A Short Note Regarding the Number of Bound Molecules of Oxygen to Hemoglobin

Oxygen, a molecule essential to many biological functions in the human body, binds coop?eratively to a protein known as hemoglobin. This cooperative binding of oxygen to hemoglobin can be described by a binding polynomial of degree n = 4. In this paper, I theoretically prove that a molecule of hemoglobin must have at least one molecule of oxygen bound to its subunits at any given point in time. I remove a condition for the equilibrium constants K_R and K_T in the binding polynomial for the binding of oxygen to hemoglobin. Removing the condition partially proves the proposed statement in this paper. I then make use of the cubic formula to derive the concentration of oxygen for which the number of bound oxygen molecules tohemoglobin is zero, thus completing a comprehensive mathematical justification of the proposed theoretical statement. Through this paper, I hope to provide a further insight into the mechanisms of oxygen and hemoglobin with regards to the respiratory system.

Use of the F test for determining the degree of enzyme-kinetic and ligand-binding data. A Monte Carlo simulation study

1. Initial-rate data were simulated for 13 representative enzyme mechanisms with the use of several distributions of rate constants in order to locate conditions leading to v([S]) curves in physiological ranges of substrate concentration. 2. In all, 420 sets of such v([S]) curves were generated with the use of several choices of substrate concentration range (two, three or four orders of magnitude), number of experimental points (10, 15 or 20), error on v (5-10%) and standard deviation on v (5-9%) in order to simulate experimental results in a number of possible ways. 3. Curve-fitting was carried out to rational functions of degree 1:1, 2:2, …, 5:5 until there was no statistically significant decrease in the sum of weighted squared residuals as judged by the F test at 95% and 99% confidence levels. 4. It was checked whether the non-linear regression program had located a good minimum in the sum of squares by also fitting the data with the correct values of parameters as starting estimates. 5. A similar procedure was adopted with 110 sets of binding data simulated for 11 models, and the F test was used to see if fractional-saturation data generated by a binding polynomial of order n could be adequately fitted by one of order m, m less than n. 6. From the 530 simulations the F test was successful in fixing the correct degree with a probability of 0.62 at the 95% confidence level, but this fell with increase in degree as follows: 1:1 (0.98), 2:2 (0.71), 3:3 (0.43) and 4:4 (0.34), the first numbers being the degree of the rate equation and those in parentheses referring to the 95% confidence level. 7. It made little difference whether the 95% or the 99% confidence level was consulted, as there were very few borderline cases. 8. The chance of detecting deviations from Michaelis-Menten kinetics, i.e. terms of at least second-order in a rate equation of degree n:n, n greater than 1, was estimated to be about 0.8. 9. The probability of the F test leading to a spurious result due to error in the data was found to be about 0.04. 10. The probability with which 4:4 mechanisms can lead to v([S]) plots with no, one, two or three turning points was computed, and it was established that there is a small but finite chance that the increase in degree that occurs in some mechanisms when ES in equilibrium EP interconversions are explicitly allowed for can be detected by the F test.