Transition State Ensemble for the Folding of B Domain of Protein A: A Comparison of Distributed Molecular Dynamics Simulations with Experiments

Implications of the unfolded state in the folding energetics of heterogeneous-backbone protein mimetics

Sequence-encoded folding is the foundation of protein structure and is also possible in synthetic chains of artificial chemical composition. In natural proteins, the characteristics of the unfolded state are as important as those of the folded state in determining folding energetics. While much is known about folded structures adopted by artificial protein-like chains, corresponding information about the unfolded states of these molecules is lacking. Here, we report the consequences of altered backbone composition on the structure, stability, and dynamics of the folded and unfolded states of a compact helix-rich protein. Characterization through a combination of biophysical experiments and atomistic simulation reveals effects of backbone modification that depend on both the type of artificial monomers employed and where they are applied in sequence. In general, introducing artificial connectivity in a way that reinforces characteristics of the unfolded state ensemble of the prototype natural protein minimizes the impact of chemical changes on folded stability. These findings have implications in the design of protein mimetics and provide an atomically detailed picture of the unfolded state of a natural protein and artificial analogues under non-denaturing conditions.

Biophysical experiments and atomistic simulation reveal impacts of protein backbone alteration on the ensemble that defines the unfolded state. These effects have implications on folded stability of protein mimetics.

How low-resolution structural data predict the conformational changes of a protein: a study on data-driven molecular dynamics simulations

Parallel cascade selection molecular dynamics (PaCS-MD) is a conformational sampling method for generating transition pathways between a given reactant and a product. PaCS-MD repeats the following two steps: (1) selections of initial structures relevant to transitions and (2) their conformational resampling. When selecting the initial structures, several measures are utilized to identify their potential to undergo transitions. In the present study, low-resolution structural data obtained from small angle scattering (SAXS) and cryo-electron microscopy (EM) are adopted as the measures in PaCS-MD to promote the conformational transitions of proteins, which is defined as SAXS-/EM-driven targeted PaCS-MD. By selecting the essential structures that have high correlations with the low-resolution structural data, the SAXS-/EM-driven targeted PaCS-MD identifies a set of transition pathways between the reactant and the product. As a demonstration, the present method successfully predicted the open-closed transition pathway of the lysine-, arginine-, ornithine-binding protein with a ns-order simulation time, indicating that the data-driven PaCS-MD simulation might work to promote the conformational transitions of proteins efficiently.

Fast helix formation in the B domain of protein A revealed by site-specific infrared probes

Comparison of experimental and computational protein folding studies can be difficult because of differences in structural resolution. Isotope-edited infrared spectroscopy offers a direct measure of structural changes involved in protein folding at the single-residue level. Here we demonstrate the increased resolution of site-specific infrared probes to the peptide backbone in the B domain of staphylococcal protein A (BdpA). (13)C═(18)O-labeled methionine was incorporated into each of the helices using recombinant protein expression. Laser-induced temperature jumps coupled with infrared spectroscopy were used to probe changes in the peptide backbone on the submillisecond time scale. The relaxation kinetics of the buried helices, solvated helices, and labeled positions were measured independently by probing the corresponding bands assigned in the amide I region. Using these wavelength-dependent measurements, we observe a fast nanosecond phase and slower microsecond phase at each position. We find at least partial formation of helices 1-3 in the fast intermediate state that precedes the transition state. These measurements provide direct, time-resolved experimental evidence of the early formation of partial helical structure in helices 1 and 3, supporting folding models proposed by computer simulations.

Hidden protein folding pathways in free-energy landscapes uncovered by network analysis

A network analysis is used to uncover hidden folding pathways in free-energy landscapes usually defined in terms of such arbitrary order parameters as root-mean-square deviation from the native structure, radius of gyration, etc. The analysis has been applied to molecular dynamics (MD) trajectories of the B-domain of staphylococcal protein A, generated with the coarse-grained united-residue (UNRES) force field in a broad range of temperatures (270K ≤ T ≤ 325K). Thousands of folding pathways have been identified at each temperature. Out of these many folding pathways, several most probable ones were selected for investigation of the conformational transitions during protein folding. Unlike other conformational space network (CSN) methods, a node in the CSN variant implemented in this work is defined according to the nativelikeness class of the structure, which defines the similarity of segments of the compared structures in terms of secondary-structure, contact-pattern, and local geometry, as well as the overall geometric similarity of the conformation under consideration to that of the reference (experimental) structure. Our previous findings, regarding the folding model and conformations found at the folding-transition temperature for protein A (Maisuradze et al., J. Am. Chem. Soc. 132, 9444, 2010), were confirmed by the conformational space network analysis. In the methodology and in the analysis of the results, the shortest path identified by using the shortest-path algorithm corresponds to the most probable folding pathway in the conformational space network.

