Theoretical and experimental demonstration of the importance of specific nonnative interactions in protein folding

Importance of Inter-residue Contacts for Understanding Protein Folding and Unfolding Rates, Remote Homology, and Drug Design

Inter-residue interactions in protein structures provide valuable insights into protein folding and stability. Understanding these interactions can be helpful in many crucial applications, including rational design of therapeutic small molecules and biologics, locating functional protein sites, and predicting protein-protein and protein-ligand interactions. The process of developing machine learning models incorporating inter-residue interactions has been improved recently. This review highlights the theoretical models incorporating inter-residue interactions in predicting folding and unfolding rates of proteins. Utilizing contact maps to depict inter-residue interactions aids researchers in developing computer models for detecting remote homologs and interface residues within protein-protein complexes which, in turn, enhances our knowledge of the relationship between sequence and structure of proteins. Further, the application of contact maps derived from inter-residue interactions is highlighted in the field of drug discovery. Overall, this review presents an extensive assessment of the significant models that use inter-residue interactions to investigate folding rates, unfolding rates, remote homology, and drug development, providing potential future advancements in constructing efficient computational models in structural biology.

Gadolinium-Based NMR Spin Relaxation Measurements of Near-Surface Electrostatic Potentials of Biomolecules

NMR spectroscopy is an important tool for the measurement of the electrostatic properties of biomolecules. To this point, paramagnetic relaxation enhancements (PREs) of 1H nuclei arising from nitroxide cosolutes in biomolecular solutions have been used to measure effective near-surface electrostatic potentials (ϕENS) of proteins and nucleic acids. Here, we present a gadolinium (Gd)-based NMR method, exploiting Gd chelates with different net charges, for measuring ϕENS values and demonstrate its utility through applications to a number of biomolecular systems. The use of Gd-based cosolutes offers several advantages over nitroxides for ϕENS measurements. First, unlike nitroxide compounds, Gd chelates enable electrostatic potential measurements on oxidation-sensitive proteins that require reducing agents. Second, the large electron spin quantum number of Gd (7/2) results in notably larger PREs for Gd chelates when used at the same concentrations as nitroxide radicals. Thus, it is possible to measure ϕENS values exclusively from + and - charged compounds even for highly charged biomolecules, avoiding the use of neutral cosolutes that, as we further establish here, limits the accuracy of the measured electrostatic potentials. In addition, the smaller concentrations of cosolutes required minimize potential binding to sites on macromolecules. Fourth, the closer proximity of the paramagnetic center and charged groups within Gd chelates, in comparison to the corresponding nitroxide compounds, enables more accurate predictions of ϕENS potentials for cross-validation of the experimental results. The Gd-based method described here, thus, broadens the applicability of studies of biomolecular electrostatics using solution NMR spectroscopy.

Targeting the protein folding transition state by mutation: Large scale (un)folding rate accelerations without altering native stability

Proteins are constantly undergoing folding and unfolding transitions, with rates that determine their homeostasis in vivo and modulate their biological function. The ability to optimize these rates without affecting overall native stability is hence highly desirable for protein engineering and design. The great challenge is, however, that mutations generally affect folding and unfolding rates with inversely complementary fractions of the net free energy change they inflict on the native state. Here we address this challenge by targeting the folding transition state (FTS) of chymotrypsin inhibitor 2 (CI2), a very slow and stable two-state folding protein with an FTS known to be refractory to change by mutation. We first discovered that the CI2's FTS is energetically taxed by the desolvation of several, highly conserved, charges that form a buried salt bridge network in the native structure. Based on these findings, we designed a CI2 variant that bears just four mutations and aims to selectively stabilize the FTS. This variant has >250-fold faster rates in both directions and hence identical native stability, demonstrating the success of our FTS-centric design strategy. With an optimized FTS, CI2 also becomes 250-fold more sensitive to proteolytic degradation by its natural substrate chymotrypsin, and completely loses its activity as inhibitor. These results indicate that CI2 has been selected through evolution to have a very unstable FTS in order to attain the kinetic stability needed to effectively function as protease inhibitor. Moreover, the CI2 case showcases that protein (un)folding rates can critically pivot around a few key residues-interactions, which can strongly modify the general effects of known structural factors such as domain size and fold topology. From a practical standpoint, our results suggest that future efforts should perhaps focus on identifying such critical residues-interactions in proteins as best strategy to significantly improve our ability to predict and engineer protein (un)folding rates.

Effects of sequence-dependent non-native interactions in equilibrium and kinetic folding properties of knotted proteins

Determining the role of non-native interactions in folding dynamics, kinetics, and mechanisms is a classic problem in protein folding. More recently, this question has witnessed a renewed interest in light of the hypothesis that knotted proteins require the assistance of non-native interactions to fold efficiently. Here, we conduct extensive equilibrium and kinetic Monte Carlo simulations of a simple off-lattice C-alpha model to explore the role of non-native interactions in the thermodynamics and kinetics of three proteins embedding a trefoil knot in their native structure. We find that equilibrium knotted conformations are stabilized by non-native interactions that are non-local, and proximal to native ones, thus enhancing them. Additionally, non-native interactions increase the knotting frequency at high temperatures, and in partially folded conformations below the transition temperatures. Although non-native interactions clearly enhance the efficiency of transition from an unfolded conformation to a partially folded knotted one, they are not required to efficiently fold a knotted protein. Indeed, a native-centric interaction potential drives the most efficient folding transition, provided that the simulation temperature is well below the transition temperature of the considered model system.

Protein-Inspired Control over Synthetic Polymer Folding for Structured Functional Nanoparticles in Water

The folding of proteins into functional nanoparticles with defined 3D structures has inspired chemists to create simple synthetic systems mimicking protein properties. The folding of polymers into nanoparticles in water proceeds via different strategies, resulting in the global compaction of the polymer chain. Herein, we review the different methods available to control the conformation of synthetic polymers and collapse/fold them into structured, functional nanoparticles, such as hydrophobic collapse, supramolecular self-assembly, and covalent cross-linking. A comparison is made between the design principles of protein folding to synthetic polymer folding and the formation of structured nanocompartments in water, highlighting similarities and differences in design and function. We also focus on the importance of structure for functional stability and diverse applications in complex media and cellular environments.

