Mechanical measurement of gravitropic bending force in pea sprouts

Abstract

Environmental stimuli such as gravity and light modify the plant development to optimize overall architecture. Many physiological and molecular biological studies of gravitropism and phototropism have been carried out. However, sufficient analysis has not been performed from a mechanical point of view. If the biological and mechanical characteristics of gravitropism and phototropism can be accurately grasped, then controlling the environmental conditions would be helpful to control the growth of plants into a specific shape. In this study, to clarify the mechanical characteristics of gravitropism, we examined the transverse bending moment occurring in cantilevered pea (Pisum sativum) sprouts in response to gravistimulation. The force of the pea sprouts lifting themselves during gravitropism was measured using an electronic balance. The gravitropic bending force of the pea sprouts was in the order of 10⁰ Nmm in the conditions set for this study, although there were wide variations due to individual differences.

Various environmental stimuli such as gravity and light modify internal and genetically encoded developmental programs that control plant development to optimize overall plant architecture. Plant organs grow in response to the direction of the stimulation, which is known as tropism. In the gravitropic response, plant organs sense the direction of gravity using amyloplasts, which are types of plastids containing a large amount of starch. The amyloplasts in endodermal cells of aerial organs, including stems and branches, or in columella cells of the root cap, sediment in the direction of gravity and transfer the signal downstream, probably by stimulating the cytoskeleton and/or cellular membrane system (Morita 2010; Vandenbrink and Kiss 2019). After gravity sensing, a differential auxin gradient along the direction of gravity is established, which promotes the differential growth of organs (Morita 2010; Vandenbrink and Kiss 2019). As a result, the aerial organs grow against the direction of gravity (negative gravitropism), while the roots grow in the direction of gravity (positive gravitropism). Like herbaceous plants, the apex of Populus seedlings placed horizontally turn upright through elongation growth within a few hours (Groover 2016). The factors involved in the gravity response in herbaceous plants are also involved in the shoot architecture of woody plants (Hill and Hollender 2019). These results suggest that the responsive mechanism to gravistimulation is common to some extent between herbaceous and woody plants. Therefore, the unilateral gravity of the earth is the basis for plants to control their architecture. In the phototropic response, plants grow toward the direction of light, thereby promoting efficient photosynthesis. Unlike in animal cells, plasma membranes of plant cells are surrounded by thick cell walls including cellulose fibers and lignin. The shape and the size of the cell are limited by the cell wall. Plant organ growth is caused by cell division and expansion that occurs via water uptake (Cosgrove 2005; Gonzalez et al. 2012). The motive force for water uptake is the osmotic pressure of the vacuolar fluid, which occupies most of the cell volume, and is caused by the movement of water into the vacuole with high solute concentration through the semipermeable vacuolar membrane. When water is absorbed by osmotic pressure, cells generate a turgor pressure pushing outward against the cell wall, while the cell wall generates a force that pushes back due to an action-reaction relationship. Cell expansion via water uptake is determined by the balance between osmotic pressure and the mechanical property of the cell wall (Hamann 2015). Therefore, plant growth via water uptake is promoted when the physical strength of the cell wall is weakened, or when the osmotic pressure is increased. The auxin activates plasma membrane H⁺-ATPase to acidify the extracellular space, which is thought to play a role in relaxation of the cell wall and promotion of cell expansion (Hager 2003; Rayle and Cleland 1992). Many physiological and molecular biological studies of gravitropism and phototropism have been carried out, but sufficient analysis has not been performed from a mechanical point of view. To identify the stiffness of Arabidopsis inflorescence stems, the force to flex the free end of a cantilevered stem by forcing to move the tip was measured (Yoshihara and Spalding 2020) and the vibration characteristics of stems was analyzed (Nakata et al. 2018). Also, the force of the pea sprouts lifting themselves upward during gravitropism was measured (Arimoto et al. 2019, 2020). However, the gravitropic bending force, the moments occurring at both ends of the differential growth zone that cause the flexuous movement in response to gravity, has not been examined. Therefore, we calculated the gravitropic bending force via bending moment diagram in this paper. If the biological and mechanical characteristics can be accurately grasped, then controlling the environmental conditions would be helpful to control the growth of plants into a specific shape. In this study, to clarify the mechanical characteristics of gravitropism, we analyzed the transverse bending force occurring in cantilevered pea (Pisum sativum) sprouts in response to gravistimulation as a first step.