A Comparison of Three Perturbation Molecular Dynamics Methods for Modeling Conformational Transitions

Targeted, steered, and biased molecular dynamics (MD) are widely used methods for studying transition processes of biomolecules. They share the common feature of adding external perturbations along a conformational progress variable to guide the transition in a predefined direction in conformational space, yet differ in how these perturbations are applied. In the present paper, we report a comparison of these three methods on generating transition paths for two different processes: the unfolding of the B domain of protein A and a conformational transition of the catalytic domain of a Src kinase Lyn. Transition pathways were calculated with different simulation parameters including the choice of progress variable and the simulation length or biasing force constant. A comparison of the generated paths based on structural similarity finds that the three perturbation MD methods generate similar transition paths for a given progress variable in most cases. On the other hand, the path depends more strongly on the choice of progress variable used to move the system between the initial and final states. Potentials of mean force (PMF) were calculated starting from unfolding trajectories to estimate the relative probabilities of the paths. A lower PMF was found for the lowest biasing force constant with BMD.

Quantifying the structural requirements of the folding transition state of protein A and other systems

The B-domain of protein A is a small three-helix bundle that has been the subject of considerable experimental and theoretical investigation. Nevertheless, a unified view of the structure of the transition-state ensemble (TSE) is still lacking. To characterize the TSE of this surprisingly challenging protein, we apply a combination of psi analysis (which probes the role of specific side-chain to side-chain contacts) and kinetic H/D amide isotope effects (which measures hydrogen-bond content), building upon previous studies using mutational phi analysis (which probes the energetic influence of side-chain substitutions). The second helix is folded in the TSE, while helix formation appears just at the carboxy and amino termini of the first and third helices, respectively. The experimental data suggest a homogenous yet plastic TS with a native-like topology. This study generalizes our earlier conclusion, based on two larger alpha/beta proteins, that the TSEs of most small proteins achieve approximately 70% of their native state's relative contact order. This high percentage limits the degree of possible TS heterogeneity and requires a reevaluation of the structural content of the TSE of other proteins, especially when they are characterized as small or polarized.

The complex folding pathways of protein A suggest a multiple-funnelled energy landscape

Folding proteins into their native states requires the formation of both secondary and tertiary structures. Many questions remain, however, as to whether these form into a precise order, and various pictures have been proposed that place the emphasis on the first or the second level of structure in describing folding. One of the favorite test models for studying this question is the B domain of protein A, which has been characterized by numerous experiments and simulations. Using the activation-relaxation technique coupled with a generic energy model (optimized potential for efficient peptide structure prediction), we generate more than 50 folding trajectories for this 60-residue protein. While the folding pathways to the native state are fully consistent with the funnel-like description of the free energy landscape, we find a wide range of mechanisms in which secondary and tertiary structures form in various orders. Our nonbiased simulations also reveal the presence of a significant number of non-native beta and alpha conformations both on and off pathway, including the visit, for a non-negligible fraction of trajectories, of fully ordered structures resembling the native state of nonhomologous proteins.

Universality and diversity of folding mechanics for three-helix bundle proteins

In this study we evaluate, at full atomic detail, the folding processes of two small helical proteins, the B domain of protein A and the Villin headpiece. Folding kinetics are studied by performing a large number of ab initio Monte Carlo folding simulations using a single transferable all-atom potential. Using these trajectories, we examine the relaxation behavior, secondary structure formation, and transition-state ensembles (TSEs) of the two proteins and compare our results with experimental data and previous computational studies. To obtain a detailed structural information on the folding dynamics viewed as an ensemble process, we perform a clustering analysis procedure based on graph theory. Moreover, rigorous p(fold) analysis is used to obtain representative samples of the TSEs and a good quantitative agreement between experimental and simulated Phi values is obtained for protein A. Phi values for Villin also are obtained and left as predictions to be tested by future experiments. Our analysis shows that the two-helix hairpin is a common partially stable structural motif that gets formed before entering the TSE in the studied proteins. These results together with our earlier study of Engrailed Homeodomain and recent experimental studies provide a comprehensive, atomic-level picture of folding mechanics of three-helix bundle proteins.

