Mechanical network in titin immunoglobulin from force distribution analysis

JEDI: A versatile code for strain analysis of molecular and periodic systems under deformation

Stretching or compression can induce significant energetic, geometric, and spectroscopic changes in materials. To fully exploit these effects in the design of mechano- or piezo-chromic materials, self-healing polymers, and other mechanoresponsive devices, a detailed knowledge about the distribution of mechanical strain in the material is essential. Within the past decade, Judgement of Energy DIstribution (JEDI) analysis has emerged as a useful tool for this purpose. Based on the harmonic approximation, the strain energy in each bond length, bond angle, and dihedral angle of the deformed system is calculated using quantum chemical methods. This allows the identification of the force-bearing scaffold of the system, leading to an understanding of mechanochemical processes at the most fundamental level. Here, we present a publicly available code that generalizes the JEDI analysis, which has previously only been available for isolated molecules. Now, the code has been extended to two- and three-dimensional periodic systems, supramolecular clusters, and substructures of chemical systems under various types of deformation. Due to the implementation of JEDI into the Atomic Simulation Environment, the JEDI analysis can be interfaced with a plethora of program packages that allow the calculation of electronic energies for molecular systems and systems with periodic boundary conditions. The automated generation of a color-coded three-dimensional structure via the Visual Molecular Dynamics program allows insightful visual analyses of the force-bearing scaffold of the strained system.

Tuning Protein Hydrogel Mechanics through Modulation of Nanoscale Unfolding and Entanglement in Postgelation Relaxation

Globular folded proteins are versatile nanoscale building blocks to create biomaterials with mechanical robustness and inherent biological functionality due to their specific and well-defined folded structures. Modulating the nanoscale unfolding of protein building blocks during network formation (in situ protein unfolding) provides potent opportunities to control the protein network structure and mechanics. Here, we control protein unfolding during the formation of hydrogels constructed from chemically cross-linked maltose binding protein using ligand binding and the addition of cosolutes to modulate protein kinetic and thermodynamic stability. Bulk shear rheology characterizes the storage moduli of the bound and unbound protein hydrogels and reveals a correlation between network rigidity, characterized as an increase in the storage modulus, and protein thermodynamic stability. Furthermore, analysis of the network relaxation behavior identifies a crossover from an unfolding dominated regime to an entanglement dominated regime. Control of in situ protein unfolding and entanglement provides an important route to finely tune the architecture, mechanics, and dynamic relaxation of protein hydrogels. Such predictive control will be advantageous for future smart biomaterials for applications which require responsive and dynamic modulation of mechanical properties and biological function.

Contribution of Hydrophobic Interactions to Protein Mechanical Stability

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

Electrostatic interactions contribute to the control of intramolecular thiol-disulfide isomerization in a protein

The roles of structural factors and of electrostatic interactions with the environment on the outcome of thiol-disulfide exchange reactions were investigated in a mutated immunoglobulin domain (I27*) under mechanical stress. An extensive ensemble of molecular dynamics trajectories was generated by means of QM/MM simulations for a total sampling of 5.7 μs. A significant number of thiol-disulfide exchanges were observed, and the Cys32 thiolate preferred to attack Cys55 over Cys24, in agreement with previous experimental and computational studies. The structural features as well as electronic structures of the thiol-disulfide system along the reaction were analyzed, as were the electrostatic interactions with the environment. The previous findings of better accessibility of Cys55 were confirmed. Additionally, the reaction was found to be directed by the electrostatic interactions of the involved sulfur atoms with the molecular environment. The relationships of atomic charges, which stem from the electrostatic interactions, lead to the kinetic preference of the attack on Cys55. Further, QM/MM metadynamics simulations of thiol-disulfide exchange in a small model system with varied artificial external electric potentials revealed changes in reaction kinetics of the same magnitude as in I27*. Therefore, the electrostatic interactions are confirmed to play a role in the regioselectivity of the thiol-disulfide exchange reactions in the protein.

Unexpected Low Mechanical Stability of Titin I27 Domain at Physiologically Relevant Temperature

The extensively studied immunoglobulin (Ig) domain I27 of the giant force-bearing protein titin has provided a basis for our current understanding of the structural stability, dynamics, and function of the numerous mechanically stretched Ig domains in the force-bearing I-band of titin. The current consensus is that titin I27 has a high mechanical stability characterized by very low unfolding rate (<10^-3 s^-1) in physiological force range and high unfolding forces (>100 pN) at typical physiological force loading rates from experiments at typical laboratory temperatures. Here, we report that when the temperature is increased from 23 to 37 °C, the unfolding rate of I27 drastically increases by ∼100-fold at the physiological level of forces, indicating a low mechanical stability of I27 at physiological conditions. The result provides new insights into the structural states and the associated functions of I27 and other similar titin I-band Ig domains.