Collagen-like Motifs of SasG: A Novel Fold for Protein Mechanical Strength

The Staphylococcus aureus surface protein G (SasG) is associated with host colonisation and biofilm formation. As colonisation occurs at the liquid-substrate interface bacteria are subject to a myriad of external forces and, presumably as a consequence, SasG displays extreme mechanical strength. This mechanical phenotype arises from the B-domain; a repetitive region composed of alternating E and G5 subdomains. These subdomains have an unusual structure comprising collagen-like regions capped by triple-stranded β-sheets. To identify the determinants of SasG mechanical strength, we characterised the mechanical phenotype and thermodynamic stability of 18 single substitution variants of a pseudo-wildtype protein. Visualising the mechanically-induced transition state at a residue-level by ϕ-value analysis reveals that the main force-bearing regions are the N- and C-terminal 'Mechanical Clamps' and their side-chain interactions. This is tailored by contacts at the pseudo-hydrophobic core interface. We also describe a novel mechanical motif - the collagen-like region and show that glycine to alanine substitutions, analogous to those found in Osteogenesis Imperfecta (brittle bone disease), result in a significantly reduced mechanical strength.

Probing the Energy Landscape of Spectrin R15 and R16 and the Effects of Non-native Interactions

Understanding the details of a protein folding mechanism can be a challenging and complex task. One system with an interesting folding behavior is the α-spectrin domain, where the R15 folds three-orders of magnitude faster than its homologues R16 and R17, despite having similar structures. The molecular origins that explain these folding rate differences remain unclear, but our previous work revealed that a combined effect produced by non-native interactions could be a reasonable cause for these differences. In this study, we explore further the folding process by identifying the molecular paths, metastable states, and the collective motions that lead these unfolded proteins to their native state conformation. Our results uncovered the differences between the folding pathways for the wild-type R15 and R16 and an R16 mutant. The metastable ensembles that speed down the folding were identified using an energy landscape visualization method (ELViM). These ensembles correspond to similar experimentally reported configurations. Our observations indicate that the non-native interactions are also associated with secondary structure misdocking. This computational methodology can be used as a fast, straightforward protocol for shedding light on systems with unclear folding or conformational traps.

Effects of Surface Tethering on the Thermodynamics and Kinetics of Frustrated Protein Folding

The interaction between the protein and surface plays an important role in biology and biotechnology. To understand how surface tethering influences the folding behavior of frustrated proteins, in this work, we systematically study the thermodynamics and folding kinetics of the bacterial immunity protein Im7 and Fyn SH3 domain tethered to a surface using Langevin dynamics simulations. Upon surface tethering, the stabilization often results from the entropic effect, whereas the destabilization is usually caused by either an energetic or entropic effect. For the Fyn SH3 domain with a two-state folding manner, the influence of nonnative interactions on thermodynamic stability is not significant, while nonnative interactions can weaken the effect of surface tethering on the change in the folding rate. By contrast, for the frustrated protein Im7, depending on where the protein is tethered, the surface tethering can promote or suppress misfolding by modulating specific nonnative contacts, thereby altering the folding rate and folding mechanism. Because surface tethering can change the intrachain diffusivity of unfolding, the kinetic stability cannot be well captured by the thermodynamic stability at some tether points. This study should be helpful in general to understand how surface tethering affects the folding energy landscape of frustrated proteins.

Crowding-induced protein destabilization in the absence of soft attractions

It is generally assumed that volume exclusion by macromolecular crowders universally stabilizes the native states of proteins and destabilization suggests soft attractions between crowders and protein. Here we show that proteins can be destabilized even by crowders that are purely repulsive. With a coarse-grained sequence-based model, we study the folding thermodynamics of two sequences with different native folds, a helical hairpin and a β-barrel, in a range of crowder volume fractions, φ_c. We find that the native state, N, remains structurally unchanged under crowded conditions, while the size of the unfolded state, U, decreases monotonically with φ_c. Hence, for all φ_c>0, U is entropically disfavored relative to N. This entropy-centric view holds for the helical hairpin protein, which is stabilized under all crowded conditions as quantified by changes in either the folding midpoint temperature, T_m, or the free energy of folding. We find, however, that the β-barrel protein is destabilized under low-T, low-φ_c conditions. This destabilization can be understood from two characteristics of its folding: 1) a relatively compact U at T<T_m, such that U is only weakly disfavored entropically by the crowders; and 2) a transient, compact, and relatively low-energy nonnative state that has a maximum population of only a few percent at φ_c=0, but increasing monotonically with φ_c. Overall, protein destabilization driven by hard-core effects appears possible when a compaction of U leads to even a modest population of compact nonnative states that are energetically competitive with N.

An Unusual Aspartic Acid Cluster in the Reovirus Attachment Fiber σ1 Mediates Stability at Low pH and Preserves Trimeric Organization

The reovirus attachment protein σ1 mediates cell attachment and receptor binding and is thought to undergo conformational changes during viral disassembly. σ1 is a trimeric filamentous protein with an α-helical coiled-coil tail, a triple-β-spiral body, and a globular head. At the trimer interface, the head domain features an unusual and conserved aspartic acid cluster, which forms the only significant intratrimer interactions in the head and must be protonated to allow trimer formation. To define the role of pH on σ1 stability and conformation, we tested its domains over a wide range of pH values. We show that all domains of σ1 are remarkably thermostable, even at the low pH of the stomach. We determined the optimal pH for stability to be between pHs 5 and 6, a value close to the pH of the endosome and of the jejunum. The σ1 head is stable at acidic and neutral pH but detrimerizes at basic pH. When Asp³⁴⁵ in the aspartic acid cluster is mutated to asparagine (D345N), the σ1 head loses stability at low pH and is more prone to detrimerize. Although the D345N mutation does not affect σ1 binding affinity for the JAM-A receptor, the overall binding stoichiometry is reduced by one-third. The additional replacement of the neighboring His³⁴⁹ with alanine disrupts inner trimer surface interactions, leading to a less thermostable and monomeric σ1 D345N head that fails to bind the JAM-A receptor. When the body is expressed together with the head domain, the thermostability is restored and the stoichiometry of the binding to JAM-A receptor is preserved. Our results confirm a fundamental role of the aspartic acid cluster as a pH-dependent molecular switch controlling trimerization and enhancing thermostability of σ1, which represent essential requirements to accomplish reovirus infection and entry and might be common mechanisms among other enteric viruses. IMPORTANCE Enteric viruses withstand the highly acidic environment of the stomach during transmission, and many of them use low pH as a trigger for conformational changes associated with entry. For many nonenveloped viruses, the structural basis of these effects is not clear. We have investigated the stability of the reovirus attachment protein σ1 over a range of pHs and find it to be remarkably thermostable, especially at low pH. We identify a role for the aspartic acid cluster in maintaining σ1 thermostability, trimeric organization, and binding to JAM-A receptor especially at the gastric pH reovirus has to withstand while passing the stomach. The understanding of monomer-trimer dynamics within σ1 enhances our knowledge of reovirus entry and has implications for stability and transmission of other enteric viruses.

