the interaction of a partner molecule with a distant binding site, and it has been studied in depth in the field of enzymology. Here, we discuss the concept of action at a distance in relation to the folding and function of the solenoid class of tandem-repeat proteins such as tetratricopeptide repeats (TPRs) and ankyrin repeats. Distantly located repeats fold cooperatively, even though only nearest-neighbour interactions exist in these proteins. A number of repeat-protein scaffolds have been reported to display allosteric effects, transferred through the repeat array, that enable them to direct the activity of the multi-subunit enzymes within which they reside. We also highlight a recently identified group of tandem-repeat proteins, the RRPNN subclass of TPRs, recent crystal structures of which indicate that they function as allosteric switches to modulate multiple bacterial quorum-sensing mechanisms. We believe that the folding cooperativity of tandem-repeat proteins and the biophysical mechanisms that transform them into allosteric switches are intimately intertwined. This opinion piece aims to combine our understanding of the two areas and develop ideas on their common underlying principles.This article is part of a discussion meeting issue 'Allostery and molecular machines'.

PyFolding: Open-Source Graphing, Simulation, and Analysis of the Biophysical Properties of Proteins

For many years, curve-fitting software has been heavily utilized to fit simple models to various types of biophysical data. Although such software packages are easy to use for simple functions, they are often expensive and present substantial impediments to applying more complex models or for the analysis of large data sets. One field that is reliant on such data analysis is the thermodynamics and kinetics of protein folding. Over the past decade, increasingly sophisticated analytical models have been generated, but without simple tools to enable routine analysis. Consequently, users have needed to generate their own tools or otherwise find willing collaborators. Here we present PyFolding, a free, open-source, and extensible Python framework for graphing, analysis, and simulation of the biophysical properties of proteins. To demonstrate the utility of PyFolding, we have used it to analyze and model experimental protein folding and thermodynamic data. Examples include: 1) multiphase kinetic folding fitted to linked equations, 2) global fitting of multiple data sets, and 3) analysis of repeat protein thermodynamics with Ising model variants. Moreover, we demonstrate how PyFolding is easily extensible to novel functionality beyond applications in protein folding via the addition of new models. Example scripts to perform these and other operations are supplied with the software, and we encourage users to contribute notebooks and models to create a community resource. Finally, we show that PyFolding can be used in conjunction with Jupyter notebooks as an easy way to share methods and analysis for publication and among research teams.

Lessons from pressure denaturation of proteins

Although it is now relatively well understood how sequence defines and impacts global protein stability in specific structural contexts, the question of how sequence modulates the configurational landscape of proteins remains to be defined. Protein configurational equilibria are generally characterized by using various chemical denaturants or by changing temperature or pH. Another thermodynamic parameter which is less often used in such studies is high hydrostatic pressure. This review discusses the basis for pressure effects on protein structure and stability, and describes how the unique mechanisms of pressure-induced unfolding can provide unique insights into protein conformational landscapes.

Extreme stability in de novo-designed repeat arrays is determined by unusually stable short-range interactions

Designed helical repeats (DHRs) are modular helix-loop-helix-loop protein structures that are tandemly repeated to form a superhelical array. Structures combining tandem DHRs demonstrate a wide range of molecular geometries, many of which are not observed in nature. Understanding cooperativity of DHR proteins provides insight into the molecular origins of Rosetta-based protein design hyperstability and facilitates comparison of energy distributions in artificial and naturally occurring protein folds. Here, we use a nearest-neighbor Ising model to quantify the intrinsic and interfacial free energies of four different DHRs. We measure the folding free energies of constructs with varying numbers of internal and terminal capping repeats for four different DHR folds, using guanidine-HCl and glycerol as destabilizing and solubilizing cosolvents. One-dimensional Ising analysis of these series reveals that, although interrepeat coupling energies are within the range seen for naturally occurring repeat proteins, the individual repeats of DHR proteins are intrinsically stable. This favorable intrinsic stability, which has not been observed for naturally occurring repeat proteins, adds to stabilizing interfaces, resulting in extraordinarily high stability. Stable repeats also impart a downhill shape to the energy landscape for DHR folding. These intrinsic stability differences suggest that part of the success of Rosetta-based design results from capturing favorable local interactions.

Globular Protein Folding In Vitro and In Vivo

In vitro, computational, and theoretical studies of protein folding have converged to paint a rich and complex energy landscape. This landscape is sensitively modulated by environmental conditions and subject to evolutionary pressure on protein function. Of these environments, none is more complex than the cell itself, where proteins function in the cytosol, in membranes, and in different compartments. A wide variety of kinetic and thermodynamics experiments, ranging from single-molecule studies to jump kinetics and from nuclear magnetic resonance to imaging on the microscope, have elucidated how protein energy landscapes facilitate folding and how they are subject to evolutionary constraints and environmental perturbation. Here we review some recent developments in the field and refer the reader to some original work and additional reviews that cover this broad topic in protein science.

Meandering Down the Energy Landscape of Protein Folding: Are We There Yet?

