Transcript No Slide Title

Bi 1 Session 5
Tuesday, April 4, 2006
“Deriving” ion concentration gradients and fluxes
1
What is the most abundant molecule in an organism?
Molecule
Class Vote
water
Ethanol
90
Comments
2
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.
3
Ionic compositions inside and outside a typical mammalian cell
Extracellular
Na+
K+
Cl-
145 mM
4 mM
110 mM
Intracellular
(Cytosol)
15 mM
150 mM
10 mM
Ca2+
Mg2+
2 mM
2 mM
10-8 M
0.5 mM
Pi
H+
Protein
2 mM
10-7 M
0.2 mM
40 mM
10-7 M
4 mM
4
One clue to a cell’s ionic concentrations:
Sea Water
Sea Water
Na+
K+
Cl-
457 mM
9.7 mM
536 mM
Extracellular
Conc
145 mM
4 mM
110 mM
Intracellular
(Cytosol)
15 mM
150 mM
10 mM
Ca2+
Mg2+
10 mM
56 mM
2 mM
2 mM
10-8 M
0.5 mM
Pi
H+
Protein
0.7 mM
10-7 M
2 mM
10-7 M
0.2 mM
40 mM
10-7 M
4 mM
5
Membranes provide a barrier to diffusion around cells,
forming compartments
Little Alberts 2-20
© Garland
Little Alberts 12-2
© Garland
. . . But specialized proteins
(channels and transporters)
control the permeation of
many molecules
Little Alberts 12-1
© Garland
6
One Benefit of Compartmentalization and Membranes:
molecules can be improved by selection
7
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!
8
A Cell that Lacks Concentration Gradients
External
Monovalent cations:
High Na+
Low K+
Na+
Na+
Na+ +
Na
Internal:
same as
External
Na+
Na+
Na+
Na+
Na+
K+
Na+
Na+
Na+
Na+
K+
9
Storing energy in a concentration gradient
without osmotic stress:
Simply reverse the ratio of Na+ and K+
External
Monovalent cations:
High Na+
Low K+
Na+
Na+
K+
K+
Internal:
Low Na+
High K+
Na+
Na+
Na+
Na+
K+
K+
K+
Na+
Na+
K+
10
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 12-10 © Garland
11
Converting a concentration gradient
to an electrical potential:
Create permeability to one ionic species (K+)
Na+
Na+
Na+
K+
Na+
Lost positive charge
leads to net negative
interior potential
K+
K+
K+
K+
Na+
Na+
K+ channels
Hundreds or thousands of ions flow through a channel protein for each opening
Na+
Na+
12
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+
13
Chem 1 textbook (OGN)
Figure 12-10
14
Deriving the Nernst potential (chemical notation)
G  RT ln
Ki
 zFV ; at equilibrium G  0 ; therefore
Ko
V 
RT  K i 

ln
zF  K o 
(we’ll assume that z = +1)
An e-fold ratio of K+ concentration ( Ki  Ko )
therefore leads to a potential difference of 
RT
.
F
R = 1.99 cal/mol oC; T = 300o; F = 9.65 x 104 C/mol (C is abbrev for coulomb).
OGN Figure 7-7
1.99 cal
 300
RT
mol


Therefore
=
F
9.965104 C
mol
 6 103 cal/C.
(C is the abbreviation for coulombs)
Now, 1 cal = 4.18 J (J is the abbreviation for joule),
and 1 J = 1 V x 1 C.
Therefore
RT
= 6 103 cal/C 4.18 V  C cal  25 mV.
F
Thus an e-fold concentration ratio gives a -25 mV membrane potential.
15
Deriving the Nernst potential
(for physicists and electrical engineers)
R = Nk, where N is Avogadro’s number and k is Boltzmann’s constant;
And F = Ne, where e is the charge on the electron.
23 J
 300
RT kT 1.38  10



 25 mV
Therefore
19
F
e
1.6  10 C
(we are familiar with the statement that kT = 25 meV)
----------------------------------------------
And a 10-fold concentration ratio leads to a membrane potential of
ln 10
RT
 58 mV
F
16
Deriving the Nernst potential
(for Biologists)
Class votes here:
Strategy
Vote
Don’t derive; Just measure
2
Look in Little Alberts Ch 12 p. 410
Or Nestler p. 37
7
Ask a physicist
35
Measure; then do IPO on NASDAQ
3
Comments
17
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+
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.
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+
18
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).
19
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)
http://www.its.caltech.edu/~lester/Bi-1/kcsa.pdb
20
H2O
carbonyl
K+ ion
K+ ions lose their waters of hydration and
are co-ordinated by backbone carbonyl groups
when they travel through a channel.
21
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 > 1000fold greater than Mg2+
Mg2+ is suitable for
transporters, but not for
channels.
22
Cells have evolved elaborate processes for pumping out intracellular
Na+ and Ca2+
These gradients can be used in two ways:
Next image
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!
23
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
Na+-coupled
cell membrane
serotonin
transporter
Attention-deficit
disorder medications:
Trademarks:
Ritalin, Dexedrine,
Adderall,
Strattera (?)
Presynaptic
terminals
Drugs of abuse:
cocaine
amphetamine
Na+-coupled
cell membrane
dopamine
transporter
cytosol
NH3+
HO
outside
HO
N
H
HO
H2
C
C
H2
NH3+
24
Some ideas about ion-coupled transporters
25
Some ideas about ion-coupled transporters
“alternating access”
26
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+.
27
Hot news from the human genome 2001 - 2006
Transport proteins (transporters, pumps, and channels)
are 5% of the human genome . . .
~ 1500 genes
28
End of Lecture 5
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