Cooperativity in mechano-calcium feedbacks in the myocardium: Some conceptual discrepancies and overcoming inconsistency within the framework of a mathematical model

Mechano-calcium feedbacks that provide fine tuning of electrical and calcium activation of the heart muscle to mechanical conditions of contractions are an important element of electromechanical coupling as a key mechanism of the autoregulation of the contractile activity of the myocardium. A large quantity of experimental and theoretical evidence supports the cooperative dependence of the calcium-troponin complex kinetics on the cross-bridge concentration as a principal mechanism that underlies the mechano-calcium feedback in the intact myocardium. At the same time, experiments performed using skinned myocardial preparations have demonstrated that mechanical conditions significantly affected only the calcium sensitivity of the Ca²⁺–force relationship rather than its Hill coefficient of cooperativity. These data make some investigators doubt the contribution of cooperativity to the mechano-calcium feedbacks. To overcome these arising discrepancies, we propose an improved conception of cooperativity that reveals the extent of intensity differently in the steady state and in transitional processes. The proposed conception enables us to reproduce and explain both the mechanodependence of calcium activation in the intact myocardium and the results with skinned muscle within the framework of a mathematical model.     

Evidence for extracellular localization of activator calcium in dog coronary artery smooth muscle as studied by the pyroantimonate method

Summary Correlated physiological and electron-microscopic studies were made on the source of calcium activating the contractile system (activator calcium) in dog coronary artery smooth muscle fibers. The magnitude of contracture tension induced by 100 mM K⁺ was dependent on external Ca²⁺ concentration and reduced or eliminated by factors known to reduce the Ca²⁺ spike or ca²⁺ influx. Little or no mechanical response was elicited by treatments known to cause release of intracellularly stored calcium. These results indicated that the contractile system is mainly activated by the inward movement of extracellular calcium. In accordance with the physiological experiments, electron-opaque pyroantimonate precipitate containing calcium was found in the lumina of caveolae, but not in any intracellular structures close to the plasma membrane, when the relaxed fibers were fixed in a 1% osmium tetroxide solution containing 2% potassium pyroantimonate. If the contracted fibers were fixed in the same solution, the pyroantimonate precipitate was diffusely distributed in the myoplasm in the form of numerous particles, while the precipitate in the caveolar lumina was scarcely seen. These findings are discussed in connection with the regulation of intracellular Ca²⁺ concentration in dog coronary artery smooth muscle.     

The association between K+ and H+ distribution in skeletal muscles: implication to linked transport.

Data from the literature and results from a mathematical model of steady state fluid-electrolyte balance are used to support the observation that a relationship exists between the concentration gradients of K⁺ and H⁺ in the fluids of skeletal muscle over a range of acid-base disturbances. This relationship is shown to be consistent with the premise that the steady state electrochemical potential gradients for these ions remain constant under these conditions. Using a pump-leak model of ion transport, and the constant electric field assumption, it is also demonstrated that the steady state rates of active transport of K⁺ and H⁺ are related. These results suggest that the relations between both the steady state concentration gradients and the active transport rates for these ions are not necessarily the result of fixed biochemical mechanisms, but may come about simply from coupling through macroscopic thermodynamic processes.     

Simplified Velocity Equations for Characterizing the Partial Inhibition or Nonessential Activation of Bireactant Enzymes

The steady state velocity equation for a bireactant enzyme in the presence of a partial inhibitor or nonessential activator, M, contains squared substrate concentration and higher-ordered M concentration terms. The equation is too complex to be useful in kinetic analyses. Simplification by the method of Cha (J. Biol. Chem. 243, 820–825 (1968)) eliminates squared substrate concentration terms, but retains higher-ordered terms in [M]. It is shown that if strict equilibrium is assumed between free E, M, and EM and for all but one other M-binding reaction, a velocity equation is obtained for an ordered bireactant enzyme that is first degree in all ligands in the absence of products. The equation is an approximation (because it was derived assuming only one M-binding reaction in the steady state), but it contains five inhibition (or activation) constants associated with M, all of which can be obtained by diagnostic replots and/or curve-fitting procedures. The equation also provides a framework for obtaining limiting constants (V¹_max, K¹_ia, K¹_mA,K¹_mB) that characterize the enzyme at saturating M. The same approach is applicable to an enzyme that catalyzes a steady state ping pong reaction.     

