Distribution of calcium during contraction and relaxation of crayfish skeletal muscle fibre.

A model of activation of muscle contraction has been applied to the crayfish isolated skeletal muscle fibre. The model is based on calcium diffusion and binding to specific regulatory sites in a sarcomere. Calcium ions activate interactions of contractile proteins and thus the generation of force. The model quantifies the relation between calcium released from intracellular stores and force elicited. Experimental tension records from isolated crayfish skeletal muscle fibres under voltage clamp conditions are analyzed. Model parameters were determined either via approximation of the onset of tension by the model solution or from the model based relations between the tension maximum, and depolarizing pulse length and amplitude. This allowed to determine time changes of free and bound calcium distribution in the sarcomere and the calcium release from terminal cisternae. The steady state calcium concentration at terminal cisternae showed S-shaped voltage dependence with saturation below approx. 10 mumol/l at positive membrane potentials.     

Relation of muscle cell contraction and calcium distribution in sarcomere

A model of activation of muscle contraction has been proposed. It is based on calcium diffusion and binding to specific regulatory sites in a sarcomere. Calcium ions activate interactions of contractile proteins and thus the generation of force. The model quantifies the relation between calcium released from intracellular stores and the elicited force.     

The positional stability of thick filaments in activated skeletal muscle depends on sarcomere length: evidence for the role of titin filaments

Electron microscopy was used to study the positional stability of thick filaments in isometrically contracting skinned rabbit psoas muscle as a function of sarcomere length at 7 degrees C. After calcium activation at a sarcomere length of 2.6 micron, where resting stiffness is low, sarcomeres become nonuniform in length. The dispersion in sarcomere length is complete by the time maximum tension is reached. A-bands generally move from their central position and continue moving toward one of the Z-discs after tension has reached a plateau at its maximum level. The lengths of the thick and thin filaments remain constant during this movement. The extent of A-band movement during contraction depends on the final length of the individual sarcomere. After prolonged activation, all sarcomeres between 1.9 and 2.5 micron long exhibit A-bands that are adjacent to a Z-disc, with no intervening I-band. Sarcomeres 2.6 or 2.7 micron long exhibit a partial movement of A-bands. At longer sarcomere lengths, where the resting stiffness exceeds the slope of the active tension-length relation, the A-bands remain perfectly centered during contraction. Sarcomere symmetry and length uniformity are restored upon relaxation. These results indicate that the central position of the thick filaments in the resting sarcomere becomes unstable upon activation. In addition, they provide evidence that the elastic titin filaments, which join thick filaments to Z-discs, produce almost all of the resting tension in skinned rabbit psoas fibers and act to resist the movement of thick filaments away from the center of the sarcomere during contraction.     

Model of calcium movements during activation in the sarcomere of frog skeletal muscle

A model of calcium movement during activation of frog skeletal muscle is described. The model was based on the half sarcomere of a myofibril and included compartments representing the terminal cisternae, the longitudinal sarcoplasmic reticulum, the extramyofibrillar space, and the myofibrillar space. The calcium-binding proteins troponin, parvalbumin, and calsequestrin were present in appropriate locations and with realistic binding kinetics. During activation a time-dependent permeability in the terminal cisternal wall led to calcium release into the myoplasm and its diffusion through the myoplasm longitudinally and radially was computed. After adjustment of three parameters, the model produced a myoplasmic free-calcium concentration that was very similar to those recorded experimentally with calcium indicators. The model has been used to demonstrate the importance of parvalbumin in the relaxation of skeletal muscle, to describe the time course and magnitude of calcium gradients associated with diffusion across the sarcomere, and to estimate the errors associated with the use of aequorin as an intracellular calcium indicator in muscle.     

The active state of cross-striated muscle cell sarcomere (an imitation model)]

An index of the sarcomere active state is introduced. It reflects the most important processes of sarcomere contraction, such as calcium diffusion taking into account permeability of calcium channels and its binding with troponin, formation of energy supplies and interaction of sarcomere contractile proteins. The effect of changes of the values of diffusion coefficients and chemical reactions rates was studied theoretically.     

