Sub-piconewton force fluctuations of actomyosin in vitro

Mechanisms of myosin II force generation: insights from novel experimental techniques and approaches

Myosin II is a molecular motor that converts chemical energy derived from ATP hydrolysis into mechanical work. Myosin II isoforms are responsible for muscle contraction and a range of cell functions relying on the development of force and motion. When the motor attaches to actin, ATP is hydrolyzed and inorganic phosphate (Pi) and ADP are released from its active site. These reactions are coordinated with changes in the structure of myosin, promoting the so-called "power stroke" that causes the sliding of actin filaments. The general features of the myosin-actin interactions are well accepted, but there are critical issues that remain poorly understood, mostly due to technological limitations. In recent years, there has been a significant advance in structural, biochemical, and mechanical methods that have advanced the field considerably. New modeling approaches have also allowed researchers to understand actomyosin interactions at different levels of analysis. This paper reviews recent studies looking into the interaction between myosin II and actin filaments, which leads to power stroke and force generation. It reviews studies conducted with single myosin molecules, myosins working in filaments, muscle sarcomeres, myofibrils, and fibers. It also reviews the mathematical models that have been used to understand the mechanics of myosin II in approaches focusing on single molecules to ensembles. Finally, it includes brief sections on translational aspects, how changes in the myosin motor by mutations and/or posttranslational modifications may cause detrimental effects in diseases and aging, among other conditions, and how myosin II has become an emerging drug target.

KnotResolver: tracking self-intersecting filaments in microscopy using directed graphs

MOTIVATION

Quantification of microscopy time series of in vitro reconstituted motor-driven microtubule transport in "gliding assays" is typically performed using computational object tracking tools. However, these are limited to non-intersecting and rod-like filaments.

RESULTS

Here, we describe a novel computational image-analysis pipeline, KnotResolver, to track image time series of highly curved self-intersecting looped filaments (knots) by resolving cross-overs. The code integrates filament segmentation and cross-over or "knot" identification based on directed graph representation, where nodes represent cross-overs and edges represent the path connecting them. The graphs are mapped back to contours and the distance to a reference minimized. The accuracy of contour detection is sub-pixel with a robustness to noise. We demonstrate the utility of KnotResolver by automatically quantifying "flagella-like" curvature dynamics and wave-like oscillations of clamped microtubules in a "gliding assay."

AVAILABILITY AND IMPLEMENTATION

The MATLAB-based source code is released as OpenSource and is available at https://github.com/CyCelsLab/MTKnotResolver.

One must reconstitute the functions of interest from purified proteins

I am often asked by students and younger colleagues and now by the editors of this issue to tell the history of the development of the in vitro motility assay and the dual-beam single-molecule laser trap assay for myosin-driven actin filament movement, used widely as key assays for understanding how both muscle and nonmuscle myosin molecular motors work. As for all discoveries, the history of the development of the myosin assays involves many people who are not authors of the final publications, but without whom the assays would not have been developed as they are. Also, early experiences shape how one develops ideas and experiments, and influence future discoveries in major ways. I am pleased here to trace my own path and acknowledge the many individuals involved and my early science experiences that led to the work I and my students, postdoctoral fellows, and sabbatical visitors did to develop these assays. Mentors are too often overlooked in historical descriptions of discoveries, and my story starts with those who mentored me.

Mechanical Stress Decreases the Amplitude of Twisting and Bending Fluctuations of Actin Filaments

A variety of biological roles of mechanical forces have been proposed in cell biology, such as cell signaling pathways for survival, development, growth, and differentiation. Mechanical forces alter the mechanical conditions within cells and their environment, which strongly influences the reorganization of the actin cytoskeleton. Single-molecule imaging studies of actin filaments have led to the hypothesis that the actin filament acts as a mechanosensor; e.g., increases in actin filament tension alter their conformation and affinity for regulatory proteins. However, our understanding of the molecular mechanisms underlying how tension modulates the mechanical behavior of a single actin filament is still incomplete. In this study, a direct measurement of the twisting and bending of a fluorescently labeled single actin filament under different tension levels by force application (0.8-3.4 pN) was performed using single-molecule fluorescence polarization (SMFP) microscopy. The results showed that the amplitude of twisting and bending fluctuations of a single actin filament decreased with increasing tension. Electron micrograph analysis of tensed filaments also revealed that the fluctuations in the crossover length of actin filaments decreased with increasing filament tension. Possible molecular mechanisms underlying these results involving the binding of actin-binding proteins, such as cofilin, to the filament are discussed.

A statistical mechanics model for determining the length distribution of actin filaments under cellular tensional homeostasis

Tensional homeostasis is a cellular process whereby nonmuscle cells such as fibroblasts keep a constant level of intracellular tension and signaling activities. Cells are allowed thanks to tensional homeostasis to adapt to mechanical stress, but the detailed mechanism remains unclear. Here we address from a theoretical point of view what is required for maintaining cellular tensional homeostasis. A constrained optimization problem is formulated to analytically determine the probability function of the length of individual actin filaments (AFs) responsible for sustaining cellular tension. An objective function composed of two entropic quantities measuring the extent of formation and dispersion of AFs within cells is optimized under two constraint functions dictating a constant amount of actin molecules and tension that are arguably the two most salient features of tensional homeostasis. We then derive a specific probability function of AFs that is qualitatively consistent with previous experimental observations, in which short AF populations preferably appear. Regarding the underlying mechanism, our analyses suggest that the constraint for keeping the constant tension level makes long AF populations smaller in number because long AFs have a higher chance to be involved in bearing larger forces. The specific length distribution of AFs is thus required for achieving the constrained objectives, by which individual cells are endowed with the ability to stably maintain a homeostatic tension throughout the cell, thereby potentially allowing cells to locally detect deviation in the tension, keep resulting biological functions, and hence enable subsequent adaptation to mechanical stress. Although minimal essential factors are included given the actual complexity of cells, our approach would provide a theoretical basis for understanding complicated homeostatic and adaptive behavior of the cell.