Photosynthesis and calcification in the calcifying algae Halimeda discoidea studied with microsensors

With microsensors, we measured the steady‐state microprofiles of O₂, pH and Ca²⁺ on the topside of young segments of Halimeda discoidea, as well as the surface dynamics upon light–dark shifts. The effect of several inhibitors was studied. The steady‐state measurements showed that under high light intensity, calcium and protons were taken up, while O₂ was produced. In the dark, O₂ was consumed, the pH decreased to below seawater level and Ca²⁺ uptake was reduced to 50%. At low light intensity (12 mmol photons m^‐2 s^‐1), Ca²⁺ efflux was observed. Upon light–dark shifts, a complicated pattern of both the pH and calcium surface dynamics was observed. Illumination caused an initial pH decrease, followed by a gradual pH increase: this indicated that the surface pH of H. discoidea is determined by more than one light‐induced process. When photosynthesis was inhibited by dichlorophenyl dimethyl urea (DCMU), a strong acidification was observed upon illumination. The nature and physiological function of this putative pump is not known. The calcium dynamics followed all pH dynamics closely, both in the presence and absence of DCMU. The Ca‐channel blockers verapamil and nifedipine had no effect on the Ca²⁺ dynamics and steady‐state profiles. Thus, in H. discoidea, calcification is not regulated by the alga, but is a consequence of pH increase during photosynthesis. Acetazolamide had no effect on photosynthesis, whereas ethoxyzolamide inhibited photosynthesis at higher light intensities. Therefore, all carbonic anhydrase activity is intracellular. Carbonic anhydrase is required to alleviate the CO₂ limitation. Calcification cannot supply sufficient protons and CO₂ to sustain photosynthesis.     

A mathematical model of airway and pulmonary arteriole smooth muscle

Airway hyperresponsiveness is a major characteristic of asthma and is believed to result from the excessive contraction of airway smooth muscle cells (SMCs). However, the identification of the mechanisms responsible for airway hyperresponsiveness is hindered by our limited understanding of how calcium (Ca²⁺), myosin light chain kinase (MLCK), and myosin light chain phosphatase (MLCP) interact to regulate airway SMC contraction. In this work, we present a modified Hai-Murphy cross-bridge model of SMC contraction that incorporates Ca²⁺ regulation of MLCK and MLCP. A comparative fit of the model simulations to experimental data predicts 1), that airway and arteriole SMC contraction is initiated by fast activation by Ca²⁺ of MLCK; 2), that airway SMC, but not arteriole SMC, is inhibited by a slower activation by Ca²⁺ of MLCP; and 3), that the presence of a contractile agonist inhibits MLCP to enhance the Ca²⁺ sensitivity of airway and arteriole SMCs. The implication of these findings is that murine airway SMCs exploit a Ca²⁺-dependent mechanism to favor a default state of relaxation. The rate of SMC relaxation is determined principally by the rate of release of the latch-bridge state, which is predicted to be faster in airway than in arteriole. In addition, the model also predicts that oscillations in calcium concentration, commonly observed during agonist-induced smooth muscle contraction, cause a significantly greater contraction than an elevated steady calcium concentration.     

Pitfalls of the 45Ca uptake method

The interpretation of the data derived from ⁴⁵Ca uptake measurements by cells and tissues can be difficult. Several of these difficulties and possible misinterpretations are described: 1) ⁴⁵Ca uptake is not equivalent to calcium influx; 2) interpretations based on the sole visual examination of ⁴⁵Ca uptake curves can be misleading because an increased tracer uptake can coexist with a decreased calcium transport and vice-versa; 3) drugs and hormones can have diametrically opposite effects when they are tested at steady state on in nonsteady state conditions. It is concluded that ⁴⁵Ca uptake curves must be kinetically analyzed and that the steady or non-steady state of the system must be known for a valid interpretation of such data.     

The effect of external calcium and lanthanum on platelet calcium content and on the release reaction

Calcium compartments in calf platelets were studied using a lanthanum washout procedure to distinguish between surface-bound calcium and intracellular calcium. The calcium content of calf platelets ranges from 20 to 60 nmol/10⁹ platelets and is sensitive to the calcium concentration of the suspending medium. With 1 mM calcium in the medium, calcium uptake is rapid and reaches steady state within 1–2 min. Results obtained with the lanthanum procedure indicate that it is the surface compartment which is most affected by the extracellular calcium concentration. The surface compartment appears to be saturable and is highly exchangeable. Although the total calcium as well as the calcium content of the surface and internal compartments are variable, the ratio of calcium in either compartment to the total saturated calcium is quite constant. The data indicate that 68–85% of the platelet calcium is located internally. Thrombin produces an immediate release of platelet calcium and labeled serotonin and an increase in the ⁴⁵Ca²⁺ uptake of both the surface and internal compartments. The release reaction is not dependent upon exogenous calcium or an influx of exogenous calcium since it occurs even in the presence of $\text{ethyleneglycol-bis-(β-aminoethylether)}\text{-N,N′-}\text{tetraacetic}$ acid. Lanthanum, however, inhibits the release reaction possibly by blocking surface calcium site and reducing the mobility of endogenous platelet calcium.     