Bios2cor: an R package integrating dynamic and evolutionary correlations to identify functionally important residues in proteins

SUMMARY

Both dynamic correlations in protein sidechain motions during molecular dynamics (MD) simulations and evolutionary correlations in multiple sequence alignments (MSA) of homologous proteins may reveal functionally important residues. We developed the R package Bios2cor that provides a unique framework to investigate and, possibly, integrate both analyses. Bios2cor starts with an MSA or a MD trajectory and computes correlation/covariation scores between positions in the MSA or between sidechain dihedral angles or rotamers in the MD trajectory. In addition, Bios2cor provides a variety of tools for the analysis, the visualization and the interpretation of the data.

AVAILABILITY

The R package Bios2cor is available from the Comprehensive R Archive Network, at http://cran.r-project.org/ web/packages/Bios2cor/index.html.

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.

The Work of Titin Protein Folding as a Major Driver in Muscle Contraction

Single-molecule atomic force microscopy and magnetic tweezers experiments have demonstrated that titin immunoglobulin (Ig) domains are capable of folding against a pulling force, generating mechanical work that exceeds that produced by a myosin motor. We hypothesize that upon muscle activation, formation of actomyosin cross bridges reduces the force on titin, causing entropic recoil of the titin polymer and triggering the folding of the titin Ig domains. In the physiological force range of 4-15 pN under which titin operates in muscle, the folding contraction of a single Ig domain can generate 200% of the work of entropic recoil and occurs at forces that exceed the maximum stalling force of single myosin motors. Thus, titin operates like a mechanical battery, storing elastic energy efficiently by unfolding Ig domains and delivering the charge back by folding when the motors are activated during a contraction. We advance the hypothesis that titin folding and myosin activation act as inextricable partners during muscle contraction.

Implementing the mechanical force into the conceptual DFT framework: understanding and predicting molecular mechanochemical properties

Studying mechanochemical properties through the implementation of the mechanical force into the conceptual DFT framework (E = E[N,v,F_ext]).

Probing molecular forces in multi-component physiological membranes

Biological membranes are remarkably heterogeneous, composed of diverse lipid mixtures with distinct chemical structure and composition. By combining molecular dynamics simulations and the newly developed Lipid-Force Distribution Analysis (L-FDA), we explore force transmission in complex multi-component membrane models mimicking eukaryotic organelles. We found that the chemical-moiety based segmentation at membrane interfaces revealed a distinctive distribution of bonded and non-bonded forces in diverse membrane environment. Our molecular stress analysis could have far-reaching implications in describing the relationship between membrane mechanical properties and functional states of chemically distinct lipids.

Accessibility explains preferred thiol-disulfide isomerization in a protein domain

Disulfide bonds are key stabilizing and yet potentially labile cross-links in proteins. While spontaneous disulfide rearrangement through thiol-disulfide exchange is increasingly recognized to play an important physiological role, its molecular determinants are still largely unknown. Here, we used a novel hybrid Monte Carlo and Molecular Dynamics scheme to elucidate the molecular principles of thiol-disulfide exchange in proteins, for a mutated immunoglobulin domain as a model system. Unexpectedly, using simple proximity as the criterion for thiol-disulfide exchange, our method correctly predicts the experimentally observed regiospecificity and selectivity of the cysteine-rich protein. While redox reactivity has been examined primarily on the level of transition states and activation barriers, our results argue for accessibility of the disulfide by the attacking thiol given the highly dynamic and sterically demanding protein as a major bottleneck of thiol-disulfide exchange. This scenario may be similarly at play in other proteins with or without an evolutionarily designed active site.

Effect of directional pulling on mechanical protein degradation by ATP-dependent proteolytic machines

AAA+ proteases and remodeling machines couple hydrolysis of ATP to mechanical unfolding and translocation of proteins following recognition of sequence tags called degrons. Here, we use single-molecule optical trapping to determine the mechanochemistry of two AAA+ proteases, Escherichia coli ClpXP and ClpAP, as they unfold and translocate substrates containing multiple copies of the titin^I27 domain during degradation initiated from the N terminus. Previous studies characterized degradation of related substrates with C-terminal degrons. We find that ClpXP and ClpAP unfold the wild-type titin^I27 domain and a destabilized variant far more rapidly when pulling from the N terminus, whereas translocation speed is reduced only modestly in the N-to-C direction. These measurements establish the role of directionality in mechanical protein degradation, show that degron placement can change whether unfolding or translocation is rate limiting, and establish that one or a few power strokes are sufficient to unfold some protein domains.

