The Fiber Walk: A Model of Tip-Driven Growth with Lateral Expansion

TL;DR

The paper introduces 'fiber walks', a new model for tip-driven growth that incorporates lateral expansion, providing a more physically plausible way to simulate biological growth processes with finite thickness.

Contribution

It presents a novel self-avoiding random walk model that includes lateral expansion, addressing limitations of previous models that lacked physical plausibility.

Findings

Fiber walks generate fibers with well-defined curvatures.

The model enables the identification of space occupancy processes.

It offers a basis for modeling biological objects with finite thickness.

Abstract

Tip-driven growth processes underlie the development of many plants. To date, tip-driven growth processes have been modelled as an elongating path or series of segments without taking into account lateral expansion during elongation. Instead, models of growth often introduce an explicit thickness by expanding the area around the completed elongated path. Modelling expansion in this way can lead to contradictions in the physical plausibility of the resulting surface and to uncertainty about how the object reached certain regions of space. Here, we introduce "fiber walks" as a self-avoiding random walk model for tip-driven growth processes that includes lateral expansion. In 2D, the fiber walk takes place on a square lattice and the space occupied by the fiber is modelled as a lateral contraction of the lattice. This contraction influences the possible follow-up steps of the fiber walk. The boundary of the area consumed by the contraction is derived as the dual of the lattice faces adjacent to the fiber. We show that fiber walks generate fibers that have well-defined curvatures, enable the identification of the process underlying the occupancy of physical space. Hence, fiber walks provide a base from which to model both the extension and expansion of physical biological objects with finite thickness.