How to grow a flat leaf

TL;DR

This paper combines elastic plate physics with feedback control theory to understand how leaves grow flat, accounting for spatial and temporal feedback effects, and explains observed growth features in tobacco leaves.

Contribution

It introduces a linearized feedback model integrating nonlocal and delayed effects to stabilize leaf growth shape, advancing understanding of laminar object regulation.

Findings

Linear feedback theory effectively suppresses long wavelength fluctuations.

Model explains statistical features observed in tobacco leaf growth.

Framework applicable to other laminar biological structures.

Abstract

Growing a flat lamina such as a leaf is almost impossible without some feedback to stabilize long wavelength modes that are easy to trigger since they are energetically cheap. Here we combine the physics of thin elastic plates with feedback control theory to explore how a leaf can remain flat while growing. We investigate both in-plane (metric) and out-of-plane (curvature) growth variation and account for both local and nonlocal feedback laws. We show that a linearized feedback theory that accounts for both spatially nonlocal and temporally delayed effects suffices to suppress long wavelength fluctuations effectively and explains recently observed statistical features of growth in tobacco leaves. Our work provides a framework for understanding the regulation of the shape of leaves and other laminar objects.