Unfolding of titin domains studied by molecular dynamics simulations

Differences in stability and calcium sensitivity of the Ig domains in titin's N2A region

Titin is a large filamentous protein that spans half a sarcomere, from Z-disk to M-line. The N2A region within the titin molecule exists between the proximal immunoglobulin (Ig) region and the PEVK region and protein-protein interactions involving this region are required for normal muscle function. The N2A region consists of four Ig domains (I80-I83) with a 105 amino acid linker region between I80 and I81 that has a helical nature. Using chemical stability measurements, we show that predicted differences between the adjacent Ig domains (I81-I83) correlate with experimentally determined differences in chemical stability and refolding kinetics. Our work further shows that I83 has the lowest ΔG_unfolding , which is increased in the presence of calcium (pCa 4.3), indicating that Ca²⁺ plays a role in stabilizing this immunoglobulin domain. The characteristics of N2A's three Ig domains provide insight into the stability of the binding sites for proteins that interact with the N2A region. This work also provides insights into how Ca²⁺ might influence binding events involving N2A.

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.

Unraveling the Mechanobiology of Extracellular Matrix

Cells need to be anchored to extracellular matrix (ECM) to survive, yet the role of ECM in guiding developmental processes, tissue homeostasis, and aging has long been underestimated. How ECM orchestrates the deterioration of healthy to pathological tissues, including fibrosis and cancer, also remains poorly understood. Inquiring how alterations in ECM fiber tension might drive these processes is timely, as mechanobiology is a rapidly growing field, and many novel mechanisms behind the mechanical forces that can regulate protein, cell, and tissue functions have recently been deciphered. The goal of this article is to review how forces can switch protein functions, and thus cell signaling, and thereby inspire new approaches to exploit the mechanobiology of ECM in regenerative medicine as well as for diagnostic and therapeutic applications. Some of the mechanochemical switching concepts described here for ECM proteins are more general and apply to intracellular proteins as well.

Combined molecular/continuum modeling reveals the role of friction during fast unfolding of coiled-coil proteins

Coiled-coils are filamentous proteins that form the basic building block of important force-bearing cellular elements, such as intermediate filaments and myosin motors. In addition to their biological importance, coiled-coil proteins are increasingly used in new biomaterials including fibers, nanotubes, or hydrogels. Coiled-coils undergo a structural transition from an α-helical coil to an unfolded state upon extension, which allows them to sustain large strains and is critical for their biological function. By performing equilibrium and out-of-equilibrium all-atom molecular dynamics (MD) simulations of coiled-coils in explicit solvent, we show that two-state models based on Kramers' or Bell's theories fail to predict the rate of unfolding at high pulling rates. We further show that an atomistically informed continuum rod model accounting for phase transformations and for the hydrodynamic interactions with the solvent can reconcile two-state models with our MD results. Our results show that frictional forces, usually neglected in theories of fibrous protein unfolding, reduce the thermodynamic force acting on the interface, and thus control the dynamics of unfolding at different pulling rates. Our results may help interpret MD simulations at high pulling rates, and could be pertinent to cytoskeletal networks or protein-based artificial materials subjected to shocks or blasts.

Insights and Challenges of Multi-Scale Modeling of Sarcomere Mechanics in cTn and Tm DCM Mutants-Genotype to Cellular Phenotype

Dilated Cardiomyopathy (DCM) is a leading cause of sudden cardiac death characterized by impaired pump function and dilatation of cardiac ventricles. In this review we discuss various in silico approaches to elucidating the mechanisms of genetic mutations leading to DCM. The approaches covered in this review focus on bridging the spatial and temporal gaps that exist between molecular and cellular processes. Mutations in sarcomeric regulatory thin filament proteins such as the troponin complex (cTn) and Tropomyosin (Tm) have been associated with DCM. Despite the experimentally-observed myofilament measures of contractility in the case of these mutations, the mechanisms by which the underlying molecular changes and protein interactions scale up to organ failure by these mutations remains elusive. The review highlights multi-scale modeling approaches and their applicability to study the effects of sarcomeric gene mutations in-silico. We discuss some of the insights that can be gained from computational models of cardiac biomechanics when scaling from molecular states to cellular level.

