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In other words, the Hill's plot should be symmetric around the origin. The
experimental measurements of Roughton et al. gave:
and
which are reasonably close to the above requirement. For this interesting
reason, Pauling's model has been “re-discovered” after more than 60 years.
Using the average of these two numbers, we get K' = 0.021 and
which are reasonably close to what Pauling got originally.
THREE-CONSTANT MODEL
The most commonly quoted theoretical model in biochemistry textbooks for
equilibrium hemoglobin saturation with oxygen is the MWC model
proposed by Monod et al. (1965). They made the following assumptions:
1. The
and
are the same.
2. Hemoglobin molecules exist in two different states: T for tense (or taut)
and R for relaxed. These two states are in equilibrium.
3. Oxygen molecules bind to the hemoglobin subunits sequentially. The
equilibrium constants are the same, one for the T-state and another for
the R-state.
4. At low oxygen pressure, hemoglobin is in the T-state. Transition
occurs from the T-state to the R-state as the oxygen pressure is
increase.
The T- and R-states of hemoglobin are designated as and
respectively with the subscripts indicating the number of
oxygen molecules bound to that state. Thus,
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