Molecule-to-Material-to-Bio Nanoarchitectonics with Biomedical Fullerene Nanoparticles

Nanoarchitectonics integrates nanotechnology with various other fields, with the goal of creating functional material systems from nanoscale units such as atoms, molecules, and nanomaterials. The concept bears strong similarities to the processes and functions seen in biological systems. Therefore, it is natural for materials designed through nanoarchitectonics to truly shine in bio-related applications. In this review, we present an overview of recent work exemplifying how nanoarchitectonics relates to biology and how it is being applied in biomedical research. First, we present nanoscale interactions being studied in basic biology and how they parallel nanoarchitectonics concepts. Then, we overview the state-of-the-art in biomedical applications pursuant to the nanoarchitectonics framework. On this basis, we take a deep dive into a particular building-block material frequently seen in nanoarchitectonics approaches: fullerene. We take a closer look at recent research on fullerene nanoparticles, paying special attention to biomedical applications in biosensing, gene delivery, and radical scavenging. With these subjects, we aim to illustrate the power of nanomaterials and biomimetic nanoarchitectonics when applied to bio-related applications, and we offer some considerations for future perspectives.

Biomimetic and Biological Nanoarchitectonics

A post-nanotechnology concept has been assigned to an emerging concept, nanoarchitectonics. Nanoarchitectonics aims to establish a discipline in which functional materials are fabricated from nano-scale components such as atoms, molecules, and nanomaterials using various techniques. Nanoarchitectonics opens ways to form a more unified paradigm by integrating nanotechnology with organic chemistry, supramolecular chemistry, material chemistry, microfabrication technology, and biotechnology. On the other hand, biological systems consist of rational organization of constituent molecules. Their structures have highly asymmetric and hierarchical features that allow for chained functional coordination, signal amplification, and vector-like energy and signal flow. The process of nanoarchitectonics is based on the premise of combining several different processes, which makes it easier to obtain a hierarchical structure. Therefore, nanoarchitectonics is a more suitable methodology for creating highly functional systems based on structural asymmetry and hierarchy like biosystems. The creation of functional materials by nanoarchitectonics is somewhat similar to the creation of functional systems in biological systems. It can be said that the goal of nanoarchitectonics is to create highly functional systems similar to those found in biological systems. This review article summarizes the synthesis of biomimetic and biological molecules and their functional structure formation from various viewpoints, from the molecular level to the cellular level. Several recent examples are arranged and categorized to illustrate such a trend with sections of (i) synthetic nanoarchitectonics for bio-related units, (ii) self-assembly nanoarchitectonics with bio-related units, (iii) nanoarchitectonics with nucleic acids, (iv) nanoarchitectonics with peptides, (v) nanoarchitectonics with proteins, and (vi) bio-related nanoarchitectonics in conjugation with materials.

Single-Molecule Biophysical Techniques to Study Actomyosin Force Transduction

Inside the cellular environment, molecular motors can work in concert to conduct a variety of important physiological functions and processes that are vital for the survival of a cell. However, in order to decipher the mechanism of how these molecular motors work, single-molecule microscopy techniques have been popular methods to understand the molecular basis of the emerging ensemble behavior of these motor proteins.In this chapter, we discuss various single-molecule biophysical imaging techniques that have been used to expose the mechanics and kinetics of myosins. The chapter should be taken as a general overview and introductory guide to the many existing techniques; however, since other chapters will discuss some of these techniques more thoroughly, the readership should refer to those chapters for further details and discussions. In particular, we will focus on scattering-based single-molecule microscopy methods, some of which have become more popular in the recent years and around which the work in our laboratories has been centered.

Fibronectin fiber creep under constant force loading

Viscoelasticity is a fundamental property of virtually all biological materials, and proteinaceous, fibrous materials that constitute the extracellular matrix (ECM) are no exception. Viscoelasticity may be particularly important in the ECM since cells can apply mechanical stress resulting from cell contractility over very long periods of time. However, measurements of ECM fiber response to long-term constant force loading are scarce, despite the increasing recognition that mechanical strain regulates the biological function of some ECM fibers. We developed a dual micropipette system that applies constant force to single fibers for up to 8 h. We utilized this system to study the time dependent response of fibronectin (Fn) fibers to constant force, as Fn fibers exhibit tremendous extensibility before mechanical failure as well as strain dependent alterations in biological properties. These data demonstrate the Fn fibers continue to stretch under constant force loading for at least 8 h and that this long-term creep results in plastic deformation of Fn fibers, in contrast to elastic deformation of Fn fibers under short-term, but fast loading rate extension. These data demonstrate that physiologically-relevant loading may impart mechanical features to Fn fibers by switching them into an extended state that may have altered biological functions. STATEMENT OF SIGNIFICANCE: Measurements of extracellular matrix (ECM) fiber response to constant force loading are scarce, so we developed a novel technique for applying constant force to single ECM fibers. We used this technique to measure constant force creep of fibronectin fibers since these fibers have been shown to be mechanotransducers whose functions can be altered by mechanical strain. We found that fibronectin fibers creep under constant force loading for the duration of the experiment and that this creep behavior resembles a power law. Furthermore, we found that constant force creep results in plastic deformation of the fibers, which suggests that the mechanobiological switching of fibronectin can only occur once after long-term loading.