Quantum Chemical Strain Analysis For Mechanochemical Processes

The use of mechanical force to initiate a chemical reaction is an efficient alternative to the conventional sources of activation energy, i.e., heat, light, and electricity. Applications of mechanochemistry in academic and industrial laboratories are diverse, ranging from chemical syntheses in ball mills and ultrasound baths to direct activation of covalent bonds using an atomic force microscope. The vectorial nature of force is advantageous because specific covalent bonds can be preconditioned for rupture by selective stretching. However, the influence of mechanical force on single molecules is still not understood at a fundamental level, which limits the applicability of mechanochemistry. As a result, many chemists still resort to rules of thumb when it comes to conducting mechanochemical syntheses. In this Account, we show that comprehension of mechanochemistry at the molecular level can be tremendously advanced by quantum chemistry, in particular by using quantum chemical force analysis tools. One such tool is the JEDI (Judgement of Energy DIstribution) analysis, which provides a convenient approach to analyze the distribution of strain energy in a mechanically deformed molecule. Based on the harmonic approximation, the strain energy contribution is calculated for each bond length, bond angle and dihedral angle, thus providing a comprehensive picture of how force affects molecules. This Account examines the theoretical foundations of quantum chemical force analysis and provides a critical overview of the performance of the JEDI analysis in various mechanochemical applications. We explain in detail how this analysis tool is to be used to identify the "force-bearing scaffold" of a distorted molecule, which allows both the rationalization and the optimization of diverse mechanochemical processes. More precisely, we show that the inclusion of every bond, bending and torsion of a molecule allows a particularly insightful discussion of the distribution of mechanical strain in deformed molecules. We illustrate the usefulness of the JEDI analysis by rationalizing the finding that a knot tremendously weakens a polymer strand via a "choking" motion of the torsions in the curved part of the knot, thus leading to facilitated bond rupture in the immediate vicinity of the knot. Moreover, we demonstrate that the JEDI analysis can be exploited to devise methods for the stabilization of inherently strained molecules. In addition to applications in the electronic ground state, the JEDI analysis can also be used in the electronically excited state to determine the mechanical energy that a molecular photoswitch can release into its environment during photoisomerization. This approach allows the quantification of the mechanical efficiency of a photoswitch, i.e., the part of the energy that becomes available for the motion into a specific direction, which enables us to judge whether a photoswitch is capable of performing a desired switching function.

One-Way Allosteric Communication between the Two Disulfide Bonds in Tissue Factor

Tissue factor (TF) is a transmembrane glycoprotein that plays distinct roles in the initiation of extrinsic coagulation cascade and thrombosis. TF contains two disulfide bonds, one each in the N-terminal and C-terminal extracellular domains. The C-domain disulfide, Cys186-Cys209, has a -RHStaple configuration in crystal structures, suggesting that this disulfide carries high pre-stress. The redox state of this disulfide has been proposed to regulate TF encryption/decryption. Ablating the N-domain Cys49-Cys57 disulfide bond was found to increase the redox potential of the Cys186-Cys209 bond, implying an allosteric communication between the domains. Using molecular dynamics simulations, we observed that the Cys186-Cys209 disulfide bond retained the -RHStaple configuration, whereas the Cys49-Cys57 disulfide bond fluctuated widely. The Cys186-Cys209 bond featured the typical -RHStaple disulfide properties, such as a longer S-S bond length, larger C-S-S angles, and higher bonded prestress, in comparison to the Cys49-Cys57 bond. Force distribution analysis was used to sense the subtle structural changes upon ablating the disulfide bonds, and allowed us to identify a one-way allosteric communication mechanism from the N-terminal to the C-terminal domain. We propose a force propagation pathway using a shortest-pathway algorithm, which we suggest is a useful method for searching allosteric signal transduction pathways in proteins. As a possible explanation for the pathway being one-way, we identified a pronounced lower degree of conformational fluctuation, or effectively higher stiffness, in the N-terminal domain. Thus, the changes of the rigid domain (N-terminal domain) can induce mechanical force propagation to the soft domain (C-terminal domain), but not vice versa.

Advances in Quantum Mechanochemistry: Electronic Structure Methods and Force Analysis

In quantum mechanochemistry, quantum chemical methods are used to describe molecules under the influence of an external force. The calculation of geometries, energies, transition states, reaction rates, and spectroscopic properties of molecules on the force-modified potential energy surfaces is the key to gain an in-depth understanding of mechanochemical processes at the molecular level. In this review, we present recent advances in the field of quantum mechanochemistry and introduce the quantum chemical methods used to calculate the properties of molecules under an external force. We place special emphasis on quantum chemical force analysis tools, which can be used to identify the mechanochemically relevant degrees of freedom in a deformed molecule, and spotlight selected applications of quantum mechanochemical methods to point out their synergistic relationship with experiments.

Release of Entropic Spring Reveals Conformational Coupling Mechanism in the ABC Transporter BtuCD-F

Substrate translocation by ATP-binding cassette (ABC) transporters involves coupling of ATP binding and hydrolysis in the nucleotide-binding domains (NBDs) to conformational changes in the transmembrane domains. We used molecular dynamics simulations to investigate the atomic-level mechanism of conformational coupling in the ABC transporter BtuCD-F, which imports vitamin B12 across the inner membrane of Escherichia coli. Our simulations show how an engineered disulfide bond across the NBD dimer interface reduces conformational fluctuations and hence configurational entropy. As a result, the disulfide bond is under substantial mechanical stress. Releasing this entropic spring, as is the case in the wild-type transporter, combined with analyzing the pairwise forces between individual residues, unravels the coupling mechanism. The identified pathways along which force is propagated from the NBDs via the coupling helix to the transmembrane domains are composed of highly conserved residues, underlining their functional relevance. This study not only reveals the details of conformational coupling in BtuCD-F, it also provides a promising approach to other long-range conformational couplings, e.g., in ABC exporters or other ATP-driven molecular machines.

