Hierarchical Helical Order in the Twisted Growth of Plant Organs

The molecular and cellular basis of left-right asymmetry in plant morphogenesis is a fundamental issue in biology. A rapidly elongating root or hypocotyl of twisting mutants of Arabidopsis thaliana exhibits a helical growth with a handedness opposite to that of the underlying cortical microtubule arrays in epidermal cells. However, how such a hierarchical helical order emerges is currently unknown. We propose a model for investigating macroscopic chiral asymmetry in Arabidopsis mutants. Our elastic model suggests that the helical pattern observed is a direct consequence of the simultaneous presence of anisotropic growth and tilting of cortical microtubule arrays. We predict that the root helical pitch angle is a function of the microtubule helical angle and elastic moduli of the tissues. The proposed model is versatile and is potentially important for other biological systems ranging from protein fibrous structures to tree trunks.