As judged by a single publication metric, the activity in the protein folding field has been declining over the past 5 years, after enjoying a decade-long growth. Does this development indicate that the field is sunsetting or is this decline only temporary? Upon surveying a small territory of its landscape, we find that the protein folding field is still quite active and many important findings have emerged from recent experimental studies. However, it is also clear that only continued development of new techniques and methods, especially those enabling dissection of the fine details and features of the protein folding energy landscape, will fuel this old field to move forward.

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.

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.

Dissecting and reprogramming the folding and assembly of tandem-repeat proteins

Studying protein folding and protein design in globular proteins presents significant challenges because of the two related features, topological complexity and co-operativity. In contrast, tandem-repeat proteins have regular and modular structures composed of linearly arrayed motifs. This means that the biophysics of even giant repeat proteins is highly amenable to dissection and to rational design. Here we discuss what has been learnt about the folding mechanisms of tandem-repeat proteins. The defining features that have emerged are: (i) accessibility of multiple distinct routes between denatured and native states, both at equilibrium and under kinetic conditions; (ii) different routes are favoured for folding compared with unfolding; (iii) unfolding energy barriers are broad, reflecting stepwise unravelling of an array repeat by repeat; (iv) highly co-operative unfolding at equilibrium and the potential for exceptionally high thermodynamic stabilities by introducing consensus residues; (v) under force, helical-repeat structures are very weak with non-co-operative unfolding leading to elasticity and buffering effects. This level of understanding should enable us to create repeat proteins with made-to-measure folding mechanisms, in which one can dial into the sequence the order of repeat folding, number of pathways taken, step size (co-operativity) and fine-structure of the kinetic energy barriers.

Infrared and Fluorescence Assessment of Protein Dynamics: From Folding to Function

While folding or performing functions, a protein can sample a rich set of conformational space. However, experimentally capturing all of the important motions with sufficient detail to allow a mechanistic description of their dynamics is nontrivial since such conformational events often occur over a wide range of time and length scales. Therefore, many methods have been employed to assess protein conformational dynamics, and depending on the nature of the conformational transition in question, some may be more advantageous than others. Herein, we describe our recent efforts, and also those of others, wherever appropriate, to use infrared- and fluorescence-based techniques to interrogate protein folding and functional dynamics. Specifically, we focus on discussing how to use extrinsic spectroscopic probes to enhance the structural resolution of these techniques and how to exploit various cross-linking strategies to acquire dynamic and mechanistic information that was previously difficult to attain.

Ising Model Reprogramming of a Repeat Protein's Equilibrium Unfolding Pathway

Repeat proteins are formed from units of 20-40 aa that stack together into quasi one-dimensional non-globular structures. This modular repetitive construction means that, unlike globular proteins, a repeat protein's equilibrium folding and thus thermodynamic stability can be analysed using linear Ising models. Typically, homozipper Ising models have been used. These treat the repeat protein as a series of identical interacting subunits (the repeated motifs) that couple together to form the folded protein. However, they cannot describe subunits of differing stabilities. Here we show that a more sophisticated heteropolymer Ising model can be constructed and fitted to two new helix deletion series of consensus tetratricopeptide repeat proteins (CTPRs). This analysis, showing an asymmetric spread of stability between helices within CTPR ensembles, coupled with the Ising model's predictive qualities was then used to guide reprogramming of the unfolding pathway of a variant CTPR protein. The designed behaviour was engineered by introducing destabilising mutations that increased the thermodynamic asymmetry within a CTPR ensemble. The asymmetry caused the terminal α-helix to thermodynamically uncouple from the rest of the protein and preferentially unfold. This produced a specific, highly populated stable intermediate with a putative dimerisation interface. As such it is the first step in designing repeat proteins with function regulated by a conformational switch.

Force-dependent switch in protein unfolding pathways and transition-state movements

Although it is known that single-domain proteins fold and unfold by parallel pathways, demonstration of this expectation has been difficult to establish in experiments. Unfolding rate, [Formula: see text], as a function of force f, obtained in single-molecule pulling experiments on src SH3 domain, exhibits upward curvature on a [Formula: see text] plot. Similar observations were reported for other proteins for the unfolding rate [Formula: see text]. These findings imply unfolding in these single-domain proteins involves a switch in the pathway as f or [Formula: see text] is increased from a low to a high value. We provide a unified theory demonstrating that if [Formula: see text] as a function of a perturbation (f or [Formula: see text]) exhibits upward curvature then the underlying energy landscape must be strongly multidimensional. Using molecular simulations we provide a structural basis for the switch in the pathways and dramatic shifts in the transition-state ensemble (TSE) in src SH3 domain as f is increased. We show that a single-point mutation shifts the upward curvature in [Formula: see text] to a lower force, thus establishing the malleability of the underlying folding landscape. Our theory, applicable to any perturbation that affects the free energy of the protein linearly, readily explains movement in the TSE in a β-sandwich (I27) protein and single-chain monellin as the denaturant concentration is varied. We predict that in the force range accessible in laser optical tweezer experiments there should be a switch in the unfolding pathways in I27 or its mutants.

