Quantifying the motor power of trees

Abstract

Key Message

Wood maturation strains can be estimated from the change in curvature that occurs when a stem grown staked in tilted position is released from the stake.

Abstract

Trees have a motor system to enable upright growth in the field of gravity. This motor function is taken on by reaction wood, a special kind of wood that typically develops in leaning axes and generates mechanical force during its formation, curving up the stem and counteracting the effect of gravity or other mechanical disturbances. Quantifying the mechanical stress induced in wood during maturation is essential to many areas of research ranging from tree architecture to functional genomics. Here, we present a new method for quantifying wood maturation stress. It consists of tilting a tree, tying it to a stake, letting it grow in tilted position, and recording the change in stem curvature that occurs when the stem is released from the stake. A mechanical model is developed to make explicit the link between the change in curvature, maturation strain and morphological traits of the stem section. A parametric study is conducted to analyse how different parameters influence the change in curvature. This method is applied to the estimation of maturation strain in two different datasets. Results show that the method is able to detect genotypic variations in motor power expression. As predicted by the model, we observe that the change in stem curvature is correlated to stem diameter and diameter growth. In contrast, wood maturation strain is independent from these dimensional effects, and is suitable as an intrinsic parameter characterising the magnitude of the plant’s gravitropic reaction.

Appendix

Integrals of cosine powers:

$${\phi _0}\left( {{\theta _1},{\theta _2}} \right)=\mathop \smallint \limits_{{{\theta _1}}}^{{{\theta _2}}} {\text{d}}\theta ={\theta _2} - {\theta _1},$$

$${\phi _1}\left( {{\theta _1},{\theta _2}} \right)=\mathop \smallint \limits_{{{\theta _1}}}^{{{\theta _2}}} {\text{cos}}\theta {\text{d}}\theta =\left[ { - {\text{sin}}\theta } \right]_{{{\theta _1}}}^{{{\theta _2}}},$$

$${\phi _2}\left( {{\theta _1},{\theta _2}} \right)=\mathop \smallint \limits_{{{\theta _1}}}^{{{\theta _2}}} {\text{co}}{{\text{s}}^2}\theta {\text{d}}\theta =\left[ {\frac{{2\theta +\pi +{\text{sin}}2\theta }}{4}} \right]_{{{\theta _1}}}^{{{\theta _2}}},$$

$${\phi _3}\left( {{\theta _1},{\theta _2}} \right)=\mathop \smallint \limits_{{{\theta _1}}}^{{{\theta _2}}} {\text{co}}{{\text{s}}^3}\theta {\text{d}}\theta =\left[ {\frac{{ - {\text{sin}}\theta (2+{\text{co}}{{\text{s}}^2}\theta )}}{3}} \right]_{{{\theta _1}}}^{{{\theta _2}}}.$$