Electrical properties of cell membrane I

(Diffusion & Equilibrium Potential)

OBJECTIVES

1. Define diffusion potential of an ion and simply conclude how to calculate it

2. Discuss the concept of charge separation.

3. Explain the methods of calculation of equilibrium potential when the membrane is permeable to several ions.

4. Define Donnan equilibrium and discuss its consequences

5. Apply this knowledge to a practical instance.

BASICS FACTSMolecular Gradients

Na+

K+

Mg2+

Ca2+

H+

HCO3-

Cl-

SO42-

PO3-

protein

inside(in mM)

14

140

0.5

10-4

(pH 7.2)

10

5-15

2

75

40

outside(in mM)

142

4

1-2

1-2

(pH 7.4)

28

110

1

4

5

ions glucose H2Ourea

Lipid Bilayer

CO2

O2N2

halothane

1. lipid-soluble molecules move readily across the membrane (rate depends on lipid solubility)

2. H2O soluble molecules cross via channels or pores

(a) (b)

Diffusion

1. Ungated Determined by size, shape, distribution of charge, et2.Gated voltage (e.g. voltage-dependent Na+ channels) chemically (e.g. nicotinic ACh receptor channels.

Characteristics:

Na+

in

outNa+ and other ions

Ion Channels

Ion concentrations

Cell Membrane in resting state

K+

Na+Cl-K+ A-

Outside of Cell

Inside of Cell

Na+ Cl-

Cell Membrane is Semi-Permeable

Cell Membrane at rest

Na+ Cl-K+

Na+ Cl-K+ A-

Outside of Cell

Inside of Cell

(K+) can pass through to equalize its concentration

Na+ and Cl- cannot pass through

Result - inside is negative relative to outside

- 55 to -100mv

- +- +- +

- +

Hydration Shells

- +

- +

- +

- +

- +- +

- +

-

+

- +

- +-

+ -

+

- +

- +

- +

- +

- +

- +

- + -

+

- +

- +

In H2O, without a membrane

hydrated Cl- is smaller than hydrated Na+ therefore faster:

Cl-Cl-

Na+

Basic ConceptsForces that determine ionic movement

Volt;- A charge difference between 2 points in space

1. Electrostatic forces1. Opposite charges attract2. Identical charges repel

2. Concentration forces1. Diffusion – movement of ions through semipermeable

membrane2. Osmosis – movement of water from region of high

concentration to low

ELECTRONEUTRAL DIFFUSSION

HIGH SALT CONC;

LOW SALT CONC;

+

-

BARRIER SEPARATES THE TWO SOLUTIONS

+

-+

-

+

-+

-+

-+

-+

-

ELECTRONEUTRAL DIFFUSSION

HIGH SALT CONC;

LOW SALT CONC;

+

-

BARRIER REMOVED

+

-

+-

+-

+-+

-+

-+

-

+ -

CHARGE SEPARATION = ELECTRICAL POTENTIAL

is the potential difference generated across a membrane when a charged solute (an ion) diffuses down its concentration gradient.

( caused by diffusion of ions.)

can be generated only if the membrane is permeable to that ion.

FEATURES;-1. if not permeable to the ion, no DP will be generated no matter how large a conc; gradient is present.

2. magnitude/Unit =, measured in mV,

3. depends on the size of the concentration gradient, where the concentration gradient is the driving force.

4. Sign of the DP depends on the charge of the diffusing ion.

5. DP are created by the movement of only a few ions, and they do not cause changes in the concentration of ions in bulk solution.

Diffusion Potentials(DP)

EP(electrochemical equilibrium), is the DIFFUSION POTENTIAL that exactly balances or opposes the tendency for diffusion down the concentration difference. At the chemical and electrical driving

forces acting on an ion are equal and opposite, FEATURES;-

1.1.Membrane is polarizedpolarized

2.More –ve particles in than out

3. Bioelectric Potential i.e,battery1. Potential for ion movement2. Current

EQUILIBRIUM POTENTIAL (EP)

At Electrochemical EquilibriumAt Electrochemical Equilibrium:

4.Concentration gradient for

the ion is exactly balanced

by the electrical gradient

5.No net flux of the ion

6.No requirement for any

sort of energy-driven pump

to maintain the concentration

gradient

Electrical potential (EMF)

The Nernst potential (equilibrium potential) is the theoretical intracellular electrical potential that would be equal in magnitude but opposite in direction to the concentration force.

When will the

negatively charged molecules stop entering the cell?

- at which an ion will be in electrochemical equilibrium.

