Load-dependent Kinetics Research Articles

A mutation in switch I alters the load-dependent kinetics of myosin Va

Myosin Va is the molecular motor that drives intracellular vesicular transport, powered by the transduction of chemical energy from ATP into mechanical work. The coupling of the powerstroke and phosphate (Pi) release is key to understanding the transduction process, and crucial details of this process remain unclear. Therefore, we determined the effect of elevated Pi on the force-generating capacity of a mini-ensemble of myosin Va S1 (WT) in a laser trap assay. By increasing the stiffness of the laser trap we determined the effect of increasing resistive loads on the rate of Pi-induced detachment from actin, and quantified this effect using the Bell approximation. We observed that WT myosin generated higher forces and larger displacements at the higher laser trap stiffnesses in the presence of 30 mM Pi, but binding event lifetimes decreased dramatically, which is most consistent with the powerstroke preceding the release of Pi from the active site. Repeating these experiments using a construct with a mutation in switch I of the active site (S217A) caused a seven-fold increase in the load-dependence of the Pi-induced detachment rate, suggesting that the S217A region of switch I may help mediate the load-dependence of Pi-rebinding.

Single-molecule mechanics and kinetics of cardiac myosin interacting with regulated thin filaments

The cardiac cycle is a tightly regulated process wherein the heart generates force to pump blood to the body during systole and then relaxes during diastole. Disruption of this finely tuned cycle can lead to a range of diseases including cardiomyopathies and heart failure. Cardiac contraction is driven by the molecular motor myosin, which pulls regulated thin filaments in a calcium-dependent manner. In some muscle and nonmuscle myosins, regulatory proteins on actin tune the kinetics, mechanics, and load dependence of the myosin working stroke; however, it is not well understood whether or how thin-filament regulatory proteins tune the mechanics of the cardiac myosin motor. To address this critical gap in knowledge, we used single-molecule techniques to measure the kinetics and mechanics of the substeps of the cardiac myosin working stroke in the presence and absence of thin filament regulatory proteins. We found that regulatory proteins gate the calcium-dependent interactions between myosin and the thin filament. At physiologically relevant ATP concentrations, cardiac myosin’s mechanics and unloaded kinetics are not affected by thin-filament regulatory proteins. We also measured the load-dependent kinetics of cardiac myosin at physiologically relevant ATP concentrations using an isometric optical clamp, and we found that thin-filament regulatory proteins do not affect either the identity or magnitude of myosin’s primary load-dependent transition. Interestingly, at low ATP concentrations at both saturating and physiologically relevant subsaturating calcium concentrations, thin-filament regulatory proteins have a small effect on actomyosin dissociation kinetics, suggesting a mechanism beyond simple steric blocking. These results have important implications for the modeling of cardiac physiology and diseases.

Cardiac myosin's mechanics and load dependent kinetics are not altered by the thin-filament proteins.

The force necessary to power human heart contraction is generated by beta cardiac myosin pulling on regulated thin filaments. Myosin's force generation is a tightly regulated process, and its disruption causes diseases including genetic cardiomyopathies. Deciphering the details of force generation at the molecular scale is critical for our understanding of both cardiac physiology and disease. While excellent studies have elucidated the mechanics and kinetics underlying the interactions between cardiac myosin and actin at the single molecule scale, the majority of these studies have been conducted in the absence of regulatory proteins. In the case of several other myosin isoforms, regulatory proteins alter the mechanics and load-dependent kinetics of the myosin working stroke, and it is not clear what role, if any they play in tuning the cardiac myosin working stroke and load-dependent kinetics. Here, we used a single molecule optical trapping assay to measure myosin's mechanics in the presence and absence of reconstituted thin-filaments (RTFs). We observed that regulatory proteins do not affect the myosin working stroke or its substeps. Interestingly, at low ATP, we observed that regulatory proteins slow the rate of actomyosin dissociation, and we showed using stopped flow kinetics that this is due to tuning of the rate of ATP-induced dissociation. The difference in the dissociation rate disappears at physiologically relevant ATP concentrations. We also used an isometric force clamp to investigate the load dependence of the myosin working stroke at physiologically relevant ATP concentrations, and this was also unchanged with RTFs. Taken together, these results show that cardiac myosin's mechanics are not altered by regulatory proteins at physiologically relevant ATP concentrations, and they provide important insights into the molecular mechanisms underlying heart contraction.

Myocardial Contractility: Historical and Contemporary Considerations.

