Roles of non‐native hydrogen‐bonding interaction in helix‐coil transition of a single polypeptide as revealed by comparison between Gō‐like and non‐Gō models

To explore the role of non‐native interactions in the helix‐coil transition, a detailed comparison between a Gō‐like model and a non‐Gō model has been performed via lattice Monte Carlo simulations. Only native hydrogen bonding interactions occur in the Gō‐like model, and the non‐native ones with sequence interval more than 4 is also included into the non‐Gō model. Some significant differences between the results from those two models have been found. The non‐native hydrogen bonds were found most populated at temperature around the helix‐coil transition. The rearrangement of non‐native hydrogen bonds into native ones in the formation of α‐helix leads to the increase of susceptibility of chain conformation, and even two peaks of susceptibility of radius of gyration versus temperature exist in the case of non‐Gō model for a non‐short peptide, while just a single peak exists in the case of Gō model for a single polypeptide chain with various chain lengths. The non‐native hydrogen bonds have complicated the temperature‐dependence of Zimm‐Bragg nucleation constant. The increase of relative probability of non‐native hydrogen bonding for long polypeptide chains leads to non‐monotonous chain length effect on the transition temperature. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Minimalist models for protein folding and design

Protein folding research during the past decade has emphasized the dominant role of native state topology in determining the speed and mechanism of folding for small proteins; this has been illustrated by simulations using minimalist protein models. The advantages of minimalist protein models lie in their ability to rapidly collect meaningful statistics about folding pathways and kinetics, their ease of characterization with coarse-grained order parameters and their concentration on the essential physics of the problem to connect with experimental observables for a target protein. The maturation of experimental protein folding has driven the need for more quantitative protein simulations to better understand the balance between sequence details and fold topology. In the past year, we have seen the emergence of more complex minimalist models, ranging from all-atom Gō potentials to coarse-grained bead models in which Gō interactions are replaced or supplemented by more physically motivated potentials. The reduced computational cost at the coarse-grained level of abstraction will potentially enable both folding studies on a genomic scale and systematic application in protein design.     

The Role of Backbone Hydrogen Bonds in the Transition State for Protein Folding of a PDZ Domain

Backbone hydrogen bonds are important for the structure and stability of proteins. However, since conventional site-directed mutagenesis cannot be applied to perturb the backbone, the contribution of these hydrogen bonds in protein folding and stability has been assessed only for a very limited set of small proteins. We have here investigated effects of five amide-to-ester mutations in the backbone of a PDZ domain, a 90-residue globular protein domain, to probe the influence of hydrogen bonds in a β-sheet for folding and stability. The amide-to-ester mutation removes NH-mediated hydrogen bonds and destabilizes hydrogen bonds formed by the carbonyl oxygen. The overall stability of the PDZ domain generally decreased for all amide-to-ester mutants due to an increase in the unfolding rate constant. For this particular region of the PDZ domain, it is therefore clear that native hydrogen bonds are formed after crossing of the rate-limiting barrier for folding. Moreover, three of the five amide-to-ester mutants displayed an increase in the folding rate constant suggesting that the hydrogen bonds are involved in non-native interactions in the transition state for folding.     

Sequence of events in folding mechanism: beyond the Gō model

Simplified Gō models, where only native contacts interact favorably, have proven useful to characterize some aspects of the folding of small proteins. The success of these models is limited by the fact that all residues interact in the same way so that the folding features of a protein are determined only by the geometry of its native conformation. We present an extended version of a Calpha-based Gō model where different residues interact with different energies. The model is used to calculate the thermodynamics of three small proteins (Protein G, Src-SH3, and CI2) and the effect of mutations (DeltaDeltaGU-N, DeltaDeltaGdouble dagger-N, DeltaDeltaGdouble dagger-U, and phi-values) on the wild-type sequence. The model allows us to investigate some of the most controversial areas in protein folding, such as its earliest stages and the nature of the unfolded state, subjects that have lately received particular attention.     

