Practical differentiation using ultrasensitive molecular circuits

Biological systems compute spatial and temporal gradients with a variety of mechanisms, some of which have been shown to include integral feedback. In traditional engineering fields, it is well known that integral components within a negative feedback loop can be used to perform a derivative action. In this paper, we define the concept of a practical differentiator that is inspired by this design principle. We then consider three simple biological circuit examples in which we prove that feedback combined with ultrasensitive, quasi-integral components yields a practical differential network under some assumptions. These examples include phosphory-lation/dephosphorylation cycles, and two networks relying on molecular sequestration.