The term myocardial contractility is thought to have originated more than 125 years ago and has remained and enigma ever since. Although the term is frequently used in textbooks, editorials and contemporary manuscripts its definition remains illusive often being conflated with cardiac performance or inotropy. The absence of a universally accepted definition has led to confusion, disagreement and misconceptions among physiologists, cardiologists and safety pharmacologists regarding its definition particularly in light of new discoveries regarding the load dependent kinetics of cardiac contraction and their translation to cardiac force-velocity and ventricular pressure-volume measurements. Importantly, the Starling interpretation of force development is length-dependent while contractility is length independent. Most historical definitions employ an operational approach and define cardiac contractility in terms of the hearts mechanical properties independent of loading conditions. Literally defined the term contract infers that something has become smaller, shrunk or shortened. The addition of the suffix “ility” implies the quality of this process. The discovery and clinical investigation of small molecules that bind to sarcomeric proteins independently altering force or velocity requires that a modern definition of the term myocardial contractility be developed if the term is to persist. This review reconsiders the historical and contemporary interpretations of the terms cardiac performance and inotropy and recommends a modern definition of myocardial contractility as the preload, afterload and length-independent intrinsic kinetically controlled, chemo-mechanical processes responsible for the development of force and velocity.

Design of An Optical Tweezers System with Fast Digital Feedback for Studying the Mechanochemistry of Cardiac Myosin

Cardiac myosin powers the contraction of the heart and has load dependent kinetics that enable it to adjust its power output in response to load. Dysfunction of cardiac myosin's mechanochemistry can lead to diseases including heart failure, and therefore, there is an outstanding need to probe how mutations and potential therapeutic compounds affect myosin's mechanochemistry under load. Given that cardiac myosin has fast cycling kinetics, we have developed a fast optical trapping system specifically tailored towards probing the mechanochemistry of cardiac myosin. A field programmable gate array (FPGA) board digitizes force signals, applies tunable digital filtering for feedback clamping, controls trap positions through fast interfaces to direct digital synthesizer (DDS) boards, and oscillates the sample stage. Amplified frequencies from each DDS drive acousto-optic deflectors for steering the trapping laser beams. This FPGA-DDS feedback system can respond to changes in bead position due to myosin binding in <33 microseconds. The synchronously acquired data include internal trap position commands, calculated feedback errors, and sample stage position. To demonstrate the system capabilities, we examined the mechanochemical properties of cardiac myosin using the three-bead-assay developed by the Spudich lab. Using our system, it is possible to clearly resolve the kinetics and mechanics of the cardiac myosin working stroke. We use an improved methodology for binding event identification and synchronization, enabling better resolution of the substeps of the myosin working stroke. We also demonstrate the ability of this system to probe the load dependent kinetics of cardiac myosin using both an isometric force feedback clamp and harmonic force spectroscopy. The speed of the system enables measurement of these parameters at physiologically relevant ATP concentrations despite the short lived binding interactions between actin and myosin.

Controlling load-dependent kinetics of β-cardiac myosin at the single-molecule level.

Concepts in molecular tension sensing in biology are growing and have their origins in studies of muscle contraction. In the heart muscle, a key parameter of contractility is the detachment rate from actin of myosin, which determines the time that myosin is bound to actin in a force-producing state and, importantly, depends on the load (force) against which myosin works. Here, we measure the detachment rate of single molecules of human β-cardiac myosin and its load dependence. We find that both can be modulated by both small molecule compounds and cardiomyopathy-causing mutations. Furthermore, effects of mutations can be reversed by introducing appropriate compounds. Our results suggest that activating vs. inhibitory perturbations of cardiac myosin are discriminated by the aggregate result on duty ratio, average force, and ultimately average power output and that cardiac contractility can be controlled by tuning the load-dependent kinetics of single myosin molecules.

Observing Single RNA Polymerase Molecules Down to Base-Pair Resolution.

During transcriptional elongation, RNA polymerases (RNAP) employ a stepping mechanism to translocate along the DNA template while synthesizing RNA. Optical trapping assays permit the progress of single molecules of RNA polymerase to be monitored in real time, at resolutions down to the level of individual base pairs. Additionally, optical trapping assays permit the application of exquisitely controlled, external forces on RNAP. Responses to such forces can reveal details of the load-dependent kinetics of transcriptional elongation and pausing. Traditionally, the bacterial form of RNAP from E. coli has served as a model for the study of transcriptional elongation using optical traps. However, it is now feasible to perform optical trapping experiments using the eukaryotic polymerase, RNAPII, as well. In this report, we describe the methods to perform optical trapping transcriptional elongation assays with both prokaryotic RNAP and eukaryotic RNAPII. We provide detailed instructions on how to reconstitute transcription elongation complexes, derivatize beads used in the assays, and perform optical trapping measurements.

