The elastic properties of the structurally characterized myosin II S2 subdomain: a molecular dynamics and normal mode analysis

Conformational dynamics and mechanical properties of biomimetic RNA, DNA, and RNA-DNA hybrid nanotubes: an atomistic molecular dynamics study

With the nanotechnology boom, artificially designed nucleic acid nanotubes have aroused interest due to their practical applications in nanorobotics, vaccine design, membrane channels, drug delivery, and force sensing. In this paper, computational study was performed to investigate the structural dynamics and mechanical properties of RNA nanotubes (RNTs), DNA nanotubes (DNTs), and RNA-DNA hybrid nanotubes (RDHNTs). So far, the structural and mechanical properties of RDHNTs have not been examined in experiments or theoretical calculations, and there is limited knowledge regarding these properties for RNTs. Here, the simulations were carried out using the equilibrium molecular dynamics (MD) and steered molecular dynamics (SMD) approaches. Using in-house scripting, we modeled hexagonal nanotubes composed of six double-stranded molecules connected by four-way Holliday junctions. Classical MD analyses were performed on the collected trajectory data to investigate structural properties. Analyses of the microscopic structural parameters of RDHNT indicated a structural transition from the A-form to a conformation between the A- and B-forms, which may be attributable to the increased rigidity of RNA scaffolds compared to DNA staples. Comprehensive research on the elastic mechanical properties was also conducted based on spontaneous thermal fluctuations of nanotubes and employing the equipartition theorem. The Young's modulus of RDHNT (E = 165 MPa) and RNT (E = 144 MPa) was found to be almost the same and nearly half of that found for DNT (E = 325 MPa). Furthermore, the results showed that RNT was more resistant to bending, torsional, and volumetric deformations than DNT and RDHNT. We also used non-equilibrium SMD simulations to acquire comprehensive knowledge of the mechanical response of nanotubes to tensile stress.

Using Multiscale Simulations as a Tool to Interpret Equatorial X-ray Fiber Diffraction Patterns from Skeletal Muscle

Synchrotron small-angle X-ray diffraction is the method of choice for nm-scale structural studies of striated muscle under physiological conditions and on millisecond time scales. The lack of generally applicable computational tools for modeling X-ray diffraction patterns from intact muscles has been a significant barrier to exploiting the full potential of this technique. Here, we report a novel "forward problem" approach using the spatially explicit computational simulation platform MUSICO to predict equatorial small-angle X-ray diffraction patterns and the force output simultaneously from resting and isometrically contracting rat skeletal muscle that can be compared to experimental data. The simulation generates families of thick-thin filament repeating units, each with their individually predicted occupancies of different populations of active and inactive myosin heads that can be used to generate 2D-projected electron density models based on known Protein Data Bank structures. We show how, by adjusting only a few selected parameters, we can achieve a good correspondence between experimental and predicted X-ray intensities. The developments presented here demonstrate the feasibility of combining X-ray diffraction and spatially explicit modeling to form a powerful hypothesis-generating tool that can be used to motivate experiments that can reveal emergent properties of muscle.

Contraction of the rigor actomyosin complex drives bulk hemoglobin expulsion from hemolyzing erythrocytes

Erythrocyte ghost formation via hemolysis is a key event in the physiological clearance of senescent red blood cells (RBCs) in the spleen. The turnover rate of millions of RBCs per second necessitates a rapid efflux of hemoglobin (Hb) from RBCs by a not yet identified mechanism. Using high-speed video-microscopy of isolated RBCs, we show that electroporation-induced efflux of cytosolic ATP and other small solutes leads to transient cell shrinkage and echinocytosis, followed by osmotic swelling to the critical hemolytic volume. The onset of hemolysis coincided with a sudden self-propelled cell motion, accompanied by cell contraction and Hb-jet ejection. Our biomechanical model, which relates the Hb-jet-driven cell motion to the cytosolic pressure generation via elastic contraction of the RBC membrane, showed that the contributions of the bilayer and the bilayer-anchored spectrin cytoskeleton to the hemolytic cell motion are negligible. Consistent with the biomechanical analysis, our biochemical experiments, involving extracellular ATP and the myosin inhibitor blebbistatin, identify the low abundant non-muscle myosin 2A (NM2A) as the key contributor to the Hb-jet emission and fast hemolytic cell motion. Thus, our data reveal a rapid myosin-based mechanism of hemolysis, as opposed to a much slower diffusive Hb efflux.

Insights into Muscle Contraction Derived from the Effects of Small-Molecular Actomyosin-Modulating Compounds

Bottom-up mechanokinetic models predict ensemble function of actin and myosin based on parameter values derived from studies using isolated proteins. To be generally useful, e.g., to analyze disease effects, such models must also be able to predict ensemble function when actomyosin interaction kinetics are modified differently from normal. Here, we test this capability for a model recently shown to predict several physiological phenomena along with the effects of the small molecular compound blebbistatin. We demonstrate that this model also qualitatively predicts effects of other well-characterized drugs as well as varied concentrations of MgATP. However, the effects of one compound, amrinone, are not well accounted for quantitatively. We therefore systematically varied key model parameters to address this issue, leading to the increased amplitude of the second sub-stroke of the power stroke from 1 nm to 2.2 nm, an unchanged first sub-stroke (5.3−5.5 nm), and an effective cross-bridge attachment rate that more than doubled. In addition to better accounting for the effects of amrinone, the modified model also accounts well for normal physiological ensemble function. Moreover, a Monte Carlo simulation-based version of the model was used to evaluate force−velocity data from small myosin ensembles. We discuss our findings in relation to key aspects of actin−myosin operation mechanisms causing a non-hyperbolic shape of the force−velocity relationship at high loads. We also discuss remaining limitations of the model, including uncertainty of whether the cross-bridge elasticity is linear or not, the capability to account for contractile properties of very small actomyosin ensembles (<20 myosin heads), and the mechanism for requirements of a higher cross-bridge attachment rate during shortening compared to during isometric contraction.

Anisotropic Elasticity of the Myosin Motor in Muscle

To define the mechanics and energetics of the myosin motor action in muscles, it is mandatory to know fundamental parameters such as the stiffness and the force of the single myosin motor, and the fraction of motors attached during contraction. These parameters can be defined in situ using sarcomere-level mechanics in single muscle fibers under the assumption that the stiffness of a myosin dimer with both motors attached (as occurs in rigor, when all motors are attached) is twice that of a single motor (as occurs in the isometric contraction). We use a mechanical/structural model to identify the constraints that underpin the stiffness of the myosin dimer with both motors attached to actin. By comparing the results of the model with the data in the literature, we conclude that the two-fold axial stiffness of the dimers with both motors attached is justified by a stiffness of the myosin motor that is anisotropic and higher along the axis of the myofilaments. A lower azimuthal stiffness of the motor plays an important role in the complex architecture of the sarcomere by allowing the motors to attach to actin filaments at different azimuthal angles relative to the thick filament.

