A ghostbursting model is a mathematical model (a system of coupled nonlinear ordinary differential equations) that is based on the Hodgkin-Huxley formalism. The ghostbursting model describes bursting similar to the in...A ghostbursting model is a mathematical model (a system of coupled nonlinear ordinary differential equations) that is based on the Hodgkin-Huxley formalism. The ghostbursting model describes bursting similar to the in vitro bursting of electrosensory neurons of weakly electric fish. Doiron and coworkers have focused on two system parameters of the model: maximal conductance of the dendritic potassium current and the current injected into the somatic compartment . They performed bifurcation analysis and revealed that the -parameter space was divided into three dynamical states: quiescence, periodic tonic spiking, and bursting. The present study focused on a third system parameter: the time constant of dendritic potassium current inactivation . A computer simulation of the model revealed how the dynamical states of the -parameter space changed in response to variations of .展开更多
Sim and Forger have proposed a mathematical model of circadian pacemaker neurons in the suprachiasmatic nucleus (SCN). This model, which has been formulated on the Hodgkin-Huxley mo-del, is described by a system of no...Sim and Forger have proposed a mathematical model of circadian pacemaker neurons in the suprachiasmatic nucleus (SCN). This model, which has been formulated on the Hodgkin-Huxley mo-del, is described by a system of nonlinear ordinary differential equations. An important feature of the SCN neurons observed in electrophysiological recording is spontaneous repetitive spiking, which is reproduced using this model. In the present study, numerical simulation analysis of this model was performed to evaluate variations in two system parameters of this model: the maximal conductance of calcium current (gCa) and the maximal conductance of sodium current (gNa). Simulation results revealed the spontaneous repetitive spiking states of the model in the (gCa, gNa)-pa-rameter space.展开更多
A mathematical model of vibrissa motoneurons (vMN), which has been developed by Harish and Golomb, can show repetitive spiking in response to a transient external stimulation. The vMN model is described by a system of...A mathematical model of vibrissa motoneurons (vMN), which has been developed by Harish and Golomb, can show repetitive spiking in response to a transient external stimulation. The vMN model is described by a system of nonlinear ordinary differential equations based on the Hodgkin-Huxley scheme. The vMN model is regulated by various types of ionic conductances, such as persistent sodium, transient sodium, delayed-rectifier potassium, and slow ionic conductances (e.g., slowly activating potassium afterhyperpolarization (AHP) conductance and h conductance). In the present study, a numerical simulation analysis of the vMN model was performed to investigate the effect of variations in the transient sodium and the slow ionic conductance values on the response of the vMN model to a transient external stimulation. Numerical simulations revealed that when both the transient sodium and the AHP conductances are eliminated, the vMN model shows a bistable behavior (i.e., a stimulation-triggered transition between dynamic states). In contrast, none of the following induce the transition alone: 1) elimination of the transient sodium conductance;2) elimination of the AHP conductance;3) elimination of the h conductance;or 4) elimination of both the transient sodium and the h conductances.展开更多
A previous study has proposed a mathematical model of type-A medial vestibular nucleus neurons (mVNn). This model is described by a system of nonlinear ordinary differential equations, which is based on the Hodgkin-Hu...A previous study has proposed a mathematical model of type-A medial vestibular nucleus neurons (mVNn). This model is described by a system of nonlinear ordinary differential equations, which is based on the Hodgkin-Huxley formalism. The type-A mVNn model contains several ionic conductances, such as the sodium conductance, calcium conductance, delayed-rectifier potassium conductance, transient potassium conductance, and calcium-dependent potassium conductance. The previous study revealed that spontaneous repetitive spiking in the type-A mVNn model can be suppressed by hyperpolarizing stimulation. However, how this suppression is affected by the ionic conductances has not been clarified in the previous study. The present study performed numerical simulation analysis of the type-A mVNn model to clarify how variations in the different ionic conductance values affect the suppression of repetitive spiking. The present study revealed that the threshold for the transition from a repetitive spiking state to a quiescent state is differentially sensitive to variations in the ionic conductances among the different types of ionic conductance.展开更多
