1. All potassium channels are open. All other channels are closed

[K+]=150mM[Na+]=15mM

[K+]=4mM[Na+]=145mM

• Na+ – K+ pump generated high [K+] concentration inside, low [Na+] concentration inside.

• Potassium is leaking out through leakage channels.• How will charge distribution across cell membrane look at equilibrium?

(compare to the iPhone touchscreen capacitive display)• What voltage will we measure across cell membrane at equilibrium?

-96mV1. All potassium channels are open. All other channels are closed

• Every time another potassium ion leaves the cell, it adds to the force that pushes potassium ions back into the cell.

• At some point (and quite fast) an equilibrium is reached• It is reached after just 2 million out of 0.5 trillion potassium ions leave the cell = 0.0005%• If you now insert an electrode and measure electrical potential what number will you

measure?• Potassium equilibrium potential it the voltage across cell membrane at which the net

flow of potassium across cell membrane is zero.

––

–– –

– ––

++ + +

?-96mV

[K+]=150mM[Na+]=15mM

[K+]=4mM[Na+]=145mM

• Will sodium concentration equilibrate across cell membrane?

2. All Potassium channels are closed. All sodium channels are open.

[K+]=150mM[Na+]=15mM

[K+]=4mM[Na+]=145mM

• What voltage will we measure across cell membrane now at equilibrium?

[K+]=150mM[Na+]=15mM

[K+]=4mM[Na+]=145mM

• What voltage will we measure across cell membrane at equilibrium? Why?

0mV3. Equal number of potassium and sodium channels are open.

[K+]=150mM[Na+]=15mM

[K+]=4mM[Na+]=145mM

4. A more real scenario: # of open potassium channels / # of open sodium channels = 100 / 1

[K+]=150mM[Na+]=15mM

[K+]=4mM[Na+]=145mM

5. Another real scenario: # of open potassium channels / # of open sodium channels = 1 / 100

• At rest some potassium always leaks out• Thus outflux is counterbalanced by Na+ – K+ pump• Note: in the first approximation:

Na+ permeability (PNa) is proportional to # of opens Na+ channels; K+ permeability (PK) is proportional to # of opens K+ channels

-96mV PNa<< PK

0mV PNa= PK

+58mV PNa / PK = 100 / 1

+60mV PNa>> PK

Depolarized

HyperpolarizedResting membrane potentialPNa / PK = 1 / 100

Respect membrane potential

• Electric ray – electric discharge can paralyze or disorient a prey• Discharge originates from electrocytes (modified muscle cells• Peak voltage = 50 Volts

• Most important: cells can regulate membrane potential by changing PNa / PK ratio over time

• Increase to 100/1 for 1ms. What happens? • Voltage jumps to +58mV• Reduce to 1/100 -- What happens? • Voltage drops to -88mV

PNa<< PK

PNa= PK

PNa / PK = 100 / 1

PNa>> PK

Depolarized

• We have just found a way to transmit information• All neurons communicate with these transient

(1ms long) spikes called action potentials

PNa<< PK

PNa= PK

PNa / PK = 100 / 1

PNa>> PK

Depolarized

How to transmit information over long distance?

1. make one long cell:

-80mV -80mV -80mV -80mV -80mV

At rest:

Change membrane potential at cell body:

+30mV +10 -80mV -80mV -80mV-20 -40

• Signal dies without reveling to the cell terminal• In a real cell, signal dies over 2 mm (1/1000 of the distance to the muscle of the toe)• Why?

We will consider two hypothetical solutions:

+30mV +10 -80mV -80mV -80mV-20 -40

K+ K+ K+

• Analogy: heat transmission along a metal rod immersed in water

• Did you transmit any heat to the far end of the rod?

300°C

200°C

120°C

Water temperature=20°C

Metal rodHeat escapes from the metal rod

+30mV +10 -80mV -80mV -80mV-20 -40 • Ions escape from a long neuron

K+ K+ K+

Possible solution #2: Connect many cells sequentially

• Each cell amplifies the spike to +30mV, then activates to following cell.

