Lecture 7: Resting Membrane Potential II
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Questions and Answers

What is the formula for calculating the total current through the membrane?

  • 𝐼𝑇𝑜𝑡𝑎𝑙 = 𝐺𝐾+ ∙ 𝑉𝑀 − 𝐸𝐾+ + 𝐺𝑁𝑎+ ∙ 𝑉𝑀 − 𝐸𝑁𝑎+
  • 𝐼𝑇𝑜𝑡𝑎𝑙 = 𝐼𝐶 + 𝐼𝑘 + 𝐼𝑁𝑎 + 𝐼𝐶𝑎 + 𝐼𝐶𝑙
  • 𝐼𝑇𝑜𝑡𝑎𝑙 = 𝐼𝐶 + 𝐼1 + 𝐼2 + 𝐼3 + ext{...} + 𝐼𝑁 (correct)
  • 𝐼𝑇𝑜𝑡𝑎𝑙 = 𝐷 + 𝐸 + 𝐹 + 𝐺

In steady state, what equals zero for the membrane?

  • 𝐶
  • 𝐼𝑇𝑜𝑡𝑎𝑙 (correct)
  • 𝑉𝑀
  • 𝐷𝑉

What does the equilibrium potential represent in relation to ionic flow?

  • It is the voltage at which the ion concentration gradient is neutral.
  • It is the voltage at which current ceases to flow.
  • It is the voltage at which ions can flow equally in both directions. (correct)
  • It is the voltage at which ions flow solely into the cell.

What is the basis for the direction of transport in the sodium-calcium exchanger?

<p>The energy difference between sodium and calcium ion gradients. (B)</p> Signup and view all the answers

How is the energy needed to extrude calcium ions from the cell determined?

<p>It is equal to the equilibrium potential of calcium ions minus the membrane potential. (C)</p> Signup and view all the answers

Under what condition can the sodium-calcium exchanger run backwards?

<p>When physiological conditions are altered. (C)</p> Signup and view all the answers

If 3 ∙ 𝐸𝑁𝑎 − 𝑉𝑀 is greater than 2 ∙ 𝐸𝐶𝑎 − 𝑉𝑀, what occurs?

<p>Ca2+ ions leave the cell and Na+ ions enter. (B)</p> Signup and view all the answers

What does the variable 𝐷 in the total current equation typically denote?

<p>The total capacitance of the membrane. (A)</p> Signup and view all the answers

What is true about the term 𝑉𝑀 in the context of the membrane potential?

<p>It represents the net voltage across the membrane. (C)</p> Signup and view all the answers

What does the term 𝐼𝑖 represent in the context of ionic currents?

<p>The specific current of a particular ion. (C)</p> Signup and view all the answers

What does the Goldman-Hodgkin-Kat (GHK) equation primarily calculate?

<p>Resting membrane potential (D)</p> Signup and view all the answers

What role does the permeability of an ion play in the GHK equation?

<p>It determines the degree to which the ion contributes to resting potential. (B)</p> Signup and view all the answers

Which assumption of the GHK model can limit its applicability?

<p>All ions move through the membrane at the same rate. (B)</p> Signup and view all the answers

How does the GHK equation account for chloride ions (Cl-)?

<p>It is included but reversed due to being an anion. (D)</p> Signup and view all the answers

What does conductance represent in the context of the membrane?

<p>The capacity of ions to move through the membrane. (A)</p> Signup and view all the answers

At which temperature is the constant 58 mV considered in the GHK equation?

<p>20°C (D)</p> Signup and view all the answers

Which element is NOT a primary ion considered in the GHK equation?

<p>Calcium (Ca2+) (D)</p> Signup and view all the answers

What is the role of the Sodium-Potassium ATPase in maintaining resting membrane potential?

<p>It maintains the ion gradients necessary for potential. (D)</p> Signup and view all the answers

What determines the energy released by Na+ moving into the cell?

<p>The driving force on Na+ ions (D)</p> Signup and view all the answers

What is the relationship between the reversal potential (VR) and the energy needed to move Ca2+ out of the cell?

<p>VR is where the energies for Na+ and Ca2+ transport are equal (D)</p> Signup and view all the answers

How many Na+ ions are transported out of the cell for every ATP molecule hydrolyzed by the sodium potassium ATPase?

