Super-relaxed Research Articles

Age affects myosin relaxation states in skeletal muscle fibers of female but not male mice.

The recent discovery that myosin has two distinct states in relaxed muscle–disordered relaxed (DRX) and super-relaxed (SRX)–provides another factor to consider in our fundamental understanding of the aging mechanism in skeletal muscle, since myosin is thought to be a potential contributor to dynapenia (age-associated loss of muscle strength independent of atrophy). The primary goal of this study was to determine the effects of age on DRX and SRX states and to examine their sex specificity. We have used quantitative fluorescence microscopy of the fluorescent nucleotide analog 2′/3′-O-(N-methylanthraniloyl) ATP (mantATP) to measure single-nucleotide turnover kinetics of myosin in skinned skeletal muscle fibers under relaxing conditions. We examined changes in DRX and SRX in response to the natural aging process by measuring the turnover of mantATP in skinned fibers isolated from psoas muscle of adult young (3–4 months old) and aged (26–28 months old) C57BL/6 female and male mice. Fluorescence decays were fitted to a multi-exponential decay function to determine both the time constants and mole fractions of fast and slow turnover populations, and significance was analyzed by a t-test. We found that in females, both the DRX and SRX lifetimes of myosin ATP turnover at steady state were shorter in aged muscle fibers compared to young muscle fibers (p ≤ 0.033). However, there was no significant difference in relaxation lifetime of either DRX (p = 0.202) or SRX (p = 0.804) between young and aged male mice. No significant effects were measured on the mole fractions (populations) of these states, as a function of sex or age (females, p = 0.100; males, p = 0.929). The effect of age on the order of myosin heads at rest and their ATPase function is sex specific, affecting only females. These findings provide new insight into the molecular factors and mechanisms that contribute to aging muscle dysfunction in a sex-specific manner.

Time-Resolved FRET Detection of the Myosin Super-Relaxed off State in Cardiac Thick Filament

We developed time-resolved fluorescence resonance energy transfer (FRET) sensors to detect the structural state of myosin in cardiac thick filaments. Cardiac myosin thick filaments are hypothesized to isomerize between an active state, termed RX (relaxed) that interacts with actin and generates force in the sarcomere, and an inactive state, termed SRX (super-relaxed) that does not bind actin and exhibits inhibited ATP hydrolysis compared to soluble myosin without actin. Regulation of the transition between these states is hypothesized to underlie the Frank-Starling law of the heart, and dysregulation of the transition to lead to genetically-driven hypertrophic cardiomyopathy; however, exactly how remains unclear, because the structural basis of the SRX is poorly understood. To investigate the structural transition between RX and SRX, we developed a time-resolved FRET assay that measures the intermolecular distance between two adjacent myosin regulatory light chains. Based on proposed structural models, formation of the SRX increases FRET while disruption decreases FRET. We tested this model with known modulators of the SRX biochemical kinetics, including temperature and ionic strength, and with two physiologically relevant SRX modulators, RLC phosphorylation and myosin-binding protein-C. This work was supported by National Institute of Health grants AR032961 and AR057220 (DDT), and American Heart Association Scientist Development Grant (JMM).

The Super Relaxed State of Myosin in Human Muscle

The Super Relaxed State of myosin (SRX) plays a role in maintaining the low resting metabolic rate of skeletal muscle. Pharmaceuticals that destabilize this state could increase resting muscle and whole body metabolic rate by as much as 1000 Calories/day, providing an effective treatment for obesity and type 2 diabetes. Our previous work on this state in skeletal muscle has all been in animal models. Here we extend this approach to human muscle. Biopsies from the quadriceps lateralis of both lean and obese subjects were used. Measurements of single turnovers showed an SRX with a population of 0.27 ± 0.02 and a lifetime of 150 ± 8 sec in lean subjects and a population of 0.28 ± 0.02 and a lifetime of 158 ± 10 sec in obese subjects. Piperine is a small molecule that has been shown to destabilize the SRX in rabbit fast twitch fibers, with no effect on slow twitch fibers. In human muscle, addition 100μM piperine reduced the population of the SRX by 34% in lean subjects and 25% in obese subjects, with little change in the lifetimes. The human quadriceps lateralis contains ∼50% fast twitch and ∼50% slow twitch fibers. Data obtained with piperine showed two responses with ∼50% of fibers showing a strong inhibition of the SRX and the remaining fibers showing very little, in both lean and obese subjects. Presumably the fibers showing strong inhibition are fast twitch, but this remains to be proven. We conclude that in human muscle the SRX and its response to piperine are similar to those seen previously in rabbit muscle, with little difference between lean and obese subjects. This shows that analogs of piperine that have higher affinity would provide effective treatment for metabolic diseases.

