Mechanical resistance of proteins explained using simple molecular models

Uncovering and engineering the mechanical properties of the adhesion GPCR ADGRG1 GAIN domain

Key cellular functions depend on the transduction of extracellular mechanical signals by specialized membrane receptors including adhesion G-protein coupled receptors (aGPCRs). While recently solved structures support aGPCR activation through shedding of the extracellular GAIN domain, the molecular mechanisms underpinning receptor mechanosensing remain poorly understood. When probed using single-molecule atomic force spectroscopy and molecular simulations, ADGRG1 GAIN dissociated from its tethered agonist at forces significantly higher than other reported signaling mechanoreceptors. Strong mechanical resistance was achieved through specific structural deformations and force propagation pathways under mechanical load. ADGRG1 GAIN variants computationally designed to lock the alpha and beta subdomains and rewire mechanically-induced structural deformations were found to modulate the GPS-Stachel rupture forces. Our study provides unprecedented insights into the molecular underpinnings of GAIN mechanical stability and paves the way for engineering mechanosensors, better understanding aGPCR function, and informing drug-discovery efforts targeting this important receptor class.

A proteome scale study reveals how plastic surfaces and agitation promote protein aggregation

Protein aggregation in biotherapeutics can reduce their activity and effectiveness. It may also promote immune reactions responsible for severe adverse effects. The impact of plastic materials on protein destabilization is not totally understood. Here, we propose to deconvolve the effects of material surface, air/liquid interface, and agitation to decipher their respective role in protein destabilization and aggregation. We analyzed the effect of polypropylene, TEFLON, glass and LOBIND surfaces on the stability of purified proteins (bovine serum albumin, hemoglobin and α-synuclein) and on a cell extract composed of 6000 soluble proteins during agitation (P = 0.1-1.2 W/kg). Proteomic analysis revealed that chaperonins, intrinsically disordered proteins and ribosomes were more sensitive to the combined effects of material surfaces and agitation while small metabolic oligomers could be protected in the same conditions. Protein loss observations coupled to Raman microscopy, dynamic light scattering and proteomic allowed us to propose a mechanistic model of protein destabilization by plastics. Our results suggest that protein loss is not primarily due to the nucleation of small aggregates in solution, but to the destabilization of proteins exposed to material surfaces and their subsequent aggregation at the sheared air/liquid interface, an effect that cannot be prevented by using LOBIND tubes. A guidance can be established on how to minimize these adverse effects. Remove one of the components of this combined stress - material, air (even partially), or agitation - and proteins will be preserved.

Factors underlying asymmetric pore dynamics of disaggregase and microtubule-severing AAA+ machines

Disaggregation and microtubule-severing nanomachines from the AAA+ (ATPases associated with various cellular activities) superfamily assemble into ring-shaped hexamers that enable protein remodeling by coupling large-scale conformational changes with application of mechanical forces within a central pore by loops protruding within the pore. We probed the asymmetric pore motions and intraring interactions that support them by performing extensive molecular dynamics simulations of single-ring severing proteins and the double-ring disaggregase ClpB. Simulations reveal that dynamic stability of hexameric pores of severing proteins and of the nucleotide-binding domain 1 (NBD1) ring of ClpB, which belong to the same clade, involves a network of salt bridges that connect conserved motifs of central pore loops. Clustering analysis of ClpB highlights correlated motions of domains of neighboring protomers supporting strong interprotomer collaboration. Severing proteins have weaker interprotomer coupling and stronger intraprotomer stabilization through salt bridges involving pore loops. Distinct mechanisms are identified in the NBD2 ring of ClpB involving weaker interprotomer coupling through salt bridges formed by noncanonical loops and stronger intraprotomer coupling. Analysis of collective motions of PL1 loops indicates that the largest amplitude motions in the spiral complex of spastin and ClpB involve axial excursions of the loops, whereas for katanin they involve opening and closing of the central pore. All three motors execute primarily axial excursions in the ring complex. These results suggest distinct substrate processing mechanisms of remodeling and translocation by ClpB and spastin compared to katanin, thus providing dynamic support for the differential action of the two severing proteins. Relaxation dynamics of the distance between the PL1 loops and the center of mass of protomers reveals observation-time-dependent dynamics, leading to predicted relaxation times of tens to hundreds of microseconds on millisecond experimental timescales. For ClpB, the predicted relaxation time is in excellent agreement with the extracted time from smFRET experiments.

Synonymous codon substitutions perturb cotranslational protein folding in vivo and impair cell fitness

In the cell, proteins are synthesized from N to C terminus and begin to fold during translation. Cotranslational folding mechanisms are therefore linked to elongation rate, which varies as a function of synonymous codon usage. However, synonymous codon substitutions can affect many distinct cellular processes, which has complicated attempts to deconvolve the extent to which synonymous codon usage can promote or frustrate proper protein folding in vivo. Although previous studies have shown that some synonymous changes can lead to different final structures, other substitutions will likely be more subtle, perturbing predominantly the protein folding pathway without radically altering the final structure. Here we show that synonymous codon substitutions encoding a single essential enzyme lead to dramatically slower cell growth. These mutations do not prevent active enzyme formation; instead, they predominantly alter the protein folding mechanism, leading to enhanced degradation in vivo. These results support a model in which synonymous codon substitutions can impair cell fitness by significantly perturbing cotranslational protein folding mechanisms, despite the chaperoning provided by the cellular protein homeostasis network.

