Monday April 9, 2014.

Nervous system and biological electricity II

1. Pre-lecture quiz2. A review of resting potential and Nernst equation3. Goldman equation4. Action potential

Information flow through neurons

Nucleus

DendritesCollectelectricalsignals

Cell bodyIntegrates incoming signalsand generates outgoingsignal to axon

AxonPasses electrical signalsto dendrites of anothercell or to an effector cell

Neurons form networks for information flow

Animation of resting potential

• https://www.youtube.com/watch?v=YP_P6bYvEjE

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 cell Outside cell

[K+] 400 mM 20 mM

[Na+] 50 mM 440 mM

[Cl-] 51 mM 560 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 - ContinuedImportant Point #1: They measured actual membrane potential (E-membrane) for the squid axon.

voltage meter

SW

nerve1mm diameter

axon0.1mm diameter

Emembrane-measured = -65 mV

Squid Neuron - ContinuedImportant Point #2: They measured the concentrations of Na+, K+, and Cl- inside thesquid neuron and outside of it.

voltage meter

SW

nerve1mm diameter

axon0.1mm diamter

Emembrane-measured = -65 mV

In Out

[K+] 400 mM 20 mM

[Na+] 50 mM 440 mM

[Cl-] 51 mM 560 mM

Squid Neuron - ContinuedImportant Point #2: They measured the concentrations of Na+, K+, and Cl- inside thesquid neuron and outside of it.

In Out

[K+] 400 mM 20 mM

[Na+] 50 mM 440 mM

[Cl-] 51 mM 560 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+.

[ ]58 *log

[ ]membrane

outE mV

inside

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+?

In Out

[K+] 400 mM 20 mM

[Na+] 50 mM 440 mM

[Cl-] 51 mM 560 mM

[ ]58 *log

[ ]membrane

outE mV

inside

A. -75mVB. +75 mVC. -173mVD. -1.3 mVE. +173mV

Squid Neuron - ContinuedImportant Point #2: They measured the concentrations of Na+, K+, and Cl- inside thesquid neuron and outside of it.

Emembrane-measured = -65 mV

In Out

[K+] 400 mM 20 mM

[Na+] 50 mM 440 mM

[Cl-] 51 mM 560 mM

Emembrane -K+ = -75 mV

E membrane -Na+ = 55 mV

Emembrane- Cl- = -60 mV

Predicted E-membrane from Nernst

Measured E-membrane

Squid Neuron - SolutionSolution: 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?

Emembrane-measured = -65 mV

In Out

[K+] 400 mM 20 mM

[Na+] 50 mM 440 mM

[Cl-] 51 mM 560 mM

Emembrane -K+ = -75

E membrane -Na+ = 55

Emembrane- Cl- = -60

Emembrane-sum= -80

Predicted E-membrane from Nernst

Measured E-membrane

[ ] [ ] [ ]58 *log

[ ] [ ] [ ]

K o Na o Cl i

membrane

K i Na i Cl o

P K P Na P ClE mV

P K P Na P Cl

at 20° C

The Goldman Equation extends the Nernst Equation to consider the relativepermeabilities of the ions (P): Ions with higher P have a larger effect on Emembrane

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=ifD1YG07fB8

Voltage-gated channels

How voltage-gated channels work

At the resting potential, voltage-gated Na+ channels are closed.

Conformational changes openvoltage-gated channels whenthe membrane is depolarized.

Two important types:1.) Na+ voltage gated channels2.) K+ voltage gated channels

Patch Clamping Allows Researchers to Record from Individual Channels

Currents through isolated channels can be measured duringan action potential.

Na

+ infl

ow K

+ outflow

Inwardcurrentfrom Na+

channels

Outwardcurrentfrom 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

NeuronAxon

1. Na+ enters axon.

2. Charge spreads;membrane“downstream”depolarizes.

Depolarization atnext ion channel

3. Voltage-gatedchannel opens inresponse todepolarization.

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 membranewrapped around axon

Action potential jumpsfrom node to node

Wider axons have higher conduction velocities.

Myelinated axons have higher conduction velocities.