Optical recording of action potential propagation in demyelinated frog nerve.

Conduction in focally demyelinated frog nerves has been measured optically using potential-sensitive dyes. Absorption changes were recorded with an array of photodiodes positioned in the image plane of a microscope. Both the amplitude and conduction velocity of the optical signals decreased in the demyelinated region. Conduction was improved after exposure to the potassium channel blocking agent 4-aminopyridine.     

Changes in the Raman spectrum of frog sciatic nerve during action potential propagation.

Raman spectra of frog sciatic nerves were recorded in different states of functioning. During excitation reversible changes were observed in the C₄₀-carotenoid peaks enhanced by the resonance Raman effect. This change can be explained by transient carbon-carbon bond equalization of the polyene chain. Possible biological consequences are also discussed.     

Computer simulation study of the shape of motor unit action potential

Motor unit action potentials (MUAPs) of brachial biceps were simulated. A simulated MUAP was obtained as a sum of single fibre action potentials (SFAPs) from all the muscle fibres of a motor unit (MU). The influence of the following factors on MUAP shape for different kinds of recording electrode was studied: fibre density, neuromuscular jitter, temporal dispersion and electrode displacements. The simulation confirms that typical MUAPs recorded with needle electrodes from muscles of low fibre density such as brachial biceps are usually triphasic. Increased fibre density produces MUAPs of more complex shape and higher amplitude. Normal neuromuscular jitter is responsible for the variability of shape of subsequent potentials from the same MU as well as for electromyographic shimmer. Pathologic (increased) jitter makes the shapes of subsequent potentials unrecognizable. The influence of temporal dispersion is interconnected with other factors but rather of minor importance. The simulation shows how big changes in MUAP shape can be expected due to electrode displacements during single experiment or during estimation of MU territory.     

Simulation of action potential propagation in complex terminal arborizations.

Action potential propagation in complex terminal arborizations was simulated using SPICE, a general purpose circuit simulation program. The Hodgkin-Huxley equations were used to simulate excitable membrane compartments. Conduction failure was common at branch points and regularly spaced boutons en passant. More complex arborizations had proportionally more inactive synapses than less complex arborizations. At lower temperature the safety factor for impulse propagation increased, reducing the number of silent synapses in a particular arborization. Small structural differences as well as minute changes in the discharge frequency of the action potential resulted in very different activation patterns of the arborization and terminal boutons. The results suggest that the structural diversity of terminal arborizations allows a wide range of presynaptic information processing. The results from this simulation study are discussed in the context of experimental results on the modulation of synaptic transmission.     

The effects of static magnetic field on action potential propagation and excitation recovery in nerve

Calculations using the Hodgkin–Huxley and one-dimensional cable equations have been performed to determine the expected sensitivity of conduction and refractoriness to changes in the time constant of sodium channel deactivation at negative potentials, as reported experimentally by Rosen (Bioelectromagnetics 24 (2003) 517) when voltage-gated sodium channels are exposed to a 125 mT static magnetic field. The predicted changes in speed of conduction and refractory period are very small.     

Energetic aspects of propagation of action potential

On the basis of the electrical analogue of an action potential suggested previously, the distribution of electrical field outside and inside the membrane was obtained. The energy released upon the propagation of a single action potential along the nerve fibre was calculated. A comparison of the results with the available data showed the correctness of the calculations performed.     

Development of action potential in larval muscle fibers in Drosophila melanogaster.

In the presence of tetraethylammonium or barium ions, the larval muscle fibers of Drosophila melanogaster were found to produce an all-or-none action potential operated by the calcium channels. The development of this distinctive membrane property during the maturation of muscle cells was studied by measuring the maximum rate of rise of the action potential in the larval muscle fibers at different stages of development from the sixteenth to ninety-sixth hours after hatching. The value increased significantly with age until a peak was reached at the sixty-fourth hour, although it became lower again as puparium formation neared at about the ninety-sixth hour. This suggests that during larval development the muscle fibers develop the ability to generate an action potential due to an inward current through the calcium channels, although the ability became lower at the later stage of larval development.     

Computer simulation of bend propagation by axoplasmic microtubules

The generation of bending waves by microtubules in squid nerve axoplasm has been modelled using appropriately modified versions of computer programs developed previously for simulation of flagellar bending waves. The results confirm that a constant longitudinal force directed along the axis of the microtubule is sufficient to cause the generation of regular oscillations and propagated bending waves when the forward gliding movement of the microtubule is obstructed. No control mechanism is required to modulate the active force-generating system. In order to obtain bending waves similar to those observed experimentally, it was necessary to use a model for the force-generating system in which the active force decreases with increasing sliding velocity. If the elastic bending resistance of axoplasmic microtubules is similar to that of microtubules in sperm terminal filaments, the longitudinal force per unit length generated by the axoplasmic microtubules must be of the same order of magnitude as the force generated by dynein arms along the doublet microtubules of eukaryotic flagella.     