The nanomechanics of individual proteins

This tutorial review provides an overview of the single protein force spectroscopy field, including the main techniques and the basic tools for analysing the data obtained from the single molecule experiments.

A comparative study for the intermediate states of myelin oligodendrocyte glycoprotein in the absence and presence of glycan - A computational approach

Myelin Oligodendrocyte glycoprotein (MOG) is found to play an important role in providing structural integrity to myelin sheath at the same time it acts as an auto-antigen which might lead to Multiple Sclerosis (MS). What causes this specific property of being an auto-antigen is still not known. Here we present molecular dynamics simulation studies of unfolding and folding of the protein MOG in both the absence and presence of N-glycan in order to understand the role of glycosylation in the stability and flexibility of the protein. The main results from these studies show that the glycosylation increases the stability of the protein MOG and inhibits the complete unfolding of MOG in the SMD. From the folding studies using TMD, it was observed that the glycan helps the protein to attain the near-native folded conformation. However, it was also observed from the direct TMD studies that the pathway of protein folding was enhanced by the trace-back of intermediate states in the presence of glycan.

Three Weaknesses for Three Perturbations: Comparing Protein Unfolding Under Shear, Force, and Thermal Stresses

The perturbation of a protein conformation by a physiological fluid flow is crucial in various biological processes including blood clotting and bacterial adhesion to human tissues. Investigating such mechanisms by computer simulations is thus of great interest, but it requires development of ad hoc strategies to mimic the complex hydrodynamic interactions acting on the protein from the surrounding flow. In this study, we apply the Lattice Boltzmann Molecular Dynamics (LBMD) technique built on the implicit solvent coarse-grained model for protein Optimized Potential for Efficient peptide structure Prediction (OPEP) and a mesoscopic representation of the fluid solvent, to simulate the unfolding of a small globular cold-shock protein in shear flow and to compare it to the unfolding mechanisms caused either by mechanical or thermal perturbations. We show that each perturbation probes a specific weakness of the protein and causes the disruption of the native fold along different unfolding pathways. Notably, the shear flow and the thermal unfolding exhibit very similar pathways, while because of the directionality of the perturbation, the unfolding under force is quite different. For force and thermal disruption of the native state, the coarse-grained simulations are compared to all-atom simulations in explicit solvent, showing an excellent agreement in the explored unfolding mechanisms. These findings encourage the use of LBMD based on the OPEP model to investigate how a flow can affect the function of larger proteins, for example, in catch-bond systems.

Molecular Mechanism of Protein Unfolding under Shear: A Lattice Boltzmann Molecular Dynamics Study

Proteins are marginally stable soft-matter entities that can be disrupted using a variety of perturbative stresses, including thermal, chemical, or mechanical ones. Fluid under extreme flow conditions is a possible route to probe the weakness of biomolecules and collect information on the molecular cohesive interactions that secure their stability. Moreover, in many cases, physiological flow triggers the functional response of specialized proteins as occurring in blood coagulation or cell adhesion. We deploy the Lattice Boltzmann molecular dynamics technique based on the coarse-grained model for protein OPEP to study the mechanism of protein unfolding under Couette flow. Our simulations provide a clear view of how structural elements of the proteins are affected by shear, and for the simple study case, the β-hairpin, we exploited the analogy to pulling experiments to quantify the mechanical forces acting on the protein under shear.

Soft Vibrational Modes Predict Breaking Events during Force-Induced Protein Unfolding

We investigate the correlation between soft vibrational modes and unfolding events in simulated force spectroscopy of proteins. Unfolding trajectories are obtained from molecular dynamics simulations of a Gō model of a monomer of a mutant of superoxide dismutase 1 protein containing all heavy atoms in the protein, and a normal mode analysis is performed based on the anisotropic network model. We show that a softness map constructed from the superposition of the amplitudes of localized soft modes correlates with unfolding events at different stages of the unfolding process. Soft residues are up to eight times more likely to undergo disruption of native structure than the average amino acid. The memory of the softness map is retained for extensions of up to several nanometers, but decorrelates more rapidly during force drops.

Periodic forces trigger knot untying during translocation of knotted proteins

Proteins need to be unfolded when translocated through the pores in mitochondrial and other cellular membranes. Knotted proteins, however, might get stuck during this process, jamming the pore, since the diameter of the pore is smaller than the size of maximally tightened knot. The jamming probability dramatically increases as the magnitude of the driving force exceeds a critical value, F_c. In this numerical study, we show that for deep knots F_c lies below the force range over which molecular import motors operate, which suggest that in these cases the knots will tighten and block the pores. Next, we show how such topological traps might be prevented by using a pulling protocol of a repetitive, on-off character. Such a repetitive pulling is biologically relevant, since the mitochondrial import motor, like other molecular motors transforms chemical energy into directed motions via nucleotide-hydrolysis-mediated conformational changes, which are cyclic in character.

