Ion channel density and threshold dynamics of repetitive firing in a cortical neuron model

Biosystems ◽  
2007 ◽  
Vol 89 (1-3) ◽  
pp. 117-125 ◽  
Author(s):  
Peter Århem ◽  
Clas Blomberg
2006 ◽  
Vol 90 (12) ◽  
pp. 4392-4404 ◽  
Author(s):  
P. Århem ◽  
G. Klement ◽  
C. Blomberg

2003 ◽  
Vol 13 (12) ◽  
pp. 3827-3834
Author(s):  
ROBERT HINCH

Wolff–Parkinson–White syndrome is a disease where an arrhythmia is caused by the ventricles being electrically excited by an additional accessory pathway that links the atria to the ventricles. The spread of the activation wave from this pathway to the ventricles is modeled using a simplified model of Hodgkin–Huxley sodium channel kinetics, in a two ion-channel model. The model is investigated both analytically (using an asymptotic analysis) and numerically, and both methods are shown to give the same result. It is found that for a given width of the accessory pathway, there is a critical sodium channel density needed for the activation wave to spread from the pathway to the tissue. This result provides an explanation for the success of class-I anti-arrhythmic drugs in treating Wolff–Parkinson–White syndrome.


2015 ◽  
Vol 113 (2) ◽  
pp. 537-549 ◽  
Author(s):  
Hugo Zeberg ◽  
Hugh P. C. Robinson ◽  
Peter Århem

Several types of intrinsic dynamics have been identified in brain neurons. Type 1 excitability is characterized by a continuous frequency-stimulus relationship and, thus, an arbitrarily low frequency at threshold current. Conversely, Type 2 excitability is characterized by a discontinuous frequency-stimulus relationship and a nonzero threshold frequency. In previous theoretical work we showed that the density of Kv channels is a bifurcation parameter, such that increasing the Kv channel density in a neuron model transforms Type 1 excitability into Type 2 excitability. Here we test this finding experimentally, using the dynamic clamp technique on Type 1 pyramidal cells in rat cortex. We found that increasing the density of slow Kv channels leads to a shift from Type 1 to Type 2 threshold dynamics, i.e., a distinct onset frequency, subthreshold oscillations, and reduced latency to first spike. In addition, the action potential was resculptured, with a narrower spike width and more pronounced afterhyperpolarization. All changes could be captured with a two-dimensional model. It may seem paradoxical that an increase in slow K channel density can lead to a higher threshold firing frequency; however, this can be explained in terms of bifurcation theory. In contrast to previous work, we argue that an increased outward current leads to a change in dynamics in these neurons without a rectification of the current-voltage curve. These results demonstrate that the behavior of neurons is determined by the global interactions of their dynamical elements and not necessarily simply by individual types of ion channels.


2020 ◽  
pp. 2150035
Author(s):  
Marifi Güler

A stochastic differential formulation for the collective dynamics of ion channel clusters in excitable membranes is developed from the so-called “reduced strong diffusion formulation”. In this error bound optimizing reduced formulation, the potassium channel states [Formula: see text] and [Formula: see text], and, the sodium channel states [Formula: see text] and [Formula: see text] are the retained states; consequently, the formulation accommodates only four channel variables and five white noises. The accuracy of the formulation is tested over the standard deviations and autocorrelation times of the channel density fluctuations. The findings are seen to be virtually identical to the corresponding results from the exact microscopic Markov simulations. The formulation arises as the most accurate model with that structural simplicity, thus making it an important model for both analytic analyses and numerical simulations in the study of finite-sized membranes.


1989 ◽  
Vol 257 (6) ◽  
pp. R1354-R1358 ◽  
Author(s):  
R. A. Edwards ◽  
P. L. Lutz ◽  
D. G. Baden

Synaptosomes were isolated from turtle and rat brains to determine whether differences in brain ion channel densities accounted for the turtle's ability to survive anoxia compared with the mammal. The Na(+)-channel binding neurotoxin brevetoxin showed high-affinity specific binding in both turtle and rat synaptosomes, suggesting specific ligand-receptor interaction. The maximum binding capacity (Bmax) value for the turtle was only about one-third of that found for the rat synaptosomes, suggesting that the turtle synaptosome has a correspondingly lower Na+ channel density than the rat. This apparent difference in Na+ channel density is not reflected in metabolic rates, since at the same temperature (31 degrees C) the O2 consumption of both the rat and turtle synaptosome was almost identical. The large reductions in energy expenditure seen in synaptosomes incubated in Na(+)-free media and in media containing ouabain (approximately 50% turtle, 80% rat) are probably related to the halting of transmembrane Na(+)-K+ exchange. The greater reduction in the rat may be related to the apparent greater density of Na+ channels in the rat brain. However, compared with the 90% reduction in brain metabolism that occurs when the turtle brain becomes anoxic, the differences in ion channel density and in the costs of ion pumping between the rat and turtle brain are trivial. Closing Na+ channels with tetrodotoxin and increasing Na+ channel activation with veratridine caused substantial decreases and increases in synaptosome energy consumption, respectively. This suggests that the modulation of ion channel conductance has a significant effect on metabolic cost and may be an important mechanism to reduce energy consumption and electrical activity in the anoxic turtle brain, while still maintaining ionic gradients.


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