Simulated refolding of stretched titin immunoglobulin domains

Contribution of Hydrophobic Interactions to Protein Mechanical Stability

The role of hydrophobic and polar interactions in providing thermodynamic stability to folded proteins has been intensively studied, but the relative contribution of these interactions to the mechanical stability is less explored. We used steered molecular dynamics simulations with constant-velocity pulling to generate force-extension curves of selected protein domains and monitor hydrophobic surface unravelling upon extension. Hydrophobic contribution was found to vary between one fifth and one third of the total force while the rest of the contribution is attributed primarily to hydrogen bonds. Moreover, hydrophobic force peaks were shifted towards larger protein extensions with respect to the force peaks attributed to hydrogen bonds. The higher importance of hydrogen bonds compared to hydrophobic interactions in providing mechanical resistance is in contrast with the relative importance of the hydrophobic interactions in providing thermodynamic stability of proteins. The different contributions of these interactions to the mechanical stability are explained by the steeper free energy dependence of hydrogen bonds compared to hydrophobic interactions on the relative positions of interacting atoms. Comparative analyses for several protein domains revealed that the variation of hydrophobic forces is modest, while the contribution of hydrogen bonds to the force peaks becomes increasingly important for mechanically resistant protein domains.

Prediction of the initial folding sites and the entire folding processes for Ig-like beta-sandwich proteins

Describing the whole story of protein folding is currently the main enigmatic problem in molecular bioinformatics study. Protein folding mechanisms have been intensively investigated with experimental as well as simulation techniques. Since a protein folds into its specific 3D structure from a unique amino acid sequence, it is interesting to extract as much information as possible from the amino acid sequence of a protein. Analyses based on inter-residue average distance statistics and a coarse-grained Gō-model simulation were conducted on Ig and FN3 domains of a titin protein to decode the folding mechanisms from their sequence data and native structure data, respectively. The central region of all domains was predicted to be an initial folding unit, that is, stable in an early state of folding. This common feature coincides well with the experimental results and underscores the significance of the β-sandwich proteins' common structure, namely, the key strands for folding and the Greek-key motif, which is located in the central region. We confirmed that our sequence-based techniques were able to predict the initial folding event just next to the denatured state and that a 3D-based Gō-model simulation can be used to investigate the whole process of protein folding.

Monitoring Unfolding of Titin I27 Single and Bi Domain with High-Pressure NMR Spectroscopy

A complete description of the pathways and mechanisms of protein folding requires a detailed structural and energetic characterization of the folding energy landscape. Simulations, when corroborated by experimental data yielding global information on the folding process, can provide this level of insight. Molecular dynamics (MD) has often been combined with force spectroscopy experiments to decipher the unfolding mechanism of titin immunoglobulin-like single or multidomain, the giant multimodular protein from sarcomeres, yielding information on the sequential events during titin unfolding under stretching. Here, we used high-pressure NMR to monitor the unfolding of titin I27 Ig-like single domain and tandem. Because this method brings residue-specific information on the folding process, it can provide quasiatomic details on this process without the help of MD simulations. Globally, the results of our high-pressure analysis are in agreement with previous results obtained by the combination of experimental measurements and MD simulation and/or protein engineering, although the intermediate folding state caused by the early detachment of the AB β-sheet, often reported in previous works based on MD or force spectroscopy, cannot be detected. On the other hand, the A'G parallel β-sheet of the β-sandwich has been confirmed as the Achilles heel of the three-dimensional scaffold: its disruption yields complete unfolding with very similar characteristics (free energy, unfolding volume, kinetics rate constants) for the two constructs.

Prediction of folding mechanisms for Ig-like beta sandwich proteins based on inter-residue average distance statistics methods

To understand the folding mechanism of a protein is one of the goals in bioinformatics study. Nowadays, it is enigmatic and difficult to extract folding information from amino acid sequence using standard bioinformatics techniques or even experimental protocols which can be time consuming. To overcome these problems, we aim to extract the initial folding unit for titin protein (Ig and fnIII domains) by means of inter-residue average distance statistics, Average Distance Map (ADM) and contact frequency analysis (F-value). TI I27 and TNfn3 domains are used to represent the Ig-domain and fnIII-domain, respectively. Beta-strands 2, 3, 5, and 6 are significant for the initial folding processes of TI I27. The central strands of TNfn3 were predicted as a primary folding segment. Known 3D structure and unknown 3D structure domains were investigated by structure or non-structure based multiple sequence alignment, respectively, to learn the conserved hydrophobic residues and predicted compact region relevant to evolution. Our results show good correspondence to experimental data, phi-value and protection factor from H-D exchange experiments. The significance of conserved hydrophobic residues near F-value peaks for structural stability using hydrophobic packing is confirmed. Our prediction methods once again could extract a folding mechanism only knowing the amino acid sequence.