Refolding simulations of an isolated fragment of barnase into a native-like β hairpin: Evidence for compactness and hydrogen bonding as concurrent stabilizing factors

Experimental evidence and theoretical models both suggest that protein folding is initiated within specific fragments intermittently adopting conformations close to that found in the protein native structure. These folding initiation sites encompassing short portions of the protein are ideally suited for study in isolation by computational methods aimed at peering into the very early events of folding. We have used Molecular Dynamics (MD) technique to investigate the behavior of an isolated protein fragment formed by residues 85 to 102 of barnase that folds into a β hairpin in the protein native structure. Three independent MD simulations of 1.3 to 1.8 ns starting from unfolded conformations of the peptide portrayed with an all-atom model in water were carried out at gradually decreasing temperature. A detailed analysis of the conformational preferences adopted by this peptide in the course of the simulations is presented. Two of the unfolded peptide conformations fold into a hairpin characterized by native and a larger bulk of nonnative interactions. Both refolding simulations substantiate the close relationship between interstrand compactness and hydrogen bonding network involving backbone atoms. Persistent compactness witnessed by side-chain interactions always occurs concomitantly with the formation of backbone hydrogen bonds. No highly populated conformations generated in a third simulation starting from the remotest unfolded conformer relative to the native structure are observed. However, nonnative long-range and medium-range contacts with the aromatic moiety of Trp94 are spotted, which are in fair agreement with a former nuclear magnetic resonance study of a denaturing solution of an isolated barnase fragment encompassing the β hairpin. All this lends reason to believe that the 85–102 barnase fragment is a strong initiation site for folding. Proteins 29:212–227, 1997. © 1997 Wiley-Liss, Inc.     

Direct analysis of backbone-backbone hydrogen bond formation in protein folding transition states

Here we investigate the role of backbone-backbone hydrogen bonding interactions in stabilizing the protein folding transition states of two model protein systems, the B1 domain of protein L (ProtL) and the P22 Arc repressor. A backbone modified analogue of ProtL containing an amide-to-ester bond substitution between residues 105 and 106 was prepared by total chemical synthesis, and the thermodynamic and kinetic parameters associated with its folding reaction were evaluated. Ultimately, these parameters were used in a Phi-value analysis to determine if the native backbone-backbone hydrogen bonding interaction perturbed in this analogue (i.e. a hydrogen bond in the first beta-turn of ProtL's beta-beta-alpha-beta-beta fold) was formed in the transition state of ProtL's folding reaction. Also determined were the kinetic parameters associated with the folding reactions of two Arc repressor analogues, each containing an amide-to-ester bond substitution in the backbone of their polypeptide chains. These parameters were used together with previously established thermodynamic parameters for the folding of these analogues in Phi-value analyses to determine if the native backbone-backbone hydrogen bonding interactions perturbed in these analogues (i.e. a hydrogen bond at the end of the intersubunit beta-sheet interface and hydrogen bonds at the beginning of the second alpha-helix in Arc repressor's beta-alpha-alpha structure) were formed in the transition state of Arc repressor's folding reaction. Our results reveal that backbone-backbone hydrogen bonding interactions are formed in the beta-turn and alpha-helical transition state structures of ProtL and Arc repressor, respectively; and they were not formed in the intersubunit beta-sheet interface of Arc repressor, a region of Arc repressor's polypeptide chain previously shown to have other non-native-like conformations in Arc's protein folding transition state.     

The Gō model revisited: Native structure and the geometric coupling between local and long-range contacts

Monte Carlo simulations show that long-range interactions play a major role in determining the folding rates of 48-mer three-dimensional lattice polymers modeled by the Gō potential. For three target structures with different native geometries we found a sharp increase in the folding time when the relative contribution of the long-range interactions to the native state's energy is decreased from approximately 50% towards zero. However, the dispersion of the simulated folding times is strongly dependent on native geometry and Gō polymers folding to one of the target structures exhibits folding times spanning three orders of magnitude. We have also found that, depending on the target geometry, a strong geometric coupling may exist between local and long-range contacts, which means that, when this coupling exists, the formation of long-range contacts is forced by the previous formation of local contacts. The absence of a strong geometric coupling results in a kinetics that is more sensitive to the interaction energy parameters; in this case, the formation of local contacts is not capable of promoting the establishment of long-range ones when the latter are strongly penalized energetically and this results in longer folding times.     

