Spiking efficiency of electrically stimulated pyramidal cells: a modeling study

Abstract

During electrical stimulation of the pyramidal cell (PC), the spiking efficiency increases from 0 to 1 at the lower threshold and decreases from 1 to 0 at the upper threshold as the stimulus amplitude increases. Spiking efficiency as a function of stimulus amplitude follows a sigmoidal or reverse sigmoidal shape, respectively.Many modeling studies examine the threshold and origin of spike i.e., action potential (AP) initiation in PCs in relation to different positions and configurations of the stimulation electrode using deterministic models in which the spiking efficiency as a function of the stimulus amplitude reduces to the step function. Fewer studies deal with modeling that includes a stochastic component in the model. Here, this was achieved by injecting a maximum-sodium-conductance-dependent noise current into each compartment with an active membrane. The spiking efficiency was examined in relation to different positions and configurations of the stimulation electrode, where the threshold and origin of AP initiation were observed, and the geometric and electrophysiological properties of the model were changed. Dynamic range (DR) and relative spread (RS) were used to measure the increase in spiking efficiency with a stimulus intensity. A simplified geometry of the PC was used, with two basic electrophysiological configurations. The first is a standard model that contains three voltage gated active channels: high-threshold 〖Na〗_v 1.2 and low-threshold 〖Na〗_v 1.6 sodium and fast K_v potassium channels. The second is an extended model that additionally contains two potassium channels, slow non-inactivating potassium current K_m and calcium dependent K_Ca, then high-voltage activated 〖Ca〗_v channel and internal calcium concentration mechanism 〖Ca〗_cm.The following can be concluded from the simulation experiments in this thesis. In general, a larger DR is expected by stimulating more excitable parts of the PC, with a few exceptions. It seems that when stimulating highly excitable parts of the PC, there is a competition between responsiveness and noisiness, which can reduce DR. DR is the largest between the unmyelinated axon and the first node of Ranvier, and the smallest at the dendrite. In addition to the geometric and electrophysiological properties of the cell, the activating function and the origin of AP initiation should also be considered for the prediction of DR. Additional channels in the extended model have almost no effect on the threshold, and a slightly larger, but still small, effect on the DR.