-80mV -80mV -80mV -80mV -80mV

-80mV +30mV -80mV -80mV -80mV -80mV

-80mV -80mV +30mV -80mV -80mV -80mV

-80mV -80mV -80mV -80mV +30mV-80mV

Possible solution #2: Connect many cells sequentially

• The downside of this system:• There is a delay at every electrical junction

between the cells.• From motor cortex in the brain to the toe

muscle = 2meters.• 2meters / 20micrometers cells = 100,000 cells• Assume that inside a cell electrical signal is

transmitted instantaneously• Delay between cells = 1millisecond• Total transmission time = 100,000 x 1ms = 100s• Too long!• This mechanism is only used

– over very short distances in animals – over long distances in plants

Solution: make one long cell and amplify along the way

-80mV -80mV -80mV -80mV -80mV

At rest:

Change membrane potential at cell body:

+30mV -80mV -80mV -80mV-80mV

Amplify along the way:

-80mV +30mV -80mV -80mV -80mV

-80mV +30mV -80mV -80mV

-80mV -80mV +30mV -80mV

-80mV -80mV -80mV +30mV-80mV

amplified

• Make one long cell and amplify along the way• This principle is used throughout the nervous system

• An action potential visualization. An action potential traveling along an axon can be visualized as a flame racing along a fuse or a sparkler, each segment igniting the next until the action potential reaches the end of the axon.

Cell body

Dendrites

Initial segment

Axoncollateral

Axonterminals

Golgi stain

Camillo Golgi (1843 – 1926) accidentally elbowed over a beaker of silver solution onto some brain slices. To his surprised, silver stained the slice in peculiar manner. Under the microscope, he saw neuronal cell bodies, dendrites and axons … But Golgi thought that all neurons are fused together, therefore he maintained that neurons of the brain act together working as a reticulum.

Spanish neuroanatomist Santiago Ramón y Cajal (1852–1934)

Cajal was the first to see discrete neurons Neuronal doctrine: neurons are electrically isolated

Ramon y Cajal improved Golgi' staining by using a method he termed "double impregnation." Ramon y Cajal's staining technique, still in use, is called Cajal's Stain.

Like the entomologist hunting for brightly colored butterflies, my attention was drawn to the flower garden of the gray matter that contained cells with delicate and elegant forms, the mysterious butterflies of the soul, the beating of whose wings may some day (who knows?) clarify the secret of mental life. […] Even from the aesthetic point of view, the nervous tissue contains the most charming attractions. In our parks is there any tree more elegant and luxurious than the Purkinje cell from the cerebellum or the psychic cell, that is the famous cerebral pyramid?" Santiago Ramón y Cajal, 1894

Purkinje cell located in the cerebellum

• Still Cajal found his neuronal doctrine hard to sell.• He had to launch his own journal to propagate his

ideas.• Eventually Cajal’s drawings got attention and Cajal

and Golgi (two scientific rivals) shared a Nobel prize in 1906.

Dendritic spines• Nice 3D visualization of neurons: https://youtu.be/Zqtng0AfHFY

Dendritic spines

Branch of Neuroscience: Cellular neuroscience

A smarter way to amplify signal along the axon

• Instead of amplifying continuously• Amplify only here.

Amplifications stations (sodium channels)

• Electrically isolate everywhere else.

• Isolation does not let charges (ions) escape from the cell • It allows a cell to amplify signal less frequently • Faster signal transmission• Most neurons in mammalian CNS are myelinated

amplified

Oligodendrocyte

• One myelin-forming cell (oligodendrocyte) can wrap around a number of axons (up to 40)

• The number of layers is 10 to 160 (what is the number of membranes?)

• Analogy: metal rod immersed in water, but this time we put layers of thermal isolation over the rod

Heat cannot escape

300°C

Optic nerve

Example of axonal transport

Functional differences of axons and dendrites hinge upon differences in their molecular composition. Membrane proteins destined to either of the domains leave the Golgi in tubulovesicular carriers that are transported by molecular motors along microtubular tracks. axonal and dendritic cell surface proteins were tagged with fluorescent proteins (FP’s).

This neuron expresses an FP-tagged protein (NgCAM) that turns up exclusively on the axonal cell surface. Interestingly, carriers containing this axonal protein enter freely into all the processes radiating from the cell body, i.e. the axon (top right) and all dendrites. Transport of carriers is bi-directional, both away and towards the cell body. The bright spot in the cell body corresponds to the Golgi area where the carriers originate.

