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     

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.     

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.     

Depth-resolved measurement of transient structural changes during action potential propagation

We report noncontact optical measurement of fast transient structural changes in the crustacean nerve during action potential propagation without the need for exogenous chemicals or reflection coatings. The technique, spectral domain optical coherence tomography, provides real-time cross-sectional images of the nerve with micron-scale resolution to select a specific region for functional assessment and interferometric phase sensitivity for subnanometer-scale motion detection. Noncontact optical measurements demonstrate nanometer-scale transient movement on a 1-ms timescale associated with action potential propagation in crayfish and lobster nerves.     

Cardiac dynamics: a simplified model for action potential propagation

This paper analyzes a new semiphysiological ionic model, used recently to study reexitations and reentry in cardiac tissue [I.R. Cantalapiedra et al, PRE 82 011907 (2010)]. The aim of the model is to reproduce action potencial morphologies and restitution curves obtained, either from experimental data, or from more complex electrophysiological models. The model divides all ion currents into four groups according to their function, thus resulting into fast-slow and inward-outward currents. We show that this simplified model is flexible enough as to accurately capture the electrical properties of cardiac myocytes, having the advantage of being less computational demanding than detailed electrophysiological models. Under some conditions, it has been shown to be amenable to mathematical analysis. The model reproduces the action potential (AP) change with stimulation rate observed both experimentally and in realistic models of healthy human and guinea pig myocytes (TNNP and LRd models, respectively). When simulated in a cable it also gives the right dependence of the conduction velocity (CV) with stimulation rate. Besides reproducing correctly these restitution properties, it also gives a good fit for the morphology of the AP, including the notch typical of phase 1. Finally, we perform simulations in a realistic geometric model of the rabbit’s ventricles, finding a good qualitative agreement in AP propagation and the ECG. Thus, this simplified model represents an alternative to more complex models when studying instabilities in wave propagation.     

Computer simulation of action potential propagation in septated nerve fibers.

The nonlinear, core-conductor model of action potential propagation down axisymmetric nerve fibers is adapted for an implicit, numerical simulation by computer solution of the differential equations. The calculation allows a septum to be inserted in the model fiber; the thin, passive septum is characterized by series resistance Rsz and shunt resistance Rss to the grounded bath. If Rsz is too large or Rss too small, the signal fails to propagate through the septum. Plots of the action potential profiles for various axial positions are obtained and show distortions due to the presence of the septum. A simple linear model, developed from these simulations, relates propagation delay through the septum and the preseptal risetime to Rsz and Rss. This model agrees with the simulations for a wide range of parameters and allows estimation of Rsz and Rss from measured propagation delays at the septum. Plots of the axial current as a function of both time and position demonstrate how the presence of the septum can cause prominent local reversals of the current. This result, not previously described, suggests that extracellular magnetic measurements of cellular action currents could be useful in the biophysical study of septated fibers.     

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.     

Fast pacing facilitates discontinuous action potential propagation between rabbit atrial cells

We examined the critical coupling conductance (G(C)) for propagation at different pacing cycle lengths (CLs) (1,000 and 400 ms). As G(C) was progressively reduced, propagation failed at a CL of 1,000 ms, whereas propagation succeeded at a CL of 400 ms over a range of G(C) values before failing at a CL of 400 ms at a lower G(C), showing facilitation of propagation at the shorter CL. Critical G(C) was (means +/- SE) 0.8 +/- 0.1 nS for a CL of 400 ms and 1.3 +/- 0.1 nS for a CL of 1,000 ms (a 63% increase, P < 0.002, n = 9 cell pairs). In 14 uncoupled cells, action potential duration at 30% repolarization (APD(30)) increased from 19.9 +/- 2.5 to 41.8 +/- 2.6 ms (P < 0.001) as CL decreased from 1,000 to 400 ms. In five cell pairs, critical G(C) with 4-aminopyridine (4-AP) was reduced to 0.4 +/- 0.1 nS at a CL of 1,000 ms (P < 0.05 compared with control solution), and critical G(C) in 4-AP was unchanged by decreasing CL to 400 ms. It is possible that the "remodeling" of atrial cells due to atrial fibrillation or tachycardia, which has been shown to produce a decrease in the transient outward current, may result in an enhanced ability to propagate, possibly facilitating further development of fibrillation under conditions of decreased cellular coupling.     

