SME
Cell & Molecular Biology
Membrane biology
Use this for “K⁺ is 5 mM outside a neuron and 140 mM inside. What is its equilibrium potential at 37 °C?”
Diagram
V = −89 mV: the inside is negative, so + charges line the outside face and − the inside.
One pair per 10 mV: 8 a side (8 at most).
Dots on one scale, one dot ≈ 3.5: Ion 5 out, 140 in.
This is an example. Type your own values to start a new problem.
E
mV
=
61.5
z
×
log₁₀
Cₒ (mM)
Cᵢ (mM)
Formulas
E
=
61.5
z
×
log₁₀(
Cₒ
Cᵢ
)
−89
=
61.5
1
×
log₁₀(
5
140
)
Assumptions
•
Only this ion crosses the membrane, and it is at equilibrium: no net flow either way.
•
E is the inside relative to the outside; 61.5 mV is 2.303RT ÷ F at 37 °C.
•
z is the ion’s charge with its sign: K⁺ and Na⁺ +1, Ca²⁺ +2, Cl⁻ −1.
•
At 20 °C the factor is 58 mV instead of 61.5 mV.
Step-by-step
WE KNOW
z = 1, Cₒ = 5 mM, Cᵢ = 140 mM
FIND
equilibrium potential (E)
Step 1 · Find equilibrium potential (E)
Use E = 61.5 ÷ z × log₁₀(Cₒ ÷ Cᵢ)
Each
tenfold
step
in
the
ratio
is
worth
61.5
mV
z
;
the
charge’s
sign
sets
the
direction.
E
=
61.5
1
×
log₁₀(
5
140
)
E
=
61.5
×
log₁₀(0.03571)
E
=
61.5
×
(−1.447)
E
=
−89
mV
Check
Put the numbers back in. Both sides should match.
−89
=
61.5
1
×
log₁₀(
5
140
)
✓
Topic check
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