• Biological membrane is a dynamic structure• Diffusion of phospholipids and some

transmembrane proteins is possible inside the 2-dimentional surface of a membrane

Example of fusion of membrane protein with cell membrane

Delivery of membrane proteins to the cell surface occurs by fusion of the carriers with the plasma membrane. Two fusion events have been captured fortuitously in this movie. Upon fusion, the contents of the carriers very rapidly diffuse in the plasma membrane, resulting in a fleeting impression of a railroad track due to the optical sectioning power of the microscope.

Time lapse: 30 seconds (one loop of movie)

• The internodal distance is ~100 x external diameter of the axon• Usually from 200 micrometers to 2 mm

Conduction velocity Time to cover 2 meters

Myelinated 5 to 120 m/s (10-270 miles/hour) 2meters / 100m/s = 20ms

Unmyelinated <2m/s(<4 miles/hour) 2meters / 2m/s = 1s

• Myelin sheath does not let ions escape, • so that current flows only at nodes of Ranvier• Excitation jumps from node to node: • saltatory conduction (from the Latin saltare, to hop or leap)• Fewer ions enter and leave the cell • less metabolic energy is required to restore intracellular

concentration of potassium and sodium

• DEFINITION: Action potential is the jump of membrane potential (Em) from resting Em of -80mV to +30mV for 1ms during the amplification process.

• How do we measure action potential?

-96mv PNa<< PK

0mv PNa= PK

+58mv PNa / PK = 100 / 1+60mv PNa>> PK

Depolarized

Amplification process

• Main player: voltage activated Na+ channel

• At rest: PNa/PK = 1/100 and Em is close to EK (Em=-88mV)

• Na+ channel is closed at Em=Em resting

• As Em is increasing to -40mV, Na channels start to open.

• We say -40mV is a threshold for Na channels.

[K+]=150mM[Na+]=15mM

[K+]=4mM[Na+]=145mM

Recall: Voltage-gated channels

Resting membrane potential: inside is negative Cell is depolarized: inside is positive

inside

outside

Voltage-gated Na+ channel

• What ions are coming into the cell through an open Na+ channel?• Positive ions.• How are they changing membrane potential?• They make the membrane potential even more positive.

– ––– ––

+ +++ ++ – ––– ––

+ +++ ++

VNa+ channel closed Na+ channel open

• membrane potential more positive• Even more sodium channels open • Even more sodium ions enter the cells • membrane potential even more positive on so on ==• Positive feedback loop == explosion == gun powder

––

[K+]=150mM[Na+]=15mM

[K+]=4mM[Na+]=145mM

Node of Ranvier

• So as Em reaches -40mV Em quickly jumps to +30mV because practically all sodium channels open

• Why doesn’t Em stay at +30mV?

––

• Why doesn’t Em stay at +30mV?• Sodium channel inactivation!• After 1ms the ball (protein)

blocks the channel • Sodium ions inflow stops • PNa / PK = 1 / 100 • Em goes back to Em resting

– ––– ––

+ +++ ++

– ––– ––

+ +++ ++

• The 2nd mechanism (less important) that pulls Em back to Em resting involves delayed rectifying potassium channel

[K+]=150mM[Na+]=15mM

[K+]=4mM[Na+]=145mM

Afterhypopolarization

• Find two errors:

InactivatedClosed Open

• Information is coded in frequency of action potentials (firing frequency)

• Refractory period analogy = toiler flush

• An action potential spike is initiated at axon hillock

• There are more than 250,000 sodium channels in axon hillock – gun powder, explosion

• Axon transmits signal actively (amplifies action potential along the way)

• Dendrites transmit signal passively (no amplification) – there are exceptions

Lesions: the MS plaques in CNS white matter

• Multiple sclerosis• Symptoms: weakness• Lack of coordination• Impairment of vision and

speech

Diagnosis of MS: visual evoked potential

• Profound slowing of conduction velocity and block in some fibers

Light flash

100msNormal

MSdelayed

EEG EEG amplitude

• Stop here

• The ONLY way for neurons to communicate over long distance is by sending action potentials.

• Over short distance, everything is used: action potentials, chemicals and small changes in electrical potential.

– ––– ––

+ +++ ++

– ––– ––

+ +++ ++

Inactivationgate

InactivatedClosed Open

1. All potassium channels are open. All other channels are closed

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