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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PubMed Central - PubMed
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: As in the previous section, we first investigate the properties of the passive membrane. The fractional-order passive cable equation is given by Eq 6 with the additional of a voltage diffusion term:Cmα∂αVm∂tα+1RmVm=g∂2Vm∂x2+I(x,t),(19)where g is a longitudinal cable conductance. Eq 19 can be written in standard form,τα∂αVm∂tα=λ2∂2Vm∂x2−Vm+RmI(x,t),(20)where time constant and space constant . The membrane potential Vm(x, t) can be determined byVm(x,t)=Rm∫0t∫−∞∞G(x−x′,t−t′)I(x′,t′)dx′dt′,(21)the convolution of the applied current I(x, t) and G(x, t), the impulse response, scaled by Rm. We solve for G(x, t) using an analytical-numerical approach using the Laplace-Fourier transform (see S1 Text), shown in Fig 7A and 7B. At early time points, for small α, G(x, t) is more “spread out” in space, while G(x, t) is less spread out at later time points (Fig 7A). At the site of the impulse (x = 0) and one length constant away (x = λ), the impulse is also more spread out in time for small α (Fig 7B). |
View Article: PubMed Central - PubMed
Affiliation: Virginia Modeling, Analysis and Simulation Center, Old Dominion University, 1030 University Boulevard, Suffolk, Virginia, USA.
No MeSH data available.