The Molecular Mechanism of Domain Swapping of the C-Terminal Domain of the SARS-Coronavirus Main Protease

In three-dimensional domain swapping, two protein monomers exchange a part of their structures to form an intertwined homodimer, whose subunits resemble the monomer. Several viral proteins domain swap to increase their structural complexity or functional avidity. The main protease (M^pro) of the severe acute respiratory syndrome (SARS) coronavirus proteolyzes viral polyproteins and has been a target for anti-SARS drug design. Domain swapping in the α-helical C-terminal domain of M^pro (M^proC) locks M^pro into a hyperactive octameric form that is hypothesized to promote the early stages of viral replication. However, in the absence of a complete molecular understanding of the mechanism of domain swapping, investigations into the biological relevance of this octameric M^pro have stalled. Isolated M^proC can exist as a monomer or a domain-swapped dimer. Here, we investigate the mechanism of domain swapping of M^proC using coarse-grained structure-based models and molecular dynamics simulations. Our simulations recapitulate several experimental features of M^proC folding. Further, we find that a contact between a tryptophan in the M^proC domain-swapping hinge and an arginine elsewhere forms early during folding, modulates the folding route, and promotes domain swapping to the native structure. An examination of the sequence and the structure of the tryptophan containing hinge loop shows that it has a propensity to form multiple secondary structures and contacts, indicating that it could be stabilized into either the monomer- or dimer-promoting conformations by mutations or ligand binding. Finally, because all residues in the tryptophan loop are identical in SARS-CoV and SARS-CoV-2, mutations that modulate domain swapping may provide insights into the role of octameric M^pro in the early-stage viral replication of both viruses.

Slow Folding of a Helical Protein: Large Barriers, Strong Internal Friction, or a Shallow, Bumpy Landscape?

The rate at which a protein molecule folds is determined by opposing energetic and entropic contributions to the free energy that shape the folding landscape. Delineating the extent to which they impact the diffusional barrier-crossing events, including the magnitude of internal friction and barrier height, has largely been a challenging task. In this work, we extract the underlying thermodynamic and dynamic contributions to the folding rate of an unusually slow-folding helical DNA-binding domain, PurR, which shares the characteristics of ultrafast downhill-folding proteins but nonetheless appears to exhibit an apparent two-state equilibrium. We combine equilibrium spectroscopy, temperature-viscosity-dependent kinetics, statistical mechanical modeling, and coarse-grained simulations to show that the conformational behavior of PurR is highly heterogeneous characterized by a large spread in melting temperatures, marginal thermodynamic barriers, and populated partially structured states. PurR appears to be at the threshold of disorder arising from frustrated electrostatics and weak packing that in turn slows down folding due to a shallow, bumpy landscape and not due to large thermodynamic barriers or strong internal friction. Our work highlights how a strong temperature dependence on the pre-exponential could signal a shallow landscape and not necessarily a slow-folding diffusion coefficient, thus determining the folding timescales of even millisecond folding proteins and hints at possible structural origins for the shallow landscape.

Effects of Topology and Sequence in Protein Folding Linked via Conformational Fluctuations

Experiments have compared the folding of proteins with different amino acid sequences but the same basic structure, or fold. Results indicate that folding is robust to sequence variations for proteins with some nonlocal folds, such as all-β, whereas the folding of more local, all-α proteins typically exhibits a stronger sequence dependence. Here, we use a coarse-grained model to systematically study how variations in sequence perturb the folding energy landscapes of three model sequences with 3α, 4β + α, and β-barrel folds, respectively. These three proteins exhibit folding features in line with experiments, including expected rank order in the cooperativity of the folding transition and stability-dependent shifts in the location of the free-energy barrier to folding. Using a generalized-ensemble simulation approach, we determine the thermodynamics of around 2000 sequence variants representing all possible hydrophobic or polar single- and double-point mutations. From an analysis of the subset of stability-neutral mutations, we find that folding is perturbed in a topology-dependent manner, with the β-barrel protein being the most robust. Our analysis shows, in particular, that the magnitude of mutational perturbations of the transition state is controlled in part by the size or "width" of the underlying conformational ensemble. This result suggests that the mutational robustness of the folding of the β-barrel protein is underpinned by its conformationally restricted transition state ensemble, revealing a link between sequence and topological effects in protein folding.

Disordered linkers in multidomain allosteric proteins: Entropic effect to favor the open state or enhanced local concentration to favor the closed state?

There are many multidomain allosteric proteins where an allosteric signal at the allosteric domain modifies the activity of the functional domain. Intrinsically disordered regions (linkers) are widely involved in this kind of regulation process, but the essential role they play therein is not well understood. Here, we investigated the effect of linkers in stabilizing the open or the closed states of multidomain proteins using combined thermodynamic deduction and coarse-grained molecular dynamics simulations. We revealed that the influence of linker can be fully characterized by an effective local concentration [B]₀ . When K_d is smaller than [B]₀ , the closed state would be favored; while the open state would be preferred when K_d is larger than [B]₀ . We used four protein systems with markedly different domain-domain binding affinity and structural order/disorder as model systems to understand the relationship between [B]₀ and the linker length as well as its flexibility. The linker length is the main practical determinant of [B]₀ . [B]₀ of a flexible linker with 40-60 residues was determined to be in a narrow range of 0.2-0.6 mM, while a too short or too long length would dramatically decrease [B]₀ . With the revealed [B]₀ range, the introduction of a flexible linker makes the regulation of weakly interacting partners possible.

