Suppression of soft spots and excited modes in the shape deformation model with spatio-temporal growth noise

The shapes of plant organs such as sepals are precise and reproducible, although the cells composing these organs are highly heterogeneous. We investigate the collective behavior of a shape deformation model with spatio-temporal fluctuations in elasticity (Hong et al., Dev. Cell, 38, 15, 2016). It is shown that the spatio-temporal growth noise has two opposing effect: the temporal noise promotes the reproducibility of the organ shape, whereas the spatial noise disturbs it, leading to the organ undergoing an abnormal shape deformation. To understand how such abnormality can emerge, we study the eigenvectors of the correlation matrix of the growth velocity. It is revealed that the anomalous shape deformations can be created by two independent factors: (1) excited modes where the orientations of the eigenvectors with m ≥ 2 are spatially correlated, and/or (2) soft spots where spot structures with high fluctuations in the magnitudes of the eigenvectors appear non-uniformly.