Communication between cells

1. Communication between cells

2. Electrical equivalent Biology R I2 I1 I I = I1 + I2

3. Nernst Equation The Nernst equation relates the potential difference to the concentration difference in equilibrium: Ci / Co = exp { - Z e (Vi -Vo )/kT } or Vi - Vo = (kT/Ze) ln (Co/Ci) with e = charge electron Z = valence of ion k = Boltzmann constant T = temperature Ci (Co) = concentration inside (outside) membrane

4. Example of Nernst equation t=0 t >> 0 R+ 50 Na+ 50 Cl- 100 Na + 100 Cl- 100 R+ 50 Na+ 64 Cl- 114 Na+ 86 Cl- 86 ΔV = 0 ΔV = - 10 If both Na and Cl, but not R+ can migrate through the membrane.

5. Nernst equation for squid axon

6. Problems with Nernst equation • considers only a single ion. • If multiple ions are involved, it assumes equal permeability for all ions • Applies only to passive transport • ions migrate independently of each other

7. Goldman/Hodgkin/Katz equation The Nernst equation relates the potential difference to the concentration difference in equilibrium for a single neuron. When several ions are involved, we obtain for equilibrium : Pk [K]o+PNa[Na]o+PCl[Cl]i ΔV = (RT/F) ln --------------------------------- Pk [K]i+PNa[Na]i+PCl[Cl]o with Pi = permeability of ion i [K]i/o = concentration inside/outside F = Faraday constant T = temperature ΔV = potential difference across membrane

8. Current through an ion channel

9. Schematic overview of the active membrane

10. 0 mV outside V mV inside Hodgkin & Huxley: Current through an ion-channel 0 mV R I I Vion V mV Ohm’s law Conductance G=1/R Conductance G is a product of maximal conductance gCa and the fraction of open channels m3h

11. Gating kinetics State:

12. Gating kinetics Open State:

13. Gating kinetics m Open Closed State: m m (1-m) Probability: m m

14. V (mV) Gating kinetics m Open m m Closed State: m m (1-m) Probability: m m Channel Open Probability:

15. -3 x 10 1 8 t 0.8 (V) m (V) 6 m ¥ 0.6 (s) 4 m t 0.4 2 0.2 0 0 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 1.2 10 1 8 h (V) t (V) ¥ h 0.8 6 (s) h t 0.6 4 0.4 2 0.2 0 -150 -100 -50 0 50 100 150 -100 -50 0 50 100 V (mV) V (mV) clamp clamp Parameter fitting (2)

16. -3 x 10 1 8 t 0.8 (V) m (V) 6 m ¥ 0.6 (s) 4 m t 0.4 2 0.2 0 0 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 1.2 10 1 8 h (V) t (V) ¥ h 0.8 6 (s) h t 0.6 4 0.4 2 0.2 0 -150 -100 -50 0 50 100 150 -100 -50 0 50 100 V (mV) V (mV) clamp clamp Parameter fitting (2)

17. V (mV) Gating kinetics m Open m m Closed State: m m (1-m) Probability: m m gm(t) = gm, max(m∞ - m0)(1 - e-t/τ) gh(t) = gh, max(h∞- h0)e-t/τ gm gh g Channel Open Probability: m3h gNa time

18. Membrane voltage equation 0 mV 0 mV INa IC V mV V mV INa = gmax, Nam3h(V- VNa) Kirchoff’s law: -Cm dV/dt = gmax, Nam3h(V-Vna) + gmax, K n4 (V-VK ) + g leak(V-Vna)

19. Actionpotential