Modulation of structure and dynamics by disulfide bond formation in unfolded states

During oxidative folding, the formation of disulfide bonds has profound effects on guiding the protein folding pathway. Until now, comparatively little is known about the changes in the conformational dynamics in folding intermediates of proteins that contain only a subset of their native disulfide bonds. In this comprehensive study, we probe the conformational landscape of non-native states of lysozyme containing a single native disulfide bond utilizing nuclear magnetic resonance (NMR) spectroscopy, small-angle X-ray scattering (SAXS), circular dichroism (CD) data, and modeling approaches. The impact on conformational dynamics varies widely depending on the loop size of the single disulfide variants and deviates significantly from random coil predictions for both NMR and SAXS data. From these experiments, we conclude that the introduction of single disulfides spanning a large portion of the polypeptide chain shifts the structure and dynamics of hydrophobic core residues of the protein so that these regions exhibit levels of order comparable to the native state on the nanosecond time scale.     

Amyloid Polymorphism in the Protein Folding and Aggregation Energy Landscape

Protein folding involves a large number of steps and conformations in which the folding protein samples different thermodynamic states characterized by local minima. Kinetically trapped on‐ or off‐pathway intermediates are metastable folding intermediates towards the lowest absolute energy minima, which have been postulated to be the natively folded state where intramolecular interactions dominate, and the amyloid state where intermolecular interactions dominate. However, this view largely neglects the rich polymorphism found within amyloid species. We review the protein folding energy landscape in view of recent findings identifying specific transition routes among different amyloid polymorphs. Observed transitions such as twisted ribbon→crystal or helical ribbon→nanotube, and forbidden transitions such helical ribbon?crystal, are discussed and positioned within the protein folding and aggregation energy landscape. Finally, amyloid crystals are identified as the ground state of the protein folding and aggregation energy landscape.     

Inherent structure analysis of protein folding

An analysis in terms of the inherent structures (IS, local minima) of the multidimensional potential energy landscape is applied to proteins. Detailed calculations are performed for the 46 bead BLN model, which folds into a four-stranded beta-barrel. Enhanced sampling has allowed determination of 239 199 IS states, believed to encompass nearly all the compact, low-energy states, and of well-averaged thermodynamic quantities at low temperature. The density of states shows distinct lobes for compact and extended states, and entropic barriers for the collapse and local ordering transitions. A two-dimensional scatterplot or density of states clearly shows the multifunnel structure of the energy landscape. The anharmonic vibrational free energy is found to play a crucial role in protein folding. The problem of determining the folding transition in a multifunnel system is discussed, and novel indicators of folding are introduced. A particularly clear picture is obtained through the occupation probabilities, pi, of individual low-lying IS, which become finite below the collapse temperature; it is suggested that poor foldability corresponds to a large "misfolding interval" where the excited state pi>0 exceeds that of the native state p0.     

Temperature dependent free energy surface of polymer folding from equilibrium and quench studies

Langevin dynamics simulation studies have been employed to calculate the temperature dependent free energy surface and folding characteristics of a 500 monomer long linear alkane (polyethylene) chain with a realistic interaction potential. Both equilibrium and temperature quench simulation studies have been carried out. Using the shape anisotropy parameter (S) of the folded molecule as the order parameter, we find a weakly first order phase transition between the high-temperature molten globule and low-temperature rodlike crystalline states separated by a small barrier of the order of k(B)T. Near the melting temperature (580 K), we observe an intriguing intermittent fluctuation with pronounced "1/f noise characteristics" between these two states with large difference in shape and structure. We have also studied the possibilities of different pathways of folding to states much below the melting point. At 300 K starting from the all-trans linear configuration, the chain folds stepwise into a very regular fourfold crystallite with very high shape anisotropy. Whereas, when quenched from a high temperature (900 K) random coil regime, we identify a two step transition from the random coiled state to a molten globulelike state and, further, to a anisotropic rodlike state. The trajectory reveals an interesting coupling between the two order parameters, namely, radius of gyration (R(g)) and the shape anisotropy parameter (S). The rodlike final state of the quench trajectory is characterized by lower shape anisotropy parameter and significantly larger number of gauche defects as compared to the final state obtained through equilibrium simulation starting from all-trans linear chain. The quench study shows indication of a nucleationlike pathway from the molten globule to the rodlike state involving an underlying rugged energy landscape.     

