Folding-unfolding Equilibrium Research Articles

Retrospective study for the universal applicability of the residue-based linear free energy relationship in the two-state exchange of protein molecules

Multiprobe measurements, such as NMR and hydrogen exchange studies, can provide the equilibrium constant, K, and rate constants for forward and backward processes, k and k′, of the two-state structural changes of a polypeptide on a per-residue basis. We previously found a linear relationship between log K and log k and between log K and log k′ for the topological exchange of a 27-residue bioactive peptide. To test the general applicability of the residue-based linear free energy relationship (rbLEFR), we performed a literature search to collect residue-specific K, k, and k′ values in various exchange processes, including folding-unfolding equilibrium, coupled folding and binding of intrinsically disordered peptides, and structural fluctuations of folded proteins. The good linearity in a substantial number of the log–log plots proved that the rbLFER holds for the structural changes in a wide variety of protein-related phenomena. Among the successful cases, the hydrogen exchange study of apomyoglobin folding intermediates is particularly interesting. We found that the residues that deviated from the linear relationship corresponded to the α-helix, for which transient translocation had been identified by other experiments. Thus, the rbLFER is useful for studying the structures and energetics of the dynamic states of protein molecules.

In silico study of osmolytic effects of choline-O-sulfate on urea induced unfolding of Trp-cage mini-protein: An atomistic view from replica exchange molecular dynamics simulation

The event of protein folding is associated with essential biological functionalities and unfolding of protein native state can cause intra-cellular toxicity leading to biological dysfunctions and even cell death. The present study discusses the folding-unfolding equilibrium of the small globular protein Trp-cage in presence of denaturing and protecting osmolytes urea and choline-O-sulfate (COS), respectively, employing Replica Exchange Molecular Dynamics (REMD), extensive free energy calculations and temperature scanned free energy landscapes. It is shown that, while 6 M urea quite easily denatures the protein, 0.5 M and 1 M COS is able to protect the protein from urea induced denaturation at room temperature. However, REMD simulations reveal that while the protein in pure water can withstand a simulation temperature as high as 420 K without melting, the protecting effect of 0.5 M and 1 M COS is operative up to 300 and 340 K respectively. This study furnishes evidences to shed light into the protecting mechanism of COS regarding urea induced protein unfolding, thereby putting forward the use of COS as a proper protecting osmolyte towards different types of proteins.

Thermal versus mechanical unfolding in a model protein.

Force spectroscopy techniques are often used to learn about the free energy landscape of single biomolecules, typically by recovering free energy quantities that, extrapolated to zero force, are compared to those measured in bulk experiments. However, it is not always clear how the information obtained from a mechanically perturbed system can be related to the information obtained using other denaturants since tensioned molecules unfold and refold along a reaction coordinate imposed by the force, which is not likely to be meaningful in its absence. Here, we explore this dichotomy by investigating the unfolding landscape of a model protein, which is unfolded first mechanically through typical force spectroscopy-like protocols and next thermally. When unfolded by nonequilibrium force extension and constant force protocols, we recover a simple two-barrier landscape as the protein reaches the extended conformation through a metastable intermediate. Interestingly, folding-unfolding equilibrium simulations at low forces suggested a totally different scenario, where this metastable state plays little role in the unfolding mechanism, and the protein unfolds through two competing pathways [R. Tapia-Rojo et al., J. Chem. Phys. 141, 135102 (2014)]. Finally, we use Markov state models to describe the configurational space of the unperturbed protein close to the critical temperature. The thermal dynamics is well understood by a one-dimensional landscape along an appropriate reaction coordinate, however it is very different from the mechanical picture. In this sense, the results of our protein model for the mechanical and thermal descriptions provide incompatible views of the folding/unfolding landscape of the system, and the estimated quantities to zero force result are hard to interpret.

Computational scrutiny of the effect of N-terminal proline and residue stereochemistry in the nucleation of α-helix fold

N-Terminal l- to d-residue mutation nucleate helical fold in Ac–DAla–LAla3–NHMe (Ib, m2), Ac–DPro–LAla3–NHMe (IIb, m1), and Ac–DPro–LPro–LAla2–NHMe (IIIb, m2) peptides.

Impact of crystal packing on coiled-coil flexibility.