Modeling action potential generation and propagation in NRK fibroblasts

Normal rat kidney (NRK) fibroblasts change their excitability properties through the various stages of cell proliferation. The present mathematical model has been developed to explain excitability of quiescent (serum deprived) NRK cells. It includes as cell membrane components, on the basis of patch-clamp experiments, an inwardly rectifying potassium conductance (G_Kir), an L-type calcium conductance (G_CaL), a leak conductance (G_leak), an intracellular calcium-activated chloride conductance [G_Cl(Ca)], and a gap junctional conductance (G_gj), coupling neighboring cells in a hexagonal pattern. This membrane model has been extended with simple intracellular calcium dynamics resulting from calcium entry via G_CaL channels, intracellular buffering, and calcium extrusion. It reproduces excitability of single NRK cells and cell clusters and intercellular action potential (AP) propagation in NRK cell monolayers. Excitation can be evoked by electrical stimulation, external potassium-induced depolarization, or hormone-induced intracellular calcium release. Analysis shows the roles of the various ion channels in the ultralong (30 s) NRK cell AP and reveals the particular role of intracellular calcium dynamics in this AP. We support our earlier conclusion (De Roos A, Willems PH, van Zoelen EJ, and Theuvenet AP. Am J Physiol Cell Physiol 273: C1900–C1907, 1997) that AP generation and propagation may act as a rapid mechanism for the propagation of intracellular calcium waves, thus contributing to fast intercellular calcium signaling. The present model serves as a starting point to further analyze excitability changes during contact inhibition and cell transformation. Hodgkin-Huxley model; intracellular calcium dynamics; L-type calcium conductance; inward rectifier; calcium-activated chloride conductance; gap junctional coupling     

An eikonal-curvature equation for action potential propagation in myocardium

We derive an eikonal-curvature equation to describe the propagation of action potential wavefronts in myocardium. This equation is used to study the effects of fiber orientation on propagation in the myocardial wall. There are significant computational advantages to the use of an eikonal-curvature equation over a full ionic model of action potential spread. With this model, it is shown that the experimentally observed misalignment of spreading action potential ellipses from fiber orientation in level myocardial surfaces is adequately explained by the rotation of fiber orientation through the myocardial wall. Additionally, it is shown that apparently high propagation velocities on the epicardial and endocardial surfaces are the result of propagation into the midwall region and acceleration along midwall fibers before reemergence at an outer surface at a time preceding what could be accomplished with propagation along the surface alone.Research was supported in part by NSF Grant DMS-8801446     

Conduction in bundles of demyelinated nerve fibers: computer simulation

This study presents a model of action potential propagation in bundles of myelinated nerve fibers. The model combines the single-cable formulation of Goldman and Albus (1967) with a basic representation of the ephaptic interaction among the fibers. We analyze first the behavior of the conduction velocity (CV) under the change of the various conductance parameters and temperature. The main parameter influencing the CV is the fast sodium conductance, and the dependence of CV on the temperature is linear up to 30 degrees C. The increase of myelin thickness above its normal value (5 microm) gives a slight increase in CV. The CV of the single fiber decreases monotonically with the disruption of myelin, but the breakdown is abrupt. There is always conduction until the thickness is larger than 2% of its original value, at which with at this point a sharp transition of CV to zero occurs. Also, the increase of temperature can block conduction. At 5% of the original thickness there is still spike propagation, but an increase of 2 degrees C causes conduction block. These results are consistent with clinical observations. Computer simulations are performed to show how the CV is affected by local damage to the myelin sheath, temperature alterations, and increased ephaptic coupling (i.e., coupling of electrical origin due to the electric neutrality of all the nerve) in the case of fiber bundles. The ephaptic interaction is included in the model. Synchronous impulse transmission and the formation of "condensed" pulse states are found. Electric impulses with a delay of 0.5 ms are presented to the system, and the numerical results show that, for increasing coupling, the impulses tend to adjust their speed and become synchronized. Other interesting phenomena are that spurious spikes are likely to be generated when ephaptic interaction is raised and that damaged axons suffering conduction block can be brought into conduction by the normal functioning fibers surrounding them. This is seen also in the case of a large number of fibers (N=500). When all the fibers are stimulated simultaneously, the conduction velocity is found to be strongly dependent on the level of ephaptic coupling and a sensible reduction is observed with respect to the propagation along an isolated axon even for low coupling level. As in the case of three fibers, spikes tend to lock and form collective impulses that propagate slowly in the nerve. On the other hand, if only 10% of fibers are stimulated by an external input, the conduction velocity is only 2% less than that along a single axon. We found a threshold value for the ephaptic coupling such that for lower values it is impossible to recruit the damaged fibers into conduction, for values of the coupling equal to this threshold only one fiber can be restored by the nondamaged fibers, and for values larger than the threshold an increasing number of fibers can return to normal functioning. We get values of the ephaptic coupling such that 25% of axons can be damaged without change of the collective conduction.     

