Growing plant stems and shoots exhibit a variety of shapes that embody
growth in response to various stimuli. Building on experimental observations,
we provide a quantitative biophysical theory for these shapes by accounting
for the inherent observed passive and active effects: (i) the active controllable
growth response of the shoot in response to its orientation relative to gravity,
(ii) proprioception, the shoot’s growth response to its own observable current
shape, and (iii) the passive elastic deflection of the shoot due to its own weight,
which determines the current shape of the shoot. Our theory separates the
sensed and actuated variables in a growing shoot and results in a morphospace diagram in terms of two dimensionless parameters representing a
scaled local active gravitropic sensitivity, and a scaled passive elastic sag.
Our computational results allow us to explain the variety of observed transient
and steady morphologies with effective positive, negative and even oscillatory
gravitropic behaviours, without the need for ad hoc complex spatio-temporal
control strategies in terms of these parameters. More broadly, our theory is
applicable to the growth of soft, floppy organs where sensing and actuation
are dynamically coupled through growth processes via shape.