Monday April 9, 2014. Nervous system and biological electricity II 1. Pre-lecture quiz 2. A review of resting potential and Nernst equation 3. Goldman equation 4. Action potential Information flow through neurons Nucleus Dendrites Cell body Axon Collect electrical signals Passes electrical signals to dendrites of another cell or to an effector cell Integrates incoming signals and generates outgoing signal to axon Neurons form networks for information flow Animation of resting potential • https://www.youtube.com/watch?v=YP_P6bY vEjE Outside of cell Increasing [K+] outside the neuron Microelectrode Equilibrium! 0 mV K channel – 65 mV Increasingly negative charge inside the neuron Inside of cell The Nernst equation can be used to calculate the equilibrium potential of a given ion æéX ùö æéX ùö RT ë 1û ÷ ë 1û ÷ ç ç E = 2.3 log = 58mV *log çé X ù÷ çé X ù÷ ZF èë 2 ûø èë 2 ûø Inside cell Outside cell [K+] 400 mM 20 mM [Na+] 50 mM 440 mM [Cl-] 51 mM 560 mM at 20° C Alan Hodgkin Andrew Huxley Squid have axons about 1,000 X wider than humans. This allowed them to do the early experiments that provided critical insights into how neurons work. Squid Neuron - Continued Important Point #1: They measured actual membrane potential (E-membrane) for the squid axon. voltage meter SW nerve 1mm diameter axon 0.1mm diameter Emembrane-measured = -65 mV Squid Neuron - Continued Important Point #2: They measured the concentrations of Na+, K+, and Cl- inside the squid neuron and outside of it. Emembrane-measured = -65 mV voltage meter SW nerve 1mm diameter axon 0.1mm diamter In Out [K+] 400 mM 20 mM [Na+] 50 mM 440 mM [Cl-] 51 mM 560 mM Squid Neuron - Continued Important Point #2: They measured the concentrations of Na+, K+, and Cl- inside the squid neuron and outside of it. What is the predicted membrane potential based on each of these ions? To answer . . . we simplify the Nernst equation to the following for Na+ and K+. E m em brane [ out ] 58 m V * log [ inside ] In Out [K+] 400 mM 20 mM [Na+] 50 mM 440 mM [Cl-] 51 mM 560 mM For Cl-, we alter the ratio due to the negative charge (valence). The formula is the following . . . æ [inside] ö Emembrane = 58mV *log ç ÷ è [outside] ø Remember: -log (x) = log (1/x) What's the e-membrane potential based on K+? E m em brane A. B. C. D. E. [ out ] 58 m V * log [ inside ] -75mV +75 mV -173mV -1.3 mV +173mV In Out [K+] 400 mM 20 mM [Na+] 50 mM 440 mM [Cl-] 51 mM 560 mM Squid Neuron - Continued Important Point #2: They measured the concentrations of Na+, K+, and Cl- inside the squid neuron and outside of it. In Out Predicted E-membrane from Nernst Emembrane -K+ = -75 mV [K+] 400 mM 20 mM [Na+] 50 mM 440 mM [Cl-] 51 mM 560 mM E membrane -Na+ = 55 mV Emembrane- Cl- = -60 mV Measured E-membrane Emembrane-measured = -65 mV Squid Neuron - Solution Solution: We need a way to consider the effects of all 3 ions on the membrane potential. Will the sum of these predicted values equal the measured membrane potential? In Out Predicted E-membrane from Nernst Emembrane -K+ = -75 [K+] 400 mM 20 mM [Na+] 50 mM 440 mM [Cl-] 51 mM 560 mM E membrane -Na+ = 55 Emembrane- Cl- = -60 Emembrane-sum= -80 Measured E-membrane Emembrane-measured = -65 mV Calculating the total resting potential – the Goldman Equation The Goldman Equation extends the Nernst Equation to consider the relative permeabilities of the ions (P): Ions with higher P have a larger effect on Emembrane E m em brane PK [ K ] o PN a [ N a ] o PC l [ C l ]i at 20° C 58 m V * log PK [ K ]i PN a [ N a ]i PC l [ C l ] o Permeabilities change during an action potential and how this allows neurons to “fire”. More key points on equilibrium & membrane potential • The equilibrium potential for an ion is the voltage at which the concentration and electrical gradients acting on that ion balance out. • The Nernst equation is a formula that converts energy stored in a concentration gradient to the energy stored as an electrical potential. This is calculated independently for each ion. • The Goldman equation calculates a membrane potential by combining the effects of key individual ions. The Action Potential Is a Rapid Change in Membrane Potential 1. Depolarization phase 2. Repolarization phase Threshold potential Resting potential 3. Hyperpolarization phase Outside of cell Increasing [K+] outside the neuron Microelectrode Equilibrium! 0 mV K channel – 65 mV Increasingly negative charge inside the neuron Inside of cell Voltage-gated sodium channels allow the action potential to occur • https://www.youtube.com/watch?v=ifD1YG07 fB8 Voltage-gated channels Two important types: 1.) Na+ voltage gated channels 2.) K+ voltage gated channels How voltage-gated channels work At the resting potential, voltagegated Na+ channels are closed. Conformational changes open voltage-gated channels when the membrane is depolarized. Patch Clamping Allows Researchers to Record from Individual Channels Currents through isolated channels can be measured during an action potential. Inward current from Na+ channels Outward current from K+ channels Resting Potential - Both voltage gated Na+ and K+ channels are closed. Initial Depolarization - Some Na+ channels open. If enough Na+ channels open, then the threshold is surpassed and an action potential is initiated. Na+ channels open quickly. K+ channels are still closed. PNa+ > PK+ Na+ channels self-inactivate, K+ channels are open. PK+ >> PNa+ Emembrane ≈ E K+ PK+ > PK+ at resting state Resting Potential - Both Na+ and K+ channels are closed. Action Potentials Propagate because Charge Spreads down the Membrane PROPAGATION OF ACTION POTENTIAL Axon Neuron 1. Na+ enters axon. 2. Charge spreads; membrane “downstream” depolarizes. Depolarization at next ion channel 3. Voltage-gated channel opens in response to depolarization. Action Potentials Propagate Quickly in Myelinated Axons Action potentials jump down axon. Action potential jumps from node to node Nodes of Ranvier Schwann cells (glia) wrap around axon, forming myelin sheath Axon Schwann cell membrane wrapped around axon Wider axons have higher conduction velocities. Myelinated axons have higher conduction velocities.