Tuning protein mechanics through an ionic cluster graft from an extremophilic protein

Proteins from extremophilic organisms provide excellent model systems to determine the role of non-covalent interactions in defining protein stability and dynamics as well as being attractive targets for the development of robust biomaterials. Hyperthermophilic proteins have a prevalence of salt bridges, relative to their mesophilic homologues, which are thought to be important for enhanced thermal stability. However, the impact of salt bridges on the mechanical properties of proteins is far from understood. Here, a combination of protein engineering, biophysical characterisation, single molecule force spectroscopy (SMFS) and molecular dynamics (MD) simulations directly investigates the role of salt bridges in the mechanical stability of two cold shock proteins; BsCSP from the mesophilic organism Bacillus subtilis and TmCSP from the hyperthermophilic organism Thermotoga maritima. Single molecule force spectroscopy shows that at ambient temperatures TmCSP is mechanically stronger yet, counter-intuitively, its native state can withstand greater deformation before unfolding (i.e. it is mechanically soft) compared with BsCSP. MD simulations were used to identify the location and quantify the population of salt bridges, and reveal that TmCSP contains a larger number of highly occupied salt bridges than BsCSP. To test the hypothesis that salt-bridges endow these mechanical properties on the hyperthermophilic CSP, a charged triple mutant (CTM) variant of BsCSP was generated by grafting an ionic cluster from TmCSP into the BsCSP scaffold. As expected CTM is thermodynamically more stable and mechanically softer than BsCSP. We show that a grafted ionic cluster can increase the mechanical softness of a protein and speculate that it could provide a mechanical recovery mechanism and that it may be a design feature applicable to other proteins.

Reduction of All-Atom Protein Folding Dynamics to One-Dimensional Diffusion

Theoretical models have often modeled protein folding dynamics as diffusion on a low-dimensional free energy surface, a remarkable simplification. However, the accuracy of such an approximation and the number of dimensions required were not clear. For all-atom folding simulations of ten small proteins in explicit solvent we show that the folding dynamics can indeed be accurately described as diffusion on just a single coordinate, the fraction of native contacts (Q). The diffusion models reproduce both folding rates, and finer details such as transition-path durations and diffusive propagators. The Q-averaged diffusion coefficients decrease with chain length, as anticipated from energy landscape theory. Although the Q-diffusion model does not capture transition-path durations for the protein NuG2, we show that this can be accomplished by designing an improved coordinate Qopt. Overall, one-dimensional diffusion on a suitable coordinate turns out to be a remarkably faithful model for the dynamics of the proteins considered.

Mechanical dissociation of the M-band titin/obscurin complex is directionally dependent

Titin and obscurin, two giant muscle proteins, bind to each other in an antiparallel Ig-Ig fashion at the M-band. This interaction must be able to withstand the mechanical strain that the M-band typically experiences and remain intact. The mechanical force on these domains is likely exerted along one of two axes: a longitudinal axis, resulting in a 'shearing' force, or a lateral axis, resulting in a 'peeling' force. Here we present molecular dynamics data suggesting that these forces result in distinct unraveling pathways of the titin/obscurin complex and that peeling the domains apart requires less work and force.

Identifying sequential substrate binding at the single-molecule level by enzyme mechanical stabilization

Enzyme-substrate binding is a dynamic process intimately coupled to protein structural changes, which in turn changes the unfolding energy landscape. By the use of single-molecule force spectroscopy (SMFS), we characterize the open-to-closed conformational transition experienced by the hyperthermophilic adenine diphosphate (ADP)-dependent glucokinase from Thermococcus litoralis triggered by the sequential binding of substrates. In the absence of substrates, the mechanical unfolding of TlGK shows an intermediate 1, which is stabilized in the presence of Mg·ADP(-), the first substrate to bind to the enzyme. However, in the presence of this substrate, an additional unfolding event is observed, intermediate 1*. Finally, in the presence of both substrates, the unfolding force of intermediates 1 and 1* increases as a consequence of the domain closure. These results show that SMFS can be used as a powerful experimental tool to investigate binding mechanisms of different enzymes with more than one ligand, expanding the repertoire of protocols traditionally used in enzymology.

Mechanical stability analysis of the protein L immunoglobulin-binding domain by full alanine screening using molecular dynamics simulations

This article is the first to study the mechanical properties of the immunoglobulin-binding domain of protein L (referred to as protein L) and its mutants at the atomic level. In the structure of protein L, each amino acid residue (except for alanines and glycines) was replaced sequentially by alanine. Thus, 49 mutants of protein L were obtained. The proteins were stretched at their termini at constant velocity using molecular dynamics simulations in water, i.e. by forced unfolding. 19 out of 49 mutations resulted in a large decrease of mechanical protein stability. These amino acids were affecting either the secondary structure (11 mutations) or loop structures (8 mutations) of protein L. Analysis of mechanical unfolding of the generated protein that has the same topology as protein L but consists of only alanines and glycines allows us to suggest that the mechanical stability of proteins, and specifically protein L, is determined by interactions between certain amino acid residues, although the unfolding pathway depends on the protein topology. This insight can now be used to modulate the mechanical properties of proteins and their unfolding pathways in the desired direction for using them in various biochips, biosensors and biomaterials for medicine, industry, and household purposes.