Allosteric Modulation of Binding Specificity by Alternative Packing of Protein Cores

Hydrophobic cores are often viewed as tightly packed and rigid, but they do show some plasticity and could thus be attractive targets for protein design. Here we explored the role of different functional pressures on the core packing and ligand recognition of the SH3 domain from human Fyn tyrosine kinase. We randomized the hydrophobic core and used phage display to select variants that bound to each of three distinct ligands. The three evolved groups showed remarkable differences in core composition, illustrating the effect of different selective pressures on the core. Changes in the core did not significantly alter protein stability, but were linked closely to changes in binding affinity and specificity. Structural analysis and molecular dynamics simulations revealed the structural basis for altered specificity. The evolved domains had significantly reduced core volumes, which in turn induced increased backbone flexibility. These motions were propagated from the core to the binding surface and induced significant conformational changes. These results show that alternative core packing and consequent allosteric modulation of binding interfaces could be used to engineer proteins with novel functions.

Size and topology modulate the effects of frustration in protein folding

The presence of conflicting interactions, or frustration, determines how fast biomolecules can explore their configurational landscapes. Recent experiments have provided cases of systems with slow reconfiguration dynamics, perhaps arising from frustration. While it is well known that protein folding speed and mechanism are strongly affected by the protein native structure, it is still unknown how the response to frustration is modulated by the protein topology. We explore the effects of nonnative interactions in the reconfigurational and folding dynamics of proteins with different sizes and topologies. We find that structural correlations related to the folded state size and topology play an important role in determining the folding kinetics of proteins that otherwise have the same amount of nonnative interactions. In particular, we find that the reconfiguration dynamics of α-helical proteins are more susceptible to frustration than β-sheet proteins of the same size. Our results may explain recent experimental findings and suggest that attempts to measure the degree of frustration due to nonnative interactions might be more successful with α-helical proteins.

A critical comparison of coarse-grained structure-based approaches and atomic models of protein folding

Structure-based coarse-grained Gō-like models have been used extensively in deciphering protein folding mechanisms because of their simplicity and tractability. Meanwhile, explicit-solvent molecular dynamics (MD) simulations with physics-based all-atom force fields have been applied successfully to simulate folding/unfolding transitions for several small, fast-folding proteins. To explore the degree to which coarse-grained Gō-like models and their extensions to incorporate nonnative interactions are capable of producing folding processes similar to those in all-atom MD simulations, here we systematically compare the computed unfolded states, transition states, and transition paths obtained using coarse-grained models and all-atom explicit-solvent MD simulations. The conformations in the unfolded state in common Gō models are more extended, and are thus more in line with experiment, than those from all-atom MD simulations. Nevertheless, the structural features of transition states obtained by the two types of models are largely similar. In contrast, the folding transition paths are significantly more sensitive to modeling details. In particular, when common Gō-like models are augmented with nonnative interactions, the predicted dimensions of the unfolded conformations become similar to those computed using all-atom MD. With this connection, the large deviations of all-atom MD from simple diffusion theory are likely caused in part by the presence of significant nonnative effects in folding processes modelled by current atomic force fields. The ramifications of our findings to the application of coarse-grained modeling to more complex biomolecular systems are discussed.

Nonnative Energetic Frustrations in Protein Folding at Residual Level: A Simulation Study of Homologous Immunoglobulin-like β-Sandwich Proteins

Nonnative interactions cause energetic frustrations in protein folding and were found to dominate key events in folding intermediates. However, systematically characterizing energetic frustrations that are caused by nonnative intra-residue interactions at residual resolution is still lacking. Recently, we studied the folding of a set of homologous all-α proteins and found that nonnative-contact-based energetic frustrations are highly correlated to topology of the protein native-contact network. Here, we studied the folding of nine homologous immunoglobulin-like (Ig-like) β-sandwich proteins, and examined nonnative-contact-based energetic frustrations Gō-like model. Our calculations showed that nonnative-interaction-based energetic frustrations in β-sandwich proteins are much more complicated than those in all-α proteins, and they exhibit highly heterogeneous effects on the folding of secondary structures. Further, the nonnative interactions introduced distinct correlations in the folding of different folding-patches of β-sandwich proteins. Taken together, a strong interplay might exist between nonnative-interaction energetic frustrations and the protein native-contact networks, which ensures that β-sandwich domains adopt a common folding mechanism.

Extracting the Hidden Distributions Underlying the Mean Transition State Structures in Protein Folding

The inherent conflict between noncovalent interactions and the large conformational entropy of the polypeptide chain forces folding reactions and their mechanisms to deviate significantly from chemical reactions. Accordingly, measures of structure in the transition state ensemble (TSE) are strongly influenced by the underlying distributions of microscopic folding pathways that are challenging to discern experimentally. Here, we present a detailed analysis of 150,000 folding transition paths of five proteins at three different thermodynamic conditions from an experimentally consistent statistical mechanical model. We find that the underlying TSE structural distributions are rarely unimodal, and the average experimental measures arise from complex underlying distributions. Unfolding pathways also exhibit subtle differences from folding counterparts due to a combination of Hammond behavior and native-state movements. Local interactions and topological complexity, to a lesser extent, are found to determine pathway heterogeneity, underscoring the importance of the balance between local and nonlocal energetics in protein folding.

