Hill Equation modified to allow slow binding to hemoglobin

Description

The Hill Equation assumes instantaneous equilibrative binding
of oxygen to Hb, but if there is delay due to diffusion or a membrane barrier, then 
the reaction is slowed. Antonini and Brunori (1971) and Frauenfelder (Austin et al 1975; 
Mourant et al 1993) showed that 
the rebinding of O2 to Hb involved a family of rate constants (including a fractal
scaling region) and the the reaction was complete in less than 50 msec Here we apply
a trick,  surrounding the Hb with a barrier to allow accounting for slow rates 
of association and dissociation, and which gives a fairly realistic sccounting for O2
exchange across RBC membranes. It is purely descriptive.
                        ---------------------
                     PS |                    |
               pO2 <------>pO2in + Hb <-> HbO|
                        |  Vol               |
                        ---------------------

The time constant of the delay is Vol/PS.

 AV Hill's empirical description of the hemoglobin-oxygen 
dissociation curve was based on data before the van Slyke apparatus for measuring 
the content of O2 in blood equilibrated with air at known PO2 and PCO2 was developed.
The simplicity of the equation led to its wide utility, even though it is too low 
at saturations below 30% (a region not often visited physiologically). Other models,
Adair's, Severinghaus', etc. offer improvements over this two parameter
power law relationship.

Equations

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.