Bounds on the Ultrasensitivity of Biochemical Reaction Cascades

We examined an upper bound for the Hill coefficient of the composition of two functions, namely the product of their individual Hill coefficients. We proved that this upper bound holds for compositions of Hill functions, and that there are instances of counterexamples that exist for more general sigmoidal functions. Additionally, we tested computationally other types of sigmoidal functions, such as the logistic and inverse trigonometric functions, and we provided computational evidence that in these cases the inequality also holds. We show that in large generality there is a limit to how ultrasensitive the composition of two functions can be, which has applications to understanding signaling cascades in biochemical reactions.PMID:38637362 | DOI:10.1007/s11538-024-01287-z
Source: Bulletin of Mathematical Biology - Category: Bioinformatics Authors: Source Type: research