Mapping the cytochrome C folding landscape

The solution to the riddle of how a protein folds is encoded in the conformational energy landscape for the constituent polypeptide. Employing fluorescence energy transfer kinetics, we have mapped the S.cerevisiae iso-1 cytochrome c landscape by monitoring the distance between a C-terminal fluorophore and the heme during folding. Within 1 ms after denaturant dilution to native conditions, unfolded protein molecules have evolved into two distinct and rapidly equilibrating populations: a collection of collapsed structures with an average fluorophore-heme distance (r) of 27 A and a roughly equal population of extended polypeptides with r > 50 A. Molecules with the native fold appear on a time scale regulated by heme ligation events ( approximately 300 ms, pH 7). The experimentally derived landscape for folding has a narrow central funnel with a flat upper rim on which collapsed and extended polypeptides interchange rapidly in a search for the native structure.     

Protein folding through kinetic discrimination

Proteins fold on a micros-ms time scale. However, the number of possible conformations of the polypeptide backbone is so large that random sampling would not allow the protein to fold within the lifetime of the universe, the Levinthal paradox. We show here that a protein chain can fold efficiently with high fidelity if on average native contacts survive longer than non-native ones, that is, if the dissociation rate constant for breakage of a contact is lower for native than for non-native interactions. An important consequence of this finding is that no pathway needs to be specified for a protein to fold. Instead, kinetic discrimination among formed contacts is a sufficient criterion for folding to proceed to the native state. Successful protein folding requires that productive contacts survive long enough to obtain a certain level of probability that other native contacts form before the first interacting unit dissociates. If native contacts survive longer than non-native ones, this prevents misfolding and provides the folding process with directionality toward the native state. If on average all contacts survive equally long, the protein chain is deemed to fold through random search through all possible conformations (i.e., the Levinthal paradox). A modest degree of cooperativity among the native contacts, that is, decreased dissociation rate next to neighboring contacts, shifts the required ratio of dissociation rates into a realistic regime and makes folding a stochastic process with a nucleation step. No kinetic discrimination needs to be invoked in regards to the association process, which is modeled as dependent on the diffusion rate of chain segments.     

Ubiquitin: a small protein folding paradigm

For the past twenty years, the small, 76-residue protein ubiquitin has been used as a model system to study protein structure, stability, folding and dynamics. In this time, ubiquitin has become a paradigm for both the experimental and computational folding communities. The folding energy landscape is now uniquely characterised with a plethora of information available on not only the native and denatured states, but partially structured states, alternatively folded states and locally unfolded states, in addition to the transition state ensemble. This Perspective focuses on the experimental characterisation of ubiquitin using a comprehensive range of biophysical techniques.     

Kinetics of cooperative protein folding involving two separate conformational families

The master equation that describes the kinetics of protein folding is solved numerically for a portion of Staphylococcal Protein A by a Laplace transformation. The calculations are carried out with 50 local-minimum conformations belonging to two conformational families. The master equation allows for transitions among all the 50 conformations in the evolution toward the final folded equilibrium distribution of conformations. It is concluded that the native protein folds in a fast cooperative process. The global energy minimum of a native protein can be reached after a sufficiently long folding time regardless of the initial state and the existence of a large number of local energy minima. Conformations representing non-native states of the protein can transform to the native state even if they do not belong to the native conformational family. Given a starting conformation, the protein molecule can fold to its final conformation through different paths. Finally, when the folding reaches the equilibrium distribution, the protein molecule adopts a set of conformations in which the global minimum has the largest average probability.     

Enhanced Wang Landau sampling of adsorbed protein conformations

Using computer simulations to model the folding of proteins into their native states is computationally expensive due to the extraordinarily low degeneracy of the ground state. In this paper, we develop an efficient way to sample these folded conformations using Wang Landau sampling coupled with the configurational bias method (which uses an unphysical "temperature" that lies between the collapse and folding transition temperatures of the protein). This method speeds up the folding process by roughly an order of magnitude over existing algorithms for the sequences studied. We apply this method to study the adsorption of intrinsically disordered hydrophobic polar protein fragments on a hydrophobic surface. We find that these fragments, which are unstructured in the bulk, acquire secondary structure upon adsorption onto a strong hydrophobic surface. Apparently, the presence of a hydrophobic surface allows these random coil fragments to fold by providing hydrophobic contacts that were lost in protein fragmentation.     