Molecular dynamics simulations of a beta-hairpin fragment of protein G: balance between side-chain and backbone forces

How is the native structure encoded in the amino acid sequence? For the traditional backbone centric view, the dominant forces are hydrogen bonds (backbone) and phi-psi propensity. The role of hydrophobicity is non-specific. For the side-chain centric view, the dominant force of protein folding is hydrophobicity. In order to understand the balance between backbone and side-chain forces, we have studied the contributions of three components of a beta-hairpin peptide: turn, backbone hydrogen bonding and side-chain interactions, of a 16-residue fragment of protein G. The peptide folds rapidly and cooperatively to a conformation with a defined secondary structure and a packed hydrophobic cluster of aromatic side-chains. Our strategy is to observe the structural stability of the beta-hairpin under systematic perturbations of the turn region, backbone hydrogen bonds and the hydrophobic core formed by the side-chains, respectively. In our molecular dynamics simulations, the peptides are solvated. with explicit water molecules, and an all-atom force field (CFF91) is used. Starting from the original peptide (G41EWTYDDATKTFTVTE56), we carried out the following MD simulations. (1) unfolding at 350 K; (2) forcing the distance between the C(alpha) atoms of ASP47 and LYS50 to be 8 A; (3) deleting two turn residues (Ala48 and Thr49) to form a beta-sheet complex of two short peptides, GEWTYDD and KTFTVTE; (4) four hydrophobic residues (W43, Y45, F52 and T53) are replaced by a glycine residue step-by-step; and (5) most importantly, four amide hydrogen atoms (T44, D46, T53, and T55, which are crucial for backbone hydrogen bonding), are substituted by fluorine atoms. The fluorination not only makes it impossible to form attractive hydrogen bonding between the two beta-hairpin strands, but also introduces a repulsive force between the two strands due to the negative charges on the fluorine and oxygen atoms. Throughout all simulations, we observe that backbone hydrogen bonds are very sensitive to the perturbations and are easily broken. In contrast, the hydrophobic core survives most perturbations. In the decisive test of fluorination, the fluorinated peptide remains folded under our simulation conditions (5 ns, 278 K). Hydrophobic interactions keep the peptide folded, even with a repulsive force between the beta-strands. Thus, our results strongly support a side-chain centric view for protein folding.     

Engineering a compact non-native state of intestinal fatty acid-binding protein

The last three C-terminal residues (129-131) of intestinal fatty acid-binding protein (IFABP) participate in four main-chain hydrogen bonds and two electrostatic interactions to sequentially distant backbone and side-chain atoms. To assess if these interactions are involved in the final adjustment of the tertiary structure during folding, we engineered an IFABP variant truncated at residue 128. An additional mutation, Trp-6-->Phe, was introduced to simplify the conformational analysis by optical methods. Although the changes were limited to a small region of the protein surface, they resulted in an IFABP with altered secondary and tertiary structure. Truncated IFABP retains some cooperativity, is monomeric, highly compact, and has the molecular dimensions and shape of the native protein. Our results indicated that residues 129-131 are part of a crucial conformational determinant in which several long-range interactions, essential for the acquisition of the native state, are established. This work suggests that carefully controlled truncation can populate equilibrium non-native states under physiological conditions. These non-native states hold a great promise as experimental models for protein folding.     