Calcium pool size modulates the sensitivity of the ryanodine receptor channel and calcium-dependent ATPase of heavy sarcoplasmic reticulum to extravesicular free calcium concentration

We have examined calcium cycling and associated ATP consumption by isolated heavy sarcoplasmic reticulum (HSR) vesicles incubated in conditions believed to exist in resting muscle. Our goals were to estimate the magnitude of calcium cycling under those conditions and identify the main mechanisms involved in its regulation. The integrity of the HSR vesicles was documented by the retention of [¹⁴C]-sucrose and electron microscopy. HSR actively exchanged Ca²⁺ with the medium through a partially open ryanodine-binding channel (RyR), as evidenced by the rapid attainment of a steady-state gradient between HSR and medium, which was promptly increased by the closure of the channel with ruthenium red (RR) or collapsed by its opening with caffeine. The ATP dependency was evidenced by the sustained ATP consumption after the steady state was attained and by the abrogation of the gradient following inhibition of the pump with thapsigargin (Tg) or the omission of ATP. When HSR vesicles were incubated in a comparatively large pool of calcium (≈1 μmol/mg HSR protein), ATP consumption was 1–1.5 μmol × [min × mg protein]⁻¹ at 0.1 μM free Ca²⁺. Under such conditions, the main regulator of the sarcoplasmic Ca²⁺-dependent ATPase (SERCA) was extravesicular-free Ca²⁺ concentration, with a four- to fivefold increase between 0.1 and 2 μM Ca²⁺, whereas RyR channel activity and the replenishment of the HSR vesicles had only a modest effect on ATP consumption. When calcium pool size was reduced to 0.1 μmol/mg HSR protein, a steady state was established at a lower level of HSR calcium. In spite of a slightly lower free extravesicular Ca²⁺ at equilibrium (≈0.07 μM following an initial concentration of 0.1 μM), both ATP consumption and the open probability of the RyR channel were increased by a factor of three to five. Compared to the large calcium pool, the sensitivity of both RyR channel and SERCA to extravesicular free Ca²⁺ concentration as well as to caffeine and RR was markedly enhanced. Conclusions: (1) In conditions present in resting muscle, HSR calcium is in dynamic equilibrium with the medium through a partially open RyR channel, which requires continuous ATP hydrolysis. (2) The availability of calcium is a major determinant of the sensitivity of both RyR channel and SERCA to free extravesicular Ca²⁺ and possibly other stimuli. (3) These observations are consistent with the concept that calcium cycling in resting muscle may account for a significant fraction of muscle energy demands and further suggest that restricting calcium availability may enhance the energetic demands of this process. J. Cell. Physiol. 175:283–294, 1998. © 1998 Wiley-Liss, Inc.     

Analysis of steady state photosynthesis in alfalfa leaves

A method for carrying out kinetic tracer studies of steady state photosynthesis in whole leaves has been developed. An apparatus that exposes whole leaves to ¹⁴CO₂ under steady state conditions, while allowing individual leaf samples to be removed as a function of time, has been constructed. Labeling data on the incorporation of ¹⁴C into Medicago sativa L. metabolite pools are reported. A carbon dioxide uptake rate of 79 micromoles ¹⁴CO₂ per milligram chlorophyll per hour was observed at a CO₂ level slightly below that of air. Several actively turning over pools of early and intermediate metabolites, including 3-phosphoglyceric acid, glycerate, citrate, and uridine diphosphoglucose, showed label saturation after approximately 10 to 20 minutes of photosynthesis with ¹⁴CO₂ under steady state conditions. Alanine labeling increased more rapidly at first, and then at a lower rate as saturation was approached. Sucrose was a major product of photosynthesis and label saturation of the sucrose pool was not observed. Labeled carbon appeared rapidly in secondary metabolites. The steady state apparatus used has numerous advantages, including leaf temperature control, protection against leaf dehydration, high illumination, known ¹⁴CO₂ specific radioactivity, and provision for control and adjustment of ¹⁴CO₂ concentration. The apparatus allows for experiments of long duration and for sufficient sample points to define clearly the metabolic steady state.     

