Pacman percolation: a model for enzyme gel degradation

TL;DR

This paper introduces a lattice-based model for enzyme-driven gel degradation, revealing a unique percolation transition with critical exponents matching experimental data, advancing understanding of enzymatic gel breakdown.

Contribution

It presents a novel lattice model simulating enzyme activity on gels, identifying a distinct universality class for the percolation transition.

Findings

Critical exponent beta=1.0±0.1 measured, matching experiments.

The model exhibits a different universality class from random percolation.

The transition is characterized as a reverse percolation process.

Abstract

We study a model for the gel degradation by an enzyme, where the gel is schematized as a cubic lattice, and the enzyme as a random walker, that cuts the bonds over which it passes. The model undergoes a (reverse) percolation transition, which for low density of enzymes falls in a universality class different from random percolation. In particular we have measured a gel fraction critical exponent beta=1.0+-0.1, in excellent agreement with experiments made on the real system.