Membrane Potential (Vm): - charge difference across the membrane -

K+

Na+

K+

Na+

inside outside…how can passive diffusion of potassium and sodium lead to development of negative membrane potential?

Simplest Case

If a membrane were permeable to only K+ then…

inside outside

K+ K+

K+ would diffuse down its concentration gradient until the electrical potential across the membrane countered diffusion.

Simplest Case

K+ K+

If a membrane were permeable to only K+ then…

The electrical potential that counters net diffusion of K+ is called the K+ equilibrium potential (EK).

inside outside

The Potassium Nernst Potential

Example: If Ko = 5 mM and Ki = 140 mM

EK = -61 log(140/4)

EK = -61 log(35)

EK = -94 mV

EK = 61 log  

Ki

Ko

So, if the membrane were permeable only to K+, Vm would be -94 mV

…also called the equilibrium potential

Simplest Case

Na+Na+

If a membrane were permeable to only Na+ then…

The electrical potential that counters net diffusion of Na+ is called the Na+ equilibrium potential (ENa).

inside outside

Na+ would diffuse down its concentration gradient until potential across the membrane countered diffusion.

The Sodium Nernst Potential

Example: If Nao = 142 mM and Nai = 14 mM

EK = -61 log(14/142)

EK = -61 log(0.1)

EK = +61 mV

EK = 61 log  

Nai

Nao

So, if the membrane were permeable only to Na+, Vm would be +61 mV

Resting Membrane Potential

0 mV

EK -94 ENa +61

Vm -90 to -70

Why is Vm so close to EK?Ans. The membrane is far more permeable to K than Na..

The Goldman-Hodgkin-Katz Equation (also called the Goldman Field Equation)

Calculates Vm when more than one ion is involved.

oCliNaiK

iCloNaoKm

ClpNapKp

ClpNapKpV

]['][']['

]['][']['log. -++

-++

++++

=61

NOTE:P’ = permeability

iCloNaoK

oCliNaiKm

ClpNapKp

ClpNapKpV

]['][']['

]['][']['log. -++

-++

++++

= -61

or

The Goldman-Hodgkin-Katz Equation

The resting membrane potential is closest to the equilibrium potential for the ion with the highest permeability!

ATP

3 Na+

2 K+

ADP

Active Transport

K+ Na+

Na+ K+

inside outside

Remember: sodium is pumped out of the cell, potassium is pumped in...

Resting Membrane Potential Summary

Cells: contain high a K+ concentration have membranes that are essentially

permeable to K+ at rest

Membrane electrical potential difference (membrane potential) is generated by diffusion of K+ ions and charge separation measured in mV (=1/1000th of 1V) typically resting membrane potentials in

neurons are -70 to 90 mV

Resting and action potentials

++

+

+

+ +

+

+

+

++

–

–

–– –

–

–

–––

–

Voltmeter

– +0 mV-80 mV +

Nerve Action Potential

Nerve signals are transmitted by action potentials, which are rapid changes in the membrane potential that spread rapidly along the nerve fiber membrane

Action potential begins with a sudden change from the normal resting negative membrane potential to a positive potential and then ends with an almost equally rapid change back to the negative potential

Changes that occur at the membrane during the action potential Transfer positive

charges to the interior of the fiber at the onset and return positive charges to the exterior at its end

Nerve Action Potential

Stages of action potential

Resting Stage. This is the resting membrane potential before the action potential begins. The membrane is said to be "polarized" during this stage because of the -90 millivolts negative membrane potential that is present

Depolarization Stage

The membrane suddenly becomes very permeable to sodium ions, allowing tremendous numbers of positively charged sodium ions to diffuse to the interior of the axon.

The normal "polarized" state is neutralized by the inflowing positively charged sodium ions, with the potential rising rapidly in the positive direction

This is called depolarization

Repolarization Stage

After the membrane becomes highly permeable to sodium ions, the sodium channels begin to close and the potassium channels open more than normal

Rapid diffusion of potassium ions to the exterior re-establishes the normal negative resting membrane potential

This is called repolarization of the membrane

The AP - membrane permeability

• During the upstroke of an action potential: Na permeability increases

due to opening of Na+ channels memb. potential approaches

ENa

Num

ber

of o

pen

chan

nel s

Na+ channels

upst

roke

K permeability increases due to opening of K+ channels

mem. potential approaches EK

downstroke

• After hyperpolarization of membrane following an action potential:

Membranehyperpolarized

resting potential

K+ channels

There is increased K+ conductance due to delayed closure of K+

channels

• During the downstroke of an action potential: Na permeability decreases

due to inactivation of Na+ channels

1 ms

+61

0

(mV)

-90

ENa

EK

Properties of action potentials Action potentials: are all-or-none events

threshold voltage (sudden increase in the membrane potential) threshold

-70

+60

mV

Stim

ulus

0

non- myelinated

0 800400

have constant conduction velocity Fibers with large diameter conduct

faster than small fibers

Fiber diameter (mm)

Vel

ocity

(m

/s)

0 3 6 9

Myelinated

12

75

15

50

25

0

are initiated by depolarization action potentials can be induced in nerve

and muscle by extrinsic stimulation

Propagation:

Rest

Opening of Na+ channels generates local current circuit that depolarizes adjacent membrane, opening more Na+ channels…

Stimulated(local depolarization)

Propagation(current spread)

Signal Transmission:

Myelination• Schwann cells surround the nerve

axon forming a myelin sheath

• Sphingomyelin decreases membrane capacitance and ion flow 5,000-fold

• Sheath is interrupted every 1-3 mm : node of Ranvier

Saltatory Conduction• AP’s only occur at the nodes (Na

channels concentrated here!)• increased velocity• energy conservation

Conduction velocity

non-myelinated

myelinated

- non-myelinated vs myelinated -