Inferring Active Noise Characteristics from the Paired Observations of Anomalous Diffusion

Anomalous diffusion has been most often argued in terms of a position fluctuation of a tracer. We here propose the other fluctuating observable, i.e., momentum transfer defined as the time integral of applied force to hold a tracer’s position. Being a conjugated variable, the momentum transfer is thought of as generating the anomalous diffusion paired with the position’s one. By putting together the paired anomalous diffusions, we aim to extract useful information in complex systems, which can be applied to experiments like tagged monomer observations in chromatin. The polymer being in the equilibrium, the mean square displacement (or variance) of position displacement or momentum transfer exhibits the sub- or superdiffusion, respectively, in which the sum of the anomalous diffusion indices is conserved quite generally, but the nonequilibrium media that generate the active noise may manifest the derivations from the equilibrium relation. We discuss the deviations that reflect the characteristics of the active noise.

Physical driving force of actomyosin motility based on the hydration effect

We propose a driving force hypothesis based on previous thermodynamics, kinetics and structural data as well as additional experiments and calculations presented here on water-related phenomena in the actomyosin systems. Although Szent-Györgyi pointed out the importance of water in muscle contraction in 1951, few studies have focused on the water science of muscle because of the difficulty of analyzing hydration properties of the muscle proteins, actin, and myosin. The thermodynamics and energetics of muscle contraction are linked to the water-mediated regulation of protein-ligand and protein-protein interactions along with structural changes in protein molecules. In this study, we assume the following two points: (1) the periodic electric field distribution along an actin filament (F-actin) is unidirectionally modified upon binding of myosin subfragment 1 (M or myosin S1) with ADP and inorganic phosphate Pi (M.ADP.Pi complex) and (2) the solvation free energy of myosin S1 depends on the external electric field strength and the solvation free energy of myosin S1 in close proximity to F-actin can become the potential force to drive myosin S1 along F-actin. The first assumption is supported by integration of experimental reports. The second assumption is supported by model calculations utilizing molecular dynamics (MD) simulation to determine solvation free energies of a small organic molecule and two small proteins. MD simulations utilize the energy representation method (ER) and the roughly proportional relationship between the solvation free energy and the solvent-accessible surface area (SASA) of the protein. The estimated driving force acting on myosin S1 is as high as several piconewtons (pN), which is consistent with the experimentally observed force.

Single molecule detection, thermal fluctuation and life

Single molecule detection has contributed to our understanding of the unique mechanisms of life. Unlike artificial man-made machines, biological molecular machines integrate thermal noises rather than avoid them. For example, single molecule detection has demonstrated that myosin motors undergo biased Brownian motion for stepwise movement and that single protein molecules spontaneously change their conformation, for switching to interactions with other proteins, in response to thermal fluctuation. Thus, molecular machines have flexibility and efficiency not seen in artificial machines.

A chemo-mechanical free-energy-based approach to model durotaxis and extracellular stiffness-dependent contraction and polarization of cells

We propose a chemo-mechanical model based on stress-dependent recruitment of myosin motors to describe how the contractility, polarization and strain in cells vary with the stiffness of their surroundings and their shape. A contractility tensor, which depends on the distribution of myosin motors, is introduced to describe the chemical free energy of the cell due to myosin recruitment. We explicitly include the contributions to the free energy that arise from mechanosensitive signalling pathways (such as the SFX, Rho-Rock and MLCK pathways) through chemo-mechanical coupling parameters. Taking the variations of the total free energy, which consists of the chemical and mechanical components, in accordance with the second law of thermodynamics provides equations for the temporal evolution of the active stress and the contractility tensor. Following this approach, we are able to recover the well-known Hill relation for active stresses, based on the fundamental principles of irreversible thermodynamics rather than phenomenology. We have numerically implemented our free energy-based approach to model spatial distribution of strain and contractility in (i) cells supported by flexible microposts, (ii) cells on two-dimensional substrates, and (iii) cells in three-dimensional matrices. We demonstrate how the polarization of the cells and the orientation of stress fibres can be deduced from the eigenvalues and eigenvectors of the contractility tensor. Our calculations suggest that the chemical free energy of the cell decreases with the stiffness of the extracellular environment as the cytoskeleton polarizes in response to stress-dependent recruitment of molecular motors. The mechanical energy, which includes the strain energy and motor potential energy, however, increases with stiffness, but the overall energy is lower for cells in stiffer environments. This provides a thermodynamic basis for durotaxis, whereby cells preferentially migrate towards stiffer regions of the extracellular environment. Our models also explain, from an energetic perspective, why the shape of the cells can change in response to stiffness of the surroundings. The effect of the stiffness of the nucleus on its shape and the orientation of the stress fibres is also studied for all the above geometries. Along with making testable predictions, we have estimated the magnitudes of the chemo-mechanical coupling parameters for myofibroblasts based on data reported in the literature.

