Strength and lifetime of the bond between actin and skeletal muscle alpha-actinin studied with an optical trapping technique

Dilated cardiomyopathy mutation in beta-cardiac myosin enhances actin activation of the power stroke and phosphate release

Inherited mutations in human beta-cardiac myosin (M2β) can lead to severe forms of heart failure. The E525K mutation in M2β is associated with dilated cardiomyopathy (DCM) and was found to stabilize the interacting heads motif (IHM) and autoinhibited super-relaxed (SRX) state in dimeric heavy meromyosin. However, in monomeric M2β subfragment 1 (S1) we found that E525K enhances (3-fold) the maximum steady-state actin-activated ATPase activity ( k cat ) and decreases (6-fold) the actin concentration at which ATPase is one-half maximal ( K ATPase ). We also found a 3 to 4-fold increase in the actin-activated power stroke and phosphate release rate constants at 30 μM actin, which overall enhanced the duty ratio 3-fold. Loaded motility assays revealed that the enhanced intrinsic motor activity translates to increased ensemble force in M2β S1. Glutamate 525, located near the actin binding region in the so-called activation loop, is highly conserved and predicted to form a salt-bridge with another conserved residue (lysine 484) in the relay helix. Enhanced sampling molecular dynamics simulations predict that the charge reversal mutation disrupts the E525-K484 salt-bridge, inducing conformations with a more flexible relay helix and a wide phosphate release tunnel. Our results highlight a highly conserved allosteric pathway associated with actin activation of the power stroke and phosphate release and suggest an important feature of the autoinhibited IHM is to prevent this region of myosin from interacting with actin. The ability of the E525K mutation to stabilize the IHM likely overrides the enhanced intrinsic motor properties, which may be key to triggering DCM pathogenesis.

Significance Statement

Heart disease can be caused by inherited mutations in beta-cardiac myosin, the molecular motor that powers systolic contraction in the ventricles of the heart. However, it remains unclear how these mutations lead to contractile dysfunction and pathogenic remodeling of the heart. We investigated a unique dilated cardiomyopathy mutation (E525K) that dramatically stabilizes the autoinhibited state while enhancing intrinsic motor function. Thus, we examined how this mutation impacts transient kinetic steps of the ATPase cycle, motile properties, and structural changes associated with the power stroke and phosphate release. Our results provide a kinetic and structural basis for how beta-cardiac myosin mutations may disrupt molecular-level contractile function in complex ways, which may inform the development of targeted therapeutics.

Three-dimensional mechanical characterization of murine skeletal muscle using quantitative micro-elastography

Skeletal muscle function is governed by both the mechanical and structural properties of its constituent tissues, which are both modified by disease. Characterizing the mechanical properties of skeletal muscle tissue at an intermediate scale, i.e., between that of cells and organs, can provide insight into diseases such as muscular dystrophies. In this study, we use quantitative micro-elastography (QME) to characterize the micro-scale elasticity of ex vivo murine skeletal muscle in three-dimensions in whole muscles. To address the challenge of achieving high QME image quality with samples featuring uneven surfaces and geometry, we encapsulate the muscles in transparent hydrogels with flat surfaces. Using this method, we study aging and disease in quadriceps tissue by comparing normal wild-type (C57BL/6J) mice with dysferlin-deficient BLAJ mice, a model for the muscular dystrophy dysferlinopathy, at 3, 10, and 24 months of age (sample size of three per group). We observe a 77% decrease in elasticity at 24 months in dysferlin-deficient quadriceps compared to wild-type quadriceps.

A computational modeling of invadopodia protrusion into an extracellular matrix fiber network

Invadopodia are dynamic actin-rich membrane protrusions that have been implicated in cancer cell invasion and metastasis. In addition, invasiveness of cancer cells is strongly correlated with invadopodia formation, which are observed during extravasation and colonization of metastatic cancer cells at secondary sites. However, quantitative understanding of the interaction of invadopodia with extracellular matrix (ECM) is lacking, and how invadopodia protrusion speed is associated with the frequency of protrusion-retraction cycles remains unknown. Here, we present a computational framework for the characterization of invadopodia protrusions which allows two way interactions between intracellular branched actin network and ECM fibers network. We have applied this approach to predicting the invasiveness of cancer cells by computationally knocking out actin-crosslinking molecules, such as α-actinin, filamin and fascin. The resulting simulations reveal distinct invadopodia dynamics with cycles of protrusion and retraction. Specifically, we found that (1) increasing accumulation of MT1-MMP at tips of invadopodia as the duration of protrusive phase is increased, and (2) the movement of nucleus toward the leading edge of the cell becomes unstable as duration of the retractile phase (or myosin turnover time) is longer than 1 min.

Binding Dynamics of α-Actinin-4 in Dependence of Actin Cortex Tension

Mechanosensation of cells is an important prerequisite for cellular function, e.g., in the context of cell migration, tissue organization, and morphogenesis. An important mechanochemical transducer is the actin cytoskeleton. In fact, previous studies have shown that actin cross-linkers such as α-actinin-4 exhibit mechanosensitive properties in their binding dynamics to actin polymers. However, to date, a quantitative analysis of tension-dependent binding dynamics in live cells is lacking. Here, we present a, to our knowledge, new technique that allows us to quantitatively characterize the dependence of cross-linking lifetime of actin cross-linkers on mechanical tension in the actin cortex of live cells. We use an approach that combines parallel plate confinement of round cells, fluorescence recovery after photobleaching, and a mathematical mean-field model of cross-linker binding. We apply our approach to the actin cross-linker α-actinin-4 and show that the cross-linking time of α-actinin-4 homodimers increases approximately twofold within the cellular range of cortical mechanical tension, rendering α-actinin-4 a catch bond in physiological tension ranges.

