Cross-bridge mechanics estimated from skeletal muscles’ work-loop responses to impacts in legged locomotion

Legged locomotion has evolved as the most common form of terrestrial locomotion. When the leg makes contact with a solid surface, muscles absorb some of the shock-wave accelerations (impacts) that propagate through the body. We built a custom-made frame to which we fixated a rat (Rattus norvegicus, Wistar) muscle (m. gastrocnemius medialis and lateralis: GAS) for emulating an impact. We found that the fibre material of the muscle dissipates between 3.5 and $$23\,\upmu \hbox {J}$$ 23 μ J ranging from fresh, fully active to passive muscle material, respectively. Accordingly, the corresponding dissipated energy in a half-sarcomere ranges between 10.4 and $$68\,z\hbox {J}$$ 68 z J , respectively. At maximum activity, a single cross-bridge would, thus, dissipate 0.6% of the mechanical work available per ATP split per impact, and up to 16% energy in common, submaximal, activities. We also found the cross-bridge stiffness as low as $$2.2\,\hbox {pN}\,\hbox {nm}^{-1}$$ 2.2 pN nm - 1 , which can be explained by the Coulomb-actuating cross-bridge part dominating the sarcomere stiffness. Results of the study provide a deeper understanding of contractile dynamics during early ground contact in bouncy gait.

The Energy of Muscle Contraction. III. Kinetic Energy During Cyclic Contractions

During muscle contraction, chemical energy is converted to mechanical energy when ATP is hydrolysed during cross-bridge cycling. This mechanical energy is then distributed and stored in the tissue as the muscle deforms or is used to perform external work. We previously showed how energy is distributed through contracting muscle during fixed-end contractions; however, it is not clear how the distribution of tissue energy is altered by the kinetic energy of muscle mass during dynamic contractions. In this study we conducted simulations of a 3D continuum muscle model that accounts for tissue mass, as well as force-velocity effects, in which the muscle underwent sinusoidal work-loop contractions coupled with bursts of excitation. We found that increasing muscle size, and therefore mass, increased the kinetic energy per unit volume of the muscle. In addition to greater relative kinetic energy per cycle, relatively more energy was also stored in the aponeurosis, and less was stored in the base material, which represented the intra and extracellular tissue components apart from the myofibrils. These energy changes in larger muscles due to greater mass were associated lower mass-specific mechanical work output per cycle, and this reduction in mass-specific work was greatest for smaller initial pennation angles. When we compared the effects of mass on the model tissue behaviour to that of in situ muscle with added mass during comparable work-loop trials, we found that greater mass led to lower maximum and higher minimum acceleration in the longitudinal (x) direction near the middle of the muscle compared to at the non-fixed end, which indicates that greater mass contributes to tissue non-uniformity in whole muscle. These comparable results for the simulated and in situ muscle also show that this modelling framework behaves in ways that are consistent with experimental muscle. Overall, the results of this study highlight that muscle mass is an important determinant of whole muscle behaviour.

Conformal evolution of phantom dominated final stages of the universe in higher dimensions

Friedmann solutions and higher-dimensional 5D Kaluza–Klein solutions using mathematical packages such as Sagemath and Cadabra are calculated. A modified Friedmann equation powered by loop quantum gravity in higher dimensions is calculated in this work. Loop quantization in extra-dimensional space is predicted. Modified equation of state for non-interacting dark matter and dark energy are calculated. It has been predicted that the higher curvature due to phantom density would be a local kind of quantized curvature. The modified Friedmann solutions with Kaluza–Klein interpretation are found. To achieve a conformal exit, the non-interacting solutions are discussed in this work. The obtained results are compared with the ΛCDM and quintessence models. The results support conformal cyclic cosmology, which predicts the conformal evolution of the universe without facing any singularity as the result of topological effects.

Mathematical model for β1-adrenergic regulation of the mouse ventricular myocyte contraction

The β1-adrenergic regulation of cardiac myocyte contraction plays an important role in regulating heart function. Activation of this system leads to an increased heart rate and stronger myocyte contraction. However, chronic stimulation of the β1-adrenergic signaling system can lead to cardiac hypertrophy and heart failure. To understand the mechanisms of action of β1-adrenoceptors, a mathematical model of cardiac myocyte contraction that includes the β1-adrenergic system was developed and studied. The model was able to simulate major experimental protocols for measurements of steady-state force-calcium relationships, cross-bridge release rate and force development rate, force-velocity relationship, and force redevelopment rate. It also reproduced quite well frequency and isoproterenol dependencies for intracellular Ca2+ concentration ([Ca2+]i) transients, total contraction force, and sarcomere shortening. The mathematical model suggested the mechanisms of increased contraction force and myocyte shortening on stimulation of β1-adrenergic receptors is due to phosphorylation of troponin I and myosin-binding protein C and increased [Ca2+]i transient resulting from activation of the β1-adrenergic signaling system. The model was used to simulate work-loop contractions and estimate the power during the cardiac cycle as well as the effects of 4-aminopyridine and tedisamil on the myocyte contraction. The developed mathematical model can be used further for simulations of contraction of ventricular myocytes from genetically modified mice and myocytes from mice with chronic cardiac diseases. NEW & NOTEWORTHY A new mathematical model of mouse ventricular myocyte contraction that includes the β1-adrenergic system was developed. The model simulated major experimental protocols for myocyte contraction and predicted the effects of 4-aminopyridine and tedisamil on the myocyte contraction. The model also allowed for simulations of work-loop contractions and estimation of the power during the cardiac cycle.