In silico insights into protein-protein interactions and folding dynamics of the saposin-like domain of Solanum tuberosum aspartic protease

The plant-specific insert is an approximately 100-residue domain found exclusively within the C-terminal lobe of some plant aspartic proteases. Structurally, this domain is a member of the saposin-like protein family, and is involved in plant pathogen defense as well as vacuolar targeting of the parent protease molecule. Similar to other members of the saposin-like protein family, most notably saposins A and C, the recently resolved crystal structure of potato (Solanum tuberosum) plant-specific insert has been shown to exist in a substrate-bound open conformation in which the plant-specific insert oligomerizes to form homodimers. In addition to the open structure, a closed conformation also exists having the classic saposin fold of the saposin-like protein family as observed in the crystal structure of barley (Hordeum vulgare L.) plant-specific insert. In the present study, the mechanisms of tertiary and quaternary conformation changes of potato plant-specific insert were investigated in silico as a function of pH. Umbrella sampling and determination of the free energy change of dissociation of the plant-specific insert homodimer revealed that increasing the pH of the system to near physiological levels reduced the free energy barrier to dissociation. Furthermore, principal component analysis was used to characterize conformational changes at both acidic and neutral pH. The results indicated that the plant-specific insert may adopt a tertiary structure similar to the characteristic saposin fold and suggest a potential new structural motif among saposin-like proteins. To our knowledge, this acidified PSI structure presents the first example of an alternative saposin-fold motif for any member of the large and diverse SAPLIP family.

Nanomechanics of β-rich proteins related to neuronal disorders studied by AFM, all-atom and coarse-grained MD methods

Computer simulations of protein unfolding substantially help to interpret force-extension curves measured in single-molecule atomic force microscope (AFM) experiments. Standard all-atom (AA) molecular dynamics simulations (MD) give a good qualitative mechanical unfolding picture but predict values too large for the maximum AFM forces with the common pulling speeds adopted here. Fine tuned coarse-grain MD computations (CG MD) offer quantitative agreement with experimental forces. In this paper we address an important methodological aspect of MD modeling, namely the impact of numerical noise generated by random assignments of bead velocities on maximum forces (F_max) calculated within the CG MD approach. Distributions of CG forces from 2000 MD runs for several model proteins rich in β structures and having folds with increasing complexity are presented. It is shown that F_max have nearly Gaussian distributions and that values of F_max for each of those β-structures may vary from 93.2 ± 28.9 pN (neurexin) to 198.3 ± 25.2 pN (fibronectin). The CG unfolding spectra are compared with AA steered MD data and with results of our AFM experiments for modules present in contactin, fibronectin and neurexin. The stability of these proteins is critical for the proper functioning of neuronal synaptic clefts. Our results confirm that CG modeling of a single molecule unfolding is a good auxiliary tool in nanomechanics but large sets of data have to be collected before reliable comparisons of protein mechanical stabilities are made.

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Experimental and theoretical studies of mechanical unfolding of different proteins

Mechanical properties of proteins are important for a wide range of biological processes including cell adhesion, muscle contraction, and protein translocation across biological membranes. It is necessary to reveal how proteins achieve their required mechanical stability under natural conditions in order to understand the biological processes and also to use the knowledge for constructing new biomaterials for medical and industrial purposes. In this connection, it is important to know how a protein will behave in response to various impacts. Theoretical and experimental works on mechanical unfolding of globular proteins will be considered in detail in this review.

The molecular mechanism underlying mechanical anisotropy of the protein GB1

Mechanical responses of elastic proteins are crucial for their biological function and nanotechnological use. Loading direction has been identified as one key determinant for the mechanical responses of proteins. However, it is not clear how a change in pulling direction changes the mechanical unfolding mechanism of the protein. Here, we combine protein engineering, single-molecule force spectroscopy, and steered molecular dynamics simulations to systematically investigate the mechanical response of a small globular protein GB1. Force versus extension profiles from both experiments and simulations reveal marked mechanical anisotropy of GB1. Using native contact analysis, we relate the mechanically robust shearing geometry with concurrent rupture of native contacts. This clearly contrasts the sequential rupture observed in simulations for the mechanically labile peeling geometry. Moreover, we identify multiple distinct mechanical unfolding pathways in two loading directions. Implications of such diverse unfolding mechanisms are discussed. Our results may also provide some insights for designing elastomeric proteins with tailored mechanical properties.

Cooperativity in thermal and force-induced protein unfolding: integration of crack propagation and network elasticity models

We investigate force-induced and temperature-induced unfolding of proteins using the combination of a gaussian network model and a crack propagation model based on "bond"-breaking independent events. We assume the existence of threshold values for the mean strain and strain fluctuations that dictate bond rupture. Surprisingly, we find that this stepwise process usually leads to a few cooperative, first-order-like, transitions in which several bonds break simultaneously, reminiscent of the "avalanches" seen in disordered networks.

