Changes of protein stiffness during folding detect protein folding intermediates

Single-molecule force-quench atomic force microscopy (FQ-AFM) is used to detect folding intermediates of a simple protein by detecting changes of molecular stiffness of the protein during its folding process. Those stiffness changes are obtained from shape and peaks of an autocorrelation of fluctuations in end-to-end length of the folding molecule. The results are supported by predictions of the equipartition theorem and agree with existing Langevin dynamics simulations of a simplified model of a protein folding. In the light of the Langevin simulations the experimental data probe an ensemble of random-coiled collapsed states of the protein, which are present both in the force-quench and thermal-quench folding pathways.     

The folding pathway of ubiquitin from all-atom molecular dynamics simulations

The folding (unfolding) pathway of ubiquitin is probed using all-atom molecular dynamics simulations. We dissect the folding pathway using two techniques: first, we probe the folding pathway of ubiquitin by calculating the evolution of structural properties over time and second, we identify the rate determining transition state for folding. The structural properties that we look at are hydrophobic solvent accessible surface area (SASA) and Calpha-root-mean-square deviation (rmsd). These properties on their own tell us relatively little about the folding pathway of ubiquitin; however, when plotted against each other, they become powerful tools for dissecting ubiquitin's folding mechanism. Plots of Calpha-rmsd against SASA serve as a phase space trajectories for the folding of ubiquitin. In this study, these plots show that ubiquitin folds to the native state via the population of an intermediate state. This is shown by an initial hydrophobic collapse phase followed by a second phase of secondary structure arrangement. Analysis of the structure of the intermediate state shows that it is a collapsed species with very little secondary structure. In reconciling these observations with recent experimental data, the transition that we observe in our simulations from the unfolded state (U) to the intermediate state (I) most likely occurs in the dead-time of the stopped flow instrument. The folding pathway of ubiquitin is probed further by identification of the rate-determining transition state for folding. The method used for this is essential dynamics, which utilizes a principal component analysis (PCA) on the atomic fluctuations throughout the simulation. The five transition state structures identified in silico are in good agreement with the experimentally determined transition state. The calculation of phi-values from the structures generated in the simulations is also carried out and it shows a good correlation with the experimentally measured values. An initial analysis of the denatured state shows that it is compact with fluctuating regions of nonnative secondary structure. It is found that the compactness in the denatured state is due to the burial of some hydrophobic residues. We conclude by looking at a correlation between folding kinetics and residual structure in the denatured state. A hierarchical folding mechanism is then proposed for ubiquitin.     

Refolding upon force quench and pathways of mechanical and thermal unfolding of ubiquitin

The refolding from stretched initial conformations of ubiquitin (PDB ID: 1ubq) under the quenched force is studied using the C(alpha)-Gō model and the Langevin dynamics. It is shown that the refolding decouples the collapse and folding kinetics. The force-quench refolding-times scale as tau(F) approximately exp(f(q)Deltax(F)/k(B)T), where f(q) is the quench force and Deltax(F) approximately 0.96 nm is the location of the average transition state along the reaction coordinate given by the end-to-end distance. This value is close to Deltax(F) approximately 0.8 nm obtained from the force-clamp experiments. The mechanical and thermal unfolding pathways are studied and compared with the experimental and all-atom simulation results in detail. The sequencing of thermal unfolding was found to be markedly different from the mechanical one. It is found that fixing the N-terminus of ubiquitin changes its mechanical unfolding pathways much more drastically compared to the case when the C-end is anchored. We obtained the distance between the native state and the transition state Deltax(UF) approximately 0.24 nm, which is in reasonable agreement with the experimental data.     

Is there an en route folding intermediate for cold shock proteins?

Cold shock proteins (Csps) play an important role in cold shock response of a diverse number of organisms ranging from bacteria to humans. Numerous studies of the Csp from various species showed that a two-state folding mechanism is conserved and the transition state (TS) appears to be very compact. However, the atomic details of the folding mechanism of Csp remain unclear. This study presents the folding mechanism of Csp in atomic detail using an all-atom Go model-based simulations. Our simulations predict that there may exist an en route intermediate, in which β strands 1-2-3 are well ordered and the contacts between β1 and β4 are almost developed. Such an intermediate might be too unstable to be detected in the previous fluorescence energy transfer experiments. The transition state ensemble has been determined from the P(fold) analysis and the TS appears even more compact than the intermediate state.     