On the folding of a structurally complex protein to its metastable active state

For successful protease inhibition, the reactive center loop (RCL) of the two-domain serine protease inhibitor, α1-antitrypsin (α1-AT), needs to remain exposed in a metastable active conformation. The α1-AT RCL is sequestered in a β-sheet in the stable latent conformation. Thus, to be functional, α1-AT must always fold to a metastable conformation while avoiding folding to a stable conformation. We explore the structural basis of this choice using folding simulations of coarse-grained structure-based models of the two α1-AT conformations. Our simulations capture the key features of folding experiments performed on both conformations. The simulations also show that the free energy barrier to fold to the latent conformation is much larger than the barrier to fold to the active conformation. An entropically stabilized on-pathway intermediate lowers the barrier for folding to the active conformation. In this intermediate, the RCL is in an exposed configuration, and only one of the two α1-AT domains is folded. In contrast, early conversion of the RCL into a β-strand increases the coupling between the two α1-AT domains in the transition state and creates a larger barrier for folding to the latent conformation. Thus, unlike what happens in several proteins, where separate regions promote folding and function, the structure of the RCL, formed early during folding, determines both the conformational and the functional fate of α1-AT. Further, the short 12-residue RCL modulates the free energy barrier and the folding cooperativity of the large 370-residue α1-AT. Finally, we suggest experiments to test the predicted folding mechanism for the latent state.

Quantifying Nonnative Interactions in the Protein-Folding Free-Energy Landscape

Protein folding is a central problem in biological physics. Energetic roughness is an important aspect that controls protein-folding stability and kinetics. The roughness is associated with conflicting interactions in the protein and is also known as frustration. Recent studies indicate that an addition of a small amount of energetic frustration may enhance folding speed for certain proteins. In this study, we have investigated the conditions under which frustration increases the folding rate. We used a Cα structure-based model to simulate a group of proteins. We found that the free-energy barrier at the transition state (ΔF) correlates with nonnative-contact variation (ΔA), and the simulated proteins are clustered according to their fold motifs. These findings are corroborated by the Clementi-Plotkin analytical model. As a consequence, the optimum frustration regime for protein folding can be predicted analytically.

Exploring the sequence-structure-function relationship for the intrinsically disordered βγ-crystallin Hahellin

βγ-Crystallins are a superfamily of proteins containing crystallin-type Greek key motifs. Some βγ-crystallin domains have been shown to bind Ca²⁺. Hahellin is a newly identified intrinsically disordered βγ-crystallin domain from Hahella chejuensis. It folds into a typical βγ-crystallin structure upon Ca²⁺ binding and acts as a Ca²⁺-regulated conformational switch. Besides Hahellin, another two putative βγ-crystallins from Caulobacter crescentus and Yersinia pestis are shown to be partially disordered in their apo-form and undergo large conformational changes upon Ca²⁺ binding, although whether they acquire a βγ-crystallin fold is not known. The extent of conformational disorder/order of a protein is determined by its amino acid sequence. To date how this sequence-structure relationship is reflected in the βγ-crystallin superfamily has not been investigated. In this work, we comparatively studied the sequence and structure of Hahellin with those of Protein S, an ordered βγ-crystallin, via various computational biophysical techniques. We found that several factors, including presence of a C-terminal disorder prone region, high content of energetic frustrations, and low contact density, may promote the formation of the disordered state of apo-Hahellin. We also analyzed the disorder propensities for other putative disordered βγ-crystallin domains. This study provides new clues for further understanding the sequence-structure-function relationship of βγ-crystallins.

Evidence for the principle of minimal frustration in the evolution of protein folding landscapes

Theoretical and experimental studies have firmly established that protein folding can be described by a funneled energy landscape. This funneled energy landscape is the result of foldable protein sequences evolving following the principle of minimal frustration, which allows proteins to rapidly fold to their native biologically functional conformations. For a protein family with a given functional fold, the principle of minimal frustration suggests that, independent of sequence, all proteins within this family should fold with similar rates. However, depending on the optimal living temperature of the organism, proteins also need to modulate their thermodynamic stability. Consequently, the difference in thermodynamic stability should be primarily caused by differences in the unfolding rates. To test this hypothesis experimentally, we performed comprehensive thermodynamic and kinetic analyses of 15 different proteins from the thioredoxin family. Eight of these thioredoxins were extant proteins from psychrophilic, mesophilic, or thermophilic organisms. The other seven protein sequences were obtained using ancestral sequence reconstruction and can be dated back over 4 billion years. We found that all studied proteins fold with very similar rates but unfold with rates that differ up to three orders of magnitude. The unfolding rates correlate well with the thermodynamic stability of the proteins. Moreover, proteins that unfold slower are more resistant to proteolysis. These results provide direct experimental support to the principle of minimal frustration hypothesis.

The low populated folding intermediate of a mutant of the Fyn SH3 domain identified by a simple model

The low populated on-pathway folding intermediate of the A39V/N53P/V55L Fyn SH3 domain is captured by a native-centric model augmented by sequence-dependent nonnative hydrophobic interactions.

Conformations of a Metastable SH3 Domain Characterized by smFRET and an Excluded-Volume Polymer Model

Conformational states of the metastable drkN SH3 domain were characterized using single-molecule fluorescence techniques. Under nondenaturing conditions, two Förster resonance energy transfer (FRET) populations were observed that corresponded to a folded and an unfolded state. FRET-estimated radii of gyration and hydrodynamic radii estimated by fluorescence correlation spectroscopy of the two coexisting conformations are in agreement with previous ensemble x-ray scattering and NMR measurements. Surprisingly, when exposed to high concentrations of urea and GdmCl denaturants, the protein still exhibits two distinct FRET populations. The dominant conformation is expanded, showing a low FRET efficiency, consistent with the expected behavior of a random chain with excluded volume. However, approximately one-third of the drkN SH3 conformations showed high, nearly 100%, FRET efficiency, which is shown to correspond to denaturation-induced looped conformations that remain stable on a timescale of at least 100 μs. These loops may contain interconverting conformations that are more globally collapsed, hairpin-like, or circular, giving rise to the observed heterogeneous broadening of this population. Although the underlying mechanism of chain looping remains elusive, FRET experiments in formamide and dimethyl sulfoxide suggest that interactions between hydrophobic groups in the distal regions may play a significant role in the formation of the looped state.

