The key event in force-induced unfolding of Titin's immunoglobulin domains

Steered molecular dynamics simulation of force-induced titin immunoglobulin domain I27 unfolding led to the discovery of a significant potential energy barrier at an extension of approximately 14 A on the unfolding pathway that protects the domain against stretching. Previous simulations showed that this barrier is due to the concurrent breaking of six interstrand hydrogen bonds (H-bonds) between beta-strands A' and G that is preceded by the breaking of two to three hydrogen bonds between strands A and B, the latter leading to an unfolding intermediate. The simulation results are supported by Angstrom-resolution atomic force microscopy data. Here we perform a structural and energetic analysis of the H-bonds breaking. It is confirmed that H-bonds between strands A and B break rapidly. However, the breaking of the H-bond between strands A' and G needs to be assisted by fluctuations of water molecules. In nanosecond simulations, water molecules are found to repeatedly interact with the protein backbone atoms, weakening individual interstrand H-bonds until all six A'-G H-bonds break simultaneously under the influence of external stretching forces. Only when those bonds are broken can the generic unfolding take place, which involves hydrophobic interactions of the protein core and exerts weaker resistance against stretching than the key event.     

Protein dynamics: From the native to the unfolded state and back again

Simulations to study protein unfolding and folding were performed. The unfolding simulations make use of molecular dynamics and treat an atomic model of barnase in aqueous solvent. The cooperative nature of the unfolding transition and the important role of water are described. The folding simulations are based on a bead model of the protein on a cubic lattice. It is shown for the 27-mer model that a large energy gap between the lowest energy (native) state and the excited states is a necessary and sufficient condition for fast folding.     

Energy landscape distortions and the mechanical unfolding of proteins

Molecular simulations and an energy landscape analysis are used to examine the stretching of a model protein. A mapping of the energy landscape shows that stretching the protein causes energy minima and energy barriers to flatten out and disappear, and new energy minima to be created. The implications of these landscape distortions depend on the timescale regime under which the protein is stretched. When the timescale for thermally activated processes is longer than the timescale of stretching, the disappearances of energy barriers provide the mechanism for protein unfolding. When the timescale for thermally activated processes is shorter than the timescale of stretching, the landscape distortions influence the stretching process by changing the number and types of energy minima in which the system can exist.     

Comparison of Generalised Born/Surface Area with Periodic Boundary Simulations to Study Protein Unfolding

Simulations comparing the rapid unfolding behaviour of the model protein barnase under explicit and implicit solvent systems have been undertaken in order to validate a faster implicit solvent method for studying proteins which are kinetically stable in silico. A comparison is made between all-atom explicitly solvated simulations of barnase undertaken using Particle Mesh Ewald electrostatic interactions with all-atom implicit solvent simulations undertaken using the generalised born/surface area (GBSA) method with a long non-bonded cut-off. The two explicit solvent unfolding trajectories appear to explore slightly different pathways showing the importance of having statistically valid ensembles which are not accessible from a single trajectory. The 500?K GBSA trajectory is unsuitable for exploring intermediate structures on the unfolding pathway of barnase, as the protein almost immediately jumps to a predominately random coil conformation. However, dropping the temperature to 400?K gives rise to trajectories where the protein is unable to climb out of the energy well containing the first intermediate state, in a reasonable timescale. A similar pattern to the explicit solvent unfolding trajectories is seen in 450?K GBSA runs, with the intermediate states differing between trajectories. The development of computer simulation methods suitable for application to more kinetically stable proteins will offer insight into the atomic detail of the conformational changes associated with protein unfolding diseases.     

Geofold: topology-based protein unfolding pathways capture the effects of engineered disulfides on kinetic stability

Protein unfolding is modeled as an ensemble of pathways, where each step in each pathway is the addition of one topologically possible conformational degree of freedom. Starting with a known protein structure, GeoFold hierarchically partitions (cuts) the native structure into substructures using revolute joints and translations. The energy of each cut and its activation barrier are calculated using buried solvent accessible surface area, side chain entropy, hydrogen bonding, buried cavities, and backbone degrees of freedom. A directed acyclic graph is constructed from the cuts, representing a network of simultaneous equilibria. Finite difference simulations on this graph simulate native unfolding pathways. Experimentally observed changes in the unfolding rates for disulfide mutants of barnase, T4 lysozyme, dihydrofolate reductase, and factor for inversion stimulation were qualitatively reproduced in these simulations. Detailed unfolding pathways for each case explain the effects of changes in the chain topology on the folding energy landscape. GeoFold is a useful tool for the inference of the effects of disulfide engineering on the energy landscape of protein unfolding.     

