membranes and transport topic ii-1 biophysics. nernst equation f = 96,400 coulomb/mole simplest...
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Nernst Equation
i
o
i
oB
CCln
F
RTC
Clnq
TkV
i
o
C
Clog mV 60Vget K 300 At
• F = 96,400 Coulomb/mole
•Simplest equation for membrane potential – one ion
www.kcl.ac.uk/teares/gktvc/vc/lt/nol/Nernst.htm
Goldman-Hodgkin-Katz Equation
• There is one membrane potential that counters all concentration gradients for permeable ions
• Pi = (ikBT)/d = Di/d, with D – diffusion constant [cm2/sec]
1i i
ii2ii
2i i
ii1iiB
CPCP
CPCPln
q
TkV
oCliNaik
iCloNaokB
ClPNaPKP
ClPNaPKPln
q
TkV
Example – simple Neuron
• Note: Can define Nernst potential for each ion, Vk = -80 mV; VNa = +58 mV. Relative permeabilities make membrane potential closer to Vk
ii
oo
NabK
NabKlog mV 58V
b = 0.02 for many neurons (at rest).
[K]i = 125 mM [K]o = 5 mM
[Na]i = 12 mM [Na]o = 120 mM
What is V?
with b = PNa/PK
Do Soma 1 (Nernst)
Electrical Model
g is like conductance (=1/R) and like permeability
This equation is equivalent to Godman-Hodgkin-Katz equation.
CaNaKCl
CaCaNaNaKKClCl
i
iim gggg
VgVgVgVg
g
VgV
(from Kirchoff’s laws)
Example squid axon
• Remember electric field points in direction of force on positive test charge
• E always points from higher potential (for ions)
[K]in =125mM
[K]out = 5 mM
Vm = -60 VK = -75
IK = gK (Vm – VK), Vm = -60 mV
IK = gK (-60 – (-75)) mV = gK(+15 mV).
g always positive.
V = Vin – Vout
positive current = positive ions flowing out of the cell.
Vm not sufficient to hold off K flow so ions flow out. When Vm = Vk then no flow.
thisopposes potentialNernst ;sdEVVVin
outoutinions
[K]in =125 mM
[K]out = 5 mM
E Eds
Do Soma 3 (Resting Potential)
Donnan Rule and other considerations Example of two permeable ions and one
impermeable one inside
• KoClo = KiCli Donnan Rule
• Electroneutrality
• Osmolarity
• Goldman- Hodgkin-Katz
• Apply electroneutrality inside and out and plug in Donnan rule and get
AZZAK4
K2log mV 58
[K]
[K]log mV 58 V 2/1222
o
o
i
om
Animal Cell ModelCi (mM)* Co (mM) P>0?
K+ 125 5 Y
Na+ 12 120 N**
Cl- 5 125 Y
A- 108 0 N
H2O 55,000 55,000 Y
* Should really use Molality (moles solute/ kg solvent) instead of per liter – accounts for how molecules displace water (non-ideality).
Maintenance of Cell Volume
• Osmolarity must be same inside and out• Concentration of permeable solutes must be
same inside and out• Si = So and Si + Pi = So (Osmolarity)• Solutions: cell wall, Pwater = 0, Pextra cellular solutes = 0
Cell impermeable to sucrose
www.lib.mcg.edu/.../section1/1ch2/s1ch2_25.ht
http://www.himalayancrystalsalt.com/html/images/PAGE-osmosis.gif
Animal Na impermeable model
• Apply electroneutrality outside, Donnan, and osmolarity
• Get unknowns and Vm = -81 mV
Active Transport
• Na-K Pump
- Two sets of two membrane spanning subunits- Phosphorylation by ATP induces a conformational change in the protein allowing pumping- Each conformation has different ion affinities. Binding of ion triggers phosphorylation. - Shift of a couple of angstroms shifts affinity.- Exhibits enzymatic behavior such as saturation.
student.ccbcmd.edu/.../eustruct/sppump.html
ii
ooom
iNaik
oNaokBm
NaK
NaKlnVV
NaPKP
NaPKPln
q
TkV
with = (n/m)(PNa/PK),n/m = 2/3 Vm VK.
Electrical Model
CaNaKCl
pCaCaNaNaKKClClm gggg
IIVgVgVgVgV
Now include current for pump, Ip as well as input current I.
Do Soma conductance and Na pump)
Patch Clamping
www.essen-instruments.com/Images/figure2.gif
• Invented by Sakmann and Neher [Pflugers Arch 375: 219-228, 1978]
•Can be used for whole cell clamp (measure currents in whole cell, placing electrode in cell) like on left or pulled patch as on right (potentially measure single channel).
•Can control [ions].
•Usually voltage clamp (command voltage or holding voltage) and observe current (I = gV). Ix = g(Vh-Vx) where x is for each ion and Vx is Nernst potential for that ion. With equal concentration of permeable ion on both sides, get g easily
Voltage Gated Channels
• When [ions] not limiting, can get nernst potential when current reverses
I = gx*(Vh – Vx)
• There is a degree of randomness in opening and closing of channels
•Proportion of time open is proportional to Voltage for some channels
•Average of many channels is predictable
Multiple Channels
• Get several channels on a patch– Gives quantized currents
• Parallel: geq = gi; Series: 1/geq = 1/gi
– g = 1/R
I
t
Ligand gated channels
• When Ach binds, gate opens and lets in Na+ and K+.
• I is proportional to [Ach]2 (binds 2 Ach)
Nicotine also binds to Ach receptor – called nicotinic receptor
Do Patch Cl, K, Multiple K, ligated)