Spectroscopic Monitoring of Mechanical Forces during Protein Folding by using Molecular Force Probes

Detailed folding pathways of proteins are still largely unknown. Real-time monitoring of mechanical forces acting in proteins during structural transitions would provide deep insights into these highly complex processes. Here, we propose two molecular force probes that can be incorporated into the protein backbone to gain insight into the magnitude and direction of mechanical forces acting in proteins during natural folding and unfolding through their optical spectroscopic response. In fact, changes in the infrared and Raman spectra are proportional to the mechanical force deforming the force probes, and the relevant bands can be intensified and shifted to a transparent window in the protein spectrum by isotopic substitution. As a result, the proposed molecular force probes can act as "force rulers", allowing the spectroscopic observation and measurement of mechanical forces acting within the proteins under natural conditions without external perturbation.

Some studies on generalized coordinate sets for polyatomic molecules

Generalized coordinates are widely used in various analyses of the trajectories of polyatomic molecules from molecular dynamics simulations, such as normal mode analysis and force distribution analysis. Here, we presented detailed discussions on the properties of some specific sets of generalized coordinates, which separate translational, rotational, and vibrational motions of a molecule from one another once the trajectories of dynamical systems are known. Efficient methods were suggested for estimating the transformation matrix between generalized and Cartesian coordinates. Some properties of the well-known BAT coordinates (bond length, angle, and torsional coordinates) were discussed as well.

Geometry Dynamics of α -Helices in Different Class I Major Histocompatibility Complexes

MHC α-helices form the antigen-binding cleft and are of particular interest for immunological reactions. To monitor these helices in molecular dynamics simulations, we applied a parsimonious fragment-fitting method to trace the axes of the α-helices. Each resulting axis was fitted by polynomials in a least-squares sense and the curvature integral was computed. To find the appropriate polynomial degree, the method was tested on two artificially modelled helices, one performing a bending movement and another a hinge movement. We found that second-order polynomials retrieve predefined parameters of helical motion with minimal relative error. From MD simulations we selected those parts of α-helices that were stable and also close to the TCR/MHC interface. We monitored the curvature integral, generated a ruled surface between the two MHC α-helices, and computed interhelical area and surface torsion, as they changed over time. We found that MHC α-helices undergo rapid but small changes in conformation. The curvature integral of helices proved to be a sensitive measure, which was closely related to changes in shape over time as confirmed by RMSD analysis. We speculate that small changes in the conformation of individual MHC α-helices are part of the intrinsic dynamics induced by engagement with the TCR.

Mapping Mechanical Force Propagation through Biomolecular Complexes

Here we employ single-molecule force spectroscopy with an atomic force microscope (AFM) and steered molecular dynamics (SMD) simulations to reveal force propagation pathways through a mechanically ultrastable multidomain cellulosome protein complex. We demonstrate a new combination of network-based correlation analysis supported by AFM directional pulling experiments, which allowed us to visualize stiff paths through the protein complex along which force is transmitted. The results implicate specific force-propagation routes nonparallel to the pulling axis that are advantageous for achieving high dissociation forces.

On the use of different coordinate systems in mechanochemical force analyses

Force analyses are crucial for a comprehensive understanding of mechanochemical processes. The choice of coordinate system in these kinds of analyses is a nontrivial task that determines the quality and validity of the obtained results. Here, we study the suitability of different sets of coordinates for mechanical force analyses, i.e., normal modes, delocalized internal, redundant internal, and Z-matrix coordinates. After discussing the theoretical foundations of force analyses using different coordinate systems, we investigate a number of test molecules. We show that normal modes and Z-matrix coordinates deliver useful results only if certain requirements are fulfilled and that only redundant internal coordinates yield meaningful results in all cases.

Energy exchange network of inter-residue interactions within a thermally fluctuating protein molecule: A computational study

Protein function is regulated not only by the structure but also by physical dynamics and thermal fluctuations. We have developed the computer program, CURrent calculation for proteins (CURP), for the flow analysis of physical quantities within thermally fluctuating protein media. The CURP program was used to calculate the energy flow within the third PDZ domain of the neuronal protein PSD-95, and the results were used to illustrate the energy exchange network of inter-residue interactions based on atomistic molecular dynamics simulations. The removal of the α3 helix is known to decrease ligand affinity by 21-fold without changing the overall protein structure; nevertheless, we demonstrated that the helix constitutes an essential part of the network graph.

