1. Lecture 15
Passive and active transport
Channels and transporters
Osmosis

2. <x2> - mean square distance (cm2)
Diffusion across exchange epithelium
“random walk”
Einstein eqn:
<x2> - mean square distance (cm2)
D – diffusion coefficient (cm2/s)
t – time interval (s)

3. The Einstein relationship is non-liner:
For a small molecule diffusing in the cytoplasm:
D = 0.5·10-5 cm2/s
x = 1 mm t = 1 ms
x = 10 mm t = 100 ms
x = 100 mm t = 10 s
x = 1 m t = 107 s = 3.2 yr
Need for circulation!

4. Ability to Move by Diffusion
substance MW
r (nm)
D cm2sec-1
μm in sec
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 27

5. Diffusion across membranes1 2
Diffusion rate
concentration gradient
14C-glycerol
Flux J C1
 J = P C1
(2)
time
rate
J = P C2
Does rate change with C2?
Jnet = P ΔC

6. The NET flux is the difference of the two unidirectional fluxes
Independent diffusion
Single-file diffusion through a channel
Electric potential DE DE
where n is the maximal number of ions interacting in the pore
H.H. Ussing, 1949

7. Permeation Through the Phospholipid Membrane
defect propagation or solubility diffusion
volume of substance
ability to dissolve into membrane
oil
water
Partition coef.
membrane: Jnet = P ΔC
bulk: Jnet = D ΔC/Δx

8. e2=2-6
Born energy
e1=80

10. Enough to cause cell lysis
Poorly permeable

11. J = v × concentration = u×c×Force……general flux equation
Flux with Force +
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

12. Free Energy/ mole = chemical potential (μ=dG/dc)
μ = μo + RT lnc + zFφ + VP + mgh +….
For simple diffusion of uncharged substance… z = 0; P=0; ignore gravity
…same as Fick’s Law if D = uRT

13. Transport…catalyzed translocation across membranes
Simple diffusion is not a transport process
Passive: energy independent
Active: energy dependent
Coupled to an energy source: light, ATP, redox, gradient
Transport against an electrochemical gradient 1 2 S
Equilibrium: ΔμS = 0
Note: [S]1 not necessarily equal to [S]2 at equilibrium!!

14. initial
final
S+1
-60 mV
-60 mV
S+1
S+1
[S+1]out = 1 mM
[S+1]in = 0 mM
[S+1]out = 1 mM
[S+1]in = 10 mM
Active or passive transport?
Nernst Equation...valid at equilibrium

15. K+ Cl- K+ Cl- K+ Cl- Equilibrium (reversal) potential let K+ cross #2#1 K+
Cl- + -
equilibrium #3
(Boltzmann)
(Nernst)
At 37oC:

16. Which are passive?
passive
passive

17. 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)

18. Non-specific water-filled channels Example: Bacterial PORIN, OmpF
Water-filled pore
(the first crystallized membrane protein, b-barrel)

19. Porin OmpX
Permeation of solutes by size and/or charge

20. MscL closed
MscL open
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.
(from Chiang et al., 2005)

21. Gap junctions
connexins
(from Sosinsky)

22. Gap Junction Channel
From Unger et al., 1999

23. Oocyte injected with aquaporin mRNA

24. C1 = C2 C1 > C2 C1 > C2 P1 = P2 P1 = P2 P1 > P2 H2O
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.

25. C1 > C2 P1 = P2 P1 > P2 P2-P1 = RT(C2-C1) p1 = RTC1 p2= RTC2
H2O
P1 > P2
pressure gauge
Equilibrium is achieved quicker if we close the left compartment
Hydrostatic pressure difference at equilibrium:
P2-P1 = RT(C2-C1)
Osmotic pressures
of individual solutions:
p1 = RTC1
p2= RTC2
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

26. Aquaporins and aquaglyceroporins

27. Aquaporin = water channel
The salient property of aquaporins is that pass only water (occasionally glycerol), but NO ions!
From Agre and Kozono, 2004

28. The Grotthuss mechanism
Proton-hopping mechanism is prevented in aquaporins by strict orientation of water in each half of the channel
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.
Cation Mobility cm2 V-1 s-1 in water
NH ×10-3
Na ×10-3
K ×10-3
H ×10-3
T. Grotthuss, 1806