<p>Three (B)</p> Signup and view all the answers

What change does the sodium potassium ATPase cause in the membrane potential?

<p>A small change due to unequal ion transport (A)</p> Signup and view all the answers

What is the significance of the value of r in the GHK equation?

<p>It reflects the activity of the sodium potassium pump (B)</p> Signup and view all the answers

Under which condition does the sodium calcium exchanger run in reverse?

<p>When the membrane potential is more positive than the reversal potential (C)</p> Signup and view all the answers

What type of pump is the sodium potassium ATPase considered to be?

<p>Electrogenic (A)</p> Signup and view all the answers

What does the GHK equation represent about the cell membrane?

<p>It describes membrane voltage based on ionic conductances and equilibrium potentials (D)</p> Signup and view all the answers

Flashcards

Goldman-Hodgkin-Katz (GHK) Equation

An equation determining the resting membrane potential, considering ion permeabilities and concentrations.

Resting Membrane Potential

The voltage difference across a cell membrane when the cell is at rest.

Ion Permeability

The ease with which an ion can cross the cell membrane.

Nernst Equation

Calculates the equilibrium potential for a specific ion across a membrane.

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Equivalent Circuit Representation

A model of the cell membrane that compares electrical properties to an electrical circuit.

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Conductance (G)

The reciprocal of resistance, representing the ability of a channel to allow ion flow.

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Equilibrium Potential

The membrane potential where the net flow of a particular ion is zero (due to chemical and electrical forces being balanced).

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Membrane Current

The movement of ions across a cell membrane.

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Sodium Calcium Exchanger

A membrane protein that exchanges sodium (Na+) ions entering the cell for calcium (Ca2+) ions exiting the cell. This process is used to remove Ca2+ from the cell and maintain low intracellular Ca2+ levels.

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Reversal Potential (VR)

The membrane potential at which the energy required to move three Na+ ions into the cell equals the energy needed to move one Ca2+ ion out of the cell. At this potential, the sodium calcium exchanger does not actively transport ions.

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Sodium Potassium ATPase

An active transport protein that pumps sodium ions (Na+) out of the cell and potassium ions (K+) into the cell using energy from ATP hydrolysis. This process helps maintain the resting membrane potential and cell volume.

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Electrogenic Pump

A pump that creates a small electrical current across the cell membrane because it moves an unequal number of ions in and out of the cell. The sodium potassium pump is electrogenic.

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How Does the Sodium Potassium Pump Affect the GHK Equation?

The GHK equation is modified to include the sodium potassium pump's effect on potassium permeability by multiplying the original permeability term by a factor (r). This factor (r) is typically 1.5 and represents the pump's activity.

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GHK Equation for Membrane Potential

The Goldman-Hodgkin-Katz equation describes the resting membrane potential based on the permeability and concentrations of different ions across the membrane. It considers the contributions of sodium, potassium, and other ions.

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Constant Field Assumption

The assumption that the electric field across the cell membrane is consistent, allowing the GHK equation to describe the membrane potential.

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Membrane current (I)

The net flow of ions across the cell membrane. It's the sum of all individual ion currents, like sodium, potassium, and calcium currents.

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Individual ion current (Ii)

The flow of a specific ion (like sodium or potassium) across the cell membrane. It depends on the ion's conductance and the difference between the membrane potential and the equilibrium potential for that ion.

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Equilibrium Potential (Ei)

The membrane potential at which there is no net movement of a specific ion across the membrane. At this point, electrical and chemical forces are balanced.

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Resting Membrane Potential (Vm)

The voltage difference across the cell membrane when the cell is at rest. It's determined by the equilibrium potentials of all ions and their respective conductances.

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How does the Na+/Ca2+ exchanger work?

The direction of transport is determined by the energy provided by the movement of sodium ions. If the energy released by 𝑁𝑎+ moving into the cell is greater, then 𝐶𝑎2+ ions move out. If the energy needed to move 𝐶𝑎2+ out is greater, then 𝑁𝑎+ ions move out and 𝐶𝑎2+ ions move in.

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What determines the direction of transport in the Na+/Ca2+ exchanger?

The direction of transport depends on the difference in energy provided by the movement of sodium ions and the energy needed to move calcium ions. If the difference favors sodium, calcium moves out, and vice versa.

