Michael C. Baxa

Benchmarking all-atom simulations using hydrogen exchange

Significance Molecular dynamics simulations have recently become capable of observing multiple protein unfolding and refolding events in a single-millisecond–long trajectory. This major advance produces atomic-level information with nanosecond resolution, a feat unmatched by experimental methods. Such simulations are being extensively analyzed to assess their description of protein folding, yet the results remain difficult to validate experimentally. We apply a combination of hydrogen exchange, NMR, and other techniques to test the simulations with a resolution of single H-bonds. Several significant discrepancies between the simulations and experimental data were uncovered for regions of the energy surface outside of the native basin. This comparison yields suggestions for improving the force fields and provides a general method for experimentally validating folding simulations. Long-time molecular dynamics (MD) simulations are now able to fold small proteins reversibly to their native structures [Lindorff-Larsen K, Piana S, Dror RO, Shaw DE (2011) Science 334(6055):517–520]. These results indicate that modern force fields can reproduce the energy surface near the native structure. To test how well the force fields recapitulate the other regions of the energy surface, MD trajectories for a variant of protein G are compared with data from site-resolved hydrogen exchange (HX) and other biophysical measurements. Because HX monitors the breaking of individual H-bonds, this experimental technique identifies the stability and H-bond content of excited states, thus enabling quantitative comparison with the simulations. Contrary to experimental findings of a cooperative, all-or-none unfolding process, the simulated denatured state ensemble, on average, is highly collapsed with some transient or persistent native 2° structure. The MD trajectories of this protein G variant and other small proteins exhibit excessive intramolecular H-bonding even for the most expanded conformations, suggesting that the force fields require improvements in describing H-bonding and backbone hydration. Moreover, these comparisons provide a general protocol for validating the ability of simulations to accurately capture rare structural fluctuations.

Loss of conformational entropy in protein folding calculated using realistic ensembles and its implications for NMR-based calculations

Significance Despite 40 years of study, no consensus has been achieved on the magnitude of the loss of backbone (BB) and side-chain (SC) entropies upon folding, even though these quantities are essential for characterizing the energetics of folding and conformational change. We calculate the loss using experimentally validated denatured and native state ensembles, avoiding the drastic assumptions used in many past analyses. By also accounting for correlated motions, we find that the loss of BB entropy is three- to fourfold larger than the SC contribution. Our values differ with some calculations by up to a factor of 3 and depend strongly on 2° structure. These results have implications upon other thermodynamic properties, the estimation of entropy using NMR methods, and coarse-grained simulations. The loss of conformational entropy is a major contribution in the thermodynamics of protein folding. However, accurate determination of the quantity has proven challenging. We calculate this loss using molecular dynamic simulations of both the native protein and a realistic denatured state ensemble. For ubiquitin, the total change in entropy is TΔSTotal = 1.4 kcal⋅mol−1 per residue at 300 K with only 20% from the loss of side-chain entropy. Our analysis exhibits mixed agreement with prior studies because of the use of more accurate ensembles and contributions from correlated motions. Buried side chains lose only a factor of 1.4 in the number of conformations available per rotamer upon folding (ΩU/ΩN). The entropy loss for helical and sheet residues differs due to the smaller motions of helical residues (TΔShelix−sheet = 0.5 kcal⋅mol−1), a property not fully reflected in the amide N-H and carbonyl C=O bond NMR order parameters. The results have implications for the thermodynamics of folding and binding, including estimates of solvent ordering and microscopic entropies obtained from NMR.

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 states 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.

Metal binding kinetics of bi-histidine sites used in psi analysis: evidence of high-energy protein folding intermediates.