Cross-bridge mechanics estimated from skeletal muscles' work-loop responses to impacts in legged locomotion

Legged locomotion has evolved as the most common form of terrestrial locomotion. When the leg makes contact with a solid surface, muscles absorb some of the shock-wave accelerations (impacts) that propagate through the body. We built a custom-made frame to which we fixated a rat (Rattus norvegicus, Wistar) muscle (m. gastrocnemius medialis and lateralis: GAS) for emulating an impact. We found that the fibre material of the muscle dissipates between 3.5 and [Formula: see text] ranging from fresh, fully active to passive muscle material, respectively. Accordingly, the corresponding dissipated energy in a half-sarcomere ranges between 10.4 and [Formula: see text], respectively. At maximum activity, a single cross-bridge would, thus, dissipate 0.6% of the mechanical work available per ATP split per impact, and up to 16% energy in common, submaximal, activities. We also found the cross-bridge stiffness as low as [Formula: see text], which can be explained by the Coulomb-actuating cross-bridge part dominating the sarcomere stiffness. Results of the study provide a deeper understanding of contractile dynamics during early ground contact in bouncy gait.

Specific osteogenesis imperfecta-related Gly substitutions in type I collagen induce distinct structural, mechanical, and dynamic characteristics

The stiffnesses, β-structures, hydrogen bonds, and vibrational modes of wild-type collagen triple helices are compared with osteogenesis imperfecta-related mutants using integrative structural and dynamic analysis via molecular dynamics simulations and Markov state models. Differences in these characteristics are strongly related to the unwound structural states in the mutated regions that are specific to each mutation.

Evidence for S2 flexibility by direct visualization of quantum dot-labeled myosin heads and rods within smooth muscle myosin filaments moving on actin in vitro

Myosins in muscle assemble into filaments by interactions between the C-terminal light meromyosin (LMM) subdomains of the coiled-coil rod domain. The two head domains are connected to LMM by the subfragment-2 (S2) subdomain of the rod. Our mixed kinetic model predicts that the flexibility and length of S2 that can be pulled away from the filament affects the maximum distance working heads can move a filament unimpeded by actin-attached heads. It also suggests that it should be possible to observe a head remain stationary relative to the filament backbone while bound to actin (dwell), followed immediately by a measurable jump upon detachment to regain the backbone trajectory. We tested these predictions by observing filaments moving along actin at varying ATP using TIRF microscopy. We simultaneously tracked two different color quantum dots (QDs), one attached to a regulatory light chain on the lever arm and the other attached to an LMM in the filament backbone. We identified events (dwells followed by jumps) by comparing the trajectories of the QDs. The average dwell times were consistent with known kinetics of the actomyosin system, and the distribution of the waiting time between observed events was consistent with a Poisson process and the expected ATPase rate. Geometric constraints suggest a maximum of ∼26 nm of S2 can be unzipped from the filament, presumably involving disruption in the coiled-coil S2, a result consistent with observations by others of S2 protruding from the filament in muscle. We propose that sufficient force is available from the working heads in the filament to overcome the stiffness imposed by filament-S2 interactions.

Steered molecular dynamic simulations reveal Marfan syndrome mutations disrupt fibrillin-1 cbEGF domain mechanosensitive calcium binding

Marfan syndrome (MFS) is a highly variable genetic connective tissue disorder caused by mutations in the calcium binding extracellular matrix glycoprotein fibrillin-1. Patients with the most severe form of MFS (neonatal MFS; nMFS) tend to have mutations that cluster in an internal region of fibrillin-1 called the neonatal region. This region is predominantly composed of eight calcium-binding epidermal growth factor-like (cbEGF) domains, each of which binds one calcium ion and is stabilized by three highly conserved disulfide bonds. Crucially, calcium plays a fundamental role in stabilizing cbEGF domains. Perturbed calcium binding caused by cbEGF domain mutations is thus thought to be a central driver of MFS pathophysiology. Using steered molecular dynamics (SMD) simulations, we demonstrate that cbEGF domain calcium binding decreases under mechanical stress (i.e. cbEGF domains are mechanosensitive). We further demonstrate the disulfide bonds in cbEGF domains uniquely orchestrate protein unfolding by showing that MFS disulfide bond mutations markedly disrupt normal mechanosensitive calcium binding dynamics. These results point to a potential mechanosensitive mechanism for fibrillin-1 in regulating extracellular transforming growth factor beta (TGFB) bioavailability and microfibril integrity. Such mechanosensitive “smart” features may represent novel mechanisms for mechanical hemostasis regulation in extracellular matrix that are pathologically activated in MFS.

Straightening Out the Elasticity of Myosin Cross-Bridges

In a contracting muscle, myosin cross-bridges extending from thick filaments pull the interdigitating thin (actin-containing) filaments during cyclical ATP-driven interactions toward the center of the sarcomere, the structural unit of striated muscle. Cross-bridge attachments in the sarcomere have been reported to exhibit a similar stiffness under both positive and negative forces. However, in vitro measurements on filaments with a sparse complement of heads detected a decrease of the cross-bridge stiffness at negative forces attributed to the buckling of the subfragment 2 tail portion. Here, we review some old and new data that confirm that cross-bridge stiffness is nearly linear in the muscle filament lattice. The implications of high myosin stiffness at positive and negative strains are considered in muscle fibers and in nonmuscle intracellular cargo transport.

Comparing models with one versus multiple myosin-binding sites per actin target zone: The power of simplicity

Mechanokinetic statistical models describe the mechanisms of muscle contraction on the basis of the average behavior of a large ensemble of actin-myosin motors. Such models often assume that myosin II motor domains bind to regularly spaced, discrete target zones along the actin-based thin filaments and develop force in a series of strain-dependent transitions under the turnover of ATP. The simplest models assume that there is just one myosin-binding site per target zone and a uniform spatial distribution of the myosin motor domains in relation to each site. However, most of the recently developed models assume three myosin-binding sites per target zone, and some models include a spatially explicit 3-D treatment of the myofilament lattice and thereby of the geometry of the actin-myosin contact points. Here, I show that the predictions for steady-state contractile behavior of muscle are very similar whether one or three myosin-binding sites per target zone is assumed, provided that the model responses are appropriately scaled to the number of sites. Comparison of the model predictions for isometrically contracting mammalian muscle cells suggests that each target zone contains three or more myosin-binding sites. Finally, I discuss the strengths and weaknesses of one-site spatially inexplicit models in relation to three-site models, including those that take into account the detailed 3-D geometry of the myofilament lattice. The results of this study suggest that single-site models, with reduced computational cost compared with multisite models, are useful for several purposes, e.g., facilitated molecular mechanistic insights.