A quantitative quantum-chemical analysis tool for the distribution of mechanical force in molecules

The promising field of mechanochemistry suffers from a general lack of understanding of the distribution and propagation of force in a stretched molecule, which limits its applicability up to the present day. In this article, we introduce the JEDI (Judgement of Energy DIstribution) analysis, which is the first quantum chemical method that provides a quantitative understanding of the distribution of mechanical stress energy among all degrees of freedom in a molecule. The method is carried out on the basis of static or dynamic calculations under the influence of an external force and makes use of a Hessian matrix in redundant internal coordinates (bond lengths, bond angles, and dihedral angles), so that all relevant degrees of freedom of a molecule are included and mechanochemical processes can be interpreted in a chemically intuitive way. The JEDI method is characterized by its modest computational effort, with the calculation of the Hessian being the rate-determining step, and delivers, except for the harmonic approximation, exact ab initio results. We apply the JEDI analysis to several example molecules in both static quantum chemical calculations and Born-Oppenheimer Molecular Dynamics simulations in which molecules are subject to an external force, thus studying not only the distribution and the propagation of strain in mechanically deformed systems, but also gaining valuable insights into the mechanochemically induced isomerization of trans-3,4-dimethylcyclobutene to trans,trans-2,4-hexadiene. The JEDI analysis can potentially be used in the discussion of sonochemical reactions, molecular motors, mechanophores, and photoswitches as well as in the development of molecular force probes.

Calculation and visualization of atomistic mechanical stresses in nanomaterials and biomolecules

Many biomolecules have machine-like functions, and accordingly are discussed in terms of mechanical properties like force and motion. However, the concept of stress, a mechanical property that is of fundamental importance in the study of macroscopic mechanics, is not commonly applied in the biomolecular context. We anticipate that microscopical stress analyses of biomolecules and nanomaterials will provide useful mechanistic insights and help guide molecular design. To enable such applications, we have developed Calculator of Atomistic Mechanical Stress (CAMS), an open-source software package for computing atomic resolution stresses from molecular dynamics (MD) simulations. The software also enables decomposition of stress into contributions from bonded, nonbonded and Generalized Born potential terms. CAMS reads GROMACS topology and trajectory files, which are easily generated from AMBER files as well; and time-varying stresses may be animated and visualized in the VMD viewer. Here, we review relevant theory and present illustrative applications.

Identification of allosteric disulfides from prestress analysis

Disulfide bonds serve to form physical cross-links between residues in protein structures, thereby stabilizing the protein fold. Apart from this purely structural role, they can also be chemically active, participating in redox reactions, and they may even potentially act as allosteric switches controlling protein functions. Specific types of disulfide bonds have been identified in static protein structures from their distinctive pattern of dihedral bond angles, and the allosteric function of such bonds is purported to be related to the torsional strain they store. Using all-atom molecular-dynamics simulations for ∼700 disulfide bonded proteins, we analyzed the intramolecular mechanical forces in 20 classes of disulfide bonds. We found that two particular classes, the -RHStaple and the -/+RHHook disulfides, are indeed more stressed than other disulfide bonds, but the stress is carried primarily by stretching of the S-S bond and bending of the neighboring bond angles, rather than by dihedral torsion. This stress corresponds to a tension force of magnitude ∼200 pN, which is balanced by repulsive van der Waals interactions between the cysteine Cα atoms. We confirm stretching of the S-S bond to be a general feature of the -RHStaples and the -/+RHHooks by analyzing ∼20,000 static protein structures. Given that forced stretching of S-S bonds is known to accelerate their cleavage, we propose that prestress of allosteric disulfide bonds has the potential to alter the reactivity of a disulfide, thereby allowing us to readily switch between functional states.

Using THz time-scale infrared spectroscopy to examine the role of collective, thermal fluctuations in the formation of myoglobin allosteric communication pathways and ligand specificity

In this investigation we use THz time-scale spectroscopy to conduct an initial set of studies on myoglobin with the aim of providing further insight into the global, collective thermal fluctuations in the protein that have been hypothesized to play a prominent role in the dynamic formation of transient ligand channels as well as in shaping the molecular level basis for ligand discrimination. Using the two ligands O2 and CO, we have determined that the perturbation from the heme-ligand complex has a strong influence on the characteristics of the myoglobin collective dynamics that are excited upon binding. Further, the differences detected in the collective protein motions in Mb-O2 compared with those in Mb-CO appear to be intimately tied with the pathways of long-range allosteric communication in the protein, which ultimately determine the trajectories selected by the respective ligands on the path to and from the heme-binding cavity.

Structure of giant muscle proteins

Giant muscle proteins (e.g., titin, nebulin, and obscurin) play a seminal role in muscle elasticity, stretch response, and sarcomeric organization. Each giant protein consists of multiple tandem structural domains, usually arranged in a modular fashion spanning 500 kDa to 4 MDa. Although many of the domains are similar in structure, subtle differences create a unique function of each domain. Recent high and low resolution structural and dynamic studies now suggest more nuanced overall protein structures than previously realized. These findings show that atomic structure, interactions between tandem domains, and intrasarcomeric environment all influence the shape, motion, and therefore function of giant proteins. In this article we will review the current understanding of titin, obscurin, and nebulin structure, from the atomic level through the molecular level.