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...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.展开更多
Stern et al. have developed a mathematical model describing pseudo-plateau bursting of pituitary cells. This model is formulated based on the Hodgkin-Huxley scheme and described by a system of nonlinear ordinary diffe...Stern et al. have developed a mathematical model describing pseudo-plateau bursting of pituitary cells. This model is formulated based on the Hodgkin-Huxley scheme and described by a system of nonlinear ordinary differential equations. In the present study, computer simulation analysis of this model was performed to evaluate the correlation between the dynamic states of the model and two system parameters: long-lasting external stimulation (Iapp) and the time constant of delayed-rectifier potassium conductance activation (τn). Computer simulation results revealed that the model showed four different dynamic states: a hyperpolarized steady state, a depolarized steady state, a repetitive spiking state, and a bursting state. An increase in Iapp changed the dynamic states from the hyperpolarized steady state to bursting state to depolarized steady state when τn was fixed at smaller values, whereas it changed the dynamic states from the hyperpolarized steady state to bursting state to repetitive spiking state when τn was fixed at larger values. An increase in τn 1) did not change the dynamic states when Iapp was fixed at a very small value, 2) changed the dynamic states from the depolarized steady state to repetitive spiking state when Iapp was fixed at a very large value, and 3) changed the dynamic states from the depolarized steady state to bursting state to repetitive spiking state when Iapp was fixed at an intermediate value.展开更多
A previous study proposed a mathematical model of A-type horizontal cells in the rabbit retina. This model, which was constructed based on the Hodgkin-Huxley model, was described by a system of nonlinear ordinary diff...A previous study proposed a mathematical model of A-type horizontal cells in the rabbit retina. This model, which was constructed based on the Hodgkin-Huxley model, was described by a system of nonlinear ordinary differential equations. The model contained five types of voltage-dependent ionic conductances: sodium, calcium, delayed rectifier potassium, transient outward potassium, and anomalous rectifier potassium conductances. The previous study indicated that when the delayed rectifier potassium conductance had a small value, depolarizing stimulation could change the dynamic state of the model from a hyperpolarized steady state to a depolarized steady state. However, how this change was affected by variations in the ionic conductance values was not clarified in detail in the previous study. To clarify this issue, in the present study, we performed numerical simulation analysis of the model and revealed the differences among the five types of ionic conductances.展开更多
文摘A ghostbursting model is a mathematical model (a system of coupled nonlinear ordinary differential equations) that is based on the Hodgkin-Huxley formalism. The ghostbursting model describes bursting similar to the in vitro bursting of electrosensory neurons of weakly electric fish. Doiron and coworkers have focused on two system parameters of the model: maximal conductance of the dendritic potassium current and the current injected into the somatic compartment . They performed bifurcation analysis and revealed that the -parameter space was divided into three dynamical states: quiescence, periodic tonic spiking, and bursting. The present study focused on a third system parameter: the time constant of dendritic potassium current inactivation . A computer simulation of the model revealed how the dynamical states of the -parameter space changed in response to variations of .
文摘Sim and Forger have proposed a mathematical model of circadian pacemaker neurons in the suprachiasmatic nucleus (SCN). This model, which has been formulated on the Hodgkin-Huxley mo-del, is described by a system of nonlinear ordinary differential equations. An important feature of the SCN neurons observed in electrophysiological recording is spontaneous repetitive spiking, which is reproduced using this model. In the present study, numerical simulation analysis of this model was performed to evaluate variations in two system parameters of this model: the maximal conductance of calcium current (gCa) and the maximal conductance of sodium current (gNa). Simulation results revealed the spontaneous repetitive spiking states of the model in the (gCa, gNa)-pa-rameter space.