Harmonic force spectroscopy measures load-dependent kinetics of individual human β-cardiac myosin molecules.

Molecular motors are responsible for numerous cellular processes from cargo transport to heart contraction. Their interactions with other cellular components are often transient and exhibit kinetics that depend on load. Here, we measure such interactions using ‘harmonic force spectroscopy'. In this method, harmonic oscillation of the sample stage of a laser trap immediately, automatically and randomly applies sinusoidally varying loads to a single motor molecule interacting with a single track along which it moves. The experimental protocol and the data analysis are simple, fast and efficient. The protocol accumulates statistics fast enough to deliver single-molecule results from single-molecule experiments. We demonstrate the method's performance by measuring the force-dependent kinetics of individual human β-cardiac myosin molecules interacting with an actin filament at physiological ATP concentration. We show that a molecule's ADP release rate depends exponentially on the applied load, in qualitative agreement with cardiac muscle, which contracts with a velocity inversely proportional to external load.

Muscle Shortening Velocity is Modulated by Alternative Myosin Converters

The myosin converter has been proposed to be critical for setting muscle shortening velocity by influencing the amplification of small conformational changes at the ATPase site into the larger lever arm swing. To test this hypothesis, we exploited the natural variation of the converter region found in Drosophila muscle types. In Drosophila, a single myosin heavy chain gene is alternatively spliced to generate myosin isoforms. The converter region is encoded by five alternative versions of exon 11 that are expressed in different muscle types. Through genetic modification we forced the expression of the alternative versions in the Drosophila jump muscle and found that two of the three versions tested to date, 11a (native to indirect flight muscles) and 11e (embryonic muscles), caused faster maximum shortening velocities of skinned jump muscle fibers relative to the native control 11c. Increases in velocity were primarily responsible for 70.9% and 79.0% higher power outputs for 11a and 11e fibers, respectively, because maximum force generation was not significantly different from control fibers. The fibers expressing 11a and 11e also exhibited a straighter force-velocity curve, as shown by increased Hill equation parameters a (95.4% and 84.5% higher, respectively) and b (72.6% and 65.5% higher, respectively) relative to control fibers, indicating that the converter modulates load dependent cross-bridge kinetics. The higher power and shortening velocity of 11a and 11e fibers enabled increased jumping ability, 76.0% and 48.8% farther, respectively. Converter homology models, using the new Drosophila myosin S1 crystal structure (pdb 4QBD), revealed minimal tertiary structure differences suggesting residue specific interactions with the relay, N-terminus, or essential light chain are critical. Overall, our data support the hypothesis that the converter helps set muscle shortening velocity under loaded and unloaded conditions and thus contributes to muscle fiber type diversity.

Symmetric Modulation of Cross-Bridge Kinetics by Sarcomere Velocity during Shortening and Lengthening in Cardiac Trabeculae; A New Insight on Sarcomere Dynamics

There is a controversy whether cross-bridge (XB) dynamics is determined by XB displacement, filaments velocity or the load experienced by each XB. The study tests these three hypotheses at the sarcomere level. Methods: Trabeculae were isolated from rat right ventricles (n=9). Sarcomere length was measured by laser diffraction. Changes in the number of strong XBs (NXB) were evaluated by measuring the dynamic stiffness. Ramp stretches and releases at different velocities and onset times were imposed over isometric sarcomere contractions. Results: Stretches yielded parallel increase in the force and stiffness, at all stretch velocities. The force per XB during stretch was constant, independent of the velocity, and equal to the isometric force per XB. This observation is incongruent with a load dependent kinetics. The instantaneous stiffness during the ramp stretches and releases was normalized by the isometric stiffness. Identical changes in the normalized stiffness were observed when identical ramp perturbations (stretch or release) were imposed at different onset times during the twitches. Thus changes in the normalized NXB are not dominated by XB recruitment processes, although the number of available XBs varies with time during the twitch. The normalized stiffness development rate linearly depended on the lengthening velocity with a slope of 6.73±0.98 [1/μm]. During shortening the normalize stiffness decline rate depended linearly on the shortening velocity with identical slope of 6.70±1.43 [1/μm]. Conclusions: The symmetrical dependence of the normalized stiffness development rate on the velocity and the independence on the perturbation onset time are conveniently explained by the velocity dependent hypothesis in the framework of an integrated sarcomere, where there is a cooperative interaction between the XBs. This mechanism explains the force-velocity relationship and the muscle high contractile efficiency.