Searching for Multiple Folding Pathways of a Nearly Symmetrical Protein: Temperature Dependent Φ-Value Analysis of the B Domain of Protein A

The B domain of protein A (BdpA) is a popular paradigm for simulating protein folding pathways. The discrepancies between so many simulations and subsequent experimental testing may be attributable to the protein being highly symmetrical: changing experimental conditions could perturb the subtle interplay between the effects of symmetry in the native structure and the effects of asymmetry from specific interactions in a given sequence. If the protein folds via multiple pathways, perturbations, such as temperature, denaturant concentration, and mutation, should change the flux of micro pathways, leading to changes in the bulk properties of the transition state. We tested this hypothesis by conducting a Phi-analysis of BdpA as a function of temperature from 25.0 degrees C to 60.0 degrees C. The Phi-values had no significant dependence on temperature and the values at 55.0 degrees C (denaturing conditions) are very similar to those at 25.0 degrees C (folding conditions), indicating the structure of the transition state does not significantly change although the experimental conditions are considerably altered. The results suggest that BdpA folds via a single dominant folding pathway.

Influence of temperature, friction, and random forces on folding of the B-domain of staphylococcal protein A: All-atom molecular dynamics in implicit solvent

The influences of temperature, friction, and random forces on the folding of protein A have been analyzed. A series of all-atom molecular dynamics folding simulations with the Amber ff99 potential and Generalized Born solvation, starting from the fully extended chain, were carried out for temperatures from 300 to 500 K, using (a) the Berendsen thermostat (with no explicit friction or random forces) and (b) Langevin dynamics (with friction and stochastic forces explicitly present in the system). The simulation temperature influences the relative time scale of the major events on the folding pathways of protein A. At lower temperatures, helix 2 folds significantly later than helices 1 and 3. However, with increasing temperature, the folding time of helix 2 approaches the folding times of helices 1 and 3. At lower temperatures, the complete formation of secondary and tertiary structure is significantly separated in time whereas, at higher temperatures, they occur simultaneously. These results suggest that some earlier experimental and theoretical observations of folding events, e.g., the order of helix formation, could depend on the temperature used in those studies. Therefore, the differences in temperature used could be one of the reasons for the discrepancies among published experimental and computational studies of the folding of protein A. Friction and random forces do not change the folding pathway that was observed in the simulations with the Berendsen thermostat, but their explicit presence in the system extends the folding time of protein A.

Phi-analysis of the folding of the B domain of protein A using multiple optical probes

We examined the co-operativity of ultra-fast folding of a protein and whether the Phi-value analysis of its transition state depended on the location of the optical probe. We incorporated in turn a tryptophan residue into each of the three helices of the B domain of Protein A. Each Trp mutant of the three-helix bundle protein was used as a pseudo-wild-type parent for Phi-analysis in which the intrinsic Trp fluorescence probed the formation of each helix during the transition state. Apart from local effects in the immediate vicinity of the probe, the three separate sets of Phi-values were in excellent agreement, demonstrating the overall co-operativity of folding and the robustness of the Phi-analysis. The transition state of folding of Protein A contains the second helix being well formed with many stabilizing tertiary hydrophobic interactions. In contrast, the first and the third helices are more poorly structured in the transition state. The mechanism of folding thus involves the concurrent formation of secondary and tertiary interactions, and is towards the nucleation-condensation extreme in the nucleation-condensation-framework continuum of mechanism, with helix 2 being the nucleus. We provide an error analysis of Phi-values derived purely from the kinetics of two-state chevron plots.

Flexibly varying folding mechanism of a nearly symmetrical protein: B domain of protein A

The folding pathway of the B domain of protein A is the pathway most intensively studied by computer simulations. Recent systematic measurement of Phi values by Sato et al., however, has shown that none of the published computational predictions is consistent with the detailed features of the experimentally observed folding mechanism. In this article we use a statistical mechanical model of folding to show that sensitive dependence of multiple transition state ensembles on temperature and the denaturant concentration is the key to resolving the inconsistency among simulations and the experiment. Such sensitivity in multiple transition state ensembles is a natural consequence of symmetry-breaking in a nearly symmetrical protein.