Modified discontinuous deformation analysis for rock failure: Crack propagation

Deformation of rock masses is not only related to rock itself, but also related to discontinuities, the latter maybe greater. Study on crack propagation at discontinuities is important to reveal the damage law of rock masses. DDARF is a discontinuous deformation analysis method for rock failure and some modified algorithms are proposed in this study. Firstly, coupled modeling methods of AutoCAD-DDARF and ANSYS-DDARF are introduced, which could improve the modeling efficiency of DDARF compared to its original program. Secondly, a convergence criterion for automatically judging the computation equilibrium is established, it could overcome subjective drawbacks of ending one calculation by time steps. Lastly but not the least, relationship between the super relaxation factor and the calculation convergence is analyzed, and reasonable value range of the super relaxation factor is obtained. Based on these above modified programs, influences on crack propagation of joint angle, joint parameters and geo-stresses

The Nekrasov diagonally dominant degree on the Schur complement of Nekrasov matrices and its applications

In this paper, we estimate the Nekrasov diagonally dominant degree on the Schur complement of Nekrasov matrices. As an application, we offer new bounds of the determinant for several special matrices, which improve the related results in certain case. Further, we give an estimation on the infinity norm bounds for the inverse of Schur complement of Nekrasov matrices. Finally, we introduce new methods called Schur-based super relaxation iteration (SSSOR) method and Schur-based conjugate gradient (SCG) method to solve the linear equation by reducing order. The numerical examples illustrate the effectiveness of the derived result.

Effects of myosin variants on interacting-heads motif explain distinct hypertrophic and dilated cardiomyopathy phenotypes.

Cardiac β-myosin variants cause hypertrophic (HCM) or dilated (DCM) cardiomyopathy by disrupting sarcomere contraction and relaxation. The locations of variants on isolated myosin head structures predict contractility effects but not the prominent relaxation and energetic deficits that characterize HCM. During relaxation, pairs of myosins form interacting-heads motif (IHM) structures that with other sarcomere proteins establish an energy-saving, super-relaxed (SRX) state. Using a human β-cardiac myosin IHM quasi-atomic model, we defined interactions sites between adjacent myosin heads and associated protein partners, and then analyzed rare variants from 6112 HCM and 1315 DCM patients and 33,370 ExAC controls. HCM variants, 72% that changed electrostatic charges, disproportionately altered IHM interaction residues (expected 23%; HCM 54%, p=2.6×10-19; DCM 26%, p=0.66; controls 20%, p=0.23). HCM variant locations predict impaired IHM formation and stability, and attenuation of the SRX state - accounting for altered contractility, reduced diastolic relaxation, and increased energy consumption, that fully characterizes HCM pathogenesis.

Phosphorylation of Myosin Increases the ATPase Activity of Relaxed Skeletal Muscle Fibers

Myosin in skeletal muscle is phosphorylated by a calcium-calmodulin dependent kinase during periods of sustained activity. Phosphorylation of myosin is known to destabilize the array of myosin heads bound to the core of the thick filament in relaxed muscle, known as the interacting heads motif. Myosin heads in this array are associated with a state with a highly inhibited ATPase activity, known as the Super Relaxed State (SRX). To determine whether phosphorylation of myosin increases the ATPase activity, we measured the ATPase activity of relaxed, skinned skeletal fibers in the presence and absence of myosin phosphorylation. Fibers were phosphorylated, >50%, by including phosphatase inhibitors in the glycerinating solution. Control fibers had an ATPase activity of 0.040 ± 0.004 s−1. Phosphorylated fibers had an ATPase activity of 0.060 ± 0.002 s−1, a 50 % increase. We have recently found a small molecule, piperine that destabilizes the SRX, increasing relaxed fiber ATPase activity. In the presence of 100μM piperine the control fibers had an ATPase activity of 0.064 ± 0.004 s−1, the phosphorylated fibers had an ATPase activity of 0.057 ± 0.001 s−1. Thus both phosphorylation and piperine increase the ATPase activity of resting fibers by destabilizing a fraction of myosin heads in the SRX, 30-50%, but their effects are not additive, suggesting that they are each affecting the same population of myosin heads. One candidate for this population may be the “free” head of the interacting heads motif, which is known to be less stable than the other head. As myosin remains in a phosphorylated state for several minutes following a period of activity, the effect described above will contribute to the energetic cost of physical activity, particularly during light activity.

Spectroscopic Studies of the Super Relaxed State of Skeletal Muscle.