Mutation of conserved histidines alters tertiary structure and nanomechanics of consensus ankyrin repeats

The conserved TPLH tetrapeptide motif of ankyrin repeats (ARs) plays an important role in stabilizing AR proteins, and histidine (TPLH)-to-arginine (TPLR) mutations in this motif have been associated with a hereditary human anemia, spherocytosis. Here, we used a combination of atomic force microscopy-based single-molecule force spectroscopy and molecular dynamics simulations to examine the mechanical effects of His → Arg substitutions in TPLH motifs in a model AR protein, NI6C. Our molecular dynamics results show that the mutant protein is less mechanically stable than the WT protein. Our atomic force microscopy results indicate that the mechanical energy input necessary to fully unfold the mutant protein is only half of that necessary to unfold the WT protein (53 versus 106 kcal/mol). In addition, the ability of the mutant to generate refolding forces is also reduced. Moreover, the mutant protein subjected to cyclic stretch-relax measurements displays mechanical fatigue, which is absent in the WT protein. Taken together, these results indicate that the His → Arg substitutions in TPLH motifs compromise mechanical properties of ARs and suggest that the origin of hereditary spherocytosis may be related to mechanical failure of ARs.

Mechanical anisotropy of ankyrin repeats

Red blood cells are frequently deformed and their cytoskeletal proteins such as spectrin and ankyrin-R are repeatedly subjected to mechanical forces. While the mechanics of spectrin was thoroughly investigated in vitro and in vivo, little is known about the mechanical behavior of ankyrin-R. In this study, we combine coarse-grained steered molecular dynamics simulations and atomic force spectroscopy to examine the mechanical response of ankyrin repeats (ARs) in a model synthetic AR protein NI6C, and in the D34 fragment of native ankyrin-R when these proteins are subjected to various stretching geometry conditions. Our steered molecular dynamics results, supported by AFM measurements, reveal an unusual mechanical anisotropy of ARs: their mechanical stability is greater when their unfolding is forced to propagate from the N-terminus toward the C-terminus (repeats unfold at ~60 pN), as compared to the unfolding in the opposite direction (unfolding force ∼ 30 pN). This anisotropy is also reflected in the complex refolding behavior of ARs. The origin of this unfolding and refolding anisotropy is in the various numbers of native contacts that are broken and formed at the interfaces between neighboring repeats depending on the unfolding/refolding propagation directions. Finally, we discuss how these complex mechanical properties of ARs in D34 may affect its behavior in vivo.

An improved strategy for generating forces in steered molecular dynamics: the mechanical unfolding of titin, e2lip3 and ubiquitin

One of the applications of Molecular Dynamics (MD) simulations is to explore the energetic barriers to mechanical unfolding of proteins such as occurs in response to the mechanical pulling of single molecules in Atomic Force Microscopy (AFM) experiments. Although Steered Molecular Dynamics simulations have provided microscopic details of the unfolding process during the pulling, the simulated forces required for unfolding are typically far in excess of the measured values. To rectify this, we have developed the Pulsed Unconstrained Fluctuating Forces (PUFF) method, which induces constant-momentum motions by applying forces directly to the instantaneous velocity of selected atoms in a protein system. The driving forces are applied in pulses, which allows the system to relax between pulses, resulting in more accurate unfolding force estimations than in previous methods. In the cases of titin, ubiquitin and e2lip3, the PUFF trajectories produce force fluctuations that agree quantitatively with AFM experiments. Another useful property of PUFF is that simulations get trapped if the target momentum is too low, simplifying the discovery and analysis of unfolding intermediates.

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 is [corrected] under severe conformational constraints [corrected] dictated by the one-dimensional geometry of the tunnel. [corrected] 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.