Fast collapse but slow formation of secondary structure elements in the refolding transition of E. coli adenylate kinase

The various models proposed for protein folding transition differ in their order of appearance of the basic steps during this process. In this study, steady state and time-resolved dynamic non-radiative excitation energy transfer (FRET and trFRET) combined with site specific labeling experiments were applied in order to characterize the initial transient ensemble of Escherichia coli adenylate kinase (AK) molecules upon shifting conditions from those favoring denaturation to refolding and from folding to denaturing. Three sets of labeled AK mutants were prepared, which were designed to probe the equilibrium and transient distributions of intramolecular segmental end-to-end distances. A 176 residue section (residues 28-203), which spans most of the 214 residue molecule, and two short secondary structure chain segments including an alpha-helix (residues 169-188) and a predominantly beta-strand region (residues 188-203), were labeled. Upon fast change of conditions from denaturing to folding, the end-to-end distance of the 176 residue chain section showed an immediate collapse to a mean value of 26 A. Under the same conditions, the two short secondary structure elements did not respond to this shift within the first ten milliseconds, and retained the characteristics of a fully unfolded state. Within the first 10 ms after changes of the solvent from folding to denaturing, only minor changes were observed at the local environments of residues 203 and 169. The response of these same local environments to the shift of conditions from denaturing to folding occurred within the dead time of the mixing device. Thus, the response of the CORE domain of AK to fast transfer from folding to unfolding conditions is slow at all three conformational levels that were probed, and for at least a few milliseconds the ensemble of folded molecules is maintained under unfolding conditions. A different order of the changes was observed upon initiation of refolding. The AK molecules undergo fast collapse to an ensemble of compact structures where the local environment of surface probes seems to be native-like but the two labeled secondary structure elements remain unfolded.     

Population of on-pathway intermediates in the folding of ubiquitin

The role that intermediate states play in protein folding is the subject of intense investigation and in the case of ubiquitin has been controversial. We present fluorescence-detected kinetic data derived from single and double mixing stopped-flow experiments to show that the F45W mutant of ubiquitin (WT*), a well-studied single-domain protein and most recently regarded as a simple two-state system, folds via on-pathway intermediates. To account for the discrepancy we observe between equilibrium and kinetic stabilities and m-values, we show that the polypeptide chain undergoes rapid collapse to an intermediate whose presence we infer from a fast lag phase in interrupted refolding experiments. Double-jump kinetic experiments identify two direct folding phases that are not associated with slow isomerisation reactions in the unfolded state. These two phases are explained by kinetic partitioning which allows molecules to reach the native state from the collapsed state via two possible competing routes, which we further examine using two destabilised ubiquitin mutants. Interrupted refolding experiments allow us to observe the formation and decay of an intermediate along one of these pathways. A plausible model for the folding pathway of ubiquitin is presented that demonstrates that obligatory intermediates and/or chain collapse are important events in restricting the conformational search for the native state of ubiquitin.     

Unstructured intermediate states in single protein force experiments

Recent single-molecule force measurements on single-domain proteins have highlighted a three-state folding mechanism where a stabilized intermediate state (I) is observed on the folding trajectory between the stretched state and the native state. Here we investigate on-lattice protein-like heteropolymer models that lead to a three-state mechanism and show that force experiments can be useful to determine the structure of I. We have mostly found that I is composed of a core stabilized by a high number of native contacts, plus an unstructured extended chain. The lifetime of I is shown to be sensitive to modifications of the protein that spoil the core. We then propose three types of modifications--point mutations, cuts, and circular permutations--aiming at: (1) confirming the presence of the core and (2) determining its location, within one amino acid accuracy, along the polypeptide chain. We also propose force jump protocols aiming to probe the on/off-pathway nature of I.     

Full Reconstruction of a Vectorial Protein Folding Pathway by Atomic Force Microscopy and Molecular Dynamics Simulations

During co-translational folding, the nascent polypeptide chain is extruded sequentially from the ribosome exit tunnel and, under severe conformational constraints, is dictated by its one-dimensional geometry. How do such vectorial constraints impact the folding pathway? Here, we combine single-molecule atomic force spectroscopy and steered molecular dynamics simulations to examine protein folding in the presence of one-dimensional constraints that are similar to those imposed on the nascent polypeptide chain. The simulations exquisitely reproduced the experimental unfolding and refolding force extension relationships and led to the full reconstruction of the vectorial folding pathway of a large polypeptide, the 253-residue consensus ankyrin repeat protein, NI6C. We show that fully stretched and then relaxed NI6C starts folding by the formation of local secondary structures, followed by the nucleation of three N-terminal repeats. This rate-limiting step is then followed by the vectorial and sequential folding of the remaining repeats. However, after partial unfolding, when allowed to refold, the C-terminal repeats successively regain structures without any nucleation step by using the intact N-terminal repeats as a template. These results suggest a pathway for the co-translational folding of repeat proteins and have implications for mechanotransduction.     