Single-molecule experiments reveal the flexibility of a Per-ARNT-Sim domain and the kinetic partitioning in the unfolding pathway under force

Per-ARNT-Sim (PAS) domains serve as versatile binding motifs in many signal-transduction proteins and are able to respond to a wide spectrum of chemical or physical signals. Despite their diverse functions, PAS domains share a conserved structure. It has been suggested that the structure of PAS domains is flexible and thus adaptable to many binding partners. However, direct measurement of the flexibility of PAS domains has not yet been provided. Here, we quantitatively measure the mechanical unfolding of a PAS domain, ARNT PAS-B, using single-molecule atomic force microscopy. Our force spectroscopy results indicate that the structure of ARNT PAS-B can be unraveled under mechanical forces as low as ~30 pN due to its broad potential well for the mechanical unfolding transition of ~2 nm. This allows the PAS-B domain to extend by up to 75% of its resting end-to-end distance without unfolding. Moreover, we found that the ARNT PAS-B domain unfolds in two distinct pathways via a kinetic partitioning mechanism. Sixty-seven percent of ARNT PAS-B unfolds through a simple two-state pathway, whereas the other 33% unfolds with a well-defined intermediate state in which the C-terminal β-hairpin is detached. We propose that the structural flexibility and force-induced partial unfolding of PAS-B domains may provide a unique mechanism for them to recruit diverse binding partners and lower the free-energy barrier for the formation of the binding interface.

Direct observation of proteolytic cleavage at the S2 site upon forced unfolding of the Notch negative regulatory region

The conserved Notch signaling pathway plays crucial roles in developing and self-renewing tissues. Notch is activated upon ligand-induced conformation change of the Notch negative regulatory region (NRR) unmasking a key proteolytic site (S2) and facilitating downstream events. Thus far, the molecular mechanism of this signal activation is not defined. However, strong indirect evidence favors a model whereby transendocytosis of the Notch extracellular domain, in tight association with ligand into the ligand-bearing cell, exerts a force on the NRR to drive the required structure change. Here, we demonstrate that force applied to the human Notch2 NRR can indeed expose the S2 site and, crucially, allow cleavage by the metalloprotease TACE (TNF-alpha-converting enzyme). Molecular insight into this process is achieved using atomic force microscopy and molecular dynamics simulations on the human Notch2 NRR. The data show near-sequential unfolding of its constituent LNR (Lin12-Notch repeat) and HD (heterodimerization) domains, at forces similar to those observed for other protein domains with a load-bearing role. Exposure of the S2 site is the first force "barrier" on the unfolding pathway, occurring prior to unfolding of any domain, and achieved via removal of the LNRAB linker region from the HD domain. Metal ions increase the resistance of the Notch2 NRR to forced unfolding, their removal clearly facilitating unfolding at lower forces. The results provide direct demonstration of force-mediated exposure and cleavage of the Notch S2 site and thus firmly establish the feasibility of a mechanotransduction mechanism for ligand-induced Notch activation.

Evolution of the potential energy landscape with static pulling force for two model proteins

The energy landscape is analyzed for off-lattice bead models of protein L and protein G as a function of a static pulling force. Two different pairs of attachment points (pulling directions) are compared in each case, namely, residues 1/56 and 10/32. For the terminal residue pulling direction 1/56, the distinct global minimum structures are all extended, aside from the compact geometry that correlates with zero force. The helical turns finally disappear at the highest pulling forces considered. For the 10/32 pulling direction, the changes are more complicated, with a variety of competing arrangements for beads outside the region where the force is directly applied. These alternatives produce frustrated energy landscapes, with low-lying minima separated by high barriers. The calculated folding pathways in the absence of force are in good agreement with previous work. The N-terminal hairpin folds first for protein L and the C-terminal hairpin for protein G, which exhibits an intermediate. However, for a relatively low static force, where the global minimum retains its structure, the folding mechanisms change, sometimes dramatically, depending on the protein and the attachment points. The scaling relations predicted by catastrophe theory are found to hold in the limit of short path lengths.

Protein unfolding under force: crack propagation in a network

The mechanical unfolding of a set of 12 proteins with diverse topologies is investigated using an all-atom constraint-based model. Proteins are represented as polypeptides cross-linked by hydrogen bonds, salt bridges, and hydrophobic contacts, each modeled as a harmonic inequality constraint capable of supporting a finite load before breaking. Stereochemically acceptable unfolding pathways are generated by minimally overloading the network in an iterative fashion, analogous to crack propagation in solids. By comparing the pathways to those from molecular dynamics simulations and intermediates identified from experiment, it is demonstrated that the dominant unfolding pathways for 9 of the 12 proteins studied are well described by crack propagation in a network.

Transient-state fluctuationlike relation for the driving force on a biomolecule

In experiments and simulations the force acting on a single biomolecular system has been observed as a fluctuating quantity if the system is driven under constant velocity. We ask the question that is analogous to transient state entropy production and work fluctuation relations whether the force fluctuations observed in the single biomolecular system satisfy a transient state fluctuationlike relation, and the answer is in the affirmative. Using a constant velocity pulling steered molecular dynamics simulation study for protein unfolding, we confirm that the force fluctuations of this single biomolecular system satisfy a transient-state fluctuationlike relation 1/γ(T,v) ln[P(v)(+f)/P(v)(-f)] = f. P(v)(±f) is the probability of positive and negative values of forces f = f · for a given unfolding velocity of magnitude v and the pulling direction n, nis the unit vector of n, and γ(T,v) is a factor that depends on initial equilibrium temperature T and the unfolding velocity. For different unfolding velocities we find that the system in the nonequilibrium pulling region displays substantial negative fluctuation in its unfolding force when velocity decreases. A negative value of force may indicate the emergence of refolding behavior during protein unfolding. We also find that γ(T,v) ~ T(-δ)v(α) and the system relaxation time τ(T,v) ~ T(δ)v(-(1+α), where α and δ are scaling exponents.

