# Understanding of the saturation function in the Monod-Wyman-Changeux Model

I am reading Mathematical Physiology, Sneyd. I am a undergraduate mathematician interested in pursuing the field, so forgive me if my terminology is off. In this example, the writer considers a protein with two binding sites. The subscript $i$ indicates the number of bound ligands. This expression, called the saturation function, appears on page 18:

$$Y = \frac{r_1 + 2r_2 + t_1 + 2t_2}{2(r_0+r_1 + r_2 + t_0 + t_1 + t_2)}$$

Where, $r_i, t_i$ denote the concentrations of chemical species $R_i, T_i$ respectively.
It looks like the weighted average of the ezymes that have occupied binding sites.

The fact that $t_0, r_0$ do not appear in the numerator suggest that it is the saturation of enzyme binding sites, the $2$ in front of the $r_2,t_2$ indicates that the enzyme with both binding sites occupied is "double concentrated". The two on the denominator indicates the number of available binding sites in the enzyme. Perhaps, if we were considering an enzyme with three binding sites:

$$Y = \frac{r_1 + 2r_2 + 3r_3 + t_1 + 2t_2 + 3t_3}{3(r_0+r_1 + r_2+ r_3 + t_0 + t_1 + t_2 + t_3)}$$

Would this description be correct?

• can you give a more precise reference to the book (Sneyd has apparently authored/co-authored several books ...) ? Oct 3, 2016 at 0:14
• ISBN 978-0-387-75846-6 Mathematical Physiology Volume 1: Cellular Physiology
– user21915
Oct 3, 2016 at 18:46