Reversal of contractility as a signature of self-organization in cytoskeletal bundles

Bundles of cytoskeletal filaments and molecular motors generate motion in living cells, and have internal structures ranging from very organized to apparently disordered. The mechanisms powering the disordered structures are debated, and existing models predominantly predict that they are contractile. We reexamine this prediction through a theoretical treatment of the interplay between three well-characterized internal dynamical processes in cytoskeletal bundles: filament assembly and disassembly, the attachement-detachment dynamics of motors and that of crosslinking proteins. The resulting self-organization is easily understood in terms of motor and crosslink localization, and allows for an extensive control of the active bundle mechanics, including reversals of the filaments’ apparent velocities and the possibility of generating extension instead of contraction. This reversal mirrors some recent experimental observations, and provides a robust criterion to experimentally elucidate the underpinnings of both actomyosin activity and the dynamics of microtubule/motor assemblies in vitro as well as in diverse intracellular structures ranging from contractile bundles to the mitotic spindle.

Frustrated binding of biopolymer crosslinkers

Transiently crosslinked actin filament networks allow cells to combine elastic rigidity with the ability to deform viscoelastically. Theoretical models of semiflexible polymer networks predict that the crosslinker unbinding rate governs the timescale beyond which viscoelastic flow occurs. However a direct comparison between network and crosslinker dynamics is lacking. Here we measure the network's stress relaxation timescale using rheology and the lifetime of bound crosslinkers using fluorescence recovery after photobleaching (FRAP). Intriguingly, we observe that the crosslinker unbinding rate measured by FRAP is more than an order of magnitude slower than the rate measured by rheology. We rationalize this difference with a three-state model where crosslinkers are bound to either 0, 1 or 2 filaments, which allows us to extract crosslinker transition rates that are otherwise difficult to access. We find that the unbinding rate of singly bound crosslinkers is nearly two orders of magnitude slower than for doubly bound ones. We attribute the increased unbinding rate of doubly bound crosslinkers to the high stiffness of biopolymers, which frustrates crosslinker binding.

Systematic Nanoscale Analysis of Endocytosis Links Efficient Vesicle Formation to Patterned Actin Nucleation

Clathrin-mediated endocytosis is an essential cellular function in all eukaryotes that is driven by a self-assembled macromolecular machine of over 50 different proteins in tens to hundreds of copies. How these proteins are organized to produce endocytic vesicles with high precision and efficiency is not understood. Here, we developed high-throughput superresolution microscopy to reconstruct the nanoscale structural organization of 23 endocytic proteins from over 100,000 endocytic sites in yeast. We found that proteins assemble by radially ordered recruitment according to function. WASP family proteins form a circular nanoscale template on the membrane to spatially control actin nucleation during vesicle formation. Mathematical modeling of actin polymerization showed that this WASP nano-template optimizes force generation for membrane invagination and substantially increases the efficiency of endocytosis. Such nanoscale pre-patterning of actin nucleation may represent a general design principle for directional force generation in membrane remodeling processes such as during cell migration and division.

Manipulation of cells with laser microbeam scissors and optical tweezers: a review

The use of laser microbeams and optical tweezers in a wide field of biological applications from genomic to immunology is discussed. Microperforation is used to introduce a well-defined amount of molecules into cells for genetic engineering and optical imaging. The microwelding of two cells induced by a laser microbeam combines their genetic outfit. Microdissection allows specific regions of genomes to be isolated from a whole set of chromosomes. Handling the cells with optical tweezers supports investigation on the attack of immune systems against diseased or cancerous cells. With the help of laser microbeams, heart infarction can be simulated, and optical tweezers support studies on the heartbeat. Finally, laser microbeams are used to induce DNA damage in living cells for studies on cancer and ageing.

The dynamics of filament assembly define cytoskeletal network morphology

The actin cytoskeleton is a key component in the machinery of eukaryotic cells, and it self-assembles out of equilibrium into a wide variety of biologically crucial structures. Although the molecular mechanisms involved are well characterized, the physical principles governing the spatial arrangement of actin filaments are not understood. Here we propose that the dynamics of actin network assembly from growing filaments results from a competition between diffusion, bundling and steric hindrance, and is responsible for the range of observed morphologies. Our model and simulations thus predict an abrupt dynamical transition between homogeneous and strongly bundled networks as a function of the actin polymerization rate. This suggests that cells may effect dramatic changes to their internal architecture through minute modifications of their nonequilibrium dynamics. Our results are consistent with available experimental data.

The dynamics of actin cytoskeleton is essential to the function of living cells. Here, Foffano et al. describe a nonequilibrium filament model to mimic the formation of cytoskeleton and pinpoint the key role played by the actin entanglement during the transition from homogeneous to bundled networks.

