SME
Inorganic Chemistry
Bioinorganic chemistry
Use this for “Hemoglobin has P₅₀ = 26 torr and n = 2.8. How saturated is it at 40 torr of O₂?”
Chart
Y(40) ≈ 77
Half bound at pO₂ = K = 26: Y(K) = 50, half of 100
This is an example. Type your own values to start a new problem.
pO₂
Oxygen pressure
example · torr
P₅₀
Half-saturation pressure
example · torr
n
Hill coefficient
example
Y
Oxygen saturation
calculated · %
Formulas
Y
=
100
×
pO₂^
n
÷
(
P₅₀
n
+
pO₂^
n
)
76.96
=
100
×
40
2.8
26
2.8
+
40
2.8
Assumptions
•
Y = pO₂ⁿ ÷ (P₅₀ⁿ + pO₂ⁿ), the Hill equation, with both pressures in torr and Y as a percent.
•
P₅₀ is the O₂ pressure at half saturation: a lower P₅₀ means the protein holds O₂ more tightly.
•
n above 1 means O₂ binding at one heme helps the next; myoglobin, with one heme, has n = 1.
•
The odds Y ÷ (100 − Y) equal (pO₂ ÷ P₅₀)ⁿ, which the steps use to work backward.
Step-by-step
WE KNOW
pO₂ = 40 torr, P₅₀ = 26 torr, n = 2.8
FIND
oxygen saturation (Y)
Step 1 · Find oxygen saturation (Y)
Use Y = 100 × pO₂ⁿ ÷ (P₅₀ⁿ + pO₂ⁿ)
Raise each pressure to the Hill coefficient, then take the share held by O₂.
Y
=
100
×
40
2.8
26
2.8
+
40
2.8
Y
=
100
×
40
2.8
9,161 + 30,600
Y
=
100
×
40
2.8
39,761
Y
=
100
×
30,600
39,761
Y
=
3,060,000
39,761
Y
=
76.96%
→
Myoglobin
(
P₅₀
=
2.8
torr,
n
=
1)
would
be
93.5%
full
at
this
pressure:
it
holds
O₂
that
hemoglobin
lets
go.
Check
Put the numbers back in. Both sides should match.
76.96
=
100
×
40
2.8
26
2.8
+
40
2.8
✓
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