On the theory of action potential propagation in plant cells

The distribution of an electric field in plant cells and zooblasts has been investigated during propagation of the action potential. The behavior of ions in the cytoplasm and in the extracellular fluid has been described with the equations of electric charge motion in electrolytes. It has been shown that the action potential causes an electric potential change not only in the depth of the cytoplasm but also in the extracellular area far from the lipid bilayer. The biomembrane resistance has been expressed by physical parameters of a cell, such as ionic diffusion coefficient in fluid, Debye-Hückel radius, dielectric constant etc. The presence of breaks in the action potential diagrams has been explained as a result of insufficient resolving power of the measuring devices at the instant the sodium ion channels of the bilayer open.     

Energy transfer and molecular switching. I. The nerve action potential

In previous papers (Barrett, 1977b, 1980), the concept of chemical paramemetric excitation was applied to a number of diverse chemical phenomena and contrasted with the concept of chemical resonance, which is a special case of parametric excitation. In the present paper, its status as the fundamental concept of energy transfer and molecular switching is indicated, providing a mechanically sound explanation of nerve excitation at a basic level.The mechanism addressed by the parametric excitation concept is intermediate between macroscopic models of membrane assymetry and molecular models. No assumptions are made concerning the related macroscopic processes, but a systematic approach to organizational aspects of the processes involved in energy transfer is proposed.The chemical analog of the Manley-Rowe relations, which are the power conservation relations for parametrically excited electrical networks, is also derived. The demonstration of such Manley-Rowe relations for chemical systems indicates, for the first time, an explanation for the directionality of flow of power, and thus designates a pumping role. The generalized Manley-Rowe relations translated into flow, reaction, as well as oscillatory system terms, are suggested to be a universal law. Non-linearity is due to the coupling of three systems—each separately describable by Onsager linear relations—by the generalized Manley-Rowe conditions relating flows/reactions/oscillations.All phenomena considered are treated in accordance with a principle of power transfer optimization (Odum & Pinkerton, 1955). Parametric excitation involves three-body interaction, with one system as energy donor, the pump, another as energy receiving, the idler, and a third as mediator of this energy flow, the signal. A conservation law is mandatory for flows/reactions/oscillations, ω_i so that ω_pump= ω_idler±ω_signal. The macroscopic structure, which sets up the conditions for this law to be in operation, may be of diverse kinds, e.g. membrane-bounded compartments, macromolecules capable of multiple conformations and bound cations, etc. All are non-linear.     

External potassium and action potential propagation in rat fast and slow twitch muscles.

The role of extracellular K+ concentration in the propagation velocity of action potential was tested in isolated rat skeletal muscles. Different K+ concentrations were produced by KCl additions to extracellular solution. Action potentials were measured extracellularly by means of two annular platinum electrodes. Fibre bundles of m. soleus (SOL), m. extensor digitorum longus (EDL), red (SMR) and white (SMW) part of m. sternomastoideus were maximum stimulated. The conduction velocity (c.v.) was calculated from the distance between the electrodes and the time delay of the potentials measured at 22 degrees C. In Tyrode solution containing 5 mmol/l K+, the c.v. was close to 1 m.s-1. Bundles of the fast muscle type seemed to have a somewhat higher c.v. The differences observed in these studies were not significant. At higher temperatures, the c.v. increased (Q10 of approx. 2) and a dissociation between SMR and SMW muscles appeared. An elevation of K+ concentration to 10 mmol/l induced a drop of the c.v. by approx. 25% and 15% in EDL and SOL muscles, respectively. After return to normal solution, the recovery was not complete within 30 min. In K+ free solution the c.v. of EDL and SM muscles rose by a factor of 1.5, but less in SOL muscles. The weaker response of SOL to K+ modification was related to the higher resistance of this muscle to fatigue. This suggestion was supported by experiments on fatigued fibre bundles. Immediately after a tetanic stimulation producing fatigue, the c.v. of EDL and SOL muscles dropped similarly as in 10 mmol/l K+; again, the drop was less for SOL muscles. Adrenaline (0.5-10.0 mumol/l) enhanced both the c.v. and the twitch amplitude. The results support the suggestion that extracellular K+ accumulation during activity is an essential factor of muscle fatigue.     

Computer simulation for teaching membrane potential fundamentals

A computer simulation of membrane potential generation is presented. It allows the user to vary the intra and extracellular concentrations of sodium, potassium and chloride ions (Na⁺, K⁺ and Cl⁻), and determine the membrane potential and the equilibrium potential for each ion. The permeability coefficients for the ionic species considered, and the temperature may also be changed at will. Concentration-potential curves may be obtained at any time. The user may also select a voltage clamp option, which allows him to impose a certain membrane potential value, and study the resulting driving force for each ion. The use of the program in general physiology courses has shown it to be a useful aid for teaching the principles of membrane potential generation.     

A calculation of the magnetic field of a nerve action potential.

The magnetic field outside an isolated axon is calculated using transmembrane potential data to specify the boundary conditions to a solution of Laplace's equation. It is shown that the contribution to the magnetic field from the current inside the membrane is two orders of magnitude larger than that from the external current. The contribution from current within the membrane is negligible. Comparisons are made between waveforms calculated for a crayfish lateral axon and those measured for a frog sciatic nerve. This calculation suggests that the magnetic field measured outside nerves can be used to determine their internal current without puncturing the nerve membrane.