10 Equations in Biology:
The Nernst Equation
RT [ion]outside
E=
ln
zF [ion]inside
R = 8.314 J / K  mol
F = 9.648 C / mol e–s
+
–
Focal Teaching Strategies
1. Informally derive an equation, step by step,
from prior scientific knowledge.
2. Verbally deconstruct an equation,
and interpret individual components.
3. Analyze an equation’s quantitative behavior,
and translate the results into clear biological
predictions.
Intro: The Nernst Equation
Determine the amount of elec.
potential E needed across a
membrane to prevent an ion
from diffusing in response to
its concentration gradient.
Example
• 2-compartment electrical cell
• [Na+] higher on right, so net
diffusion occurs toward the left.
• Apply elec. current  ERHS < 0:
equilibrium b/n diffusion &
electrostatic attraction
e–s
+
–
Background Knowledge
What familiar scientific principles might be
most relevant to understanding this system?
• Individual ions have diff. charges.
• Like charges repel; opposite charges attract.
• Molecules diffuse down their conc. gradient.
• There are certain universal physical constants.
• Absolute zero temp. means no molecular movement.
• others?
1. Informal Derivation
• List 3-4 specific
parameters that you
would expect to
influence a membrane’s
equilibrium potential E
for a particular ion.
• For each parameter,
would you expect it to
have a positive or a
negative effect on E?
Parameter
Effect on E
(+ or –)
1. Informal Derivation
• Now write an equation
for E that includes all the
parameters you listed,
and in which each
parameter has the effect
you predicted.
• Use dimensional
analysis to verify that
units are combined
appropriately.
E = T - d +... ?
(degrees
Kelvin)
(micrometers)
2. Verbal Deconstruction
RT [ion]outside
E=
ln
zF [ion]inside
• Dimensional analysis: units for E?
• What do the constants R and F actually measure?
Why are they present in the Nernst equation?
3. Mathematical Analysis &
Biological Interpretation
Compare & contrast the behavior of the actual
Nernst equation with the variants shown below.
Nernst:
RT [ion]outside
E=
ln
zF [ion]inside Why the log ratio?
Variant 1:
RT æ [ion]outside ö
E=
çç
÷÷
zF è [ion]inside ø
Variant 2:
RT
E=
[ion]outside - [ion]inside
zF
(
)
3. Mathematical Analysis &
Biological Interpretation
RT [ion]outside
E=
ln
zF [ion]inside
• Under what conditions does the Nernst
equation predict E = 0 ? Do those
predictions make sense biologically?
• What does the Nernst equation predict
about the behavior of uncharged solutes?
Is this prediction biologically reasonable?
3. Mathematical Analysis &
Biological Interpretation
• Assuming that the Nernst
equation is an accurate
model, predict the equilibrium
potential for Na+ ions in a
human skeletal muscle cell.
RT [ion]outside
E=
ln
zF [ion]inside
• [Na+]cell  15 mM; [Na+]extracellular fluid  145 mM.
• Intepret your result: effect of the membrane potential?
how is it maintained by the cell?
Take-home message
• Informal derivation is faster than full derivation
using word & formal equations, but less thorough.
• Verbal deconstruction helps identify & remedy
gaps in prior knowledge, and gives abstract
concepts a more concrete foundation.
• Mathematical analysis can be used to shift focus
away from manipulating an equation to interpreting
the underlying model and its outcomes.