Equilibrium sampling for biomolecules under mechanical tension

In the studies of force-induced conformational transitions of biomolecules, the large timescale difference from experiments presents the challenge of obtaining convergent sampling for molecular dynamics simulations. To circumvent this fundamental problem, an approach combining the replica-exchange method and umbrella sampling (REM-US) was developed to simulate mechanical stretching of biomolecules under equilibrium conditions. Equilibrium properties of conformational transitions can be obtained directly from simulations without further assumptions. To test the performance, we carried out REM-US simulations of atomic force microscope (AFM) stretching and relaxing measurements on the polysaccharide pustulan, a (1-->6)-beta-D-glucan, which undergoes well-characterized rotameric transitions in the backbone bonds. With significantly enhanced sampling convergence and efficiency, the REM-US approach closely reproduced the equilibrium force-extension curves measured in AFM experiments. Consistent with the reversibility in the AFM measurements, the new approach generated identical force-extension curves in both stretching and relaxing simulations-an outcome not reported in previous studies, proving that equilibrium conditions were achieved in the simulations. REM-US may provide a robust approach to modeling of mechanical stretching on polysaccharides and even nucleic acids.

Interplay of mechanical and binding properties of Fibronectin type I

Fibronectins (FNs) are a major component of the extracellular matrix (ECM), and provide important binding sites for a variety of ligands outside and on the surface of the cell. Similar to other ECM proteins, FNs are consistently subject to mechanical stress in the ECM. Therefore, it is important to study their structure and binding properties under mechanical stress and understand how their binding and mechanical properties might affect each other. Although certain FN modules have been extensively investigated, no simulation studies have been reported for the FN type I (Fn1) domains, despite their prominent role in binding of various protein modules to FN polymers in the ECM. Using equilibrium and steered molecular dynamics simulations, we have studied mechanical properties of Fn1 modules in the presence or the absence of a specific FN-binding peptide (FnBP). We have also investigated how the binding of the FnBP peptide to Fn1 might be affected by tensile force. Despite the presence of disulfide bonds within individual Fn1 modules that are presumed to prevent their extension, it is found that significant internal structural changes within individual modules are induced by the forces applied in our simulations. These internal structural changes result in significant variations in the accessibility of different residues of the Fn1 modules, which affect their exposure, and, thus, the binding properties of the Fn1 modules. Binding of the FnBP appears to reduce the flexibility of the linker region connecting individual Fn1 modules (exhibited in the form of reduced fluctuation and motion of the linker region), both with regard to bending and stretching motions, and hence stabilizes the inter-domain configuration under force. Under large tensile forces, the FnBP peptide unbinds from Fn1. The results suggest that Fn1 modules in FN polymers do contribute to the overall extension caused by force-induced stretching of the polymer in the ECM, and that binding properties of Fn1 modules can be affected by mechanically induced internal protein conformational changes in spite of the presence of disulfide bonds which were presumed to completely abolish the capacity of Fn1 modules to undergo extension in response to external forces.

Discovery through the computational microscope

All-atom molecular dynamics simulations have become increasingly popular as a tool to investigate protein function and dynamics. However, researchers are concerned about the short time scales covered by simulations, the apparent impossibility to model large and integral biomolecular systems, and the actual predictive power of the molecular dynamics methodology. Here we review simulations that were in the past both hotly disputed and considered key successes, namely of proteins with mainly mechanical functions (titin, fibrinogen, ankyrin, and cadherin). The simulation work covered shows how state-of-the-art modeling alleviates some of the prior concerns and how unrefuted discoveries are made through the "computational microscope."

Mechanochemistry: one bond at a time

Single-molecule force-clamp spectroscopy offers a novel platform for mechanically denaturing proteins by applying a constant force to a polyprotein. A powerful emerging application of the technique is that, by introducing a disulfide bond in each protein module, the chemical kinetics of disulfide bond cleavage under different stretching forces can be probed at the single-bond level. Even at forces much lower than that which can rupture the chemical bond, the breaking of the S-S bond at the presence of various chemical reducing agents is significantly accelerated. Our previous work demonstrated that the rate of thiol/disulfide exchange reaction is force-dependent and well-described by an Arrhenius term of the form r = A(exp((FΔx(r) - E(a))/k(B)T)[nucleophile]). From Arrhenius fits to the force dependency of the reduction rate, we measured the bond elongation parameter, Δx(r), along the reaction coordinate to the transition state of the S(N)2 reaction cleaved by different nucleophiles and enzymes, never before observed by any other technique. For S-S cleavage by various reducing agents, obtaining the Δx(r) value can help depicting the energy landscapes and elucidating the mechanisms of the reactions at the single-molecule level. Small nucleophiles, such as 1,4-dl-dithiothreitol (DTT), tris(2-carboxyethyl)phosphine (TCEP), and l-cysteine, react with the S-S bond with monotonically increasing rates under the applied force, while thioredoxin enzymes exhibit both stretching-favored and -resistant reaction-rate regimes. These measurements demonstrate the power of the single-molecule force-clamp spectroscopy approach in providing unprecedented access to chemical reactions.