Backbone dynamics, fast folding, and secondary structure formation in helical proteins and peptides

We discuss the construction of a simple, off-lattice model protein with a comparatively detailed representation of the protein backbone, and use it to address some general aspects of the folding kinetics of a small helical protein and two peptide fragments. The model makes use of an associative memory hamiltonian to smoothly interpolate between the limits of a native contact only, or Go, potential and a statistical pair potential derived from a database of known structures. We have observed qualitatively different behavior in these two limits. In the Go limit, we see apparently barrier-less folding. As we increase the roughness of the model energy landscape, we can observe the emergence of the characteristic activated temperature dependence previously seen in lattice studies and analytical theories. We are also able to study the dependence of the folding kinetics on local interactions such as hydrogen bonds, and we discuss the implications of these results for the formation of secondary structure at intermediate stages of the folding reaction.     

Mechanical unfolding of a beta-hairpin using molecular dynamics

Single-molecule mechanical unfolding experiments have the potential to provide insights into the details of protein folding pathways. To investigate the relationship between force-extension unfolding curves and microscopic events, we performed molecular dynamics simulations of the mechanical unfolding of the C-terminal hairpin of protein G. We have studied the dependence of the unfolding pathway on pulling speed, cantilever stiffness, and attachment points. Under conditions that generate low forces, the unfolding trajectory mimics the untethered, thermally accessible pathway previously proposed based on high-temperature studies. In this stepwise pathway, complete breakdown of backbone hydrogen bonds precedes dissociation of the hydrophobic cluster. Under more extreme conditions, the cluster and hydrogen bonds break simultaneously. Transitions between folding intermediates can be identified in our simulations as features of the calculated force-extension curves.     

Common Structural Transitions in Explicit-Solvent Simulations of Villin Headpiece Folding

Molecular dynamics simulations of protein folding can provide very high-resolution data on the folding process; however, due to computational challenges most studies of protein folding have been limited to small peptides, or made use of approximations such as Gō potentials or implicit solvent models. We have performed a set of molecular dynamics simulations totaling >50 μs on the villin headpiece subdomain, one of the most stable and fastest-folding naturally occurring proteins, in explicit solvent. We find that the wild-type villin headpiece reliably folds to a native conformation on timescales similar to experimentally observed folding, but that a fast folding double-norleucine mutant shows significantly more heterogeneous behavior. Along with other recent simulation studies, we note the occurrence of nonnative structures intermediates, which may yield a nativelike signal in the fluorescence measurements typically used to study villin folding. Based on the wild-type simulations, we propose alternative approaches to measure the formation of the native state.     

Cooperativity,smooth energy landscapes and the origins of topology-dependent protein folding rates

The relative folding rates of simple, single-domain proteins, proteins whose folding energy landscapes are smooth, are highly dispersed and strongly correlated with native-state topology. In contrast, the relative folding rates of small, Gō-potential lattice polymers, which also exhibit smooth energy landscapes, are poorly dispersed and insignificantly correlated with native-state topology. Here, we investigate this discrepancy in light of a recent, quantitative theory of two-state folding kinetics, the topomer search model. This model stipulates that the topology-dependence of two-state folding rates is a direct consequence of the extraordinarily cooperative equilibrium folding of simple proteins. We demonstrate that traditional Gō polymers lack the extreme cooperativity that characterizes the folding of naturally occurring, two-state proteins and confirm that the folding rates of a diverse set of Gō 27-mers are poorly dispersed and effectively uncorrelated with native state topology. Upon modestly increasing the cooperativity of the Gō-potential, however, significantly increased dispersion and strongly topology-dependent kinetics are observed. These results support previous arguments that the cooperative folding of simple, single-domain proteins gives rise to their topology-dependent folding rates. We speculate that this cooperativity, and thus, indirectly, the topology-rate relationship, may have arisen in order to generate the smooth energetic landscapes upon which rapid folding can occur.     

