First Passage and Cooperativity of Queuing Kinetics

TL;DR

This paper investigates the kinetics of ligand-receptor binding, revealing how sequential and random binding modes differ in saturation and speed, especially near critical energies where kinetic traps occur.

Contribution

It introduces a model comparing sequential and random ligand binding, highlighting the effects of cooperativity and revealing kinetic traps near critical energies.

Findings

Sequential binding leads to higher saturation at equilibrium.

Random binding reaches full occupancy faster at low cooperativity.

Kinetic traps significantly slow down random binding near critical energies for N≥8.

Abstract

We model the kinetics of ligand-receptor systems, where multiple ligands may bind and unbind to the receptor, either randomly or in a specific order. Equilibrium occupation and first occurrence of complete filling of the receptor are determined and compared. At equilibrium, receptors that bind ligands sequentially are more likely to be saturated than those that bind in random order. Surprisingly however, for low cooperativity, the random process first reaches full occupancy faster than the sequential one. This is true {\it except} near a critical binding energy where a 'kinetic trap' arises and the random process dramatically slows down when the number of binding sites $N\geq 8$. These results demonstrate the subtle interplay between cooperativity and sequentiality for a wide class of kinetic phenomena, including chemical binding, nucleation, and assembly line strategies.