Lecture 15

Passive and active transport

Channels and transporters

Osmosis

Diffusion across exchange epithelium

bas ila r m em brane

10 m vascularendothe lium

B LO O D

IN TE R S TIT IU M

Dtx 22 Einstein eqn:

<x2> - mean square distance (cm2)D – diffusion coefficient (cm2/s)t – time interval (s)

“random walk”

The Einstein relationship is non-liner:

For a small molecule diffusing in the cytoplasm:

D = 0.5·10-5 cm2/s

Dxt2

2

x = 1 m t = 1 ms

x = 10 m t = 100 ms

x = 100 m t = 10 s

x = 1 m t = 107 s = 3.2 yrNeed

for

circ

ula

tion!

Ability to Move by Diffusion

substance MW r (nm)D cm2sec-1

μm in 1sec

μm in 1 hour

water 18 0.15 2.0E-05 63.2 3795

oxygen 32 0.2 1.0E-05 44.7 2683

urea 60 0.4 1.1E-05 46.9 2814

glucose 180 0.5 7.0E-06 37.4 2245

RNAse 13700 1.8 1.0E-06 14.1 849

Hemoglobin 68000 3.1 7.0E-07 11.8 710

TMV 30,000,000 5.0E-08 3.2 190

vesicle 500 4.0E-09 0.9 54

mitochondrion 2000 1.0E-09 0.4 27

Diffusion across membranes

1 2

Flux J C1

Jnet = P ΔC

J = P C1

Diffusion rate concentration gradient

14C-glycerol

(2)

time

rate

Does rate change with C2?

J = P C2

The NET flux is the difference of the two unidirectional fluxes

RT

EzF

c

c

o

i exp][

][

*

Independent diffusion Single-file diffusion through a channel E

lect

ric p

oten

tial

n

o

iRT

EzF

c

c

exp][

][

*

where n is the maximal number of ions interacting in the pore

H.H. Ussing, 1949

*

*

E E

Permeation Through the Phospholipid Membrane

defect propagation or solubility diffusion

volume of substance ability to dissolve into membrane

membrane: Jnet = P ΔC

x

DKP wo

/

bulk: Jnet = D ΔC/Δx

oilwater

water

oilwo C

CK /Partition coef.

r

qqdqG

q

el 0

2

00 84

1

120

2

10

2

20

2 11

888 r

q

r

q

r

qGBorn =2-6

=80Born energy

Poorly permeable

Enough to cause cell lysis

Flux with Force

+

0 5 10 15 20 25 mV (voltage φ)

Electric field = dφ/dx

Direction of force on ion?

Force causes….? Acceleration? No…velocity…? friction

Velocity, v = Force × mobility = u×Force; u is mobility

J = v × concentration = u×c×Force……general flux equation

Free Energy/ mole = chemical potential (μ=dG/dc)

μ = μo + RT lnc + zFφ + VP + mgh +….

...1

dx

dhmg

dx

dPV

dx

dzF

dx

dc

cRT

dx

dForce

For simple diffusion of uncharged substance… z = 0; P=0; ignore gravity

dx

dcuRT

dx

dc

cucRTJ

1…same as Fick’s Law if D = uRT

Transport…catalyzed translocation across membranes

Passive: energy independent

Active: energy dependent

•Coupled to an energy source: light, ATP, redox, gradient

•Transport against an electrochemical gradient

Simple diffusion is not a transport process

Equilibrium: ΔμS = 0

12

SS

FzS

SRT SS )

][

][ln(

2

1

Note: [S]1 not necessarily equal to [S]2 at equilibrium!!

initial final

S+1

-60 mV

[S+1]out = 1 mM

[S+1]in = 0 mM

[S+1]out = 1 mM

[S+1]in = 10 mM

S+1

S+1

-60 mV

Active or passive transport?

)][

][log(60

1

2

1

S

SmV

zS Nernst Equation...valid at equilibrium

K+Cl-

K+

Cl-

#1

kT

z

out

in ec

c

(mV) log5.61

ln

out

inrev

out

in

c

c

zE

c

c

zF

RT

(Boltzmann)

(Nernst)

K+Cl-

K+

Cl-

let K+ cross#2

K+Cl-

K+

Cl-

+

+

+

-

-

-

equilibrium#3

Equilibrium (reversal) potential

At 37oC:

passive

passive

Which are passive?

Solute transport Channels and Facilitators

• Water channels (aquaporins)• Intercellular gap junctions (connexins)• Mitochondrial channels (ATP/ADP

exchange)• ABC transporters (MDR proteins,

CFTR)

• Diffusion Facilitators: Glucose transporters (GLUT1-12)

Water-filled pore

Non-specific water-filled channels

Example: Bacterial PORIN, OmpF

(the first crystallized membrane protein, -barrel)

Porin OmpX

Permeation of solutes by size and/or charge

WT MscL has one single Tyrosine (Y) per subunit in position 79. If we insert second aromatic residue (Y or W) in position 93, the channel becomes non-functional. If we move the second Y (or W) to position 102, this partially rescues the defect.

MscL closed MscL open

(from Chiang et al., 2005)

Gap junctions

connexins

(from Sosinsky)

Gap Junction Channel

From Unger et al., 1999

Oocyte injected with aquaporin mRNA

C1 = C2 C1 > C2

P1 = P2 P1 > P2

Water flows into the left compartment through the semi-permeable membrane down its own concentration gradient. It tends to dilute the contents of the left compartment raising the level of fluid at the same time. The increased hydrostatic pressure eventually counters the water influx and at equilibrium the net water flow is zero.

C1 > C2

P1 = P2

H2O

1 = RTC1 2= RTC2

Hydrostatic pressure difference at equilibrium:

Osmotic pressuresof individual solutions:

P2-P1 = RT(C2-C1)

C1 > C2

P1 = P2

H2O

P1 > P2

pressure gaugeC1 > C2

P1 = P2

H2O

P1 > P2

pressure gauge

A difference of C = 1 mOsm creates pressure of 18.4 mm Hg

100 mOsm is equivalent to 1840 mm Hg or 2.42 atm

Equilibrium is achieved quicker if we close the left compartment

Aquaporins and aquaglyceroporins

Aquaporin = water channel

From Agre and Kozono, 2004

The salient property of aquaporins is that pass only water (occasionally glycerol), but NO ions!

The Grotthuss mechanism

Proton-hopping mechanism is prevented in aquaporins by strict orientation of water in each half of the channel

Cation Mobility cm2 V-1 s-1 in water

NH4+ 0.763×10-3

Na+ 0.519×10-3

K+ 0.762×10-3

H+ 3.62×10-3

Proton has abnormally high mobility in water and other dissociating fluids because it does not diffuse all the way, protons are re-distributed by binding and dissociation.

T. Grotthuss, 1806