A model for thermal exchange in axons during action potential propagation

Several experiments have shown that during propagation of the action potential in axons, thermal energy is locally exchanged. In this paper, we use a simple model based on statistical physics to show that an important part of this exchange comes from the physics of the effusion. We evaluate, during the action potential propagation, the variation of internal energy and of the energy associated with the chemical potential of the effusion of water and ions to extract the thermal energy exchanged. The temperature exchanged is then evaluated on the area where the action potential is active. Results give a good correspondence between experimental work and this model, showing that an important part of the thermal energy exchange comes from the statistical cooling power of the effusion.     

Stochastic simulations on the reliability of action potential propagation in thin axons

It is generally assumed that axons use action potentials (APs) to transmit information fast and reliably to synapses. Yet, the reliability of transmission along fibers below 0.5 μm diameter, such as cortical and cerebellar axons, is unknown. Using detailed models of rodent cortical and squid axons and stochastic simulations, we show how conduction along such thin axons is affected by the probabilistic nature of voltage-gated ion channels (channel noise). We identify four distinct effects that corrupt propagating spike trains in thin axons: spikes were added, deleted, jittered, or split into groups depending upon the temporal pattern of spikes. Additional APs may appear spontaneously; however, APs in general seldom fail (<1%). Spike timing is jittered on the order of milliseconds over distances of millimeters, as conduction velocity fluctuates in two ways. First, variability in the number of Na channels opening in the early rising phase of the AP cause propagation speed to fluctuate gradually. Second, a novel mode of AP propagation (stochastic microsaltatory conduction), where the AP leaps ahead toward spontaneously formed clusters of open Na channels, produces random discrete jumps in spike time reliability. The combined effect of these two mechanisms depends on the pattern of spikes. Our results show that axonal variability is a general problem and should be taken into account when considering both neural coding and the reliability of synaptic transmission in densely connected cortical networks, where small synapses are typically innervated by thin axons. In contrast we find that thicker axons above 0.5 μm diameter are reliable.     

Influence of anisotropic conduction properties in the propagation of the cardiac action potential

Anisotropy, the property of being directionally dependent, is ubiquitous in nature. Propagation of the electrical impulse in cardiac tissue is anisotropic, a property that is determined by molecular, cellular, and histological determinants. The properties and spatial arrangement of connexin molecules, the cell size and geometry, and the fiber orientation and arrangement are examples of structural determinants of anisotropy. Anisotropy is not a static property but is subject to dynamic functional regulation, mediated by modulation of gap junctional conductance. Tissue repolarization is also anisotropic. The relevance of anisotropy extends beyond normal propagation and has important implications in pathological states, as a potential substrate for abnormal rhythms and reentry.     

Energetic aspects of the gliding mitility of mycoplasmas

This report reviews the question of whether mycoplasma gliding is an active form of surface translocation or a biased Brownian motion. The theoretical calculations presented here, along with recently described experimental observations, unequivocally prove that the motility of some mycoplasmas—at least, however, ofMycoplasma mobile—requires a cellular energy source. In an accompanying report we present further experimental evidence supporting this conclusion.     

Long-term activity-dependent plasticity of action potential propagation delay and amplitude in cortical networks

Background

The precise temporal control of neuronal action potentials is essential for regulating many brain functions. From the viewpoint of a neuron, the specific timings of afferent input from the action potentials of its synaptic partners determines whether or not and when that neuron will fire its own action potential. Tuning such input would provide a powerful mechanism to adjust neuron function and in turn, that of the brain. However, axonal plasticity of action potential timing is counter to conventional notions of stable propagation and to the dominant theories of activity-dependent plasticity focusing on synaptic efficacies.