Effect of Chain Conformation on the Single-Molecule Melting Force in Polymer Single Crystals: Steered Molecular Dynamics Simulations Study

Understanding the relationship between polymer chain conformation as well as the chain composition within the single crystal and the mechanical properties of the corresponding single polymer chain will facilitate the rational design of high performance polymer materials. Here three model systems of polymer single crystals, namely poly(ethylene oxide) (PEO), polyethylene (PE), and nylon-66 (PA66) have been chosen to study the effects of chain conformation, helical (PEO) versus planar zigzag conformation (PE, PA66), and chain composition (PE versus PA66) on the mechanical properties of a single polymer chain. To do that, steered molecular dynamics simulations were performed on those polymer single crystals by pulling individual polymer chains out of the crystals. Our results show that the patterns of force-extension curve as well as the chain moving mode are closely related to the conformation of the polymer chain in the single crystal. In addition, hydrogen bonds can enhance greatly the force required to stretch the polymer chain out of the single crystal. The dynamic breaking and reformation of multivalent hydrogen bonds have been observed for the first time in PA66 at the single molecule level.

Computing Average Passive Forces in Sarcomeres in Length-Ramp Simulations

Passive forces in sarcomeres are mainly related to the giant protein titin. Titin’s extensible region consists of spring-like elements acting in series. In skeletal muscles these elements are the PEVK segment, two distinct immunoglobulin (Ig) domain regions (proximal and distal), and a N2A portion. While distal Ig domains are thought to form inextensible end filaments in intact sarcomeres, proximal Ig domains unfold in a force- and time-dependent manner. In length-ramp experiments of single titin strands, sequential unfolding of Ig domains leads to a typical saw-tooth pattern in force-elongation curves which can be simulated by Monte Carlo simulations. In sarcomeres, where more than a thousand titin strands are arranged in parallel, numerous Monte Carlo simulations are required to estimate the resultant force of all titin filaments based on the non-uniform titin elongations. To simplify calculations, the stochastic model of passive forces is often replaced by linear or non-linear deterministic and phenomenological functions. However, new theories of muscle contraction are based on the hypothesized binding of titin to the actin filament upon activation, and thereby on a prominent role of the structural properties of titin. Therefore, these theories necessitate a detailed analysis of titin forces in length-ramp experiments. In our study we present a simple and efficient alternative to Monte Carlo simulations. Based on a structural titin model, we calculate the exact probability distributions of unfolded Ig domains under length-ramp conditions needed for rigorous analysis of expected forces, distribution of unfolding forces, etc. Due to the generality of our model, the approach is applicable to a wide range of stochastic protein unfolding problems.

We provide a simple and stable algorithm to determine the exact solution of passive forces in a half sarcomere in length-ramp simulations. The approach is applicable to a wide range of stochastic models of protein unfolding.

Atomic resolution probe for allostery in the regulatory thin filament

Calcium binding and dissociation within the cardiac thin filament (CTF) is a fundamental regulator of normal contraction and relaxation. Although the disruption of this complex, allosterically mediated process has long been implicated in human disease, the precise atomic-level mechanisms remain opaque, greatly hampering the development of novel targeted therapies. To address this question, we used a fully atomistic CTF model to test both Ca(2+) binding strength and the energy required to remove Ca(2+) from the N-lobe binding site in WT and mutant troponin complexes that have been linked to genetic cardiomyopathies. This computational approach is combined with measurements of in vitro Ca(2+) dissociation rates in fully reconstituted WT and cardiac troponin T R92L and R92W thin filaments. These human disease mutations represent known substitutions at the same residue, reside at a significant distance from the calcium binding site in cardiac troponin C, and do not affect either the binding pocket affinity or EF-hand structure of the binding domain. Both have been shown to have significantly different effects on cardiac function in vivo. We now show that these mutations independently alter the interaction between the Ca(2+) ion and cardiac troponin I subunit. This interaction is a previously unidentified mechanism, in which mutations in one protein of a complex indirectly affect a third via structural and dynamic changes in a second to yield a pathogenic change in thin filament function that results in mutation-specific disease states. We can now provide atom-level insight that is potentially highly actionable in drug design.

