A reverse stroke characterizes the force generation of cardiac myofilaments, leading to an understanding of heart function

Modeling thick filament activation suggests a molecular basis for force depression

Multiscale models aiming to connect muscle's molecular and cellular function have been difficult to develop, in part due to a lack of self-consistent multiscale data. To address this gap, we measured the force response from single, skinned rabbit psoas muscle fibers to ramp shortenings and step stretches performed on the plateau region of the force-length relationship. We isolated myosin from the same muscles and, under similar conditions, performed single-molecule and ensemble measurements of myosin's ATP-dependent interaction with actin using laser trapping and in vitro motility assays. We fit the fiber data by developing a partial differential equation model that includes thick filament activation, whereby an increase in force on the thick filament pulls myosin out of an inhibited state. The model also includes a series elastic element and a parallel elastic element. This parallel elastic element models a titin-actin interaction proposed to account for the increase in isometric force after stretch (residual force enhancement). By optimizing the model fit to a subset of our fiber measurements, we specified seven unknown parameters. The model then successfully predicted the remainder of our fiber measurements and also our molecular measurements from the laser trap and in vitro motility. The success of the model suggests that our multiscale data are self-consistent and can serve as a testbed for other multiscale models. Moreover, the model captures the decrease in isometric force observed in our muscle fibers after active shortening (force depression), suggesting a molecular mechanism for force depression, whereby a parallel elastic element combines with thick filament activation to decrease the number of cycling cross-bridges.

Fully Active Delivery of Nanodrugs In Vivo via Remote Optical Manipulation

The active delivery of nanodrugs has been a bottleneck problem in nanomedicine. While modification of nanodrugs with targeting agents can enhance their retention at the lesion location, the transportation of nanodrugs in the circulation system is still a passive process. The navigation of nanodrugs with external forces such as magnetic field has been shown to be effective for active delivery, but the existing techniques are limited to specific materials like magnetic nanoparticles. In this study, an alternative actuation method is proposed based on optical manipulation for remote navigation of nanodrugs in vivo, which is compatible with most of the common drug carriers and exhibits significantly higher manipulation precision. By the programmable scanning of the laser beam, the motion trajectory and velocity of the nanodrugs can be precisely controlled in real time, making it possible for intelligent drug delivery, such as inverse-flow transportation, selective entry into specific vascular branch, and dynamic circumvention across obstacles. In addition, the controlled mass delivery of nanodrugs can be realized through indirect actuation by the microflow field. The developed optical manipulation method provides a new solution for the active delivery of nanodrugs, with promising potential for the treatment of blood diseases such as leukemia and thrombosis.

Modeling Thick Filament Activation Suggests a Molecular Basis for Force Depression

Multiscale models aiming to connect muscle's molecular and cellular function have been difficult to develop, in part, due to a lack of self-consistent multiscale data. To address this gap, we measured the force response from single skinned rabbit psoas muscle fibers to ramp shortenings and step stretches performed on the plateau region of the force-length relationship. We isolated myosin from the same muscles and, under similar conditions, performed single molecule and ensemble measurements of myosin's ATP-dependent interaction with actin using laser trapping and in vitro motility assays. We fit the fiber data by developing a partial differential equation model that includes thick filament activation, whereby an increase in force on the thick filament pulls myosin out of an inhibited state. The model also includes a series elastic element and a parallel elastic element. This parallel elastic element models a titin-actin interaction proposed to account for the increase in isometric force following stretch (residual force enhancement). By optimizing the model fit to a subset of our fiber measurements, we specified seven unknown parameters. The model then successfully predicted the remainder of our fiber measurements and also our molecular measurements from the laser trap and in vitro motility. The success of the model suggests that our multiscale data are self-consistent and can serve as a testbed for other multiscale models. Moreover, the model captures the decrease in isometric force observed in our muscle fibers after active shortening (force depression), suggesting a molecular mechanism for force depression, whereby a parallel elastic element combines with thick filament activation to decrease the number of cycling cross-bridges.

New paradigms in actomyosin energy transduction: Critical evaluation of non-traditional models for orthophosphate release

Release of the ATP hydrolysis product ortophosphate (Pi) from the active site of myosin is central in chemo-mechanical energy transduction and closely associated with the main force-generating structural change, the power-stroke. Despite intense investigations, the relative timing between Pi-release and the power-stroke remains poorly understood. This hampers in depth understanding of force production by myosin in health and disease and our understanding of myosin-active drugs. Since the 1990s and up to today, models that incorporate the Pi-release either distinctly before or after the power-stroke, in unbranched kinetic schemes, have dominated the literature. However, in recent years, alternative models have emerged to explain apparently contradictory findings. Here, we first compare and critically analyze three influential alternative models proposed previously. These are either characterized by a branched kinetic scheme or by partial uncoupling of Pi-release and the power-stroke. Finally, we suggest critical tests of the models aiming for a unified picture.