Methodology/Principal Findings

Here we show the occurrence of activity-dependent plasticity of action potential propagation delays (up to 4 ms or 40% after minutes and 13 ms or 74% after hours) and amplitudes (up to 87%). We used a multi-electrode array to induce, detect, and track changes in propagation in multiple neurons while they adapted to different patterned stimuli in controlled neocortical networks in vitro. The changes did not occur when the same stimulation was repeated while blocking ionotropic gabaergic and glutamatergic receptors. Even though induction of changes in action potential timing and amplitude depended on synaptic transmission, the expression of these changes persisted in the presence of the synaptic receptor blockers.

Conclusions/Significance

We conclude that, along with changes in synaptic efficacy, propagation plasticity provides a cellular mechanism to tune neuronal network function in vitro and potentially learning and memory in the brain.     

Energetic aspects of spore germination in filamentous fungi

The antifungal activity of substances interfering with the function and biogenesis of mitochondria was studied. Strict anaerobiosis, cyanide, azide, oligomycin, bongkrekic acid and ethidium bromide were found to prevent spore germination ofAspergillus niger andPenicillium italicum in liquid germination medium. The effect of azide, oligomycin and ethidium bromide was fungicidal. Cyanide and azide completely inhibited the incorporation of¹⁴C-leucine and¹⁴C-uracil into germinating conidia ofA. niger. Oligomycin and ethidium bromide reduced the extent of incorporation of both precursors in the first few hours of conidial germination and at later stages stopped it completely. The inhibition of both spore germination and macromolecules synthesis during the germination ofA. niger conidia were in relation to the specific inhibitory effect of the agents on respiratory activity of dormant conidia and mycelial cells. The results indicate that both the function of mitochondrial genetic and protein synthesizing systems and the function of oxidative phosphorylation are essential for normal spore germination and fungal growth.     

Energetic aspects of CO oxidation in desulfovibrio desulfuricans

In cell suspension of Desulfovibrio desulfuricans B-1388, oxidation of CO as the only energy source is associated with reduction of SO42-. After a 2-h incubation of cells in 8% CO, 81% of the gas is converted. Oxidation of 1 mole CO results in formation of 0.23 mole H2S. Intracellular ATP content increases from 2.5 (control) to 8.3 nmoles/mg (during CO conversion). Dinitrophenol inhibits sulfate reduction and CO oxidation. CO dehydrogenase was detected in cytoplasmic and membrane cell fractions (59 and 34%, respectively).     

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.     

Radial propagation of muscle action potential along the tubular system examined by potential-sensitive dyes

Isolated single (Xenopus) muscle fibers were stained with a non-permeant potential-probing dye, merocyanine rhodanine (WW375) or merocyanine oxazolone (NK2367). When the fiber was massively stimulated, an absorption change (wave a), which seemed to reflect the action potential, occurred. Simultaneous recording of optical changes and intracellular action potentials revealed that the time-course of wave a was slower than the action potential: the peak of wave a was attained at 1 ms, and the peak of action potential was reached at 0.5 ms after the stimulation. This difference suggests that wave a represents the potential changes of the whole tubular membrane and the surface membrane, whereas the action potential represents a surface potential change. This idea was substantiated by recording absorption signals preferentially from the surface membrane by recording the absorption changes at the edge of the fiber. Wave a obtained by this method was as quick as the intracellular action potential. The value of radial conduction velocity of action potential along the T system, calculated by comparing the action potential with wave a, was 6.4 cm/s at 24.5 degrees C, in fair agreement with González-Serratos (1971. J. Physiol. [Lond.]. 212:777-799). The shape of wave a suggests the existence of an access delay (a conduction delay at the orifice of the T system) of 130 microseconds.