Molecular basis of the mechanical hierarchy in myomesin dimers for sarcomere integrity

Myomesin is one of the most important structural molecules constructing the M-band in the force-generating unit of striated muscle, and a critical structural maintainer of the sarcomere. Using molecular dynamics simulations, we here dissect the mechanical properties of the structurally known building blocks of myomesin, namely α-helices, immunoglobulin (Ig) domains, and the dimer interface at myomesin's 13th Ig domain, covering the mechanically important C-terminal part of the molecule. We find the interdomain α-helices to be stabilized by the hydrophobic interface formed between the N-terminal half of these helices and adjacent Ig domains, and, interestingly, to show a rapid unfolding and refolding equilibrium especially under low axial forces up to ∼ 15 pN. These results support and yield atomic details for the notion of recent atomic-force microscopy experiments, namely, that the unique helices inserted between Ig domains in myomesin function as elastomers and force buffers. Our results also explain how the C-terminal dimer of two myomesin molecules is mechanically outperforming the helices and Ig domains in myomesin and elsewhere, explaining former experimental findings. This study provides a fresh view onto how myomesin integrates elastic helices, rigid immunoglobulin domains, and an extraordinarily resistant dimer into a molecular structure, to feature a mechanical hierarchy that represents a firm and yet extensible molecular anchor to guard the stability of the sarcomere.

A structure-based model fails to probe the mechanical unfolding pathways of the titin I27 domain

We discuss the use of a structure based Cα-Go model and Langevin dynamics to study in detail the mechanical properties and unfolding pathway of the titin I27 domain. We show that a simple Go-model does detect correctly the origin of the mechanical stability of this domain. The unfolding free energy landscape parameters x(u) and ΔG(‡), extracted from dependencies of unfolding forces on pulling speeds, are found to agree reasonably well with experiments. We predict that above v = 10(4) nm/s the additional force-induced intermediate state is populated at an end-to-end extension of about 75 Å. The force-induced switch in the unfolding pathway occurs at the critical pulling speed v(crit) ≈ 10(6)-10(7) nm/s. We argue that this critical pulling speed is an upper limit of the interval where Bell's theory works. However, our results suggest that the Go-model fails to reproduce the experimentally observed mechanical unfolding pathway properly, yielding an incomplete picture of the free energy landscape. Surprisingly, the experimentally observed intermediate state with the A strand detached is not populated in Go-model simulations over a wide range of pulling speeds. The discrepancy between simulation and experiment is clearly seen from the early stage of the unfolding process which shows the limitation of the Go model in reproducing unfolding pathways and deciphering the complete picture of the free energy landscape.

Dissecting the structural determinants for the difference in mechanical stability of silk and amyloid beta-sheet stacks

Stacking of β-sheets results in a protein super secondary structure with remarkable mechanical properties. β-Stacks are the determinants of a silk fiber's resilience and are also the building blocks of amyloid fibrils. While both silk and amyloid-type crystals are known to feature a high resistance against rupture, their structural and mechanical similarities and particularities are yet to be fully understood. Here, we systematically compare the rupture force and stiffness of amyloid and spider silk poly-alanine β-stacks of comparable sizes using Molecular Dynamics simulations. We identify the direction of force application as the primary determinant of the rupture strength; β-sheets in silk are orientated along the fiber axis, i.e. the pulling direction, and consequently require high forces in the several nanoNewton range for shearing β-strands apart, while β-sheets in amyloid are oriented vertically to the fiber, allowing a zipper-like rupture at sub-nanoNewton forces. A secondary factor rendering amyloid β-stacks softer and weaker than their spider silk counterparts is the sub-optimal side-chain packing between β-sheets due to the sequence variations of amyloid-forming proteins as opposed to the perfectly packed poly-alanine β-sheets of silk. Taken together, amyloid fibers can reach the stiffness of silk fibers in spite of their softer and weaker β-sheet arrangement as they are missing a softening amorphous matrix.