The structural characterization of various constructs of the Measles virus (MeV) Phosphoprotein (P) multimerization domain (PMD) has brought to light significant discrepancies in the quaternary structure due to both crystal constraints and the flexible nature of this coiled-coil. Indeed, despite a conserved tetrameric parallel coiled-coil core, structural comparison unveiled significant deformations in the C-terminal extremities that even led to the partial unfolding of the coiled-coil. These deformations were induced by intermolecular interactions within the crystal, as well as by the crystallization condition. These deformations also suggest that PMD has the ability to adapt to external mechanical constrains. Using a combination of biophysical methods (size-exclusion chromatography, circular dichroism and small angle X-ray scattering), we assessed the differential flexibility of the C-terminal region of the MeV PMD in solution. Taken together, these results show that crystal packing can be used to "freeze" in a certain state, parts of proteins known to be in a dynamic folding-unfolding equilibrium. They also bring awareness that conclusions about function and mechanism based on analysis of a single crystal structure of a known dynamic protein can be easily biased, and they challenge to some extent the assumption that coiled-coil structures can be reliably predicted from the amino acid sequence.

Interactions of main chain in folding and self assembly of unfolded protein structure: Enquiries with a serine solubilized nonapeptide

Interactions of the protein main chain are probed for their role in folding and self-assembly. The interactions are assessed with serine nonapeptide Ac-(Ser-Ala)4-Ser-NH2 in poly-L and alternating-L,D structure variations. Being a neutral molecule, Serine nonapeptide has been found to display not only folding-unfolding equilibrium, but also association-dissociation equilibrium as a function of solvent and concentration. Thus scrutiny of intra- and inter-molecular interactions have been undertaken in water, methanol, and DMSO solvents. In water, poly-L peptide displays a PPII-helix conformation which unfolds to extended β-conformation with increase of temperature, apparently in a two-state equilibrium. Poly-L peptide at high concentration and on transfer to the low polarity solvent, methanol, displays ordering as a β-hairpin. This implies folding of the peptide by self assembly. Self assembly and ordering possibly as double-stranded β-helix is also evidence for alternating-L,D peptide. Both isomers were observed to be unfolded in high polarity solvent DMSO. Dynamic light scattering suggests that assembly in both isomers may involve large size aggregates. The results have established that folding and self-assembly can be coupled equilibria dependent upon solute structure, concentration, and solvent. The interactions of the protein main chain involved in folding and self assembly of unfolded structure are illuminated and have been discussed.

Isolation and characterization of Korean pine (Pinus koraiensis) convicilin

A vicilin-like globulin seed storage protein, termed convicilin, was isolated for the first time from Korean pine (Pinus koraiensis). SDS-PAGE analysis revealed that Korean pine convicilin was post-translationally processed. The N-terminal peptide sequences of its components were determined. These peptides could be mapped to a protein translated from an embryo abundant transcript isolated in this study. Similar to vicilin, native convicilin appeared to be homotrimeric. Differential scanning calorimetry (DSC) analyses revealed that this protein is less resistant to thermal treatment than Korean pine vicilin. Its transition temperature was 75.57 °C compared with 84.13 °C for vicilin. The urea induced folding-unfolding equilibrium of pine convicilin monitored by intrinsic fluorescence could be interpreted in terms of a two-state model, with a Cm of 4.41 ± 0.15 M.

Folding Dynamics of the Trp-Cage Miniprotein: Evidence for a Native-Like Intermediate from Combined Time-Resolved Vibrational Spectroscopy and Molecular Dynamics Simulations