The Limited Role of Nonnative Contacts in the Folding Pathways of a Lattice Protein

Models of protein energetics that neglect interactions between amino acids that are not adjacent in the native state, such as the Gō model, encode or underlie many influential ideas on protein folding. Implicit in this simplification is a crucial assumption that has never been critically evaluated in a broad context: Detailed mechanisms of protein folding are not biased by nonnative contacts, typically argued to be a consequence of sequence design and/or topology. Here we present, using computer simulations of a well-studied lattice heteropolymer model, the first systematic test of this oft-assumed correspondence over the statistically significant range of hundreds of thousands of amino acid sequences that fold to the same native structure. Contrary to previous conjectures, we find a multiplicity of folding mechanisms, suggesting that Gō-like models cannot be justified by considerations of topology alone. Instead, we find that the crucial factor in discriminating among topological pathways is the heterogeneity of native contact energies: The order in which native contacts accumulate is profoundly insensitive to omission of nonnative interactions, provided that native contact heterogeneity is retained. This robustness holds over a surprisingly wide range of folding rates for our designed sequences. Mirroring predictions based on the principle of minimum frustration, fast-folding sequences match their Gō-like counterparts in both topological mechanism and transit times. Less optimized sequences dwell much longer in the unfolded state and/or off-pathway intermediates than do Gō-like models. For dynamics that bridge unfolded and unfolded states, however, even slow folders exhibit topological mechanisms and transit times nearly identical with those of their Gō-like counterparts. Our results do not imply a direct correspondence between folding trajectories of Gō-like models and those of real proteins, but they do help to clarify key topological and energetic assumptions that are commonly used to justify such caricatures.     

Cysteine-cysteine contact preference leads to target-focusing in protein folding

We perform a statistical analysis of amino-acid contacts to investigate possible preferences of amino-acid interactions. We include in the analysis only tertiary contacts, because they are less constrained--compared to secondary contacts--by proteins' backbone rigidity. Using proteins from the protein data bank, our analysis reveals an unusually high frequency of cysteine pairings relative to that expected from random. To elucidate the possible effects of cysteine interactions in folding, we perform molecular simulations on three cysteine-rich proteins. In particular, we investigate the difference in folding dynamics between a Gō-like model (where attraction only occurs between amino acids forming a native contact) and a variant model (where attraction between any two cysteines is introduced to mimic the formation/dissociation of native/nonnative disulfide bonds). We find that when attraction among cysteines is nonspecific and comparable to a solvent-averaged interaction, they produce a target-focusing effect that expedites folding of cysteine-rich proteins as a result of a reduction of conformational search space. In addition, the target-focusing effect also helps reduce glassiness by lowering activation energy barriers and kinetic frustration in the system. The concept of target-focusing also provides a qualitative understanding of a correlation between the rates of protein folding and parameters such as contact order and total contact distance.     

Backbone-driven collapse in unfolded protein chains

Collapse of unfolded protein chains is an early event in folding. It affects structural properties of intrinsically disordered proteins, which take a considerable fraction of the human proteome. Collapse is generally believed to be driven by hydrophobic forces imposed by the presence of nonpolar amino acid side chains. Contributions from backbone hydrogen bonds to protein folding and stability, however, are controversial. To date, the experimental dissection of side-chain and backbone contributions has not yet been achieved because both types of interactions are integral parts of protein structure. Here, we realized this goal by applying mutagenesis and chemical modification on a set of disordered peptides and proteins. We measured the protein dimensions and kinetics of intra-chain diffusion of modified polypeptides at the level of individual molecules using fluorescence correlation spectroscopy, thereby avoiding artifacts commonly caused by aggregation of unfolded protein material in bulk. We found no contributions from side chains to collapse but, instead, identified backbone interactions as a source sufficient to form globules of native-like dimensions. The presence of backbone hydrogen bonds decreased polypeptide water solubility dramatically and accelerated the nanosecond kinetics of loop closure, in agreement with recent predictions from computer simulation. The presence of side chains, instead, slowed loop closure and modulated the dimensions of intrinsically disordered domains. It appeared that the transient formation of backbone interactions facilitates the diffusive search for productive conformations at the early stage of folding and within intrinsically disordered proteins.