At this potential: total energy inside = total energy outside

Electrical Energy Term: zFV

Chemical Energy Term: RT.ln[Ion]

Z is the charge, 1 for Na+ and K+, 2 for Ca2+ and Mg2+, -1 for Cl-

F is Faraday’s Constant = 9.648 x 104 Coulombs / mole

R is the Universal gas constant = 8.315 Joules / °Kelvin * mole

T is the absolute temperature in °Kelvin

Equilibrium potential (mV) , Eion =

EK = -90mV ENa = +60mv

i

o

K K

K

ZF

RTE

][

][log

1. Cell membranes form an insulating barrier that acts

like a parallel plate capacitor (1 μF /cm2)

2. Only a small number of ions must cross the membrane to create a significant voltage difference

3. Bulk neutrality of internal and external solution

4. Cells need channels to regulate their volume

5. Permeable ions move toward electrochemical equilibrium

6. Eion =calculated as NERST POTENTIAL

7. Electrochemical equilibrium does not depend on permeability,

only on the concentration gradient

CAPACITANCE

Electrical properties

The membrane potential

In the resting state, the intracellular space contains more negative ions than the extracellular space

difference of -50 to +120mV

THE MEMBRANE POTENTIAL

MEMBRANE

ExtracellularFluid Intracellular

Fluid

Na+

K+K+

Sodium channel is less open causing sodium to be slower

Potassium channel is more open causing potassium to be faster

+ - MEMRANE POTENTIAL(ABOUT 90 -120 mv)

1. Cell membrane acts as a barrier--ICF from mixing with ECF2. 2 solutions have different concentrations of their ions. Furthermore, this difference in

concentrations leads to a difference in charge of the solutions..

3. Therefore,+ve ions will tend to gravitate towards -ve solution. Likewise, -ve ions will tend to gravitate towards +ve solution.

4. Then the difference between the inside voltage and outside voltage is determined membrane potential.

When a membrane is permeable to several different ions, DP developed depends on:

1.Polarity of the electrical charge of ions.

2. Permeability of the membrane (P) to each ion.

3. Concentration of each ion in two compartments separated by the membrane.

MP is calculated by Goldman-Hodgkin-Katz equation.

icliNaiK

ocloNaoK

m ClPNaPKP

ClPNaPKP

F

RTV

][][][

][][][log

Membrane Potential: Goldman Equation

1. P = permeabilityAt rest: PK: PNa: PCl = 1.0 : 0.4 : 0.45

2. Net potential movement for all ions 3. Known Vm:Can predict direction of movement of any ion ~

NOTE:P’ = permeability

EQUIVALENT ELECTRICAL CIRCUIT MODEL

1. With unequal distribution of ions and differential resting conductances to those ions,

2. We can use the Nernst equation and Ohm’s law in an equivalent circuit model to predict a stable resting membrane potential of -75 mV, as is seen in many cells

NB, this is a steady state and not an equilibrium, since K+ and Na+ are not at their equilibrium potentials; there is a continuous flux of those ions at the RMP

RMP Em = (EK * gK) + (ENa * gNa) + (ECl * gCl)gNa + gK + gCl

Chord Conductance Equation

ClE

Clg

Nag

Kg

Clg

NaE

Clg

Nag

Kg

Nag

KE

Clg

Nag

Kg

Kg

Vm

1.Vm = EK+ +ENa+ + ECl-....

Vm = membrane potential, not equal to Eion;

2.Weighted avg of equilibrium potentials of all ions to which membrane is

permeable

3.Esp. K+, Na+, Cl-; changes in ECF K+ alters RMP in all cells

Passive distribution Donnan equilibrium

The ratio of positively charged permeable ions equals the ratio of negatively charged permeable ions

III

K+

Cl-

III

[K+] = [K+]

[Cl-] = [Cl-]

Start Equilibrium

Mathematically expressed:

•Another way of saying the number of positive charges must equal the number of negative charges on each side of the membrane

[ ] [ ]

[ ] [ ]I II

II I

K Cl

K Cl

1. BUT, in real cells there are a large number of negatively charged, impermeable molecules (proteins, nucleic acids, other ions)

2. call them A-

III

K+

Cl-

Start

A- III

[K+] > [K+]

[Cl-] < [Cl-]

Equilibrium

A-

III

[K+] > [K+]

[Cl-] < [Cl-]

Equilibrium

A- [K+]I = [A-]I + [Cl-]I

[K+]II = [Cl-]II

If [A-]I is large, [K+]I must also be largeA=phosphate anions+ protiens macromolecules

+’ve = -’ve+’ve = -’ve

space-charge neutrality

-----------

+++++++++++

EXAMPLE

1. The product of Diffusible Ions is the same on the two sides of a membrane.

33 K+

33 Cl-

67 K+

50 Pr -

17 Cl-Step 2

66 Osmoles 134 Osmoles

50 K+ 50 K+

50 Cl- 50 Pr -Initial

100 Osmoles 100 Osmoles

Final

33 ml 67 ml

33 K+

33 Cl-

67 K+

50 Pr -

17 Cl-

Total Volume100 ml

IonsMove

H2Omoves

Human Potentials

1. Strong potentials in muscles--EMG, ECG (electromyogram

and electrocardiogram).

2. Weaker potentials from brain--EEGs.

3. Evoked potentials allow study of changes.

4. Computer averaging allows study of deep brain potentials:

Event-related potentials in sensory systems and cognition.