membrane transport of electrolytes

7/28/2019 Membrane Transport of Electrolytes

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Prof. Wei-Shou Hu lecture notes 1

Communications BetweenCells and Environment:

Transport across Membrane

ChEn 3701

Topic 19

I.PERMEABILITY AND DIFFUSION THROUGH MEMBRANE

A.Chemical potential gradient

B.Electric potential gradient

II.FICKS LAW OF DIFFUSION

A.Estimation of diffusion coefficient

B.Diffusion across the membrane

III.TRANSPORT PROTEINS

A.Transporters-uniporter, symporter and antiporter

B Uniporters

C Symporters and antiporters in active transport

Mass Transfer

Convection

Movement of materials dueto fluid flow, e.g.

Delivery of oxygen in thebody fluid

Diffusion

Transfer of material in astagnant medium due toconcentration difference ofsolute

Ficks Law of Diffusion

Diffusion flux is proportional toconcentration gradient

C

x

x1 x2

C1

C2

Flux J

slope isc

x

2 1

2 1

c cc

x x x

=

cJ D

x

=

The solute diffuses from a

position with a high

concentration to another

position with a low

concentration; i.e. when

concentration c1>c2, flux is

positive from x1 to x2


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Estimation of Diffusion Coefficient

The Stokes-Einstein equation is written as

where kis Boltzmans constant, Tis absolute temperature, is the viscosity of thesolvent, and ris the radius of solute molecule.

For a spherical molecule, the molecule mass is:

For proteins, can be assumed to be constant.

Thus the diffusion coefficient of a solute in a liquid is approximately inverselyproportional to the cubic root of the molecular weight.

6

kTD

r=

34

3r =

1/3 1/3 1/3

2( ) =constant, thus,

3 6

kTDM D M

=

1/3

2( )

3 6

kTD

=

Partition Coefficient and Solubility

When two materials or two mixture ofmaterials are brought together, and

yet they cannot be completely mixed

to become homogeneous, then

different phases coexist

A solute that can be dissolved in both

phases eventually reaches equilibrium

in the two phases

The concentrations of the solute in the

two phases at equilibrium are related

by a partition coefficient

C

HC

Phase 1

Phase 2

Two phases in equilibrium

H is the partition coefficient

Diffusion across Cell Membrane

x1 x2

c1 c2

HcHc11 HcHc22

Side 1 Side 2

Diffusion of c from x1 to x2 is from the solutions on theopposite sides of the membrane. The concentrationdifference between the two sides causes diffusionacross the membrane proportional to c1-c2; it isproportional to Hc1-Hc2

Membrane is treated as a distinct phase

HC1

x2

C1

x1

C2

HC2

Diffusion Across the Membrane

H is the partition coefficient

( )= = AA

1 2 2 1DH

J C C x x

A: Permeability

DH

Flux across the membrane is described by

l

C1

C2

Outside Inside

HcHc11

HcHc22

Concentration in the membrane is

hard to measure. The concentration

in the solutions C is often used. The

concentration in the membrane is

calculated using the value of H.


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10 2 cm/s in P~3.6 x107 cm2/s in Do2

Cells use transporters for transport of most

compounds, including water (water can

also diffuse through membrane).

Transporter is selective for different solutes,

and in the transporter, the permeability is

not that in the membrane.

Permeability is too lowto sustain cellsnutritional needs

Using transporters the solute either interacts with the

molecular recognition mechanism of the transporter

protein and move across, or being convected with fluid

flow through the interior of the transporter protein

molecules, instead of simply diffusing through the lipid

bilayer membrane. So, even though the cross sectional

area of transporters is much smaller than that of lipid

bilayer membrane, the flux can be much higher. It

follows saturation type of kinetics.

Transporter mediate solute

transfer differs from diffusion

across membraneMost ionic species (like other species) have different concentrations inside and

outside the plasmic membrane.

The gradient of sodium and potassium across cytoplasmic membrane haveopposite directions.


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Transport of Electrolyte and

Membrane Potential

Strong electrolytes completely dissociate inaqueous solution and exist in ion-counter ionpair

Transport of ionic species in pairs to maintainelectric neutrality;

Otherwise charge imbalance occurs over adistance and electric potential is created

In living systems charges are slightly imbalancedacross cellular membranes to create an electricpotential gradient

Electric Membrane Potential

Gradient

When a electric potential gradient exists over aspace, there is a high propensity to draw ionicspecies to move in the direction that will result inreverting to electric neutrality

In cellular membranes the electric potentialdrives attractively charged molecules to moveacross the membrane via transporter

For charged molecules, there are thus two

potential gradient to drive their transfer acrossthe membrane: chemical potential gradient, (i.e.concentration difference) electric potentialgradient (measured in mV)

Diffusion of Electrolytes

The flux equation for an electrolyte can be written as(Nernst-Planck equation)

The flux is affected by both concentration gradient andelectric potential gradient

is the electrostatic potential, zis the valence of charge,is Faradays constant (96500 coulomb/volt).