Similarity and difference in the unfolding of thermophilic and mesophilic cold shock proteins studied by molecular dynamics simulations

Molecular dynamics simulations were performed to unfold a homologous pair of thermophilic and mesophilic cold shock proteins at high temperatures. The two proteins differ in just 11 of 66 residues and have very similar structures with a closed five-stranded antiparallel beta-barrel. A long flexible loop connects the N-terminal side of the barrel, formed by three strands (beta1-beta3), with the C-terminal side, formed by two strands (beta4-beta5). The two proteins were found to follow the same unfolding pathway, but with the thermophilic protein showing much slower unfolding. Unfolding started with the melting of C-terminal strands, leading to exposure of the hydrophobic core. Subsequent melting of beta3 and the beta-hairpin formed by the first two strands then resulted in unfolding of the whole protein. The slower unfolding of the thermophilic protein could be attributed to ion pair formation of Arg-3 with Glu-46, Glu-21, and the C-terminal. These ion pairs were also found to be important for the difference in folding stability between the pair of proteins. Thus electrostatic interactions appear to play similar roles in the difference in folding stability and kinetics between the pair of proteins.     

600 ps Molecular dynamics reveals stable substructures and flexible hinge points in cAMP dependent protein kinase

Molecular dynamics simulations of the catalytic subunit of cAMP dependent protein kinase (cAPK) have been performed in an aqueous environment. The relations among the protein hydrogen‐bonding network, secondary structural elements, and the internal motions of rigid domains were examined. The values of fluctuations of protein dihedral angles during dynamics show quite distinct maxima in the regions of loops and minima in the regions of α‐helices and β‐strands. Analyses of conformation snapshots throughout the run show stable subdomains and indicate that these rigid domains are constrained during the dynamics by a stable network of hydrogen bonds. The most stable subdomain during the dynamics was in the small lobe including part of the carboxy‐terminal tail. The most significant flexible region was the highly conserved glycine‐rich loop between β strands 1 and 2 in the small lobe. Many of the main chain dihedral angle changes measured in a comparison of the crystallographic structures of “open” and “closed” conformations of cAPK correspond to the highly flexible residues found during dynamics. © 1999 John Wiley & Sons, Inc. Biopoly 50: 513–524, 1999     

Temperature dependence of the free energy landscape of the src-SH3 protein domain

The temperature dependence of the free energy landscape of the src-SH3 protein domain is investigated through fully atomic simulations in explicit solvent. Simulations are performed above and below the folding transition temperature, enabling an analysis of both protein folding and unfolding. The transition state for folding and unfolding, identified from the free energy surfaces, is found to be very similar, with structure in the central hydrophobic sheet and little structure throughout the rest of the protein. This is a result of a polarized folding (unfolding) mechanism involving early formation (late loss) of the central hydrophobic sheet at the transition state. Unfolding simulations map qualitatively well onto low-temperature free energy surfaces but appear, however, to miss important features observed in folding simulations. In particular, details of the folding mechanism involving the opening and closing of the hydrophobic core are not captured by unfolding simulations performed under strongly denaturing conditions. In addition, free energy surfaces at high temperatures do not display a desolvation barrier found at lower temperatures, involving the expulsion of water molecules from the hydrophobic core.     

Beta-hairpin folding mechanism of a nine-residue peptide revealed from molecular dynamics simulations in explicit water

The beta-hairpin fold mechanism of a nine-residue peptide, which is modified from the beta-hairpin of alpha-amylase inhibitor tendamistat (residues 15-23), is studied through direct folding simulations in explicit water at native folding conditions. Three 300-nanosecond self-guided molecular dynamics (SGMD) simulations have revealed a series of beta-hairpin folding events. During these simulations, the peptide folds repeatedly into a major cluster of beta-hairpin structures, which agree well with nuclear magnetic resonance experimental observations. This major cluster is found to have the minimum conformational free energy among all sampled conformations. This peptide also folds into many other beta-hairpin structures, which represent some local free energy minimum states. In the unfolded state, the N-terminal residues of the peptide, Tyr-1, Gln-2, and Asn-3, have a confined conformational distribution. This confinement makes beta-hairpin the only energetically favored structure to fold. The unfolded state of this peptide is populated with conformations with non-native intrapeptide interactions. This peptide goes through fully hydrated conformations to eliminate non-native interactions before folding into a beta-hairpin. The folding of a beta-hairpin starts with side-chain interactions, which bring two strands together to form interstrand hydrogen bonds. The unfolding of the beta-hairpin is not simply the reverse of the folding process. Comparing unfolding simulations using MD and SGMD methods demonstrate that SGMD simulations can qualitatively reproduce the kinetics of the peptide system.     