Trp-cage is a synthetic 20-residue miniprotein which folds rapidly and spontaneously to a well-defined globular structure more typical of larger proteins. Due to its small size and fast folding, it is an ideal model system for experimental and theoretical investigations of protein folding mechanisms. However, Trp-cage's exact folding mechanism is still a matter of debate. Here we investigate Trp-cage's relaxation dynamics in the amide I' spectral region (1530-1700 cm(-1)) using time-resolved infrared spectroscopy. Residue-specific information was obtained by incorporating an isotopic label ((13)C═(18)O) into the amide carbonyl group of residue Gly11, thereby spectrally isolating an individual 310-helical residue. The folding-unfolding equilibrium is perturbed using a nanosecond temperature-jump (T-jump), and the subsequent re-equilibration is probed by observing the time-dependent vibrational response in the amide I' region. We observe bimodal relaxation kinetics with time constants of 100 ± 10 and 770 ± 40 ns at 322 K, suggesting that the folding involves an intermediate state, the character of which can be determined from the time- and frequency-resolved data. We find that the relaxation dynamics close to the melting temperature involve fast fluctuations in the polyproline II region, whereas the slower process can be attributed to conformational rearrangements due to the global (un)folding transition of the protein. Combined analysis of our T-jump data and molecular dynamics simulations indicates that the formation of a well-defined α-helix precedes the rapid formation of the hydrophobic cage structure, implying a native-like folding intermediate, that mainly differs from the folded conformation in the orientation of the C-terminal polyproline II helix relative to the N-terminal part of the backbone. We find that the main free-energy barrier is positioned between the folding intermediate and the unfolded state ensemble, and that it involves the formation of the α-helix, the 310-helix, and the Asp9-Arg16 salt bridge. Our results suggest that at low temperature (T ≪ Tm) a folding path via formation of α-helical contacts followed by hydrophobic clustering becomes more important.

Evidence against a Permanently Folded Nucleation Sequence in the Intrinsically Disordered Protein Stathmin Measured by Site-Directed Spin Labeling EPR Spectroscopy

After their relatively recent discovery and classification, it has been shown that intrinsically disordered proteins (IDPs) play essential roles in cellular regulation and signal transduction. Stathmin is a eukaryotic IDP responsible for regulating the polymerization equilibrium between the tubulin heterodimer and microtubules, and is also highly expressed in cancerous cells. Stathmin exists in a highly-ordered folded state when bound to its binding partner tubulin; however, alone in solution, as an IDP lacking those stabilizing binding interactions, stathmin is likely to explore conformational space in various equilibria between partially and completely folded states. Interestingly, it has been suggested that soluble stathmin has a short helical region (Glu55-Ala73) of persistent foldedness, and that this region might act as an α-helical ‘nucleation sequence' necessary for further folding in the C-terminal direction. Alternatively, we believe that the complete length of stathmin exists in a folding-unfolding equilibrium, and here we report data supporting this hypothesis. Nitroxide spin labeled mutants of stathmin throughout the Glu55-Ala73 region - rotationally immobilized through coupling to CNBr-activated sepharose beads - were studied by electron paramagnetic resonance (EPR) spectroscopy. The continuous wave EPR spectra for all 19 spin labeled mutants unambiguously indicate that this region of stathmin exists in a dynamic equilibrium between folded (ordered) and unfolded (disordered) states, and that no such helical nucleation sequence exists. We also show that this folding equilibrium in stathmin is shifted by the common biochemical viscosity modifiers sucrose, glycerol, and Ficoll-70.

Membrane Anchoring Amplifies Osmosensing by the Inner Membrane Receptor EnvZ

A fundamental question in signalling biology is how do receptors transmit the effects of extracellular stimuli across membranes? Transmembrane segments that connect a receptor extracellular domain to its intracellular domain are often considered to be critical elements for transmitting these signals. The dynamics of receptor signalling is not clearly understood, as there are few biophysical probes to directly monitor transmembrane regions. Amide Deuterium Exchange Mass Spectrometry (HDXMS) provides an excellent method to describe the conformational dynamics of membrane bound proteins. Our recently published studies with the cytoplasmic domain of the bacterial inner membrane osmosensor kinase EnvZ (EnvZc) have revealed the molecular basis for osmosensing through modulation of helix-coil transitions in a critical four helix bundle subdomain (Wang, LC, Morgan, L, Godakumbura, P, Kenney, LJ and Anand, GS EMBO J. 31(11):2648-59, 2012). This study highlighted the importance of local folding-unfolding equilibria in the functioning of EnvZ signalling. Most surprising was that a cytoplasmic deletion fragment of EnvZ lacking the transmembrane helices was able to fully rescue the osmosensing function in a strain lacking the envZ gene. This immediately raised the question as to what is the function of membrane anchoring? Our preliminary results indicate that the helix-coil transitions and associated local unfolding we observed in EnvZc also occur in transmembrane helix regions in EnvZ. Conformational dynamics of full-length EnvZ embedded within nanodiscs indicate that the osmosensing core of EnvZ shows greater deuterium exchange compared to EnvZc, suggesting a regulatory role of the membrane in modulating the autokinase activity of EnvZ. Our results reveal that membrane anchoring is responsible for ‘damping down' the helix-coil transitions and likely increases the sensitivity range for the receptor. These results are broadly relevant to all receptors. Supported by Mechanobiology RCE and VA-1IOBX000372 to LJK.