Theoretical Insights into the Biophysics of Protein Bi-stability and Evolutionary Switches

Deciphering the effects of nonsynonymous mutations on protein structure is central to many areas of biomedical research and is of fundamental importance to the study of molecular evolution. Much of the investigation of protein evolution has focused on mutations that leave a protein’s folded structure essentially unchanged. However, to evolve novel folds of proteins, mutations that lead to large conformational modifications have to be involved. Unraveling the basic biophysics of such mutations is a challenge to theory, especially when only one or two amino acid substitutions cause a large-scale conformational switch. Among the few such mutational switches identified experimentally, the one between the G_A all-α and G_B α+β folds is extensively characterized; but all-atom simulations using fully transferrable potentials have not been able to account for this striking switching behavior. Here we introduce an explicit-chain model that combines structure-based native biases for multiple alternative structures with a general physical atomic force field, and apply this construct to twelve mutants spanning the sequence variation between G_A and G_B. In agreement with experiment, we observe conformational switching from G_A to G_B upon a single L45Y substitution in the GA98 mutant. In line with the latent evolutionary potential concept, our model shows a gradual sequence-dependent change in fold preference in the mutants before this switch. Our analysis also indicates that a sharp G_A/G_B switch may arise from the orientation dependence of aromatic π-interactions. These findings provide physical insights toward rationalizing, predicting and designing evolutionary conformational switches.

The biological functions of globular proteins are intimately related to their folded structures and their associated conformational fluctuations. Evolution of new structures is an important avenue to new functions. Although many mutations do not change the folded state, experiments indicate that a single amino acid substitution can lead to a drastic change in the folded structure. The physics of this switch-like behavior remains to be elucidated. Here we develop a computational model for the relevant physical forces, showing that mutations can lead to new folds by passing through intermediate sequences where the old and new folds occur with varying probabilities. Our approach helps provide a general physical account of conformational switching in evolution and mutational effects on conformational dynamics.

Design, Synthesis, Assembly, and Engineering of Peptoid Nanosheets

Two-dimensional (2D) atomically defined organic nanomaterials are an important material class with broad applications. However, few general synthetic methods exist to produce such materials in high yields and to precisely functionalize them. One strategy to form ordered 2D organic nanomaterials is through the supramolecular assembly of sequence-defined synthetic polymers. Peptoids, one such class of polymer, are designable bioinspired heteropolymers whose main-chain length and monomer sequence can be precisely controlled. We have recently discovered that individual peptoid polymers with a simple sequence of alternating hydrophobic and ionic monomers can self-assemble into highly ordered, free-floating nanosheets. A detailed understanding of their molecular structure and supramolecular assembly dynamics provides a robust platform for the discovery of new classes of nanosheets with tunable properties and novel applications. In this Account, we discuss the discovery, characterization, assembly, molecular modeling, and functionalization of peptoid nanosheets. The fundamental properties of peptoid nanosheets, their mechanism of formation, and their application as robust scaffolds for molecular recognition and as templates for the growth of inorganic minerals have been probed by an arsenal of experimental characterization techniques (e.g., scanning probe, electron, and optical microscopy, X-ray diffraction, surface-selective vibrational spectroscopy, and surface tensiometry) and computational techniques (coarse-grained and atomistic modeling). Peptoid nanosheets are supramolecular assemblies of 16-42-mer chains that form molecular bilayers. They span tens of microns in lateral dimensions and freely float in water. Their component chains are highly ordered, with chains nearly fully extended and packed parallel to one another as a result of hydrophobic and electrostatic interactions. Nanosheets form via a novel interface-catalyzed monolayer collapse mechanism. Peptoid chains first assemble into a monolayer at either an air-water or oil-water interface, on which peptoid chains extend, order, and pack into a brick-like pattern. Upon mechanical compression of the interface, the monolayer buckles into stable bilayer structures. Recent work has focused on the design of nanosheets with tunable properties and functionality. They are readily engineerable, as functional monomers can be readily incorporated onto the nanosheet surface or into the interior. For example, functional hydrophilic "loops" have been displayed on the surfaces of nanosheets. These loops can interact with specific protein targets, serving as a potentially general platform for molecular recognition. Nanosheets can also bind metal ions and serve as 2D templates for mineral growth. Through our understanding of the formation mechanism, along with predicted features ascertained from molecular modeling, we aim to further design and synthesize nanosheets as robust protein mimetics with the potential for unprecedented functionality and stability.

Constructing sequence-dependent protein models using coevolutionary information

Recent developments in global statistical methodologies have advanced the analysis of large collections of protein sequences for coevolutionary information. Coevolution between amino acids in a protein arises from compensatory mutations that are needed to maintain the stability or function of a protein over the course of evolution. This gives rise to quantifiable correlations between amino acid sites within the multiple sequence alignment of a protein family. Here, we use the maximum entropy-based approach called mean field Direct Coupling Analysis (mfDCA) to infer a Potts model Hamiltonian governing the correlated mutations in a protein family. We use the inferred pairwise statistical couplings to generate the sequence-dependent heterogeneous interaction energies of a structure-based model (SBM) where only native contacts are considered. Considering the ribosomal S6 protein and its circular permutants as well as the SH3 protein, we demonstrate that these models quantitatively agree with experimental data on folding mechanisms. This work serves as a new framework for generating coevolutionary data-enriched models that can potentially be used to engineer key functional motions and novel interactions in protein systems.

Influences of heterogeneous native contact energy and many-body interactions on the prediction of protein folding mechanisms

Combining heterogenous native contact energies and many-body interactions could improve the prediction of Brønsted plots using a structure-based model.

Knotted proteins: A tangled tale of Structural Biology

Knotted proteins have their native structures arranged in the form of an open knot. In the last ten years researchers have been making significant efforts to reveal their folding mechanism and understand which functional advantage(s) knots convey to their carriers. Molecular simulations have been playing a fundamental role in this endeavor, and early computational predictions about the knotting mechanism have just been confirmed in wet lab experiments. Here we review a collection of simulation results that allow outlining the current status of the field of knotted proteins, and discuss directions for future research.