= +

j D C Cz

RT

Membrane Electric Potential

Gradient

Electric potential gradient provides much higher

energetic potential than chemical gradient for

ionic species to migrate at a given concentration

difference It takes only a small amount of ion to migrate

over a distance to create a electric potential, as

compared to chemical gradient

Conversely, it takes only a small amount of ionic

species to migrate to neutralize the electric

potential


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Diffusion of a strong-one-electrolyte

solution

In a solution with only one electrolyte of single

valence, the two ions have the same chemical

gradient.

Their diffusion is interactive, because in addition

to responding to chemical gradient, they also

must maintain electric neutrality

The effective diffusion coefficient for theinteractive diffusion is the harmonic average of

their diffusion coefficient

1 2

2

1 1D

D D

= +

To transport only one ion without its

counter ion has a very high energentic

cost

Membrane as a capacitor

Q=C Q is the amount of charge, C is the capacitance that has unitsof Farads, is the electropotential10 m diameter cell with a surface area of 3.14 x 10-6 cm2 has a capacitance

typical of a cytoplasmic membrane of about 1 microfarads per cm2

Electropotential difference of 50 mV across the membrane

The amount of charges moved across in terms of number of moles this

quantity becomes

The intracellular potassium concentration is about 100 mM. In a cell of 10 m diameter,

the volume is (10 m)3/6. Thus, the total amount of K+ in a cell is 5.2 x 10 -14 mole. It

can be seen that it takes of transferring a very tiny fraction of the intracellular K+ ion,

(less than 3 x 10-5) to create a 50 mV electropotential across the membrane.

2 6 2

13

13

18

1 / (3.14 10 ) 0.05

1.57 10

1.57 10

96500

1.65 10

Q Farad cm x x cm x v

x coulomb

xmole

x mole

=

=

=

=

=-RT/Vln(1-x)

For dilute solutio

=- RTC

Another Driving force for transport across

membrane: Osmotic PressureGeneral Classification of Transporters


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Different Mechanisms of

Membrane Transport

Passive Diffusion (only O2, N2, CO2 , H2O)

Facilitated Diffusion (facilitated transport)

Uniporters

Ion channels and water channel

Active Transport

ATP dependent pump

Co-transporters

Symporters, Antiporters

CELLs strategy in controlling Membrane Traffic

1. Use Na-K ATPase to create Na+, K+ and electric gradient

At the expense of ATP

2. Use channel protein to maintain the electric potential within a range

When the channel opens

quickly more along

changing membrane quickly

1&2. Sustain the Na+, K+ gradient and electric potential

3. Use uniporter to move unchanged solute along the gradient

4. Use co-transporter (transporting also H+) with charged solute along thegradient

5. Use co-transporter (K+

or Na+

co- transport) for active transport.As Na+ moves along the gradient, it also drives glucose against thegradient

Driving Forces in Membrane Transport Chemical potential gradient

Ionic species

Uncharged species

Electric potential

Osmotic pressure

Energy for Active TransportATP

Na+, K+, H+ gradient

Capacity or Reservoir of driving forceATP: 1mM

Na+: (140-12)=130 mM100 mM

K+: 100 mM

H+

10-4

mMCa2+ 0.2 M in solution, 10 M in reservoir (conjugated wth protein or store in ER)

Magnitude of concentration gradient

Glucose: 5 mM

Amino acid: 1 mM

Na+: 130 mM

K+: 100 mM

Ca2+: 1 mM

H+: 10-4 mM

Compounds transportedNutrients

Osmotant, electrolytes

Signaling:

Ca2+: low concentration

K+: altering electric potential

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Different types of Membrane

Transport Systems


Uniporters


Active Transport

ATP dependent pump

CotransporterSymporters, Antiporters

A+ B-

A+ B-

B+

B+A+

A+

General Classification of Transport Systems

Uniporters

Transport uncharged molecules, such as

sugar, or molecules with no net charge,

eg. Neutral amino acids

Transport along the concentration gradient

(i.e. facilitated diffusion)Different glucose transporters have different Km. Different cells or cells under

different conditions express different levels of transporter proteins to regulate

its Vmax for transport.

Some glucose transporters respond to insulin.

Example of uniporters

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Uinporter: GLUT1 GLUT2

Kinetics of uniporter can be described by a saturation type of kinetics

Cotransporters

Two different roles for different types of co-transporters

1. Co-transport ionic molecules to maintaincharge neutrality

-otherwise electric gradient will be created or perturbed

2. Co-transport a solute with Na+ or K+

- Use the chemical potential of Na+ or K+ gradient totransport a solute

- The transport of the solute is coupled to Na+ or K+transport

- As Na+ or K+ is driven to migrate along its gradient,glucose is driven to move against its gradient

Sodium dependent glucose symporter

Because of its concentration gradient Na+ is driven to enter the cell. As they

enter the cells, the transporter also carries glucose molecule across against the

glucose gradient. It allows glucose to go from the low glucose side of intestine

to enter the epithelial cells in which glucose has accumulated.

Each mole of glucose is co-transported with two moles of Na+.

