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Computation of Mechanical Stress in Melon (Cucumis melo L.)

Hypocotyls during Transplant Preconditioning by Brushing

L.F. Hernández

Lab. de Morfología Vegetal

Depto. de Agronomía, UNSur

Bahía Blanca, 8000

and

Comisión de Investigaciones Científicas

de la Pcia. de Buenos Aires (CIC)

La Plata1900

Argentina

M.E. Ayastuy and M.A. Cantamutto

Horticultura Especial y Cultivos Intensivos

Depto. de Agronomía, UNSur

Bahía Blanca 8000

Argentina

Keywords: Bending stress, Finite element, mechanostimulus, thigmomorphogenesis

Abstract

Pretransplant brushing is a recommended horticultural technique to control stem

elongation. In melon (Cucumis melo L., inodorus group), when applied at fully expanded

cotyledon stage (15 days after emergence) it promotes hypocotyl shortening and significantly

improves postransplant performance.

Thigmomorphogenesis has been attributed to the physiological response for fast

developmental changes observed in the hypocotyl after its flexure by brushing. The

mechanostimulus signal transduction pathway leading to thigmomorphogenesis is not yet well

defined but it has been proposed that an efficient thigmo stimulus transport to growth centers

should be present.

In this contribution it is hypothesized that hypocotyl bending by brushing induces a

significant mechanical stress at a vascular level. That would contribute to the rapid long

distance intra-plant signaling transport. For validating this hypothesis, tensions generated on

the surface and in the vascular tissues during bending by brushing were dynamically simulated,

located, and calculated in a 3D model of the hypocotyl using the finite element method.

From the simulation a significant high bending stress at the ground level parenchyma

near the xylem and phloem was observed. The proximity of stressed cells to the phloem and

xylem elements support the hypothesis that mechanical stimulus cannot only act at the stem

surface but at the vascular tissue level.

INTRODUCTION Pretransplant brushing is a recommended horticultural technique to control stem elongation in

several plant species (Mitchell, 1996; Latimer, 1998). In melon (Cucumis melo L., inodorus group) we

have found that daily brushing during 10 days, at a rate of 10 to 40 strokes per minute (back and forth)

and at fully expanded cotyledon stage (15 days after emergence) (Fig. 1a; Ayastuy, 2004), promotes

hypocotyl shortening, reducing the its length by 20%, and significantly improves its postransplant

performance (Ayastuy, 2004). Thigmomorphogenesis (Jaffe et al., 2002) can explain these developmental changes observed in the hypocotyl after its flexure by brushing.

The mechanostimulus signal transduction pathway leading to thigmomorphogenesis is not yet

well defined and the exact mechanism of the thigmoresponse is unknown. Moreover it has still not been properly determined whether the growth response is restricted to the stimulated areas or whether

the whole plant is affected.

The first sign of the mechano-response is an increase of Ca2+cyt followed by the release of

ethylene (Biro et al., 1980; Erner et al., 1980; Huberman y Jaffe, 1981; Biro and Jaffe, 1984).

However it has been stated that this hormone is unlikely to be involved in either the molecular or

Proc. IIIrd IS on HORTIMODEL2006

Eds. L.F.M. Marcelis et al.

Acta Hort. 718, ISHS 2006

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developmental responses of plants to mechanical stimuli. Plants exposed to touch or shaking show a rapid (1 to 3 min) reduction in the rate of shoot elongation whereas ethylene release takes 30 to 45 min

to be detected (Johnson et al., 1998).

To rapidly transduce the thigmo stimulus from the site of perception to distant apical

meristems where active cell reproduction and expansion is taking place, an efficient transport system,

other than cell to cell communication pathways via plasmodesmata, has to be available (Jaffe et al.,

2002). The phloem long-distance translocation system of plants could play an important role in whole-

plant development as a conduit for the delivery of signaling molecules (Yoo et al., 2002). It could then

be appropriate to assume that the vascular system, particularly at the phloem sieve elements (SE)

level, could be the best route for the signals to be mobilized.

