Modelling action potentials and membrane currents of mammalian skeletal muscle fibres in coherence with potassium concentration changes in the T-tubular system.

During prolonged activity the action potentials of skeletal muscle fibres change their shape. A model study was made as to whether potassium accumulation and removal in the tubular space is important with respect to those variations. Classical Hodgkin-Huxley type sodium and (potassium) delayed rectifier currents were used to determine the sarcolemmal and tubular action potentials. The resting membrane potential was described with a chloride conductance, a potassium conductance (inward rather than outward rectifier) and a sodium conductance (minor influence) in both sarcolemmal and tubular membranes. The two potassium conductances, the Na-K pump and the potassium diffusion between tubular compartments and to the external medium contributed to the settlement of the potassium concentration in the tubular space. This space was divided into 20 coupled concentric compartments. In the longitudinal direction the fibre was a cable series of 56 short segments. All the results are concerned with one of the middle segments. During action potentials, potassium accumulates in the tubular space by outward current through both the delayed and inward rectifier potassium conductances. In between the action potentials the potassium concentration decreases in all compartments owing to potassium removal processes. In the outer tubular compartment the diffusion-driven potassium export to the bathing solution is the main process. In the inner tubular compartment, potassium removal is mainly effected by re-uptake into the sarcoplasm by means of the inward rectifier and the Na-K pump. This inward transport of potassium strongly reduces the positive shift of the tubular resting membrane potential and the consequent decrease of the action potential amplitude caused by inactivation of the sodium channels. Therefore, both potassium removal processes maintain excitability of the tubular membrane in the centre of the fibre, promote excitation-contraction coupling and contribute to the prevention of fatigue.

Influence of inhomogeneities in muscle tissue on single-fibre action potentials: a model study.

The influence of changes in electrical conductivity, due to the muscle boundary, layers and compartments of intramuscular connective tissue and blood vessels, on computed single-muscle fibre action potentials (SFAPs) in rat hindleg muscle is calculated. The position of the active fibre is varied throughout the muscle. For fibres close to the muscle boundary, peak-to-peak voltages of SFAPs increase by up to a factor of 3 compared with the unbounded situation. For inner fibres, the presence of nearby connective tissue compartments causes an increase of up to 40%. A blood vessel in the neighbourhood of the active fibre leads to a decrease of at most 20%, for recording sites between the active fibre and the blood vessel. For recording sites beyond the blood vessel, peak-to-peak voltages increase by up to 20%.

Ionic currents during action potentials in mammalian skeletal muscle fibers analyzed with loose patch clamp.

The loose patch-clamp technique was applied to analyze transmembrane currents during propagating action potentials in superficial fibers of musculi extensor digitorum longus of the mouse in vitro. Experimentally three components were identified in the transmembrane current: 1) a capacitive, 2) an inward sodium, and 3) an outward potassium current. Other components were negligible. The capacitive current was similar in shape to the first derivative of the intracellularly measured action potential. Tetrodotoxin, tetraethylammonium, and 4-aminopyridine, applied in the pipette, were used to identify the contribution in the current by sodium and potassium ions. With extracellularly applied depolarization steps only a sodium current was observed, not a potassium current. Occasionally found outward currents were artifactual. The behaviour of delayed rectifier potassium channels in muscle fiber membranes is discussed in the light of these unexpected findings. We conclude that potassium channel activity contributing to and measured during action potential generation is in some way inaccessible to loose patch extracellular voltage-clamp stimulation and that loose patch action current recording is a useful noninvasive method to analyze membrane conductances involved in action potential generation.

Single fibre action potentials in skeletal muscle related to recording distances.

Single muscle fibre action potentials (SFAPs) are considered to be functions of a bioelectrical source and electrical conductivity parameters of the medium. In most model studies SFAPs are computed as a convolution of the bioelectrical source with a transfer function. Calculated peak-to-peak amplitudes of SFAPs decrease with increasing recording distances. In this paper an experimental validation of model results is presented. Experiments were carried out on the m. extensor digitorum longus (EDL) of the rat. Using a method including fluorescent labelling of the active fibre, the distance between the active fibre and the recording electrode was derived. With another method, the decline of the peak-to-peak amplitude of SFAPs detected along a multi-electrode was obtained. With both experimental methods, in general peak-to-peak amplitudes of SFAPs decreased with increasing recording distances, as was found in model results with present volume conduction theory. However, this behaviour was not found in all experiments. The rate of decline of the peak-to-peak amplitudes with recording distance was always less than in models.

The bioelectrical source in computing single muscle fiber action potentials.

Generally, single muscle fiber action potentials (SFAPs) are modeled as a convolution of the bioelectrical source (being the transmembrane current) with a weighting or transfer function, representing the electrical volume conduction. In practice, the intracellular action potential (IAP) rather than the transmembrane current is often used as the source, because the IAP is relatively easy to obtain under experimental conditions. Using a core conductor assumption, the transmembrane current equals the second derivative of the IAP. In previous articles, discrepancies were found between experimental and simulated SFAPs. Adaptations in the volume conductor slightly altered the simulation results. Another origin of discrepancy might be an erroneous description of the source. Therefore, in the present article, different sources were studied. First, an analytical description of the IAP was used. Furthermore, an experimental IAP, a special experimental SFAP, and a measured transmembrane current scaled to our experimental situation were applied. The results for the experimental IAP were comparable to those with the analytical IAP. The best agreement between experimental and simulated data was found for a measured transmembrane current as source, but differences are still apparent.

Potential distribution and single-fibre action potentials in a radially bounded muscle model.

In modelling the electrical behaviour of muscle tissue, we used to employ a frequency-dependent volume conductor network model, which was infinitely extended in all directions. Equations in this model could be solved using a finite-difference approach. The most important restriction of this model was the fact that no boundary effects could be incorporated. Analytical models of muscle tissue normally do not have this disadvantage, but in those models the microscopic structure of muscle tissue cannot be taken into account. In the paper, we present a combined numerical/analytical approach, which enables the study of potential distributions and SFAPs in simulated microscopic muscle tissue in which the influence of the muscle boundary has been considered. We considered muscle models with radii of 1.5 mm and 10 mm. Both models were compared with an unbounded network model. In the model with a radius of 1.5 mm we varied the position of the active fibre relative to the muscle surface. It appeared that in most cases the presence of a boundary had a considerable effect on the potential distribution. An increase in the peak-to-peak value of the SFAP amplitude up to 300 per cent was noticed when the active fibre was positioned 500 microns beneath the muscle surface in a model with a radius of 1.5 mm.

Quantitative analysis of single muscle fibre action potentials recorded at known distances.

In vivo records of single fibre action potentials (SFAPs) have always been obtained at unknown distance from the active muscle fibre. A new experimental method has been developed enabling the derivation of the recording distance in animal experiments. A single fibre is stimulated with an intracellular micropipette electrode. The same electrode is used thereafter for labelling with an auto-fluorescent dye, Lucifer Yellow. In this method there is no use of chemical fixation. The tissue structure is kept as well as possible. In cross-sections the fluorescent fibre is seen and its position is quantitized with respect to the tip of one or more recording wire electrodes. Morphometric data, such as the recording distance and the fibre cross-sectional area, are used for the interpretation of parameters of the SFAPs (peak-peak amplitude, time between the first positive and negative peaks). The present results show that within 300 microns recording distance is not as dominant for the SFAP shape as expected. The method offers also a direct check of the relation between the muscle fibre; diameter and the conduction velocity of the action potential. In the present small set of data there is no simple linear relationship.