The Dynamics of Zeroth-Order Ultrasensitivity: A Critical Phenomenon in Cell Biology

TL;DR

This paper investigates the dynamic behavior of zeroth-order ultrasensitivity in cellular phosphorylation cycles, revealing a critical slowdown similar to phase transitions, and introduces a simple mathematical model to capture this phenomenon.

Contribution

It provides a dynamic analysis of ultrasensitivity in PdPC, highlighting a phase transition-like slowdown and proposing a simple model for broader application and education.

Findings

Identification of critical slowdown near ultrasensitivity transition

Development of a simple mathematical model capturing ultrasensitivity dynamics

Demonstration of ultrasensitivity as a phase transition phenomenon

Abstract

It is well known since the pioneering work of Goldbeter and Koshland [Proc. Natl. Acad. Sci. USA, vol. 78, pp. 6840-6844 (1981)] that cellular phosphorylation- dephosphorylation cycle (PdPC), catalyzed by kinase and phosphatase under saturated condition with zeroth order enzyme kinetics, exhibits ultrasensitivity, sharp transition. We analyse the dynamics aspects of the zeroth order PdPC kinetics and show a critical slowdown akin to the phase transition in condensed matter physics. We demonstrate that an extremely simple, though somewhat mathematically "singular" model is a faithful representation of the ultrasentivity phenomenon. The simplified mathematical model will be valuable, as a component, in developing complex cellular signaling network theory as well as having a pedagogic value.