Molecularly resolved label-free sensing of single nucleobase mismatches by interfacial LNA probes

So far, there has been no report on molecularly resolved discrimination of single nucleobase mismatches using surface-confined single stranded locked nucleic acid (ssLNA) probes. Herein, it is exemplified using a label-independent force-sensing approach that an optimal coverage of 12-mer ssLNA sensor probes formed onto gold(111) surface allows recognition of ssDNA targets with twice stronger force sensitivity than 12-mer ssDNA sensor probes. The force distributions are reproducible and the molecule-by-molecule force measurements are largely in agreement with ensemble on-surface melting temperature data. Importantly, the molecularly resolved detection is responsive to the presence of single nucleobase mismatches in target sequences. Since the labelling steps can be eliminated from protocol, and each force-based detection event occurs within milliseconds' time scale, the force-sensing assay is potentially capable of rapid detection. The LNA probe performance is indicative of versatility in terms of substrate choice - be it gold (for basic research and array-based applications) or silicon (for ‘lab-on-a-chip’ type devices). The nucleic acid microarray technologies could therefore be generally benefited by adopting the LNA films, in place of DNA. Since LNA is nuclease-resistant, unlike DNA, and the LNA-based assay is sensitive to single nucleobase mismatches, the possibilities for label-free in vitro rapid diagnostics based on the LNA probes may be explored.

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.

Study of the influence of actin-binding proteins using linear analyses of cell deformability

The actin cytoskeleton plays a key role in the deformability of the cell and in mechanosensing. Here we analyze the contributions of three major actin cross-linking proteins, myosin II, α-actinin and filamin, to cell deformability, by using micropipette aspiration of Dictyostelium cells. We examine the applicability of three simple mechanical models: for small deformation, linear viscoelasticity and drop of liquid with a tense cortex; and for large deformation, a Newtonian viscous fluid. For these models, we have derived linearized equations and we provide a novel, straightforward methodology to analyze the experiments. This methodology allowed us to differentiate the effects of the cross-linking proteins in the different regimes of deformation. Our results confirm some previous observations and suggest important relations between the molecular characteristics of the actin-binding proteins and the cell behavior: the effect of myosin is explained in terms of the relation between the lifetime of the bond to actin and the resistive force; the presence of α-actinin obstructs the deformation of the cytoskeleton, presumably mainly due to the higher molecular stiffness and to the lower dissociation rate constants; and filamin contributes critically to the global connectivity of the network, possibly by rapidly turning over cross-links during the remodeling of the cytoskeletal network, thanks to the higher rate constants, flexibility and larger size. The results suggest a sophisticated relationship between the expression levels of actin-binding proteins, deformability and mechanosensing.

Isoforms Confer Characteristic Force Generation and Mechanosensation by Myosin II Filaments

Myosin II isoforms with varying mechanochemistry and filament size interact with filamentous actin (F-actin) arrays to generate contractile forces in muscle and nonmuscle cells. How myosin II force production is shaped by isoform-specific motor properties and environmental stiffness remains poorly understood. Here, we used computer simulations to analyze force production by an ensemble of myosin motors against an elastically tethered actin filament. We found that force output depends on two timescales: the duration of F-actin attachment, which varies sharply with the ensemble size, motor duty ratio, and external load; and the time to build force, which scales with the ensemble stall force, gliding speed, and environmental stiffness. Although force-dependent kinetics were not required to sense changes in stiffness, the myosin catch bond produced positive feedback between the attachment time and force to trigger switch-like transitions from transient attachments, generating small forces, to high-force-generating runs. Using parameters representative of skeletal muscle myosin, nonmuscle myosin IIB, and nonmuscle myosin IIA revealed three distinct regimes of behavior, respectively: 1) large assemblies of fast, low-duty ratio motors rapidly build stable forces over a large range of environmental stiffness; 2) ensembles of slow, high-duty ratio motors serve as high-affinity cross-links with force buildup times that exceed physiological timescales; and 3) small assemblies of low-duty ratio motors operating at intermediate speeds are poised to respond sharply to changes in mechanical context-at low force or stiffness, they serve as low-affinity cross-links, but they can transition to force production via the positive-feedback mechanism described above. Together, these results reveal how myosin isoform properties may be tuned to produce force and respond to mechanical cues in their environment.

The path to visualization of walking myosin V by high-speed atomic force microscopy

The quest for understanding the mechanism of myosin-based motility started with studies on muscle contraction. From numerous studies, the basic frameworks for this mechanism were constructed and brilliant hypotheses were put forward. However, the argument about the most crucial issue of how the actin-myosin interaction generates contractile force and shortening has not been definitive. To increase the "directness of measurement", in vitro motility assays and single-molecule optical techniques were created and used. Consequently, detailed knowledge of the motility of muscle myosin evolved, which resulted in provoking more arguments to a higher level. In parallel with technical progress, advances in cell biology led to the discovery of many classes of myosins. Myosin V was discovered to be a processive motor, unlike myosin II. The processivity reduced experimental difficulties because it allowed continuous tracing of the motor action of single myosin V molecules. Extensive studies of myosin V were expected to resolve arguments and build a consensus but did not necessarily do so. The directness of measurement was further enhanced by the recent advent of high-speed atomic force microscopy capable of directly visualizing biological molecules in action at high spatiotemporal resolution. This microscopy clearly visualized myosin V molecules walking on actin filaments and at last provided irrefutable evidence for the swinging lever-arm motion propelling the molecules. However, a peculiar foot stomp behavior also appeared in the AFM movie, raising new questions of the chemo-mechanical coupling in this motor and myosin motors in general. This article reviews these changes in the research of myosin motility and proposes new ideas to resolve the newly raised questions.

