Asymmetries in leaf branch are associated with differential speeds along growth axes: A theoretical prediction

Abstract

When different growth speeds along axes of a divaricating leaf were introduced into our previous model, robust and directed asymmetries were reproduced. The differences in growth speed could be predicted from the distributions of leaf segments in actual leaves. Developmental Dynamics 246:981-991, 2017. © 2017 Wiley Periodicals, Inc.

Theoretical models for branch formation in plants

“…Such divaricated leaves are categorized as serrations, lobes, and leaflets mainly according to their degree of protrusion. Simple and compound leaves are sharply distinguished from one another, though the arrangement of lobes or leaflets in divarications often show commonalities (Nakamasu et al 2017). A heterophyllous plant, Rorippa aquatica, has sequential peripheral complexity from an elliptically shaped simple leaf to a finely dissected leaf (Nakayama et al 2012).…”

“…1b-d, 3b). In the case of lateral branching, the sequence of regular arrangements observed in the intact (i.e., not modified) branches was described using recurrence formulas (Nakamasu et al 2014(Nakamasu et al , 2017, and is coincidentally comparable to a specific parameter in (tD)OL-systems with a delay (Prusinkiewicz and Lindenmayer 1990), though these models are completely different systems. The former utilizes the spatial scale to make form, whereas the latter model repeatedly adds a stable unit as measured in time to adjust the branch arrangement.…”

“…The former utilizes the spatial scale to make form, whereas the latter model repeatedly adds a stable unit as measured in time to adjust the branch arrangement. This rule is appropriate to explain branch arrangements that include asymmetry observed in actual leaves (Nakamasu et al 2014(Nakamasu et al , 2017. Degree of branch asymmetry can be expressed as subtractions of sequential steps of the recurrence formula.…”

Expansive growths with uniaxial gradients can explain formation of oblong diversity observed in two-dimensional leaf shapes

“…Therefore, the growth speed at the point P ij is determined as a function of ( u i + u j ) and/or w y . For description of the growth caused by cell expansion without cell proliferation had been treated in (Nakamasu et al ., 2017), though, for its biased case, the connection point P ij ( t ) is propagated along the vector from the geometrical center of the initial condition as . Here, is defined as the vector on each point in the direction mentioned above and with a length of the distance from the origin is divided by a representative length l of the shape ( l is the length of the tallest vector) (Fig.…”

Developmental analyses of divarications in leaves of an aquatic fern Microsorum pteropus and its varieties

“…The leaves are critical for photosynthesis and vary widely in size and shape, although they all develop similarly from a small group of cells, called leaf primordia, which locate on shoot apical meristems. Mathematical models have been used to understand complex natures of leaf-shape formation [1], [2], [3], [4]. Developmental patterns in leaf primordia that determine leaf shapes are highly diverse among species [5].…”