Nerve Excitation Biophysics

Neurons Nerve signals due to modulations of membrane potential Motor neuron Sensory neuron Nerve signals due to modulations of membrane potential Motor Neurons have dendrites

History Action potential is electrical pulse that travels much slower than electrical current K+ and especially Na+ play big role Hodgkin and Katz: as [Na+] decreases velocity of action potential decreases Calamari Alan Lloyd Hodgkin Andrew Fielding Huxley Hodgkin and Huxley observe membrane potential reverses during pulse and goes to +100 mV They also see that conductance of membrane increases 40X and propose have transient changes in Na and K conductance → Nobel Prize Skip 2016

Voltage Clamp Measure current to keep voltage constant Positive current: + ions out of axon VK = -72 mV, VNa = + 55 mV DV = Vin - Vout Measure current to keep voltage constant INa = gNa(Vm – VNa), IK = gK(Vm -VK), IL = gL(Vm – Vk) Voltage Clamp makes IC = Cm dV/dt = 0 Itot = INa + IK + IL (with clamp) Vm = Vh = 1/gtot (gKVK + gNaVNa + gLVL + I), clamp and look at I See notes on conventions re current etc.

Voltage Clamp experiments Set concentrations of ions so can get Nernst potentials equal membrane potential and reduce variables gNa, gK ~ 0 at resting potential and they are only activated when the axon is depolarized (becomes less negative). H&H get gL when hyperpolarize I = IL = gL (Vm – VL), VL < Vresting (-60 mV)

Action Potential Resting Na m gate closed h gate open; n-gate closed Sufficient initial depolarization → open m-gate, Vm → VNa; h gate closes (inactivation) and K n-gate opens, Vm → Vk n-gate closes and h-gate opens (de-inactivation), Vm → Vrest h Do Axon 1 Dynamics

Axon 1 Dynamics

H&H Voltage Clamp experiments When depolarize, get early negative current and later positive current As DV increases Amplitude of Ineg decreases; DV = 115 have Ineg = 0; DV > 115 have early positive current Rate of current development increases (both + and -) Switch from negative current to positive gets earlier Note: VK = -72 mV, VNa = +55 mV, Vresting = -60mV; INa = gNa(Vm – VNa), IK = gK(Vm – VK) So IK always positive; INa negative for small DV but becomes positive for DV>115 mV I reversal could be due to cessation of early I- or stronger/earlier I+ H&H isolate currents by setting Vm = VNa so get voltage dependence of IK Deduce voltage dependence of INa since Itot = INa + IK Do axon 1 and 2 Then 3

Example You are working with a colossal squid axon resting at -60 mV. VNa = 55 mV. VK = -72 mV. Assuming gNa = gk, is the net current positive, negative or zero when you apply the following voltage steps: - 10 mV (hyperpolarize to -70 mV) + 20 mV + 115 mV + 130 mV

Axon 2&3 Axon 2 – Voltage Clamp and Currents Screen shows graph with membrane potential steps and currents vs time. Current is sum of Na and K currents. Ieak is subtracted out. 1. Run. Start at -60 mV. Have Vstep = 10 mV. 2. Step up Vstep by 20 mV up to 140 mV. What do you see? 3. Find voltage when only have positive current. (~115 mV). What is happening here? Axon 3 – Voltage Clamp and Separate Currents 4. Repeat Vsteps like in Axon 2. Set Vstep to 60 mV just to show general currents. Why no sodium current at 115 mV? 5. Go to parameters in top parameters window. See that VNa is 55 mV (so when step 115 mV = -60 + 115 = 55 mV). 6. Now, like H&H, can change VNa (would be changing Na concentrations) and study voltage dependence of gk alone. Take both VNa and Vstep down by 20 (go to 35 mV and 95 mV). 7. Could keep doing this. H&H get INa by subtracting IK from Itotal.

Na activation and inactivation and deinactivation DV  activation , time inactivation  deinactivation deinactivation is also voltage dependent H&H use conditioning steps: Brief conditioning depolarization  reduced INa during 2nd step As Dt for conditioning step increases  INa 2nd step decreases (more sodium channels inactivated during conditioning step)  H&H find time and voltage dependence of inactivation ex – conditioning step + 29 mV  tinactivation = 2 ms (nearly complete) step + 8 mV  tinactivation > 8 ms (less inactivation) They found that even at resting potential, many sodium channel are inactive. H&H used long conditioning steps to study de-inactivation This turned off (closed) Na channels then set 2nd voltage to recovery voltage – vary time to 3rd voltage to look at current. Axon 4

Axon 4 Voltage Clamp Na inactivation

Empirical Equations Generally dg/dt = a(1-g) – bg; a = opening (fwd rate), b = closing Potassium, have gk = gkmaxn4; gkmax = max conductance (all open) Sodium, have gNa = gNamaxm3h, m is like n for K, h describes inactivation Each has time dependence like n m3 = fraction activated, h is fraction de-inactivated Axon 5 Do axon 6 and review Do in Maple? Skip rest 2016? If know parameters (max g, taus, nernst potentials etc) can get action potential and explain all observed phenomenon.

Axon 5 Na K conductances This is like previous exercises except, now look at conductances which you would get from the currents divided by the potential. Remember can get g from I = gV.   Play. Have 10 mV Vstep. See nothing in gNa and small effect on gK. Increase step 30, 50 , 70, 115 [Vstep in middle parameter – increase]. What is happening here? Why is gNA so high when Vm = VNa (Vstep = 115 mv) even though we saw there is no current then?

Axon 6 Current clamp Summary Hit Stop/Go Explain what you see.

Threshold and Refractory Period http://www.biocrawler.com/encyclopedia/Action_potential http://cwx.prenhall.com/bookbind/pubbooks/morris5/medialib/images/F02_03.gif Axon 7 and 8 There is a minimum initial depolarization you need to get action potential – this is the threshold. “All or none” aspect of action potential After action potential, threshold is infinity (Na h gates closed), this leads to a refractory period.

Axon 7 Impulse Threshold

Axon 8 Absolute and Refractory Periods

Spread of Action Potential http://www.arts.uwaterloo.ca/~bfleming/psych261/image25.gif Na comes in and causes depolarization at neighboring sites. Refractory period insures unidirectional event. Want current to go along axon, not out of axon Invertebrates: large radius → small R Vertebrates: large R along axon (myelin sheath and nodes of Ranier)

Have ligand gated channel (eg Ach receptor that needs two Ach to open). When open both Na and K can get through → get depolzarization