文摘A mathematical model of vibrissa motoneurons (vMN), which has been developed by Harish and Golomb, can show repetitive spiking in response to a transient external stimulation. The vMN model is described by a system of nonlinear ordinary differential equations based on the Hodgkin-Huxley scheme. The vMN model is regulated by various types of ionic conductances, such as persistent sodium, transient sodium, delayed-rectifier potassium, and slow ionic conductances (e.g., slowly activating potassium afterhyperpolarization (AHP) conductance and h conductance). In the present study, a numerical simulation analysis of the vMN model was performed to investigate the effect of variations in the transient sodium and the slow ionic conductance values on the response of the vMN model to a transient external stimulation. Numerical simulations revealed that when both the transient sodium and the AHP conductances are eliminated, the vMN model shows a bistable behavior (i.e., a stimulation-triggered transition between dynamic states). In contrast, none of the following induce the transition alone: 1) elimination of the transient sodium conductance;2) elimination of the AHP conductance;3) elimination of the h conductance;or 4) elimination of both the transient sodium and the h conductances.
文摘A previous study has proposed a mathematical model of type-A medial vestibular nucleus neurons (mVNn). This model is described by a system of nonlinear ordinary differential equations, which is based on the Hodgkin-Huxley formalism. The type-A mVNn model contains several ionic conductances, such as the sodium conductance, calcium conductance, delayed-rectifier potassium conductance, transient potassium conductance, and calcium-dependent potassium conductance. The previous study revealed that spontaneous repetitive spiking in the type-A mVNn model can be suppressed by hyperpolarizing stimulation. However, how this suppression is affected by the ionic conductances has not been clarified in the previous study. The present study performed numerical simulation analysis of the type-A mVNn model to clarify how variations in the different ionic conductance values affect the suppression of repetitive spiking. The present study revealed that the threshold for the transition from a repetitive spiking state to a quiescent state is differentially sensitive to variations in the ionic conductances among the different types of ionic conductance.
文摘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.
文摘Stern et al. have developed a mathematical model describing pseudo-plateau bursting of pituitary cells. This model is formulated based on the Hodgkin-Huxley scheme and described by a system of nonlinear ordinary differential equations. In the present study, computer simulation analysis of this model was performed to evaluate the correlation between the dynamic states of the model and two system parameters: long-lasting external stimulation (Iapp) and the time constant of delayed-rectifier potassium conductance activation (τn). Computer simulation results revealed that the model showed four different dynamic states: a hyperpolarized steady state, a depolarized steady state, a repetitive spiking state, and a bursting state. An increase in Iapp changed the dynamic states from the hyperpolarized steady state to bursting state to depolarized steady state when τn was fixed at smaller values, whereas it changed the dynamic states from the hyperpolarized steady state to bursting state to repetitive spiking state when τn was fixed at larger values. An increase in τn 1) did not change the dynamic states when Iapp was fixed at a very small value, 2) changed the dynamic states from the depolarized steady state to repetitive spiking state when Iapp was fixed at a very large value, and 3) changed the dynamic states from the depolarized steady state to bursting state to repetitive spiking state when Iapp was fixed at an intermediate value.
文摘A previous study proposed a mathematical model of A-type horizontal cells in the rabbit retina. This model, which was constructed based on the Hodgkin-Huxley model, was described by a system of nonlinear ordinary differential equations. The model contained five types of voltage-dependent ionic conductances: sodium, calcium, delayed rectifier potassium, transient outward potassium, and anomalous rectifier potassium conductances. The previous study indicated that when the delayed rectifier potassium conductance had a small value, depolarizing stimulation could change the dynamic state of the model from a hyperpolarized steady state to a depolarized steady state. However, how this change was affected by variations in the ionic conductance values was not clarified in detail in the previous study. To clarify this issue, in the present study, we performed numerical simulation analysis of the model and revealed the differences among the five types of ionic conductances.