Force-induced unfolding simulations of the human Notch1 negative regulatory region: possible roles of the heterodimerization domain in mechanosensing

Notch receptors are core components of the Notch signaling pathway and play a central role in cell fate decisions during development as well as tissue homeostasis. Upon ligand binding, Notch is sequentially cleaved at the S2 site by an ADAM protease and at the S3 site by the γ-secretase complex. Recent X-ray structures of the negative regulatory region (NRR) of the Notch receptor reveal an auto-inhibited fold where three protective Lin12/Notch repeats (LNR) of the NRR shield the S2 cleavage site housed in the heterodimerization (HD) domain. One of the models explaining how ligand binding drives the NRR conformation from a protease-resistant state to a protease-sensitive one invokes a mechanical force exerted on the NRR upon ligand endocytosis. Here, we combined physics-based atomistic simulations and topology-based coarse-grained modeling to investigate the intrinsic and force-induced folding and unfolding mechanisms of the human Notch1 NRR. The simulations support that external force applied to the termini of the NRR disengages the LNR modules from the heterodimerization (HD) domain in a well-defined, largely sequential manner. Importantly, the mechanical force can further drive local unfolding of the HD domain in a functionally relevant fashion that would provide full proteolytic access to the S2 site prior to heterodimer disassociation. We further analyzed local structural features, intrinsic folding free energy surfaces, and correlated motions of the HD domain. The results are consistent with a model in which the HD domain possesses inherent mechanosensing characteristics that could be utilized during Notch activation. This potential role of the HD domain in ligand-dependent Notch activation may have implications for understanding normal and aberrant Notch signaling.

Cooperative dynamics of proteins unraveled by network models

Recent years have seen a significant increase in the number of computational studies that adopted network models for investigating biomolecular systems dynamics and interactions. In particular, elastic network models have proven useful in elucidating the dynamics and allosteric signaling mechanisms of proteins and their complexes. Here we present an overview of two most widely used elastic network models, the Gaussian Network Model (GNM) and Anisotropic Network Model (ANM). We illustrate their use in (i) explaining the anisotropic response of proteins observed in external pulling experiments, (ii) identifying residues that possess high allosteric potentials, and demonstrating in this context the propensity of catalytic sites and metal-binding sites for enabling efficient signal transduction, and (iii) assisting in structure refinement, molecular replacement and comparative modeling of ligand-bound forms via efficient sampling of energetically favored conformers.

Hydrodynamic effects in proteins

Experimental and numerical results pertaining to flow-induced effects in proteins are reviewed. Special emphasis is placed on shear-induced unfolding and on the role of solvent mediated hydrodynamic interactions in the conformational transitions in proteins.

Molecular basis for the structural stability of an enclosed β-barrel loop

We present molecular dynamics simulation studies of the structural stability of an enclosed loop in the β domain of the Escherichia coli O157:H7 autotransporter EspP. Our investigation revealed that, in addition to its excellent resistance to thermal perturbations, EspP loop 5 (L5) also has remarkable mechanical stability against pulling forces along the membrane norm. These findings are consistent with the experimental report that EspP L5 helps to maintain the permeability barrier in the outer membrane. In contrast to the major secondary structure elements of globular proteins such as ubiquitin, whose resistance to thermal and mechanical perturbations depends mainly on backbone hydrogen bonds and hydrophobic interactions, the structural stability of EspP L5 can be attributed mainly to geometric constraints and side-chain interactions dominated by hydrogen bonds. Examination of B-factors from available high-resolution structures of membrane-embedded β barrels indicates that most of the enclosed loops have stable structures. This finding suggests that loops stabilized by geometric constraints and side-chain interactions might be used more generally to restrict β-barrel channels for various functional purposes.

Energy landscape, structure and rate effects on strength properties of alpha-helical proteins

The strength of protein domains is crucial to identify the mechanical role of protein domains in biological processes such as mechanotransduction, tissue mechanics and tissue remodeling. Whereas the concept of strength has been widely investigated for engineered materials, the strength of fundamental protein material building blocks and how it depends on structural parameters such as the chemical bonding, the protein filament length and the timescale of observation or deformation velocity remains poorly understood. Here we report a systematic analysis of the influence of key parameters that define the energy landscape of the strength properties of alpha-helical protein domains, including energy barriers, unfolding and refolding distances, the locations of folded and unfolded states, as well as variations of the length and pulling velocity of alpha-helical protein filaments. The analysis is facilitated by the development of a double-well mesoscale potential formulation, utilized here to carry out a systematic numerical analysis of the behavior of alpha-helices. We compare the results against widely used protein strength models based on the Bell model, one of the simplest models used to characterize the strength of protein filaments. We find that, whereas Bell-type models are a reasonable approximation to describe the rupture of alpha-helical protein domains for a certain range of pulling speeds and values of energy barriers, the model ceases to hold for very large energy barriers and for very small pulling speeds, in agreement with earlier findings. We conclude with an application of our mesoscale model to investigate the effect of the length of alpha-helices on their mechanical strength. We find a weakening effect as the length of alpha-helical proteins increases, followed by an asymptotic regime in which the strength remains constant. We compare strand lengths found in biological proteins with the scaling law of strength versus alpha-helix filament length. The mesoscale model reported here is generally applicable to other protein filaments that feature a serial array of domains that unfold under applied strain, where a similar length-dependent strength could be observed.