The zinc-specific fluorophore, Zinpyr-1, is used in competition assays to determine the kinetic and thermodynamic parameters of Zn2+ binding to engineered bi-histidine sites located in ubiquitin and the B domain of protein A (BdpA). These binding sites are used in psi analysis studies to investigate structure formation in the folding transition state identified by the change in folding rate upon addition of metal ions. For ubiquitin, the on-rate binding constant and binding affinity for a site located along an alpha-helix are measured to be approximately 10(7) M-1 s-1 and 3 microM, respectively. For a site located across two beta-strands, the metal binding affinity was too weak to measure in the dye competition assays (Kd > 55 microM). The equilibrium-determined values for the Zn2+-induced stabilization of ubiquitin and BdpA match the values derived from changes in the global folding and unfolding rates. Therefore, metal ion binding is in fast equilibrium during the transit over the free energy barrier. Accordingly, the folding rate must be slower than the product of the fractional population of a high-energy intermediate with the metal site formed and the metal binding on-rate constant. The known folding rate of 20 s-1 at 1.5 M guanidinium chloride in 400 microM Zn2+ provides an upper bound for the stability of such intermediates (DeltaG(U-I) < 4 kcal/mol). These results support a view of the apparent two-state protein folding reaction surface as a fast pre-equilibrium between the denatured state and a series of high-energy species. The net folding rate is a product of the equilibrium constant of the highest-energy species and a transmission rate. For ubiquitin, we estimate the transmission rate to be approximately 10(4) s-1. Implications for the role of unfolded chain diffusion on folding rates and barrier heights are discussed.

Even with nonnative interactions, the updated folding transition states of the homologs Proteins G & L are extensive and similar

Significance An outstanding issue in protein science is identifying the relationship between sequence and folding, e.g., do sequences having similar structures have similar folding pathways? The homologs Proteins G & L have been cited as a primary example where sequence variations dramatically affect folding dynamics. However, our new results indicate that the homologs have similar folding behavior. At the highest point on the reaction surface, the pathways converge to similar ensembles. These findings are distinct from descriptions based on the widely used mutational ϕ analysis, partly due to nonnative behavior. Our study emphasizes that significant challenges remain both in characterizing and predicting transition state ensembles even for relatively simple proteins whose folding behavior is believed to be well understood. Experimental and computational folding studies of Proteins L & G and NuG2 typically find that sequence differences determine which of the two hairpins is formed in the transition state ensemble (TSE). However, our recent work on Protein L finds that its TSE contains both hairpins, compelling a reassessment of the influence of sequence on the folding behavior of the other two homologs. We characterize the TSEs for Protein G and NuG2b, a triple mutant of NuG2, using ψ analysis, a method for identifying contacts in the TSE. All three homologs are found to share a common and near-native TSE topology with interactions between all four strands. However, the helical content varies in the TSE, being largely absent in Proteins G & L but partially present in NuG2b. The variability likely arises from competing propensities for the formation of nonnative β turns in the naturally occurring proteins, as observed in our TerItFix folding algorithm. All-atom folding simulations of NuG2b recapitulate the observed TSEs with four strands for 5 of 27 transition paths [Lindorff-Larsen K, Piana S, Dror RO, Shaw DE (2011) Science 334(6055):517–520]. Our data support the view that homologous proteins have similar folding mechanisms, even when nonnative interactions are present in the transition state. These findings emphasize the ongoing challenge of accurately characterizing and predicting TSEs, even for relatively simple proteins.

A “Link‐Psi” strategy using crosslinking indicates that the folding transition state of ubiquitin is not very malleable

Using a combined crosslinking‐ψ analysis strategy, we examine whether the structural content of the transition state of ubiquitin can be altered. A synthetic dichloroacetone crosslink is first introduced across two β strands. Whether the structural content in the transition state ensemble has shifted towards the region containing the crosslink is probed by remeasuring the ψ value at another region (ψ identifies the degree to which an inserted bi‐Histidine metal ion binding site is formed in the transition state). For sites around the periphery of the obligate transition state nucleus, we find that the resulting changes in ψ values are near or at our detection limit, thereby indicating that the structural content of the transition state has not measurably changed upon crosslinking. This work demonstrates the utility of the simultaneous application of crosslinking and ψ‐analysis for examining potential transition state heterogeneity in globular proteins.