Constriction model of actomyosin ring for cytokinesis by fission yeast using a two-state sliding filament mechanism

We developed a model describing the structure and contractile mechanism of the actomyosin ring in fission yeast, Schizosaccharomyces pombe. The proposed ring includes actin, myosin, and α-actinin, and is organized into a structure similar to that of muscle sarcomeres. This structure justifies the use of the sliding-filament mechanism developed by Huxley and Hill, but it is probably less organized relative to that of muscle sarcomeres. Ring contraction tension was generated via the same fundamental mechanism used to generate muscle tension, but some physicochemical parameters were adjusted to be consistent with the proposed ring structure. Simulations allowed an estimate of ring constriction tension that reproduced the observed ring constriction velocity using a physiologically possible, self-consistent set of parameters. Proposed molecular-level properties responsible for the thousand-fold slower constriction velocity of the ring relative to that of muscle sarcomeres include fewer myosin molecules involved, a less organized contractile configuration, a low α-actinin concentration, and a high resistance membrane tension. Ring constriction velocity is demonstrated as an exponential function of time despite a near linear appearance. We proposed a hypothesis to explain why excess myosin heads inhibit constriction velocity rather than enhance it. The model revealed how myosin concentration and elastic resistance tension are balanced during cytokinesis in S. pombe.

The Arabidopsis alkaline ceramidase TOD1 is a key turgor pressure regulator in plant cells

Turgor pressure plays pivotal roles in the growth and movement of walled cells that make up plants and fungi. However, the molecular mechanisms regulating turgor pressure and the coordination between turgor pressure and cell wall remodelling for cell growth remain poorly understood. Here, we report the characterization of Arabidopsis TurgOr regulation Defect 1 (TOD1), which is preferentially expressed in pollen tubes and silique guard cells. We demonstrate that TOD1 is a Golgi-localized alkaline ceramidase. tod1 mutant pollen tubes have higher turgor than wild type and show growth retardation both in pistils and in agarose medium. In addition, tod1 guard cells are insensitive to abscisic acid (ABA)-induced stomatal closure, whereas sphingosine-1-phosphate, a putative downstream component of ABA signalling and product of alkaline ceramidases, promotes closure in both wild type and tod1. Our data suggest that TOD1 acts in turgor pressure regulation in both guard cells and pollen tubes.

The force-velocity relationship at negative loads (assisted shortening) studied in isolated, intact muscle fibres of the frog

AIM

The study was undertaken to explore the force-velocity relationship under conditions where the myofilament system is subjected to an external force that serves as a negative load and assists the shortening movement.

METHODS

The experiments were carried out on single muscle fibres isolated from the anterior tibialis muscle of Rana temporaria. The fibres, being operated under load-clamp control, were released to shorten during tetanic stimulation at sarcomere lengths where the fibres carried different degrees of passive tension. The shortening thus occurred while the sarcomeres were subjected to a force that may be characterized as a 'negative load', that is, a force assisting the shortening movement.

RESULTS

The force-velocity relationship below zero load was found to be a smooth continuation of the force-velocity curve recorded at positive loads with the shortening velocity increasing steeply at loads below zero. A negative load amounting to merely 10% of the isometric force, thus raised the shortening velocity to a level two to three times higher than V0 , the velocity recorded at zero load.

CONCLUSIONS

The results provide evidence that, even in the presence of a longitudinal compressive force, the speed of shortening of the muscle fibre is determined by the cycling rate of the interacting cross-bridges. The force-velocity relationship at negative loads may play a relevant part during fast movements of striated muscle as pointed out in the discussion.

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.

Quantification of cellular penetrative forces using lab-on-a-chip technology and finite element modeling

Tip-growing cells have the unique property of invading living tissues and abiotic growth matrices. To do so, they exert significant penetrative forces. In plant and fungal cells, these forces are generated by the hydrostatic turgor pressure. Using the TipChip, a microfluidic lab-on-a-chip device developed for tip-growing cells, we tested the ability to exert penetrative forces generated in pollen tubes, the fastest-growing plant cells. The tubes were guided to grow through microscopic gaps made of elastic polydimethylsiloxane material. Based on the deformation of the gaps, the force exerted by the elongating tubes to permit passage was determined using finite element methods. The data revealed that increasing mechanical impedance was met by the pollen tubes through modulation of the cell wall compliance and, thus, a change in the force acting on the obstacle. Tubes that successfully passed a narrow gap frequently burst, raising questions about the sperm discharge mechanism in the flowering plants.

Velocity-dependent actomyosin ATPase cycle revealed by in vitro motility assay with kinetic analysis

The actomyosin interaction plays a key role in a number of cellular functions. Single-molecule measurement techniques have been developed to study the mechanism of the actomyosin contractile system. However, the behavior of isolated single molecules does not always reflect that of molecules in a complex system such as a muscle fiber. Here, we developed a simple method for studying the kinetic parameters of the actomyosin interaction using small numbers of molecules. This approach does not require the specialized equipment needed for single-molecule measurements, and permits us to observe behavior that is more similar to that of a complex system. Using an in vitro motility assay, we examined the duration of continuous sliding of actin filaments on a sparsely distributed heavy meromyosin-coated surface. To estimate the association rate constant of the actomyosin motile system, we compared the distribution of experimentally obtained duration times with a computationally simulated distribution. We found that the association rate constant depends on the sliding velocity of the actin filaments. This technique may be used to reveal new aspects of the kinetics of various motor proteins in complex systems.

