Mechanically unfolding the small, topologically simple protein L

Mechanical unbinding of abeta peptides from amyloid fibrils

Using the experimental structures of Abeta amyloid fibrils and all-atom molecular dynamics, we study the force-induced unbinding of Abeta peptides from the fibril. We show that the mechanical dissociation of Abeta peptides is highly anisotropic and proceeds via different pathways when force is applied in parallel or perpendicular direction with respect to the fibril axis. The threshold forces associated with lateral unbinding of Abeta peptides exceed those observed during the mechanical dissociation along the fibril axis. In addition, Abeta fibrils are found to be brittle in the lateral direction of unbinding and soft along the fibril axis. Lateral mechanical unbinding and the unbinding along the fibril axis load different types of fibril interactions. Lateral unbinding is primarily determined by the cooperative rupture of fibril backbone hydrogen bonds. The unbinding along the fibril axis largely depends on the interpeptide Lys-Asp electrostatic contacts and the hydrophobic interactions formed by the Abeta C terminal. Due to universality of the amyloid beta structure, the anisotropic mechanical dissociation observed for Abeta fibrils is likely to be applicable to other amyloid assemblies. The estimates of equilibrium forces required to dissociate Abeta peptide from the amyloid fibril suggest that these supramolecular structures are mechanically stronger than most protein domains.

Stretching to understand proteins - a survey of the protein data bank

We make a survey of resistance of 7510 proteins to mechanical stretching at constant speed as studied within a coarse-grained molecular dynamics model. We correlate the maximum force of resistance with the native structure, predict proteins which should be especially strong, and identify the nature of their force clamps.

Secondary structure, mechanical stability, and location of transition state of proteins

It is well known that the unfolding times of proteins, tauu, scales with the external mechanical force f as tauu=tauu0exp(-fxu/kBT), where xu is the location of the average transition state along the reaction coordinate given by the end-to-end distance. Using the off-lattice Go-like models, we have shown that in terms of xu, proteins may be divided into two classes. The first class, which includes beta- and beta/alpha-proteins, has xu approximately 2-5 A whereas the second class of alpha-proteins has xu about three times larger than that of the first class, xu approximately 7-15 A. These results are in good agreement with the experimental data. The secondary structure is found to play the key role in determining the shape of the free energy landscape. Namely, the distance between the native state and the transition state depends on the helix content linearly. It is shown that xu has a strong correlation with mechanical stability of proteins. Defining the unfolding force, fu, from the constant velocity pulling measurements as a measure of the mechanical stability, we predict that xu decays with fu by a power law, xu approximately fu(-mu), where the exponent mu is approximately 0.4. We have demonstrated that the unfolding force correlates with the helix content of a protein. The contact order, which is a measure of fraction of local contacts, was found to strongly correlate with the mechanical stability and the distance between the transition state and native state. Our study reveals that xu and fu might be estimated using either the helicity or the contact order.

Mechanical unfolding revisited through a simple but realistic model

Single-molecule experiments and their application to probe the mechanical resistance and related properties of proteins provide a new dimension in our knowledge of these important and complex biological molecules. Single-molecule techniques may not have yet overridden solution experiments as a method of choice to characterize biophysical and biological properties of proteins, but have stimulated a debate and contributed considerably to bridge theory and experiment. Here we demonstrate this latter contribution by illustrating the reach of some theoretical findings using a solvable but nontrivial molecular model whose properties are analogous to those of the corresponding experimental systems. In particular, we show the relationship between the thermodynamic and the mechanical properties of a protein. The simulations presented here also illustrate how forced and spontaneous unfolding occur through different pathways and that folding and unfolding rates at equilibrium cannot in general be obtained from forced unfolding experiments or simulations. We also study the relationship between the energy surface and the mechanical resistance of a protein and show how a simple analysis of the native state can predict much of the mechanical properties of a protein.

Force-clamp spectroscopy of single-protein monomers reveals the individual unfolding and folding pathways of I27 and ubiquitin

Single-protein force experiments have relied on a molecular fingerprint based on tethering multiple single-protein domains in a polyprotein chain. However, correlations between these domains remain an issue in interpreting force spectroscopy data, particularly during protein folding. Here we first show that force-clamp spectroscopy is a sensitive technique that provides a molecular fingerprint based on the unfolding step size of four single-monomer proteins. We then measure the force-dependent unfolding rate kinetics of ubiquitin and I27 monomers and find a good agreement with the data obtained for the respective polyproteins over a wide range of forces, in support of the Markovian hypothesis. Moreover, with a large statistical ensemble at a single force, we show that ubiquitin monomers also exhibit a broad distribution of unfolding times as a signature of disorder in the folded protein landscape. Furthermore, we readily capture the folding trajectories of monomers that exhibit the same stages in folding observed for polyproteins, thus eliminating the possibility of entropic masking by other unfolded modules in the chain or domain-domain interactions. On average, the time to reach the I27 folded length increases with increasing quenching force at a rate similar to that of the polyproteins. Force-clamp spectroscopy at the single-monomer level reproduces the kinetics of unfolding and refolding measured using polyproteins, which proves that there is no mechanical effect of tethering proteins to one another in the case of ubiquitin and I27.