Functional significance of HCM mutants of tropomyosin, V95A and D175N, studied with in vitro motility assays

The majority of hypertrophic cardiomyopathy (HCM) is caused by mutations in sarcomere proteins. We examined tropomyosin (Tpm)’s HCM mutants in humans, V95A and D175N, with in vitro motility assay using optical tweezers to evaluate the effects of the Tpm mutations on the actomyosin interaction at the single molecular level. Thin filaments were reconstituted using these Tpm mutants, and their sliding velocity and force were measured at varying Ca²⁺ concentrations. Our results indicate that the sliding velocity at pCa ≥8.0 was significantly increased in mutants, which is expected to cause a diastolic problem. The velocity that can be activated by Ca²⁺ decreased significantly in mutants causing a systolic problem. With sliding force, Ca²⁺ activatable force decreased in V95A and increased in D175N, which may cause a systolic problem. Our results further demonstrate that the duty ratio determined at the steady state of force generation in saturating [Ca²⁺] decreased in V95A and increased in D175N. The Ca²⁺ sensitivity and cooperativity were not significantly affected by the mutations. These results suggest that the two mutants modulate molecular processes of the actomyosin interaction differently, but to result in the same pathology known as HCM.

Nonlinear Actomyosin Elasticity in Muscle?

Cyclic interactions between myosin II motor domains and actin filaments that are powered by turnover of ATP underlie muscle contraction and have key roles in motility of nonmuscle cells. The elastic characteristics of actin-myosin cross-bridges are central in the force-generating process, and disturbances in these properties may lead to disease. Although the prevailing paradigm is that the cross-bridge elasticity is linear (Hookean), recent single-molecule studies suggest otherwise. Despite convincing evidence for substantial nonlinearity of the cross-bridge elasticity in the single-molecule work, this finding has had limited influence on muscle physiology and physiology of other ordered cellular actin-myosin ensembles. Here, we use a biophysical modeling approach to close the gap between single molecules and physiology. The model is used for analysis of available experimental results in the light of possible nonlinearity of the cross-bridge elasticity. We consider results obtained both under rigor conditions (in the absence of ATP) and during active muscle contraction. Our results suggest that a wide range of experimental findings from mechanical experiments on muscle cells are consistent with nonlinear actin-myosin elasticity similar to that previously found in single molecules. Indeed, the introduction of nonlinear cross-bridge elasticity into the model improves the reproduction of key experimental results and eliminates the need for force dependence of the ATP-induced detachment rate, consistent with observations in other single-molecule studies. The findings have significant implications for the understanding of key features of actin-myosin-based production of force and motion in living cells, particularly in muscle, and for the interpretation of experimental results that rely on stiffness measurements on cells or myofibrils.

Do Actomyosin Single-Molecule Mechanics Data Predict Mechanics of Contracting Muscle?

In muscle, but not in single-molecule mechanics studies, actin, myosin and accessory proteins are incorporated into a highly ordered myofilament lattice. In view of this difference we compare results from single-molecule studies and muscle mechanics and analyze to what degree data from the two types of studies agree with each other. There is reasonable correspondence in estimates of the cross-bridge power-stroke distance (7–13 nm), cross-bridge stiffness (~2 pN/nm) and average isometric force per cross-bridge (6–9 pN). Furthermore, models defined on the basis of single-molecule mechanics and solution biochemistry give good fits to experimental data from muscle. This suggests that the ordered myofilament lattice, accessory proteins and emergent effects of the sarcomere organization have only minor modulatory roles. However, such factors may be of greater importance under e.g., disease conditions. We also identify areas where single-molecule and muscle data are conflicting: (1) whether force generation is an Eyring or Kramers process with just one major power-stroke or several sub-strokes; (2) whether the myofilaments and the cross-bridges have Hookean or non-linear elasticity; (3) if individual myosin heads slip between actin sites under certain conditions, e.g., in lengthening; or (4) if the two heads of myosin cooperate.

Nanomechanics of actin filament: A molecular dynamics simulation

Actin is known as the most abundant essentially protein in eukaryotic cells. Actin plays a crucial role in many cellular processes involving mechanical forces such as cell motility, adhesion, muscle contraction, and intracellular transport. However, little is known about the mechanical properties of this protein when subjected to mechanical forces in cellular processes. In this article, a series of large-scale molecular dynamics simulations are carried out to elucidate nanomechanical behavior such as elastic and viscoelastic properties of a single actin filament. Here, we used two individual methods namely, all-atoms and coarse-grained molecular dynamics, to evaluate elastic properties of a single actin filament. In the other word, based on Brownian motions of the filament and using the principle of the equipartition theorem, in aqueous solution, tensile stiffness, torsional rigidity, and bending rigidity of the single actin filament are studied. The results revealed that increasing the sampling window time leads to convergence of obtained mechanical properties to the experimental values. Moreover, in order to investigate viscoelastic properties of a single actin filament, constant force steered molecular dynamics method is used to apply different external tensile loads and perform five individual creep tests on the molecule. The strain-time response of the filament for each creep test is obtained. Based on the Kelvin-Voigt model, the results reveal that a single actin filament shows a nonlinear viscoelastic behavior, with a Young's modulus of 2.85 GPa, a viscosity of 4.06 GPa.ns, and a relaxation time in the range of 1.42 ns which were measured here for the first time at the single filament level. The findings of this article suggest that molecular dynamics simulations could also be a useful tool for investigating the mechanical behavior of bio-nanomaterials.

Multiscale and Multiaxial Mechanics of Vascular Smooth Muscle

Mathematical models can facilitate an integrative understanding of the complexity underlying biological structure and function, but they must be informed and validated by empirical data. Uniaxial contraction of an arterial ring is a well-used in vitro approach for studying characteristics of smooth muscle contractility even though this experimental arrangement does not mimic the in vivo vascular geometry or loading. In contrast, biaxial contraction of an inflated and axially extended excised vessel provides broader information, both passive and active, under more realistic conditions. Few investigations have compared these two in vitro approaches directly, namely how their results overlap, how they differ, or if each provides unique complementary information. Toward this end, we present, to our knowledge, a new multiscale mathematical model of arterial contractility accounting for structural and functional constituents at molecular, cellular, and tissue levels. The artery is assumed to be a thick-walled incompressible cylinder described by an anisotropic model of the extracellular matrix and, to our knowledge, novel model of smooth muscle contractility. The latter includes a 3D structural sensitivity to deformation, including microscale muscle filament overlap and filament lattice spacing. The overall model captures uniaxial and biaxial experimental contraction data, which was not possible when accounting for filament overlap alone. The model also enables parameter sensitivity studies, which confirmed that uniaxial contraction tests are not as efficient as biaxial tests for identifying changes in vascular smooth muscle function.