Cooperativity of myosin II motors in the non-regulated and regulated thin filaments investigated with high-speed AFM

Skeletal myosins II are non-processive molecular motors that work in ensembles to produce muscle contraction while binding to the actin filament. Although the molecular properties of myosin II are well known, there is still debate about the collective work of the motors: is there cooperativity between myosin motors while binding to the actin filaments? In this study, we use high-speed AFM to evaluate this issue. We observed that the initial binding of small arrays of myosin heads to the non-regulated actin filaments did not affect the cooperative probability of subsequent bindings and did not lead to an increase in the fractional occupancy of the actin binding sites. These results suggest that myosin motors are independent force generators when connected in small arrays, and that the binding of one myosin does not alter the kinetics of other myosins. In contrast, the probability of binding of myosin heads to regulated thin filaments under activating conditions (at high Ca2+ concentration in the presence of 2 μM ATP) was increased with the initial binding of one myosin, leading to a larger occupancy of available binding sites at the next half-helical pitch of the filament. The result suggests that myosin cooperativity is observed over five pseudo-repeats and defined by the activation status of the thin filaments.

Thermodynamics and Kinetics of a Binary Mechanical System: Mechanisms of Muscle Contraction

Biological motors function at the interface of biology, physics, and chemistry, and it remains unsettled what rules from which disciplines account for how these motors work. Myosin motors are enzymes that catalyze the hydrolysis of ATP through a mechanism involving a switch-like myosin structural change (a lever arm rotation) induced by actin binding that generates a small displacement of an actin filament. In muscle, individual myosin motors are widely assumed to function as molecular machines having mechanical properties that resemble those of muscle. In a fundamental departure from this perspective, here, I show that muscle more closely resembles a heat engine with mechanical properties that emerge from the thermodynamics of a myosin motor ensemble. The transformative impact of thermodynamics on our understanding of how a heat engine works guides a parallel transformation in our understanding of how muscle works. I consider the simplest possible model of force generation: a binary mechanical system. I develop the mechanics, energetics, and kinetics of this system and show that a single binding reaction generates force when muscle is held at a fixed length and performs work when muscle is allowed to shorten. This creates a network of thermodynamic binding pathways that resembles many of the characteristic mechanical and energetic behaviors of muscle including the muscle force-velocity relationship, heat output by shortening muscle, four phases of a muscle tension transient, spontaneous oscillatory contractions, and force redevelopment. Analogous to the thermodynamic (Carnot) cycle for a heat engine, isothermal and adiabatic binding and detachment reactions create a thermodynamic cycle for muscle that resembles cardiac pressure-volume loops (i.e., how the heart works). This paper provides an outline for how to re-interpret muscle mechanic data using thermodynamics - an ongoing effort that will continue providing novel insights into how muscle and molecular motors work.

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

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

A thermodynamically consistent monte carlo cross-bridge model with a trapping mechanism reveals the role of stretch activation in heart pumping

Changes in intracellular calcium concentrations regulate heart beats. However, the decline in the left ventricular pressure during early diastole is much sharper than that of the Ca²⁺ transient, resulting in a rapid supply of blood to the left ventricle during the diastole. At the tissue level, cardiac muscles have a distinct characteristic, known as stretch activation, similar to the function of insect flight muscles. Stretch activation, which is a delayed increase in force following a rapid muscle length increase, has been thought to be related to autonomous control in these muscles. In this numerical simulation study, we introduced a molecular mechanism of stretch activation and investigated the role of this mechanism in the pumping function of the heart, using the previously developed coupling multiple-step active stiffness integration scheme for a Monte Carlo (MC) cross-bridge model and a bi-ventricular finite element model. In the MC cross-bridge model, we introduced a mechanism for trapping the myosin molecule in its post-power stroke state. We then determined the rate constants of transitions for trapping and escaping in a thermodynamically consistent manner. Based on our numerical analysis, we draw the following conclusions regarding the stretch activation mechanism: (i) the delayed force becomes larger than the original isometric force because the population of trapped myosin molecules and their average force increase after stretching; (ii) the delayed force has a duration of more than a few seconds owing to a fairly small rate constant of escape from the trapped state. For the role of stretch activation in heart pumping, we draw the following conclusions: (iii) for the regions in which the contraction force decreases earlier than the neighboring region in the end-systole phase, the trapped myosin molecules prevent further lengthening of the myocytes, which then prevents further shortening of neighboring myocytes; (iv) as a result, the contraction forces are sustained longer, resulting in a larger blood ejection, and their degeneration is synchronized.

Application of optical tweezers in cardiovascular research: More than just a measuring tool

Recent advances in the field of optical tweezer technology have shown intriguing potential for applications in cardiovascular medicine, bringing this laboratory nanomechanical instrument into the spotlight of translational medicine. This article summarizes cardiovascular system findings generated using optical tweezers, including not only rigorous nanomechanical measurements but also multifunctional manipulation of biologically active molecules such as myosin and actin, of cells such as red blood cells and cardiomyocytes, of subcellular organelles, and of microvessels in vivo. The implications of these findings in the diagnosis and treatment of diseases, as well as potential perspectives that could also benefit from this tool, are also discussed.

