1. Week 3a: Ion gradients and equilibrium potentials
BIOL3833
Week 3a: Ion gradients and equilibrium potentials

2. Preview: Where are we headed?

3. Action potentials carry information in the nervous system:

4. Understanding the single Action Potential

5. Ohm’s Law again

6. These two expressions of Ohms Law govern all neural function:
V = I*R
I = V*G

7. Driving force (Voltage): Separation of Charge Across the Membrane
Two forces at work: Diffusion and Electromotive
Particles of same identity diffuse to areas of lower concentration
Different charges attract, similar charges repel
Neural membranes maintain different concentrations of ions inside vs. outside
What are the consequences of these events?
Set up the question by drawing the diagram of an impermeable cell with high KCl inside and low KCl outside. Then open K+ permeable pores:
The question is: What happens now?

8. Now the Equilibrium Game!
Reeses = Kisses = -1 (This is their relative charge)
You can only move Reeses
Chem Teams: Score = 30–abs(#reeses[inside] – #reeses[outside])
Electrical Teams: Score = 30 - abs(sum[inside] - sum[outside])
Record your starting reeses[inside] and reeses[outside]
Record your starting sum[inside] - sum[outside]
Try to find the compromise that is best for both teams
Record the final sum[inside] - sum[outside]
This is your equilibrium potential

9. Exploring the consequences:

10. Nernst Equation for Equilibrium Potentials
R = Gas constant (quantifies gas diffusion pressure)
T = Temperature (everything slows down when cold and speeds up when hot)
F = Faradays constant (quantifies electrical force on charged particles)
Zx = Valence (+1 for Na K; -1 for Cl-, and +2 for Ca++

11. Nernst Equation for Equilibrium Potentials

12. Example: Calculate EK
Ko = 3 mM
Ki = 130 mM

13. Example: Calculate ENa
Nao = 144 mM
Nai = 22 mM

14. Significance of equilibrium potentials
If the membrane potential is at Eion there will be no net movement of that ion species across the membrane If the membrane is exclusively permeable to one type of ion, the membrane potential will move to Eion

15. The concept of driving force
The electromotive force on an ion species is a function of the membrane voltage and Eion Iion = (Vm – Eion) * Gion

16. What happens when the membrane is permeable to more than one ion?

17. The Goldman Hodgkin Katz (GHK) Equation
Membrane potential is determined by the relative membrane
permeability of each ion species and its Equilibrium potential.

18. The Goldman Hodgkin Katz (GHK) Equation
Simplified by ignoring chloride