Mechanical Coupling between Myosin Molecules Causes Differences between Ensemble and Single-Molecule Measurements

In contracting muscle, individual myosin molecules function as part of a large ensemble, hydrolyzing ATP to power the relative sliding of actin filaments. The technological advances that have enabled direct observation and manipulation of single molecules, including recent experiments that have explored myosin's force-dependent properties, provide detailed insight into the kinetics of myosin's mechanochemical interaction with actin. However, it has been difficult to reconcile these single-molecule observations with the behavior of myosin in an ensemble. Here, using a combination of simulations and theory, we show that the kinetic mechanism derived from single-molecule experiments describes ensemble behavior; but the connection between single molecule and ensemble is complex. In particular, even in the absence of external force, internal forces generated between myosin molecules in a large ensemble accelerate ADP release and increase how far actin moves during a single myosin attachment. These myosin-induced changes in strong binding lifetime and attachment distance cause measurable properties, such as actin speed in the motility assay, to vary depending on the number of myosin molecules interacting with an actin filament. This ensemble-size effect challenges the simple detachment limited model of motility, because even when motility speed is limited by ADP release, increasing attachment rate can increase motility speed.     

Local Control Model of Excitation–Contraction Coupling in Skeletal Muscle

The voltage-activated H⁺ selective conductance of rat alveolar epithelial cells was studied using whole-cell and excised-patch voltage-clamp techniques. The effects of substituting deuterium oxide, D₂O, for water, H₂O, on both the conductance and the pH dependence of gating were explored. D⁺ was able to permeate proton channels, but with a conductance only about 50% that of H⁺. The conductance in D₂O was reduced more than could be accounted for by bulk solvent isotope effects (i.e., the lower mobility of D⁺ than H⁺), suggesting that D⁺ interacts specifically with the channel during permeation. Evidently the H⁺ or D⁺ current is not diffusion limited, and the H⁺ channel does not behave like a water-filled pore. This result indirectly strengthens the hypothesis that H⁺ (or D⁺) and not OH⁻ is the ionic species carrying current. The voltage dependence of H⁺ channel gating characteristically is sensitive to pH_o and pH_i and was regulated by pD_o and pD_i in an analogous manner, shifting 40 mV/U change in the pD gradient. The time constant of H⁺ current activation was about three times slower (τ_act was larger) in D₂O than in H₂O. The size of the isotope effect is consistent with deuterium isotope effects for proton abstraction reactions, suggesting that H⁺ channel activation requires deprotonation of the channel. In contrast, deactivation (τ_tail) was slowed only by a factor ≤1.5 in D₂O. The results are interpreted within the context of a model for the regulation of H⁺ channel gating by mutually exclusive protonation at internal and external sites (Cherny, V.V., V.S. Markin, and T.E. DeCoursey. 1995. J. Gen. Physiol. 105:861–896). Most of the kinetic effects of D₂O can be explained if the pK _a of the external regulatory site is ∼0.5 pH U higher in D₂O.     

Direct Observation of Phosphate Inhibiting the Force-Generating Capacity of a Miniensemble of Myosin Molecules

Elevated levels of phosphate (P_i) reduce isometric force, providing support for the notion that the release of P_i from myosin is closely associated with the generation of muscular force. P_i is thought to rebind to actomyosin in an ADP-bound state and reverse the force-generating steps, including the rotation of the lever arm (i.e., the powerstroke). Despite extensive study, this mechanism remains controversial, in part because it fails to explain the effects of P_i on isometric ATPase and unloaded shortening velocity. To gain new insight into this process, we determined the effect of P_i on the force-generating capacity of a small ensemble of myosin (∼12 myosin heads) using a three-bead laser trap assay. In the absence of P_i, myosin pulled the actin filament out of the laser trap an average distance of 54 ± 4 nm, translating into an average peak force of 1.2 pN. By contrast, in the presence of 30 mM P_i, myosin generated only enough force to displace the actin filament by 13 ± 1 nm, generating just 0.2 pN of force. The elevated P_i also caused a >65% reduction in binding-event lifetime, suggesting that P_i induces premature detachment from a strongly bound state. Definitive evidence of a P_i-induced powerstroke reversal was not observed, therefore we determined if a branched kinetic model in which P_i induces detachment from a strongly bound, postpowerstroke state could explain these observations. The model was able to accurately reproduce not only the data presented here, but also the effects of P_i on both isometric ATPase in muscle fibers and actin filament velocity in a motility assay. The ability of the model to capture the findings presented here as well as previous findings suggests that P_i-induced inhibition of force may proceed along a kinetic pathway different from that of force generation.     

