Membrane capacitive memory alters spiking in neurons described by the fractional-order Hodgkin-Huxley model.
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We find that in the membrane patch model, as fractional-order decreases, i.e., a greater influence of membrane potential memory, peak sodium and potassium currents are altered, and spike frequency and amplitude are generally reduced.In the nerve axon, the velocity of spike propagation increases as fractional-order decreases, while in a neural network, electrical activity is more likely to cease for smaller fractional-order.Importantly, we demonstrate that the modulation of the peak ionic currents that occurs for reduced fractional-order alone fails to reproduce many of the key alterations in spiking properties, suggesting that membrane capacitive memory and fractional-order membrane potential dynamics are important and necessary to reproduce neuronal electrical activity.
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Affiliation: Virginia Modeling, Analysis and Simulation Center, Old Dominion University, 1030 University Boulevard, Suffolk, Virginia, USA.
ABSTRACT
Excitable cells and cell membranes are often modeled by the simple yet elegant parallel resistor-capacitor circuit. However, studies have shown that the passive properties of membranes may be more appropriately modeled with a non-ideal capacitor, in which the current-voltage relationship is given by a fractional-order derivative. Fractional-order membrane potential dynamics introduce capacitive memory effects, i.e., dynamics are influenced by a weighted sum of the membrane potential prior history. However, it is not clear to what extent fractional-order dynamics may alter the properties of active excitable cells. In this study, we investigate the spiking properties of the neuronal membrane patch, nerve axon, and neural networks described by the fractional-order Hodgkin-Huxley neuron model. We find that in the membrane patch model, as fractional-order decreases, i.e., a greater influence of membrane potential memory, peak sodium and potassium currents are altered, and spike frequency and amplitude are generally reduced. In the nerve axon, the velocity of spike propagation increases as fractional-order decreases, while in a neural network, electrical activity is more likely to cease for smaller fractional-order. Importantly, we demonstrate that the modulation of the peak ionic currents that occurs for reduced fractional-order alone fails to reproduce many of the key alterations in spiking properties, suggesting that membrane capacitive memory and fractional-order membrane potential dynamics are important and necessary to reproduce neuronal electrical activity. No MeSH data available. Related in: MedlinePlus |
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Mentions: We next investigate the influence of fractional-order α on spike propagation during a constant stimulus, in which capacitive memory may alter propagation over successive spikes. In Fig 9A (top), we plot spike propagation velocity as a function of the spike number for different values of α and the applied current amplitude Iapp. In general, spike propagation velocity decreases as a function of the spike number, and in most cases, approaches an asymptotic value after 3–4 spikes. For a small value of Iapp (left), velocity decreases to a small extent as spike number increases, and this decrease is approximately the same for all values of α. We characterize this decrease by calculating the difference between the velocity for a given spike number and between the final (asymptotic) velocity, as a percentage of the final velocity (Fig 9A, bottom). This small change in velocity is due to the fact that, as in the membrane patch, spike frequency is small for small Iapp (Fig 6), such that the time between propagating spikes in the nerve axon is sufficiently long for sodium channel recovery (see Fig. D in S1 Text for further analysis of the relationship between spike frequency and propagation velocity). However, for α = 0.4, propagation fails after a single spike, since the sodium channel recovery is insufficient to maintain the fast propagation velocity over many spikes. |
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Affiliation: Virginia Modeling, Analysis and Simulation Center, Old Dominion University, 1030 University Boulevard, Suffolk, Virginia, USA.
No MeSH data available.