Complex In Vitro Motility Characteristics Emerge from Mechanical Coupling of Myosin Motors via a Commonly Propelled Actin Filament

Background: Collective propulsion of actin by myosin motors is fundamental to most muscle contraction models. Single myosin load-dependent mechanochemistry as well as cooperative action of small numbers of motors are increasingly well-understood. Deducing macroscopic actin propulsion from microscopic actomyosin interaction would help to connect both scales. We developed and tested experimentally a model that explains the emergence of complex features of in vitro actin sliding from mechanical coupling of a high but not statistical number of myosins via actin.Methods: Smooth muscle myosin load-dependent kinetics were modeled based on single molecule experiments [Veigel; NatCellBiol(2003), 5(11):980]; the coupling parameter “I” quantifies the acceleration of the rate-limiting ADP-release/detachment step by the phosphate release-associated main power stroke, as hypothesized by others [Jackson; PhysChemChemPhys(2009), 11:4808]. A simplified two-state model exhibited a saddle-node bifurcation into fast/slow bistable filament motion above a critical number of coupled myosins for I>0, leading to an acceleration relative to the non-coupled I=0 case. Chemical Master Equation and Gillespie-type simulations of the full three state model (Pre Power Stroke, Post Power Stroke, Non-Bound) further predicted a characteristic deviation of velocity fluctuations from the law of large numbers as well as increased sliding velocity autocorrelation times. We developed video analysis software for increased throughput and detail, allowing length-resolved quantification of sliding velocities, velocity fluctuations, and autocorrelation times in in vitro motility assays with myosin purified from phasic smooth muscle.Results: A previously reported acceleration of in vitro actin sliding [Baker; JBiolChem(2003), 278(31):28533] emerges from our model. Qualitative predictions on velocity fluctuations and autocorrelation time were confirmed experimentally.Conclusions: These results support the hypothesis of actin sliding acceleration by mechanical coupling between different actomyosin kinetic steps.

High-Throughput Single Molecule Measurements Confirm a Load-Dependent Association Rate for E-Selectin and Sialyl Lewisa

We previously reported the association rate between E-selectin and sialyl Lewisa, two molecules involved in leukocyte adhesion and rolling, to be accelerated by compressive loads acting between them (Snook and Guilford, 2010). To improve and expand these studies, we have built a magnetic bond pulling system for high-throughput data collection from single molecules for studies of load-dependent kinetics. The system allows us to replicate laser trap and biomembrane force probe experiments on a larger scale. Four electromagnets are arranged in a tetrahedron, two above and two below a flow cell. These provide uniform upward and downward forces, respectively. The system is controlled through a LabVIEW interface and is capable of producing vertical pushing and pulling forces up to ∼40 pN between receptor-coated surfaces and 3 μm ligand-coated superparamagnetic beads. Loads are applied to dozens of beads simultaneously, which are tracked through video microscopy with a temporal resolution of 11 ms. We used the device to investigate the possibility of a load-dependent rate of association between E-selectin and sialyl Lewisa. The fraction of contacts forming a bond (“adhesion probability”) can be fitted as a function of contact time to determine the 2-dimensional on-rate. This was done over a range of compressive forces to determine the effect of compressive force on 2D on-rate. We confirmed that compressive force does indeed increase the rate of association between E-selectin and sialyl Lewisa. This high-throughput approach will allow us to more rapidly investigate the origin of this phenomenon.

Cardiomyopathy-linked myosin regulatory light chain mutations disrupt myosin strain-dependent biochemistry.

Familial hypertrophic cardiomyopathy (FHC) is caused by mutations in sarcomeric proteins including the myosin regulatory light chain (RLC). Two such FHC mutations, R58Q and N47K, located near the cationic binding site of the RLC, have been identified from population studies. To examine the molecular basis for the observed phenotypes, we exchanged endogenous RLC from native porcine cardiac myosin with recombinant human ventricular wild type (WT) or FHC mutant RLC and examined the ability of the reconstituted myosin to propel actin filament sliding using the in vitro motility assay. We find that, whereas the mutant myosins are indistinguishable from the controls (WT or native myosin) under unloaded conditions, both R58Q- and N47K-exchanged myosins show reductions in force and power output compared with WT or native myosin. We also show that the changes in loaded kinetics are a result of mutation-induced loss of myosin strain sensitivity of ADP affinity. We propose that the R58Q and N47K mutations alter the mechanical properties of the myosin neck region, leading to altered load-dependent kinetics that may explain the observed mutant-induced FHC phenotypes.