Solvent-induced free energy landscape and solute-solvent dynamic coupling in a multielement solute

Molecular dynamics simulations using a simple multielement model solute with internal degrees of freedom and accounting for solvent-induced interactions to all orders in explicit water are reported. The potential energy landscape of the solute is flat in vacuo. However, the sole untruncated solvent-induced interactions between apolar (hydrophobic) and charged elements generate a rich landscape of potential of mean force exhibiting typical features of protein landscapes. Despite the simplicity of our solute, the depth of minima in this landscape is not far in size from free energies that stabilize protein conformations. Dynamical coupling between configurational switching of the system and hydration reconfiguration is also elicited. Switching is seen to occur on a time scale two orders of magnitude longer than that of the reconfiguration time of the solute taken alone, or that of the unperturbed solvent. Qualitatively, these results are unaffected by a different choice of the water-water interaction potential. They show that already at an elementary level, solvent-induced interactions alone, when fully accounted for, can be responsible for configurational and dynamical features essential to protein folding and function.     

Refolding molecular dynamics simulations of small- and middle-sized proteins in an explicit solvent

In order to elucidate the protein folding problem, we performed molecular dynamics simulations for small- and middle-sized two unfolding and six refolding proteins in an explicit solvent. Histidine-containing phosphocarrier protein and small designed protein were chosen for the simulations. We found that the protein folding process of these proteins was divided into three phases: an α -helix formation phase, a packing phase and a β -sheet formation phase. In the α -helix formation phase, an α -helix was developed from a β -turn structure through a 3₁₀-helix state. In the packing phase, proteins became compact, and tertiary structures (α / α or pre- β / β packing) were formed. Formation of a hydrophobic nucleus occurred concomitant with the α -helix formation and packing phase. Finally, in the β -sheet formation phase, a β -sheet was developed owing to the sequential formation of hydrogen bonds between two neighbouring strands, just like a "closing zipper".     

Role of extracellular glutamic acids in the stability and energy landscape of bacteriorhodopsin

Bacteriorhodopsin (BR), a specialized nanomachine, converts light energy into a proton gradient to power Halobacterium salinarum. In this work, we analyze the mechanical stability of a BR triple mutant in which three key extracellular residues, Glu⁹, Glu¹⁹⁴, and Glu²⁰⁴, were mutated simultaneously to Gln. These three Glu residues are involved in a network of hydrogen bonds, in cation binding, and form part of the proton release pathway of BR. Changes in these features and the robust photocycle dynamics of wild-type (WT) BR are apparent when the three extracellular Glu residues are mutated to Gln. It is speculated that such functional changes of proteins go hand in hand with changes in their mechanical properties. Here, we apply single-molecule dynamic force spectroscopy to investigate how the Glu to Gln mutations change interactions, reaction pathways, and the energy barriers of the structural regions of WT BR. The altered heights and positions of individual energy barriers unravel the changes in the mechanical and the unfolding kinetic properties of the secondary structures of WT BR. These changes in the mechanical unfolding energy landscape cause the proton pump to choose unfolding pathways differently. We suggest that, in a similar manner, the changed mechanical properties of mutated BR alter the functional energy landscape favoring different reaction pathways in the light-induced proton pumping mechanism.     

Mechanical unfolding of TNfn3: the unfolding pathway of a fnIII domain probed by protein engineering, AFM and MD simulation

Protein engineering Phi-value analysis combined with single molecule atomic force microscopy (AFM) was used to probe the molecular basis for the mechanical stability of TNfn3, the third fibronectin type III domain from human tenascin. This approach has been adopted previously to solve the forced unfolding pathway of a titin immunoglobulin domain, TI I27. TNfn3 and TI I27 are members of different protein superfamilies and have no sequence identity but they have the same beta-sandwich structure consisting of two antiparallel beta-sheets. TNfn3, however, unfolds at significantly lower forces than TI I27. We compare the response of these proteins to mechanical force. Mutational analysis shows that, as is the case with TI I27, TNfn3 unfolds via a force-stabilised intermediate. The key event in forced unfolding in TI I27 is largely the breaking of hydrogen bonds and hydrophobic interactions between the A' and G-strands. The mechanical Phi-value analysis and molecular dynamics simulations reported here reveal that significantly more of the TNfn3 molecule contributes to its resistance to force. Both AFM experimental data and molecular dynamics simulations suggest that the rate-limiting step of TNfn3 forced unfolding reflects a transition from the extended early intermediate to an aligned intermediate state. As well as losses of interactions of the A and G-strands and associated loops there are rearrangements throughout the core. As was the case for TI I27, the forced unfolding pathway of TNfn3 is different from that observed in denaturant studies in the absence of force.     

