Eden model with nonlocal growth rules and the kinetic roughening in biological systems

TL;DR

This paper introduces a nonlocal Eden model influenced by external nutrient availability, revealing transient KPZ universality in plentiful environments and a crossover to unstable growth under scarcity, relevant to biological growth experiments.

Contribution

It presents a novel off-lattice Eden model with nonlocal growth rules based on nutrient concentration, exploring kinetic roughening universality classes in biological systems.

Findings

KPZ universality class appears as a long transient in nutrient-rich conditions.

Nutrient scarcity causes a crossover from KPZ to unstable growth.

Quenched KPZ behavior observed at the pinning transition.

Abstract

We investigate an off-lattice Eden model where the growth of new cells is performed with a probability dependent on the availability of resources coming externally towards the growing aggregate. Concentration of nutrients necessary for replication is assumed to be proportional to the voids connecting the replicating cells to the outer region, introducing therefore an nonlocal dependence on the replication rule. Our simulations point out that the Kadar-Parisi-Zhang (KPZ) universality class is a transient that can last for long periods in plentiful environments. For conditions of nutrient scarcity we observe a crossover from regular KPZ to unstable growth, passing by a transient consistent with the quenched KPZ class at the pinning transition. Our analysis sheds light on results reporting on the universality class of kinetic roughening in akin experiments of biological growth.