Action of La3+ on the systems providing contractility of vertebrate myocardium

The inotropic action of La³⁺ on frog myocardium was studied with taking into account its effect on mitochondria of cardiomyocytes (CM). It has been established that in the range of studied concentrations (0.2–6.0 mM), La³⁺ decreases dose-dependently the force of cardiac contractions (by 3.3–92.2%). In parallel experiments on isolated rat heart mitochondria (RHM), La³⁺ at a concentration of 25 μM has been shown to cause swelling of non-energized and energized mitochondria incubated in isotonic medium with 125 mM NH₄NO₃ and in hypotonic medium with 25 mM CH₃COOK. The study of oxidative processes in mitochondria with aid of polarographic method of measurement of oxygen concentration has shown that La³⁺ at concentrations of 50 and 100 μM increases the oxygen consumption rate by mitochondria in the state 2. However, La³⁺ does not decrease the respiration rate of isolated mitochondria in the state 3, as this takes place in the case of use of Cd²⁺ or at the Ca²⁺-overloading of mitochondria. The rate of endogenous respiration of isolated mitochondria in the medium with La³⁺ was higher than in control, which suggests its effect on ion permeability of the inner membrane. The data obtained in this work indicate that the La³⁺-produced decrease of contractility of cardiac muscle is not only due to the direct blocking effect on the potential-controlled Ca²⁺-channels, but is also mediated by its unspecific action on the CM mitochondria. This action is manifested as an acceleration of the energy-dependent K⁺ transport in matrix and as an increase of ion permeability of the inner mitochondrial membrane (IMM).     

Stretch-induced Increase in Activation of Skinned Muscle Fibres by Calcium

IT is well known that the active tetanic tension of a living striated muscle fibre decreases linearly with increase of fibre length beyond its slack length^1,2 and this has been explained² by the decreased number of interacting sites between thick (myosin-containing) and thin (actin-containing) filaments. Skinned fibres³ have been shown to behave similarly at high concentrations of calcium⁴. But examination of the mechanical properties, of partially activated skinned muscle fibres showed that the isometric tension increased with the increase of fibre length beyond its slack length if contraction was induced by a low concentration of calcium ions.     

A Spatially Detailed Model of Isometric Contraction Based on Competitive Binding of Troponin I Explains Cooperative Interactions between Tropomyosin and Crossbridges

Biophysical models of cardiac tension development provide a succinct representation of our understanding of force generation in the heart. The link between protein kinetics and interactions that gives rise to high cooperativity is not yet fully explained from experiments or previous biophysical models. We propose a biophysical ODE-based representation of cross-bridge (XB), tropomyosin and troponin within a contractile regulatory unit (RU) to investigate the mechanisms behind cooperative activation, as well as the role of cooperativity in dynamic tension generation across different species. The model includes cooperative interactions between regulatory units (RU-RU), between crossbridges (XB-XB), as well more complex interactions between crossbridges and regulatory units (XB-RU interactions). For the steady-state force-calcium relationship, our framework predicts that: (1) XB-RU effects are key in shifting the half-activation value of the force-calcium relationship towards lower [Ca²⁺], but have only small effects on cooperativity. (2) XB-XB effects approximately double the duty ratio of myosin, but do not significantly affect cooperativity. (3) RU-RU effects derived from the long-range action of tropomyosin are a major factor in cooperative activation, with each additional unblocked RU increasing the rate of additional RU’s unblocking. (4) Myosin affinity for short (1–4 RU) unblocked stretches of actin of is very low, and the resulting suppression of force at low [Ca²⁺] is a major contributor in the biphasic force-calcium relationship. We also reproduce isometric tension development across mouse, rat and human at physiological temperature and pacing rate, and conclude that species differences require only changes in myosin affinity and troponin I/troponin C affinity. Furthermore, we show that the calcium dependence of the rate of tension redevelopment k_tr is explained by transient blocking of RU’s by a temporary decrease in XB-RU effects.     

Slow adaptation in spider mechanoreceptor neurons

Slow adaptation of action potential firing is a common but poorly understood property of sensory neurons. We quantified slow adaptation in a cuticular mechanoreceptor organ of the spider, Cupiennius salei, by stimulating with continuous pseudorandom mechanical displacements while recording action potentials intracellularly from the cell bodies. Firing rate declined over a period of several minutes before reaching a steady level at about half the initial rate. This slow adaptation was fitted by an exponential decay with mean time constant of 18.5 s. Recovery from slow adaptation was also fitted by an exponential process, but with a longer time constant of 167 s. The receptor potential produced by the same stimulation protocol did not change its amplitude or dynamics, showing that slow adaptation occurs during action potential encoding from the receptor potential. Experiments with chemical blockers of calcium entry or the known potassium currents failed to reduce the slow adaptation. The Na⁺/K⁺ pump blocker Ouabain decreased the time constant of slow adaptation, suggesting that ion accumulation is involved. In some experiments, a second class of small action potentials were observed, which were tentatively attributed to failed conduction from the sensory dendrite through the soma to the axon.     

