Goldman-Hodgkin-Katz Equation Quiz

Membrane Potential and Action Potential

• Membrane potential is the electrical potential difference across a cell membrane.
• Membrane permeability refers to the ability of a membrane to allow specific ions to pass through.
• Goldman-Hodgkin-Katz (GHK) model describes membrane potential for multiple permeant ions.
• The application of the GHK equation determines reversal potential.
• Resting potential describes the membrane potential of a neuron at rest.
• Action potential describes the rapid change in membrane potential of a neuron during an impulse.
• Neurons are nerve cells.

Determination of Membrane Potential

• If a membrane is only permeable to one ion, the membrane potential equals the Nernst potential for that ion.
• If a membrane is permeable to two ions and an impermeant ion is also present, the two permeant ions equilibrate with unequal distribution across the membrane.
• The resting membrane of a typical cell is highly permeable to potassium ions (K+) compared to sodium (Na+), calcium (Ca2+), or chloride (Cl-) ions.
• The resting membrane potential (Vrest) of a squid giant axon is not equal to the equilibrium potential for K+ (EK), sodium (ENa), or chloride (ECl), but instead sits within those values.

Effects of Changing [Cl-]out on Vm

• At rest, the membrane is permeable to both potassium (K+) and chloride (Cl-) ions.
• A sudden decrease in extracellular chloride concentration affects the membrane potential (Vm), causing a drop in Vm to a value between the equilibrium potentials of K+ and Cl-.
• The cell will continue to adjust to restore the Donnan equilibrium.
• A new equilibrium will be reached when the chloride concentration inside the cell is 2.4 mM.

Membrane Permeability

• Transmembrane permeability of an ion (P) depends on the diffusion coefficient (D), the water-membrane solubility (β), and the thickness of the membrane (l).
• Permeability also depends on ion mobility (µ) and the temperature (T).
• Fick's first law describes the diffusion of ions across a membrane.
• A homogeneous membrane with a linear drop in concentration across a membrane results in a linear equation for permeability.

Goldman-Hodgkin-Katz Model

• The Goldman-Hodgkin-Katz (GHK) model describes membrane potential given ion permeabilities and ion concentrations.
• This model assumes that ions move across the membrane independently, and the electric field within the membrane is constant.
• At steady state (resting state), the total current for a cell with permeability to K+, Na+, and Cl-, is zero.
• An equation relates membrane potential to the permeability and concentration of various ions involved. This equation is called the constant field equation.

Goldman-Hodgkin-Katz Model, Membrane Current

• The Goldman-Hodgkin-Katz (GHK) model, describes how the transmembrane current changes when the membrane potential is shifted.
• In a membrane, the current exhibits a nonlinear function of membrane potential.
• The relation of current to voltage is linear only if the extracellular ion concentration equals the intracellular ion concentration.
• This relation is nonlinear with inward rectification or outward rectification depending on the ion involved.

Example: Effects of Extracellular [K+] on Vm

• In the squid giant axon, the membrane permeability ratios are approximately K+ : Na+ : Cl- = 1 : 0.03 : 0.1
• The membrane is most permeable to potassium ions (K+), less to chloride (Cl-) ions, and least permeable to sodium ions (Na+).
• The resting membrane potential (Vrest) is influenced by the extracellular K+ concentration, and a change in extracellular K+ concentrations results in significant changes in Vrest.
• The calculated Vrest values from the GHK equation are in agreement with experimental values and more dependent on K+ when extracellular K+ concentrations increase.

Examples: Effect of Pump Current on Vm

• The resting membrane potential (Vrest) of a squid giant axon is slightly less than the one calculated without taking pumps into consideration (e.g. Na+/K+ pump).
• The Na+-K+ pump moves 3 sodium ions out and 2 potassium ions in for each pump cycle.
• The effect of the pump on the resting membrane potential is less than 15%.
• The resting membrane potential is influenced by the Na+-K+ pump, and the driving force of this pump plays a critical role in maintaining the resting state.

Resting Membrane Potential

• Resting membrane potential (Vrest) is the membrane potential in the absence of external stimulus, a steady state condition.
• K+ plays a significant role in the value of resting membrane potential.
• Ion concentrations both inside and outside the cell membrane and their permeabilities, determine the resting membrane potential.
• Resting membrane potential is used in various cellular processes such as the cell cycle, cell volume regulation, proliferation, and muscle contraction.

Electrical Communication

• Neurons use action potentials and graded potentials for communication.
• Action potentials are all-or-nothing signals, and their frequency encodes information, whereas graded potentials amplitude-encode information.
• Action potentials have higher information content per second.
• Graded potentials' amplitude is proportional to the stimulus strength, and they are crucial for short-distance signal encoding.

A Typical Neuron

• Dendrites (receiving part) and dendritic spines receive signals.
• The soma (cell body) is the central part.
• Axon hillock is the origin of action potentials.
• The axon (transmitting part) conducts the action potential.
• Axon terminals release neurotransmitters at synapses (connections with other neurons or target cells).

Generation of Action Potential

• Hodgkin and Huxley's work involved intracellular recordings of squid giant axons showing action potentials (rapid changes in membrane voltage).
• Action potentials result from transient increases in sodium (Na+) and potassium (K+) membrane conductances.
• Cole and Curtis studies established the importance of ionic conductance changes in generating action potentials.

Increase in Na+ and K+ Conductance Generates APs

• The voltage-clamp technique isolates Na+ and K+ currents.
• Na+ current rapidly activates and inactivates, while K+ current slowly activates.
• Pharmacological blockers (e.g., tetrodotoxin (TTX) for Na+ channels, tetraethylammonium (TEA) for K+ channels) helped isolate specific ionic currents underlying action potentials.

Ionic Currents in Na+ and K+ Conductance Generates APs

• Pharmacological blockers can isolate ionic currents and membrane conductances.
• Conductance measurements and blockers help study voltage changes in neurons.

Equivalent Circuit Representation

• Biological membranes act like resistances and capacitances in parallel.
• The membrane specific capacitance (Cm), membrane specific resistance (Rm), and membrane specific conductance (Gm) are key electrical parameters.

Parallel Conductance Model

• The parallel conductance model describes membrane current as the sum of currents from various ionic conductances.
• The model is crucial in understanding how different ionic conductances contribute to the membrane potential.

Current-Voltage Relations

• Current-voltage (I/V) curves relate membrane current to the membrane potential.
• I/V curves are typically nonlinear, and different ionic currents can be isolated using pharmacological blockers.
• Various voltage protocols to study I/V relations and investigate ionic currents can be used.

Isolation of Different Ca2+ Currents

• Specific blockers can isolate different calcium (Ca2+) current types, such as the L-type and T-type channels.
• Calcium currents can be studied using blocking protocols and current measurement.