A systematic muscle model covering regions from the fast ramp stretches in the muscle fibres to the relatively slow stretches in the human triceps surae

Acetylation of conserved lysines fine-tunes mitochondrial malate dehydrogenase activity in land plants

Plants need to rapidly and flexibly adjust their metabolism to changes of their immediate environment. Since this necessity results from the sessile lifestyle of land plants, key mechanisms for orchestrating central metabolic acclimation are likely to have evolved early. Here, we explore the role of lysine acetylation as a post-translational modification to directly modulate metabolic function. We generated a lysine acetylome of the moss Physcomitrium patens and identified 638 lysine acetylation sites, mostly found in mitochondrial and plastidial proteins. A comparison with available angiosperm data pinpointed lysine acetylation as a conserved regulatory strategy in land plants. Focusing on mitochondrial central metabolism, we functionally analyzed acetylation of mitochondrial malate dehydrogenase (mMDH), which acts as a hub of plant metabolic flexibility. In P. patens mMDH1, we detected a single acetylated lysine located next to one of the four acetylation sites detected in Arabidopsis thaliana mMDH1. We assessed the kinetic behavior of recombinant A. thaliana and P. patens mMDH1 with site-specifically incorporated acetyl-lysines. Acetylation of A. thaliana mMDH1 at K169, K170, and K334 decreases its oxaloacetate reduction activity, while acetylation of P. patens mMDH1 at K172 increases this activity. We found modulation of the malate oxidation activity only in A. thaliana mMDH1, where acetylation of K334 strongly activated it. Comparative homology modeling of MDH proteins revealed that evolutionarily conserved lysines serve as hotspots of acetylation. Our combined analyses indicate lysine acetylation as a common strategy to fine-tune the activity of central metabolic enzymes with likely impact on plant acclimation capacity.

A model of muscle contraction based on the Langevin equation with actomyosin potentials

We propose a muscle contraction model that is essentially a model of the motion of myosin motors as described by a Langevin equation. This model involves one-dimensional numerical calculations wherein the total force is the sum of a viscous force proportional to the myosin head velocity, a white Gaussian noise produced by random forces and other potential forces originating from the actomyosin structure and intra-molecular charges. We calculate the velocity of a single myosin on an actin filament to be 4.9-49 μm/s, depending on the viscosity between the actomyosin molecules. A myosin filament with a hundred myosin heads is used to simulate the contractions of a half-sarcomere within the skeletal muscle. The force response due to a quick release in the isometric contraction is simulated using a process wherein crossbridges are changed forcibly from one state to another. In contrast, the force response to a quick stretch is simulated using purely mechanical characteristics. We simulate the force-velocity relation and energy efficiency in the isotonic contraction and adenosine triphosphate consumption. The simulation results are in good agreement with the experimental results. We show that the Langevin equation for the actomyosin potentials can be modified statistically to become an existing muscle model that uses Maxwell elements.

Muscle as a molecular machine for protecting joints and bones by absorbing mechanical impacts

We hypothesize that dissipation of mechanical energy of external impact to absorb mechanical shock is a fundamental function of skeletal muscle in addition to its primary function to convert chemical energy into mechanical energy. In physical systems, the common mechanism for absorbing mechanical shock is achieved with the use of both elastic and viscous elements and we hypothesize that the viscosity of the skeletal muscle is a variable parameter which can be voluntarily controlled by changing the tension of the contracting muscle. We further hypothesize that an ability of muscle to absorb shock has been an important factor in biological evolution, allowing the life to move from the ocean to land, from hydrodynamic to aerodynamic environment with dramatically different loading conditions for musculoskeletal system. The ability of muscle to redistribute the energy of mechanical shock in time and space and unload skeletal joints is of key importance in physical activities. We developed a mathematical model explaining the absorption of mechanical shock energy due to the increased viscosity of contracting skeletal muscles. The developed model, based on the classical theory of sliding filaments, demonstrates that the increased muscle viscosity is a result of the time delay (or phase shift) between the mechanical impact and the attachment/detachment of myosin heads to binding sites on the actin filaments. The increase in the contracted muscle's viscosity is time dependent. Since the forward and backward rate constants for binding the myosin heads to the actin filaments are on the order of 100s(-1), the viscosity of the contracted muscle starts to significantly increase with an impact time greater than 0.01s. The impact time is one of the key parameters in generating destructive stress in the colliding objects. In order to successfully dampen a short high power impact, muscles must first slow it down to engage the molecular mechanism of muscle viscosity. Muscle carries out two functions, acting first as a nonlinear spring to slow down impact and second as a viscous damper to absorb the impact. Exploring the ability of muscle to absorb mechanical shock may shed light to many problems of medical biomechanics and sports medicine. Currently there are no clinical devices for real-time quantitative assessment of viscoelastic properties of contracting muscles in vivo. Such assessment may be important for diagnosis and monitoring of treatment of various muscle disorders such as muscle dystrophy, motor neuron diseases, inflammatory and metabolic myopathies and many more.