A kinetic model for determining the consequences of electrogenic active transport in cardiac muscle

When active transport is electrogenic in a tissue that is continuously active, such as cardiac muscle, the active transport current is as important in the generation of the action potential as are the passive currents. A thermodynamically constrained kinetic model of electrogenic active transport of sodium and potassium ions has been developed in which the influences of voltage and chemical composition are explicitly defined. This model is coupled to a system of passive permeabilities, of the minimum degree of complexity, to simulate the integrated activity of active and passive ion transport in the generation of the cardiac action potential. Results of preliminary simulations indicate that electrogenic active transport provides a mechanism for slowly changing currents both within the time scale of an action potential as well as of many action potentials. The presence of active transport also complicates the interpretation of isotopic flux measurements and the separation of currents.     

A model for the oxygen-paradox in mouse cardiac muscle

1. Mouse ventricle strips provide a good model system for studying cellular damage in mammalian cardiac muscle. 2. Anoxia rapidly causes destruction of the myofilament apparatus that is characteristic of calcium-triggered damage in muscle cells, and it is suggested that anoxia promotes release of calcium from the mitochondria. 3. Oxygen exacerbates this damage which is independent of extracellular calcium; it is suggested that it initiates myofilament damage by activation at an intracellular site, probably the sarcoplasmic reticulum.     

A model for the active site of skeletal muscle myosin.

A model for a main element of the active site of skeletal muscle myosin is presented that relates directly to the 92 amino acid fragment (p₁₀) of myosin recently described by Elzinga &; Collins (1977). In this model, the substrate, an eight-membered cyclic complex of MgATP, fits tightly into a 16 amino acid segment of p₁₀ and interacts with seven of its amino acids. A main feature of the model is the important role played by the one molecule of N^τ-methylhistidine² that is present in each myosin heavy chain. At the site, it is postulated that this rare amino acid functions as a donor ligand to Mg²⁺. Once N^τ-methylhistidine is put in place next to the metal, the other amino acids that appear to form a pocket come easily into position around the MgATP. These amino acids with their postulated functions are: tyrosine 72, which through a Mg-bound water, or perhaps directly, is attached to the Mg; histidine 76, which donates a proton to the P_γ of ATP; lysine 78, which binds electrostatically to P_β of ATP; phenylalanines 80 and 81, which flank the purine ring of ATP; and aspartate 66, which forms a hydrogen bond to the 6-amino group of adenine. The Mg-coordination role ascribed to N^τ-methylhistidine 69 in skeletal muscle myosin could be taken by histidine 69 in cardiac myosin and in other muscle myosins that do not contain the methylated amino acid.The choice of p₁₀ to contain a main element of the active site is based on: (a) the presence in p₁₀ of the essential sulfhydryl groups, SH1 and SH2, whose modification affects the ATPase activity of myosin; (b) the presence in ρ₁₀ of N^τ-methylhistidine, an unusual amino acid whose methylation in skeletal muscle we take as an indicator for a special function at the active site; (c) the position of p₁₀ in the primary structure near the junction between subfragment 1 and subfragment 2 (the hinge region) where, we postulate, enzymatic events at the active site are coupled to movements of the hinge that occur during contraction; (d) indications that the DTNB light chain, probably involved in regulation, is also near the hinge; (e) the effects of MgATP at the active site on the chemical reactivity of three SH groups (SH1, SH2 and SH3) located near the hinge; and (f) the effect of hinge cleavage on the oxygen exchange reaction catalyzed at the active site. The correlation of all these observations forms the basis for our placement of part of the active site on p₁₀ near the subfragment 1-subfragment 2 hinge.     