Desmosomes and Intermediate Filaments: Their Consequences for Tissue Mechanics

Adherens junctions (AJs) and desmosomes connect the actin and keratin filament networks of adjacent cells into a mechanical unit. Whereas AJs function in mechanosensing and in transducing mechanical forces between the plasma membrane and the actomyosin cytoskeleton, desmosomes and intermediate filaments (IFs) provide mechanical stability required to maintain tissue architecture and integrity when the tissues are exposed to mechanical stress. Desmosomes are essential for stable intercellular cohesion, whereas keratins determine cell mechanics but are not involved in generating tension. Here, we summarize the current knowledge of the role of IFs and desmosomes in tissue mechanics and discuss whether the desmosome-keratin scaffold might be actively involved in mechanosensing and in the conversion of chemical signals into mechanical strength.

Intrinsic K-Ras dynamics: A novel molecular dynamics data analysis method shows causality between residue pair motions

K-Ras is the most frequently mutated oncogene in human cancers, but there are still no drugs that directly target it in the clinic. Recent studies utilizing dynamics information show promising results for selectively targeting mutant K-Ras. However, despite extensive characterization, the mechanisms by which K-Ras residue fluctuations transfer allosteric regulatory information remain unknown. Understanding the direction of information flow can provide new mechanistic insights for K-Ras targeting. Here, we present a novel approach –conditional time-delayed correlations (CTC) – using the motions of all residue pairs of a protein to predict directionality in the allosteric regulation of the protein fluctuations. Analyzing nucleotide-dependent intrinsic K-Ras motions with the new approach yields predictions that agree with the literature, showing that GTP-binding stabilizes K-Ras motions and leads to residue correlations with relatively long characteristic decay times. Furthermore, our study is the first to identify driver-follower relationships in correlated motions of K-Ras residue pairs, revealing the direction of information flow during allosteric modulation of its nucleotide-dependent intrinsic activity: active K-Ras Switch-II region motions drive Switch-I region motions, while α-helix-3L7 motions control both. Our results provide novel insights for strategies that directly target mutant K-Ras.

The Structure of the Plakin Domain of Plectin Reveals an Extended Rod-like Shape

Plakins are large multi-domain proteins that interconnect cytoskeletal structures. Plectin is a prototypical plakin that tethers intermediate filaments to membrane-associated complexes. Most plakins contain a plakin domain formed by up to nine spectrin repeats (SR1-SR9) and an SH3 domain. The plakin domains of plectin and other plakins harbor binding sites for junctional proteins. We have combined x-ray crystallography with small angle x-ray scattering (SAXS) to elucidate the structure of the plakin domain of plectin, extending our previous analysis of the SR1 to SR5 region. Two crystal structures of the SR5-SR6 region allowed us to characterize its uniquely wide inter-repeat conformational variability. We also report the crystal structures of the SR7-SR8 region, refined to 1.8 Å, and the SR7-SR9 at lower resolution. The SR7-SR9 region, which is conserved in all other plakin domains, forms a rigid segment stabilized by uniquely extensive inter-repeat contacts mediated by unusually long helices in SR8 and SR9. Using SAXS we show that in solution the SR3-SR6 and SR7-SR9 regions are rod-like segments and that SR3-SR9 of plectin has an extended shape with a small central kink. Other plakins, such as bullous pemphigoid antigen 1 and microtubule and actin cross-linking factor 1, are likely to have similar extended plakin domains. In contrast, desmoplakin has a two-segment structure with a central flexible hinge. The continuous versus segmented structures of the plakin domains of plectin and desmoplakin give insight into how different plakins might respond to tension and transmit mechanical signals.

Elastic properties of dynein motor domain obtained from all-atom molecular dynamics simulations

Dyneins are large microtubule motor proteins that convert ATP energy to mechanical power. High-resolution crystal structures of ADP-bound cytoplasmic dynein have revealed the organization of the motor domain, comprising the AAA(+) ring, the linker, the stalk/strut and the C sequence. Recently, the ADP.vanadate-bound structure, which is similar to the ATP hydrolysis transition state, revealed how the structure of dynein changes upon ATP binding. Although both the ADP- and ATP-bound state structures have been resolved, the dynamic properties at the atomic level remain unclear. In this work, we built two models named 'the ADP model' and 'the ATP model', where ADP and ATP are bound to AAA1 in the AAA(+) ring, respectively, to observe the initial procedure of the structural change from the unprimed to the primed state. We performed 200-ns molecular dynamics simulations for both models and compared their structures and dynamics. The motions of the stalk, consisting of a long coiled coil with a microtubule-binding domain, significantly differed between the two models. The elastic properties of the stalk were analyzed and compared with the experimental results.

Measuring the Elasticity of Poly-l-Proline Helices with Terahertz Spectroscopy

The rigidity of poly-l-proline is an important contributor to the stability of many protein secondary structures, where it has been shown to strongly influence bulk flexibility. The experimental Young's moduli of two known poly-l-proline helical forms, right-handed all-cis (Form I) and left-handed all-trans (Form II), were determined in the crystalline state by using an approach that combines terahertz time-domain spectroscopy, X-ray diffraction, and solid-state density functional theory. Contrary to expectations, the helices were found to be considerably less rigid than many other natural and synthetic polymers, as well as differing greatly from each other, with Young's moduli of 4.9 and 9.6 GPa for Forms I and II, respectively.

Characterization of the flexibility of the peripheral stalk of prokaryotic rotary A-ATPases by atomistic simulations

Rotary ATPases are involved in numerous physiological processes, with the three distinct types (F/A/V‐ATPases) sharing functional properties and structural features. The basic mechanism involves the counter rotation of two motors, a soluble ATP hydrolyzing/synthesizing domain and a membrane‐embedded ion pump connected through a central rotor axle and a stator complex. Within the A/V‐ATPase family conformational flexibility of the EG stators has been shown to accommodate catalytic cycling and is considered to be important to function. For the A‐ATPase three EG structures have been reported, thought to represent conformational states of the stator during different stages of rotary catalysis. Here we use long, detailed atomistic simulations to show that those structures are conformers explored through thermal fluctuations, but do not represent highly populated states of the EG stator in solution. We show that the coiled coil tail domain has a high persistence length (∼100 nm), but retains the ability to adapt to different conformational states through the presence of two hinge regions. Moreover, the stator network of the related V‐ATPase has been suggested to adapt to subunit interactions in the collar region in addition to the nucleotide occupancy of the catalytic domain. The MD simulations reported here, reinforce this observation showing that the EG stators have enough flexibility to adapt to significantly different structural re‐arrangements and accommodate structural changes in the catalytic domain whilst resisting the large torque generated by catalytic cycling. These results are important to understand the role the stators play in the rotary‐ATPase mechanism. Proteins 2016; 84:1203–1212. © 2016 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