Rupture force analysis and the associated systematic errors in force spectroscopy by AFM

Force spectroscopy is a new and valuable tool in physical chemistry and biophysics. However, data analysis has yet to be standardized, hindering the advancement of the technique. In this article, treatment of the rupture forces is described in the framework of the Bell-Evans model, and the systematic errors associated with the tether effect for approaches that utilize the most probable, the median, and the mean rupture forces are compared. It is shown that significant systematic errors in the dissociation rate can result from nonlinear loading with polymeric tethers even if the apparent loading rate is used in the analysis. Analytical expressions for the systematic errors are provided for the most probable and median forces. The use of these expressions to correct the associated systematic errors is illustrated by the analysis of the measured rupture forces between single hexadecane molecules in water. It is noted that the measured distributions of rupture forces often contain high forces that are unaccounted for by theoretical models. Experimental data indicate that the most significant effect of the high forces "tail" is on the dissociation rate obtained from the median force analysis whereas the barrier width appears to be unaffected.

Single-molecule force spectroscopy reveals a mechanically stable protein fold and the rational tuning of its mechanical stability

It is recognized that shear topology of two directly connected force-bearing terminal beta-strands is a common feature among the vast majority of mechanically stable proteins known so far. However, these proteins belong to only two distinct protein folds, Ig-like beta sandwich fold and beta-grasp fold, significantly hindering delineating molecular determinants of mechanical stability and rational tuning of mechanical properties. Here we combine single-molecule atomic force microscopy and steered molecular dynamics simulation to reveal that the de novo designed Top7 fold [Kuhlman B, Dantas G, Ireton GC, Varani G, Stoddard BL, Baker D (2003) Science 302:1364-1368] represents a mechanically stable protein fold that is distinct from Ig-like beta sandwich and beta-grasp folds. Although the two force-bearing beta strands of Top7 are not directly connected, Top7 displays significant mechanical stability, demonstrating that the direct connectivity of force-bearing beta strands in shear topology is not mandatory for mechanical stability. This finding broadens our understanding of the design of mechanically stable proteins and expands the protein fold space where mechanically stable proteins can be screened. Moreover, our results revealed a substructure-sliding mechanism for the mechanical unfolding of Top7 and the existence of two possible unfolding pathways with different height of energy barrier. Such insights enabled us to rationally tune the mechanical stability of Top7 by redesigning its mechanical unfolding pathway. Our study demonstrates that computational biology methods (including de novo design) offer great potential for designing proteins of defined topology to achieve significant and tunable mechanical properties in a rational and systematic fashion.

Unfolding cross-linkers as rheology regulators in F-actin networks

We report on the nonlinear mechanical properties of a statistically homogeneous, isotropic semiflexible network cross-linked by polymers containing numerous small unfolding domains, such as the ubiquitous F-actin cross-linker filamin. We show that the inclusion of such proteins has a dramatic effect on the large strain behavior of the network. Beyond a strain threshold, which depends on network density, the unfolding of protein domains leads to bulk shear softening. Past this critical strain, the network spontaneously organizes itself so that an appreciable fraction of the filamin cross-linkers are at the threshold of domain unfolding. We discuss via a simple mean-field model the cause of this network organization and suggest that it may be the source of power-law relaxation observed in in vitro and in intracellular microrheology experiments. We present data which fully justify our model for a simplified network architecture.

The effect of protein complexation on the mechanical stability of Im9

Force mode microscopy can be used to examine the effect of mechanical manipulation on the noncovalent interactions that stabilize proteins and their complexes. Here we describe the effect of complexation by the high affinity protein ligand E9 on the mechanical resistance of the simple four-helical protein, Im9. When concatenated into a construct of alternating I27 domains, Im9 unfolded below the thermal noise limit of the instrument ( approximately 20 pN). Complexation of E9 had little effect on the mechanical resistance of Im9 (unfolding force approximately 30 pN) despite the high avidity of this complex (K(d) approximately 10 fM).