Direct Observation of Phosphate Inhibiting the Force-Generating Capacity of a Miniensemble of Myosin Molecules

Elevated levels of phosphate (P_i) reduce isometric force, providing support for the notion that the release of P_i from myosin is closely associated with the generation of muscular force. P_i is thought to rebind to actomyosin in an ADP-bound state and reverse the force-generating steps, including the rotation of the lever arm (i.e., the powerstroke). Despite extensive study, this mechanism remains controversial, in part because it fails to explain the effects of P_i on isometric ATPase and unloaded shortening velocity. To gain new insight into this process, we determined the effect of P_i on the force-generating capacity of a small ensemble of myosin (∼12 myosin heads) using a three-bead laser trap assay. In the absence of P_i, myosin pulled the actin filament out of the laser trap an average distance of 54 ± 4 nm, translating into an average peak force of 1.2 pN. By contrast, in the presence of 30 mM P_i, myosin generated only enough force to displace the actin filament by 13 ± 1 nm, generating just 0.2 pN of force. The elevated P_i also caused a >65% reduction in binding-event lifetime, suggesting that P_i induces premature detachment from a strongly bound state. Definitive evidence of a P_i-induced powerstroke reversal was not observed, therefore we determined if a branched kinetic model in which P_i induces detachment from a strongly bound, postpowerstroke state could explain these observations. The model was able to accurately reproduce not only the data presented here, but also the effects of P_i on both isometric ATPase in muscle fibers and actin filament velocity in a motility assay. The ability of the model to capture the findings presented here as well as previous findings suggests that P_i-induced inhibition of force may proceed along a kinetic pathway different from that of force generation.     

Effects of Cardiac Myosin Binding Protein-C on Actin Motility Are Explained with a Drag-Activation-Competition Model

Although mutations in cardiac myosin binding protein-C (cMyBP-C) cause heart disease, its role in muscle contraction is not well understood. A mechanism remains elusive partly because the protein can have multiple effects, such as dual biphasic activation and inhibition observed in actin motility assays. Here we develop a mathematical model for the interaction of cMyBP-C with the contractile proteins actin and myosin and the regulatory protein tropomyosin. We use this model to show that a drag-activation-competition mechanism accurately describes actin motility measurements, while models lacking either drag or competition do not. These results suggest that complex effects can arise simply from cMyBP-C binding to actin.     

Evidence for a Complex between Myosin and ADP in Relaxed Muscle Fibres

TAYLOR and his co-workers have shown that myosin, when mixed with its substrate ATP, rapidly forms a stoichiometric complex in which the terminal phosphate bond of the ATP is already broken¹; this complex is relatively stable and lasts for nearly all of the time between successive ATP hydrolyses². The aim of the present work was to find out whether such a complex is formed in relaxed muscle.     

Eye Movement Deficits Are Consistent with a Staging Model of pTDP-43 Pathology in Amyotrophic Lateral Sclerosis

Background

The neuropathological process underlying amyotrophic lateral sclerosis (ALS) can be traced as a four-stage progression scheme of sequential corticofugal axonal spread. The examination of eye movement control gains deep insights into brain network pathology and provides the opportunity to detect both disturbance of the brainstem oculomotor circuitry as well as executive deficits of oculomotor function associated with higher brain networks.

Objective

To study systematically oculomotor characteristics in ALS and its underlying network pathology in order to determine whether eye movement deterioration can be categorized within a staging system of oculomotor decline that corresponds to the neuropathological model.