Effects of External Calcium Deprivation on Single Muscle Fibers

Deprivation of external calcium causes sudden potentiation of the twitch response of single muscle fibers. The potentiation was 64 ± 8%. Potentiation is simultaneous with membrane depolarization occurring after Ca⁺⁺ removal. This depolarization amounted to 9 ± 2 mv. Ca⁺⁺ removal also alters the action potential. 3 min after calcium withdrawal, action potential amplitude fell by 36 ± 3 mv; maximum rates of rise and fall of the spike decreased by 55 ± 5 and 63 ± 5% respectively. Changes in shape of the A. P. differ from those seen with other potentiators of the twitch response, such as Zn⁺⁺. After short exposure to calcium-free media, potassium-induced contractures show potentiation of peak tension. The S-shaped curve relating potassium contracture tension to log [K]_o shifts to the left after such treatment. Calcium deprivation also increased the rate of relaxation of the contractures. This effect depends on the duration of calcium deprivation, and is probably related to the effect of calcium lack on the membrane. The change in relaxation occurred immediately after calcium deprivation, and was reversed by sudden readmission of calcium. Relaxation of twitch and tetanus responses also were affected by Ca lack, but not as rapidly as potassium contractures. The results suggest that external calcium is not directly involved in the process responsible for tension development, supporting the view that this process is mediated by translocation of intracellular calcium. The relaxation process, however, appears to be rapidly affected by deprivation of external calcium.     

Calcium is necessary for light excitation in barnacle photoreceptors

Summary Illumination of barnacle (Balanus amphitrite) photoreceptors is known to increase the membrane permeability to sodium and Ca²⁺ ions resulting in a depolarizing receptor potential. In this report, we show that lanthanum (La³⁺), a known inhibitor of Ca-binding proteins, reversibly eliminates the receptor potential of barnacle photoreceptors when applied to the extracellular space. Similar reversible elimination of the light response was obtained by removing extracellular Ca²⁺ by application of the calcium chelating agent EGTA. Iontophoretic injection of Ca²⁺, but not K⁺ into the cells protected both the transient and the steady-state phases of the receptor potential from elimination by EGTA while only the transient phase was protected in the presence of La³⁺. The EGTA experiments suggest that internal Ca²⁺ is necessary for light excitation of barnacle photoreceptors while the La³⁺ experiments suggest that La³⁺-sensitive inward current is necessary to maintain excitation during prolonged light.Abbreviations EGTA ethylenglyol-bis-(-aminoethylether) N, N, N¹, N¹-tetraacetate - BAPTA bis-(0-aminophenoxy)-ethane-N, N, N¹, N¹-tetraacetic acid - DMSO dimethyl sulfoxide - trp transient receptor potential - nss no steady state - ASW artificial sea water     

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.     

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.     

Molecular properties of the red cell calcium pump: II. Effects of calmodulin,proteolytic digestion and drugs on the calcium-induced membrane phosphorylation by ATP in inside-out red cell membrane vesicles

In inside-out human red cell membrane vesicles /IOV/, in the absence of Mg²⁺, the only calcium-induced labelling by γ³²P-ATP occurs in a 140–150 000 molecular weight protein fraction, representing the hydroxylamine-sensitive phosphorylated intermediate /EP/ of the calcium pump. In the presence of Mg²⁺ calcium-induced phosphorylation is accelerated but several other membrane proteins are also phosphorylated through protein kinase action forming hydroxylamine-insensitive bonds. Addition of calmodulin accelerates EP formation both in the absence and presence of Mg²⁺.Treatment of the membrane with SH-group reagents significantly reduces EP formation. Mild trypsin digestion of IOVs, stimulating active calcium transport, eliminates calmodulin action and decreases the steady-state level of EP. In trypsin-digested IOVs the molecular weight of the ³²P-labelled EP is shifted to lower values /110–120 000/ We suggest that trypsin digestion cleaves off a 20–40 000 molecular weight calmodulin-binding regulatory subunit of the calcium pump molecule.