Computational and single-molecule force studies of a macro domain protein reveal a key molecular determinant for mechanical stability

Resolving molecular determinants of mechanical stability of proteins is crucial in the rational design of advanced biomaterials for use in biomedical and nanotechnological applications. Here we present an interdisciplinary study combining bioinformatics screening, steered molecular dynamics simulations, protein engineering, and single-molecule force spectroscopy that explores the mechanical properties of a macro domain protein with mixed alpha + beta topology. The unique architecture is defined by a single seven-stranded beta-sheet in the core of the protein flanked by five alpha-helices. Unlike mechanically stable proteins studied thus far, the macro domain provides the distinct advantage of having the key load-bearing hydrogen bonds (H bonds) buried in the hydrophobic core protected from water attacks. This feature allows direct measurement of the force required to break apart the load-bearing H bonds under locally hydrophobic conditions. Steered molecular dynamics simulations predicted extremely high mechanical stability of the macro domain by using constant velocity and constant force methods. Single-molecule force spectroscopy experiments confirm the exceptional mechanical strength of the macro domain, measuring a rupture force as high as 570 pN. Furthermore, through selective deletion of shielding peptide segments, we examined the same key H bonds under hydrophilic environments in which the beta-strands are exposed to solvent and verify that the high mechanical stability of the macro domain results from excellent shielding of the load-bearing H bonds from competing water. Our study reveals that shielding water accessibility to the load-bearing strands is a critical molecular determinant for enhancing the mechanical stability of proteins.

Critical examination of the inherent-structure-landscape analysis of two-state folding proteins

Recent studies attracted the attention on the inherent-structure-landscape (ISL) approach as a reduced description of proteins allowing to map their full thermodynamic properties. However, the analysis has been so far limited to a single topology of a two-state folding protein, and the simplifying assumptions of the method have not been examined. In this work, we construct the thermodynamics of four two-state folding proteins of different sizes and secondary structure by molecular dynamics (MD) simulations using the ISL method and critically examine possible limitations of the method. Our results show that the ISL approach correctly describes the thermodynamics function, such as the specific heat, on a qualitative level. Using both analytical and numerical methods, we show that some quantitative limitations cannot be overcome with enhanced sampling or the inclusion of harmonic corrections.

Hierarchical structure controls nanomechanical properties of vimentin intermediate filaments

Intermediate filaments (IFs), in addition to microtubules and microfilaments, are one of the three major components of the cytoskeleton in eukaryotic cells, playing a vital role in mechanotransduction and in providing mechanical stability to cells. Despite the importance of IF mechanics for cell biology and cell mechanics, the structural basis for their mechanical properties remains unknown. Specifically, our understanding of fundamental filament properties, such as the basis for their great extensibility, stiffening properties, and their exceptional mechanical resilience remains limited. This has prevented us from answering fundamental structure-function relationship questions related to the biomechanical role of intermediate filaments, which is crucial to link structure and function in the protein material's biological context. Here we utilize an atomistic-level model of the human vimentin dimer and tetramer to study their response to mechanical tensile stress, and describe a detailed analysis of the mechanical properties and associated deformation mechanisms. We observe a transition from alpha-helices to beta-sheets with subsequent interdimer sliding under mechanical deformation, which has been inferred previously from experimental results. By upscaling our results we report, for the first time, a quantitative comparison to experimental results of IF nanomechanics, showing good agreement. Through the identification of links between structures and deformation mechanisms at distinct hierarchical levels, we show that the multi-scale structure of IFs is crucial for their characteristic mechanical properties, in particular their ability to undergo severe deformation of ≈300% strain without breaking, facilitated by a cascaded activation of a distinct deformation mechanisms operating at different levels. This process enables IFs to combine disparate properties such as mechanosensitivity, strength and deformability. Our results enable a new paradigm in studying biological and mechanical properties of IFs from an atomistic perspective, and lay the foundation to understanding how properties of individual protein molecules can have profound effects at larger length-scales.