From mechanical force to RhoA activation

Throughout their lives, all cells constantly experience and respond to various mechanical forces. These frequently originate externally but can also arise internally as a result of the contractile actin cytoskeleton. Mechanical forces trigger multiple signaling pathways. Several converge and result in the activation of the GTPase RhoA. In this review, we focus on the pathways by which mechanical force leads to RhoA regulation, especially when force is transmitted via cell adhesion molecules that mediate either cell-matrix or cell-cell interactions. We discuss both the upstream signaling events that lead to activation of RhoA and the downstream consequences of this pathway. These include not only cytoskeletal reorganization and, in a positive feedback loop, increased myosin-generated contraction but also profound effects on gene expression and differentiation.

From single molecule fluctuations to muscle contraction: a Brownian model of A.F. Huxley's hypotheses

Muscular force generation in response to external stimuli is the result of thermally fluctuating, cyclical interactions between myosin and actin, which together form the actomyosin complex. Normally, these fluctuations are modelled using transition rate functions that are based on muscle fiber behaviour, in a phenomenological fashion. However, such a basis reduces the predictive power of these models. As an alternative, we propose a model which uses direct single molecule observations of actomyosin fluctuations reported in the literature. We precisely estimate the actomyosin potential bias and use diffusion theory to obtain a brownian ratchet model that reproduces the complete cross-bridge cycle. The model is validated by simulating several macroscopic experimental conditions, while its interpretation is compatible with two different force-generating scenarios.

An integrated in vitro and in situ study of kinetics of myosin II from frog skeletal muscle

A new efficient protocol for extraction and conservation of myosin II from frog skeletal muscle made it possible to preserve the myosin functionality for a week and apply single molecule techniques to the molecular motor that has been best characterized for its mechanical, structural and energetic parameters in situ.With the in vitro motility assay, we estimated the sliding velocity of actin on frog myosin II (VF) and its modulation by pH, myosin density, temperature (range 4-30◦C) and substrate concentration. VF was 8.88 ± 0.26 μms⁻¹ at 30.6◦C and decreased to 1.60 ± 0.09 μms⁻¹ at 4.5◦C. The in vitro mechanical and kinetic parameters were integrated with the in situ parameters of frog muscle myosin working in arrays in each half-sarcomere. By comparing VF with the shortening velocities determined in intact frog muscle fibres under different loads and their dependence on temperature, we found that VF is 40-50% less than the fibre unloaded shortening velocity (V0) at the same temperature and we determined the load that explains the reduced value of VF. With this integrated approach we could define fundamental kinetic steps of the acto-myosin ATPase cycle in situ and their relation with mechanical steps. In particular we found that at 5◦C the rate of ADP release calculated using the step size estimated from in situ experiments accounts for the rate of detachment of motors during steady shortening under low loads.

Direct manipulation of a single potassium channel gate with an atomic force microscope probe

Ion channels are membrane proteins that regulate cell functions by controlling the ion permeability of cell membranes. An ion channel contains an ion-selective pore that permeates ions and a sensor that senses a specific stimulus such as ligand binding to regulate the permeability. The detailed molecular mechanisms of this regulation, or gating, are unknown. Gating is thought to occur from conformational changes in the sensor domain in response to the stimulus, which results in opening the gate to permit ion conduction. Using an atomic force microscope and artificial bilayer system, a mechanical stimulus is applied to a potassium channel, and its gating is monitored in real time. The channel-open probability increases greatly when pushing the cytoplasmic domain toward the membrane. This result shows that a mechanical stimulus at the cytoplasmic domain causes changes in the gating and is the first to show direct evidence of coupling between conformational changes in the cytoplasmic domain and channel gating. This novel technology has the potential to be a powerful tool for investigating the activation dynamics in channel proteins.

Locomotive and reptation motion induced by internal force and friction

We propose a simple mechanical model of locomotion induced by internal force and friction. We first construct a system of two elements as an analog of the bipedal motion. The internal force does not induce a directional motion by itself because of the action-reaction law, but a directional motion becomes possible by the control of the frictional force. The efficiency of these model systems is studied using an analogy to the heat engine. As a modified version of the two-element model, we construct a model that exhibits a bipedal motion similar to kinesin's motion of molecular motor. Next, we propose a linear chain model and a ladder model as an extension of the original two-element model. We find a transition from a straight to a snake-like motion in a ladder model by changing the strength of the internal force.

Effect of tensile force on the mechanical behavior of actin filaments

Actin filaments are the most abundant components of the cellular cytoskeleton, and play critical roles in various cellular functions such as migration, division and shape control. In these activities, mechanical tension causes structural changes in the double-helical structure of the actin filament, which is a key modulator of cytoskeletal reorganization. This study performed large-scale molecular dynamics (MD) and steered MD simulations to quantitatively analyze the effects of tensile force on the mechanical behavior of actin filaments. The results revealed that when a tensile force of 200pN was applied to a filament consisting of 14 actin subunits, the twist angle of the filament decreased by approximately 20°, corresponding to a rotation of approximately -2° per subunit, representing a critical structural change in actin filaments. Based on these structural changes, the variance in filament length and twist angle was found to decrease, leading to increases in extensional and torsional stiffness. Torsional stiffness increased significantly under the tensile condition, and the ratio of filament stiffness under tensile force to that under no external force increased significantly on longer temporal scales. The results obtained from this study contribute to the understanding of mechano-chemical interactions concerning actin dynamics, showing that increased tensile force in the filament prevents actin regulatory proteins from binding to the filament.