Tensile mechanics of alanine-based helical polypeptide: force spectroscopy versus computer simulations

In nature, an alpha-helix is commonly used to build thermodynamically stable and mechanically rigid protein conformations. In view of growing interest in the mechanical rigidity of proteins, we measured the tensile profile of an alanine-based alpha-helical polypeptide on an atomic-force microscope to investigate the basic mechanics of helix extension with minimal interference from side-chain interactions. The peptide was extended to its maximum contour length with much less force than in reported cases of poly-L-Glu or poly-L-Lys, indicating that chain stiffness strongly depended on the physicochemical properties of side chains, such as their bulkiness. The low tensile-force extension originated presumably in locally unfolded parts because of spontaneous structural fluctuations. In 50% trifluoroethanol, the well-known helix-promoting agent, the rigidity of the sample polypeptide was markedly increased. Computer simulations of the peptide-stretching process showed that a majority of constituent residues underwent a transition from an alpha-helical to an extended conformation by overcoming an energy barrier around psi approximately 0 degrees on the Ramachandran plot. The observed lability of an isolated helix signified the biological importance of the lateral bundling of helices to maintain a rigid protein structure.

Analysis of the unfolding process of green fluorescent protein by molecular dynamics simulation

Molecular dynamics simulation of the enforced stretching of circularly permuted green fluorescent protein (cpGFP) was performed to observe the detailed process of unfolding of beta-sheets in cpGFP and to clarify the structural change arising from the force. The simulation using the generalized Born method with original force field parameters enabled us to observe the unfolding process of the entire region of the protein and to clarify atom motion of the individual domain during the stretching. The force required for the stretching of cpGFP was estimated from the differential of the computed potential energy. A prominent rise in force appeared three times during the stretching. The amplitude and the position of these three peaks were consistent with the observation in atomic force microscopy (AFM) experiments. Further, the movements of atoms involved in each peak were shown to be closely related to the dissociation of hydrogen bonds. Additional simulations for the unfolding process of titin and spectrin also gave satisfactory interpretation of the results of previous AFM experiments. The difference in the enforced stretching process between cpGFP and wild-type GFP was further discussed through the MD simulation.

Secondary and tertiary structure elasticity of titin Z1Z2 and a titin chain model

The giant protein titin, which is responsible for passive elasticity in muscle fibers, is built from approximately 300 regular immunoglobulin-like (Ig) domains and FN-III repeats. While the soft elasticity derived from its entropic regions, as well as the stiff mechanical resistance derived from the unfolding of the secondary structure elements of Ig- and FN-III domains have been studied extensively, less is known about the mechanical elasticity stemming from the orientation of neighboring domains relative to each other. Here we address the dynamics and energetics of interdomain arrangement of two adjacent Ig-domains of titin, Z1, and Z2, using molecular dynamics (MD) simulations. The simulations reveal conformational flexibility, due to the domain-domain geometry, that lends an intermediate force elasticity to titin. We employ adaptive biasing force MD simulations to calculate the energy required to bend the Z1Z2 tandem open to identify energetically feasible interdomain arrangements of the Z1 and Z2 domains. The finding is cast into a stochastic model for Z1Z2 interdomain elasticity that is generalized to a multiple domain chain replicating many Z1Z2-like units and representing a long titin segment. The elastic properties of this chain suggest that titin derives so-called tertiary structure elasticity from bending and twisting of its domains. Finally, we employ steered molecular dynamics simulations to stretch individual Z1 and Z2 domains and characterize the so-called secondary structure elasticity of the two domains. Our study suggests that titin's overall elastic response at weak force stems from a soft entropic spring behavior (not described here), from tertiary structure elasticity with an elastic spring constant of approximately 0.001-1 pN/A and, at strong forces, from secondary structure elasticity.