Actin dynamics, architecture, and mechanics in cell motility

Tight coupling between biochemical and mechanical properties of the actin cytoskeleton drives a large range of cellular processes including polarity establishment, morphogenesis, and motility. This is possible because actin filaments are semi-flexible polymers that, in conjunction with the molecular motor myosin, can act as biological active springs or "dashpots" (in laymen's terms, shock absorbers or fluidizers) able to exert or resist against force in a cellular environment. To modulate their mechanical properties, actin filaments can organize into a variety of architectures generating a diversity of cellular organizations including branched or crosslinked networks in the lamellipodium, parallel bundles in filopodia, and antiparallel structures in contractile fibers. In this review we describe the feedback loop between biochemical and mechanical properties of actin organization at the molecular level in vitro, then we integrate this knowledge into our current understanding of cellular actin organization and its physiological roles.

Application of atomic force microscopy for characteristics of single intermolecular interactions

Atomic force microscopy (AFM) can be used to make measurements in vacuum, air, and water. The method is able to gather information about intermolecular interaction forces at the level of single molecules. This review encompasses experimental and theoretical data on the characterization of ligand-receptor interactions by AFM. The advantage of AFM in comparison with other methods developed for the characterization of single molecular interactions is its ability to estimate not only rupture forces, but also thermodynamic and kinetic parameters of the rupture of a complex. The specific features of force spectroscopy applied to ligand-receptor interactions are examined in this review from the stage of the modification of the substrate and the cantilever up to the processing and interpretation of the data. We show the specificities of the statistical analysis of the array of data based on the results of AFM measurements, and we discuss transformation of data into thermodynamic and kinetic parameters (kinetic dissociation constant, Gibbs free energy, enthalpy, and entropy). Particular attention is paid to the study of polyvalent interactions, where the definition of the constants is hampered due to the complex stoichiometry of the reactions.

Molecular machines directly observed by high-speed atomic force microscopy

Molecular machines made of proteins are highly dynamic and carry out sophisticated biological functions. The direct and dynamic high-resolution visualization of molecular machines in action is considered to be the most straightforward approach to understanding how they function but this has long been infeasible until recently. High-speed atomic force microscopy has recently been realized, making such visualization possible. The captured images of myosin V, F1-ATPase, and bacteriorhodopsin have enabled their dynamic processes and structure dynamics to be revealed in great detail, giving unique and deep insights into their functional mechanisms.

Finding the weakest link: exploring integrin-mediated mechanical molecular pathways

From the extracellular matrix to the cytoskeleton, a network of molecular links connects cells to their environment. Molecules in this network transmit and detect mechanical forces, which subsequently determine cell behavior and fate. Here, we reconstruct the mechanical pathway followed by these forces. From matrix proteins to actin through integrins and adaptor proteins, we review how forces affect the lifetime of bonds and stretch or alter the conformation of proteins, and how these mechanical changes are converted into biochemical signals in mechanotransduction events. We evaluate which of the proteins in the network can participate in mechanotransduction and which are simply responsible for transmitting forces in a dynamic network. Besides their individual properties, we also analyze how the mechanical responses of a protein are determined by their serial connections from the matrix to actin, their parallel connections in integrin clusters and by the rate at which force is applied to them. All these define mechanical molecular pathways in cells, which are emerging as key regulators of cell function alongside better studied biochemical pathways.

Measuring forces between two single actin filaments during bundle formation

Bundles of filamentous actin are dominant cytoskeletal structures, which play a crucial role in various cellular processes. As yet quantifying the fundamental interaction between two individual actin filaments forming the smallest possible bundle has not been realized. Applying holographic optical tweezers integrated with a microfluidic platform, we were able to measure the forces between two actin filaments during bundle formation. Quantitative analysis yields forces up to 0.2 pN depending on the concentration of bundling agents.

Dynamic molecular processes mediate cellular mechanotransduction

Cellular responses to mechanical forces are crucial in embryonic development and adult physiology, and are involved in numerous diseases, including atherosclerosis, hypertension, osteoporosis, muscular dystrophy, myopathies and cancer. These responses are mediated by load-bearing subcellular structures, such as the plasma membrane, cell-adhesion complexes and the cytoskeleton. Recent work has demonstrated that these structures are dynamic, undergoing assembly, disassembly and movement, even when ostensibly stable. An emerging insight is that transduction of forces into biochemical signals occurs within the context of these processes. This framework helps to explain how forces of varying strengths or dynamic characteristics regulate distinct signalling pathways.