The mechanical unfolding of ubiquitin through all-atom Monte Carlo simulation with a Go-type potential

The mechanical unfolding of proteins under a stretching force has an important role in living systems and is a logical extension of the more general protein folding problem. Recent advances in experimental methodology have allowed the stretching of single molecules, thus rendering this process ripe for computational study. We use all-atom Monte Carlo simulation with a Gō-type potential to study the mechanical unfolding pathway of ubiquitin. A detailed, robust, well-defined pathway is found, confirming existing results in this vein though using a different model. Additionally, we identify the protein's fundamental stabilizing secondary structure interactions in the presence of a stretching force and show that this fundamental stabilizing role does not persist in the absence of mechanical stress. The apparent success of simulation methods in studying ubiquitin's mechanical unfolding pathway indicates their potential usefulness for future study of the stretching of other proteins and the relationship between protein structure and the response to mechanical deformation.

Correction of Systematic Errors in Single-Molecule Force Spectroscopy with Polymeric Tethers by Atomic Force Microscopy

Single-molecule force spectroscopy has become a valuable tool for the investigation of intermolecular energy landscapes for a wide range of molecular associations. Atomic force microscopy (AFM) is often used as an experimental technique in these measurements, and the Bell-Evans model is commonly used in the statistical analysis of rupture forces. Most applications of the Bell-Evans model consider a constant loading rate of force applied to the intermolecular bond. The data analysis is often inconsistent because either the probe velocity or the apparent loading rate is being used as an independent parameter. These approaches provide different results when used in AFM-based experiments. Significant variations in results arise from the relative stiffness of the AFM force sensor in comparison with the stiffness of polymeric tethers that link the molecules under study to the solid surfaces. An analytical model presented here accounts for the systematic errors in force-spectroscopy parameters arising from the nonlinear loading induced by polymer tethers. The presented analytical model is based on the Bell-Evans model of the kinetics of forced dissociation and on the asymptotic models of tether stretching. The two most common data reduction procedures are analyzed, and analytical expressions for the systematic errors are provided. The model shows that the barrier width is underestimated and that the dissociation rate is significantly overestimated when force-spectroscopy data are analyzed without taking into account the elasticity of the polymeric tether. Systematic error estimates for asymptotic freely jointed chain and wormlike chain polymer models are given for comparison. The analytical model based on the asymptotic freely jointed chain stretching is employed to analyze and correct the results of the double-tether force-spectroscopy experiments of disjoining "hydrophobic bonds" between individual hexadecane molecules that are covalently tethered via poly(ethylene glycol) linkers of different lengths to the substrates and to the AFM probes. Application of the correction algorithm decreases the spread of the data from the mean value, which is particularly important for measurements of the dissociation rate, and increases the barrier width to 0.43 nm, which might be indicative of the theoretically predicted hydrophobic dewetting.

Polyprotein of GB1 is an ideal artificial elastomeric protein

Naturally occurring elastomeric proteins function as molecular springs in their biological settings and show mechanical properties that underlie the elasticity of natural adhesives, cell adhesion proteins and muscle proteins. Constantly subject to repeated stretching-relaxation cycles, many elastomeric proteins demonstrate remarkable consistency and reliability in their mechanical performance. Such properties had hitherto been observed only in naturally evolved elastomeric proteins. Here we use single-molecule atomic force microscopy techniques to demonstrate that an artificial polyprotein made of tandem repeats of non-mechanical protein GB1 has mechanical properties that are comparable or superior to those of known elastomeric proteins. In addition to its mechanical stability, we show that GB1 polyprotein shows a unique combination of mechanical features, including the fastest folding kinetics measured so far for a tethered protein, high folding fidelity, low mechanical fatigue during repeated stretching-relaxation cycles and ability to fold against residual forces. These fine features make GB1 polyprotein an ideal artificial protein-based molecular spring that could function in a challenging working environment requiring repeated stretching-relaxation. This study represents a key step towards engineering artificial molecular springs with tailored nanomechanical properties for bottom-up construction of new devices and materials.

Mechanical unfolding of proteins: insights into biology, structure and folding

Since user-friendly atomic force microscopes came onto the market a few years ago, scientists have explored the response of many proteins to applied force. This field has now matured beyond the phenomenological with exciting recent developments, particularly with regards to research into biological questions. For example, detailed mechanistic studies have suggested how mechanically active proteins perform their functions. Also, in vitro forced unfolding has been compared with in vivo protein import and degradation. Additionally, investigations have been carried out that probe the relationship between protein structure and response to applied force, an area that has benefited significantly from synergy between experiments and simulations. Finally, recent technological developments offer exciting new avenues for experimental studies.