A lattice protein with an amyloidogenic latent state: stability and folding kinetics

We have designed a model lattice protein that has two stable folded states, the lower free energy native state and a latent state of somewhat higher energy. The two states have a sizable part of their structures in common (two "alpha-helices") and differ in the content of "alpha-helices" and "beta-strands" in the rest of their structures; i.e. for the native state, this part is alpha-helical, and for the latent state it is composed of beta-strands. Thus, the lattice protein free energy surface mimics that of amyloidogenic proteins that form well organized fibrils under appropriate conditions. A Go-like potential was used and the folding process was simulated with a Monte Carlo method. To gain insight into the equilibrium free energy surface and the folding kinetics, we have combined standard approaches (reduced free energy surfaces, contact maps, time-dependent populations of the characteristic states, and folding time distributions) with a new approach. The latter is based on a principal coordinate analysis of the entire set of contacts, which makes possible the introduction of unbiased reaction coordinates and the construction of a kinetic network for the folding process. The system is found to have four characteristic basins, namely a semicompact globule, an on-pathway intermediate (the bifurcation basin), and the native and latent states. The bifurcation basin is shallow and consists of the structure common to the native and latent states, with the rest disorganized. On the basis of the simulation results, a simple kinetic model describing the transitions between the characteristic states was developed, and the rate constants for the essential transitions were estimated. During the folding process the system dwells in the bifurcation basin for a relatively short time before it proceeds to the native or latent state. We suggest that such a bifurcation may occur generally for proteins in which native and latent states have a sizable part of their structures in common. Moreover, there is the possibility of introducing changes in the system (e.g., mutations), which guide the system toward the native or misfolded state.     

The protein folding network indicates that the ultrafast folding mutant of villin headpiece subdomain has a deeper folding funnel

Protein folding is a dynamic process with continuous transitions among different conformations. In this work, the dynamics in the protein folding network of villin headpiece subdomain (HP35) has been investigated based on multiple reversible folding trajectories of HP35 and its ultrafast folding mutant where sub-angstrom folding was achieved. The four folding states were clearly separated on the network, validating the classification of the states. Examination of the eight conformers with different formation of the individual helices revealed high plasticity of the three helices in all the four states. A consistent feature between the wild type and mutant protein is the dominant conformer 111 (all three helices formed) in the folded state and conformers 111 and 011 (helices II and III formed) in the major intermediate state, indicating the critical role of helices II and III in the folding mechanism. When compared to the wild type, the folding landscape of the ultrafast folding mutant exhibited a deeper folding funnel towards the folded state. The very beginning of the folding (0-10 ns) was very similar for both protein variants but it soon diverged and displayed different folding pathways. Although going through the major intermediate state is the dominant pathway for both, it was also observed that some folding went through the minor intermediate state for the mutant. The intriguing difference resulting from the mutation at two residues in helix III has been carefully analyzed and discussed in details.     

Optimum folding pathways of proteins: their determination and properties

We develop a dynamic optimization technique for determining optimum folding pathways of proteins starting from different initial configurations. A coarse-grained Go model is used. Forces acting on each bead are (i) the friction force, (ii) forces from bond length constraints, (iii) excluded volume constraints, and (iv) attractive forces between residue pairs that are in contact in the native state. An objective function is defined as the total attractive energy between nonbonded residues, which are neighbors in the native state. The objective function is minimized over all feasible paths, satisfying bond length and excluded volume constraints. The optimization problem is nonconvex and contains a large number of constraints. An augmented Lagrangian method with a penalty barrier function was used to solve the problem. The method is applied to a 36-residue protein, chicken villin headpiece. Sequences of events during folding of the protein are determined for various pathways and analyzed. The relative time scales are compared and scaled according to experimentally measured events. Formation times of the helices, turn, and the loop agree with experimental data. We obtain the overall folding time of the protein in the range of 600 ns-1.2 micros that is smaller than the experimental result of 4-5 micros, showing that the optimal folding times that we obtain may be possible lower bounds. Time dependent variables during folding and energies associated with short- and long-range interactions between secondary structures are analyzed in modal space using Karhunen-Loeve expansion.     