Protein high-force pulling simulations yield low-force results

All-atom explicit-solvent molecular dynamics simulations are used to pull with extremely large constant force (750–3000 pN) on three small proteins. The introduction of a nondimensional timescale permits direct comparison of unfolding across all forces. A crossover force of approximately 1100 pN divides unfolding dynamics into two regimes. At higher forces, residues sequentially unfold from the pulling end while maintaining the remainder of the protein force-free. Measurements of hydrodynamic viscous stresses are made easy by the high speeds of unfolding. Using an exact low-Reynolds-number scaling, these measurements can be extrapolated to provide, for the first time, an estimate of the hydrodynamic force on low-force unfolding. Below 1100 pN, but surprisingly still at extremely large applied force, intermediate states and cooperative unfoldings as seen at much lower forces are observed. The force-insensitive persistence of these structures indicates that decomposition into unfolded fragments requires a large fluctuation. This finding suggests how proteins are constructed to resist transient high force. The progression of helix and sheet unfolding is also found to be insensitive to force. The force-insensitivity of key aspects of unfolding opens the possibility that numerical simulations can be accelerated by high applied force while still maintaining critical features of unfolding.

Engineering proteins with enhanced mechanical stability by force-specific sequence motifs

Use of atomic force microscopy (AFM) has recently led to a better understanding of the molecular mechanisms of the unfolding process by mechanical forces; however, the rational design of novel proteins with specific mechanical strength remains challenging. We have approached this problem from a new perspective that generates linear physical-chemical properties (PCP) motifs from a limited AFM data set. Guided by our linear sequence analysis, we designed and analyzed four new mutants of the titin I1 domain with the goal of increasing the domain's mechanical strength. All four mutants could be cloned and expressed as soluble proteins. AFM data indicate that at least two of the mutants have increased molecular mechanical strength. This observation suggests that the PCP method is useful to graft sequences specific for high mechanical stability to weak proteins to increase their mechanical stability, and represents an additional tool in the design of novel proteins besides steered molecular dynamics calculations, coarse grained simulations, and ϕ-value analysis of the transition state.

Tertiary and secondary structure elasticity of a six-Ig titin chain

The protein titin functions as a mechanical spring conferring passive elasticity to muscle. Force spectroscopy studies have shown that titin exhibits several regimes of elasticity. Disordered segments bring about a soft, entropic spring-type elasticity; secondary structures of titin's immunoglobulin-like (Ig-) and fibronectin type III-like (FN-III) domains provide a stiff elasticity. In this study, we demonstrate a third type of elasticity due to tertiary structure and involving domain-domain interaction and reorganization along the titin chain. Through 870 ns of molecular dynamics simulations involving 29,000-635,000 atom systems, the mechanical properties of a six-Ig domain segment of titin (I65-I70), for which a crystallographic structure is available, are probed. The results reveal a soft tertiary structure elasticity. A remarkably accurate statistical mechanical description for this elasticity is derived and applied. Simulations also studied the stiff, secondary structure elasticity of the I65-I70 chain due to the unraveling of its domains and revealed how force propagates along the chain during the secondary structure elasticity response.

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."

Mechanical signaling on the single protein level studied using steered molecular dynamics

Efficient communication between the cell and its external environment is of the utmost importance to the function of multicellular organisms. While signaling events can be generally characterized as information exchange by means of controlled energy conversion, research efforts have hitherto mainly been concerned with mechanisms involving chemical and electrical energy transfer. Here, we review recent computational efforts addressing the function of mechanical force in signal transduction. Specifically, we focus on the role of steered molecular dynamics (SMD) simulations in providing details at the atomic level on a group of protein domains, which play a fundamental role in signal exchange by responding properly to mechanical strain. We start by giving a brief introduction to the SMD technique and general properties of mechanically stable protein folds, followed by specific examples illustrating three general regimes of signal transfer utilizing mechanical energy: purely mechanical, mechanical to chemical, and chemical to mechanical. Whenever possible the physiological importance of the example at hand is stressed to highlight the diversity of the processes in which mechanical signaling plays a key role. We also provide an overview of future challenges and perspectives for this rapidly developing field.

Nanomechanical strength mechanisms of hierarchical biological materials and tissues

Biological protein materials (BPMs), intriguing hierarchical structures formed by assembly of chemical building blocks, are crucial for critical functions of life. The structural details of BPMs are fascinating: They represent a combination of universally found motifs such as alpha-helices or beta-sheets with highly adapted protein structures such as cytoskeletal networks or spider silk nanocomposites. BPMs combine properties like strength and robustness, self-healing ability, adaptability, changeability, evolvability and others into multi-functional materials at a level unmatched in synthetic materials. The ability to achieve these properties depends critically on the particular traits of these materials, first and foremost their hierarchical architecture and seamless integration of material and structure, from nano to macro. Here, we provide a brief review of this field and outline new research directions, along with a review of recent research results in the development of structure-property relationships of biological protein materials exemplified in a study of vimentin intermediate filaments.