Poly-Ig tandems from I-band titin share extended domain arrangements irrespective of the distinct features of their modular constituents

The cellular function of the giant protein titin in striated muscle is a major focus of scientific attention. Particularly, its role in passive mechanics has been extensively investigated. In strong contrast, the structural details of this filament are very poorly understood. To date, only a handful of atomic models from single domain components have become available and data on poly-constructs are limited to scarce SAXS analyses. In this study, we examine the molecular parameters of poly-Ig tandems from I-band titin relevant to muscle elasticity. We revisit conservation patterns in domain and linker sequences of I-band modules and interpret these in the light of available atomic structures of Ig domains from muscle proteins. The emphasis is placed on features expected to affect inter-domain arrangements. We examine the overall conformation of a 6Ig fragment, I65-I70, from the skeletal I-band of soleus titin using SAXS and electron microscopy approaches. The possible effect of highly conserved glutamate groups at the linkers as well as the ionic strength of the medium on the overall molecular parameters of this sample is investigated. Our findings indicate that poly-Ig tandems from I-band titin tend to adopt extended arrangements with low or moderate intrinsic flexibility, independently of the specific features of linkers or component Ig domains across constitutively- and differentially-expressed tandems. Linkers do not appear to operate as free hinges so that lateral association of Ig domains must occur infrequently in samples in solution, even that inter-domain sequences of 4-5 residues length would well accommodate such geometry. It can be expected that this principle is generally applicable to all Ig-tandems from I-band titin.

Molecular mechanisms of cellular mechanics

Mechanical forces play an essential role in cellular processes as input, output, and signals. Various protein complexes in the cell are designed to handle, transform and use such forces. For instance, proteins of muscle and the extracellular matrix can withstand considerable stretching forces, hearing-related and mechanosensory proteins can transform weak mechanical stimuli into electrical signals, and regulatory proteins are suited to forcing DNA into loops to control gene expression. Here we review the structure-function relationship of four protein complexes with well defined and representative mechanical functions. The first example is titin, a protein that confers passive elasticity on muscle. The second system is the elastic extracellular matrix protein, fibronectin, and its cellular receptor integrin. The third protein system is the transduction apparatus in hearing and other mechanical senses, likely containing cadherin and ankyrin repeats. The last system is the lac repressor protein, which regulates gene expression by looping DNA. This review focuses on atomic level descriptions of the physical mechanisms underlying the various mechanical functions of the stated proteins.

Stress transmission in the lung: pathways from organ to molecule

Gas exchange, the primary function of the lung, can come about only with the application of physical forces on the macroscale and their transmission to the scale of small airway, small blood vessel, and alveolus, where they serve to distend and stabilize structures that would otherwise collapse. The pathway for force transmission then continues down to the level of cell, nucleus, and molecule; moreover, to lesser or greater degrees most cell types that are resident in the lung have the ability to generate contractile forces. At these smallest scales, physical forces serve to distend the cytoskeleton, drive cytoskeletal remodeling, expose cryptic binding domains, and ultimately modulate reaction rates and gene expression. Importantly, evidence has now accumulated suggesting that multiscale phenomena span these scales and govern integrative lung behavior.

Mechanism of titin unfolding by force: insight from quasi-equilibrium molecular dynamics calculations

We have studied the unfolding by force of one of the immunoglobulin domains of the muscle protein titin using molecular dynamics simulations at 300 K. Previous studies, done at constant pulling rates, showed that under the effect of the force two strands connected to each other by six backbone H-bonds are pulled apart. No details about the mechanism of H-bond breaking were provided. Our simulation protocol "pull and wait" was designed to correspond to very slow pulling, more similar to the rates used in experiments than are the protocols used in previous computational studies. Under these conditions interstrand backbone H-bonds are not "ripped apart" by the application of the force. Instead, small elongations produced by the force weaken specific backbone H-bonds with respect to water-backbone H-bonds. These weakened bonds allow a single water molecule to make H-bonds to the CO and the NH of the same backbone H-bond while they are still bound to each other. The backbone H-bond then breaks (distance > 3.6 A), but its donor and acceptor atoms remain bound to the same water molecule. Further separation of the chains takes place when a second water molecule makes an H-bond with either the protein backbone donor or acceptor atom. Thus, the force does not directly break the main chain H-bonds: it destabilizes them in such a way that they are replaced by H-bonds to water. With this mechanism, the force necessary to break all the H-bonds required to separate the two strands will be strongly dependent on the pulling speed. Further simulations carried out at low forces but long waiting times (> or = 500 ps, < or = 10 ns) show that, given enough time, even a very small pulling force (< 400 pN) is sufficient to destabilize the interstrand H-bonds and allow them to be replaced by H-bonds to two water molecules. As expected, increasing the temperature to 350 K allows the interstrand H-bonds to break at lower forces than those required at 300 K.