Artificial domain duplication replicates evolutionary history of ketol-acid reductoisomerases

The duplication of protein structural domains has been proposed as a common mechanism for the generation of new protein folds. A particularly interesting case is the class II ketol-acid reductoisomerase (KARI), which putatively arose from an ancestral class I KARI by duplication of the C-terminal domain and corresponding loss of obligate dimerization. As a result, the class II enzymes acquired a deeply embedded figure-of-eight knot. To test this evolutionary hypothesis we constructed a novel class II KARI by duplicating the C-terminal domain of a hyperthermostable class I KARI. The new protein is monomeric, as confirmed by gel filtration and X-ray crystallography, and has the deeply knotted class II KARI fold. Surprisingly, its catalytic activity is nearly unchanged from the parent KARI. This provides strong evidence in support of domain duplication as the mechanism for the evolution of the class II KARI fold and demonstrates the ability of domain duplication to generate topological novelty in a function-neutral manner.

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.

Even with nonnative interactions, the updated folding transition states of the homologs Proteins G & L are extensive and similar

Experimental and computational folding studies of Proteins L & G and NuG2 typically find that sequence differences determine which of the two hairpins is formed in the transition state ensemble (TSE). However, our recent work on Protein L finds that its TSE contains both hairpins, compelling a reassessment of the influence of sequence on the folding behavior of the other two homologs. We characterize the TSEs for Protein G and NuG2b, a triple mutant of NuG2, using ψ analysis, a method for identifying contacts in the TSE. All three homologs are found to share a common and near-native TSE topology with interactions between all four strands. However, the helical content varies in the TSE, being largely absent in Proteins G & L but partially present in NuG2b. The variability likely arises from competing propensities for the formation of nonnative β turns in the naturally occurring proteins, as observed in our TerItFix folding algorithm. All-atom folding simulations of NuG2b recapitulate the observed TSEs with four strands for 5 of 27 transition paths [Lindorff-Larsen K, Piana S, Dror RO, Shaw DE (2011) Science 334(6055):517-520]. Our data support the view that homologous proteins have similar folding mechanisms, even when nonnative interactions are present in the transition state. These findings emphasize the ongoing challenge of accurately characterizing and predicting TSEs, even for relatively simple proteins.

Highly polarized C-terminal transition state of the leucine-rich repeat domain of PP32 is governed by local stability

The leucine-rich repeat domain of PP32 is composed of five β-strand-containing repeats anchored by terminal caps. These repeats differ in sequence but are similar in structure, providing a means to connect topology, sequence, and folding pathway selection. Through kinetic studies of PP32, we find folding to be rate-limited by the formation of an on-pathway intermediate. Destabilizing core substitutions reveal a transition state ensemble that is highly polarized toward the C-terminal repeat and cap. To determine if this nucleus for folding corresponds to the most stable region of PP32, we monitored amide hydrogen exchange by NMR spectroscopy. Indeed, we find the highest protection to be biased toward the C terminus. Sequence manipulations that destabilize the C terminus spread out the transition state toward the middle of the protein. Consistent with results for helical ankyrin repeat proteins, these results suggest that local stabilities determine folding pathways.

Single-molecule chemo-mechanical unfolding reveals multiple transition state barriers in a small single-domain protein

A fundamental question in protein folding is whether proteins fold through one or multiple trajectories. While most experiments indicate a single pathway, simulations suggest proteins can fold through many parallel pathways. Here, we use a combination of chemical denaturant, mechanical force and site-directed mutations to demonstrate the presence of multiple unfolding pathways in a simple, two-state folding protein. We show that these multiple pathways have structurally different transition states, and that seemingly small changes in protein sequence and environment can strongly modulate the flux between the pathways. These results suggest that in vivo, the crowded cellular environment could strongly influence the mechanisms of protein folding and unfolding. Our study resolves the apparent dichotomy between experimental and theoretical studies, and highlights the advantage of using a multipronged approach to reveal the complexities of a protein's free-energy landscape.

Although most protein folding experiments can be explained by a single pathway, theoretical evidence suggests the presence of multiple pathways. Here, the authors resolve this using a combination of force, chemical denaturation and mutagenesis to modulate the flux between parallel pathways.

Structural characterization of MG and pre-MG states of proteins by MD simulations, NMR, and other techniques

Almost all proteins fold via a number of partially structured intermediates such as molten globule (MG) and pre-molten globule states. Understanding the structure of these intermediates at atomic level is often a challenge, as these states are observed under extreme conditions of pH, temperature, and chemical denaturants. Furthermore, several other processes such as chemical modification, site-directed mutagenesis (or point mutation), and cleavage of covalent bond of natural proteins often lead to MG like partially unfolded conformation. However, the dynamic nature of proteins in these states makes them unsuitable for most structure determination at atomic level. Intermediate states studied so far have been characterized mostly by circular dichroism, fluorescence, viscosity, dynamic light scattering measurements, dye binding, infrared techniques, molecular dynamics simulations, etc. There is a limited amount of structural data available on these intermediate states by nuclear magnetic resonance (NMR) and hence there is a need to characterize these states at the molecular level. In this review, we present characterization of equilibrium intermediates by biophysical techniques with special reference to NMR.