The load dependence of rate constants

As experimental techniques in biophysics have progressed at the single molecule level, there has been considerable interest in understanding how external mechanical influences (such as load) affect chemical reactions. The majority of biophysical studies investigating load-dependent kinetics use an equation where the rate constant exponentially depends on force, which is sometimes called Bell's equation. This equation requires the determination of two parameters that describe the potential energy-strain function: k(0), which is the reaction rate in the absence of load, and x(c), which is the difference in strain between the reactant and transition states. However, there have been theoretical studies based on Kramers' theory suggesting that the rate constant should have load-dependent pre-exponential terms and nonlinear load-dependent terms in the exponential. Kramers' theory requires an exact knowledge of the potential energy-strain function, which is in general not known for an experimental system. Here, we derive a general approximation of Kramers' theory where the potential energy-strain function is described by five parameters, which can, for small loads, be reduced to four-, three-, and finally to two parameters (Bell's equation). We then use an idealized physical system to validate our approximations to Kramers' theory and show how they can predict parameters of interest (such as k(0) and x(c)) better than Bell's equation. Finally, we show previously published experimental data that are not well fitted by Bell's equation but are adequately fitted by these more exact equations.

Mutation of a Conserved Glycine in the SH1-SH2 Helix Affects the Load-Dependent Kinetics of Myosin

The ATP hydrolysis rate and shortening velocity of muscle are load-dependent. At the molecular level, myosin generates force and motion by coupling ATP hydrolysis to lever arm rotation. When a laser trap was used to apply load to single heads of expressed smooth muscle myosin (S1), the ADP release kinetics accelerated with an assistive load and slowed with a resistive load; however, ATP binding was mostly unaffected. To investigate how load is communicated within the motor, a glycine located at the putative fulcrum of the lever arm was mutated to valine (G709V). In the absence of load, stopped-flow and laser trap studies showed that the mutation significantly slowed the rates of ADP release and ATP binding, accounting for the ∼270-fold decrease in actin sliding velocity. The load dependence of the mutant’s ADP release rate was the same as that of wild-type S1 (WT) despite the slower rate. In contrast, load accelerated ATP binding by ∼20-fold, irrespective of loading direction. Imparting mechanical energy to the mutant motor partially reversed the slowed ATP binding by overcoming the elevated activation energy barrier. These results imply that conformational changes near the conserved G709 are critical for the transmission of mechanochemical information between myosin’s active site and lever arm.

Load-dependent kinetics of myosin-V can explain its high processivity

Recent studies provide strong evidence that single myosin class V molecules transport vesicles and organelles processively along F-actin, taking several 36-nm steps, 'hand over hand', for each diffusional encounter. The mechanisms regulating myosin-V's processivity remain unknown. Here, we have used an optical-tweezers-based transducer to measure the effect of load on the mechanical interactions between rabbit skeletal F-actin and a single head of mouse brain myosin-V, which produces its working stroke in two phases. We found that the lifetimes of the first phase of the working stroke changed exponentially and about 10-fold over a range of pushing and pulling forces of +/- 1.5 pN. Stiffness measurements suggest that intramolecular forces could approach 3.6 pN when both heads are bound to F-actin, in which case extrapolation would predict the detachment kinetics of the front head to slow down 50-fold and the kinetics of the rear head to accelerate respectively. This synchronizing effect on the chemo-mechanical cycles of the heads increases the probability of the trail head detaching first and causes a strong increase in the number of forward steps per diffusional encounter over a system with no strain dependence.

Load-dependent kinetics of force production by smooth muscle myosin measured with optical tweezers.

Muscle contraction is driven by the cyclical interaction of myosin with actin, coupled with ATP hydrolysis. Myosin attaches to actin, forming a crossbridge that produces force and movement as it tilts or rocks into subsequent bound states before finally detaching. It has been hypothesized that the kinetics of one or more of these mechanical transitions are dependent on load, allowing muscle to shorten quickly under low load, but to sustain tension economically, with slowly cycling crossbridges under high load conditions. The idea that muscle biochemistry depends on mechanical output is termed the 'Fenn effect'. However, the molecular details of how load affects the kinetics of a single crossbridge are unknown. Here, we describe a new technique based on optical tweezers to rapidly apply force to a single smooth muscle myosin crossbridge. The crossbridge produced movement in two phases that contribute 4 nm + 2 nm of displacement. Duration of the first phase depended in an exponential manner on the amplitude of applied load. Duration of the second phase was much less affected by load, but was significantly shorter at high ATP concentration. The effect of load on the lifetime of the bound crossbridge is to prolong binding when load is high, but to accelerate release when load is low or negative.