Single-molecule measurements using microneedles

Myosin is both an enzyme and a molecular motor that hydrolyzes ATP and interacts with actin filaments for force generation. Manipulation techniques with microneedles and laser traps have recently been developed to capture and manipulate the actomyosin interaction for the purpose of revealing the mechanics of this system. Combined with single-molecule imaging techniques, the coupling between chemical processes (ATP hydrolysis) and mechanical processes (myosin force generation) has been directly determined. In this chapter, we describe these two manipulation techniques, especially microneedle method, in detail.

Mapping the classical cross-bridge theory and backward steps in a three bead laser trap setup

According to the cross-bridge theory (Huxley, 1957), the interaction between myosin and actin is governed by a deterministic process where the myosin molecule pulls the actin filament in one specific direction only. However, studies on single myosin-actin interactions produced displacements of actin not only in the preferred but also in the opposite direction. This phenomenon is typically referred to as backward steps by the myosin head. Molloy et al. (1995) speculated that these backward steps are not caused by the molecular interactions of actin with myosin but are an artifact of the Brownian motion associated with these molecular level experiments. The aim of this study was to investigate, whether a theoretical model can support Molloy's speculation. We therefore developed a theoretical model of actin-myosin based muscle contraction that was strictly based on Huxley's assumption of one stepping direction only, but incorporated Brownian motion, as observed in single cross-bridge-actin interactions. The mathematical model is based on Langevin equations describing the classical three-bead laser trap setup and uses a novel semi-analytical approach to study the percentage of backward steps. We analyzed the effects of different initial actin attachment site distribution and laser trap stiffness on the ratio of forward to backward steps. Our results demonstrate that backward steps and the classical cross-bridge theory are perfectly compatible in a three-bead laser trap setup.

Single-molecule fluorescence characterization in native environment

Single-molecule detection (SMD) with fluorescence is a widely used microscopic technique for biomolecule structure and function characterization. The modern light microscope with high numerical aperture objective and sensitive CCD camera can image the brightly emitting organic and fluorescent protein tags with reasonable time resolution. Single-molecule imaging gives an unambiguous bottom-up biomolecule characterization that avoids the "missing information" problem characteristic of ensemble measurements. It has circumvented the diffraction limit by facilitating single-particle localization to ~1 nm. Probes developed specifically for SMD applications extend the advantages of single-molecule imaging to high probe density regions of cells and tissues. These applications perform under conditions resembling the native biomolecule environment and have been used to detect both probe position and orientation. Native, high density SMD may have added significance if molecular crowding impacts native biomolecule behavior as expected inside the cell.

Classic and contemporary approaches to modeling biochemical reactions

Recent interest in modeling biochemical networks raises questions about the relationship between often complex mathematical models and familiar arithmetic concepts from classical enzymology, and also about connections between modeling and experimental data. This review addresses both topics by familiarizing readers with key concepts (and terminology) in the construction, validation, and application of deterministic biochemical models, with particular emphasis on a simple enzyme-catalyzed reaction. Networks of coupled ordinary differential equations (ODEs) are the natural language for describing enzyme kinetics in a mass action approximation. We illustrate this point by showing how the familiar Briggs-Haldane formulation of Michaelis-Menten kinetics derives from the outer (or quasi-steady-state) solution of a dynamical system of ODEs describing a simple reaction under special conditions. We discuss how parameters in the Michaelis-Menten approximation and in the underlying ODE network can be estimated from experimental data, with a special emphasis on the origins of uncertainty. Finally, we extrapolate from a simple reaction to complex models of multiprotein biochemical networks. The concepts described in this review, hitherto of interest primarily to practitioners, are likely to become important for a much broader community of cellular and molecular biologists attempting to understand the promise and challenges of "systems biology" as applied to biochemical mechanisms.

Load-dependent sliding direction change of a myosin head on an actin molecule and its energetic aspects: Energy borrowing model of a cross-bridge cycle

A model of muscle contraction is proposed, assuming loose coupling between power strokes and ATP hydrolysis of a myosin head. The energy borrowing mechanism is introduced in a cross-bridge cycle that borrows energy from the environment to cover the necessary energy for enthalpy production during sliding movement. Important premises for modeling are as follows: 1) the interaction area where a myosin head slides is supposed to be on an actin molecule; 2) the actomyosin complex is assumed to generate force F(θ), which slides the myosin head M* in the interaction area; 3) the direction of the force F(θ) varies in proportion to the load P; 4) the energy supplied by ATP hydrolysis is used to retain the myosin head in the high-energy state M*, and is not used for enthalpy production; 5) the myosin head enters a hydration state and dehydration state repeatedly during the cross-bridge cycle. The dehydrated myosin head recovers its hydrated state by hydration in the surrounding medium; 6) the energy source for work and heat production liberated by the AM* complex is of external origin. On the basis of these premises, the model adequately explains the experimental results observed at various levels in muscular samples: 1) twist in actin filaments observed in shortening muscle fibers; 2) the load-velocity relationship in single muscle fiber; 3) energy balance among enthalpy production, the borrowed energy and the energy supplied by ATP hydrolysis during muscle contraction. Force F(θ) acting on the myosin head is depicted.

