Cellular and Molecular Neuroscience

Attendance

• TopHat Code: Use the TopHat app for attendance and follow along for questions.

Topic of Discussion

• Key Topics: Focus on the Nernst Equation and the Goldman Equation as they relate to ion movement and membrane potentials.

Practice Problems on Ion Movement

First Practice Problem

• Scenario: Two chambers separated by an impermeable membrane with an ion channel permeable only to Y0, an uncharged ion.

• Ion Distribution:

  • Left side: 6 Y0 ions (uncharged)

  • Right side: 3 Y0 ions (uncharged)

• Question 1: Which way will Y0 move once the channel opens?

• Question 2: What gradient is driving the force behind ion movement?

Second Practice Problem

• Scenario: Two chambers separated by an impermeable membrane with an ion channel permeable only to X-, an anion.

• Ion Distribution:

  • Left side: 4 double-charged cations (C++) and 4 single-charged anions (X-)

  • Right side: 4 uncharged ions (Z0) and 4 single-charged anions (X-)

• Question 1: Which way will the X- ions move once the channel opens?

• Question 2: What gradient is driving the force behind ion movement?

Electrical and Concentration Gradients

• Concept Overview:

  • Predict the electrical gradient force that balances the concentration gradient.

• Key Equations:

  • Nernst Equation: Used for single ions.

  • Goldman Equation: Predicts membrane potential based on the relative permeability of several ions.

Membrane Potential (Vm) Influences Ion Fluxes

• Mechanics of Ion Movement:

  • Connecting a battery across a K+-permeable membrane allows direct control of membrane potential.

  • Scenarios:

  • Battery Off: K+ ions flow according to their concentration gradient.

  • Equilibrium Potential for K+: Setting the initial membrane potential (Vin-out) at this point yields no net K+ flux.

  • More Negative Vm: If the membrane potential is more negative than K+ equilibrium potential, K+ will flow against its concentration gradient.

Relationship Between Membrane Potential and K+ Flux

• Key Insight: When Vm approaches Eion, there will be no net movement of that ion.

Nernst Equation

• Equation:

  • E{ion} = -61 imes ext{log} \left( \frac{[ion]{outside}}{[ion]_{inside}} \right)

• Explanation of the Equation:

  • This equation calculates the equilibrium potential for a specific ion based on its concentration gradient across the membrane.

• Implication: Changes in internal and external ion concentrations can be predicted using the Nernst Equation.

  • Example: The resting membrane potential of a squid giant axon is largely determined by the K+ concentration gradient.

• Graphical Representation:

  • (A) Increasing external K+ concentration depolarizes the resting membrane potential.

  • (B) A graph representing the relationship between resting membrane potential and external K+ concentration plotted on a semi-logarithmic scale shows a straight line with a slope of +58 mV per tenfold change in concentration, derived from the Nernst equation.

Goldman Equation

• Equation:

  • Vm = 61 imes \text{log} \left( \frac{PK [K^+]{outside} + P{Na} [Na^+]{outside} + P{Cl} [Cl^-]{inside}}{PK [K^+]{inside} + P{Na} [Na^+]{inside} + P{Cl} [Cl^-]_{outside}} \right)

• Explanation of the Equation:

  • The Goldman Equation accounts for the contributions of multiple ions to the membrane potential based on their relative permeabilities.

• Constants and Variables:

  • The constant 61 is derived from physical constants including the universal gas constant and the temperature of mammalian cells.

  • Pion: Relative permeability of each ion.

  • [Ion] inside: Intracellular concentration of each ion

  • [Ion] outside: Extracellular concentration of each ion.

• Conclusion: The membrane potential (Vm) approaches Eion of the most permeable ion, influencing ion movement and gradient dynamics.

Practice Problems

• Continuing practice and application of concepts through further problems on membrane potentials and ion fluxes.