Internal protein dynamics shifts the distance to the mechanical transition state

Mechanical unfolding of polyproteins by force spectroscopy provides valuable insight into their free energy landscapes. Most experiments of the unfolding process have been fit to two-state and/or one dimensional models, with the details of the protein and its dynamics often subsumed into a zero-force unfolding rate and a distance x{u}{1D} to the transition state. We consider the entire phase space of a model protein under a constant force, and show that x{u}{1D} contains a sizeable contribution from exploring the full multidimensional energy landscape. This effect is greater for proteins with many degrees of freedom that are affected by force; and surprisingly, we predict that externally attached flexible linkers also contribute to the measured unfolding characteristics.

Nanoscale mechanical characterisation of amyloid fibrils discovered in a natural adhesive

Using the atomic force microscope, we have investigated the nanoscale mechanical response of the attachment adhesive of the terrestrial alga Prasiola linearis (Prasiolales, Chlorophyta). We were able to locate and extend highly ordered mechanical structures directly from the natural adhesive matrix of the living plant. The in vivo mechanical response of the structured biopolymer often displayed the repetitive sawtooth force-extension characteristics of a material exhibiting high mechanical strength at the molecular level. Mechanical and histological evidence leads us to propose a mechanism for mechanical strength in our sample based on amyloid fibrils. These proteinaceous, pleated β-sheet complexes are usually associated with neurodegenerative diseases. However, we now conclude that the amyloid protein quaternary structures detected in our material should be considered as a possible generic mechanism for mechanical strength in natural adhesives.

Filamin cross-linked semiflexible networks: fragility under strain

The semiflexible F-actin network of the cytoskeleton is cross-linked by a variety of proteins including filamin, which contains Ig domains that unfold under applied tension. We examine a simple filament network model cross-linked by such unfolding linkers that captures the main mechanical features of F-actin networks cross-linked by filamin proteins and show that, under sufficient strain, the network spontaneously self-organizes so that an appreciable fraction of the filamin cross-linkers are at the threshold of domain unfolding. We propose and test a mean-field model to account for this effect. We also suggest a qualitative experimental signature of this type of network reorganization under applied strain that may be observable in intracellular microrheology experiments of Crocker et al.

Mechanical Unfolding of Segment-Swapped Protein G Dimer: Results from Replica Exchange Molecular Dynamics Simulations

The protein G dimer (pdb code 1Q10) is a mutated dimeric form of the immunoglobulin-binding domain B1 of streptococcal protein G, in which the two monomeric units have swapped elements of their secondary structure. We have used replica exchange molecular dynamics simulations to study how this dimer responds to a mechanical force that pulls the N-terminus of one unit and the C-terminus of the other apart. We have further compared the mechanical response of the dimer to that of the protein G monomer. When the pulling force is low enough, the mechanical unfolding can be viewed as a thermally activated barrier crossing process. For each protein, we have computed the corresponding free energy barrier and its dependence on the pulling force. While the dimer is found to be less resistant to mechanical unfolding than its monomeric counterpart, the two proteins exhibit essentially the same mechanical unfolding mechanism involving separation of the terminal parallel strands. On the basis of our results, we speculate that the mechanical properties of natural adhesives, composites, fibers, and other materials may be optimized not only at a single molecule level but also at the mesoscopic level through the interactions among individual chains.

Mechanical resistance of proteins explained using simple molecular models

Recent experiments have demonstrated that proteins unfold when two atoms are mechanically pulled apart, and that this process is different to when heated or when a chemical denaturant is added to the solution. Experiments have also shown that the response of proteins to external forces is very diverse, some of them being "hard," and others "soft." Mechanical resistance originates from the presence of barriers on the energy landscape; together, experiment and simulation have demonstrated that unfolding occurs through alternative pathways when different pairs of atoms undergo mechanical extension. Here we use simulation to probe the mechanical resistance of six structurally diverse proteins when pulled in different directions. For this, we use two very different models: a detailed, transferable one, and a coarse-grained, structure-based one. The coarse-grained model gives results that are surprisingly similar to the detailed one and qualitatively agree with experiment; i.e., the mechanical resistance of different proteins or of a single protein pulled in different directions can be predicted by simulation. The results demonstrate the importance of pulling direction relative to the local topology in determining mechanical stability, and rationalize the effect of the location of importation/degradation tags on the rates of mitochondrial import or protein degradation in vivo.