The effect of sarcomere non-uniformity on the sarcomere length-tension relationship of skinned fibers

It has proved difficult to activate skinned muscle fibers to produce high tension (3 kg/cm² level) without loss of clear striations. A new method was developed which permits high tension production in skinned muscle fibers while retaining clear striations. Clear striations allow reliable measurement of the sarcomere lengths during contraction by microscopy and diffractometry. The method is to increase the Ca⁺⁺ concentration of the bathing solution very gradually over a time period of 5 to 10 minutes. Once the skinned fiber is conditioned by this slow activation, subsequent contractions can be elicited by ordinary quick activations without loss of striations. When the experiments are carried out with careful controls for the uniformity of the sarcomere length distribution along the entire length of the fiber, contractions are highly repeatable. Using the new method and stringent quality control of fibers, the sarcomere length-isometric tension relationship of skinned rabbit soleus fibers was obtained. The results differ from those previously obtained by conventional activation methods in that tension increases with sarcomere length not only at low (pCa = 5.8), but also at high (pCa = 5.2), calcium concentration.     

Patterns of sarcomere activation, temperature dependence, and effect of ryanodine in chemically skinned cardiac fibers

Functionally skinned and electrochemically shunted myocytes were prepared by perfusing rat hearts with collagenase in order to obtain a technically improved measurement of sarcomere dynamics and to evaluate the role of sarcoplasmic reticulum in situ with respect to contractile activation. In the presence of micromolar calcium, the myocytes exhibited phasic and propagated contraction waves beginning at one end and proceeding along the myocyte. Beating rates, the propagation velocity of the activation wave, and single sarcomere shortening and relaxation velocities were obtained by manual or automated analysis of 16-mm film recorded at 170 frames/s from a camera attached to a microscope that was equipped with a temperature-controlled stage. In parallel experiments, calcium accumulation by the sarcoplasmic reticulum of the myocytes in situ was measured by direct isotopic tracer methods. The frequency (10-38 min-1) of spontaneous contractions, the velocity (1.9-7.4 microns . s-1) of sarcomere shortening, and the velocity (1.7-6.8 microns . s-1) of sarcomere relaxation displayed identical temperature dependences (Q10 = 2.2), which are similar to that of the calcium pump of sarcoplasmic reticulum and are consistent with a rate limit imposed by enzyme-catalyzed mechanisms on all these parameters. On the other hand, the velocity (77- 159 microns . s-1) of sequential sarcomere activation displayed a lower temperature dependence (Q10 = 1.5), which is consistent with a diffusion-limited and self-propagating release of calcium from one sarcomere to the other. The phasic contractile activity of the dissociated myocytes was inhibited by 10(-8)-10(6) M ryanodine (and not by myolemmal calcium blockers) under conditions in which calcium accumulation by sarcoplasmic reticulum in situ was demonstrated to proceed optimally. The effect of ryanodine is attributed to an interaction of this drug with sarcotubular structures, producing inhibition of calcium release from the sarcoplasmic reticulum. The consequent lack of sarcomere activation underlines the role of sarcoplasmic reticulum uptake and release in the phasic contractile activation of the electrochemically shunted myocytes.     

Fluorescence anisotropy imaging microscopy maps calmodulin binding during cellular contraction and locomotion

Calmodulin is a calcium transducer that activates key regulatory and structural proteins through calcium-induced binding to the target proteins. A fluorescent analog of calmodulin in conjunction with ratio imaging, relative to a volume indicator, has demonstrated that calmodulin is uniformly distributed in serum-deprived fibroblasts and there is no immediate change in the distribution upon stimulation with complete serum. The same fluorescent analog of calmodulin together with steady state fluorescence anisotropy imaging microscopy has been used to define the temporal and spatial changes in calmodulin binding to cellular targets during stimulation of serum-deprived fibroblasts and in polarized fibroblasts during wound healing. In serum-deprived fibroblasts, which exhibit a low free calcium ion concentration, a majority of the fluorescent analog of calmodulin remained unbound (fraction bound, fB < 10%). However, upon stimulation of the serum- deprived cells with complete serum, calmodulin binding (maximum fB approximately 95%) was directly correlated with the time course of the elevation and decline of the free calcium ion concentration, while the contraction of stress fibers continued for an hour or more. Calmodulin binding was also elevated in the leading lamellae of fibroblasts (maximum FB approximately 50%) during the lamellar contraction phase of wound healing and was spatially correlated with the contraction of transverse fibers containing myosin II. Highly polarized and motile fibroblasts exhibited the highest anisotropy (calmodulin binding) in the retracting tails and in association with contracting transverse fibers in the cortex of the cell. These results suggest that local activation of myosin II-based contractions involves the local binding of calmodulin to target proteins. The results also demonstrate a powerful yet simple mode of light microscopy that will be valuable for mapping molecular binding of suitably labeled macromolecules in living cells.     