Simulations of multi-directional forced unfolding of titin I27

Mechanical resistance of a protein under external force is known to depend on the amino acid sequence, unfolding rate constant, topology and the direction of force applied. To assess the affect of force direction on mechanical resistance, molecular dynamics (MD) simulations of the partial unfolding of titin I27 have been carried out by applying a ramp of force between the N-terminus and the alpha-carbon of each amino acid, respectively. The results arbitrarily place the amino acids in a hierarchy in terms of the time at which an unfolding intermediate is formed. The onset of unfolding is indeed affected by force direction; directions that give maximum leverage (for the A strand to detach) unfold to the intermediate quicker than directions that give least leverage. Moreover, the change in the time taken to reach the intermediate, hence the change in mechanical resistance, can be attributed to beta-strand topology. The simulations indicate that experimentally multi-directional forced unfolding could be used to reveal and study strand topology, and suggests that direction of applied force, topology and mechanical resistance are all closely related.

Force spectroscopy of single multidomain biopolymers: a master equation approach

Experiments using atomic force microscopy for unfolding single multidomain biopolymers cover a broad range of time scales from equilibrium to non-equilibrium. A master equation approach allows to identify and treat coherently three dynamical regimes for increasing linear ramp velocity: i) an equilibrium regime, ii) a transient regime where refolding events still occur, and iii) a saw-tooth regime without any refolding events. For each regime, analytical approximations are derived and compared to numerically investigated examples. We analyze in the framework of this model also a periodic experimental protocol instead of a linear ramp. In this case, a major simplification arises if the dynamics can be restricted to an effectively two-dimensional subspace. For transitions with an intermediate meta-stable state, like Immunoglobulin27, a refined model allows to extract previously unknown molecular parameters related to this meta-stable state.

Origin of mechanical strength of bovine carbonic anhydrase studied by molecular dynamics simulation

The forced unfolding process of bovine carbonic anhydrase II (BCA II) was examined at the atomic level by the molecular dynamics (MD) simulation. By force spectroscopy, experimentally obtained force-extension curves (F-E curves) showed a prominent force peak after 50 nm extension. F-E curves obtained from our simulation had three force peaks appearing after extensions of 10-17 nm, 40 nm, and 53 nm, each signifying a brittle fracture of a specific local structure. Upon undergoing the final fracture at 53 nm of extension, the entire molecule became a single flexible chain and was further extended to its full theoretical length, almost as a random coil. This feature of the 53-nm peak strongly suggested its close correspondence to the experimentally observed force peak at approximately 60-nm extension. The 53-nm peak in the molecular dynamics simulation corresponded to the unfolding process of the beta-sheeted core that includes zinc-coordinating histidine residues. These results suggest that the structural change occurring at 50-60 nm in atomic force microscopy experiments corresponded to the destruction of the zinc coordination site.

Force-Clamp Spectroscopy Monitors the Folding Trajectory of a Single Protein

We used force-clamp atomic force microscopy to measure the end-to-end length of the small protein ubiquitin during its folding reaction at the single-molecule level. Ubiquitin was first unfolded and extended at a high force, then the stretching force was quenched and protein folding was observed. The folding trajectories were continuous and marked by several distinct stages. The time taken to fold was dependent on the contour length of the unfolded protein and the stretching force applied during folding. The folding collapse was marked by large fluctuations in the end-to-end length of the protein, but these fluctuations vanished upon the final folding contraction. These direct observations of the complete folding trajectory of a protein provide a benchmark to determine the physical basis of the folding reaction.

