Fast-slow asymptotics for a Markov chain model of fast sodium current

The link model is a fundamental pharmacokinetic-pharmacodynamic (PK–PD) approach to account for delayed drug responses when the observed effect does not immediately correlate with the drug's plasma concentration peak. This delay is mathematically addressed by introducing an effect compartment concentration, Ce, which is kinetically linked to the plasma concentration, Cp, via a first-order rate constant, ke0. The linkage allows for a more accurate prediction of drug effects over time. A...

Ion channels are specialized proteins on the plasma membrane that allow charged ions to pass down their electrochemical gradient. Their main function is to maintain the membrane potential which is critical for cell viability. These channels are either gated or non-gated and can transport more than a thousand ions within milliseconds for the cellular event to occur.
Compared to the gated ion channels, the non-gated channels, also known as leakage or passive channels, have no gating mechanism....

A postsynaptic neuron usually receives numerous impulses from several other presynaptic neurons. The axon hillock of the postsynaptic neuron integrates all these signals and determines the likelihood of firing an action potential.
Sometimes a single EPSP is strong enough to induce an action potential in the postsynaptic neuron. However, multiple presynaptic inputs must often create EPSPs around the same time for the postsynaptic neuron to be sufficiently depolarized to fire an action potential....

Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...

Voltage-gated ion channels are transmembrane proteins that open and close in response to changes in the membrane potential. They are present on the membranes of all electrically excitable cells such as neurons, heart, and muscle cells.
Generally, all voltage-gated ion channels have a 'voltage-sensing domain' that spans the lipid bilayer. The charged residues in the sensor move in response to the membrane potential changes that open the channel allowing ions movement. There are several types of...

The relative difference in electrical charge, or voltage, between the inside and the outside of a cell membrane, is called the membrane potential. It is generated by differences in permeability of the membrane to various ions and the concentrations of these ions across the membrane.
The Inside of a Neuron is More Negative
The membrane potential of a cell can be measured by inserting a microelectrode into a cell and comparing the charge to a reference electrode in the extracellular fluid. The...