Stereochemistry and Solvent Role in Protein Folding: Nuclear Magnetic Resonance and Molecular Dynamics Studies of Poly-l and Alternating-l,d Homopolypeptides in Dimethyl Sulfoxide

The competing interactions folding and unfolding protein structure remain obscure. Using homopolypeptides, we ask if poly-L structure may have a role. We mutate the structure to alternating-L,D stereochemistry and substitute water as the fold-promoting solvent with methanol and dimethyl sulfoxide (DMSO) as the fold-denaturing solvents. Circular dichroism and molecular dynamics established previously that, while both isomers were folded in water, the poly-L isomer was unfolded and alternating-L,D isomer folded in methanol. Nuclear magnetic resonance and molecular dynamics establish now that both isomers are unfolded in DMSO. We calculated energetics of folding-unfolding equilibrium with water and methanol as solvents. We have now calculated interactions of unfolded polypeptide structures with DMSO as solvent. Methanol was found to unfold and water fold poly-L structure as a dielectric. DMSO has now been found to unfold both poly-L and alternating-L,D structures by strong solvation of peptides to disrupt their hydrogen bonds. Accordingly, we propose that while linked peptides fold protein structure with hydrogen bonds they unfold the structure electrostatically due to the stereochemical effect of the poly-L structure. Protein folding to ordering of peptide hydrogen bonds with water as canonical solvent may thus involve two specific and independent solvent effects-one, strong screening of electrostatics of poly-L linked peptides, and two, weak dipolar solvation of peptides. Correspondingly, protein denaturation may involve two independent solvent effects-one, weak dielectric to unfold poly-L structure electrostatically, and two, strong polarity to disrupt peptide hydrogen bonds by solvation of peptides.

Environmental Effects Dominate the Folding of Oligocholates in Solution, Surfactant Micelles, and Lipid Membranes

Oligocholate foldamers with different numbers and locations of guanidinium-carboxylate salt bridges were synthesized. The salt bridges were introduced by incorporating arginine and glutamic acid residues into the foldamer sequence. The conformations of these foldamers were studied by fluorescence spectroscopy in homogeneous solution, anionic and nonionic micelles, and lipid bilayers. Environmental effects instead of inherent foldability were found to dominate the folding. As different noncovalent forces become involved in the conformations of the molecules, the best folder in one environment could turn into the worst in another. Preferential solvation was the main driving force for the folding of oligocholates in solution. The molecules behaved very differently in micelles and lipid bilayers, with the most critical factors controlling the folding-unfolding equilibrium being the solvation of ionic groups and the abilities of the surfactants/lipids to compete for the salt bridge. Because of their ability to fold into helices with a nonpolar exterior and a polar interior, the oligocholates could transport large hydrophilic molecules such as carboxyfluorescein across lipid bilayers. Both the conformational properties of the oligocholates and their binding with the guest were important to the transport efficiency.

Conformational Transition Associated with E1-E2 Interaction in Small Ubiquitin-like Modifications

Ubiquitin-like modifications regulate nearly every aspect of cellular functions. A key step in these modifications is the recognition of the carrier enzyme (E2) by the activating enzyme (E1). In this study, we have found that a critical E2-binding surface on the E1 of the small ubiquitin-like modifier has unusually high populations in both ordered and disordered states. Upon binding the E2, the disordered state is converted to the ordered state, which resembles the structure of the bound conformation, providing a mechanism to resolve the "Levinthal Paradox" search problem in a folding-upon-binding process. The significance of the folding-unfolding equilibrium is shown by the loss of functions of the mutations that shift the equilibrium to the folded state. This study highlights the importance of conformational flexibility in the molecular recognition event.