In the super-relaxed state of myosin, ATPase activity is strongly inhibited by binding of the myosin heads to the core of the thick filament in a structure known as the interacting-heads motif. In the disordered relaxed state myosin heads are not bound to the core of the thick filament and have an ATPase rate that is 10 fold greater. In the interacting-heads motif the two regulatory light chains appear to bind to each other. We have made single cysteine mutants of the regulatory light chain, placed both paramagnetic and fluorescent probes on them, and exchanged them into skinned skeletal muscle fibers. Many of the labeled light chains tended to disrupt the stability of the super-relaxed state, and showed spectral changes in the transition from the disordered relaxed state to the super-relaxed state. These data support the putative interface between the two regulatory light chains identified by cryo electron microscopy and show that both the divalent cation bound to the regulatory light chain and the N-terminus of the regulatory light chain play a role in the stability of the super-relaxed state. One probe showed a shift to shorter wavelengths in the super-relaxed state such that a ratio of intensities at 440nm to that at 520nm provided a measure of the population of the super-relaxed state amenable for high throughput screens for finding potential pharmaceuticals. The results provide a proof of concept that small molecules that bind to this region can destabilize the super-relaxed state and provide a method to search for small molecules that do so leading to a potentially effective treatment for Type 2 diabetes and obesity.

Ablation of cardiac myosin binding protein-C disrupts the super-relaxed state of myosin in murine cardiomyocytes

Cardiac myosin binding protein-C (cMyBP-C) is a structural and regulatory component of cardiac thick filaments. It is observed in electron micrographs as seven to nine transverse stripes in the central portion of each half of the A band. Its C-terminus binds tightly to the myosin rod and contributes to thick filament structure, while the N-terminus can bind both myosin S2 and actin, influencing their structure and function. Mutations in the MYBPC3 gene (encoding cMyBP-C) are commonly associated with hypertrophic cardiomyopathy (HCM). In cardiac cells there exists a population of myosin heads in the super-relaxed (SRX) state, which are bound to the thick filament core with a highly inhibited ATPase activity. This report examines the role cMyBP-C plays in regulating the population of the SRX state of cardiac myosin by using an assay that measures single ATP turnover of myosin. We report a significant decrease in the proportion of myosin heads in the SRX state in homozygous cMyBP-C knockout mice, however heterozygous cMyBP-C knockout mice do not significantly differ from the wild type. A smaller, non-significant decrease is observed when thoracic aortic constriction is used to induce cardiac hypertrophy in mutation negative mice. These results support the proposal that cMyBP-C stabilises the thick filament and that the loss of cMyBP-C results in an untethering of myosin heads. This results in an increased myosin ATP turnover, further consolidating the relationship between thick filament structure and the myosin ATPase.

Destabilizing the Super Relaxed State of Skeletal Muscle Myosin to Treat Obesity and Type 2 Diabetes

In resting skeletal muscle, myosin is found in 2 states, the super-relaxed state (SRX) and the disordered relaxed state (DRX). In the SRX the ATPase activity is strongly inhibited by binding of the myosin heads to the core of the thick filament; in the DRX the myosin heads are not bound to the core of the thick filament and have an ATPase rate that is an order of magnitude greater. We made a series of single cysteine mutants of the myosin regulatory light chain, placed fluorescent probes on them, and exchanged them into skinned rabbit fast skeletal muscle fibers. We found fluorescent probes that reported on the relative populations of the SRX and DRX, and used them to carry out a high throughput screen. The screen identified one compound, piperine, which destabilized the SRX as measured by probe fluorescence. The kd for inhibition was ∼3 μM with a maximum inhibition of ∼50% at high concentations. The compound was also shown to destabilize the SRX using single nucleotide turnover measurements. The effect was only seen in fast twitch fibers. Piperine was shown to increase the ATPase activity of relaxed fibers by 40%. It had no effect on the mechanics of either active or resting muscle fibers. Previous work has shown that piperine can attenuate both obesity and type 2 diabetes in rodent models of these conditions. We propose that these effects are due to the up-regulation of resting muscle metabolism. The results described here suggest that piperine would provide a useful lead compound for the development of therapies to treat obesity and type 2 diabetes in humans.