Mechanics of Vascular Smooth Muscle

Vascular smooth muscle (VSM; see Table 1 for a list of abbreviations) is a heterogeneous biomaterial comprised of cells and extracellular matrix. By surrounding tubes of endothelial cells, VSM forms a regulated network, the vasculature, through which oxygenated blood supplies specialized organs, permitting the development of large multicellular organisms. VSM cells, the engine of the vasculature, house a set of regulated nanomotors that permit rapid stress-development, sustained stress-maintenance and vessel constriction. Viscoelastic materials within, surrounding and attached to VSM cells, comprised largely of polymeric proteins with complex mechanical characteristics, assist the engine with countering loads imposed by the heart pump, and with control of relengthening after constriction. The complexity of this smart material can be reduced by classical mechanical studies combined with circuit modeling using spring and dashpot elements. Evaluation of the mechanical characteristics of VSM requires a more complete understanding of the mechanics and regulation of its biochemical parts, and ultimately, an understanding of how these parts work together to form the machinery of the vascular tree. Current molecular studies provide detailed mechanical data about single polymeric molecules, revealing viscoelasticity and plasticity at the protein domain level, the unique biological slip-catch bond, and a regulated two-step actomyosin power stroke. At the tissue level, new insight into acutely dynamic stress-strain behavior reveals smooth muscle to exhibit adaptive plasticity. At its core, physiology aims to describe the complex interactions of molecular systems, clarifying structure-function relationships and regulation of biological machines. The intent of this review is to provide a comprehensive presentation of one biomachine, VSM.

Coiled coils as possible models of protein structure evolution

Coiled coils are formed by two or more α-helices wrapped around one another. This structural motif often guides di-, tri- or multimerization of proteins involved in diverse biological processes such as membrane fusion, signal transduction and the organization of the cytoskeleton. Although coiled coil motifs seem conceptually simple and their existence was proposed in the early 1950s, the high variability of the motif makes coiled coil prediction from sequence a difficult task. They might be confused with intrinsically disordered sequences and even more with a recently described structural motif, the charged single α-helix. By contrast, the versatility of coiled coil structures renders them an ideal candidate for protein (re)design and many novel variants have been successfully created to date. In this paper, we review coiled coils in the light of protein evolution by putting our present understanding of the motif and its variants in the context of structural interconversions. We argue that coiled coils are ideal subjects for studies of subtle and large-scale structural changes because of their well-characterized and versatile nature.

Buckling transition in long α-helices

The treatment of bending and buckling of stiff biopolymer filaments by the popular worm-like chain model does not provide adequate understanding of these processes at the microscopic level. Thus, we have used the atomistic molecular-dynamic simulations and the Amber03 force field to examine the compression buckling of α-helix (AH) filaments at room temperature. It was found that the buckling instability occurs in AHs at the critical force f(c) in the range of tens of pN depending on the AH length. The decrease of the force f(c) with the contour length follows the prediction of the classic thin rod theory. At the force f(c) the helical filament undergoes the swift and irreversible transition from the smoothly bent structure to the buckled one. A sharp kink in the AH contour arises at the transition, accompanied by the disruption of the hydrogen bonds in its vicinity. The kink defect brings in an effective softening of the AH molecule at buckling. Nonbonded interactions between helical branches drive the rearrangement of a kinked AH into the ultimate buckled structure of a compact helical hairpin described earlier in the literature.

Multiscale impact of nucleotides and cations on the conformational equilibrium, elasticity and rheology of actin filaments and crosslinked networks

Cells are able to respond to mechanical forces and deformations. The actin cytoskeleton, a highly dynamic scaffolding structure, plays an important role in cell mechano-sensing. Thus, understanding rheological behaviors of the actin cytoskeleton is critical for delineating mechanical behaviors of cells. The actin cytoskeleton consists of interconnected actin filaments (F-actin) that form via self-assembly of actin monomers. It has been shown that molecular changes of the monomer subunits impact the rigidity of F-actin. However, it remains inconclusive whether or not the molecular changes can propagate to the network level and thus alter the rheological properties of actin networks. Here, we focus on how cation binding and nucleotide state tune the molecular conformation and rigidity of F-actin and a representative rheological behavior of actin networks, strain-stiffening. We employ a multiscale approach by combining established computational techniques: molecular dynamics, normal mode analysis and Brownian dynamics. Our findings indicate that different combinations of nucleotide (ATP, ADP or ADP-Pi) and cation [Formula: see text] or [Formula: see text] at one or multiple sites) binding change the molecular conformation of F-actin by varying inter- and intra-strand interactions which bridge adjacent subunits between and within F-actin helical strands. This is reflected in the rigidity of actin filaments against bending and stretching. We found that differences in extension and bending rigidity of F-actin induced by cation binding to the low-, intermediate- and high-affinity sites vary the strain-stiffening response of actin networks crosslinked by rigid crosslinkers, such as scruin, whereas they minimally impact the strain-stiffening response when compliant crosslinkers, such as filamin A or [Formula: see text]-actinin, are used.

The kinetics underlying the velocity of smooth muscle myosin filament sliding on actin filaments in vitro

Actin-myosin interactions are well studied using soluble myosin fragments, but little is known about effects of myosin filament structure on mechanochemistry. We stabilized unphosphorylated smooth muscle myosin (SMM) and phosphorylated smooth muscle myosin (pSMM) filaments against ATP-induced depolymerization using a cross-linker and attached fluorescent rhodamine (XL-Rh-SMM). Electron micrographs showed that these side polar filaments are very similar to unmodified filaments. They are ~0.63 μm long and contain ~176 molecules. Rate constants for ATP-induced dissociation and ADP release from acto-myosin for filaments and S1 heads were similar. Actin-activated ATPases of SMM and XL-Rh-SMM were similarly regulated. XL-Rh-pSMM filaments moved processively on F-actin that was bound to a PEG brush surface. ATP dependence of filament velocities was similar to that for solution ATPases at high [actin], suggesting that both processes are limited by the same kinetic step (weak to strong transition) and therefore are attachment- limited. This differs from actin sliding over myosin monomers, which is primarily detachment-limited. Fitting filament data to an attachment-limited model showed that approximately half of the heads are available to move the filament, consistent with a side polar structure. We suggest the low stiffness subfragment 2 (S2) domain remains unhindered during filament motion in our assay. Actin-bound negatively displaced heads will impart minimal drag force because of S2 buckling. Given the ADP release rate, the velocity, and the length of S2, these heads will detach from actin before slack is taken up into a backwardly displaced high stiffness position. This mechanism explains the lack of detachment- limited kinetics at physiological [ATP]. These findings address how nonlinear elasticity in assemblies of motors leads to efficient collective force generation.