The pea sprouts were used under two different conditions. In the first condition, the commercial pea sprouts were cut at 12 cm from the apex of the stem, and the basal part (5 cm-long in experiments 1 and 3 and 3 cm-long in experiment 2) of the 12-cm stem sections were set in a small container filled with a water-absorbed sponge (hereafter referred to as “pea sprouts without roots: WOR”). In the second condition, pea seeds were germinated on the water-absorbed sponge, and the intact pea sprouts with the 10 cm-long stems were set in a small container with a water-absorbed sponge (hereafter referred to as “pea sprouts with roots: WR”). After placing the pea sprouts horizontally for gravistimulation, fixed-point images were taken every 10 min with a digital camera (Canon EOS 9000D) with flash in all experiments in a dark room. The camera was positioned far enough from the pea sprouts to avoid the phototropic response of the plants. We conducted three kinds of experiments (Table 1). In experiment 1, the gravitropic behavior of pea sprouts were observed for 18 h after placing them horizontally. The stems of the pea sprouts were divided into 1 cm-sections from the apex and marked at the midpoint of each section in this experiment (Figure 1A). The mass of each section was measured by cutting the stems into sections with scissors after the experiments. Additionally, the distance from the bending point to each mass point of the divided sections was estimated from the fixed-point images taken during the experiments. The rotation angle at the apex of the stem defined as the angle formed between the growing direction of the apex and the horizontal base line was measured from the images every 30 min from the start of the experiment to 6 h, and thereafter it was measured every 1 h during gravistimulation. In experiment 2, to calculate the gravitropic bending force, the constraint reaction force was measured by constraining the vertical movement of the pea sprouts using a nylon thread with a weight placed on an electronic balance (Shimadzu Corporation, UX420H, 0.001 g minimum display). After setting the pea sprouts in the small container and placing them horizontally, as with experiment 1, a 0.235 mm-diameter nylon thread to which a 2.2-g weight was attached at the lower end was fixed 2 cm away from the apex with adhesive tape to be orthogonal to the stem axis (Figure 1B). The length was adjusted so that the thread was stretched at slight tension, while the weight was placed on the electronic balance. The pea sprouts were placed for 3 h, during which a reading of the electronic balance was recorded every second. The fixed-point images of the pea sprout were taken at 0 and 3 h during gravitropism (Figure 1B). In experiment 3, we increased the constraint and constrained the vertical movement of the stem at 4.5 cm from the apex using styrene board 1 with a thickness of 3 mm (Figure 1C). Additionally, we installed another styrene board 2 with the weight above the apex of the stem, such as a ceiling to constrain the upward movement of the apex. Only styrene board 2 was placed on the electronic balance and changes of the measured weight was recorded (Figure 1C).

Table 1. Experiment overview with schematic depiction of test apparatus.

Figure 1. Experimental conditions of each experiment. (A) Maximum intensity projection of time-lapse images during gravitropism of the pea sprout in experiment 1. Positions of the pea sprout at each time point are indicated by numbers; 1: 0 min, 2: 40 min, 3: 4 h 50 min, 4: 9 h, 5: 13 h 10 min, and 6: 17 h 20 min. Red markers indicate the stem sections divided every 2 cm. The circle with a dotted line indicates the bending point of the stem region after gravistimulation for 17 h 20 min. (B) Test apparatus with one-point constraint for measurement of the constraint reaction force of the pea sprout in experiment 2. A nylon thread attached to a weight (2.2 g) at the lower end was fixed with adhesive tape to be orthogonal to the stem axis 2 cm from the apex of the stem. A representative image of the experiment at 0 h and 3 h during gravitropism. The stem of the pea sprout showed unexpected adaptation by rotation at the constraint point. (C) Test apparatus with two-point constraint for measurement of the lifting force of the pea sprout in experiment 3. Styrene board 1 at 4.5 cm from the apex of the stem constrained the vertical movement of the stem. Styrene board 2 just above the apex of the stem constrained the upward movement of the apex. Styrene board 2 with a weight (2.2 g) was placed on the electronic balance.

The specification of the pea sprouts and the measured stem weight in experiment 1 are shown in Supplementary Table S1. Changes of the stem weight were regarded as negligibly small because almost no elongation of the stem was observed during the experimental period. As shown in Figure 2, the rotation angle at the apex of the stem varied widely depending on the individual specimen. The tip of each stem grew downward since the cantilever was bent down along its length under its own weight when placed horizontally. After being gravistimulated for 40 min, the tip of the stem switched direction of deflection upward (Figure 2). The bending point judged from the fixed-point images as the point where angular variation occurs in the stem was shifted from the apical to basal region during gravitropism, that is, the stem gradually bent from the tip. Each specimen achieved a maximum rotation angle at a different time from 2.5 to 10 h during gravistimulation (Figure 2). In experiment 2, the constraint reaction force in Figure 3 is the opposite value of the electronic balance whose initial value was initialized to zero. The constraint reaction force became negative at the early stage because the stem bent downward under its own weight. Supplementary Table S2 shows the test results, including the lifting force; the difference between the maximum and minimum value of the constraint force during one measurement. The observed lifting force was between 2.0×10⁻³ and 5.0×10⁻³ N, though there was individual difference. The length from the bending point to the apex was estimated from the images after the experiments. We intended to obtain the approximate value of the constraint reaction force required to calculate the gravitropic bending force in experiment 2. However, only one constraint point seemed to induce unexpected adaptation by rotation of the stem. The bending point shifted to the constrained point as the stem bent, such that the stem could continue to bend with the constraint. Therefore, the lifting force could not be accurately measured. The specification of the pea sprouts and test results of experiment 3 are shown in Supplementary Table S3. The lifting force was 2.0×10⁻³ to 1.3×10⁻² N, which was higher, in general, than those of experiment 2 by constraining the vertical movement of the bending point.

