Nerve Excitation Topic II-2 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

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; 3. h gate closes (inactivation) and K n-gate opens, Vm → Vk 4. n-gate closes and h-gate opens (de-inactivation), Vm → Vrest h Do 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 = 117 have Ineg = 0; DV > 117 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 Do Axon 2&3 Voltage Clamp Currents

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 Do Axon 4 Voltage Clamp Na Inact

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 Do Axon 5 Voltage Clamp Na K conductance Axon 5 Do axon 6 and review Do in Maple? If know parameters (max g, taus, nernst potentials etc) can get action potential and explain all observed phenomenon.

Action Potential Do Axon 6 Impulse conductance Note that at resting 40% Na channel inactivated Do axon 6 Do Axon 6 Impulse conductance

Threshold and Refractory Period http://www.biocrawler.com/encyclopedia/Action_potential Axon 7 and 8 http://cwx.prenhall.com/bookbind/pubbooks/morris5/medialib/images/F02_03.gif 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. Do Axon 7&8 Impulse Threshold and Refractory

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