Model for stretching and unfolding the giant multidomain muscle protein using single-molecule force spectroscopy

Single-molecule manipulation has allowed the forced unfolding of multidomain proteins. Here we outline a theory that not only explains these experiments but also points out a number of difficulties in their interpretation and makes suggestions for further experiments. For titin we reproduce force-extension curves, the dependence of break force on pulling speed, and break-force distributions and also validate two common experimental views: Unfolding titin Ig domains can be explained as stepwise increases in contour length, and increasing force peaks in native Ig sequences represent a hierarchy of bond strengths. Our theory is valid for essentially any molecule that can be unfolded in atomic force microscopy; as a further example, we present force-extension curves for the unfolding of RNA hairpins.

Cell adhesion to nanoligands: effects of ligand size and concentration in solution

Cells interact with both tethered and motile ligands in their extracellular environment to initiate and regulate signaling, adhesion, and migration. A quantitative and fundamental understanding of these receptor-ligand interactions is necessary for drug discovery, tissue engineering, and biomaterial fabrication. In this paper, we present a mean field approach to quantify the fundamental thermodynamics of interaction between the cell surface receptors and motile ligands in solvent. Our studies show that the free energy of interaction between the receptors and the nanosized ligands depends strongly on the ligand size and the effects at lower and higher concentrations show completely opposite trends that cannot be explained by simple scaling laws. In addition, we also observe various regimes of strong and weak adhesion as a function of ligand size and concentration. Our calculations provide insights into understanding cell-matrix interactions at a fundamental level as well as to identify potential avenues for fabrication of nanoligands for therapeutic and biotechnological purposes.

Using steered molecular dynamics simulations and single-molecule force spectroscopy to guide the rational design of biomimetic modular polymeric materials

This article describes results on using steered molecular dynamics (SMD) simulations and experimental single molecule force spectroscopy (SMFS) to investigate the relationship between hydrogen bonding and mechanical stability of a series of homodimeric β-sheet mimics. The dimers consisting of 4, 6, and 8 H-bonding sites were modeled in explicit chloroform solvent and the rupture force was studied using constant velocity SMD. The role of solvent structuring on the conformation of the dimers was analyzed and showed no significant contribution of chloroform molecules in the rupture event. The simulated stability of the dimers was validated by force data obtained with atomic force microscopy (AFM)-based SMFS in toluene. The computational model for the 8H dimer also offered insight into a possible mismatched dimer intermediate that may contribute to the lower than expected mechanical stability observed by single molecule AFM force studies. In addition, atomic level analysis of the rupture mechanism verified the dependence of mechanical strength on pulling trajectory due to the directional nature of chemical bonding under an applied force. The knowledge gained from this basic study will be used to guide further design of modular polymers having folded nanostructures through strategic programming of weak, non-covalent interactions into polymer backbones.

Stabilization provided by neighboring strands is critical for the mechanical stability of proteins

Single-molecule force spectroscopy studies and steered molecular dynamics simulations have revealed that protein topology and pulling geometry play important roles in determining the mechanical stability of proteins. Most studies have focused on local interactions that are associated with the force-bearing beta-strands. Interactions mediated by neighboring strands are often overlooked. Here we use Top7 and barstar as model systems to illustrate the critical importance of the stabilization effect provided by neighboring beta-strands on the mechanical stability. Using single-molecule atomic force microscopy, we showed that Top7 and barstar, which have similar topology in their force-bearing region, exhibit vastly different mechanical-stability characteristics. Top7 is mechanically stable and unfolds at approximately 150 pN, whereas barstar is mechanically labile and unfolds largely below 50 pN. Steered molecular dynamics simulations revealed that stretching force peels one force-bearing strand away from barstar to trigger unfolding, whereas Top7 unfolds via a substructure-sliding mechanism. This previously overlooked stabilization effect from neighboring beta-strands is likely to be a general mechanism in protein mechanics and can serve as a guideline for the de novo design of proteins with significant mechanical stability and novel protein topology.