Improving single molecule force spectroscopy through automated real-time data collection and quantification of experimental conditions

The benefits of single molecule force spectroscopy (SMFS) clearly outweigh the challenges which include small sample sizes, tedious data collection and introduction of human bias during the subjective data selection. These difficulties can be partially eliminated through automation of the experimental data collection process for atomic force microscopy (AFM). Automation can be accomplished using an algorithm that triages usable force-extension recordings quickly with positive and negative selection. We implemented an algorithm based on the windowed fast Fourier transform of force-extension traces that identifies peaks using force-extension regimes to correctly identify usable recordings from proteins composed of repeated domains. This algorithm excels as a real-time diagnostic because it involves <30 ms computational time, has high sensitivity and specificity, and efficiently detects weak unfolding events. We used the statistics provided by the automated procedure to clearly demonstrate the properties of molecular adhesion and how these properties change with differences in the cantilever tip and protein functional groups and protein age.

Protein mechanics: how force regulates molecular function

BACKGROUND

Regulation of proteins is ubiquitous and vital for any organism. Protein activity can be altered chemically, by covalent modifications or non-covalent binding of co-factors. Mechanical forces are emerging as an additional way of regulating proteins, by inducing a conformational change or by partial unfolding.

SCOPE

We review some advances in experimental and theoretical techniques to study protein allostery driven by mechanical forces, as opposed to the more conventional ligand driven allostery. In this respect, we discuss recent single molecule pulling experiments as they have substantially augmented our view on the protein allostery by mechanical signals in recent years. Finally, we present a computational analysis technique, Force Distribution Analysis, that we developed to reveal allosteric pathways in proteins.

MAJOR CONCLUSIONS

Any kind of external perturbation, being it ligand binding or mechanical stretching, can be viewed as an external force acting on the macromolecule, rendering force-based experimental or computational techniques, a very general approach to the mechanics involved in protein allostery.

GENERAL SIGNIFICANCE

This unifying view might aid to decipher how complex allosteric protein machineries are regulated on the single molecular level.

Isopeptide bonds mechanically stabilize spy0128 in bacterial pili

Pili on the surface of Streptococcus pyogenes play a crucial role in adhesion to and colonization in human cells. The major pilin subunit, Spy0128, features intramolecular covalent isopeptide bonds that autocatalytically form between the side chains of lysine and asparagine residues and are regarded as important factors in conveying structural stability. In support of this notion, single-molecule force spectroscopy experiments with Spy0128 recently demonstrated the inextensibility of these bonds under mechanical load. However, the molecular determinants of their apparent absolute durability remain unknown. Here, we studied the impact of the isopeptide bond in the Spy0128 C-terminal domain on the mechanical properties of this subunit using force-probe molecular dynamics simulations and force distribution analysis. Even in the presence of the covalent cross-link, the pili β-sandwich domain undergoes partial unfolding, albeit at ∼50% higher rupture forces and with the ability to rapidly refold on the nanosecond timescale. We find that the isopeptide bond is located right at the point of stress concentration in the protein, leading to relative, yet not absolute, mechanical stabilization by the additional cross-link. Our findings indicate how the isopeptide bond enhances the mechanical stability and refolding capability at the molecular level, ensuring that the domain remains predominantly in a potentially adhesive conformation.

Time-resolved force distribution analysis

Background

Biomolecules or other complex macromolecules undergo conformational transitions upon exposure to an external perturbation such as ligand binding or mechanical force. To follow fluctuations in pairwise forces between atoms or residues during such conformational changes as observed in Molecular Dynamics (MD) simulations, we developed Time-Resolved Force Distribution Analysis (TRFDA).

Results

The implementation focuses on computational efficiency and low-memory usage and, along with the wide range of output options, makes possible time series analysis of pairwise forces variation in long MD simulations and for large molecular systems. It also provides an exact decomposition of pairwise forces resulting from 3- and 4-body potentials and a unified treatment of pairwise forces between atoms or residues. As a proof of concept, we present a stress analysis during unfolding of ubiquitin in a force-clamp MD simulation.

Conclusions

TRFDA can be used, among others, in tracking signal propagation at atomic level, for characterizing dynamical intermolecular interactions (e.g. protein-ligand during flexible docking), in development of force fields and for following stress distribution during conformational changes.

Single molecule force spectroscopy on titin implicates immunoglobulin domain stability as a cardiac disease mechanism

Titin plays crucial roles in sarcomere organization and cardiac elasticity by acting as an intrasarcomeric molecular spring. A mutation in the tenth Ig-like domain of titin's spring region is associated with arrhythmogenic cardiomyopathy, a disease characterized by ventricular arrhythmias leading to cardiac arrest and sudden death. Titin is the first sarcomeric protein linked to arrhythmogenic cardiomyopathy. To characterize the disease mechanism, we have used atomic force microscopy to directly measure the effects that the disease-linked point mutation (T16I) has on the mechanical and kinetic stability of Ig10 at the single molecule level. The mutation decreases the force needed to unfold Ig10 and increases its rate of unfolding 4-fold. We also found that T16I Ig10 is more prone to degradation, presumably due to compromised local protein structure. Overall, the disease-linked mutation weakens the structural integrity of titin's Ig10 domain and suggests an Ig domain disease mechanism.