A new mechanokinetic model for muscle contraction, where force and movement are triggered by phosphate release

The atomic structure of myosin-S1 suggests that its working stroke, which generates tension and shortening in muscle, is triggered by the release of inorganic phosphate from the active site. This mechanism is the basis of a new mechanokinetic model for contractility, using the biochemical actomyosin ATPase cycle, strain-dependent kinetics and dimeric myosins on buckling rods. In this model, phosphate-dependent aspects of contractility arise from a rapid reversible release of phosphate from the initial bound state (A.M.ADP.Pi), which triggers the stroke. Added phosphate drives bound myosin towards this initial state, and the transient tension response to a phosphate jump reflects the rate at which it detaches from actin. Predictions for the tensile and energetic properties of striated muscle as a function of phosphate level, including the tension responses to length steps and Pi-jumps, are compared with experimental data from rabbit psoas fibres at 10 °C. The phosphate sensitivity of isometric tension is maximal when the actin affinity of M.ADP.Pi is near unity. Hence variations in actin affinity modulate the phosphate dependence of isometric tension, and may explain why phosphate sensitivity is temperature-dependent or absent in different muscles.

The contributions of filaments and cross-bridges to sarcomere compliance in skeletal muscle

Force generation in the muscle sarcomere is driven by the head domain of the myosin molecule extending from the thick filament to form cross-bridges with the actin-containing thin filament. Following attachment, a structural working stroke in the head pulls the thin filament towards the centre of the sarcomere, producing, under unloaded conditions, a filament sliding of ∼ 11 nm. The mechanism of force generation by the myosin head depends on the relationship between cross-bridge force and movement, which is determined by compliances of the cross-bridge (C(cb)) and filaments. By measuring the force dependence of the spacing of the high-order myosin- and actin-based X-ray reflections from sartorius muscles of Rana esculenta we find a combined filament compliance (Cf) of 13.1 ± 1.2 nm MPa(-1), close to recent estimates from single fibre mechanics (12.8 ± 0.5 nm MPa(-1)). C(cb) calculated using these estimates is 0.37 ± 0.12 nm pN(-1), a value fully accounted for by the compliance of the myosin head domain, 0.38 ± 0.06 nm pN(-1), obtained from the intensity changes of the 14.5 nm myosin-based X-ray reflection in response to 3 kHz oscillations imposed on single muscle fibres in rigor. Thus, a significant contribution to C(cb) from the myosin tail that joins the head to the thick filament is excluded. The low C(cb) value indicates that the myosin head generates isometric force by a small sub-step of the 11 nm stroke that drives filament sliding at low load. The implications of these results for the mechanism of force generation by myosins have general relevance for cardiac and non-muscle myosins as well as for skeletal muscle.

Breakup and then makeup: a predictive model of how cilia self-regulate hardness for posture control

Functioning as sensors and propulsors, cilia are evolutionarily conserved organelles having a highly organized internal structure. How a paramecium's cilium produces off-propulsion-plane curvature during its return stroke for symmetry breaking and drag reduction is not known. We explain these cilium deformations by developing a torsional pendulum model of beat frequency dependence on viscosity and an olivo-cerebellar model of self-regulation of posture control. The phase dependence of cilia torsion is determined, and a bio-physical model of hardness control with predictive features is offered. Crossbridge links between the central microtubule pair harden the cilium during the power stroke; this stroke's end is a critical phase during which ATP molecules soften the crossbridge-microtubule attachment at the cilium inflection point where torsion is at its maximum. A precipitous reduction in hardness ensues, signaling the start of ATP hydrolysis that re-hardens the cilium. The cilium attractor basin could be used as reference for perturbation sensing.

A computational model of the response of adherent cells to stretch and changes in substrate stiffness

Cells in the body exist in a dynamic mechanical environment where they are subject to mechanical stretch as well as changes in composition and stiffness of the underlying extracellular matrix (ECM). However, the underlying mechanisms by which cells sense and adapt to their dynamic mechanical environment, in particular to stretch, are not well understood. In this study, we hypothesized that emergent phenomena at the level of the actin network arising from active structural rearrangements driven by nonmuscle myosin II molecular motors play a major role in the cellular response to both stretch and changes in ECM stiffness. To test this hypothesis, we introduce a simple network model of actin-myosin interactions that links active self-organization of the actin network to the stiffness of the network and the traction forces generated by the network. We demonstrate that such a network replicates not only the effect of changes in substrate stiffness on cellular traction and stiffness and the dependence of rate of force development by a cell on the stiffness of its substrate, but also explains the physical response of adherent cells to transient and cyclic stretch. Our results provide strong indication that network phenomena governed by the active reorganization of the actin-myosin structure plays an important role in cellular mechanosensing and response to both changes in ECM stiffness and externally applied mechanical stretch.

Stiffness, working stroke, and force of single-myosin molecules in skeletal muscle: elucidation of these mechanical properties via nonlinear elasticity evaluation

In muscles, the arrays of skeletal myosin molecules interact with actin filaments and continuously generate force at various contraction speeds. Therefore, it is crucial for myosin molecules to generate force collectively and minimize the interference between individual myosin molecules. Knowledge of the elasticity of myosin molecules is crucial for understanding the molecular mechanisms of muscle contractions because elasticity directly affects the working and drag (resistance) force generation when myosin molecules are positively or negatively strained. The working stroke distance is also an important mechanical property necessary for elucidation of the thermodynamic efficiency of muscle contractions at the molecular level. In this review, we focus on these mechanical properties obtained from single-fiber and single-molecule studies and discuss recent findings associated with these mechanical properties. We also discuss the potential molecular mechanisms associated with reduction of the drag effect caused by negatively strained myosin molecules.

Multiscale Coarse-Graining via Normal Mode Analysis

A multiscale coarse-graining method called the normal-mode analysis based fluctuation matching (NMA-FM) is developed for constructing coarse-grained models of biomolecular systems. In the framework of normal-mode analysis, an arbitrary fine-grained model can be systematically converted to a more coarse-grained model, while the crucial low-frequency motions of the fine-grained system are able to be reproduced in the coarse-grained modeling. The method relies on the technique of fluctuation matching that has been devised earlier for parametrizing heterogeneous elastic network models based on data from atomistic molecular dynamics simulations. The new approach is quite efficient since it avoids expensive atomistic molecular dynamics simulations and can start from already coarse-grained elastic network models. In the practical aspect, the method is suitable for conformational analyses of large biomacromolecules and calculations of mechanical properties of biomaterials, which is demonstrated by the studied systems including an amyloid dimer, lysozyme and adenylate kinase proteins, and the S2 subdomain of myosin.