Rheology of myocardium. The relation between force, velocity, sarcomere length and activation in rat cardiac muscle

The relations between force, shortening velocity and sarcomere length (F-V-SL) during cardiac contraction, underlie Starling's Law of the Heart. F-V-SL were investigated in isolated, intact and skinned trabeculae and myocytes from rat heart. SL and V were measured with laser diffraction techniques; F was measured with a silicon strain gauge. The "ascending" F-SL relation appeared to result from both length dependent sensitivity of the contractile system to activator calcium ions and the presence of restoring forces (Fr), residing in the collagen skeleton of the muscle. Fr increased exponentially with decreasing SL below slack length to 25% of maximal twitch force (Ft) at SL = 1.60 microns. V was inversely proportional to the load and attained a maximum at zero load (Vo). Vo increased with factors that increased F: [Ca++], SL, and time during the twitch. Vo reached a maximum and remained constant (13.5 microns/s) when F attained or exceeded 50% of its maximum value. Viscous force in the passive muscle increased with V to a maximum of 4% of Ft at V = 40 microns/s. The relation between Vo and these factors could be predicted by a model of contraction in which the measured visco-elastic properties of myocardium were incorporated, while the truly unloaded maximal velocity of sarcomere shortening was assumed to be independent of the level of activation of the contractile filaments. A model of the cardiac cycle which explains the relation between Frank's and Starling's laws is presented.     

Sarcomere length dispersion in single skeletal muscle fibers and fiber bundles.

Light diffraction patterns produced by single skeletal muscle fibers and small fiber bundles of Rana pipiens semitendinosus have been examined at rest and during tetanic contraction. The muscle diffraction patterns were recorded with a vidicon camera interfaced to a minicomputer. Digitized video output was analyzed on-line to determine mean sarcomere length, line intensity, and the distribution of sarcomere lengths. The occurrence of first-order line intensity and peak amplitude maxima at approximately 3.0 mum is interpreted in terms of simple scattering theory. Measurements made along the length of a singel fiber reveal small variations in calculated mean sarcomere length (SD about 1.2%) and its percent dispersion (2.1% +/- 0.8%). Dispersion in small multifiber preparations increases approximately linearly with fiber number (about 0.2% per fiber) to a maximum of 8-10% in large bundles. Dispersion measurements based upon diffraction line analysis are comparable to SDs calculated from length distribution histograms obtained by light micrography of the fiber. First-order line intensity decreases by about 40% during tetanus; larger multifibered bundles exhibit substantial increases in sarcomere dispersion during contraction, but single fibers show no appreciable dispersion change. These results suggest the occurrence of asynchronous static or dynamic axial disordering of thick filaments, with a persistence in long range order of sarcomere spacing during contraction in single fibers.     

A mathematical model of the sarcomere mechanics of cross-striated muscle with consideration of the stretch and twist of actin filaments

A mathematical model of sarcomere mechanics, which takes into account the elongation of actin and myosin filaments and also twisting of the actin filaments in the sarcomere of striated muscle during contraction is presented. The model accounts for the experimentally observed phenomena of the stretch and twist of the actin filaments due to strong binding of myosin heads and the pulling force. Some model parameters were estimated from published experimental data. The results of modeling show that the twist of actin filaments can play a substantial role in the mechanical responses of contracting muscle fibers to step changes of their length.     

