Mathematical Modeling of Subthreshold Resonant Properties in Pyloric Dilator Neurons

Abstract

Various types of neurons exhibit subthreshold resonance oscillation (preferred frequency response) to fluctuating sinusoidal input currents. This phenomenon is well known to influence the synaptic plasticity and frequency of neural network oscillation. This study evaluates the resonant properties of pacemaker pyloric dilator (PD) neurons in the central pattern generator network through mathematical modeling. From the pharmacological point of view, calcium currents cannot be blocked in PD neurons without removing the calcium-dependent potassium current. Thus, the effects of calcium (I Ca) and calcium-dependent potassium (I KCa) currents on resonant properties remain unclear. By taking advantage of Hodgkin-Huxley-type model of neuron and its equivalent RLC circuit, we examine the effects of changing resting membrane potential and those ionic currents on the resonance. Results show that changing the resting membrane potential influences the amplitude and frequency of resonance so that the strength of resonance (Q-value) increases by both depolarization and hyperpolarization of the resting membrane potential. Moreover, hyperpolarization-activated inward current (I h) and I Ca (in association with I KCa) are dominant factors on resonant properties at hyperpolarized and depolarized potentials, respectively. Through mathematical analysis, results indicate that I h and I KCa affect the resonant properties of PD neurons. However, I Ca only has an amplifying effect on the resonance amplitude of these neurons.

Dynamical Mechanism of Hyperpolarization-Activated Non-specific Cation Current Induced Resonance and Spike-Timing Precision in a Neuronal Model

“…Compared with many experimental and simulation results (Zemankovics et al, 2010 ; Gastrein et al, 2011 ; Pavlov et al, 2011 ) of the subthreshold resonance and precise spike-timing induced by I h , there are much less theoretical investigations (Rotstein, 2015 ; Vazifehkhah et al, 2015 ) to explain the corresponding dynamical mechanism. It is well known that neuron is a nonlinear dynamical system which can be described by the differential equations, and bifurcation analysis has been identified as an effective method to identify the dynamical mechanism of the electrophysiological properties of neurons.…”

“…Furthermore, the experimental studies found that I h can induce subthreshold membrane resonance and enhance spike-timing precision characterized by the standard deviation ( STD ) or coefficient variation ( CV ) of the interspike intervals (ISIs) (Zemankovics et al, 2010 ; Gastrein et al, 2011 ; Pavlov et al, 2011 ; Borel et al, 2013 ; Gonzalez et al, 2015 ). Resonance means that impedance profile of a neuron to external stimulus reaches a maximal value at a certain value corresponding to an intrinsic frequency preference (Rotstein, 2015 ; Vazifehkhah et al, 2015 ), which is an important factor related to the rhythmic oscillations (Gasparini and DiFrancesco, 1997 ; Hutcheon and Yarom, 2000 ; Giocomo et al, 2007 ; Moca et al, 2014 ; Gonzalez et al, 2015 ). For example, hippocampal pyramidal neurons (Hu et al, 2002 ; Zemankovics et al, 2010 ; Gastrein et al, 2011 ; Borel et al, 2013 ) exhibit subthreshold resonance to the injection of sinusoidal current, and their resonant properties contribute to the emergence of Theta oscillations (Zemankovics et al, 2010 ; Stark et al, 2013 ).…”

“…In addition to these experimental studies, the roles of I h on the modulation of the neuronal electrophysiological activities, such as the membrane subthreshold resonance and spike-timing precision, have also been simulated in the theoretical models. The influences of the types of neurons, the different resonant currents, and the factors of I h on the subthreshold resonance have been investigated in the theoretical models (Zemankovics et al, 2010 ; Rotstein and Nadim, 2014 ; Vazifehkhah et al, 2015 ; Fox et al, 2017 ; Pena et al, 2017 ). For instance, some researchers suggested that the cell-type (pyramidal cells and interneurons) specificity of the impedance or resonance profiles in the hippocampal CA1 neurons maybe explained by the properties of I h combined with the passive membrane characteristics in a conductance-based theoretical model (Zemankovics et al, 2010 ).…”

“…For instance, some researchers suggested that the cell-type (pyramidal cells and interneurons) specificity of the impedance or resonance profiles in the hippocampal CA1 neurons maybe explained by the properties of I h combined with the passive membrane characteristics in a conductance-based theoretical model (Zemankovics et al, 2010 ). Investigations on the subthreshold resonance in theoretical models of the Pyloric Dilator neurons of the crab pyloric network found that I h and calcium current are the dominant factors to induce the resonant properties at hyperpolarized and depolarized potentials, respectively (Vazifehkhah et al, 2015 ; Fox et al, 2017 ). I h and slow potassium current were identified to play different roles in the generation of resonance (Rotstein and Nadim, 2014 ).…”

Mechanism and Applications of Electrical Stimulation Disturbance on Motoneuron Excitability Studied Using Flexible Intramuscular Electrode

“…Figure 5 A1 shows the circuit model to simulate voltage waveforms in response to electrical stimulation delivered by small‐distance stimulation electrodes. In this circuit model, motoneurons are represented by RLC (resistor, inductor, and capacitor) components (green blocks P1–P4 in Figure A1). Muscle fibers are represented by RC (resistor and capacitor) components (blue blocks in Figure A1).…”