1. “Deriving” ion concentration gradients and fluxes
Bi 1 Session 5
Tuesday, April 4, 2006
“Deriving” ion concentration gradients and fluxes

2. What is the most abundant molecule in an organism?

3. A reminder from Chem 1:
H2O MW = 18
Density ~ 1 kg/l
Therefore the concentration of water in an aqueous solution is
~ (1000 g/liter )/(18 g/mol) = 55 mol/liter or 55 M.
All other molecules in the body are at least 100 times less concentrated.

4. Ionic compositions inside and outside a typical mammalian cell

5. One clue to a cell’s ionic concentrations:
Sea Water

6. Membranes provide a barrier to diffusion around cells,
forming compartments
Little Alberts 2-20
© Garland
Little Alberts 12-2
© Garland
Little Alberts 12-1
© Garland
. . . But specialized proteins (channels and transporters) control the permeation of many molecules

7. One Benefit of Compartmentalization and Membranes:
molecules can be improved by selection

8. How much is 4 mM protein?
A typical protein has 500 amino acid residues.
An average residue has a molecular mass of 110.
Therefore the average protein has a molecular mass of 55,000.
( 4 x 10-3 mol/liter) x (5.5 x 104 g/mol) = 2.2 x 102 g/l
= 220 g/l.
The cell is ~22% protein!

9. A Cell that Lacks Concentration Gradients
Na+
Na+
Na+
External
Monovalent cations:
High Na+
Low K+
Na+
Na+
Na+
Na+ K+
Internal:
same as
External
Na+
Na+
Na+
Na+
Na+
Na+ K+

10. Storing energy in a concentration gradient without osmotic stress:
Simply reverse the ratio of Na+ and K+
Na+
Na+
Na+
External
Monovalent cations:
High Na+
Low K+ K+
Internal:
Low Na+
High K+
Na+
Na+
Na+
Na+
Na+ K+

11. Little Alberts 12-10 © Garland
The “Na+ pump” splits ATP to make a Na+ and K+ concentration gradient 3 2
A transporter protein moves a few ions for each conformational change
Little Alberts © Garland

12. Converting a concentration gradient to an electrical potential:
Create permeability to one ionic species (K+)
Na+
Na+
Na+ K+
K+ channels
Lost positive charge leads to net negative interior potential
Na+ K+ K+ K+
Na+ K+
Na+
Hundreds or thousands of ions flow through a channel protein for each opening
Na+
Na+

13. the energy of discharging the concentration gradient for K+ ions
The Nernst potential:
the energy of discharging the concentration gradient for K+ ions
balances
the energy of moving the K+ ions through the potential difference K+ K+ K+ K+ K+

14. Chem 1 textbook (OGN)
Figure 12-10

15. Deriving the Nernst potential (chemical notation)
OGN Figure 7-7

16. Deriving the Nernst potential
(for physicists and electrical engineers)

17. Deriving the Nernst potential
(for Biologists)

18. Na+ Na+ Na+ Na+ Na+ Na+ Na+ Na+ What is the selective advantage . . .
that the membrane is permeable at rest to K+ rather than to Na+?
a small inward leak of Na+ would change the internal [Na+]
by fractionally more than
a small outward leakage of K+ would change internal [K+ ]
Na+
Na+
[K+]I = 140 mM; [Na+]I = 10 mM. A leak of 10 mM:
[Na+] would increase from ~ 10 mM to 20 mM, doubling [Na+]I and causing a 17 mV change in the Nernst potential.
Na+
But a similar outward leak in K+ would decrease [K+]i from 140 mM to 130 mM, causing a < 2 mV change in the Nernst potential for [K+].
Na+
Na+
Conclusion: cell function is more stable when the resting permeability is to K+ .
Na+
Na+
Na+

19. Other monovalent ions
Under what circumstances do cells use Cl- fluxes?
 Apparently it’s not straightforward to make a permeability pathway that distinguishes among anions using protein side chains. Therefore there is no “anion pair” corresponding to K+ / Na+. Few cells use anions to set the resting potential.
But some channels do use anion (mainly Cl-) fluxes (Lecture 21, cystic fibrosis).
Could cells utilize plasma membrane H+ fluxes?
 Probably not.
There are not enough protons to make a bulk flow, required for robustly maintaining the ion concentration gradients.
(but some very small organelles (~ 0.1 mm) and bacteria do indeed store energy as H+ gradients).

20. Divalent Cations
What is the selective advantage that cells maintain Ca2+ at such low levels?
Cells made a commitment, more than a billion yr ago, to use high-energy phosphate bonds for energy storage.
Therefore cells contain a high internal phosphate concentration.
But Ca phosphate is insoluble near neutral pH.
Therefore cells cannot have appreciable concentration of Ca2+;
they typically maintain Ca2+ at < 10 –8 M.
What is the selective advantage that cells don’t use Mg2+ fluxes?
The answer derives from considering the atomic-scale structure of a K+ -selective channel (next slide), which received the 2003 Nobel Chemistry Prize:
(Swiss-prot viewer must be installed on your computer)

21. K+ ions lose their waters of hydration and
H2O
K+ ion
carbonyl
K+ ions lose their waters of hydration and
are co-ordinated by backbone carbonyl groups
when they travel through a channel.

22. Time required to exchange waters of hydration
Na+ , K+
1 ns
(~ 109/s)
Ca2+
5 ns
(2 x 108/s)
Mg2+
10 ms
(105/s)
Conclusion:
Na+ , K+, and Ca2+ can flow through single channels at rates > 1000-fold greater than Mg2+
Mg2+ is suitable for transporters, but not for channels.

23. Cells have evolved elaborate processes for pumping out intracellular
Na+ and Ca2+
These gradients can be used in two ways:
1. The gradients are used for uphill “exchange” to control the concentrations of other small molecules.
2. Transient, local increases in intracellular Ca2+ and Na+ concentrations can now be used for signaling inside cells!
Next image

24. Na+-coupled cell membrane neurotransmitter transporters:
major targets for drugs of therapy and abuse
Antidepressants
(“SSRIs” =
serotonin-selective
reuptake inhibitors):
Prozac, Zoloft, Paxil, Celexa, Luvox
Drugs of abuse:
MDMA
Attention-deficit
disorder medications:
Ritalin, Dexedrine,
Adderall,
Strattera (?)
Drugs of abuse:
cocaine
amphetamine
Trademarks:
Presynaptic
terminals
Na+-coupled
cell membrane
serotonin
transporter
Na+-coupled
cell membrane
dopamine
transporter
cytosol
outside

25. Some ideas about ion-coupled transporters

26. Some ideas about ion-coupled transporters
“alternating access”

27. 3 classes of proteins that transport ions across membranes:
(transporter)
modified from
Little Alberts 12-4
© Garland
Ion channels that flux many ions per event
Ion-coupled transporters
“Active” transporters (pumps) that split ATP
These proteins have evolved in a natural—perhaps necessary--way to provide that
The resting potential arises via selective permeability to K+
This selective permeability also leads to the Nernst potential.
Transient breakdowns in membrane potential are used as nerve signals.
Neuronal and non-neuronal cells also signal via transient influxes of Na+ and Ca2+.

28. Hot news from the human genome 2001 - 2006
Transport proteins (transporters, pumps, and channels)
are 5% of the human genome . . .
~ 1500 genes

29. End of Lecture 5