text: The classic Monod–Wyman–Changeux model (MWC) for cooperativity is generally published in an irreversible form. That is, there are no product terms in the rate equation which can be problematic for those wishing to build metabolic models since there are no product inhibition terms. However, a series of publications by Popova and Sel'kov derived the MWC rate equation for the reversible, multi-substrate, multi-product reaction.
  The same problem applies to the classic Hill equation which is almost always shown in an irreversible form. Hofmeyr and Cornish-Bowden first published the reversible form of the Hill equation. The equation  has since been discussed elsewhere and the model has also been used in a number of kinetic models such as a model of Phosphofructokinase and Glycolytic Oscillations in the Pancreatic β-cells or a model of a glucose-xylose co-utilizing S. cerevisiae strain. The model has also been discussed in modern enzyme kinetics textbooks.