Molecular dynamics simulations of synthetic peptide folding

Because the time scale of protein folding is much greater than that of the widely used simulations of native structures, a detailed report of molecular dynamics simulations of folding has not been available. In this study, we Included the average solvent effect in the potential functions to simplify the calculation of the solvent effect and carried out long molecular dynamics simulations of the alanine-based synthetic peptides at 274 K. From either an extended or a randomly generated conformation, the simulations approached a helix-coil equilibrium in about 3 ns. The multiple minima problem did not prevent helix folding. The calculated helical ratio of Ac-AAQAAAAQAAAAQAAY-NH₂ was 47%, in good agreement with the circular dichroism measurement (about 50%). A helical segment with frayed ends was the most stable conformation, but the hydrophobic interaction favored the compact, distorted helix-turn-helix conformations. The transition between the two types of conformations occurred in a much larger time scale than helix propagation. The transient hydrogen bonds between the glutamine side chain and the backbone carbonyl group could reduce the free energy barrier of helix folding and unfolding. The substitution of a single alanine residue in the middle of the peptide with valine or glycine decreased the average helical ratio significantly, in agreement with experimental observations. © 1996 Wiley-Liss, Inc.     

Mechanical Unfolding of Spectrin Repeats Induces Water-Molecule Ordering

Mechanical processes are involved at many stages of the development of living cells, and often external forces applied to a biomolecule result in its unfolding. Although our knowledge of the unfolding mechanisms and the magnitude of the forces involved has evolved, the role that water molecules play in the mechanical unfolding of biomolecules has not yet been fully elucidated. To this end, we investigated with steered molecular dynamics simulations the mechanical unfolding of dystrophin’s spectrin repeat 1 and related the changes in the protein’s structure to the ordering of the surrounding water molecules. Our results indicate that upon mechanically induced unfolding of the protein, the solvent molecules become more ordered and increase their average number of hydrogen bonds. In addition, the unfolded structures originating from mechanical pulling expose an increasing amount of the hydrophobic residues to the solvent molecules, and the uncoiled regions adapt a convex surface with a small radius of curvature. As a result, the solvent molecules reorganize around the protein’s small protrusions in structurally ordered waters that are characteristic of the so-called “small-molecule regime,” which allows water to maintain a high hydrogen bond count at the expense of an increased structural order. We also determined that the response of water to structural changes in the protein is localized to the specific regions of the protein that undergo unfolding. These results indicate that water plays an important role in the mechanically induced unfolding of biomolecules. Our findings may prove relevant to the ever-growing interest in understanding macromolecular crowding in living cells and their effects on protein folding, and suggest that the hydration layer may be exploited as a means for short-range allosteric communication.     

Complex folding pathways in a simple beta-hairpin

The determination of the folding mechanisms of proteins is critical to understand the topological change that can propagate Alzheimer and Creutzfeld-Jakobs diseases, among others. The computational community has paid considerable attention to this problem; however, the associated time scale, typically on the order of milliseconds or more, represents a formidable challenge. Ab initio protein folding from long molecular dynamics simulations or ensemble dynamics is not feasible with ordinary computing facilities and new techniques must be introduced. Here we present a detailed study of the folding of a 16-residue beta-hairpin, described by a generic energy model and using the activation-relaxation technique. From a total of 90 trajectories at 300 K, three folding pathways emerge. All involve a simultaneous optimization of the complete hydrophobic and hydrogen bonding interactions. The first two pathways follow closely those observed by previous theoretical studies (folding starting at the turn or by interactions between the termini). The third pathway, never observed by previous all-atom folding, unfolding, and equilibrium simulations, can be described as a reptation move of one strand of the beta-sheet with respect to the other. This reptation move indicates that non-native interactions can play a dominant role in the folding of secondary structures. Furthermore, such a mechanism mediated by non-native hydrogen bonds is not available for study by unfolding and Gō model simulations. The exact folding path followed by a given beta-hairpin is likely to be influenced by its sequence and the solvent conditions. Taken together, these results point to a more complex folding picture than expected for a simple beta-hairpin.     