A model of excitation-contraction coupling of mammalian cardiac muscle

A model is developed for the excitation-contraction coupling of mammalian cardiac muscle. This model assumes that upon depolarization, the calcium current not only raises the sarcoplasmic Ca²⁺ concentration, but also induces the release of Ca from cisternal sarcoplasmic reticulum, whose rate of release depends on the membrane potential. These two main sources of calcium elevate the sarcoplasmic Ca²⁺ concentration so that it activates the interaction of myosin and actin and initiates contraction in accordance with Huxley's sliding filament mechanism. The uptake and recycling of Ca²⁺ to cisternal sarcoplasmic reticulum is accomplished by the longitudinal sarcoplasmic reticulum. Mitochondria are assumed to accumulate mainly Ca²⁺. The uptake of Ca is considered to be an active process, utilizing energy.The proposed model qualitatively predicts the following electrical-mechanical events often observed in living muscle: tension-voltage-duration, staircase phenomenon, frequency-strength relationship, post-extrasystolic potentiation and contractile behavior after a period of rest.     

A model for ionic conduction in the ryanodine receptor channel of sheep cardiac muscle sarcoplasmic reticulum

A model is developed for ionic conduction in the sheep cardiac sarcoplasmic reticulum ryanodine receptor channel based on Eyring rate theory. A simple scheme is proposed founded on single-ion occupancy and an energy profile with four barriers and three binding sites. The model is able to quantitatively predict a large number of conduction properties of the purified and native receptor with monovalent and divalent cations as permeant species. It suggests that discrimination between divalent and monovalent cations is due to a high affinity central binding site and a process that favors the passage of divalent cations between binding sites. Furthermore, differences in conductance among the group Ia cations and among the alkaline earths are largely explained by differing affinity at this putative central binding site.     

An "active enzyme" muscle model

A new model of skeletal muscle contraction is presented from a unified view of muscle physiology, chemical energetics and newly obtained experimental data concerning actomyosin ATPase in vitro.In this model an interaction between actin and myosin, involving two distinct active sites, is considered to be the essential elementary mechanism for muscle contractions. These two sites are located on myosin. One site, forming a myosin-ADP-P, complex, has stored energy derived from ATP splitting before the beginning of a contraction. Another site, forming a myosin-ATP complex, upon interacting with actin, catalyzes ATP hydrolysis, using a fraction of the stored energy. The hydrolysis at the latter site is responsible for tension development, while the stored energy is released to drive the contractile reaction between actin and myosin unidirectionally. (Thus, the two sites act co-operatively and they can be viewed as forming an active enzyme.)There has been a difficulty in explaining the shortening heat production with apparent lack of corresponding chemical change at the early stage of contraction. The active enzyme model accounts for the shortening heat as the irreversible release of the stored energy. The heat production appears to precede its corresponding ATP splitting for “refueling” which occurs after complete exhaustion of the stored energy, while the actomyosin ATP hydrolysis takes place proportionally to the work. At the macroscopic level, the model is compatible with Hill's tension-velocity and heat relation.     

A silver-reducing component in rat striated muscle

Summary In previous work on rat striated muscle cells a sliver-reducing component was found selectively localized at the terminal cistern/transverse tubule system (Tandler and Pellegrino de Iraldi 1989). To further investigate that problem we performed the Hg–Ag argentaffin reaction on a sarcoplasmic reticulum fraction from rat skeletal muscle. Circular profiles corresponding to vesicular structures were found outlined by silver grains. The number of silver stained vesicles were less than the total number vesicles stained by conventional procedures. The correlation between argentaffinities in the intact muscle fiber and their subcellular organelles indicated that the Hg–Ag reactive vesicles must be those derived from the terminal cisternae of the sarcoplasmic reticulum. The silver-reducing constituent aggregates in the presence of 1 mM CaCl₂ or 0.5 M K cacodylate. The state of aggregation induced by Ca²⁺ was not affected by incubation with 0.5% Triton X-100 or by 2 mM EDTA, thus suggesting a localization at or near the membrane of the terminal cistern vesicle facing the junctional gap. In Laemmli SDS-acrylamide gels the Hg–Ag reaction stained all proteins in a manner similar to Coomasie blue. It is suggested that the selective histochemical staining is the result of differential reactivities due to steric requirements of the chemical reaction.     

