Safe uses of Hill's model: an exact comparison with the Adair model

Journal article, 2011

Background: The Hill function and related Hill's model are used frequently to study processes in the living cell. There are very few studies that focus on investigating in which situations the model can be safely used. It is investigated whether it is possible to use Hill's model to describe fluctuations in particle numbers of a more complicated reaction system. Quantitative statements are made regarding when such approach is possible. Results: The particle number distribution functions for Hill's and Adair's models were compared by solving the respective master equations. Adair's model was used as a representative of a more complicated reaction model. Three similarity measurers were introduced to compare the distributions in a quantitative way. Both time dependent and the equilibrium properties of the similarity measures were studied. Conclusions: Hill's model can be safely used to investigate noise characteristics of strongly cooperative Adair's model. For a given reaction in the reaction chain, the dissociation constant of the reaction that follows should be much smaller that the dissociation constant of the chosen reaction. However, such statement needs to be used with caution. The quantitative analysis showed that boundaries of the regions in the parameter space where the models behave in the same way, exhibit a rather rich structure.