Molecular Dynamics Simulations of a Reversibly Folding β-Heptapeptide in Methanol: Influence of the Treatment of Long-Range Electrostatic Interactions

Eight 100-ns molecular dynamics simulations of a beta-heptapeptide in methanol at 340 K (within cubic periodic computational boxes of about 6-nm edge) are reported and compared. These simulations were performed with three different charge-state combinations at the peptide termini, one of them with or without a neutralizing chloride counterion, and using either the lattice-sum (LS) or reaction-field (RF) scheme to handle electrostatic interactions. The choice of the electrostatic scheme has essentially no influence on the folding-unfolding equilibrium when the peptide termini are uncharged and only a small influence when the peptide is positively charged at its N-terminus (with or without inclusion of a neutralizing chloride counterion). However, when the peptide is zwitterionic, the LS scheme leads to preferential sampling of the high-dipole folded helical state, whereas the RF scheme leads to preferential sampling of a low-dipole unfolded salt-bridged state. A continuum electrostatics analysis based on the sampled configurations (zwitterionic case) suggests that the LS scheme stabilizes the helical state through artificial periodicity, but that the magnitude of this perturbation is essentially negligible (compared to the thermal energy) for the large box size and relatively polar solvent considered. The results thus provide clear evidence (continuum electrostatics analysis) for the absence of LS artifacts and some indications (still not definitive because of the limited sampling of the folding-unfolding transition) for the presence of RF artifacts in this specific system.

Equilibrium Thermodynamics of Urea Denaturation of Trp-cage Miniprotein

Urea is a denaturant commonly used in protein folding studies. Simulation studies of the effect of urea on protein stability have concentrated on how urea unfolds proteins - not on how urea affects the folding/unfolding equilibrium. Here we report the first simulation studies of the reversible folding and unfolding equilibrium of a protein - the Trp-Cage miniprotein. Replica exchange MD was performed in all atomic detail, starting from an unfolded (extended) configuration in three different solvent conditions viz. 2M, 4M and 6M in Urea. The Kirkwood-Buff model for Urea was employed. Fifty replicas of the system at each concentration were simulated for 150 ns per replica per urea concentration (22.5 microseconds total simulation time), enabling us to obtain folding-unfolding equilibrium data in the temperature range of 283 K to 579 K. In addition, we have performed REMD simulations in 0 M urea i.e pure water (4 microseconds total simulation time). During these simulations we observe all replicas to fold and unfold multiple times. The equilibrium properties, as a function of T and [Urea], show a clear shift in equilibrium towards the unfolded state with increasing urea concentration. Details of the solvent structure around the protein backbone and side chains will be presented.This work was supported by the NSF MCB-0543769.

Effect of Interdomain Linker Length on an Antagonistic Folding–Unfolding Equilibrium between Two Protein Domains

Fusion of one protein domain with another is a common event in both evolution and protein engineering experiments. When insertion is at an internal site (e.g., a surface loop or turn), as opposed to one of the termini, conformational strain can be introduced into both domains. Strain is manifested by an antagonistic folding–unfolding equilibrium between the two domains, which we previously showed can be parameterized by a coupling free-energy term (Δ G X). The extent of strain is predicted to depend primarily on the ratio of the N-to-C distance of the guest protein to the distance between ends of the surface loop in the host protein. Here, we test that hypothesis by inserting ubiquitin (Ub) into the bacterial ribonuclease barnase (Bn), using peptide linkers from zero to 10 amino acids each. Δ G X values are determined by measuring the extent to which Co 2+ binding to an engineered site on the Ub domain destabilizes the Bn domain. All-atom, unforced Langevin dynamics simulations are employed to gain structural insight into the mechanism of mechanically induced unfolding. Experimental and computational results find that the two domains are structurally and energetically uncoupled when linkers are long and that Δ G X increases with decreasing linker length. When the linkers are fewer than two amino acids, strain is so great that one domain unfolds the other. However, the protein is able to refold as dimers and higher-order oligomers. The likely mechanism is a three-dimensional domain swap of the Bn domain, which relieves conformational strain. The simulations suggest that an effective route to mechanical unfolding begins with disruption of the hydrophobic core of Bn near the Ub insertion site.