Hierarchies, multiple energy barriers, and robustness govern the fracture mechanics of alpha-helical and beta-sheet protein domains

The fundamental fracture mechanisms of biological protein materials remain largely unknown, in part, because of a lack of understanding of how individual protein building blocks respond to mechanical load. For instance, it remains controversial whether the free energy landscape of the unfolding behavior of proteins consists of multiple, discrete transition states or the location of the transition state changes continuously with the pulling velocity. This lack in understanding has thus far prevented us from developing predictive strength models of protein materials. Here, we report direct atomistic simulation that over four orders of magnitude in time scales of the unfolding behavior of alpha-helical (AH) and beta-sheet (BS) domains, the key building blocks of hair, hoof, and wool as well as spider silk, amyloids, and titin. We find that two discrete transition states corresponding to two fracture mechanisms exist. Whereas the unfolding mechanism at fast pulling rates is sequential rupture of individual hydrogen bonds (HBs), unfolding at slow pulling rates proceeds by simultaneous rupture of several HBs. We derive the hierarchical Bell model, a theory that explicitly considers the hierarchical architecture of proteins, providing a rigorous structure-property relationship. We exemplify our model in a study of AHs, and show that 3-4 parallel HBs per turn are favorable in light of the protein's mechanical and thermodynamical stability, in agreement with experimental findings that AHs feature 3.6 HBs per turn. Our results provide evidence that the molecular structure of AHs maximizes its robustness at minimal use of building materials.

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.

Single-Molecule Experiments in Vitro and in Silico

Single-molecule force experiments in vitro enable the characterization of the mechanical response of biological matter at the nanometer scale. However, they do not reveal the molecular mechanisms underlying mechanical function. These can only be readily studied through molecular dynamics simulations of atomic structural models: "in silico" (by computer analysis) single-molecule experiments. Steered molecular dynamics simulations, in which external forces are used to explore the response and function of macromolecules, have become a powerful tool complementing and guiding in vitro single-molecule experiments. The insights provided by in silico experiments are illustrated here through a review of recent research in three areas of protein mechanics: elasticity of the muscle protein titin and the extracellular matrix protein fibronectin; linker-mediated elasticity of the cytoskeleton protein spectrin; and elasticity of ankyrin repeats, a protein module found ubiquitously in cells but with an as-yet unclear function.

Understanding the mechanical behaviour of human enamel from its structural and compositional characteristics

As the hardest and one of the most durable load-bearing tissues of the body, enamel has attracted considerable interest from both material scientists and clinical practitioners due to its excellent mechanical properties. In this paper, possible mechanisms responsible for the excellent mechanical properties of enamel are explored and summarized, which primarily include its hierarchical structure and the nanomechanical properties of the minor protein macromolecular component. Furthermore, additional experimental and numerical evidences to support the assumptions are presented. For example, enamel shows lower elastic modulus, higher energy absorption ability and greater indentation creep behaviour than sintered hydroxyapatite material. All the data indicate that the structural and compositional characteristics of the minor protein component significantly regulate the mechanical properties of enamel to better match its functional needs.

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.

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.

Computational study of coagulation factor VIIa's affinity for phospholipid membranes

The interaction between the gamma-carboxyglutamic acid-rich domain of coagulation factor VIIa (FVIIa), a vitamin-K-dependent enzyme, and phospholipid membranes plays a major role in initiation of blood coagulation. However, despite a high sequence and structural similarity to the Gla domain of other vitamin-K-dependent enzymes with a high membrane affinity, its affinity for negatively charged phospholipids is poor. A few amino acid differences are responsible for this observation. Based on the X-ray structure of lysophosphatidylserine (lysoPS) bound to the Gla domain of bovine prothrombin (Prth), models of the Gla domain of wildtype FVIIa and mutated FVIIa Gla domains in complex with lysoPS were built. Molecular dynamics (MD) and steered molecular dynamics (SMD) simulations on the complexes were applied to investigate the significant difference in the binding affinity. The MD simulation approach provides a structural and dynamic support to the role of P10Q and K32E mutations in the improvement of the membrane contact. Hence, rotation of the Gly11 main chain generated during the MD simulation results in a hydrogen bond with Q10 side chain as well as the appearance of a hydrogen bond between E32 and Q10 forcing the loop harbouring Arg9 and Arg15 to shrink and thereby enhances the accessibility of the phospholipids to the calcium ions. Furthermore, the application of the SMD simulation method to dissociate C6-lysoPS from a series of Gla domain models exhibits a ranking of the rupture force that can be useful in the interpretation of the PS interaction with Gla domains. Finally, adiabatic mapping of Gla6 residue in FVIIa with or without insertion of Tyr4 confirms the critical role of the insertion on the conformation of the side chain Gla6 in FVIIa and the corresponding Gla7 in Prth.