Titin-based tension in the cardiac sarcomere: molecular origin and physiological adaptations

The passive stiffness of cardiac muscle plays a critical role in ventricular filling during diastole and is determined by the extracellular matrix and the sarcomeric protein titin. Titin spans from the Z-disk to the M-band of the sarcomere and also contains a large extensible region that acts as a molecular spring and develops passive force during sarcomere stretch. This extensible segment is titin's I-band region, and its force-generating mechanical properties determine titin-based passive tension. The properties of titin's I-band region can be modulated by isoform splicing and post-translational modification and are intimately linked to diastolic function. This review discusses the physical origin of titin-based passive tension, the mechanisms that alter titin stiffness, and titin's role in stress-sensing signaling pathways.

Dynamic prestress in a globular protein

A protein at equilibrium is commonly thought of as a fully relaxed structure, with the intra-molecular interactions showing fluctuations around their energy minimum. In contrast, here we find direct evidence for a protein as a molecular tensegrity structure, comprising a balance of tensed and compressed interactions, a concept that has been put forward for macroscopic structures. We quantified the distribution of inter-residue prestress in ubiquitin and immunoglobulin from all-atom molecular dynamics simulations. The network of highly fluctuating yet significant inter-residue forces in proteins is a consequence of the intrinsic frustration of a protein when sampling its rugged energy landscape. In beta sheets, this balance of forces is found to compress the intra-strand hydrogen bonds. We estimate that the observed magnitude of this pre-compression is enough to induce significant changes in the hydrogen bond lifetimes; thus, prestress, which can be as high as a few 100 pN, can be considered a key factor in determining the unfolding kinetics and pathway of proteins under force. Strong pre-tension in certain salt bridges on the other hand is connected to the thermodynamic stability of ubiquitin. Effective force profiles between some side-chains reveal the signature of multiple, distinct conformational states, and such static disorder could be one factor explaining the growing body of experiments revealing non-exponential unfolding kinetics of proteins. The design of prestress distributions in engineering proteins promises to be a new tool for tailoring the mechanical properties of made-to-order nanomaterials.

A tensegrity structure is one composed of members that are permanently under either tension or compression, and the balance of these tensile and compressive forces provides the structure with its mechanical stability. Macroscale tensegrity structures, which include Buckminster Fuller's geodesic domes, achieve exceptional structural integrity with a minimal use of resources. The question we address in this work is whether nature makes use of molecular-scale tensegrity in the design of proteins. Using Molecular Dynamics simulations of the protein ubiquitin, we measure the network of pairwise forces connecting the amino acid residues and show that this network does indeed have the character of a tensegrity structure. Furthermore, we find that the arrangement of tensile and compressive forces is such that hydrogen bonds in the protein's beta sheet, which are crucial for bearing mechanical loads, are compressed. This pre-compression is enough to significantly lengthen the lifetime of a bond under a given force, and thus should be an important factor in determining the protein's mechanical strength. The rational design of molecular prestress networks promises to be a new avenue for the engineering of proteins with made-to-order mechanical properties, for applications in medicine, materials and nanotechnology.

Implementation of force distribution analysis for molecular dynamics simulations

Background

The way mechanical stress is distributed inside and propagated by proteins and other biopolymers largely defines their function. Yet, determining the network of interactions propagating internal strain remains a challenge for both, experiment and theory. Based on molecular dynamics simulations, we developed force distribution analysis (FDA), a method that allows visualizing strain propagation in macromolecules.

Results

To be immediately applicable to a wide range of systems, FDA was implemented as an extension to Gromacs, a commonly used package for molecular simulations. The FDA code comes with an easy-to-use command line interface and can directly be applied to every system built using Gromacs. We provide an additional R-package providing functions for advanced statistical analysis and presentation of the FDA data.

Conclusions

Using FDA, we were able to explain the origin of mechanical robustness in immunoglobulin domains and silk fibers. By elucidating propagation of internal strain upon ligand binding, we previously also successfully revealed the functionality of a stiff allosteric protein. FDA thus has the potential to be a valuable tool in the investigation and rational design of mechanical properties in proteins and nano-materials.

