# Hemoglobin-Oxygen binding energy

## Main Question or Discussion Point

I'm trying to find the binding energy on an oxygen molecule bound to Hemoglobin, searching Google and Wikipedia has so far turned up nothing. The binding energy is needed to find the probability for Hemoglobin to bind 0,1,2,3 or 4 oxygen molecules.

Regards

TheMan

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Andy Resnick
A quick PubMed search turned up:

Proc Natl Acad Sci U S A. 2007 Nov 20;104(47):18451-5. Epub 2007 Nov 14.
A quantum-chemical picture of hemoglobin affinity.
Alcantara RE, Xu C, Spiro TG, Guallar V.

There's a table in it that may have what you need, but I'm not sure.

I can't reach it, seems my University don't have a subscription to PNAS.

alxm
Actually the article Andy cited studied carbon monoxide binding.
And you wouldn't want to use it anyway. It's a QM (B3LYP) calculation, so the error would be about 3-4 kcal/mol for an iron complex like this. Also, the calculated value is $$\Delta E$$, the change in electronic energy, not $$\Delta G$$, which takes entropy into account. (and normally you'd be interested in the binding energy versus aqueous solution, where entropy is a significant effect).

Since this is a case where you can get experimental data, I'd suggest you use that instead. I turned up http://dx.doi.org/10.1016/0006-291X(75)90518-5" [Broken], which obtained a value of 0.60 eV (13.8 kcal/mol) with an accuracy of 0.06 eV through Mössbauer spectroscopy. There are probably better experimental values out there, and they're all better than a QM one.

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epenguin
Homework Helper
Gold Member
I'm trying to find the binding energy on an oxygen molecule bound to Hemoglobin, searching Google and Wikipedia has so far turned up nothing. The binding energy is needed to find the probability for Hemoglobin to bind 0,1,2,3 or 4 oxygen molecules.

Regards

TheMan
I don't know why this thread was bumped after nearly a year nor whether the answers are really what the OP was looking for (and it should be in another part of the site such as biology or 'other sciences').

In a simple binding curve such as typically to myoglobin there is an equilibrium constant Km for the reaction $O_2 + Mb \rightleftharpoons MbO_2$

And the standard free energy of binding is given by

$$\Delta G^0 = - RT\ ln\ K_m$$

By simple binding curve I mean one corresponding to the formula

$$X = \frac{x}{K_m + x}$$ .....(1)

where $x$ is ligand concentration and X is saturation of the macromolecule by ligand (i.e. amount of x bound/binding sites). Km equals the ligand concentration x1/2 at half saturation. So we can rewrite

$$\Delta G^0 = - RT\ ln\ x_{1/2}$$ .....(2)

For a macromolecule with co-operativity in the binding, like hemoglobin which you ask about, which equation (1) for X above no longer describes, equation (2) is still valid as long as (to the extent that) the binding curve is symmetrical (as a function of log x). Then $\Delta G^0$ means the standard free energy change per binding site for the overall reaction

$$Hb + 4 \ O_2 \rightleftharpoons Hb(O_2)_4$$

If however the binding curve is not symmetrical you have to substitute for x1/2, xm the median ligand concentration defined as the concentration $x$ for which

$$\displaystyle\int^x_{-\infty} X\,d\ln x = \displaystyle\int^\infty_x (1 - X)\,d\ln x$$

You can get the free energy of binding therefore from any publication where you can see a Hb binding curve. Approximating them as symmetrical and using x1/2 will give you useful approximation. When you ask ‘the’ free energy for Hb O2 binding, you would have to say which Hb of which species (human alone has several not to mention natural and engineered variants etc.) and under what conditions since it varies according to pH, temperature, salt and buffer concentration and those of several ligands like diphosphoglycerate, of biological significance or not. The study of these variations is a massive literature.

The above parameters are insufficient to give you "the probability for Hemoglobin to bind 0,1,2,3 or 4 oxygen molecules". To say something about that you need either a model or futher analysis of the binding curve which however requires very accurate binding measurements over a wide saturation range, or else a different kind of experimental information.

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