Ion channels and Action Potentials

1. Ion channels and Action Potentials macroscopic currents change membrane potential Jim Huettner

2. Ion Channels and Action Potentials • The second lecture emphasized the need for channels to maintain osmotic balance. Today we consider how cells use ion channels to generate electrical signals called action potentials. • Action potentials are the fastest mechanism for transmission of signals over long distances within the body. They also allow for precise timing of events, coordination and rhythms. • In nearly all cases the final effect of an action potential is to elevate intracellular calcium.

3. The variety of Action Potentials Skeletal muscle Cardiac muscle Bean (2007) The action potential in mammalian central neurons. Nature Rev Neuroscience 8:451-465.

4. Pacemaker firing

5. Rhythmic Action Potential Bursts

6. Recording Membrane Potential

7. Changing Membrane Potential Physical Model Electrical Model

8. A simple model cell A membrane sphere with conducting pores. The sphere contains, and is bathed in saline. The equivalent circuit is a capacitor and resistor in parallel. Inject a square pulse of current with a microelectrode, some of it will charge the capacitance and some will go through the resistance of the conducting pores. ITot = IR + IC where IR = Vm / R and IC = C *dVm / dt ÞdVm /dt = (ITot /C) – (Vm / (R * C)) The solution of this equation is: Vm = ITot* R * (1 - exp (-t / t)) where t = R * C is the membrane time constant At equilibrium, when t >> tVm = ITot* R Where R = 1 / SGpores is called the Input Resistance When t = t then (1 - exp(-t / t)) becomes (1 - exp(-1)) = 0.632

9. Sample Calculation A spherical cell, 100 µm in diameter, that has 200 open channels, each with a conductance of 10 pS. Surface area of a sphere is A = 4 * p * r2 Area = 4 * 3.1416 * (50 x 10-4 cm)2 = 3.1 x 10-4 cm2 C = 3.1 x 10-4 µFarads GTot = 200 * 10 pS so Rin = 1 / GTot = 5 x 108W and t = Rin* C = 155 msec A square pulse of current, 5 pA for 1 second will produce a change in membrane potential that will reach a steady state value of V = I * R = 5 x 10-12 A * 5 x 108W = 2.5 mV

10. Plot of Potential versus Time

11. Equivalent Circuit for Sodium Entry Physical Model Electrical Model

12. Competing Batteries Model • Ohm’s Law: V = I * R, so INa = V1*gNa • IK = V2*gKICl = V3*gCl • At rest there is no net current • INa + IK + ICl = 0 • Þ V1* gNa + V2*gK + V3*gCl = 0 • Vm or Vrest = V1 + ENa = V2 + EK = V3 + ECl • Þ V1 = Vm – ENa and V2 = Vm – EK and V3 = Vm – ECl • 0 = (Vm – Ena) * gNa + (Vm – EK) * gK + (Vm – Ecl) * gCl Vm = gNaENa + gKEK + gClEClIion = gion * (Vm-Eion) gNa + gK + gCl

13. Passive v.s. Active • All cells exhibit passive changes in membrane potential when stimulated • Only excitable cells fire action potentials • Excitability depends on specialized channels

14. Specialized Channels Underlie Excitability • Ionic Selectivity - most channels show some preference among ions in solution. Some channels are highly selective for Na+, others are selectively permeable to K+, others to Ca2+ and others to Cl-. Some channels are permeable to cations (Na+, K+) but reject anions (Cl-). Excitable cells need channels with an equilibrium potential more positive than the resting potential • Gating - most channels are not open all of the time. In many cases, channel opening and closing (gating) is controlled by an external signal. Ligand-gated channels are gated by binding a chemical. Voltage-gated channels are controlled by the membrane potential and are essential for the action potential. The classic example is the voltage-gated Na+ channel. This channel is closed at rest, is activated by depolarization, and spontaneously inactivates once it has opened.

15. Sodium Current is Regenerative

16. Sodium Channel Gating States

17. Threshold and Refractory Periods • Action potentials, like other regenerative processes, exhibit a threshold – a level of depolarization that must be exceeded in order for an action potential to occur. • The cell reaches threshold when the rate of sodium entry is greater than the rate of potassium exit. • During the absolute refractory period it is impossible to elicit an action potential. • During the relative refractory period, the threshold for action potentials is higher than at rest.

18. Evidence for Channels • Na channel blockers • Tetrodotoxin • Saxitoxin • Procaine • K channel blocker • tetraethyl ammonium • Ion substitution • Single channel recordings

20. Squid Axon Voltage Clamp

21. Contribution ofK channels Currents During an Action Potential Time Course of Currents

22. Role of Deactivation

23. Propagation • Propagated action potential recorded intracellularly from two points along a squid giant axon. Recording pipettes (a) and (b) are separated by 16 mm. • Traces show a 0.75 msec propagation time between (a) and (b), corresponding to a conduction velocity of 21.3 meters / sec

24. Local Circuits • Because the action potential is a wave moving at constant velocity, the diagrams show both the time course of change at a single location and an instantaneous “snapshot” of the spatial extent of the action potential. • Local circuit currents spread forward to bring the membrane above threshold. • The figure exaggerates the diameter of the axon, it should be only 0.5 mm.

25. The Cable Equation • Originally derived for signal transmission along undersea cables • Vm decays exponentially with distance • Vm = 63.2% of V0 for x = l, one “space constant” • l is proportional to (radius)1/2, current spreads farther for larger diameter fibers • lincreases with membrane resistance • Time constant t = rm * cm does not change with fiber diameter • dV/dt increases as cm decreases • Myelination speeds propagation along nerve fibers by increasing membrane resistance and decreasing membrane capacitance

26. Myelination Alberts et al., 6th ed.

27. Transmission • Nerve Action Potential • Na and K Channels • Calcium Entry • Calcium Channels • Vesicle Fusion • Diffusion and Binding • Postsynaptic Current • Ligand-Gated Channels

28. Hoppa et al., (2014) Neuron

29. Deisseroth(2015) Nature Neuroscience

30. Summary: • Current can move across the membrane by: • Charging the membrane capacitance • Passing across the membrane resistance through ion channels • Membrane resistance and capacitance govern the time course of membrane potential change • For a spherical cell: Vm = ITot R (1- exp (-t / t) and t = RC • Action potentials require voltage-gated channels • They open with depolarization and carry a net inward current • Inactivation and / or voltage-gated outward current underlie repolarization • Inactivation imposes a refractory period • The final effect of an action potential is to elevate calcium

31. Additional Reading • Bean (2007) The action potential in mammalian central neurons. Nature Rev Neuroscience 8:451-465. • Hille, B (2001) Ion Channels of Excitable Membranes, 3rd ed. Sinauer, Sunderland, MA. • Hoppa MB, Gouzer G, Armbruster M, Ryan TA. (2014) Control and plasticity of the presynaptic action potential waveform at small CNS nerve terminals. Neuron. 84:778-89. • Deisseroth K. (2015) Optogenetics: 10 years of microbial opsins in neuroscience. Nat Neurosci. 18:1213-25.