Related papers: Stability analysis of action potential generation …
The physiology of voltage gated ion channels is complex and insights into their gating mechanism is incomplete. Their function is best represented by Markov models with relatively large number of distinct states that are connected by…
The stochastic opening and closing of voltage-gated ion channels produces noise in neurons. The effect of this noise on the neuronal performance has been modelled using either approximate or Langevin model, based on stochastic differential…
Voltage-gated sodium (Na$_\mathrm{v}$) channels are responsible for the depolarizing phase of the action potential in most nerve cells, and Na$_\mathrm{v}$ channel localization to the axon initial segment is vital to action potential…
Neuronal excitability is the phenomena that describes action potential generation due to a stimulus input. Commonly, neuronal excitability is divided into two classes: Type I and Type II, both having different properties that affect…
The action potential in a neural membrane is generated by Na+ and K+ channel ionic currents that may be calculated from a current equation and the rate equations for activation variables m and n, and the Na+ inactivation variable h.…
This paper presents in-depth analysis of the excitable membranes of a biological system. We rigorously prove from the Chay neuron model that the state dependent voltage-sensitive potassium ion-channel and calcium sensitive potassium…
In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. In this first paper, we construct…
Neuronal cells present periodic trains of localized voltage spikes involving a large amount of different ionic channels. A relevant question is whether this is a cooperative effect or it could also be an intrinsic property of individual…
A fifteen state kinetic model for Na+ channel gating that describes the coupling between three activation sensors, a two-stage fast inactivation process and slow inactivated states, may be reduced to equations for a six state system by…
In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. We seek to study these dynamics…
Noise induced excitability is studied in type I and II Morris-Lecar neurons subject to constant sub threshold input, where fluctuations arise from sodium and potassium ion channels. Ion channels open and close randomly, creating current…
To preserve strictly conservative behavior as well as model the variety of dissipative behavior displayed by solid materials, we propose a significant enhancement to the internal state variable-neural ordinary differential equation…
In this work we have theoretically investigated how the action potential generation and its associated intrinsic properties are affected in presence of ion channel blockers by adapting Gillepie's stochastic simulation technique on a very…
Many ion channels spontaneously switch between different levels of activity. Although this behaviour known as modal gating has been observed for a long time it is currently not well understood. Despite the fact that appropriately…
Dravet syndrome is a developmental and epileptic encephalopathy, characterized by the early onset of drug-resistant seizures and various comorbidities. Most cases of this severe and complex pathology are due to mutations of NaV1.1, a sodium…
Excitability is an attribute of life, and is a driving force in the descent of complexity. Cellular electrical activity as realized by membrane proteins that act as either channels or transporters is the basis of excitability. Electrical…
Stochastic Resonance in single voltage-dependent ion channels is investigated within a three state non-Markovian modeling of the ion channel conformational dynamics. In contrast to a two-state description one assumes the presence of an…
We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that…
We consider a stochastic version of an excitable system based on the Morris-Lecar model of a neuron, in which the noise originates from stochastic Sodium and Potassium ion channels opening and closing. One can analyze neural excitability in…
The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation…