1. Generation of the Membrane Potential
Experimental Biology 2004
Cellular Homeostasis Refresher Course
Generation of the
Membrane Potential
Stephen Wright
University of Arizona

2. The Starting Point: Na,K-ATPase
Jens Skou
Nobel Prize 1997
5-20 mM
140 mM
‘leak’ pathways
3Na+
ATP
3Na+
2K+ mM
4 mM
2K+
Accounts for
about 10% of
basal metabolic
rate!
Animation nice
Define BMR
1. The stoichiometry of a single ‘cycle’ of the
Na,K-ATPase is: 3 Na : 2 K : 1 ATP
2. At ‘steady-state’ active fluxes of Na and K
balance the ‘leak’ fluxes

3. 100 K+ Na+ 100 K+ 10 10 Na+ in out (110 mM Cl-)
Maybe different colors for Na and K
(110 mM Cl-)

4. 100 K+ Na+ 100 (-) (+) K+ 10 10 Na+ in out Jnet for K+ = 0
At ‘equilibrium’
(-)
(+)
K+ 10
Na+ 100
10 Na+
(110 mM Cl-)

5. Nernst Equation at Equilibrium: Electrical Force = Chemical Force
(electrical ‘voltage’ = chemical ‘gradient’)
VKzKF = -RT ln
[K+]in
[K+]out
Maybe lightning bolt for “electrical force”
Bubbling beaker/flask for “chemical force”
VK = ln
[K+]in
[K+]out
-RT
zKF
Nernst Equation

6. Walther Hermann Nernst
Nobel Prize: 1920

7. VK  -60 mV [K+]in -60 mV VK  log zK [K+]out [K+]in -RT VK = ln zKF
R = 8.31 J/(mol-deg)
T = 310o K
F= 96,500 coul/mol
ln to log (x2.303)
VK = log
[K+]in
[K+]out
-61.5 mV zK
VK  log
[K+]in
[K+]out
-60 mV zK
This would be a good place to have a diagram of a RBC or some generic cell with Kin & Kout & V(K) ~Vm
Color code Na, K, and Cl as on slide 11 throughout …. Better visual effect…. Also helps folks to keep track of the ions
[K+]in = 100 mM and [K+]out = 10 mM
VK  -60 mV

8. 60 mV  10x gradient So what? i.e., Why should I care….?
Or, ….[flashing or moving yellow/green arrow would be good here] -60 mV ~ 10 X (chemical gradient) [I think you want to minimize words]
Again, lightning bolt and bubbling beaker at the end here would “grab” folks
i.e., Why should I care….?

9. Well... 1. Underscores the equality that exists between
chemical and electrical forces
The Nernst Equation:
2. Provides a tool for predicting if ‘active’
transport processes are present...
Again cartoon showing lightning bolt “morphing” into ubbling baeker and vis versa
Some color ?
3. Conceptual ‘starting point’ for understanding
the physiological basis of all bioelectric activity

10. are ‘two sides of the same coin’
Summary to this point....
Chemical force and Electrical force
are ‘two sides of the same coin’
energy (driving forces)
Nernst equation displays the
theoretical balance between these forces
Use cartoon metaphors, e.g, coin anology lightning bolt and beaker on 2 sides of rotating coin [easily done with PPT animation]
Goldman equation reflects the real world
situation of finite and variable ionic permeabilities

11. 2 parameters of Goldman eq:
Ion Permeabilities
rapidly variable
Ion Gradients
‘stable’
PK[K+]out + PNa[Na+]out + PCl [Cl-]in
Vm  -60 mV log
PK[K+]in + PNa[Na+]in + PCl [Cl-]out
‘Goldman Equation’

12. Factors influencing the Membrane Potential at Rest
A. Ion Gradients
Ion [in] [out] Veq (Nernst)
Na mM mM mV K Cl Pi
10-9 cm/sec
10-7 cm/sec
10-8 cm/sec
B. Membrane Permeability
Goldman prediction of Vm = -84 mV

13. PK[K+]out + PNa[Na+]out + PCl [Cl-]in Vm  -60 mV log
PK[K+]in + PNa[Na+]in + PCl [Cl-]out
+50
-50
-100
Membrane Potential (mV)
VNa
‘boundary
conditions’ Vm
VCl VK

14. What is the basis of ‘PK’? 3Na+ 2K+ So, at ‘rest’ PK dominates
ATP
2K+
In large part, it reflects the
constitutive activity of a
population of K Channels
(‘inward rectifier’ - KIR channels)

15. Ventricular Action Potential KIR 2.1 overexpression Vm Vm
KIR 2.1 suppression Vm Vm
Miake et al., JCI, 2003

16. (-) 3Na+ 2K+ Then a medical student rose and said “Speak to us of Cl-”
w/apologies to Kahlil Gibran
3Na+
ATP
2K+
(-)
The cell spends its
energy building K+ and
Na+ gradients...
The Cl- gradient is largely
a passive consequence of
the PD established by
the K gradient/permeability
Cl-

17. ‘ignoring’ Cl, the resting PD
becomes a function of the ratio
of PNa to PK....
normal [K+]out Vm
Vm closely tracks [K+]out except
at very low concentrations,
or when PNa is relatively high

18. In Conclusion... A. Active transport establishes K+ and Na+ gradients
these tend to be stable
B. Electrical Potential Difference is a consequence
of these gradients and the relative permeability of
the membrane to these ions
C. At ‘rest’ the PD is dominated by the combined
influence of:
Is it possible to cartoon some of these closing concepts?
1. the outwardly direct K+ gradient
2. large PK