Multistep orthophosphate release tunes actomyosin energy transduction

Muscle contraction and a range of critical cellular functions rely on force-producing interactions between myosin motors and actin filaments, powered by turnover of adenosine triphosphate (ATP). The relationship between release of the ATP hydrolysis product ortophosphate (Pi) from the myosin active site and the force-generating structural change, the power-stroke, remains enigmatic despite its central role in energy transduction. Here, we present a model with multistep Pi-release that unifies current conflicting views while also revealing additional complexities of potential functional importance. The model is based on our evidence from kinetics, molecular modelling and single molecule fluorescence studies of Pi binding outside the active site. It is also consistent with high-speed atomic force microscopy movies of single myosin II molecules without Pi at the active site, showing consecutive snapshots of pre- and post-power stroke conformations. In addition to revealing critical features of energy transduction by actomyosin, the results suggest enzymatic mechanisms of potentially general relevance.

Release of the ATP hydrolysis product orthophosphate (Pi) from the myosin active site is central in force generation but is poorly understood. Here, Moretto et al. present evidence for multistep Pi-release reconciling apparently contradictory results.

A chemical thermodynamic model of motor enzymes unifies chemical-Fx and powerstroke models

Molecular motors play a central role in many biological processes, ranging from pumping blood and breathing to growth and wound healing. Through motor-catalyzed chemical reactions, these nanomachines convert the chemical free energy from ATP hydrolysis into two different forms of mechanical work. Motor enzymes perform reversible work, wrev, through an intermediate step in their catalyzed reaction cycle referred to as a working step, and they perform Fx work when they move a distance, x, against a force, F. In a powerstroke model, wrev is performed when the working step stretches a spring within a given motor enzyme. In a chemical-Fx model, wrev is performed in generating a conserved Fx potential defined external to the motor enzyme. It is difficult to find any common ground between these models even though both have been shown to account for mechanochemical measurements of motor enzymes with reasonable accuracy. Here, I show that, by changing one simple assumption in each model, the powerstroke and chemical-Fx model can be reconciled through a chemical thermodynamic model. The formal and experimental justifications for changing these assumptions are presented. The result is a unifying model for mechanochemical coupling in motor enzymes first presented by A.V. Hill in 1938 that is consistent with single-molecule structural and mechanical data.

Critical Evaluation of Current Hypotheses for the Pathogenesis of Hypertrophic Cardiomyopathy

Hereditary hypertrophic cardiomyopathy (HCM), due to mutations in sarcomere proteins, occurs in more than 1/500 individuals and is the leading cause of sudden cardiac death in young people. The clinical course exhibits appreciable variability. However, typically, heart morphology and function are normal at birth, with pathological remodeling developing over years to decades, leading to a phenotype characterized by asymmetric ventricular hypertrophy, scattered fibrosis and myofibrillar/cellular disarray with ultimate mechanical heart failure and/or severe arrhythmias. The identity of the primary mutation-induced changes in sarcomere function and how they trigger debilitating remodeling are poorly understood. Support for the importance of mutation-induced hypercontractility, e.g., increased calcium sensitivity and/or increased power output, has been strengthened in recent years. However, other ideas that mutation-induced hypocontractility or non-uniformities with contractile instabilities, instead, constitute primary triggers cannot yet be discarded. Here, we review evidence for and criticism against the mentioned hypotheses. In this process, we find support for previous ideas that inefficient energy usage and a blunted Frank–Starling mechanism have central roles in pathogenesis, although presumably representing effects secondary to the primary mutation-induced changes. While first trying to reconcile apparently diverging evidence for the different hypotheses in one unified model, we also identify key remaining questions and suggest how experimental systems that are built around isolated primarily expressed proteins could be useful.

A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation

In a multiscale simulation of a beating heart, the very large difference in the time scales between rapid stochastic conformational changes of contractile proteins and deterministic macroscopic outcomes, such as the ventricular pressure and volume, have hampered the implementation of an efficient coupling algorithm for the two scales. Furthermore, the consideration of dynamic changes of muscle stiffness caused by the cross-bridge activity of motor proteins have not been well established in continuum mechanics. To overcome these issues, we propose a multiple time step scheme called the multiple step active stiffness integration scheme (MusAsi) for the coupling of Monte Carlo (MC) multiple steps and an implicit finite element (FE) time integration step. The method focuses on the active tension stiffness matrix, where the active tension derivatives concerning the current displacements in the FE model are correctly integrated into the total stiffness matrix to avoid instability. A sensitivity analysis of the number of samples used in the MC model and the combination of time step sizes confirmed the accuracy and robustness of MusAsi, and we concluded that the combination of a 1.25 ms FE time step and 0.005 ms MC multiple steps using a few hundred motor proteins in each finite element was appropriate in the tradeoff between accuracy and computational time. Furthermore, for a biventricular FE model consisting of 45,000 tetrahedral elements, one heartbeat could be computed within 1.5 h using 320 cores of a conventional parallel computer system. These results support the practicality of MusAsi for uses in both the basic research of the relationship between molecular mechanisms and cardiac outputs, and clinical applications of perioperative prediction.