Image Fusion for Travel Time Tomography Inversion

Abstract The travel time tomography technology had achieved wide application, the hinge of tomography was inversion algorithm, the ray path tracing technology had a great impact on the inversion results. In order to improve the SNR of inversion image, comprehensive utilization of inversion results with different ray tracing can be used. We presented an imaging fusion method based on improved Wilkinson iteration method. Firstly, the shortest path method and the linear travel time interpolation were used for forward calculation; then combined the improved Wilkinson iteration method with super relaxation precondition method to reduce the condition number of matrix and accelerate iterative speed, the precise integration method was used to solve the inverse matrix more precisely in tomography inversion process; finally, use wavelet transform for image fusion, obtain the final image. Therefore, the ill-conditioned linear equations were changed into iterative normal system through two times of treatment and using images with different forward algorithms for image fusion, it reduced the influence effect of measurement error on imaging. Simulation results showed that, this method can eliminate the artifacts in images effectively, it had extensive practical significance.

The role of super-relaxed myosin in skeletal and cardiac muscle.

The super-relaxed (SRX) state of myosin was only recently reported in striated muscle. It is characterised by a sub-population of myosin heads with a highly inhibited rate of ATP turnover. Myosin heads in the SRX state are bound to each other along the thickfilament core producing a highly ordered arrangement. Upon activation, these heads project into the interfilament space where they can bind to theactin filaments. Thus far, the population and lifetimes of myosin heads in the SRX state have been characterised in rabbit cardiac, and fast and slow skeletal muscle, as well as in the skeletal muscle of the tarantula. These studies suggest that the role of SRX in cardiac and skeletal muscle regulation is tailored to their specific functions. In skeletal muscle, the SRX modulates the resting metabolic rate. Cardiac SRX represents a "reserve" of inactive myosin heads that may protect the heart during times of stress, e.g. hypoxia and ischaemia. These heads may also be called up when there is a sustained demand for increased power. The SRX in cardiac muscle provides a potential target for novel therapies.

Dynamical process of complex systems and fractional differential equations

Abstract Behavior of dynamical process of complex systems is investigated. Specifically we analyse two types of ideal complex systems. For analysing the ideal complex systems, we define the response functions describing the internal states to an external force. The internal states are obtained as a relaxation process showing a “power law” distribution, such as scale free behaviors observed in actual measurements. By introducing a hybrid system, the logarithmic time, and double logarithmic time, we show how the “slow relaxation” (SR) process and “super slow relaxation” (SSR) process occur. Regarding the irregular variations of the internal states as an activation process, we calculate the response function to the external force. The behaviors are classified into “power”, “exponential”, and “stretched exponential” type. Finally we construct a fractional differential equation (FDE) describing the time evolution of these complex systems. In our theory, the exponent of the FDE or that of the power law distribution is expressed in terms of the parameters characterizing the structure of the system.

A New State of Myosin in Cardiac Muscles with Very Slow ATP Turnover: A Potential Cardio-Protective Mechanism in the Heart

We used quantitative epi-fluorescence of mant-nucleotides to measure single nucleotide turnovers in small bundles of permeable rabbit ventricle cells. In relaxed cells nucleotide turnover occurs in two phases one with a short time constant, 14 ± 1 seconds, and a second with a much longer time constant, 144 ± 10 seconds. The first is compatible with the normal relaxed state and the second arises from myosin heads in the Super Relaxed State (SRX). Approximately 60% of the myosin heads were in the SRX. Recent work identified a similar state with a slow nucleotide turnover time constant, 230 seconds, in relaxed vertebrate skeletal muscle (Stewart et.al. PNAS, 2010). The SRX appears to play a similar role in relaxed skeletal fibers and cardiac cells providing a state with a very low metabolic rate. However, in active fibers the properties of the SRX differ dramatically. There is a rapid transition of myosin heads out of the SRX in active skeletal fibers. In contrast, in cardiac muscle, the population of myosin heads in the SRX is not changed when the muscle, is activated. This property allows the SRX to play a very different role in cardiac cells than in skeletal fibers. The mechanisms that control cardiac contractility are complex, leading to an output that can vary from highly active to very quiescent. The ability of myosin heads to remain in the SRX, while other heads are generating tension, allows this state to play a role in the regulation of cardiac output. In particular, the super relaxed state could provide a mechanism for decreasing the metabolic load on the heart, being cardioprotective, particularly in time of stress such as ischemia.

Super Slow Polarization Relaxation in PLZT Relaxor Ceramics

Using the method of continuous measuring of low- and infralow frequency dielectric response the features of super slow polarization relaxation processes in PLZT-8/65/35+0.1 Eu ceramics were investigated. It was shown that the time dependences of dielectric permittivity ϵ′ may be described by approximation function of the type: ϵ′(t) ∼ ϵ′(to) · exp[−ln(t/to)β] where t > to and β < 1. Also, the anomalies in temperature dependences of current i(T) in the short sample of non-poled and aged PLZT ceramics have been found. The obtained results are interpreted on the base of assumption that microelectrets (fractal clusters) appear with the course of time.