Purification and Characterization of the 7S Vicilin from Korean Pine (Pinus koraiensis)

Pine nuts are economically important as a source of human food. They are also of medical importance because numerous pine nut allergy cases have been recently reported. However, little is known about the proteins in pine nuts. The purpose of this study was to purify and characterize pine nut storage proteins. Reported here is the first detailed purification protocol of the 7S vicilin-type globulin from Korean pine (Pinus koraiensis) by gel filtration, anion exchange, and hydrophobic interaction chromatography. Reducing SDS-PAGE analysis indicated that purified vicilin consists of four major bands, reminiscent of post-translational protease cleavage of storage proteins during protein body packing in other species. The N-terminal ends of vicilin peptides were sequenced by Edman degradation. Circular dichroism (CD) and differential scanning calorimetry (DSC) analyses revealed that pine nut vicilin is stable up to 80 degrees C and its folding-unfolding equilibrium monitored by intrinsic fluorescence can be interpreted in terms of a two-state model.

A shorter peptide model from staphylococcal nuclease for the folding–unfolding equilibrium of a β-hairpin shows that unfolded state has significant contribution from compact conformational states

It is important to understand the conformational features of the unfolded state in equilibrium with folded state under physiological conditions. In this paper, we consider a short peptide model LMYKGQPM from staphylococcal nuclease to model the conformational equilibrium between a hairpin conformation and its unfolded state using molecular dynamics simulation under NVT conditions at 300K using GROMOS96 force field. The free energy landscape has overall funnel-like shape with hairpin conformations sampling the minima. The "unfolded" state has a higher free energy of approximately 12kJ/mol with respect to native hairpin minimum and occupies a plateau region. We find that the unfolded state has significant contributions from compact conformations. Many of these conformations have hairpin-like topology. Further, these compact conformational forms are stabilized by hydrophobic interactions. Conversion between native and non-native hairpins occurs via unfolded states. Frequent conversions between folded and unfolded hairpins are observed with single exponential kinetics. We compare our results with the emerging picture of unfolded state from both experimental and theoretical studies.

Efficiency reduction and pseudo-convergence in replica exchange sampling of peptide folding–unfolding equilibria

Replica exchange (RE) molecular dynamics (MD) simulations are frequently applied to sample the folding–unfolding equilibria of β-hairpin peptides in solution, because efficiency gains are expected from this technique. Using a three-state Markov model featuring key aspects of β-hairpin folding we show that RE simulations can be less efficient than conventional techniques. Furthermore we demonstrate that one is easily seduced to erroneously assign convergence to the RE sampling, because RE ensembles can rapidly reach long-lived stationary states. We conclude that typical REMD simulations covering a few tens of nanoseconds are by far too short for sufficient sampling of β-hairpin folding–unfolding equilibria.

Conformational instability of the MARK3 UBA domain compromises ubiquitin recognition and promotes interaction with the adjacent kinase domain

The Par-1/MARK protein kinases play a pivotal role in establishing cellular polarity. This family of kinases contains a unique domain architecture, in which a ubiquitin-associated (UBA) domain is located C-terminal to the kinase domain. We have used a combination of x-ray crystallography and NMR dynamics experiments to understand the interaction of the human (h) MARK3 UBA domain with the adjacent kinase domain as compared with ubiquitin. The x-ray crystal structure of the linked hMARK3 kinase and UBA domains establishes that the UBA domain forms a stable intramolecular interaction with the N-terminal lobe of the kinase domain. However, solution-state NMR studies of the isolated UBA domain indicate that it is highly dynamic, undergoing conformational transitions that can be explained by a folding-unfolding equilibrium. NMR titration experiments indicated that the hMARK3 UBA domain has a detectable but extremely weak affinity for mono ubiquitin, which suggests that conformational instability of the isolated hMARK3 UBA domain attenuates binding to ubiquitin despite the presence of residues typically involved in ubiquitin recognition. Our data identify a molecular mechanism through which the hMARK3 UBA domain has evolved to bind the kinase domain, in a fashion that stabilizes an open conformation of the N- and C-terminal lobes, at the expense of its capacity to engage ubiquitin. These results may be relevant more generally to the 30% of UBA domains that lack significant ubiquitin-binding activity, and they suggest a unique mechanism by which interaction domains may evolve new binding properties.