Abstract
Electrosensory pyramidal neurons in weakly electric fish can generate burst firing. Based on the Hodgkin-Huxley scheme, a previous study has developed a mathematical model that reproduces this burst firing. This model is called the ghostbursting model and is described by a system of non-linear ordinary differential equations. Although the dynamic state of this model is a quiescent state during low levels of electrical stimulation, an increase in the level of electrical stimulation transforms the dynamic state first into a repetitive spiking state and finally into a burst firing state. The present study performed computer simulation analysis of the ghostbursting model to evaluate the sensitivity of the three dynamic states of the model (i.e., the quiescent, repetitive spiking, and burst firing states) to variations in sodium and potassium conductance values of the model. The present numerical simulation analysis revealed the sensitivity of the electrical stimulation threshold required for eliciting the burst firing state to variations in the values of four ionic conductances (i.e., somatic sodium, dendritic sodium, somatic potassium, and dendritic potassium conductances) in the ghostbursting model.
Highlights
The ghostbursting model is a mathematical model of electrosensory pyramidal neurons in weakly electric fish, How to cite this paper: Shirahata, T. (2016) The Relationship of Sodium and Potassium Conductances with Dynamic States of a Mathematical Model of Electrosensory Pyramidal Neurons
The ghostbursting model used in this study is described by a system of Ordinary Differential Equations (ODEs), which consists of six state variables: the membrane potential of the somatic compartment [Vs(t)] [t is time], the activating variable of the potassium conductance of the somatic compartment [ns(t)], the membrane potential of the dendritic compartment [Vd(t)], the inactivating variable of the sodium conductance of the dendritic compartment [hd(t)], the activating variable of the potassium conductance of the dendritic compartment [nd(t)], and the inactivating variable of the potassium conductance of the dendritic compartment [pd(t)]
The repetitive spiking threshold (Is = 5.8) increased to 6.0 when gNa,d decreased to 95% but did not change when gNa,d increased to 105% [Figure 1(b)]
Summary
The ghostbursting model is a mathematical model of electrosensory pyramidal neurons in weakly electric fish, How to cite this paper: Shirahata, T. (2016) The Relationship of Sodium and Potassium Conductances with Dynamic States of a Mathematical Model of Electrosensory Pyramidal Neurons. Shirahata which is described by a system of nonlinear Ordinary Differential Equations (ODEs) (see Methods in [1]) This model is based on the Hodgkin-Huxley formalism and describes the time evolution of the membrane potentials of the somatic and dendritic compartments of the model. This model contains many parameters such as electrical stimulation and ionic conductances (i.e., sodium and potassium conductances), and previous studies have revealed the relationship of the dynamic states of the model with variations in parameter values. Results from these previous studies highlight the importance of extending these investigations to studies of the sensitivity of the dynamics of the ghostbursting model to parameter variations, focusing on detailed analysis of the membrane conductance ([5] and page 26 in [6])
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call