Posttransition state desolvation of the hydrophobic core of the src-SH3 protein domain

The folding thermodynamics of the src-SH3 protein domain were characterized under refolding conditions through biased fully atomic molecular dynamics simulations with explicit solvent. The calculated free energy surfaces along several reaction coordinates revealed two barriers. The first, larger barrier was identified as the transition state barrier for folding, associated with the formation of the first hydrophobic sheet of the protein. phi values calculated from structures residing at the transition state barrier agree well with experimental phi values. The microscopic information obtained from our simulations allowed us to unambiguously assign intermediate phi values as the result of multiple folding pathways. The second, smaller barrier occurs later in the folding process and is associated with the cooperative expulsion of water molecules between the hydrophobic sheets of the protein. This posttransition state desolvation barrier cannot be observed through traditional folding experiments, but is found to be critical to the correct packing of the hydrophobic core in the final stages of folding. Hydrogen exchange and NMR experiments are suggested to probe this barrier.     

Microsecond Barrier-Limited Chain Collapse Observed by Time-Resolved FRET and SAXS

It is generally held that random-coil polypeptide chains undergo a barrier-less continuous collapse when the solvent conditions are changed to favor the fully folded native conformation. We test this hypothesis by probing intramolecular distance distributions during folding in one of the paradigms of folding reactions, that of cytochrome c. The Trp59-to-heme distance was probed by time-resolved Förster resonance energy transfer in the microsecond time range of refolding. Contrary to expectation, a state with a Trp59–heme distance close to that of the guanidinium hydrochloride (GdnHCl) denatured state is present after ~ 27 μs of folding. A concomitant decrease in the population of this state and an increase in the population of a compact high-FRET (Förster resonance energy transfer) state (efficiency > 90%) show that the collapse is barrier limited. Small-angle X-ray scattering (SAXS) measurements over a similar time range show that the radius of gyration under native favoring conditions is comparable to that of the GdnHCl denatured unfolded state. An independent comprehensive global thermodynamic analysis reveals that marginally stable partially folded structures are also present in the nominally unfolded GdnHCl denatured state. These observations suggest that specifically collapsed intermediate structures with low stability in rapid equilibrium with the unfolded state may contribute to the apparent chain contraction observed in previous fluorescence studies using steady-state detection. In the absence of significant dynamic averaging of marginally stable partially folded states and with the use of probes sensitive to distance distributions, barrier-limited chain contraction is observed upon transfer of the GdnHCl denatured state ensemble to native-like conditions.     

Kinetic studies of folding of the B-domain of staphylococcal protein A with molecular dynamics and a united-residue (UNRES) model of polypeptide chains

Langevin dynamics is used with our physics-based united-residue (UNRES) force field to study the folding pathways of the B-domain of staphylococcal protein A (1BDD (alpha; 46 residues)). With 400 trajectories of protein A started from the extended state (to gather meaningful statistics), and simulated for more than 35 ns each, 380 of them folded to the native structure. The simulations were carried out at the optimal folding temperature of protein A with this force field. To the best of our knowledge, this is the first simulation study of protein-folding kinetics with a physics-based force field in which reliable statistics can be gathered. In all the simulations, the C-terminal alpha-helix forms first. The ensemble of the native basin has an average RMSD value of 4 A from the native structure. There is a stable intermediate along the folding pathway, in which the N-terminal alpha-helix is unfolded; this intermediate appears on the way to the native structure in less than one-fourth of the folding pathways, while the remaining ones proceed directly to the native state. Non-native structures persist until the end of the simulations, but the native-like structures dominate. To express the kinetics of protein A folding quantitatively, two observables were used: (i) the average alpha-helix content (averaged over all trajectories within a given time window); and (ii) the fraction of conformations (averaged over all trajectories within a given time window) with Calpha RMSD values from the native structure less than 5 A (fraction of completely folded structures). The alpha-helix content grows quickly with time, and its variation fits well to a single-exponential term, suggesting fast two-state kinetics. On the other hand, the fraction of folded structures changes more slowly with time and fits to a sum of two exponentials, in agreement with the appearance of the intermediate, found when analyzing the folding pathways. This observation demonstrates that different qualitative and quantitative conclusions about folding kinetics can be drawn depending on which observable is monitored.     

