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.

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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 Collect electrical signals Cell body Integrates incoming signals and generates outgoing signal to axon Axon Passes electrical signals to dendrites of another cell or to an effector cell

Neurons form networks for information flow

Animation of resting potential https://www.youtube.com/watch?v=YP_P6bY vEjE

Outside of cell Inside of cell Microelectrode 0 mV – 65 mV K  channel Increasingly negative charge inside the neuron Increasing [K+] outside the neuron Equilibrium!

at 20° C The Nernst equation can be used to calculate the equilibrium potential of a given ion Inside cellOutside cell [K+]400 mM20 mM [Na+]50 mM440 mM [Cl-]51 mM560 mM

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. Andrew HuxleyAlan Hodgkin

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 E membrane-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. voltage meter SW nerve 1mm diameter axon 0.1mm diamter E membrane-measured = -65 mV InOut [K+]400 mM20 mM [Na+]50 mM440 mM [Cl-]51 mM560 mM

Squid Neuron - Continued Important Point #2: They measured the concentrations of Na+, K+, and Cl- inside the squid neuron and outside of it. InOut [K+]400 mM20 mM [Na+]50 mM440 mM [Cl-]51 mM560 mM 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+. For Cl-, we alter the ratio due to the negative charge (valence). The formula is the following... Remember: -log (x) = log (1/x)

What's the e-membrane potential based on K+? InOut [K+]400 mM20 mM [Na+]50 mM440 mM [Cl-]51 mM560 mM A. -75mV B. +75 mV C. -173mV D. -1.3 mV E. +173mV

Squid Neuron - Continued Important Point #2: They measured the concentrations of Na+, K+, and Cl- inside the squid neuron and outside of it. E membrane-measured = -65 mV InOut [K+]400 mM20 mM [Na+]50 mM440 mM [Cl-]51 mM560 mM E membrane -K+ = -75 mV E membrane -Na+ = 55 mV E membrane- Cl- = -60 mV Predicted E-membrane from Nernst Measured E-membrane

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? E membrane-measured = -65 mV InOut [K+]400 mM20 mM [Na+]50 mM440 mM [Cl-]51 mM560 mM E membrane -K+ = -75 E membrane -Na+ = 55 E membrane- Cl- = -60 E membrane-sum = -80 Predicted E-membrane from Nernst Measured E-membrane

at 20° C 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 E membrane Calculating the total resting potential – the Goldman Equation 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 3. Hyperpolarization phase Resting potential Threshold potential

Outside of cell Inside of cell Microelectrode 0 mV – 65 mV K  channel Increasingly negative charge inside the neuron Increasing [K+] outside the neuron Equilibrium!

Voltage-gated sodium channels allow the action potential to occur https://www.youtube.com/watch?v=ifD1YG07 fB8

Voltage-gated channels How voltage-gated channels work At the resting potential, voltage- gated Na + channels are closed. Conformational changes open voltage-gated channels when the membrane is depolarized. Two important types: 1.) Na+ voltage gated channels 2.) K+ voltage gated channels

Patch Clamping Allows Researchers to Record from Individual Channels Currents through isolated channels can be measured during an action potential. Na + inflow K + outflow 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. P Na+ > P K+

Na + channels self-inactivate, K + channels are open. P K+ >> P Na+

E membrane ≈ E K+ P K+ > P K+ 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 Neuron Axon 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. Nodes of Ranvier Schwann cells (glia) wrap around axon, forming myelin sheath Axon Schwann cell membrane wrapped around axon Action potential jumps from node to node

Wider axons have higher conduction velocities. Myelinated axons have higher conduction velocities.

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