Oliver E. Jensen

PNAS January 5, 2021 118 (1) e2023962118

Plants integrate numerous signals in order to adapt their shape to their environment, modifying their tissues structurally and biochemically so that stems, roots, branches, and leaves have the appropriate shape, orientation, and mechanical properties to track the sun, resist gravity, and harness nutrients. In PNAS, Moulton et al. (1) present a compact mathematical description of the essential components of these tropic responses, providing a framework linking sensing, hormone transport, and growth to three-dimensional form. Their model is expressed as a set of coupled relationships between mathematical functions defined along a curve in space, yielding an elegant field theory that harnesses many of the complexities of plant tropisms.

Many physical “laws” are formulated using fields, that is, smooth mathematical functions that vary in space and time. Although they may be generated by large numbers of discrete processes operating at microscopic scales, fields vary smoothly at macroscopic length scales, allowing their spatiotemporal evolution to be described using the powerful language of vector and tensor calculus, with relationships often expressed with remarkable succinctness. Underpinning many of the triumphs of physical field theories (such as Maxwell’s equations of electromagnetism, or the Navier–Stokes equations of fluid mechanics) is the very large difference between the microscopic length scales at which fields are generated or decay and the macroscopic length scales over which we may seek to describe them, a feature known as “separation of scales.”

See more: https://www.pnas.org/content/118/1/e2023962118

Figure 1: A schematic showing the interactions between the eight primary fields in the model presented by ref. 1: Hormone concentration A and growth g vary both along and across the shoot; stretch and intrinsic curvatures γ, û 1û1, and û 2û2, realized curvatures u1u1 and u2u2, and the location of the shoot’s centerline in three-dimensional space r vary along the shoot. Interactions between these fields are described in the text as Processes i to v. The dashed arrow represents the mechanical impact of external loads (e.g., self-weight, contact with a rigid surface) in determining the shape of the plant.