Mechanical strength of the titin Z1Z2-telethonin complex

Using molecular dynamics simulations, we have explored the mechanical strength of the titin Z1Z2-telethonin complex, namely, its ability to bear strong forces such as those encountered during passive muscle stretch. Our results show that not only does this complex resist considerable mechanical force through beta strand crosslinking, suggesting that telethonin is an important component of the N-terminal titin anchor, but also that telethonin distributes these forces between its two joined titin Z2 domains to protect the proximal Z1 domains from bearing too much stress. Our simulations also reveal that without telethonin, apo-titin Z1Z2 exhibits significantly decreased resistance to mechanical stress, and that the N-terminal segment of telethonin (residues 1-89) does not exhibit a stable fold conformation when it is unbound from titin Z1Z2. Consequently, our study sheds light on a key but little studied architectural feature of biological cells-the existence of strong mechanical links that glue separate proteins together.

Mechanotransduction involving multimodular proteins: converting force into biochemical signals

Cells can sense and transduce a broad range of mechanical forces into distinct sets of biochemical signals that ultimately regulate cellular processes, including adhesion, proliferation, differentiation, and apoptosis. Deciphering at the nanoscale the design principles by which sensory elements are integrated into structural protein motifs whose conformations can be switched mechanically is crucial to understand the process of transduction of force into biochemical signals that are then integrated to regulate mechanoresponsive pathways. While the major focus in the search for mechanosensory units has been on membrane proteins such as ion channels, integrins, and associated cytoplasmic complexes, a multimodular design of tandem repeats of various structural motifs is ubiquitously found among extracellular matrix proteins, as well as cell adhesion molecules, and among many intracellular players that physically link transmembrane proteins to the contractile cytoskeleton. Single-molecule studies have revealed an unexpected richness of mechanosensory motifs, including force-regulated conformational changes of loop-exposed molecular recognition sites, intermediate states in the unraveling pathway that might either expose cryptic binding or phosphorylation sites, or regions that display enzymatic activity only when unmasked by force. Insights into mechanochemical signal conversion principles will also affect various technological fields, from biotechnology to tissue engineering and drug development.

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.

Molecular dynamics simulations of forced conformational transitions in 1,6-linked polysaccharides

Recent atomic force microscopy stretching measurements of single polysaccharide molecules suggest that their elasticity is governed by force-induced conformational transitions of the pyranose ring. However, the mechanism of these transitions and the mechanics of the pyranose ring are not fully understood. Here we use steered molecular dynamics simulations of the stretching process to unravel the mechanism of forced conformational transitions in 1,6 linked polysaccharides. In contrast to most sugars, 1,6 linked polysaccharides have an extra bond in their inter-residue linkage, C5-C6, around which restricted rotations occur and this additional degree of freedom increases the mechanical complexity of these polymers. By comparing the computational results with the atomic force microscopy data we determine that forced rotations around the C5-C6 bond have a significant and different impact on the elasticity of alpha- and beta-linked polysaccharides. Beta-linkages of a polysaccharide pustulan force the rotation around the C5-C6 bonds and produce a Hookean-like elasticity but do not affect the conformation of the pyranose rings. However, alpha-linkages of dextran induce compound conformational transitions that include simultaneous rotations around the C5-C6 bonds and chair-boat transitions of the pyranose rings. These previously not-recognized transitions are responsible for the characteristic plateau in the force-extension relationship of dextran.