Topological and sequence information predict that foldons organize a partially overlapped and hierarchical structure

It has been suggested that proteins have substructures, called foldons, which can cooperatively fold into the native structure. However, several prior investigations define foldons in various ways, citing different foldon characteristics, thereby making the concept of a foldon ambiguous. In this study, we perform a Gō model simulation and analyze the characteristics of substructures that cooperatively fold into the native-like structure. Although some results do not agree well with the experimental evidence due to the simplicity of our coarse-grained model, our results strongly suggest that cooperatively folding units sometimes organize a partially overlapped and hierarchical structure. This view makes us easy to interpret some different proposal about the foldon as a difference of the hierarchical structure. On the basis of this finding, we present a new method to assign foldons and their hierarchy, using structural and sequence information. The results show that the foldons assigned by our method correspond to the intermediate structures identified by some experimental techniques. The new method makes it easy to predict whether a protein folds sequentially into the native structure or whether some foldons fold into the native structure in parallel.

Native contact density and nonnative hydrophobic effects in the folding of bacterial immunity proteins

The bacterial colicin-immunity proteins Im7 and Im9 fold by different mechanisms. Experimentally, at pH 7.0 and 10°C, Im7 folds in a three-state manner via an intermediate but Im9 folding is two-state-like. Accordingly, Im7 exhibits a chevron rollover, whereas the chevron arm for Im9 folding is linear. Here we address the biophysical basis of their different behaviors by using native-centric models with and without additional transferrable, sequence-dependent energies. The Im7 chevron rollover is not captured by either a pure native-centric model or a model augmented by nonnative hydrophobic interactions with a uniform strength irrespective of residue type. By contrast, a more realistic nonnative interaction scheme that accounts for the difference in hydrophobicity among residues leads simultaneously to a chevron rollover for Im7 and an essentially linear folding chevron arm for Im9. Hydrophobic residues identified by published experiments to be involved in nonnative interactions during Im7 folding are found to participate in the strongest nonnative contacts in this model. Thus our observations support the experimental perspective that the Im7 folding intermediate is largely underpinned by nonnative interactions involving large hydrophobics. Our simulation suggests further that nonnative effects in Im7 are facilitated by a lower local native contact density relative to that of Im9. In a one-dimensional diffusion picture of Im7 folding with a coordinate- and stability-dependent diffusion coefficient, a significant chevron rollover is consistent with a diffusion coefficient that depends strongly on native stability at the conformational position of the folding intermediate.

In order to fold correctly, a globular protein must avoid being trapped in wrong, i.e., nonnative conformations. Thus a biophysical account of how attractive nonnative interactions are bypassed by some amino acid sequences but not others is key to deciphering protein structure and function. We examine two closely related bacterial immunity proteins, Im7 and Im9, that are experimentally known to fold very differently: Whereas Im9 folds directly, Im7 folds through a mispacked conformational intermediate. A simple model we developed accounts for their intriguingly different folding kinetics in terms of a balance between the density of native-promoting contacts and the hydrophobicity of local amino acid sequences. This emergent principle is extensible to other biomolecular recognition processes.

The hydrophobic temperature dependence of amino acids directly calculated from protein structures

The hydrophobic effect is the main driving force in protein folding. One can estimate the relative strength of this hydrophobic effect for each amino acid by mining a large set of experimentally determined protein structures. However, the hydrophobic force is known to be strongly temperature dependent. This temperature dependence is thought to explain the denaturation of proteins at low temperatures. Here we investigate if it is possible to extract this temperature dependence directly from a large set of protein structures determined at different temperatures. Using NMR structures filtered for sequence identity, we were able to extract hydrophobicity propensities for all amino acids at five different temperature ranges (spanning 265-340 K). These propensities show that the hydrophobicity becomes weaker at lower temperatures, in line with current theory. Alternatively, one can conclude that the temperature dependence of the hydrophobic effect has a measurable influence on protein structures. Moreover, this work provides a method for probing the individual temperature dependence of the different amino acid types, which is difficult to obtain by direct experiment.

In general, proteins become functional once they fold into a specific globular structure. On folding, hydrophobic amino acids get buried inside the protein such that they are shielded from the water; this hydrophobic effect makes a protein fold stable. However, the strength of the hydrophobicity is known to be strongly temperature dependent, leading for example to lower stability at lower temperatures (cold denaturation). Nevertheless, it is difficult to quantify the temperature dependence for hydrophobic amino acids. Here we are able to estimate the strength of the hydrophobic effect, by analysing the positions of a large number of amino acids from protein structures experimentally determined at different temperatures. For each amino acid type, we use the ratio between the number of residues at the inside and at the surface of the folded structures as a measure for its hydrophobicity. This approach shows that the hydrophobic effect becomes weaker at lower temperatures, as expected from theoretical predictions. Understanding the temperature dependence for amino acids, can help to make proteins (or enzymes) stable at a specific temperature range. For example, the design of enzymes that are stable and functional at low temperatures may benefit from this work.

Biophysics of protein evolution and evolutionary protein biophysics

The study of molecular evolution at the level of protein-coding genes often entails comparing large datasets of sequences to infer their evolutionary relationships. Despite the importance of a protein's structure and conformational dynamics to its function and thus its fitness, common phylogenetic methods embody minimal biophysical knowledge of proteins. To underscore the biophysical constraints on natural selection, we survey effects of protein mutations, highlighting the physical basis for marginal stability of natural globular proteins and how requirement for kinetic stability and avoidance of misfolding and misinteractions might have affected protein evolution. The biophysical underpinnings of these effects have been addressed by models with an explicit coarse-grained spatial representation of the polypeptide chain. Sequence-structure mappings based on such models are powerful conceptual tools that rationalize mutational robustness, evolvability, epistasis, promiscuous function performed by 'hidden' conformational states, resolution of adaptive conflicts and conformational switches in the evolution from one protein fold to another. Recently, protein biophysics has been applied to derive more accurate evolutionary accounts of sequence data. Methods have also been developed to exploit sequence-based evolutionary information to predict biophysical behaviours of proteins. The success of these approaches demonstrates a deep synergy between the fields of protein biophysics and protein evolution.