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What does the Na+/Ca2+ exchanger do?

The Na+/Ca2+ exchanger helps maintain the concentration of calcium inside the cell, which is crucial for cellular processes like muscle contraction and signaling.

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How does the Na+/Ca2+ exchanger help regulate cellular processes?

By controlling the flow of calcium ions in and out of the cell, the Na+/Ca2+ exchanger influences various cellular processes like muscle contraction and signaling pathways.

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Study Notes

Lecture 7: Resting Membrane Potential II

  • Topics: Goldman-Hodgkin-Katz (GHK) Equation, Equivalent Circuit Representation, Sodium calcium exchanger revisited, Sodium Potassium ATPase revisited

Goldman-Hodgkin-Katz (GHK) Equation

  • Many charged molecules influence cell membrane electrical properties
  • Higher membrane permeability for an ion leads to greater contribution to membrane potential.
  • The GHK equation expands the Nernst equation, considering ion permeabilities and concentrations inside/outside the cell.
  • The formula is: VM = 58mV * log₁₀ (PK⁺[K⁺]out + PNa⁺[Na⁺]out + PCl⁻[Cl⁻]in) / (PK⁺[K⁺]in + PNa⁺[Na⁺]in + PCl⁻[Cl⁻]out)
  • Constants are used in the formula as this version can be seen as using 58mV at 20°C and 62mV at 37°C.
  • Note that chloride's movement is reversed as it's an anion.

Goldman-Hodgkin-Katz (GHK) Equation: Assumptions

  • Ion movement within the membrane follows the Nernst equation.
  • Ions move across the membrane independently.
  • The electric field across the membrane is constant.
  • This model assumes ions don't interact when crossing the membrane.

Equivalent Circuit Representation of a Membrane

  • Biological membranes act like electrical circuits, with voltages (across the membrane), equilibrium, ion currents, and resistance.
  • Conductance is the reciprocal of resistance: G = 1/R
  • Each ion's current is calculated by multiplying the ion's conductance by the difference between the membrane potential and the ion's equilibrium potential. (I = G*(Vm - E))
  • Total current through the membrane is the sum of inward and outward currents.

Equivalent Circuit Representation of a Membrane: Steady-State

  • In steady-state, total current through the membrane is 0.
  • The membrane potential (Vm) is represented as the sum of ion currents and conductances based on ionic permeabilities and corresponding equilibrium potentials. (Vm = (GK⁺ * EK⁺ + GNa⁺ * ENa⁺ + GCa²⁺ * ECa²⁺ + GCl⁻ * ECl⁻ )/(GK⁺ + GNa⁺ + GCa²⁺ + GCl⁻))

Equilibrium Potential

  • Equilibrium potential describes the reversal potential when voltage and direction of ionic current changes.

Sodium Calcium Exchanger

  • Moves one Ca²⁺ out of the cell against its gradient for every three Na⁺ into the cell following its electrochemical gradient.
  • Can run in reverse: Ca²⁺ enters cell, Na⁺ leaves cell.
  • Direction of transport depends on the energy difference between moving Na⁺ inwards vs Ca⁺² outwards.
  • The exchanger runs back and forth, regulated by Na⁺ and Ca²⁺ concentration gradients and membrane potential.
  • Reversal potential (VR) is when energy released from moving Na⁺ inward equals energy needed to move Ca²⁺ outward. (3*|Ena-VR|=2*|Eca-VR|)

Sodium Potassium ATPase

  • Transports Na⁺ out of and K⁺ into the cell.
  • For every ATP hydrolyzed, 3 Na⁺ ions are transported out of the cell and 2K⁺ ions are transported into the cell.
  • This causes a slight change in membrane potential due to an unbalanced transfer of ions across the membrane.
  • The ATPase influences the GHK equation as it affects ion permeability.
  • r - A factor that accounts for pumping actions by the ATPase (often has a value of 1.5).

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NPB 110B Fall 2024 Lecture 7 Resting Membrane Potential II PDF

Description

This quiz covers the Goldman-Hodgkin-Katz (GHK) Equation and its implications for resting membrane potential. Understand the role of ion permeabilities and the equivalent circuit representation. Explore the sodium-potassium ATPase and sodium-calcium exchanger concepts in relation to membrane potentials.

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