Mathematical and computation modeling of self-organizing sarcomere with chaotic dynamics of the order parameter

The results of constructing a nonlinear model of sarcomere contraction are summarized. A strange attractor has been obtained, which is related to the randomness of the dynamics of the order parameter during sarcomere deformation. A hypothesis is proposed that upon fixation of the actin filaments in the sarcomere the myosin system undergoes nonlinear oscillations with dissipation, which leads to elevation of solution temperature. The increase in temperature has been determined for pulsations of the inertial range. Normalized power spectra of the pulsations of the order parameter have been constructed for the model by Fourier transform. The thermodynamics of sarcomere contraction is considered.     

Age-dependent variation in contractility of adult cardiac myocytes

This study was designed to examine the influence of the age of adults on the contractile characteristics of the myocardium and to ascertain whether the age dependent variation is related to variation in sarcolemmal calcium channels. Cardiomyocytes were isolated from 2, 6 and 12-month-old, male Sprague-Dawley rats and the extent and velocity of contraction were recorded as a function of change in cell length. Age dependent increase in cell length and sarcomere length was significant (P<0.05). Extent of contraction increased with age and the velocities of contraction and relaxation normalized to total contraction decreased with age (P<0.05). Sensitivity to the L-type channel antagonist (verapamil, 1 microM) and the T-type channel antagonist (nickel chloride, 40 microM) was significant in 6 and 12-month-old animals. This differential response to calcium channel antagonists suggests that the age-dependent variation in contractility may be mediated by the variation in the distribution/function of sarcolemmal calcium channels.     

Myofilament lattice spacing as a function of sarcomere length in isolated rat myocardium

The Frank-Starling relationship of the heart has, as its molecular basis, an increase in the activation of myofibrils by calcium as the sarcomere length increases. It has been suggested that this phenomenon may be due to myofilaments moving closer together at longer lengths, thereby enhancing the probability of favorable acto-myosin interaction, resulting in increased calcium sensitivity. Accordingly, we have developed an apparatus so as to obtain accurate measurements of myocardial interfilament spacing (by synchrotron X-ray diffraction) as a function of sarcomere length (by video microscopy) over the working range of the heart, using skinned as well as intact rat trabeculas as model systems. In both these systems, lattice spacing decreased significantly as sarcomere length was increased. Furthermore, lattice spacing in the intact muscle was significantly smaller than that in the skinned muscle at all sarcomere lengths studied. These observations are consistent with the hypothesis that lattice spacing underlies length-dependent activation in the myocardium.     

Sarcomere length nanometry in rat neonatal cardiomyocytes expressed with α-actinin–AcGFP in Z discs

Nanometry is widely used in biological sciences to analyze the movement of molecules or molecular assemblies in cells and in vivo. In cardiac muscle, a change in sarcomere length (SL) by a mere ∼100 nm causes a substantial change in contractility, indicating the need for the simultaneous measurement of SL and intracellular Ca²⁺ concentration ([Ca²⁺]_i) in cardiomyocytes at high spatial and temporal resolution. To accurately analyze the motion of individual sarcomeres with nanometer precision during excitation–contraction coupling, we applied nanometry techniques to primary-cultured rat neonatal cardiomyocytes. First, we developed an experimental system for simultaneous nanoscale analysis of single sarcomere dynamics and [Ca²⁺]_i changes via the expression of AcGFP in Z discs. We found that the averaging of the lengths of sarcomeres along the myocyte, a method generally used in today’s myocardial research, caused marked underestimation of sarcomere lengthening speed because of the superpositioning of different timings for lengthening between sequentially connected sarcomeres. Then, we found that after treatment with ionomycin, neonatal myocytes exhibited spontaneous sarcomeric oscillations (cell-SPOCs) at partial activation with blockage of sarcoplasmic reticulum functions, and the waveform properties were indistinguishable from those obtained in electric field stimulation. The myosin activator omecamtiv mecarbil markedly enhanced Z-disc displacement during cell-SPOC. Finally, we interpreted the present experimental findings in the framework of our mathematical model of SPOCs. The present experimental system has a broad range of application possibilities for unveiling single sarcomere dynamics during excitation–contraction coupling in cardiomyocytes under various settings.     

