Archibald Hill developed a mathematical way of measuring the degree of cooperativity (see the Appendix in chapter 7 of the textbook). Cooperativity for hemoglobin is measured by the Hill coefficient (n). For a non-cooperative myoglobin: n = 1. For a completely cooperative hemoglobin: n = 4. The following fractional saturation data (Y) were measured of myoglobin (Mb) and hemoglobin (Hb) samples from a human patient. po Mb 0.294 0.455 0.625 0.714 0.769 0.806 0.833 0.854 0.87 Hb 0.006 0.012 0.026 0.044 0.067 0.096 0.13 0.169 0.214 мь 0.893 0.909 0.926 0.944 0.954 0.962 0.967 0.971 0.977 нь 0.321 0.431 0.574 0.747 0.851 0.909 0.94 0.958 0.975 100 Using your favorite graphing software, make two plots, including both sets of globin data (Mb and Hb) in each plot.
(i) Plot Y as a function of the partial pressure of molecular oxygen (pO2).
(ii) Make a Hill plot of log(Os) as a function of log(Y/(1 - Y)).
What are the binding dissociation constants (Ko) and Hill coefficients (n) for these globin samples? Are these parameters normal? Explain.