Figure 2. Time course of the rotation angle at the apex of pea sprout stems. The rotation angle of the stem was defined as the angle formed between the growing direction of the apex and the horizontal base line during gravistimulaton in experiment 1.

Figure 3. Time course of the constraint reaction force in experiment 2. The lifting force is defined as the difference between the maximum and minimum value of the constraint reaction force recorded during gravistimulation.

First, we examined the bending moment, internal stress induced by differential growth, at the bending point of experiment 1 and 3. It was calculated as the product of the summation of the moments calculated by the self-weight of the stem applied to each mass point and the perpendicular distance between each mass point and the bending point in experiment 1 and the moment calculated by the downward constraint reaction force near the apex and the perpendicular distance between the constraint points in experiment 3. The bending moment at the bending point was calculated every 30 min from the start of the experiment to 6 h, and thereafter it was calculated every 1 h by regarding each section as the mass point (Figure 4). The bending moment at the bending point was highest when the stem was horizontal and decreased as it bent. The bending moment of WOR was higher than that of WR because stems of WOR had a larger diameter. In experiment 1, the averages of the maximum bending moments of WR and WOR were 7.0×10⁻³ Nmm and 3.0×10⁻² Nmm, respectively. On the other hand, in experiment 3, the bending moment at the point constrained by styrene board 1 was calculated as the product of the downward constraint reaction force near the apex of the stem and the distance between the constraint points, without considering the self-weight of the stem (Figure 5). The bending moment tended to increase over time, and the averages of the maximum bending moment of WR and WOR were 0.22 and 0.47 Nmm, respectively. Next, we regarded the transverse gravitropic bending force as the opposite and equal moments generated at both ends of the differential growth zone from cell expansion by water uptake and examined the gravitropic bending force on the assumption that the differential growth zone was 2.5 to 4.0 cm from the apex of the stem. The uniformly distributed load of 3.0×10⁻⁵ N/mm was applied as its self-weight, and the constraint reaction forces near the apex of the stem in experiment 2 and 3 were 3.6×10⁻³ and 8.0×10⁻³ N, respectively. When the stem was placed horizontally, cell expansion by water uptake was promoted in the lower part of the stem, and tension was generated in the cell wall due to the turgor pressure inside the cell. Consequently, the compressive force was generated in the upper part of the stem, and the moments generated by these resultant stresses were considered as the force that caused the bending deflection in gravitropism. Figure 6 presents the bending moment due to the self-weight of the pea sprouts, the gravitropic bending force, and the constraint reaction force when the stems were kept horizontal for each experimental condition. The gravitropic bending force was calculated according to the superposition principle. The resultant vertical displacement of the stem at the constraint point can be determined by algebraically summing the displacement calculated by each load component, namely the gravitropic bending force and constraint reaction force applied separately to the stem. Since the resultant vertical displacement at the constraint point is zero, the gravitropic bending force can be calculated. In experiment 2, the gravitropic bending force was 2.1 Nmm. On the other hand, in experiment 3, if it is assumed that the constraint reaction force near the basal part of the stem is P, then the gravitropic bending force becomes 4.6–96 P Nmm. The gravitropic bending force of the pea sprouts was in the order of 10⁰ Nmm in the conditions set for these experiments, although there were wide variations due to individual differences. By measuring the constraint reaction force near the basal part of the stem, it is implied that the gravitropic bending force could be obtained more accurately.

Figure 4. Bending moment generated by the self-weight of the pea sprouts in experiment 1. (A) Stem is modeled by a single line fixed at one end such as a cantilever. Bending moment diagram indicating that the bending moment resisted internally at a section through the stem. If they cause the bending shape of the stem to concave downward, then the bending moment is negative and the bending moment diagram is illustrated upward on the stem. The arrows with different length represent the distributed load, because the weight of each section are different in experiment 1. In this case, to consider the bending moment at the bending point, the arrows are illustrated only at the part from the bending point to the apex. (B) Time course of the bending moment at the bending point during gravistimulation.

Figure 5. Bending moment generated by the constraint reaction force in experiment 3. For simplicity, the self-weight is neglected. (A) Bending moment diagram. (B) Time course of the bending moment magnitude at the bending point during gravistimulation.

Figure 6. Bending moment diagrams of pea sprout stems for each load case. (A) Cantilevered stem subjected to uniformly distributed dead load as that in experiment 1. (B) Cantilevered stem subjected to a concentrated dead load near the apex and uniformly distributed load as that in experiment 2. (C) Cantilevered stem subjected to concentrated loads and uniformly distributed dead load as that in experiment 3. It is assumed that the constraint reaction force near the basal is P.