Pressure-induced changes in the structure and function of the kinesin-microtubule complex

Kinesin-1 is an ATP-driven molecular motor that "walks" along a microtubule by working two heads in a "hand-over-hand" fashion. The stepping motion is well-coordinated by intermolecular interactions between the kinesin head and microtubule, and is sensitively changed by applied forces. We demonstrate that hydrostatic pressure works as an inhibitory action on kinesin motility. We developed a high-pressure microscope that enables the application of hydrostatic pressures of up to 200 MPa (2000 bar). Under high-pressure conditions, taxol-stabilized microtubules were shortened from both ends at the same speed. The sliding velocity of kinesin motors was reversibly changed by pressure, and reached half-maximal value at approximately 100 MPa. The pressure-velocity relationship was very close to the force-velocity relationship of single kinesin molecules, suggesting a similar inhibitory mechanism on kinesin motility. Further analysis showed that the pressure mainly affects the stepping motion, but not the ATP binding reaction. The application of pressure is thought to enhance the structural fluctuation and/or association of water molecules with the exposed regions of the kinesin head and microtubule. These pressure-induced effects could prevent kinesin motors from completing the stepping motion.

Single molecule measurements and molecular motors

Single molecule imaging and manipulation are powerful tools in describing the operations of molecular machines like molecular motors. The single molecule measurements allow a dynamic behaviour of individual biomolecules to be measured. In this paper, we describe how we have developed single molecule measurements to understand the mechanism of molecular motors. The step movement of molecular motors associated with a single cycle of ATP hydrolysis has been identified. The single molecule measurements that have sensitivity to monitor thermal fluctuation have revealed that thermal Brownian motion is involved in the step movement of molecular motors. Several mechanisms have been suggested in different motors to bias random thermal motion to directional movement.

Measurement system for simultaneous observation of myosin V chemical and mechanical events

Myosin V is an actin-based processive molecular motor driven by the chemical energy of ATP hydrolysis. Although the chemo-mechanical coupling in processive movement has been postulated by separate structural, mechanical and biochemical studies, no experiment has been able to directly test these conclusions. Therefore the relationship between ATP-turnover and force generation remains unclear. Currently, the most direct method to measure the chemo-mechanical coupling in processive motors is to simultaneously observe ATP-turnover cycles and displacement at the single molecule level. In this study, we developed a simultaneous measurement system suitable for mechanical and chemical assays of myosin V in order to directly elucidate its chemo-mechanical coupling.

Role of multiple bonds between the single cell adhesion molecules, nectin and cadherin, revealed by high sensitive force measurements

Nectins and cadherins, members of cell adhesion molecules (CAMs), are the primary mediators for various types of cell-cell junctions. Here, intermolecular force microscopy (IFM) with force sensitivity at sub-picoNewtons is used to characterize the extracellular trans-interactions between paired nectins and paired cadherins at the single molecule level. Three and four different bound states between paired nectins and paired cadherins are, respectively, identified and characterized based on bond strength distributions where each bound state has a unique lifetime and bond length. The results indicate that multiple domains of nectins act uncooperatively, as a zipper-like multiply bonded system whereas those of cadherins act cooperatively, as a parallel-like multiply bonded system, consistent with a "fork initiation and zipper" hypothesis for the formation of cell-cell adhesion. The observed dynamic properties among multiple bonds are expected to be advantageous such that nectins search adaptively in the cell-cell exploratory recognition process while cadherins slowly stabilize in the cell-cell zippering process.

DNA mechanics as a tool to probe helicase and translocase activity

Helicases and translocases are proteins that use the energy derived from ATP hydrolysis to move along or pump nucleic acid substrates. Single molecule manipulation has proved to be a powerful tool to investigate the mechanochemistry of these motors. Here we first describe the basic mechanical properties of DNA unraveled by single molecule manipulation techniques. Then we demonstrate how the knowledge of these properties has been used to design single molecule assays to address the enzymatic mechanisms of different translocases. We report on four single molecule manipulation systems addressing the mechanism of different helicases using specifically designed DNA substrates: UvrD enzyme activity detection on a stretched nicked DNA molecule, HCV NS3 helicase unwinding of a RNA hairpin under tension, the observation of RecBCD helicase/nuclease forward and backward motion, and T7 gp4 helicase mediated opening of a synthetic DNA replication fork. We then discuss experiments on two dsDNA translocases: the RuvAB motor studied on its natural substrate, the Holliday junction, and the chromosome-segregation motor FtsK, showing its unusual coupling to DNA supercoiling.

Mechanical response analysis and power generation by single-cell stretching

To harvest useful information about cell response due to mechanical perturbations under physiological conditions, a cantilever-based technique was designed, which allowed precise application of arbitrary forces or deformation histories on a single cell in vitro. Essential requirements for these investigations are a mechanism for applying an automated cell force and an induced-deformation detection system based on fiber-optical force sensing and closed loop control. The required mechanical stability of the setup can persist for several hours since mechanical drifts due to thermal gradients can be eliminated sufficiently (these gradients are caused by local heating of the cell observation chamber to 37 degrees C). During mechanical characterization, the cell is visualized with an optical microscope, which enables the simultaneous observation of cell shape and intracellular morphological changes. Either the cell elongation is observed as a reaction against a constant load or the cell force is measured as a response to constant deformation. Passive viscoelastic deformation and active cell response can be discriminated. The active power generated during contraction is in the range of Pmax= 10(-16) Watts, which corresponds to 2500 ATP molecules s(-1) at 10 k(B)T/molecule. The ratio of contractive to dissipative power is estimated to be in the range of 10(-2). The highest forces supported by the cell suggest that about 10(4) molecular motors must be involved in contraction. This indicates an energy-conversion efficiency of approximately 0.5. Our findings propose that, in addition to the recruitment of cell-contractile elements upon mechanical stimulation, the cell cytoskeleton becomes increasingly crosslinked in response to a mechanical pull. Quantitative stress-strain data, such as those presented here, may be employed to test physical models that describe cellular responses to mechanical stimuli.