Free energy landscape of protein folding in water: explicit vs. implicit solvent

The Generalized Born (GB) continuum solvent model is arguably the most widely used implicit solvent model in protein folding and protein structure prediction simulations; however, it still remains an open question on how well the model behaves in these large-scale simulations. The current study uses the beta-hairpin from C-terminus of protein G as an example to explore the folding free energy landscape with various GB models, and the results are compared to the explicit solvent simulations and experiments. All free energy landscapes are obtained from extensive conformation space sampling with a highly parallel replica exchange method. Because solvation model parameters are strongly coupled with force fields, five different force field/solvation model combinations are examined and compared in this study, namely the explicit solvent model: OPLSAA/SPC model, and the implicit solvent models: OPLSAA/SGB (Surface GB), AMBER94/GBSA (GB with Solvent Accessible Surface Area), AMBER96/GBSA, and AMBER99/GBSA. Surprisingly, we find that the free energy landscapes from implicit solvent models are quite different from that of the explicit solvent model. Except for AMBER96/GBSA, all other implicit solvent models find the lowest free energy state not the native state. All implicit solvent models show erroneous salt-bridge effects between charged residues, particularly in OPLSAA/SGB model, where the overly strong salt-bridge effect results in an overweighting of a non-native structure with one hydrophobic residue F52 expelled from the hydrophobic core in order to make better salt bridges. On the other hand, both AMBER94/GBSA and AMBER99/GBSA models turn the beta-hairpin in to an alpha-helix, and the alpha-helical content is much higher than the previously reported alpha-helices in an explicit solvent simulation with AMBER94 (AMBER94/TIP3P). Only AMBER96/GBSA shows a reasonable free energy landscape with the lowest free energy structure the native one despite an erroneous salt-bridge between D47 and K50. Detailed results on free energy contour maps, lowest free energy structures, distribution of native contacts, alpha-helical content during the folding process, NOE comparison with NMR, and temperature dependences are reported and discussed for all five models.     

LpxA: A natural nanotube

UDP‐N‐acetylglucosamine 3‐O‐acyltransferase is a protein with a left‐handed parallel β‐helix, which is a natural nanotube. They are associated with unusual high stability. To identify the reason behind the structural stability of β‐helical nanotubular structure, we have performed a total of 4 μs molecular dynamics simulations of the protein in implicit solvent at four different temperatures and monitored the unfolding pathway. The correlation in movement between different regions of the nanotubular structure has been identified from the dynamical cross‐correlation map and contribution of some specific residues towards unfolding transition has been identified by principal component analysis. Difference in stability of the three loop regions has also been characterized. Construction of the unfolding conformational energy landscape identifies the probable intermediates that can appear in the unfolding pathway of the protein. © 2010 Wiley Periodicals, Inc. Biopolymers 93: 845–853, 2010.     

Microscopic stability of cold shock protein A examined by NMR native state hydrogen exchange as a function of urea and trimethylamine N-oxide

Native state hydrogen exchange of cold shock protein A (CspA) has been characterized as a function of the denaturant urea and of the stabilizing agent trimethylamine N-oxide (TMAO). The structure of CspA has five strands of beta-sheet. Strands beta1-beta4 have strongly protected amide protons that, based on experiments as a function of urea, exchange through a simple all-or-none global unfolding mechanism. By contrast, the protection of amide protons from strand beta5 is too weak to measure in water. Strand beta5 is hydrogen bonded to strands beta3 and beta4, both of which afford strong protection from solvent exchange. Gaussian network model (GNM) simulations, which assume that the degree of protection depends on tertiary contact density in the native structure, accurately predict the strong protection observed in strands beta1-beta4 but fail to account for the weak protection in strand beta5. The most conspicuous feature of strand beta5 is its low sequence hydrophobicity. In the presence of TMAO, there is an increase in the protection of strands beta1-beta4, and protection extends to amide protons in more hydrophilic segments of the protein, including strand beta5 and the loops connecting the beta-strands. TMAO stabilizes proteins by raising the free energy of the denatured state, due to highly unfavorable interactions between TMAO and the exposed peptide backbone. As such, the stabilizing effects of TMAO are expected to be relatively independent of sequence hydrophobicity. The present results suggest that the magnitude of solvent exchange protection depends more on solvent accessibility in the ensemble of exchange susceptible conformations than on the strength of hydrogen-bonding interactions in the native structure.