The mechanical stability of ubiquitin is linkage dependent

Ubiquitin chains are formed through the action of a set of enzymes that covalently link ubiquitin either through peptide bonds or through isopeptide bonds between their C terminus and any of four lysine residues. These naturally occurring polyproteins allow one to study the mechanical stability of a protein, when force is applied through different linkages. Here we used single-molecule force spectroscopy techniques to examine the mechanical stability of N-C-linked and Lys48-C-linked ubiquitin chains. We combined these experiments with steered molecular dynamics (SMD) simulations and found that the mechanical stability and unfolding pathway of ubiquitin strongly depend on the linkage through which the mechanical force is applied to the protein. Hence, a protein that is otherwise very stable may be easily unfolded by a relatively weak mechanical force applied through the right linkage. This may be a widespread mechanism in biological systems.

Unfolding of titin domains studied by molecular dynamics simulations

Titin, a approximately 1 micron long protein found in striated muscle myofibrils, possesses unique elastic properties. The extensible behavior of titin has been demonstrated in atomic force microscopy and optical tweezer experiments to involve the reversible unfolding of individual immunoglobulin-like (Ig) domains. We have used steered molecular dynamics (SMD), a novel computer simulation method, to investigate the mechanical response of single titin Ig domains upon stress. Simulations of stretching Ig domains I1 and I27 have been performed in a solvent of explicit water molecules. The SMD approach provides a detailed structural and dynamic description of how Ig domains react to external forces. Validation of SMD results includes both qualitative and quantitative agreement with AFM recordings. Furthermore, combining SMD with single molecule experimental data leads to a comprehensive understanding of Ig domains' mechanical properties. A set of backbone hydrogen bonds that link the domains' terminal beta-strands play a key role in the mechanical resistance to external forces. Slight differences in architecture permit a mechanical unfolding intermediate for I27, but not for I1. Refolding simulations of I27 demonstrate a locking mechanism.

Steered molecular dynamics studies of titin I1 domain unfolding

The cardiac muscle protein titin, responsible for developing passive elasticity and extensibility of muscle, possesses about 40 immunoglobulin-like (Ig) domains in its I-band region. Atomic force microscopy (AFM) and steered molecular dynamics (SMD) have been successfully combined to investigate the reversible unfolding of individual Ig domains. However, previous SMD studies of titin I-band modules have been restricted to I27, the only structurally known Ig domain from the distal region of the titin I-band. In this paper we report SMD simulations unfolding I1, the first structurally available Ig domain from the proximal region of the titin I-band. The simulations are carried out with a view toward upcoming atomic force microscopy experiments. Both constant velocity and constant force stretching have been employed to model mechanical unfolding of oxidized I1, which has a disulfide bond bridging beta-strands C and E, as well as reduced I1, in which the disulfide bridge is absent. The simulations reveal that I1 is protected against external stress mainly through six interstrand hydrogen bonds between its A and B beta-strands. The disulfide bond enhances the mechanical stability of oxidized I1 domains by restricting the rupture of backbone hydrogen bonds between the A'- and G-strands. The disulfide bond also limits the maximum extension of I1 to approximately 220 A. Comparison of the unfolding pathways of I1 and I27 are provided and implications to AFM experiments are discussed.

Identifying unfolding intermediates of FN-III(10) by steered molecular dynamics

Experimental studies have indicated that FN-III modules undergo reversible unfolding as a mechanism of elasticity. The unfolding of FN-III modules, including the cell-binding FN-III(10) module, has further been suggested to be functionally relevant by exposing buried cryptic sites or modulating cell binding. While steered molecular dynamics (SMD) simulations have provided one tool to investigate this process, computational requirements so far have limited detailed analysis to the early stages of unfolding. Here, we use an extended periodic box to probe the unfolding of FN-III(10) for extensions longer than 60A. Up to three plateaus, corresponding to three metastable intermediates, were observed in the extension-time profile from SMD stretching of FN-III(10). The first and second plateaus correspond to a twisted and an aligned state prior to unraveling FN-III(10) beta-strands. The third plateau, at an extension of approximately 100A, follows unraveling of FN-III(10) A and B-strands and precedes breaking of inter-strand hydrogen bonds between F and G-strands. The simulations revealed three forced unfolding pathways of FN-III(10), one of which is preferentially selected under physiological conditions. Implications for fibronectin fibrillogenesis are discussed.