Simulated data sets for single molecule kinetics: some limitations and complications of data analysis

When the fluorescence intensity of a chromophore attached to or bound in an enzyme relates to a specific reactive step in the enzymatic reaction, a single molecule fluorescence study of the process reveals a time sequence in the fluorescence emission that can be analyzed to derive kinetic and mechanistic information. Reports of various experimental results and corresponding theoretical studies have provided a basis for interpreting these data and understanding the methodology. We have found it useful to parallel experiments with Monte Carlo simulations of potential models hypothesized to describe the reaction kinetics. The simulations can be adapted to include experimental limitations, such as limited data sets, and complexities such as dynamic disorder, where reaction rates appear to change over time. By using models that are known a priori, the simulations reveal some of the challenges of interpreting finite single-molecule data sets by employing various statistical signatures that have been identified.

Geometrical correspondence identified and a new interaction unit suggested in striated muscle

It has long been believed that the periodic structure of the myosin helix is a consequence only of compressing the actin-myosin interaction sites. Here, we identify a length correspondence between the smallest helical unit on the thick filament and the helical pitch of the actin filaments in two different contractile muscles. This suggests a rotation/swing of the filaments that creates a new interaction unit in addition to the single interaction between an actin filament and a myosin head. Numerical characteristics of the single interaction are estimated from discussion about an in vivo interaction utilizing the new unit. The estimated twisted angle of the actin filaments is consistent with that calculated from its torsion rigidity and the evaluated step sizes per cross-bridge can be performed by a single bend of a myosin head. By comparing our evaluated step sizes with experimental results, we conclude that the most plausible mechanism at the force-recovery stage involves swings or rotations of both filaments in the same direction (clockwise).

Tracking topoisomerase activity at the single-molecule level

The recent development of new techniques to manipulate single DNA molecules has opened new opportunities for the study of the enzymes that control DNA topology: the type I and II topoisomerases. These single-molecule assays provide a unique way to study the uncoiling of single supercoiled DNA molecules and the unlinking of two intertwined DNAs. They allow for a detailed characterization of the activity of topoisomerases, including the processivity, the chiral discrimination, and the dependence of their enzymatic rate on ATP concentration, degree of supercoiling, and the tension in the molecule. These results shed new light on the mechanism of these enzymes and their function in vivo.

Fluctuation of actin sliding over myosin thick filaments in vitro

It is customarily thought that myosin motors act as independent force-generators in both isotonic unloaded shortening as well as isometric contraction of muscle. We tested this assumption regarding unloaded shortening, by analyzing the fluctuation of the actin sliding movement over long native thick filaments from molluscan smooth muscle in vitro. This analysis is based on the prediction that the effective diffusion coefficient of actin, a measure of the fluctuation, is proportional to the inverse of the number of myosin motors generating the sliding movement of an actin filament, hence proportional to the inverse of the actin length, when the actions of the motors are stochastic and statistically independent. Contrary to this prediction, we found the effective diffusion coefficient to be virtually independent of, and thus not proportional to, the inverse of the actin length. This result shows that the myosin motors are not independent force-generators when generating the continuous sliding movement of actin in vitro and that the sliding motion is a macroscopic manifestation of the cooperative actions of the microscopic ensemble motors.

A new muscle contractile system composed of a thick filament lattice and a single actin filament

To bridge the gap between the contractile system in muscle and in vitro motility assay, we have devised an A-band motility assay system. A glycerinated skeletal myofibril was treated with gelsolin to selectively remove the thin filaments and expose a single A-band. A single bead-tailed actin filament trapped by optical tweezers was made to interact with the inside or the outer surface of the A-band, and the displacement of the bead-tailed filament was measured in a physiological ionic condition by phase-contrast and fluorescence microscopy. We observed large back-and-forth displacement of the filament accompanied by a large change in developed force. Despite this large tension fluctuation, we found that the average force was proportional to the overlap inside and outside the A-band up to approximately 150 nm and 300 nm from the end of the A-band, respectively. Consistent with the difference in the density of myosin molecules, the average force per unit length of the overlap inside the A-band (the time-averaged force/myosin head was approximately 1 pN) was approximately twice as large as that outside. Thus, we conclude that the A-band motility assay system described here is suitable for studying force generation on a single actin filament, and its sliding movement within a regular three-dimensional thick filament lattice.

Single-molecule enzymology of chymotrypsin using water-in-oil emulsion

Single-molecule studies allow the study of subtle activity differences due to local folding in proteins, but are time consuming and difficult because only a few molecules are observed in one experiment. We developed an assay where we can simultaneously measure the activity of hundreds of individual molecules. The assay utilizes a synthetic chymotrypsin substrate that is nonfluorescent before cleavage by chymotrypsin, but is intensely fluorescent afterward. We encapsulated the enzyme and substrate in micron-sized droplets of water surrounded by silicone oil where each microdroplet contains <1 enzyme on average. A microscope and charge-coupled device camera are used to measure the fluorescence intensity of the same individual droplet over time. Based on these measurements, we conclude that enzymatic reactions could occur within this emulsion system, the statistical average activity of individual chymotrypsin molecules is similar to that measured in bulk, and the activity of individual chymotrypsin is heterogeneous.