A model study of the contribution of active Na-K transport to membrane repolarization in cardiac cells

A biochemical model of active Na-K transport in cardiac cells was studied in conjunction with a representation of the passive membrane currents and ion concentration changes. The active transport model is based on the thermodynamic and kinetic properties of a six-step reaction scheme for the Na,K-ATPase. It has a fixed Na:K stoechiometry of 3:2, and its activation is governed by three parameters: membrane potential intracellular Na+ concentration, and interstitial K+ concentration. The Na-K pump current is directly proportional to the density of Na,K-ATPase molecules. The passive membrane currents and ion concentration changes involve only Na+ and K+ ions, and no attempt was made to provide a precise representation of Ca2+ currents or Ca2+ concentration changes. The surface-to-volume ratio of the interstitial compartment is 55 times larger than that of the intracellular compartment. The flux balance conditions are such that the original equilibrium concentration values are re-established at each stimulation cycle. The underlying assumptions of the model were checked against experimental measurements on Na-K pump activity in a variety of preparations. In addition, the qualitative validation of the model was carried out by comparing its behavior following sudden frequency shifts to corresponding experimental observations. The overall behavior of the model is quite satisfactory and it is used to provide the following indications: (1) when the intracellular and interstitial volumes are relatively large, the ion concentration transients are small and the pumping rate depends essentially on average concentration levels. (2) An increase in internal Na+ concentration potentiates the response of the Na-K pump to rapid membrane depolarizations. (3) When the internal Na+ concentration is large enough, the Na-K pump current transient plays an important role in shaping the plateau and repolarization phase of the action potential. (4) A rapid increase in external K+ concentration during voltage clamp in multicellular preparations could saturate the Na-K pump response and lead to a fairly linear dependence of the pump activity on the internal Na+ concentration.     

A 3D skeletal muscle model coupled with active contraction of muscle fibres and hyperelastic behaviour

This paper presents a three-dimensional finite element model of skeletal muscle which was developed to simulate active and passive non-linear mechanical behaviours of the muscle during lengthening or shortening under either quasi-static or dynamic condition. Constitutive relation of the muscle was determined by using a strain energy approach, while active contraction behaviour of the muscle fibre was simulated by establishing a numerical algorithm based on the concept of the Hill's three-element muscle model. The proposed numerical algorithm could be used to predict concentric, eccentric, isometric and isotonic contraction behaviours of the muscle. The proposed numerical algorithm and constitutive model for the muscle were derived and implemented into a non-linear large deformation finite element programme ABAQUS by using user-defined material subroutines. A number of scenarios have been used to demonstrate capability of the model for simulating both quasi-static and dynamic response of the muscle. Validation of the proposed model has been performed by comparing the simulated results with the experimental ones of frog gastrocenemius muscle deformation. The effects of the fusiform muscle geometry and fibre orientation on the stress and fibre stretch distributions of frog muscle during isotonic contraction have also been investigated by using the proposed model. The predictability of the present model for dynamic response of the muscle has been demonstrated by simulating the extension of a squid tentacle during a strike to catch prey.     

A two-current model for the dynamics of cardiac membrane

In this paper we introduce and study a model for electrical activity of cardiac membrane which incorporates only an inward and an outward current. This model is useful for three reasons: (1) Its simplicity, comparable to the FitzHugh-Nagumo model, makes it useful in numerical simulations, especially in two or three spatial dimensions where numerical efficiency is so important. (2) It can be understood analytically without recourse to numerical simulations. This allows us to determine rather completely how the parameters in the model affect its behavior which in turn provides insight into the effects of the many parameters in more realistic models. (3) It naturally gives rise to a one-dimensional map which specifies the action potential duration as a function of the previous diastolic interval. For certain parameter values, this map exhibits a new phenomenon—subcritical alternans—that does not occur for the commonly used exponential map.