Methods

Sixty-eight ALS patients and 31 controls underwent video-oculographic, clinical and neuropsychological assessments.

Results

Oculomotor examinations revealed increased anti- and delayed saccades’ errors, gaze-palsy and a cerebellary type of smooth pursuit disturbance. The oculomotor disturbances occurred in a sequential manner: Stage 1, only executive control of eye movements was affected. Stage 2 indicates disturbed executive control plus ‘genuine’ oculomotor dysfunctions such as gaze-paly. We found high correlations (p<0.001) between the oculomotor stages and both, the clinical presentation as assessed by the ALS Functional Rating Scale (ALSFRS) score, and cognitive scores from the Edinburgh Cognitive and Behavioral ALS Screen (ECAS).

Conclusions

Dysfunction of eye movement control in ALS can be characterized by a two-staged sequential pattern comprising executive deficits in Stage 1 and additional impaired infratentorial oculomotor control pathways in Stage 2. This pattern parallels the neuropathological staging of ALS and may serve as a technical marker of the neuropathological spreading.     

Transcranial Direct Current Stimulation Improves Ipsilateral Selective Muscle Activation in a Frequency Dependent Manner

Failure to suppress antagonist muscles can lead to movement dysfunction, such as the abnormal muscle synergies often seen in the upper limb after stroke. A neurophysiological surrogate of upper limb synergies, the selectivity ratio (SR), can be determined from the ratio of biceps brachii (BB) motor evoked potentials to transcranial magnetic stimulation prior to forearm pronation versus elbow flexion. Surprisingly, cathodal transcranial direct current stimulation (c-TDCS) over ipsilateral primary motor cortex (M1) reduces (i.e. improves) the SR in healthy adults, and chronic stroke patients. The ability to suppress antagonist muscles may be exacerbated at high movement rates. The aim of the present study was to investigate whether the selective muscle activation of the biceps brachii (BB) is dependent on altering frequency demands, and whether the c-tDCS improvement of SR is dependent on task frequency. Seventeen healthy participants performed repetitive isometric elbow flexion and forearm pronation at three rates, before and after c-tDCS or sham delivered to ipsilateral left M1. Ipsilateral c-tDCS improved the SR in a frequency dependent manner by selectively suppressing BB antagonist excitability. Our findings confirm that c-tDCS is an effective tool for improving selective muscle activation, and provide novel evidence for its efficacy at rates of movement where it is most likely to benefit task performance.     

ATPase Activity of Myosin Correlated with Speed of Muscle Shortening

Myosin was isolated from 14 different muscles (mammals, lower vertebrates, and invertebrates) of known maximal speed of shortening. These myosin preparations were homogeneous in the analytical ultracentrifuge or, in a few cases, showed, in addition to the main myosin peak, part of the myosin in aggregated form. Actin- and Ca⁺⁺-activated ATPase activities of the myosins were generally proportional to the speed of shortening of their respective muscles; i.e. the greater the intrinsic speed, the higher the ATPase activity. This relation was found when the speed of shortening ranged from 0.1 to 24 muscle lengths/sec. The temperature coefficient of the Ca⁺⁺-activated myosin ATPase was the same as that of the speed of shortening, Q₁₀ about 2. Higher Q₁₀ values were found for the actin-activated myosin ATPase, especially below 10°C. By using myofibrils instead of reconstituted actomyosin, Q₁₀ values close to 2 could be obtained for the Mg⁺⁺-activated myofibrillar ATPase at ionic strength of 0.014. In another series of experiments, myosin was isolated from 11 different muscles of known isometric twitch contraction time. The ATPase activity of these myosins was inversely proportional to the contraction time of the muscles. These results suggest a role for the ATPase activity of myosin in determining the speed of muscle contraction. In contrast to the ATPase activity of myosin, which varied according to the speed of contraction, the F-actin-binding ability of myosin from various muscles was rather constant.     

