Facilitation Pressure

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In red muscle tissue, there is myoglobin (Mb) which reversibly binds oxygen (O2) and thus might play a role in tissue oxygen transport – note, that within tissue O2 exclusively is transported through diffusion. Tissue is far from homogeneous, but O2 is a gas and can be represented by its partial pressure P so that we can use Fick's law with (oxygen) permeability ℘. With co-diffusing myoglobin-bound oxygen MbO2, the total oxygen flux is:

J O2Tot = J O2 + J MbO2 = − ℘∇P − DMbO2 ∇[MbO2]
The reaction between Mb and O2 is not very fast, but supposedly fast enough to assume chemical equilibrium in (most of) the tissue. Then, the oxymyoglobin concentration [MbO2] can be expressed as ctS where ct is the total Mb concentration and S its saturation with oxygen:
S = P
P + P50,Mb
so that:
J O2Tot = − ℘∇P − DMbO2 ct ∇S = − ℘ {∇P + DMbO2 ct ∇S}
℘
The term DMbO2 ct /℘ is called Facilitation Pressure PF and can be interpreted as follows. Without Mb, over a certain range Δx, O2 is transported according to the difference in pressue ΔP. With facilitation, a PF ΔS is added. Since ΔS maximally can be 1 (100% against 0%), the PF tells us what the maximum addition to the driving force for diffusion is, in terms of partial pressure. Note, however, that it only tells us the driving force; it does add NOTHING to the O2 pressure itself.

Example: say, in a hard working muscle the oxygen pressure P is 5 mmHg, and that would be sufficient to overcome a diffusion distance of 10 μm. Now, with Mb with a PF = 12 mmHg and P50,Mb = 7 mmHg, S = 5/(5+7) and PFS 12×5/(5+7) = 5 mmHg, so a total driving force of 5+5 = 10 mmHg enabling to overcome a quite larger distance than 10 μm.

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