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Membrane capacitive memory alters spiking in neurons described by the fractional-order Hodgkin-Huxley model.

Weinberg SH - PLoS ONE (2015)

Bottom Line: 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.

View Article: 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

Repetitive firing in the fractional-order Hodgkin-Huxley model.(A) The membrane potential Vm, sodium current INa, potassium current IK, and voltage memory trace vmem are shown as a function of time in response to a constant applied current, Iapp = 20 (left), 100 (middle), and 140 (right) μA/cm2, for different values of fractional-order α. (B) The instantaneous spike frequency is shown as a function of the interspike interval (ISI) number for different values of α.
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pone.0126629.g004: Repetitive firing in the fractional-order Hodgkin-Huxley model.(A) The membrane potential Vm, sodium current INa, potassium current IK, and voltage memory trace vmem are shown as a function of time in response to a constant applied current, Iapp = 20 (left), 100 (middle), and 140 (right) μA/cm2, for different values of fractional-order α. (B) The instantaneous spike frequency is shown as a function of the interspike interval (ISI) number for different values of α.

Mentions: It is well-established in the classical Hodgkin-Huxley model (i.e., α = 1), the neuron will repetitively fire or spike in response to a constant applied stimulus Iapp ∈ [I1, I2], where I1 and I2 represent critical values discussed below [23]. We next investigate to what extent fractional-order α alters the properties of repetitive firing for a constant stimulus. We show the membrane potential Vm, ionic currents INa and IK, and voltage memory trace vmem as functions of time for a constant applied current, for different values of Iapp and α, during a 100-ms duration simulation (Fig 4A).


Membrane capacitive memory alters spiking in neurons described by the fractional-order Hodgkin-Huxley model.

Weinberg SH - PLoS ONE (2015)

Repetitive firing in the fractional-order Hodgkin-Huxley model.(A) The membrane potential Vm, sodium current INa, potassium current IK, and voltage memory trace vmem are shown as a function of time in response to a constant applied current, Iapp = 20 (left), 100 (middle), and 140 (right) μA/cm2, for different values of fractional-order α. (B) The instantaneous spike frequency is shown as a function of the interspike interval (ISI) number for different values of α.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4430543&req=5

pone.0126629.g004: Repetitive firing in the fractional-order Hodgkin-Huxley model.(A) The membrane potential Vm, sodium current INa, potassium current IK, and voltage memory trace vmem are shown as a function of time in response to a constant applied current, Iapp = 20 (left), 100 (middle), and 140 (right) μA/cm2, for different values of fractional-order α. (B) The instantaneous spike frequency is shown as a function of the interspike interval (ISI) number for different values of α.
Mentions: It is well-established in the classical Hodgkin-Huxley model (i.e., α = 1), the neuron will repetitively fire or spike in response to a constant applied stimulus Iapp ∈ [I1, I2], where I1 and I2 represent critical values discussed below [23]. We next investigate to what extent fractional-order α alters the properties of repetitive firing for a constant stimulus. We show the membrane potential Vm, ionic currents INa and IK, and voltage memory trace vmem as functions of time for a constant applied current, for different values of Iapp and α, during a 100-ms duration simulation (Fig 4A).

Bottom Line: 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.

View Article: 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