Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

Abstract

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.

Overcoming the Challenges to Enhancing Experimental Plant Biology With Computational Modeling

“…A variety of mathematical techniques from topology and geometry are used to describe plant shape and exploit the analytically common or distinguishing characteristics of shapes as phenotypic traits (Bucksch et al, 2017;Mao et al, 2018). Technically, morphological modeling is realized through image processing as a means to extract plant geometry, segmentation or computer simulation to characterize relations between elements like connectivity and hierarchy of branches, arrangements of cells in a space or location of molecules.…”

“…Technically, morphological modeling is realized through image processing as a means to extract plant geometry, segmentation or computer simulation to characterize relations between elements like connectivity and hierarchy of branches, arrangements of cells in a space or location of molecules. The field of morphological modeling seeks to understand how underlying mechanisms, including gene regulatory networks, cellular signaling, organ signaling, and biophysical limitations, interact with physical growth processes, and how this ultimately produces the overall size and shape of different plant organs (Chickarmane et al, 2010;Bucksch et al, 2017;Hong et al, 2018).…”

“…Mechanistic mathematical models can enhance the information content and prediction of shape development. For example, the FiberWalk (Bucksch et al, 2017) characterizes the interaction between elongation and lateral expansion processes of tip-driven growth of a branch. The model predicts that tip-driven growth does not result in an equally thick branch and can not reach all spatial locations, providing mechanistic interpretation of some of the observed variation in measured phenotyping data.…”

“…Root systems which had root tips in close proximity obtained the most additional phosphorus uptake due to organic-acid exudation. In summary, mechanistic mathematical models are also powerful vehicles to incorporate multi-scale processes, heterogeneous data such as soil, and complex geometries and are a future direction of focus for the field (Roeder et al, 2011;Bucksch et al, 2017;Hong et al, 2018;Ruiz et al, 2020b). Additionally, mechanistic models can be coupled with imaging studies and growth models to link observed plant structure to underlying function.…”

“…Here, we begin by dividing the field of mathematical modeling in plant biology into two categories: pattern-finding and mechanistic mathematical models (section 1). We then address how these types of models are used in different subfields of plant biology, and how pattern and mechanistic mathematical models complement each other (section 2) (Bucksch et al, 2017;Passot et al, 2019). Then we further describe the scientific value of modeling (section 3).…”