Single-Molecule Studies of the Im7 Folding Landscape

Under appropriate conditions, the four-helical Im7 (immunity protein 7) folds from an ensemble of unfolded conformers to a highly compact native state via an on-pathway intermediate. Here, we investigate the unfolded, intermediate, and native states populated during folding using diffusion single-pair fluorescence resonance energy transfer by measuring the efficiency of energy transfer (or proximity or P ratio) between pairs of fluorophores introduced into the side chains of cysteine residues placed in the center of helices 1 and 4, 1 and 3, or 2 and 4. We show that while the native states of each variant give rise to a single narrow distribution with high P values, the distributions of the intermediates trapped at equilibrium (denoted I^eqm) are fitted by two Gaussian distributions. Modulation of the folding conditions from those that stabilize the intermediate to those that destabilize the intermediate enabled the distribution of lower P value to be assigned to the population of the unfolded ensemble in equilibrium with the intermediate state. The reduced stability of the I^eqm variants allowed analysis of the effect of denaturant concentration on the compaction and breadth of the unfolded state ensemble to be quantified from 0 to 6 M urea. Significant compaction is observed as the concentration of urea is decreased in both the presence and absence of sodium sulfate, as previously reported for a variety of proteins. In the presence of Na₂SO₄ in 0 M urea, the P value of the unfolded state ensemble approaches that of the native state. Concurrent with compaction, the ensemble displays increased peak width of P values, possibly reflecting a reduction in the rate of conformational exchange among iso-energetic unfolded, but compact conformations. The results provide new insights into the initial stages of folding of Im7 and suggest that the unfolded state is highly conformationally constrained at the outset of folding.     

Fluctuating elastic filaments under distributed loads

Filaments under distributed loads are common in biological systems. In this paper, we study the thermo-mechanical properties of an extensible thermally fluctuating elastic filament under distributed forces. The ground state of the filament is solved first, followed by an investigation of the thermal fluctuations around the ground state. We first consider a special case where the tangential component of the distributed force tau is uniform along the filament. For the force-extension relation in this case, we show that the filament is equivalent to one under end-to-end applied force F = tauL0/2 where L0 is the length of the filament. To study the thermal fluctuations under more general distributed loadings, the filament is first discretized into segments, and its energy is approximated up to quadratic order. Then the partition function of the discretized filament, or chain, is evaluated using multi-dimensional Gaussian integrals, from which free energy and other properties of the filament are derived. We show that a filament under distributed loads suffers larger thermal fluctuations than one with the end loads of the same magnitude. We also show that our results for a discretized filament agree with continuum theory for a continuous rod. Finally, we give some applications of our ideas to the stretching and fluctuation of DNA in non-uniform microfluidic channels.     

Insights into nucleic acid conformational dynamics from massively parallel stochastic simulations

The helical hairpin is one of the most ubiquitous and elementary secondary structural motifs in nucleic acids, capable of serving functional roles and participating in long-range tertiary contacts. Yet the self-assembly of these structures has not been well-characterized at the atomic level. With this in mind, the dynamics of nucleic acid hairpin formation and disruption have been studied using a novel computational tool: large-scale, parallel, atomistic molecular dynamics simulation employing an inhomogeneous distributed computer consisting of more than 40,000 processors. Using multiple methodologies, over 500 micro s of atomistic simulation time has been collected for a large ensemble of hairpins (sequence 5'-GGGC[GCAA]GCCU-3'), allowing characterization of rare events not previously observable in simulation. From uncoupled ensemble dynamics simulations in unperturbed folding conditions, we report on 1), competing pathways between the folded and unfolded regions of the conformational space; 2), observed nonnative stacking and basepairing traps; and 3), a helix unwinding-rewinding mode that is differentiated from the unfolding and folding dynamics. A heterogeneous transition state ensemble is characterized structurally through calculations of conformer-specific folding probabilities and a multiplexed replica exchange stochastic dynamics algorithm is used to derive an approximate folding landscape. A comparison between the observed folding mechanism and that of a peptide beta-hairpin analog suggests that although native topology defines the character of the folding landscape, the statistical weighting of potential folding pathways is determined by the chemical nature of the polymer.     