The harmonic analysis of cylindrically symmetric proteins: a comparison of Dronpa and a DNA sliding clamp

The harmonic analysis of two types of proteins with cylindrical symmetry is performed by the Standard Force Field Normal Mode Analysis and by the elastic network model. For both proteins the global elastic modes are assigned to their characteristic topologies. Dronpa is a rigid β-barrel structure, presenting the twisting, bending and breathing motion of a cylindrical rod. The β sliding clamp of Escherichia coli is a hexagonal β-wheel, consisting of rigid segments. In its spectrum four classes of vibrations are identified which are characteristic of an elastic torus. Correlation diagrams and RMSF analysis are compared. The results provide not only a comprehensive validation of the use of both methods to describe the elastic behavior according to the low-frequency normal modes, but also depict the correlated motions of β-barrel and β-wheel proteins. The harmonic flexibility of the Dronpa protein is compared to the principal components of molecular dynamics (MD) simulation. A functionally important localized cleft opening mode is found, which is not detected by harmonic analysis.

Hysteresis-based mechanism for the directed motility of the Ncd motor

Ncd is a Kinesin-14 family protein that walks to the microtubule's minus end. Although available structures show its α-helical neck in either pre- or post-stroke orientations, little is known about the transition between these two states. Using a combination of molecular dynamics simulations and structural analyses, we find that the neck sequentially makes intermediate contacts with the motor head along its mostly longitudinal path, and it develops a 24° twist in the post-stroke orientation. The forward (pre-stroke to post-stroke) motion has an ∼4.5 k(B)T (where k(B) is the Boltzmann constant, and T=300 K) free-energy barrier and is a diffusion guided by the intermediate contacts. The post-stroke free-energy minimum is higher and is formed ∼10° before reaching the orientation in the post-stroke crystal structure, consistent with previous structural data. The importance of intermediate contacts correlates with the existing motility data, including those for mutant Ncds. Unlike the forward motion, the recovery stroke goes nearly downhill in free energy, powered in part by torsional relaxation of the neck. The hysteresis in the energetics of the neck motion arises from the mechanical compliance of the protein, and together with guided diffusion, it may be key to the directed motility of Ncd.

Coarse-grained modeling of conformational transitions underlying the processive stepping of myosin V dimer along filamentous actin

To explore the structural basis of processive stepping of myosin V along filamentous actin, we have performed comprehensive modeling of its key conformational states and transitions with an unprecedented residue level of details. We have built structural models for a myosin V monomer complexed with filamentous actin at four biochemical states [adenosine diphosphate (ATP)-, adenosine diphosphate (ADP)-phosphate-, ADP-bound or nucleotide-free]. Then we have modeled a myosin V dimer (consisting of lead and rear head) at various two-head-bound states with nearly straight lever arms rotated by intramolecular strain. Next, we have performed transition pathway modeling to determine the most favorable sequence of transitions (namely, phosphate release at the lead head followed by ADP release at the rear head, while ADP release at the lead head is inhibited), which underlie the kinetic coordination between the two heads. Finally, we have used transition pathway modeling to reveal the order of structural changes during three key biochemical transitions (phosphate release at the lead head, ADP release and ATP binding at the rear head), which shed lights on the strain-dependence of the allosterically coupled motions at various stages of myosin V's work cycle. Our modeling results are in agreement with and offer structural insights to many results of kinetic, single-molecule and structural studies of myosin V.

Mechanical response and conformational amplification in α-helical coiled coils

α-Helical coiled coils (CCs) are ubiquitous tertiary structural domains that are often found in mechanoproteins. CCs have mechanical rigidity and are often involved in force transmission between protein domains. Although crystal structures of CCs are available, information about their conformational flexibility is limited. The role of hydrophobic interactions in determining the CC conformation is not clear. In this work we examined the mechanical responses of typical CCs and constructed a coarse-grained mechanical model to describe the conformation of the protein. The model treats α-helices as elastic rods. Hydrophobic bonds arranged in a repeated pattern determine the CC structure. The model is compared with molecular-dynamics simulations of CCs under force. We also estimate the effective bending and twisting persistence length of the CC. The model allows us to examine unconventional responses of the CC, including significant conformational amplification upon binding of a small molecule. We find that the CC does not behave as a simple elastic rod and shows complex nonlinear responses. These results are significant for understanding the role of CC structures in chemoreceptors, motor proteins, and mechanotransduction in general.

Structural divergence of the rotary ATPases

The rotary ATPase family of membrane protein complexes may have only three members, but each one plays a fundamental role in biological energy conversion. The F1Fo-ATPase (F-ATPase) couples ATP synthesis to the electrochemical membrane potential in bacteria, mitochondria and chloroplasts, while the vacuolar H+-ATPase (V-ATPase) operates as an ATP-driven proton pump in eukaryotic membranes. In different species of archaea and bacteria, the A1Ao-ATPase (A-ATPase) can function as either an ATP synthase or an ion pump. All three of these multi-subunit complexes are rotary molecular motors, sharing a fundamentally similar mechanism in which rotational movement drives the energy conversion process. By analogy to macroscopic systems, individual subunits can be assigned to rotor, axle or stator functions. Recently, three-dimensional reconstructions from electron microscopy and single particle image processing have led to a significant step forward in understanding of the overall architecture of all three forms of these complexes and have allowed the organisation of subunits within the rotor and stator parts of the motors to be more clearly mapped out. This review describes the emerging consensus regarding the organisation of the rotor and stator components of V-, A- and F-ATPases, examining core similarities that point to a common evolutionary origin, and highlighting key differences. In particular, it discusses how newly revealed variation in the complexity of the inter-domain connections may impact on the mechanics and regulation of these molecular machines.

Two rotary motors in F-ATP synthase are elastically coupled by a flexible rotor and a stiff stator stalk

ATP is synthesized by ATP synthase (F(O)F(1)-ATPase). Its rotary electromotor (F(O)) translocates protons (in some organisms sodium cations) and generates torque to drive the rotary chemical generator (F(1)). Elastic power transmission between F(O) and F(1) is essential for smoothing the cooperation of these stepping motors, thereby increasing their kinetic efficiency. A particularly compliant elastic domain is located on the central rotor (c(10-15)/ε/γ), right between the two sites of torque generation and consumption. The hinge on the active lever on subunit β adds further compliance. It is under contention whether or not the peripheral stalk (and the "stator" as a whole) also serves as elastic buffer. In the enzyme from Escherichia coli, the most extended component of the stalk is the homodimer b(2), a right-handed α-helical coiled coil. By fluctuation analysis we determined the spring constant of the stator in response to twisting and bending, and compared wild-type with b-mutant enzymes. In both deformation modes, the stator was very stiff in the wild type. It was more compliant if b was elongated by 11 amino acid residues. Substitution of three consecutive residues in b by glycine, expected to destabilize its α-helical structure, further reduced the stiffness against bending deformation. In any case, the stator was at least 10-fold stiffer than the rotor, and the enzyme retained its proton-coupled activity.

Human essential myosin light chain isoforms revealed distinct myosin binding, sarcomeric sorting, and inotropic activity

AIMS

In this paper, we tested the hypothesis that different binding affinities of the C-terminus of human cardiac alkali (essential) myosin light chain (A1) isoforms to the IQ1 motif of the myosin lever arm provide a molecular basis for distinct sarcomeric sorting and inotropic activity.