Cytoskeletal cross-linking and bundling in motor-independent contraction

Eukaryotic and prokaryotic cells use cytoskeletal proteins to regulate and modify cell shape. During cytokinesis or eukaryotic cell crawling, contractile forces are generated inside the cell to constrict the division site or to haul the rear of the cell forward, respectively. In many cases, these forces have been attributed to the activity of molecular motors, such as myosin II, which, by pulling on actin filaments, can produce contraction of the actin cytoskeleton. However, prokaryotic division is driven by the tubulin-like protein FtsZ and does not seem to require additional molecular motors to constrict the division site. Likewise, Dictyostelium discoideum and Saccharomyces cerevisiae can perform cytokinesis under motor-free conditions. In addition, many crawling cells can translocate when myosin is inhibited or absent. In this review, we point out another force-generation mechanism that can play a significant role in driving these processes in eukaryotes and prokaryotes. This mechanism is mediated by cross-linking and bundling proteins that form effective interactions between cytoskeletal filaments. Some recent studies in this area are reviewed and the physical underpinnings of this force-generation mechanism are explained.

Cross-link-governed dynamics of biopolymer networks

Recent experiments show that networks of stiff biopolymers cross-linked by transient linker proteins exhibit complex stress relaxation, enabling network flow at long times. We present a model for the dynamics controlled by cross-links in such networks. We show that a single microscopic time scale for cross-linker unbinding leads to a broad spectrum of macroscopic relaxation times and a shear modulus G ∼ ω(1/2) for low frequencies ω. This model quantitatively describes the measured rheology of actin networks cross-linked with α-actinin-4 over more than four decades in frequency.

Molecular origin of strain softening in cross-linked F-actin networks

Two types of measurement are presented that relate molecular events to macroscopic behavior of F-actin networks. First, shear modulus is measured by oscillating an embedded microbead. Second, a microbead is translated at constant rate and transitions in the resisting force are observed. The loading rate dependence of the force at the transitions is similar to that of the molecular unbinding force, suggesting that they share a common origin. Reversibility tests of shear modulus provide further evidence that strain softening of F-actin networks is caused by force-induced rupture of cross-links.

Actin cross-link assembly and disassembly mechanics for alpha-Actinin and fascin

Self-assembly of complex structures is commonplace in biology but often poorly understood. In the case of the actin cytoskeleton, a great deal is known about the components that include higher order structures, such as lamellar meshes, filopodial bundles, and stress fibers. Each of these cytoskeletal structures contains actin filaments and cross-linking proteins, but the role of cross-linking proteins in the initial steps of structure formation has not been clearly elucidated. We employ an optical trapping assay to investigate the behaviors of two actin cross-linking proteins, fascin and alpha-actinin, during the first steps of structure assembly. Here, we show that these proteins have distinct binding characteristics that cause them to recognize and cross-link filaments that are arranged with specific geometries. alpha-Actinin is a promiscuous cross-linker, linking filaments over all angles. It retains this flexibility after cross-links are formed, maintaining a connection even when the link is rotated. Conversely, fascin is extremely selective, only cross-linking filaments in a parallel orientation. Surprisingly, bundles formed by either protein are extremely stable, persisting for over 0.5 h in a continuous wash. However, using fluorescence recovery after photobleaching and fluorescence decay experiments, we find that the stable fascin population can be rapidly competed away by free fascin. We present a simple avidity model for this cross-link dissociation behavior. Together, these results place constraints on how cytoskeletal structures assemble, organize, and disassemble in vivo.

The molecular basis of frictional loads in the in vitro motility assay with applications to the study of the loaded mechanochemistry of molecular motors

Molecular motors convert chemical energy into mechanical movement, generating forces necessary to accomplish an array of cellular functions. Since molecular motors generate force, they typically work under loaded conditions where the motor mechanochemistry is altered by the presence of a load. Several biophysical techniques have been developed to study the loaded behavior and force generating capabilities of molecular motors yet most of these techniques require specialized equipment. The frictional loading assay is a modification to the in vitro motility assay that can be performed on a standard epifluorescence microscope, permitting the high-throughput measurement of the loaded mechanochemistry of molecular motors. Here, we describe a model for the molecular basis of the frictional loading assay by modeling the load as a series of either elastic or viscoelastic elements. The model, which calculates the frictional loads imposed by different binding proteins, permits the measurement of isotonic kinetics, force-velocity relationships, and power curves in the motility assay. We show computationally and experimentally that the frictional load imposed by alpha-actinin, the most widely employed actin binding protein in frictional loading experiments, behaves as a viscoelastic rather than purely elastic load. As a test of the model, we examined the frictional loading behavior of rabbit skeletal muscle myosin under normal and fatigue-like conditions using alpha-actinin as a load. We found that, consistent with fiber studies, fatigue-like conditions cause reductions in myosin isometric force, unloaded sliding velocity, maximal power output, and shift the load at which peak power output occurs.

Statics and dynamics of the wormlike bundle model

Bundles of filamentous polymers are primary structural components of a broad range of cytoskeletal structures, and their mechanical properties play key roles in cellular functions ranging from locomotion to mechanotransduction and fertilization. We give a detailed derivation of a wormlike bundle model as a generic description for the statics and dynamics of polymer bundles consisting of semiflexible polymers interconnected by crosslinking agents. The elastic degrees of freedom include bending as well as twist deformations of the filaments and shear deformation of the crosslinks. We show that a competition between the elastic properties of the filaments and those of the crosslinks leads to renormalized effective bend and twist rigidities that become mode-number dependent. The strength and character of this dependence is found to vary with bundle architecture, such as the arrangement of filaments in the cross section and pretwist. We discuss two paradigmatic cases of bundle architecture, a uniform arrangement of filaments as found in F -actin bundles and a shell-like architecture as characteristic for microtubules. Each architecture is found to have its own universal ratio of maximal to minimal bending rigidity, independent of the specific type of crosslink-induced filament coupling; our predictions are in reasonable agreement with available experimental data for microtubules. Moreover, we analyze the predictions of the wormlike bundle model for experimental observables such as the tangent-tangent correlation function and dynamic response and correlation functions. Finally, we analyze the effect of pretwist (helicity) on the mechanical properties of bundles. We predict that microtubules with different number of protofilaments should have distinct variations in their effective bending rigidity.