Multiple sources of passive stress relaxation in muscle fibres

The forces developed during stretch of nonactivated muscle consist of velocity-sensitive (viscous/viscoelastic) and velocity-insensitive (elastic) components. At the myofibrillar level, the elastic-force component has been described in terms of the entropic-spring properties of the giant protein titin, but entropic elasticity cannot account for viscoelastic properties, such as stress relaxation. Here we examine the contribution of titin to passive stress relaxation of isolated rat-cardiac myofibrils depleted of actin by gelsolin treatment. Monte Carlo simulations show that, up to approximately 5 s after a stretch, the time course of stress relaxation can be described assuming unfolding of 1-2 immunoglobulin domains per titin molecule. For extended periods of stress relaxation, the simulations failed to correctly describe the myofibril data, suggesting that in situ, titin-Ig domains may be more stable than predicted in earlier single-molecule atomic-force-microscopy studies. The reasons behind this finding remain unknown; simply assuming a reduced unfolding probability of domains--an effect found here by AFM force spectroscopy on titin-Ig domains in the presence of a chaperone, alpha-B-crystallin--did not help correctly simulate the time course of stress relaxation. We conclude that myofibrillar stress relaxation likely has multiple sources. Evidence is provided that in intact myofibrils, an initial, rapid phase of stress relaxation results from viscous resistance due to the presence of actin filaments.

Mechanically induced titin kinase activation studied by force-probe molecular dynamics simulations

The conversion of mechanical stress into a biochemical signal in a muscle cell requires a force sensor. Titin kinase, the catalytic domain of the elastic muscle protein titin, has been suggested as a candidate. Its activation requires major conformational changes resulting in the exposure of its active site. Here, force-probe molecular dynamics simulations were used to obtain insight into the tension-induced activation mechanism. We find evidence for a sequential mechanically induced opening of the catalytic site without complete domain unfolding. Our results suggest the rupture of two terminal beta-sheets as the primary unfolding steps. The low force resistance of the C-terminal relative to the N-terminal beta-sheet is attributed to their different geometry. A subsequent rearrangement of the autoinhibitory tail is seen to lead to the exposure of the active site, as is required for titin kinase activity. These results support the hypothesis of titin kinase as a force sensor.

Evidence for a direct but sequential binding of titin to tropomyosin and actin filaments

Titin is a giant molecule that spans half a sarcomere, establishing several specific bindings with both structural and contractile myofibrillar elements. It has been demonstrated that this giant protein plays a major role in striated muscle cell passive tension and contractile filament alignment. The in vitro interaction of titin with a new partner (tropomyosin) reported here is reinforced by our recent in vitro motility study using reconstituted Ca-regulated thin filaments, myosin and a native 800-kDa titin fragment. In the presence of the tropomyosin-troponin complex, the actin filament movement onto coated S1 is improved by the titin fragment. Here, we found that two purified native titin fragments of 150 and 800 kDa, covering respectively the N1-line and the N2-line/PEVK region in the I-band and known to contain actin-binding sites, directly bind tropomyosin in the absence of actin. We have also shown that binding of the 800-kDa fragment with filamentous actin inhibited the subsequent interaction of tropomyosin with actin, as judged by cosedimentation. However, this was not the case if the complex of actin and tropomyosin was formed before the addition of the 800-kDa fragment. We thus conclude that a sequential arrangement of contacts exists between parts of the titin I-band region, tropomyosin and actin in the thin filament.

Tuning the Mechanical Stability of Fibronectin Type III Modules through Sequence Variations

Cells can switch the functional states of extracellular matrix proteins by stretching them while exerting mechanical force. Using steered molecular dynamics, we investigated how the mechanical stability of FnIII modules from the cell adhesion protein fibronectin is affected by natural variations in their amino acid sequences. Despite remarkably similar tertiary structures, FnIII modules share low sequence homology. Conversely, the sequence homology for the same FnIII module across multiple species is notably higher, suggesting that sequence variability is functionally significant. Our studies find that the mechanical stability of FnIII modules can be tuned through substitutions of just a few key amino acids by altering access of water molecules to hydrogen bonds that break early in the unfolding pathway. Furthermore, the FnIII hierarchy of mechanical unfolding can be changed by environmental conditions, such as pH for FnIII10, or by forming complexes with other molecules, such as heparin binding to FnIII13.