Catch Muscle Myorod Modulates ATPase Activity of Myosin in a Phosphorylation-Dependent Way

Myorod is expressed exclusively in molluscan catch muscle and localizes on the surface of thick filaments together with twitchin and myosin. Myorod is an alternatively spliced product of the myosin heavy-chain gene that contains the C-terminal rod part of myosin and a unique N-terminal domain. The unique domain is a target for phosphorylation by gizzard smooth myosin light chain kinase (smMLCK) and, perhaps, molluscan twitchin, which contains a MLCK-like domain. To elucidate the role of myorod and its phosphorylation in the catch muscle, the effect of chromatographically purified myorod on the actin-activated Mg²⁺-ATPase activity of myosin was studied. We found that phosphorylation at the N-terminus of myorod potentiated the actin-activated Mg²⁺-ATPase activity of mussel and rabbit myosins. This potentiation occurred only if myorod was phosphorylated and introduced into the ATPase assay as a co-filament with myosin. We suggest that myorod could be related to the catch state, a function specific to molluscan muscle.     

Activation of Store-Operated Calcium Entry in Airway Smooth Muscle Cells: Insight from a Mathematical Model

Intracellular dynamics of airway smooth muscle cells (ASMC) mediate ASMC contraction and proliferation, and thus play a key role in airway hyper-responsiveness (AHR) and remodelling in asthma. We evaluate the importance of store-operated entry (SOCE) in these dynamics by constructing a mathematical model of ASMC signaling based on experimental data from lung slices. The model confirms that SOCE is elicited upon sufficient depletion of the sarcoplasmic reticulum (SR), while receptor-operated entry (ROCE) is inhibited in such conditions. It also shows that SOCE can sustain agonist-induced oscillations in the absence of other influx. SOCE up-regulation may thus contribute to AHR by increasing the oscillation frequency that in turn regulates ASMC contraction. The model also provides an explanation for the failure of the SERCA pump blocker CPA to clamp the cytosolic of ASMC in lung slices, by showing that CPA is unable to maintain the SR empty of . This prediction is confirmed by experimental data from mouse lung slices, and strongly suggests that CPA only partially inhibits SERCA in ASMC.     

Consistent Temperature Coupling with Thermal Fluctuations of Smooth Particle Hydrodynamics and Molecular Dynamics

We propose a thermodynamically consistent and energy-conserving temperature coupling scheme between the atomistic and the continuum domain. The coupling scheme links the two domains using the DPDE (Dissipative Particle Dynamics at constant Energy) thermostat and is designed to handle strong temperature gradients across the atomistic/continuum domain interface. The fundamentally different definitions of temperature in the continuum and atomistic domain – internal energy and heat capacity versus particle velocity – are accounted for in a straightforward and conceptually intuitive way by the DPDE thermostat. We verify the here-proposed scheme using a fluid, which is simultaneously represented as a continuum using Smooth Particle Hydrodynamics, and as an atomistically resolved liquid using Molecular Dynamics. In the case of equilibrium contact between both domains, we show that the correct microscopic equilibrium properties of the atomistic fluid are obtained. As an example of a strong non-equilibrium situation, we consider the propagation of a steady shock-wave from the continuum domain into the atomistic domain, and show that the coupling scheme conserves both energy and shock-wave dynamics. To demonstrate the applicability of our scheme to real systems, we consider shock loading of a phospholipid bilayer immersed in water in a multi-scale simulation, an interesting topic of biological relevance.     

Relationship between Superprecipitating Activity and Constituents of Myosin B Prepared from Normal and PSE Porcine Muscle

Myosin B from normal and PSE porcine muscles was studied by superprecipitation and SDS polyacrylamide gel electrophoresis. Similar studies were made on the fractions derived from the myosin B preparation after ultracentrifugation. Myosin B and its fractions from PSE muscle showed much less superprecipitation than normal. This difference between normal and PSE muscle seems to reflect differences in biological activity of their myofibrillar proteins, rather than differences in myofibrillar protein composition.     