The regulatory action of alpha-actinin on actin filaments is enhanced by cofilin

We have used fluorescence recovery after photobleaching to study the effect of muscle alpha-actinin on the structure of actin filaments in dilute solutions. Unexpectedly we found that alpha-actinin partitioned filaments into two types: those with a high mobility and those with low mobility. We have determined that the high mobility (smaller sized) population is too large to be simple monomeric actin:alpha-actinin complexes. Although it is known that cofilin encourages the transformation of alpha-actinin:actin gels into large meshworks of inter-digitating actin filament bundles (Maciver et al. 1991), we have found that the presence of cofilin also increases the cross-linking of actin filaments by alpha-actinin and hypothesize that this is due to cofilin's ability to alter the filament twist. This effectively makes more potential alpha-actinin binding sites per unit of actin filament. As expected from previous work, this effect was more marked at pH 6.5 than at pH 8.0. Both effects are likely to operate in cells to deny other actin-binding proteins access to binding these particular filaments and may explain how very different actin cytoskeletal structures may co-exist in the same cell at the same time.

Cell mechanics: dissecting the physical responses of cells to force

It is now widely appreciated that normal tissue morphology and function rely upon cells' ability to sense and generate forces appropriate to their correct tissue context. Although the effects of forces on cells have been studied for decades, our understanding of how those forces propagate through and act on different cell substructures remains at an early stage. The past decade has seen a resurgence of interest, with a variety of different micromechanical methods in current use that probe cells' dynamic deformation in response to a time-varying force. The ability of researchers to carefully measure the mechanical properties of cells subjected to a variety of pharmacological and genetic interventions, however, currently outstrips our ability to quantitatively interpret the data in many cases. Despite these challenges, the stage is now set for the development of detailed models for cell deformability, motility, and mechanosensing that are rooted at the molecular level.

Nonlinear elasticity of stiff biopolymers connected by flexible linkers

Networks of the biopolymer actin, cross-linked by the compliant protein filamin, form soft gels. They can, however, withstand large shear stresses due to their pronounced nonlinear elastic behavior. The nonlinear elasticity can be controlled by varying the number of cross-links per actin filament. We propose and test a model of rigid filaments decorated by multiple flexible linkers that is in quantitative agreement with experiment. This allows us to estimate loads on individual cross-links, which we find to be less than 10 pN.

Studying Molecular Interactions at the Single Bond Level with a Laminar Flow Chamber

During the last decade, many investigators developed new methodologies allowing to study ligand-receptor interactions with unprecedented accuracy, up to the single bond level. Reported results include information on bond mechanical properties, association behaviour of surface-attached molecules, and dissection of energy landscapes and reaction pathways. The purpose of the present review is to discuss the potential and limitations of laminar flow chambers operated at low shear rates. This includes a brief review of basic principles, practical tips and problems associated with data interpretation. It is concluded that flow chambers are ideally suited to analyze weak interactions between a number of biomolecules, including the main families of adhesion receptors such as selectins, integrins, cadherins and members of the immunoglobulin superfamily. The sensitivity of the method is limited by the quality of surfaces and efficiency of the studied ligand-receptor couple rather than the hardware. Analyzing interactions with a resolution of a piconewton and a few milliseconds shows that ligand-receptor complexes may experience a number of intermediate binding states, making it necessary to examine the definition of association and dissociation rates. Finally, it is emphasized that association rates measured on surface-bound molecules are highly dependent on parameters unrelated to binding surfaces.

Transient binding and dissipation in cross-linked actin networks

In contrast with entangled actin solutions, transiently cross-linked actin networks can provide highly elastic properties while still allowing for local rearrangements in the microstructure-on biological relevant time scales. Here, we show that thermal unbinding of transient cross-links entails local stress relaxation and energy dissipation in an intermediate elasticity dominated frequency regime. We quantify the viscoelastic response of an isotropically cross-linked actin network by experimentally tuning the off rate of the transiently cross-linking molecules, their density, and the solvent viscosity. We reproduce the measured frequency response by a semiphenomenological model that is predicated on microscopic unbinding events.

Measuring molecular rupture forces between single actin filaments and actin-binding proteins

Actin-binding proteins (ABPs) regulate the assembly of actin filaments (F-actin) into networks and bundles that provide the structural integrity of the cell. Two of these ABPs, filamin and alpha-actinin, have been extensively used to model the mechanical properties of actin networks grown in vitro; however, there is a lack in the understanding of how the molecular interactions between ABPs and F-actin regulate the dynamic properties of the cytoskeleton. Here, we present a native-like assay geometry to test the rupture force of a complex formed by an ABP linking two quasiparallel actin filaments. We readily demonstrate the adaptability of this assay by testing it with two different ABPs: filamin and alpha-actinin. For filamin/actin and alpha-actinin/actin, we measured similar rupture forces of 40-80 pN for loading rates between 4 and 50 pN/s. Both ABP unfolding and conformational transition events were observed, demonstrating that both are important and may be a significant mechanism for the temporal regulation of the mechanical properties of the actin cytoskeleton. With this modular, single-molecule assay, a wide range of ABP/actin interactions can be studied to better understand cytoskeletal and cell dynamics.