METHODS AND RESULTS

We employed circular dichroism and surface plasmon resonance spectroscopy to investigate structural properties, secondary structures, and protein-protein interactions of a recombinant head-rod fragments of rat cardiac β-myosin heavy chain aa664-915 with alanine-mutated IQ2 domain (rβ-MYH(664-915)IQ(ala4)) and A1 isoforms [human atrial (hALC1) and human ventricular (hVLC-1) light chains]. Double epitope-tagging competition was used to monitor the intracellular localization of exogenously introduced hALC-1 and hVLC-1 constructs in neonatal rat cardiomyocytes. Contractile functions of A1 isoforms were investigated by monitoring shortening and intracellular-free Ca(2+) (Fura-2) of adult rat cardiomyocytes infected with adenoviral (Ad) vectors using hALC-1 or β-galactosidase as expression cassettes. hALC-1 bound more strongly (greater than three-fold lower K(D)) to rβ-MYH(664-915) than did hVLC-1. Sorting specificity of A1 isoforms to sarcomeres of cardiomyocytes rose in the order hVLC-1 to hALC-1. Replacement of endogenous VLC-1 by hALC-1 in adult rat cardiomyocytes increased contractility while the systolic Ca(2+) signal remained unchanged.

CONCLUSION

Intense myosin binding of hALC-1 provides a mechanism for preferential sarcomeric sorting and Ca(2+)-independent positive inotropic activity.

Anisotropic elastic network modeling of entire microtubules

Microtubules are supramolecular structures that make up the cytoskeleton and strongly affect the mechanical properties of the cell. Within the cytoskeleton filaments, the microtubule (MT) exhibits by far the highest bending stiffness. Bending stiffness depends on the mechanical properties and intermolecular interactions of the tubulin dimers (the MT building blocks). Computational molecular modeling has the potential for obtaining quantitative insights into this area. However, to our knowledge, standard molecular modeling techniques, such as molecular dynamics (MD) and normal mode analysis (NMA), are not yet able to simulate large molecular structures like the MTs; in fact, their possibilities are normally limited to much smaller protein complexes. In this work, we developed a multiscale approach by merging the modeling contribution from MD and NMA. In particular, MD simulations were used to refine the molecular conformation and arrangement of the tubulin dimers inside the MT lattice. Subsequently, NMA was used to investigate the vibrational properties of MTs modeled as an elastic network. The coarse-grain model here developed can describe systems of hundreds of interacting tubulin monomers (corresponding to up to 1,000,000 atoms). In particular, we were able to simulate coarse-grain models of entire MTs, with lengths up to 350 nm. A quantitative mechanical investigation was performed; from the bending and stretching modes, we estimated MT macroscopic properties such as bending stiffness, Young modulus, and persistence length, thus allowing a direct comparison with experimental data.

Second harmonic generation microscopy probes different states of motor protein interaction in myofibrils

The second harmonic generation (SHG) signal intensity sourced from skeletal muscle myosin II strongly depends on the polarization of the incident laser beam relative to the muscle fiber axis. This dependence is related to the second-order susceptibility χ((2)), which can be described by a single component ratio γ under generally assumed symmetries. We precisely extracted γ from SHG polarization dependence curves with an extended focal field model. In murine myofibrillar preparations, we have found two distinct polarization dependencies: With the actomyosin system in the rigor state, γ(rig) has a mean value of γ(rig) = 0.52 (SD = 0.04, n = 55); in a relaxed state where myosin is not bound to actin, γ(rel) has a mean value of γ(rel) = 0.24 (SD = 0.07, n = 70). We observed a similar value in an activated state where the myosin power stroke was pharmacologically inhibited using N-benzyl-p-toluene sulfonamide. In summary, different actomyosin states can be visualized noninvasively with SHG microscopy. Specifically, SHG even allows us to distinguish different actin-bound states of myosin II using γ as a parameter.

Nonlinear elasticity and an 8-nm working stroke of single myosin molecules in myofilaments

Using optical trapping and fluorescence imaging techniques, we measured the step size and stiffness of single skeletal myosins interacting with actin filaments and arranged on myosin-rod cofilaments that approximate myosin mechanics during muscle contraction. Stiffness is dramatically lower for negatively compared to positively strained myosins, consistent with buckling of myosin's subfragment 2 rod domain. Low stiffness minimizes drag of negatively strained myosins during contraction at loaded conditions. Myosin's elastic portion is stretched during active force generation, reducing apparent step size with increasing load, even though the working stroke is approximately constant at about 8 nanometers. Taking account of the nonlinear nature of myosin elasticity is essential to relate myosin's internal structural changes to physiological force generation and filament sliding.

Equilibrium sampling for biomolecules under mechanical tension

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

Alternative S2 hinge regions of the myosin rod affect myofibrillar structure and myosin kinetics

The subfragment 2/light meromyosin "hinge" region has been proposed to significantly contribute to muscle contraction force and/or speed. Transgenic replacement of the endogenous fast muscle isovariant hinge A (exon 15a) in Drosophila melanogaster indirect flight muscle with the slow muscle hinge B (exon 15b) allows examination of the structural and functional changes when only this region of the myosin molecule is different. Hinge B was previously shown to increase myosin rod length, increase A-band and sarcomere length, and decrease flight performance compared to hinge A. We applied additional measures to these transgenic lines to further evaluate the consequences of modifying this hinge region. Structurally, the longer A-band and sarcomere lengths found in the hinge B myofibrils appear to be due to the longitudinal addition of myosin heads. Functionally, hinge B, although a significant distance from the myosin catalytic domain, alters myosin kinetics in a manner consistent with this region increasing myosin rod length. These structural and functional changes combine to decrease whole fly wing-beat frequency and flight performance. Our results indicate that this hinge region plays an important role in determining myosin kinetics and in regulating thick and thin filament lengths as well as sarcomere length.

Mechanical design of translocating motor proteins

Translocating motors generate force and move along a biofilament track to achieve diverse functions including gene transcription, translation, intracellular cargo transport, protein degradation, and muscle contraction. Advances in single molecule manipulation experiments, structural biology, and computational analysis are making it possible to consider common mechanical design principles of these diverse families of motors. Here, we propose a mechanical parts list that include track, energy conversion machinery, and moving parts. Energy is supplied not just by burning of a fuel molecule, but there are other sources or sinks of free energy, by binding and release of a fuel or products, or similarly between the motor and the track. Dynamic conformational changes of the motor domain can be regarded as controlling the flow of free energy to and from the surrounding heat reservoir. Multiple motor domains are organized in distinct ways to achieve motility under imposed physical constraints. Transcending amino acid sequence and structure, physically and functionally similar mechanical parts may have evolved as nature's design strategy for these molecular engines.