Announcements:

• Last lecture1. Organization of the nervous system

2. Introduction to the neuron

• Today – electrical potential1. Generating membrane potential

2. Nernst equation

3. Goldman equation

4. Maintaining ionic distributions

Neural Signaling

Within neurons

Between neurons

electrical chemical & electrical

A Simple Circuit

Bioelectric Potentials

• Neurons have an electrical potential (voltage) across the cell membrane

• The inside of the cell is more negative than the outside – called the Resting Membrane Potential

Measuring Membrane Potential

cell

microelectrodeamplifier

0 mV

-80 mVtime

Resting potentialReferenceelectrode

Bathing solution

Electrophysiology techniques

Amplifier output

Glass micropipette

Silver / Silver chloride wire electrode

3M KCl solution

Very tiny hole (<<0.1m)

Reference electrode

Resting Membrane Potential• How is it generated?

1. differential distribution of ions inside and outside the cell

2. Selective Permeability of the membrane to some ions

• How does unequal concentration of ions give rise to membrane potential ?

Equal concentrations of ions

0.01 MKCL

0.01 MKCL

Artificial ion selective membrane (only K+, not Cl-)

I II

voltmeter

No net movement

0 volts

Cl-

Cl-

Cl-

Cl-

K+

K+

K+

K+

Unequal concentrations of ions

0.1 MKCL

0.01 MKCL

Ion selective membrane

(only K+, not Cl-)

I

K+ concentration

gradient

Cl-

Cl-Cl-

Cl-

K+

K+

K+

K+

Cl-

+-volts

K+

K+

Cl-

K+

II

CHEMICAL

K+

K+

K+

K+

K+

K+

Initial

ELECTRICAL

K+

K+

K+K+

++++

+

+

New Equilibrium

CHEMICAL

K+ K+Cl-

Cl- Cl-

Cl-

Cl-

Cl-

K+

Cl-

Cl-

Cl-

Cl- K+

Cl-

Cl-

Cl-

Cl-

Cl-Cl-

Cl-

Cl-

Unequal concentrations of ions

• Initial diffusion of K+ down concentration gradient from I to II

• This causes + charge to accumulate in II because + and - charges are separated– Remember that Cl- can’t cross the

membrane !

• Therefore II becomes positive relative to I

Equilibrium Potential

• As II becomes +, movement of K+ is repelled

• Every K+ near the membrane has two opposing forces acting on it:

1. Chemical gradient2. Electrical gradient

• These two forces exactly balance each other

• Called the electrochemical equilibrium

• The electrical potential that develops is called the equilibrium potential for the ion.

• Electrical potential at which there is no net movement of the ion

• Note: 1. only a very small number of ions actually contribute

to the electrical potential

2. the overall concentrations of K and Cl in solution do not change.

• To calculate the equilibrium potential of any ion (eg. K, Na, Ca,) at any concentration– we use the Nernst Equation:

Nernst Equation

Equilibrium Potentialof X ion (eg. K+) in Volts

Valence ofion (-1, +1, +2)Faraday constant

Gas Constant Temp (K) Ion Concentration I

Ion Concentration II

[ ]ln

[ ]

I

II

RT XEx

zF X

Nernst Equation

• At 18C, for a monovalent ion, and converting to log10 ,the equation simplifies to:

0.058log

IX

II

XE

z X

0.058 [ ]log

[ ]

I

II

XEx

z X

• By convention electrical potential inside of cells is expressed relative to the outside of the cell

0.058 [ ]log

[ ]

outside

inside

XEx

z X

Example: K+

0.058log

IK

II

XE

z X

0.1 MKCL

0.02 MKCL

outin

= -0.040 Volts = - 40 mV

0.058 [ ]log

[ ]K

X outE

z X in

0.020.058log

0.1KE

• Therefore, – initial movement of K+ down concentration

gradient– When electrical potential of -40 mV develops,

there will be no net movement of K+– Thus K+ is in electrochemical equilibrium

What if there is more than one permeable ion?

0.1 M KCl0.02 M NaCl

0.01 M KCl0.2 M NaCl

outinNa+

K+Na+

Na+

Na+

Na+

Na+

Permeable to K+ and Na+, but not Cl-

K+

K+

K+

K+

K+

• To calculate the overall potential of multiple ions

• use the Goldman Equation

• Considers the permeability of ions and their concentrations

Goldman equation

Permeability Ion concentrationBecause Cl is negative

Voltage

[ ] [ ] [ ]0.058log

[ ] [ ] [ ]

K outside Na outside Cl inside

K inside Na inside Cl outside

P K P Na P ClVm

P K P Na P Cl

Goldman equation

• Example, typical mammalian cell:1. Assume permeability for Na is 1/100 of permeability

for K, and permeability of Cl is 0

2. Assume [K]in= 140, [K]out=5

[Na]in =10, [Na]out=120

1[5] 0.01[120] 00.058log

1[140] 0.01[10] 0

78

Vm

Vm mV

Goldman equation

• The resting membrane potential of most cells is predicted by the Goldman equation

Summary & Key Concepts

1. Unequal distributions of an ion across a selective membrane

• causes an electrochemical potential called the equilibrium potential

2. Two opposing forces act on ions at the membrane

1. A chemical force down the concentration gradient

2. An opposing electrical force

Summary & Key Concepts

3. The equilibrium potential for an ion is described by the Nernst equation

4. Cell membranes are permeable to more than one ion

5. the membrane electrical potential is described by the Goldman equation

So What???

• Everything the nervous system and muscles do depends on the resting membrane potential

Sample question• If two concentrations of KCl solution

across a membrane give an equilibrium potential for K+ of -60 mV, what will the equilibrium potential be if the concentrations on each side are reversed

A. -120 mVB. 0C. +60 mVD. -30 mV