Fragility and mechanosensing in a thermalized cytoskeleton model with forced protein unfolding

We describe a model of cytoskeletal mechanics based on the force-induced conformational change of protein cross-links in a stressed polymer network. Slow deformation of simulated networks containing cross-links that undergo repeated, serial domain unfolding leads to an unusual state-with many cross-links accumulating near the critical force for further unfolding. This state is robust to thermalization and does not occur in similar protein unbinding based simulations. Moreover, we note that the unusual configuration of near-critical protein cross-links in the fragile state provides a physical mechanism for the chemical transduction of cell-level mechanical strain and extra-cellular matrix stiffness.

Cross-linker unbinding and self-similarity in bundled cytoskeletal networks

The macromechanical properties of purely bundled in vitro actin networks are not only determined by the micromechanical properties of individual bundles but also by molecular unbinding events of the actin-binding protein (ABP) fascin. Under high mechanical load the network elasticity depends on the forced unbinding of individual ABPs in a rate dependent manner. Cross-linker unbinding in combination with the structural self-similarity of the network enables the introduction of a concentration-time superposition principle--broadening the mechanically accessible frequency range over 8 orders of magnitude.

Viscoelasticity of isotropically cross-linked actin networks

Despite their importance for the proper function of living cells, the physical properties of cross-linked actin networks remain poorly understood as the occurrence of heterogeneities hamper a quantitative physical description. The isotropic homogeneously cross-linked actin network presented here enables us to quantitatively relate the network response to a single filament model by determining the dominating length scale. The frequency dependence of the linear response and nonuniversal form of the nonlinear response reveal the importance of cross-linker unbinding events.

A stochastic, cantilever approach to the evaluation of solution phase thermodynamic quantities

A cantilever device based on competitive binding of an immobilized receptor to immobilized and soluble ligand and capable of measuring solution-phase thermodynamic quantities is described. Through multiple binary queries, the device stochastically measures the probability of the formation of a bound complex between immobilized protein and immobilized ligand as a function of soluble ligand concentration. The resulting binding isotherm is described by a binding polynomial consisting of the activities of soluble and immobilized ligand and binding constants for the association of immobilized protein with free and immobilized ligand. Evaluation of the polynomial reveals an association constant for the formation of a complex between immobilized ligand and immobilized protein close to that for the formation of complex between soluble protein and soluble ligand. The methodology lays the foundation for construction of practical portable sensing devices.

Interlaced optical force-fluorescence measurements for single molecule biophysics

Combining optical tweezers with single molecule fluorescence offers a powerful technique to study the biophysical properties of single proteins and molecules. However, such integration into a combined, coincident arrangement has been severely limited by the dramatic reduction in fluorescence longevity of common dyes under simultaneous exposure to trapping and fluorescence excitation beams. We present a novel approach to overcome this problem by alternately modulating the optical trap and excitation beams to prevent simultaneous exposure of the fluorescent dye. We demonstrate the dramatic reduction of trap-induced photobleaching effects on the common single molecule fluorescence dye Cy3, which is highly susceptible to this destructive pathway. The extension in characteristic fluorophore longevity, a 20-fold improvement when compared to simultaneous exposure to both beams, prolongs the fluorescence emission to several tens of seconds in a combined, coincident arrangement. Furthermore, we show that this scheme, interlaced optical force-fluorescence, does not compromise the trap stiffness or single molecule fluorescence sensitivity at sufficiently high modulation frequencies. Such improvement permits the simultaneous measurement of the mechanical state of a system with optical tweezers and the localization of molecular changes with single molecule fluorescence, as demonstrated by mechanically unzipping a 15-basepair DNA segment labeled with Cy3.

Multi-step fibrinogen binding to the integrin (alpha)IIb(beta)3 detected using force spectroscopy

The regulated ability of integrin alphaIIbbeta3 to bind fibrinogen plays a crucial role in platelet aggregation and hemostasis. We have developed a model system based on laser tweezers, enabling us to measure specific rupture forces needed to separate single receptor-ligand complexes. First of all, we performed a thorough and statistically representative analysis of nonspecific protein-protein binding versus specific alphaIIbbeta3-fibrinogen interactions in combination with experimental evidence for single-molecule measurements. The rupture force distribution of purified alphaIIbbeta3 and fibrinogen, covalently attached to underlying surfaces, ranged from approximately 20 to 150 pN. This distribution could be fit with a sum of an exponential curve for weak to moderate (20-60 pN) forces, and a Gaussian curve for strong (>60 pN) rupture forces that peaked at 80-90 pN. The interactions corresponding to these rupture force regimes differed in their susceptibility to alphaIIbbeta3 antagonists or Mn2+, an alphaIIbbeta3 activator. Varying the surface density of fibrinogen changed the total binding probability linearly >3.5-fold but did not affect the shape of the rupture force distribution, indicating that the measurements represent single-molecule binding. The yield strength of alphaIIbbeta3-fibrinogen interactions was independent of the loading rate (160-16,000 pN/s), whereas their binding probability markedly correlated with the duration of contact. The aggregate of data provides evidence for complex multi-step binding/unbinding pathways of alphaIIbbeta3 and fibrinogen revealed at the single-molecule level.