Multiscale modeling of a conditionally disordered pH-sensing chaperone

The pH-sensing chaperone HdeA promotes the survival of enteropathogenic bacteria during transit through the harshly acidic environment of the mammalian stomach. At low pH, HdeA transitions from an inactive, folded, dimer to chaperone-active, disordered, monomers to protect against the acid-induced aggregation of periplasmic proteins. Toward achieving a detailed mechanistic understanding of the pH response of HdeA, we develop a multiscale modeling approach to capture its pH-dependent thermodynamics. Our approach combines pK(a) (logarithmic acid dissociation constant) calculations from all-atom constant pH molecular dynamics simulations with coarse-grained modeling and yields new, atomic-level, insights into HdeA chaperone function that can be directly tested by experiment. "pH triggers" that significantly destabilize the dimer are each located near the N-terminus of a helix, suggesting that their neutralization at low pH destabilizes the helix macrodipole as a mechanism of monomer disordering. Moreover, we observe a non-monotonic change in the pH-dependent stability of HdeA, with maximal stability of the dimer near pH5. This affect is attributed to the protonation Glu37, which exhibits an anomalously high pK(a) value and is located within the hydrophobic dimer interface. Finally, the pH-dependent binding pathway of HdeA comprises a partially unfolded, dimeric intermediate that becomes increasingly stable relative to the native dimer at lower pH values and displays key structural features for chaperone-substrate interaction. We anticipate that the insights from our model will help inform ongoing NMR and biochemical investigations.

Protein unfolding rates correlate as strongly as folding rates with native structure

Although the folding rates of proteins have been studied extensively, both experimentally and theoretically, and many native state topological parameters have been proposed to correlate with or predict these rates, unfolding rates have received much less attention. Moreover, unfolding rates have generally been thought either to not relate to native topology in the same manner as folding rates, perhaps depending on different topological parameters, or to be more difficult to predict. Using a dataset of 108 proteins including two-state and multistate folders, we find that both unfolding and folding rates correlate strongly, and comparably well, with well-established measures of native topology, the absolute contact order and the long range order, with correlation coefficient values of 0.75 or higher. In addition, compared to folding rates, the absolute values of unfolding rates vary more strongly with native topology, have a larger range of values, and correlate better with thermodynamic stability. Similar trends are observed for subsets of different protein structural classes. Taken together, these results suggest that choosing a scaffold for protein engineering may require a compromise between a simple topology that will fold sufficiently quickly but also unfold quickly, and a complex topology that will unfold slowly and hence have kinetic stability, but fold slowly. These observations, together with the established role of kinetic stability in determining resistance to thermal and chemical denaturation as well as proteases, have important implications for understanding fundamental aspects of protein unfolding and folding and for protein engineering and design.

Theoretical perspectives on nonnative interactions and intrinsic disorder in protein folding and binding

The diverse biological functions of intrinsically disordered proteins (IDPs) have markedly raised our appreciation of protein conformational versatility, whereas the existence of energetically favorable yet functional detrimental nonnative interactions underscores the physical limitations of evolutionary optimization. Here we survey recent advances in using biophysical modeling to gain insight into experimentally observed nonnative behaviors and IDP properties. Simulations of IDP interactions to date focus mostly on coupled folding-binding, which follows essentially the same organizing principle as the local-nonlocal coupling mechanism in cooperative folding of monomeric globular proteins. By contrast, more innovative theories of electrostatic and aromatic interactions are needed for the conceptually novel but less-explored 'fuzzy' complexes in which the functionally bound IDPs remain largely disordered.

Conserved prosegment residues stabilize a late-stage folding transition state of pepsin independently of ground states

The native folding of certain zymogen-derived enzymes is completely dependent upon a prosegment domain to stabilize the folding transition state, thereby catalyzing the folding reaction. Generally little is known about how the prosegment accomplishes this task. It was previously shown that the prosegment catalyzes a late-stage folding transition between a stable misfolded state and the native state of pepsin. In this study, the contributions of specific prosegment residues to catalyzing pepsin folding were investigated by introducing individual Ala substitutions and measuring the effects on the bimolecular folding reaction between the prosegment peptide and pepsin. The effects of mutations on the free energies of the individual misfolded and native ground states and the transition state were compared using measurements of prosegment-pepsin binding and folding kinetics. Five out of the seven prosegment residues examined yielded relatively large kinetic effects and minimal ground state perturbations upon mutation, findings which indicate that these residues form strengthened and/or non-native contacts in the transition state. These five residues are semi- to strictly conserved, while only a non-conserved residue had no kinetic effect. One conserved residue was shown to form native structure in the transition state. These results indicated that the prosegment, which is only 44 residues long, has evolved a high density of contacts that preferentially stabilize the folding transition state over the ground states. It is postulated that the prosegment forms extensive non-native contacts during the process of catalyzing correct inter- and intra-domain contacts during the final stages of folding. These results have implications for understanding the folding of multi-domain proteins and for the evolution of prosegment-catalyzed folding.

PolyUbiquitin chain linkage topology selects the functions from the underlying binding landscape

Ubiquitin (Ub) can generate versatile molecular signals and lead to different celluar fates. The functional poly-valence of Ub is believed to be resulted from its ability to form distinct polymerized chains with eight linkage types. To provide a full picture of ubiquitin code, we explore the binding landscape of two free Ub monomers and also the functional landscapes of of all eight linkage types by theoretical modeling. Remarkably, we found that most of the compact structures of covalently connected dimeric Ub chains (diUbs) pre-exist on the binding landscape. These compact functional states were subsequently validated by corresponding linkage models. This leads to the proposal that the folding architecture of Ub monomer has encoded all functional states into its binding landscape, which is further selected by different topologies of polymeric Ub chains. Moreover, our results revealed that covalent linkage leads to symmetry breaking of interfacial interactions. We further propose that topological constraint not only limits the conformational space for effective switching between functional states, but also selects the local interactions for realizing the corresponding biological function. Therefore, the topological constraint provides a way for breaking the binding symmetry and reaching the functional specificity. The simulation results also provide several predictions that qualitatively and quantitatively consistent with experiments. Importantly, the K48 linkage model successfully predicted intermediate states. The resulting multi-state energy landscape was further employed to reconcile the seemingly contradictory experimental data on the conformational equilibrium of K48-diUb. Our results further suggest that hydrophobic interactions are dominant in the functional landscapes of K6-, K11-, K33- and K48 diUbs, while electrostatic interactions play a more important role in the functional landscapes of K27, K29, K63 and linear linkages.