Nanomechanics of Ig-like domains of human contactin (BIG-2)

Contactins are modular extracellular cell matrix proteins that are present in the brain, and they are responsible for the proper development and functioning of neurons. They contain six immunoglobulin-like IgC2 domains and four fibronectin type III repeats. The interactions of contactin with other proteins are poorly understood. The mechanical properties of all IgC2 domains of human contactin 4 were studied using a steered molecular dynamics approach and CHARMM force field with an explicit TIP3P water environment on a 10-ns timescale. Force spectra of all domains were determined computationally and the nanomechanical unfolding process is described. The domains show different mechanical stabilities. The calculated maxima of the unfolding force are in the range of 900–1700 pN at a loading rate of 7 N/s. Our data indicate that critical regions of IgC2 domains 2 and 3, which are responsible for interactions with tyrosine phosphatases and are important in nervous system development, are affected by even weak mechanical stretching. Thus, tensions present in the cell may modulate cellular activities related to contactin function. The present data should facilitate the interpretation of atomic force microscope single-molecule spectra of numerous proteins with similar IgC2 motives.

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The giant protein titin: a regulatory node that integrates myocyte signaling pathways

Titin, the largest protein in the human body, is well known as a molecular spring in muscle cells and scaffold protein aiding myofibrillar assembly. However, recent evidence has established another important role for titin: that of a regulatory node integrating, and perhaps coordinating, diverse signaling pathways, particularly in cardiomyocytes. We review key findings within this emerging field, including those related to phosphorylation of the titin springs, and also discuss how titin participates in hypertrophic gene regulation and protein quality control.

Crystallographic and nuclear magnetic resonance evaluation of the impact of peptide binding to the second PDZ domain of protein tyrosine phosphatase 1E

PDZ (PSD95/Discs large/ZO-1) domains are ubiquitous protein interaction motifs found in scaffolding proteins involved in signal transduction. Despite the fact that many PDZ domains show a limited tendency to undergo structural change, the PDZ family has been associated with long-range communication and allostery. One of the PDZ domains studied most in terms of structure and biophysical properties is the second PDZ ("PDZ2") domain from protein tyrosine phosphatase 1E (PTP1E, also known as PTPL1). Previously, we showed through NMR relaxation studies that binding of the RA-GEF2 C-terminal peptide substrate results in long-range propagation of side-chain dynamic changes in human PDZ2 [Fuentes, E. J., et al. (2004) J. Mol. Biol. 335, 1105-1115]. Here, we present the first X-ray crystal structures of PDZ2 in the absence and presence of RA-GEF2 ligand, determined to resolutions of 1.65 and 1.3 Å, respectively. These structures deviate somewhat from previously determined NMR structures and indicate that very minor structural changes in PDZ2 accompany peptide binding. NMR residual dipolar couplings confirm the crystal structures to be accurate models of the time-averaged atomic coordinates of PDZ2. The impact on side-chain dynamics was further tested with a C-terminal peptide from APC, which showed results nearly identical to those of RA-GEF2. Thus, allosteric transmission in PDZ2 induced by peptide binding is conveyed purely and robustly by dynamics. (15)N relaxation dispersion measurements did not detect appreciable populations of a kinetic structural intermediate. Collectively, for ligand binding to PDZ2, these data support a lock-and-key binding model from a structural perspective and an allosteric model from a dynamical perspective, which together suggest a complex energy landscape for functional transitions within the ensemble.

Mechanical unfolding of acylphosphatase studied by single-molecule force spectroscopy and MD simulations

Single-molecule manipulation methods provide a powerful means to study protein transitions. Here we combined single-molecule force spectroscopy and steered molecular-dynamics simulations to study the mechanical properties and unfolding behavior of the small enzyme acylphosphatase (AcP). We find that mechanical unfolding of AcP occurs at relatively low forces in an all-or-none fashion and is decelerated in the presence of a ligand, as observed in solution measurements. The prominent energy barrier for the transition is separated from the native state by a distance that is unusually long for alpha/beta proteins. Unfolding is initiated at the C-terminal strand (beta(T)) that lies at one edge of the beta-sheet of AcP, followed by unraveling of the strand located at the other. The central strand of the sheet and the two helices in the protein unfold last. Ligand binding counteracts unfolding by stabilizing contacts between an arginine residue (Arg-23) and the catalytic loop, as well as with beta(T) of AcP, which renders the force-bearing units of the protein resistant to force. This stabilizing effect may also account for the decelerated unfolding of ligand-bound AcP in the absence of force.

Unravelling the design principles for single protein mechanical strength

In recent years single molecule manipulation techniques have improved to the extent that measurements of the mechanical strength of single proteins can now be undertaken routinely. This powerful new tool, coupled with theoretical frameworks to characterise the unfolding process, has enabled significant progress to be made in understanding the physical mechanisms that underlie protein mechanical strength. These design concepts have allowed the search for proteins with novel, mechanically strong folds to be automated and for previously mechanically characterised proteins to be engineered rationally. Methods to achieve the latter are diverse and include re-engineering of specific hydrophobic core residues, changing solvent conditions and the 'cross-linking' of side-chains that are separated in the rate-limiting unfolding transition. Predicting the mechanical behaviour of larger proteins and those with more complex structures remains a significant challenge while on-going instrument development is beginning to allow the examination of mechanical strength of protein across a wide range of force loading rates. The integral role of force in biology and the potential for exploitation of catalytic and structural proteins as functional bio-materials makes this a particularly important area of research.