Neurophysiology

The Resting

Membrane Potential

Intracellular Extracellular

V V

Vm

-70 mV

Vm=Vin-Vout

Three Concepts

1. Concentration Gradients

2. Electrical gradients

3. Selective permeabilityof the membrane

100 NaCl

Solid barrier in place

0 NaCl

Outside Inside

100 Na+100 Cl-

0 Na+0 Cl-

Solid barrier in place

0

0 0

Outside Inside

100 Na+100 Cl-

0 Na+0 Cl-

Outside Inside

Barrier removed

Na+ Concentration gradient = 100

0 0

Cl- Concentration gradient = 100

50 Na+50 Cl-

50 Na+50 Cl-

Outside Inside

Barrier removed

0 0

Na+ Concentration gradient = 0

Cl- Concentration gradient = 0

50 Na+50 Cl-

50 Na+50 Cl-

0 0

Outside Inside

Measure voltage difference

0

Na+ Concentration gradient = 0

Cl- Concentration gradient = 0

System at equilibrium

100 Na+100 Cl-

0 Na+0 Cl-

Solid barrier in place

0

0 0

Outside Inside

100 Na+100 Cl-

0 Na+0 Cl-

Replace with Na+ permeable membrane

0

0 0

Outside Inside

Na+ Concentration gradient = 100

50 Na+100 Cl-

50 Na+0 Cl-

Replace with Na+ permeable membrane

+100

-50 +50

Outside Inside

Na+ Concentration gradient = 0

50 Na+100 Cl-

50 Na+0 Cl-

Replace with Na+ permeable membrane

+100

-50 +50

Outside Inside

Na+ Concentration gradient = 0

75 Na+100 Cl-

25 Na+0 Cl-

Replace with Na+ permeable membrane

+50

-25 +25

Outside Inside

Na+ Concentration gradient = 50

System at equilibrium

75 Na+100 Cl-

25 Na+0 Cl-

Replace with Cl- permeable membrane

+50

-25 +25

Outside Inside

Cl- Concentration gradient = 100

75 Na+50 Cl-

25 Na+50 Cl-

Replace with Cl- permeable membrane

-50

+25 -25

Outside Inside

Cl- Concentration gradient = 0

75 Na+62.5Cl-

25 Na+37.5 Cl-

Replace with Cl- permeable membrane

-25

+12.5 -12.5

Outside Inside

Cl- Concentration gradient = 25

System at equilibrium

Ion Concentrations in Neurons

Ion [X]I [X]O

Na+ 50mM 440mM

Cl- 52mM 560mM

K+ 400mM 20mM

c

c

e

e

c

e

(Giant Squid Axon)

Nernst Equation

Ex = RT/zF * ln ([X]o/[X]i)

whereR =universal gas constant (8.31 joules/mole-oK)T = temperature (oK)z = charge of the ionF = faraday constant (96,500 coulombs/mole)

If z = 1 and T = 293o K, thenEx = 58 log ([X]o/[X]i)

If z = -1 and T = 293o K, thenEx = -58 log ([X]o/[X]i)

If z = 2 and T = 293o K, thenEx = 29 log ([X]o/[X]i)

Ion Concentrations in Neurons

Ion [X]I [X]O

Na+ 50mM 440mM

Cl- 52mM 560mM

K+ 400mM 20mM

c

c

e

e

c

e

(Giant Squid Axon)

ECl - = -60mV

EK+ = -75mV

ENa+Na+ = +55mV = +55mV

Goldman Equationor

Goldman-Katz Equation

Takes into account all ionsat the same time and thedifferent permeabilities of the membrane to those ions.

At rest:PK+ = 1.00PNa+= .04PCl- = .45

(PNa+[Na+]o + PK+[K+]o + PCl-[Cl-]i)Erm = 58 log

(PNa+[Na+]i + PK+[K+]i + PCl-[Cl-]o)

(.04(440) + 1.0 (20) + .45 (52)) = 58 log

(.04 (50) + 1.0(400) + .45(560))

(17.6 + 20 +23.4) = 58 log

(2.0 + 400 + 252)

61.0= 58 log

654.0

= 58 log (.093) = 58 (-1.03)

= -59.8mV