Revealing what gets buried first in protein folding

After decades of research, the nature of the rate-limiting step in the folding of globular proteins still elicits a range of opinions (1). The properties of the associated transition state (TS) provide critical insights into possible folding mechanisms. However, the characterization of the TS is challenging because atomic level methods cannot be applied to this minimally populated state, and lower resolution methods have produced divergent views. Even the existence of a generalized TS remains actively debated. In PNAS, Guinn et al. (2) dissect the burial properties of the TS for 13 proteins by analyzing the denaturant and temperature dependence of folding rates to distinguish the burial of hydrophobic surface from that of amide groups. With this capability, they propose that the TSs generally are very advanced and often contain the native 2° structure, a level higher than most prior methods have indicated.

Perplexing cooperative folding and stability of a low-sequence complexity, polyproline 2 protein lacking a hydrophobic core

Significance The basis of protein-folding cooperativity and stability elicits a variety of opinions, as does the existence and importance of possible residual structure in the denatured state. We examine these issues in a protein that is striking in its dearth of hydrophobic burial and its lack of canonical α and β structures, while having a low sequence complexity with 46% glycine. Unexpectedly, the protein’s folding behavior is similar to that observed for typical globular proteins. This enigma forces a reexamination of the possible combination of factors that can stabilize a protein. The burial of hydrophobic side chains in a protein core generally is thought to be the major ingredient for stable, cooperative folding. Here, we show that, for the snow flea antifreeze protein (sfAFP), stability and cooperativity can occur without a hydrophobic core, and without α-helices or β-sheets. sfAFP has low sequence complexity with 46% glycine and an interior filled only with backbone H-bonds between six polyproline 2 (PP2) helices. However, the protein folds in a kinetically two-state manner and is moderately stable at room temperature. We believe that a major part of the stability arises from the unusual match between residue-level PP2 dihedral angle bias in the unfolded state and PP2 helical structure in the native state. Additional stabilizing factors that compensate for the dearth of hydrophobic burial include shorter and stronger H-bonds, and increased entropy in the folded state. These results extend our understanding of the origins of cooperativity and stability in protein folding, including the balance between solvent and polypeptide chain entropies.

Cooperative folding near the downhill limit determined with amino acid resolution by hydrogen exchange

Significance Fast-folding proteins provide a testing ground for theories and simulations of folding at the extreme limit, in particular when it occurs on the timescale of chain diffusion and potentially in the elusive barrier-free limit. Whereas most fast-folding studies probe the reaction near the transition point with limited resolution, we apply hydrogen exchange methods to a microsecond folder, characterizing its energy landscape with amino acid precision under highly stabilizing conditions where barrier-free folding is most probable. Despite folding with τ = 5 μs, we find that the molecule folds and unfolds in a cooperative process matching the properties observed at elevated denaturant concentration, implying that much faster folding rate constants are required to reach the downhill limit. The relationship between folding cooperativity and downhill, or barrier-free, folding of proteins under highly stabilizing conditions remains an unresolved topic, especially for proteins such as λ-repressor that fold on the microsecond timescale. Under aqueous conditions where downhill folding is most likely to occur, we measure the stability of multiple H bonds, using hydrogen exchange (HX) in a λYA variant that is suggested to be an incipient downhill folder having an extrapolated folding rate constant of 2 × 105 s−1 and a stability of 7.4 kcal·mol−1 at 298 K. At least one H bond on each of the three largest helices (α1, α3, and α4) breaks during a common unfolding event that reflects global denaturation. The use of HX enables us to both examine folding under highly stabilizing, native-like conditions and probe the pretransition state region for stable species without the need to initiate the folding reaction. The equivalence of the stability determined at zero and high denaturant indicates that any residual denatured state structure minimally affects the stability even under native conditions. Using our ψ analysis method along with mutational ϕ analysis, we find that the three aforementioned helices are all present in the folding transition state. Hence, the free energy surface has a sufficiently high barrier separating the denatured and native states that folding appears cooperative even under extremely stable and fast folding conditions.