Cardiomyocytes Sense Matrix Rigidity through a Combination of Muscle and Non-muscle Myosin Contractions

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Alterations at the Cross-Bridge Level Are Associated with a Paradoxical Gain of Muscle Function In Vivo in a Mouse Model of Nemaline Myopathy

Nemaline myopathy is the most common disease entity among non-dystrophic skeletal muscle congenital diseases. The first disease causing mutation (Met9Arg) was identified in the gene encoding α-tropomyosin_slow gene (TPM3). Considering the conflicting findings of the previous studies on the transgenic (Tg) mice carrying the TPM3 ^Met9Arg mutation, we investigated carefully the effect of the Met9Arg mutation in 8–9 month-old Tg(TPM3)^Met9Arg mice on muscle function using a multiscale methodological approach including skinned muscle fibers analysis and in vivo investigations by magnetic resonance imaging and 31-phosphorus magnetic resonance spectroscopy. While in vitro maximal force production was reduced in Tg(TPM3)^Met9Arg mice as compared to controls, in vivo measurements revealed an improved mechanical performance in the transgenic mice as compared to the former. The reduced in vitro muscle force might be related to alterations occuring at the cross-bridges level with muscle-specific underlying mechanisms. In vivo muscle improvement was not associated with any changes in either muscle volume or energy metabolism. Our findings indicate that TPM3(Met9Arg) mutation leads to a mild muscle weakness in vitro related to an alteration at the cross-bridges level and a paradoxical gain of muscle function in vivo. These results clearly point out that in vitro alterations are muscle-dependent and do not necessarily translate into similar changes in vivo.     

The Distribution of the Asymptotic Number of Citations to Sets of Publications by a Researcher or from an Academic Department Are Consistent with a Discrete Lognormal Model

How to quantify the impact of a researcher’s or an institution’s body of work is a matter of increasing importance to scientists, funding agencies, and hiring committees. The use of bibliometric indicators, such as the h-index or the Journal Impact Factor, have become widespread despite their known limitations. We argue that most existing bibliometric indicators are inconsistent, biased, and, worst of all, susceptible to manipulation. Here, we pursue a principled approach to the development of an indicator to quantify the scientific impact of both individual researchers and research institutions grounded on the functional form of the distribution of the asymptotic number of citations. We validate our approach using the publication records of 1,283 researchers from seven scientific and engineering disciplines and the chemistry departments at the 106 U.S. research institutions classified as “very high research activity”. Our approach has three distinct advantages. First, it accurately captures the overall scientific impact of researchers at all career stages, as measured by asymptotic citation counts. Second, unlike other measures, our indicator is resistant to manipulation and rewards publication quality over quantity. Third, our approach captures the time-evolution of the scientific impact of research institutions.     

Coupling of Adjacent Tropomyosins Enhances Cross-Bridge-Mediated Cooperative Activation in a Markov Model of the Cardiac Thin Filament

We developed a Markov model of cardiac thin filament activation that accounts for interactions among nearest-neighbor regulatory units (RUs) in a spatially explicit manner. Interactions were assumed to arise from structural coupling of adjacent tropomyosins (Tms), such that Tm shifting within each RU was influenced by the Tm status of its neighbors. Simulations using the model demonstrate that this coupling is sufficient to produce observed cooperativity in both steady-state and dynamic force-Ca²⁺ relationships. The model was further validated by comparison with reported responses under various conditions including inhibition of myosin binding and the addition of strong-binding, non-force-producing myosin fragments. The model also reproduced the effects of 2.5 mM added P_i on Ca²⁺-activated force and the rate of force redevelopment measured in skinned rat myocardial preparations. Model analysis suggests that Tm-Tm coupling potentiates the activating effects of strongly-bound cross-bridges and contributes to force-Ca²⁺ dynamics of intact cardiac muscle. The model further predicts that activation at low Ca²⁺ concentrations is cooperatively inhibited by nearest neighbors, requiring Ca²⁺ binding to >25% of RUs to produce appreciable levels of force. Without excluding other putative cooperative mechanisms, these findings suggest that structural coupling of adjacent Tm molecules contributes to several properties of cardiac myofilament activation.