Structural insights into the two sequential folding transition states of the PB1 domain of NBR1 from Φ value analysis and biased molecular dynamics simulations

The PB1 domain of NBR1 folds via a single pathway mechanism involving two sequential energy barriers separated by a high-energy intermediate. The structural ensemble representing each of the two transition states (TS1 and TS2) has been calculated using experimental Φ values and biased molecular dynamics simulations. Both TS1 and TS2 represent compact states (β(TS1) = 0.71, and β(TS2) = 0.93) but are defined by quite different distributions of Φ values, degrees of structural heterogeneity, and nativelike secondary structure. TS1 forms a heterogeneous ensemble of dynamic structures, representing a global collapse of the polypeptide chain around a set of weak nativelike contacts. In contrast, TS2 has a high proportion of nativelike secondary structure, which is reflected in an extensive distribution of high Φ values. Two snapshots along the folding pathway of the PB1 domain reveal insights into the malleability, the solvent accessibility, and the timing of nativelike core packing that stabilizes the folded state.     

Single molecule force spectroscopy reveals a weakly populated microstate of the FnIII domains of tenascin

The native states of proteins exist as an ensemble of conformationally similar microstates. The fluctuations among different microstates are of great importance for the functions and structural stability of proteins. Here, we demonstrate that single molecule atomic force microscopy (AFM) can be used to directly probe the existence of multiple folded microstates. We used the AFM to repeatedly stretch and relax a recombinant tenascin fragment TNfnALL to allow the fibronectin type III (FnIII) domains to undergo repeated unfolding/refolding cycles. In addition to the native state, we discovered that some FnIII domains can refold from the unfolded state into a previously unrecognized microstate, N* state. This novel state is conformationally similar to the native state, but mechanically less stable. The native state unfolds at approximately 120 pN, while the N* state unfolds at approximately 50 pN. These two distinct populations of microstates constitute the ensemble of the folded states for some FnIII domains. An unfolded FnIII domain can fold into either one of the two microstates via two distinct folding routes. These results reveal the dynamic and heterogeneous picture of the folded ensemble for some FnIII domains of tenascin, which may carry important implications for the mechanical functions of tenascins in vivo.     

Is an intermediate state populated on the folding pathway of ubiquitin?

In the last couple of years, there has been increasing debate as to the presence and role of intermediate states on the folding pathways of several small proteins, including the 76-residue protein ubiquitin. Here, we present detailed kinetic studies to establish whether an intermediate state is ever populated during the folding of this protein. We show that the differences observed in previous studies are attributable to the transient aggregation of the protein during folding. Using a highly soluble construct of ubiquitin, which does not aggregate during folding, we establish the conditions in which an intermediate state is sufficiently stable to be observed by kinetic measurements.     

Direct observation of active protein folding using lock-in force spectroscopy

Direct observation of the folding of a single polypeptide chain can provide important information about the thermodynamic states populated along its folding pathway. In this study, we present a lock-in force-spectroscopy technique that improves resolution of atomic-force microscopy force spectroscopy to 400 fN. Using this technique we show that immunoglobulin domain 4 from Dictyostelium discoideum filamin (ddFLN4) refolds against forces of ∼4 pN. Our data show folding of this domain proceeds directly from an extended state and no thermodynamically distinct collapsed state of the polypeptide before folding is populated. Folding of ddFLN4 under load proceeds via an intermediate state. Three-state folding allows ddFLN4 to fold against significantly larger forces than would be possible for a mere two-state folder. We present a general model for protein folding kinetics under load that can predict refolding forces based on chain-length and zero force refolding rate.     

Monte Carlo simulation for single RNA unfolding by force

Using polymer elastic theory and known RNA free energies, we construct a Monte Carlo algorithm to simulate the single RNA folding and unfolding by mechanical force on the secondary structure level. For the constant force ensemble, we simulate the force-extension curves of the P5ab, P5abc deltaA, and P5abc molecules in equilibrium. For the constant extension ensemble, we focus on the mechanical behaviors of the RNA P5ab molecule, which include the unfolding force dependence on the pulling speed, the force-hysteresis phenomenon, and the coincidence of stretching-relaxing force-curves in thermal equilibrium. We particularly simulate the time traces of the end-to-end distance of the P5ab under the constant force in equilibrium, which also have been recorded in the recent experiment. The reaction rate constants for the folding and unfolding are calculated. Our results show that the agreement between the simulation and the experimental measurements is satisfactory.