A dynamic model of excitation-contraction coupling during acidosis in cardiac ventricular myocytes

Acidosis in cardiac myocytes is a major factor in the reduced inotropy that occurs in the ischemic heart. During acidosis, diastolic calcium concentration and the amplitude of the calcium transient increase, while the strength of contraction decreases. This has been attributed to the inhibition by protons of calcium uptake and release by the sarcoplasmic reticulum, to a rise of intracellular sodium caused by activation of sodium-hydrogen exchange, decreased calcium binding affinity to Troponin-C, and direct effects on the contractile machinery. The relative contributions and concerted action of these effects are, however, difficult to establish experimentally. We have developed a mathematical model to examine altered calcium-handling mechanisms during acidosis. Each of the alterations was incorporated into a dynamical model of pH regulation and excitation-contraction coupling to predict the time courses of key ionic species during acidosis, in particular intracellular pH, sodium and the calcium transient, and contraction. This modeling study suggests that the most significant effects are elevated sodium, inhibition of sodium-calcium exchange, and the direct interaction of protons with the contractile machinery; and shows how the experimental data on these contributions can be reconciled to understand the overall effects of acidosis in the beating heart.     

Effect of Calcium Activated Factor on Properties of Actin and Myosin of Rabbit Skeletal Muscle

The effect of calcium activated factor (CAF) on enzymatic properties of actin and myosin was investigated. SDS polyacrylamide gel electrophoresis revealed that CAF did not degrade actin, but a slight degradation was found in myosin during CAF digestion, which might have been due to contaminated protease (s) in CAF preparation. No influence was found in EDTA ATPase of myosin and polymerization of G-actin during CAF digestion. However, heavy meromyosin (HMM) ATPase activating ability of actin was slightly decreased during CAF digestion. Although CAF digestion slightly decreased the biological activity of myofibrillar proteins, a single sarcomere prepared by CAF digestion is a useful model for studying muscle contraction because of its almost intact contractility.     

A mechanism for sarcomere breathing: volume change and advective flow within the myofilament lattice

During muscle contraction, myosin motors anchored to thick filaments bind to and slide actin thin filaments. These motors rely on energy derived from ATP, supplied, in part, by diffusion from the sarcoplasm to the interior of the lattice of actin and myosin filaments. The radial spacing of filaments in this lattice may change or remain constant during contraction. If the lattice is isovolumetric, it must expand when the muscle shortens. If, however, the spacing is constant or has a different pattern of axial and radial motion, then the lattice changes volume during contraction, driving fluid motion and assisting in the transport of molecules between the contractile lattice and the surrounding intracellular space. We first create an advective-diffusive-reaction flow model and show that the flow into and out of the sarcomere lattice would be significant in the absence of lattice expansion. Advective transport coupled to diffusion has the potential to substantially enhance metabolite exchange within the crowded sarcomere. Using time-resolved x-ray diffraction of contracting muscle, we next show that the contractile lattice is neither isovolumetric nor constant in spacing. Instead, lattice spacing is time varying, depends on activation, and can manifest as an effective time-varying Poisson ratio. The resulting fluid flow in the sarcomere lattice of synchronous insect flight muscles is even greater than expected for constant lattice spacing conditions. Lattice spacing depends on a variety of factors that produce radial force, including cross-bridges, titin-like molecules, and other structural proteins. Volume change and advective transport varies with the phase of muscle stimulation during periodic contraction but remains significant at all conditions. Although varying in magnitude, advective transport will occur in all cases in which the sarcomere is not isovolumetric. Akin to “breathing,” advective-diffusive transport in sarcomeres is sufficient to promote metabolite exchange and may play a role in the regulation of contraction itself.     

Energetics of activation in frog skeletal muscle at sarcomere lengths beyond myofilament overlap.

Experiments were designed to gain information about the effects of extremely long sarcomere lengths (greater than 3.8 microns) on muscle activation. The amount of energy liberated in an isometric twitch by muscles stretched to sarcomere lengths where myofilament overlap is vanishingly small (greater than 3.6 microns) is thought to be an indirect measure of the Ca2+ cycled during contraction. The effects of altering sarcomere length from 3.8 to 4.3 microns on the amount of Ca2+ cycled was measured using twitch energy liberation as an indicator of the Ca2+ cycled. Twitch energy liberation decreased by approximately 20% over this sarcomere length region, suggesting that the amount of Ca2+ released by a single action potential is not altered dramatically when a muscle is stretched to extreme lengths.