Biomechanical modeling of gravitropic response of branches: roles of asymmetric periphery growth strain versus self-weight bending effect

Bending movement of a branch depends on the mutual interaction of gravitational disturbance, phototropic response, and gravitropic correction. Four factors are involved in gravitropic correction: asymmetric growth strain, eccentric growth increment, heterogeneous longitudinal elasticity (MOE), and initial radius which are associated with reaction wood production. In this context, we have developed a simplified model to calculate the rate of curvature change by combination of these factors. Experimental data from Taiwan red cypress were used to test the validity of the model. Our results show clearly that asymmetric growth strain is the main factor involved in correction. Eccentric growth increment has positive efficiency and increases correction in addition to growth strain, while the total effect of longitudinal MOE variation has negative efficiency and decreases correction. Spring-back strain measurement is found to be useful for the measurement of self-weight bending moment of branch. The branches studied are essentially close to a biomechanical equilibrium which maintains branches in horizontal positions. In the case of a deciduous dicotyledonous tree, flamegold, the effect of defoliating behavior on measured growth strain and curvature change was formulated by a modified model. Growth strain is the sum of measured growth strain after defoliation and spring-back strain during defoliation. The curvature change can be calculated by using measured growth strain and spring-back strain after defoliation. These results show that full-leaf branches of flamegold have a tendency to bend downward, but defoliated branches have a tendency for upward bending. The efficiency of correction increased after defoliation due to weight loss