Modulation of the folding energy landscape of cytochrome C with salt

The folding reaction of acid-unfolded cytochrome c in the presence of various amounts of KCl was investigated with Trp fluorescence and resonance Raman spectroscopies. It was found that the too-early-too-much polypeptide chain collapse induced by KCl yields some stable folding intermediates, which need to overcome a higher energy barrier to fold into their native conformation. We propose that the charge distribution on the polypeptide chain is part of the folding codon encoded in the linear amino acid sequence. The charge screening effect introduced by KCl alters the shape of the energy landscape by raising the slope of the upper rim and introduces a rugged energy surface toward the bottom of the folding funnel.     

Evidence of an intermediate and parallel pathways in protein unfolding from single-molecule fluorescence

Determining how proteins fold into their native structures is a subject of great importance, since ultimately it will allow protein structure and function to be predicted from primary sequence data. In addition, there is now a clear link between protein unfolding and misfolding events and many disease states. However, since proteins fold over rugged, multidimensional energy landscapes, this is a challenging experimental and theoretical problem. Single-molecule fluorescence methods developed over the past decade have the potential to follow the unfolding/folding of individual molecules. Mapping out the landscape without ensemble averaging will enable the identification of intermediate states which may not be significantly populated, in addition to the presence of multiple pathways. To date, there have been only a limited number of single-molecule folding/unfolding studies under nonequilibrium conditions and no intermediates have been observed. Here, for the first time, we present a single-molecule study of the unfolding of a large autofluorescent protein, Citrine, a variant of green fluorescent protein. Single-molecule fluorescence techniques are used to directly detect an intermediate on the unfolding/folding pathway and the existence of parallel unfolding pathways. This work, and the novel methods used, shows that single-molecule fluorescence can now provide new, hitherto experimentally inaccessible, insights into the folding/unfolding of proteins.     

Multidomain protein solves the folding problem by multifunnel combined landscape: theoretical investigation of a y-family DNA polymerase

Approximately three-fourths of eukaryotic proteins are composed of multiple independently folded domains. However, much of our understanding is based on single domain proteins or isolated domains whose studies directly lead to well-known energy landscape theory in which proteins fold by navigating through a funneled energy landscape toward native structure ensembles. The degrees of freedom for proteins with multiple domains are many orders of magnitude larger than that for single domain proteins. Now, the question arises: How do the multidomain proteins solve the "protein folding problem"? Here, we specifically address this issue by exploring the structure folding relationship of Sulfolobus solfataricus DNA polymerase IV (DPO4), a prototype Y-family DNA polymerase which contains a polymerase core consisting of a palm (P domain), a finger (F domain), and a thumb domain (T domain) in addition to a little finger domain (LF domain). The theoretical results are in good agreement with the experimental data and lead to several theoretical predictions. Finally, we propose that for rapid folding into well-defined conformations which carry out the biological functions, four-domain DPO4 employs a divide-and-conquer strategy, that is, combining multiple individual folding funnels into a single funnel (domains fold independently and then coalesce). In this way, the degrees of freedom for multidomain proteins are polynomial rather than exponential, and the conformational search process can be reduced effectively from a large to a smaller time scale.     

Frustration Sculpts the Early Stages of Protein Folding

The funneled energy landscape theory implies that protein structures are minimally frustrated. Yet, because of the divergent demands between folding and function, regions of frustrated patterns are present at the active site of proteins. To understand the effects of such local frustration in dictating the energy landscape of proteins, here we compare the folding mechanisms of the two alternative spliced forms of a PDZ domain (PDZ2 and PDZ2as) that share a nearly identical sequence and structure, while displaying different frustration patterns. The analysis, based on the kinetic characterization of a large number of site‐directed mutants, reveals that although the late stages for folding are very robust and biased by native topology, the early stages are more malleable and dominated by local frustration. The results are briefly discussed in the context of the energy‐landscape theory.     

Polypeptide foldings obtained with effective pair potentials

We present a model of protein folding which is based on a potential function that describes the effective interaction between two amino acids (alanines, in this case). Our model is consistent with the formation of two important secondary structures, namely, an alpha-helix and a beta-ladder. In each case, we estimate the density of states using a random walk in energy space. This function allows the direct calculation of certain thermodynamic properties. By means of the configurational temperature, we also verify that the obtained polypeptides are in their native state.