Use Na+ gradient as driving force to pump

glucose (against gradient)

The Significance of Coupling Glucose Active

Transport to Na+ co-transport

From Nernest equation =

2

1

C= nRT ln

C

eG nzF

= +

2

1

c e

{ }

= G + G

CG n RT ln zF

C

Gibbs free energy change for Na+ transport

Gibbs free energy change for uncharged solute transport. = 2

1

c

CG nRT ln

C

z = valence

R = 8.314 J/K mol

= potential energy differenceT = Absolute temperature Ge contributes nearly 25% ofG

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ATP-dependent Pump

P class pump

V class proton pump

F class proton pump

ABC transporter superfamily

Example: Na+-K+ ATPase Lysosomal proton pump

Mitochondrial ATP Synthase

Multiple drug resistance

(MDR)

P class pump: ATP-dependent Pump Na+-K+ ATPase

Km,Na+:0.6mM

Km,K+:high

Km,Na+:high

Km,K+:0.2mM

Phosphorylation of protein by ATP is key to its

pumping

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P class pump: Ca2+-ATPase in Skeletal Muscle Cellsalong the membrane of

sarcoplasmic reticulum (SR) membrane

Ca2+ ~ 10-67M

Ca2+ ~ 10-2M

SR is calcium ion reservoir, also has binding proteins to reduce soluble Ca2+

Reduce energy required to pump calcium back

P class pump: Ca2+-ATPase Calmodulin-a calcium pump regulatory

protein

Ca2+ in cytosol highly regulated to be below 0.2 M

Calmodulin is a calcium binding protein

At high calcium concentration, Ca2+ binds to calmodulin

Triggers allosteric activation of Ca2+-ATPase, pump out Ca2+

from cytosol out of the cell

V class ion pump

Many vesicles

are acidic:

e.g.lysosome

pH 4.5-5

electrogenic

Non-

electro-

genic

To generate pH gradient

And membrane potential; cannot

pump large quantities of H+

To pump proton to acidify a large

compartment

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Generate ATP using proton gradient

instead of using ATP to pump proton

ATP synthase

ATP-binding

cascade family

Channel Proteins

Ion channels

- For major ions: Na+, K+, Cl-

- Selective rapid movement alongconcentration gradient.

Water channel

Ion Channels

k+ channel

gated

ungated

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Water channel protein Aquaporin

Passive Diffusion


Uniporters


Co-transporters


Active Transport

ATP dependent pump

P class pump

V class proton pump

F class proton pump

ABC transporter superfamily

Co-transporters


Homeostasis, coordination of

different transporters

The transport of many species requires

the interactions of many transport systems

to act in concert to sustain a homeostatic

system

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The transport of glucose from intestinal lumen into intestinal epithelial cells thus

consumes Na+ gradient.

The Na+/K+ATPase sustains the gradient of Na+

Glucose moves down the gradient via Glut2 into blood

Balance of Intracellular Ion

+ + + +

+ + + +

+ + + +

+ ++

++

+

= + = +

+ = +

=

= +

( [ ] ) ([ ] ) ( )[ ] ( )

([ ] ) ( )[ ] ( )

( )(specific growth rate), then:

([ ] )

i ii K Na K ATPase K channel

ii K Na K ATPase K channel

i

K Na K ATPase K chann

d V K d K d VV K V J J

dt dt dt

d K d VK J J

dt Vdt

d Vdefine

Vdt

d KJ J

dt

+

change of intracellular concentration

=sum of fluxes (ATPase+channel) - dilution due to growth

[ ]iel

K

Homeostasis of Major Ions

+ + + +

+ + + + +

++

++

= +

= + +

= + +

- mediated transporter

- mediated transporter

[ ][ ]

[ ] 3[ ]2

[ ][ ]

iiK Na K ATPase K channel

i iK N a K ATPase Na channel Na

iiCl pump Cl channel Cl

d KJ J K

dt

d NaJ J J Nadt

d ClJ J J Cl

dt

0 0 0

[ ] [ ] [ ]n

[ ] [ ] [ ]Na i K i Cl i

Na K Cl

P Na P K P Cl RT

P Na P K P Cl

+ +

+ +

+ + =

+ + A

Intracellular concentration changes:

The changes in their concentrations is constrained by (1) the

net change of charges is zero, (2) electric potential

Where Ps are Permeabilities

Goldman-

Hodgkin-KatzGHK) equation

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Acidification of stomach lumen

HCO3-

H2O +H+

carbonic anhydrase

The kinetics of the reaction is not fast enough, use carbonic anhydrase to push reaction rightward.

Storage of sucrose in plant leaf vacuoles

Bacterial Transport System

Bacterial Transport System

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Fur

GATAATGATAATCATTATCCTATTACTATTAGTAATAG

Fur

Fur

GATAATGATAATCATTATCCTATTACTATTAGTAATAG

Iron limiting

condition

Iron rich

condition

Iron acquisition genes

Iron acquisition genes

Fur

Fe2+

Fur

Negative Regulation of Iron Uptake

Genes by Fur

Fur (the regulatory protein) is coded by gene fur.

membrane transport of electrolytes

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