Hierarchical self-assembly of actin bundle networks: Gels with surface protein skin layers

The networklike structure of actin bundles formed with the cross-linking protein alpha-actinin has been investigated via x-ray scattering and confocal fluorescence microscopy over a wide range of alpha-actinin/F-actin ratios. We describe the hierarchical structure of bundle gels formed at high ratios. Isotropic actin bundle gels form via cluster-cluster aggregation in the diffusion-limited aggregation regime at high alpha-actinin/actin ratios. This process is clearly observed by confocal fluorescence microscopy. Polylysine is investigated as an alternative bundling agent in the high-ratio regime and the effects of F-actin length are also discussed. One particularly fascinating aspect of this system is the presence of a structured skin layer at the gel/water interface. Confocal microscopy has elucidated the full three-dimensional structure of this layer and revealed several interesting morphologies. The protein skin layer is a micron-scale structure composed of a directed network of bundles and exhibits flat, crumpled, and tubelike shapes. We show that crumpling of the skin layer results from stresses due to the underlying gel. These biologically based geometric structures may detach from the gel, demonstrating potential for the generation of biological scaffolds with defined shapes for applications in cell encapsulation and tissue engineering. We demonstrate manipulation of the skin layer, producing hemispherical structures in solution.

The effect of alpha-actinin on the length distribution of F-actin

Actin filament length distribution in cells is often regulated to fit specific tasks. In comparison to the well-studied regulation of the average filament length (e.g., using capping proteins), controlling the width of the distribution is less well understood. We utilize two complementary methods to measure the effect of alpha-actinin on the width of the distribution of lengths of F-actin in vitro. Analyzing transmission electron micrographs shows that crosslinking by alpha-actinin reduces the width of the length distribution of F-actin, decreasing the coefficient of variation by two- to threefold. Analysis of fluorescence data from depolymerization assays confirms this observation. We suggest a mechanistic molecular model in which a local (weak) stabilization of crosslinked monomers in the filament is the physical origin of the decrease in the variance of lengths. Although alpha-actinin is known to bind reversibly to F-actin, our model shows that even weak binding can produce this effect, and that in fact it persists throughout a wide range of binding strengths.

Simultaneous, coincident optical trapping and single-molecule fluorescence

We constructed a microscope-based instrument capable of simultaneous, spatially coincident optical trapping and single-molecule fluorescence. The capabilities of this apparatus were demonstrated by studying the force-induced strand separation of a dye-labeled, 15-base-pair region of double-stranded DNA (dsDNA), with force applied either parallel ('unzipping' mode) or perpendicular ('shearing' mode) to the long axis of the region. Mechanical transitions corresponding to DNA hybrid rupture occurred simultaneously with discontinuous changes in the fluorescence emission. The rupture force was strongly dependent on the direction of applied force, indicating the existence of distinct unbinding pathways for the two force-loading modes. From the rupture force histograms, we determined the distance to the thermodynamic transition state and the thermal off rates in the absence of load for both processes.

Molecular Organizations of Myofibrils of Skeletal Muscle Studied by Atomic Force Microscopy

By applying AFM technology, we studied mechanical characteristics of myofibrils of skeletal muscle. The obtained results indicate that (1) the Z-band is the most rigid sarcomere component stabilizing the myofibril structures, (2) various filamentous components are inter-connected in sarcomere with sufficient mechanical strength to support the contractile force, and (3) the molecular structure of the overlap region between actin and myosin filaments is anisotropic. In any case the present studies clearly indicate that the AFM technique is a powerful tool to investigate the mechanical characteristics of sarcomere structure of muscle fiber.

Strain hardening of actin filament networks. Regulation by the dynamic cross-linking protein alpha-actinin

Mechanical stresses applied to the plasma membrane of an adherent cell induces strain hardening of the cytoskeleton, i.e. the elasticity of the cytoskeleton increases with its deformation. Strain hardening is thought to mediate the transduction of mechanical signals across the plasma membrane through the cytoskeleton. Here, we describe the strain dependence of a model system consisting of actin filaments (F-actin), a major component of the cytoskeleton, and the F-actin cross-linking protein alpha-actinin, which localizes along contractile stress fibers and at focal adhesions. We show that the amplitude and rate of shear deformations regulate the resilience of F-actin networks. At low temperatures, for which the lifetime of binding of alpha-actinin to F-actin is long, F-actin/alpha-actinin networks exhibit strong strain hardening at short time scales and soften at long time scales. For F-actin networks in the absence of alpha-actinin or for F-actin/alpha-actinin networks at high temperatures, strain hardening appears only at very short time scales. We propose a model of strain hardening for F-actin networks, based on both the intrinsic rigidity of F-actin and dynamic topological constraints formed by the cross-linkers located at filaments entanglements. This model offers an explanation for the origin of strain hardening observed when shear stresses are applied against the cellular membrane.