Ionic channel density of excitable membranes can act a bifurcation parameter
Related Experiment Video
Updated: Oct 12, 2026
10:14
Recapitulation of an Ion Channel IV Curve Using Frequency Components
Published on: February 8, 2011
Biological Cybernetics
|January 1, 1981
Abstract:
As the maximal K+-conductance (or K+-channel density) of the Hodgkin-Huxley equations is reduced, the stable resting membrane potential bifurcates at a subcritical Hopf bifurcation into small amplitude unstable oscillations. These small amplitude solutions jump to large amplitude periodic solutions that correspond to a repetitive discharge of action potentials. Thus the specific channel density can act as a bifurcation parameter, and can control the excitability and autorhythmicity of excitable membranes.
Related Concept Videos
01:19Ion Channels
The movement of ions like sodium, potassium, and calcium into and out of the cell is essential to maintain the electrochemical gradient in living cells. The ion channels—a class of membrane transport proteins—help maintain this ionic gradient for the smooth functioning of physiological activities such as maintaining cell size and volume, conducting nerve impulses, and gas and nutrient exchange.
Ion channels are specialized integral membrane proteins on the plasma membrane that allow specific...
Ion channels are specialized integral membrane proteins on the plasma membrane that allow specific...
01:24Non-gated Ion Channels
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.
Compared to the gated ion channels, the non-gated channels, also known as leakage or passive channels, have no gating mechanism.
01:19The Role of Ion Channels in Neuronal Computation
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.
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.
01:26Voltage-gated Ion Channels
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...
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...
01:24Non-gated Ion Channels
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.
Compared to the gated ion channels, the non-gated channels, also known as leakage or passive channels, have no gating mechanism.
01:26Voltage-gated Ion Channels
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...
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...