Identification of a mechanical rheostat in the hydrophobic core of protein L

The ability of proteins and their complexes to withstand or respond to mechanical stimuli is vital for cells to maintain their structural organisation, to relay external signals and to facilitate unfolding and remodelling. Force spectroscopy using the atomic force microscope allows the behaviour of single protein molecules under an applied extension to be investigated and their mechanical strength to be quantified. protein L, a simple model protein, displays moderate mechanical strength and is thought to unfold by the shearing of two mechanical sub-domains. Here, we investigate the importance of side-chain packing for the mechanical strength of protein L by measuring the mechanical strength of a series of protein L variants containing single conservative hydrophobic volume deletion mutants. Of the five thermodynamically destabilised variants characterised, only one residue (I60V) close to the interface between two mechanical sub-domains was found to differ in mechanical properties to wild type (ΔF_I60V–WT = − 36 pN at 447 nm s^− 1, Δx_uI60V–WT = 0.2 nm). Φ-value analysis of the unfolding data revealed a highly native transition state. To test whether the number of hydrophobic contacts across the mechanical interface does affect the mechanical strength of protein L, we measured the mechanical properties of two further variants. protein L L10F, which increases core packing but does not enhance interfacial contacts, increased mechanical strength by 13 ± 11 pN at 447 nm s^− 1. By contrast, protein L I60F, which increases both core and cross-interface contacts, increased mechanical strength by 72 ± 13 pN at 447 nm s^− 1. These data suggest a method by which nature can evolve a varied mechanical response from a limited number of topologies and demonstrate a generic but facile method by which the mechanical strength of proteins can be rationally modified.

Periodic forces trigger a complex mechanical response in ubiquitin

Mechanical forces govern physiological processes in all living organisms. Many cellular forces, for example, those generated in cyclic conformational changes of biological machines, have repetitive components. In apparent contrast, little is known about how dynamic protein structures respond to periodic mechanical information. Ubiquitin is a small protein found in all eukaryotes. We developed molecular dynamics simulations to unfold single and multimeric ubiquitins with periodic forces. By using a coarse-grained representation, we were able to model forces with periods about 2 orders of magnitude longer than the protein's relaxation time. We found that even a moderate periodic force weakened the protein and shifted its unfolding pathways in a frequency- and amplitude-dependent manner. A complex dynamic response with secondary structure refolding and an increasing importance of local interactions was revealed. Importantly, repetitive forces with broadly distributed frequencies elicited very similar molecular responses compared to fixed-frequency forces. When testing the influence of pulling geometry on ubiquitin's mechanical stability, it was found that the linkage involved in the mechanical degradation of cellular proteins renders the protein remarkably insensitive to periodic forces. We also devised a complementary kinetic energy landscape model that traces these observations and explains periodic-force, single-molecule measurements. In turn, this analytical model is capable of predicting dynamic protein responses. These results provide new insights into ubiquitin mechanics and a potential mechanical role during protein degradation, as well as first frameworks for dynamic protein stability and the modeling of repetitive mechanical processes.

New dynamical window onto the landscape for forced protein unfolding

The unfolding of a protein by the application of an external force pulling two atoms of the protein can be detected by atomic force and optical tweezers technologies as have been broadly demonstrated in the past decade. Variation of the applied force results in a modulation of the free-energy barrier to unfolding and thus, the rate of the process, which is often assumed to have single exponential kinetics. It has been recently shown that it is experimentally feasible, through the use of force clamps, to estimate the distribution of unfolding times for a population of proteins initially in the native state. In this Letter we show how the analysis of such distributions under a range of forces can provide unique information about the underlying free-energy surface such as the height of the free-energy barrier, the preexponential factor and the force dependence of the unfolding kinetics without resorting to ad hoc kinetic models.

Force-dependent hopping rates of RNA hairpins can be estimated from accurate measurement of the folding landscapes

The sequence-dependent folding landscapes of nucleic acid hairpins reflect much of the complexity of biomolecular folding. Folding trajectories, generated by using single-molecule force-clamp experiments by attaching semiflexible polymers to the ends of hairpins, have been used to infer their folding landscapes. Using simulations and theory, we study the effect of the dynamics of the attached handles on the handle-free RNA free-energy profile F(o)(eq)(z(m)), where z(m) is the molecular extension of the hairpin. Accurate measurements of F(o)(eq)(z(m)) requires stiff polymers with small L/l(p), where L is the contour length of the handle, and l(p) is the persistence length. Paradoxically, reliable estimates of the hopping rates can only be made by using flexible handles. Nevertheless, we show that the equilibrium free-energy profile F(o)(eq)(z(m)) at an external tension f(m), the force (f) at which the folded and unfolded states are equally populated, in conjunction with Kramers' theory, can provide accurate estimates of the force-dependent hopping rates in the absence of handles at arbitrary values of f. Our theoretical framework shows that z(m) is a good reaction coordinate for nucleic acid hairpins under tension.

Asymptotic strength limit of hydrogen-bond assemblies in proteins at vanishing pulling rates

We develop a fracture-mechanics-based theoretical framework that considers the free energy competition between entropic elasticity of polypeptide chains and rupture of peptide hydrogen bonds, which we use here to provide an explanation for the intrinsic strength limit of protein domains at vanishing rates. Our analysis predicts that individual protein domains stabilized only by hydrogen bonds cannot exhibit rupture forces larger than approximately 200 pN in the asymptotic limit. This result explains earlier experimental and computational observations that indicate an asymptotical strength limit at vanishing pulling rates.

Elastic bond network model for protein unfolding mechanics

Recent advances in single molecule mechanics have made it possible to investigate the mechanical anisotropy of protein stability in great detail. A quantitative prediction of protein unfolding forces at experimental time scales has so far been difficult. Here, we present an elastically bonded network model to describe the mechanical unfolding forces of green fluorescent protein in eight different pulling directions. The combination of an elastic network and irreversible bond fracture kinetics offers a new concept to understand the determinants of mechanical protein stability.