In fact the velocity of movement of materials in the SE range from 0.30 to 150 cm.h-1 (Taiz

and Zeiger, 1998). In an organ of 10 cm length such as a plant’s hypocotyl, the mechanosignal

generated at its base could reach the apical meristem in around 6 min, which closely agrees with the

measured times for the mechano-responses (Peacock and Berg, 1994). Moreover if the mechanical

stresses generated by brushing and shoot bending are located near the phloem strands it could

contribute even more to the mechanostimulus transport efficiency.

In this article, it is proposed that brushing induces external and internal stresses. This would

result in endogenous mechanosignals generated near the vascular strands that would then easily move

acropetally and basipetally towards growth centers. For validating this hypothesis, mechanical stresses

in the inner tissues of the Cucumis hypocotyl generated during bending were simulated and calculated using the finite element method.

MATERIALS AND METHODS

Anatomy of the hypocotyl A detailed location of the main tissues within the hypocotyl (Esau, 1977) and the relative

volumes of its constitutive tissues were defined from stained transverse serial sections (Ruzin, 1999)

taken from 15-days old hypocotyls of Cucumis plants (Fig. 2a).

Biomechanical properties of the tissues The Young's modulus of the whole hypocotyl was calculated from a three-point bending test

performed in a micromechanical testing device for small plant samples (Hernández and Bellés, 2004; 2006). A segment of 10.0 to 12.0 cm was trimmed from the hypocotyl and placed between two

opposite parallel holders. An indenter with rectangular cross section of width 1 mm was applied to the

segment in between the two supports until failure. Real time data was collected and downloaded to a PC. The hypocotyl segments were tested immediately upon removal from the plants. To prevent tissue

dehydration the specimens were coated during the test in silicone oil.

The Young's modulus of parenchyma and sclerenchyma as well as its Poisson ratios were taken from the literature (Preston, 1974; Wainwright et al., 1982; Niklas, 1992). The Young's modulus

of the xylem was from Hepworth and Vincent, (1998). Tissue density was estimated from the weight

of hypocotyl segments of known dimensions and the relative proportions of each tissue calculated

from the surface areas of each constitutive tissue measured from hypocotyl’s transverse cuts. To

calculate the force applied on a whole individual melon seedling during brushing a measuring

apparatus was assembled as described in Fig. 1b. For each biomechanical test 15 to 20 samples were

used.

Modeling and stress simulation Stresses inside the hypocotyl were calculated using the finite element (FE) method (Logan,

2001), a numerical procedure used for both static and dynamic structural analyses, suited for solving

the partial differential equations which describe stresses and strains in structures which have

heterogeneous properties.

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Based on its external dimensions and distribution of tissues (Fig. 2a) a 3-D model of the hypocotyl was constructed and properly meshed using the brick structural element (Figs. 2b and 3b;

Logan, 2001). Four strands of vascular tissue in the lower hypocotyl (0 to 4 cm) and 6 strands in its

topmost section (4 to 10 cm) (Fig. 3b) as observed from the histological analysis were considered. For

simplification purposes the model assumes isotropy and was considered to be composed by five

tissues incorporated as five independent element groups of isotropic material (Ep+Col: E(MN) = 3.5;

σ=2.5; δ (Kg.m-3)= 430; Cp: E=6.5; σ=0.25; δ= 960; Fs: E= 9.9; σ= 2.5; δ=1000; Xy: E=8.9; σ=2.5;

δ=950; Mp: E=4.0; σ=3.5; δ=600; Fig. 2b). Six and eight-nodal solid elements were used giving the model a final configuration of 7644 elements with 8560 nodes.

Calculation and localization of stresses in the model Stresses at the site of the hypocotyl’s simulated uniaxial bending were calculated. The

analysis was made using the ACCUPACK/VE routine from ALGOR (vers. 17, Algor Inc., Pittsburgh,

PA), a FE software processor for non-linear calculation. The bottom of the hypocotyl model was fixed and bending simulation applying a

displacement boundary condition (F= 0.0 to 0.04 N during 1.2 s; Fig. 3a,b) at the opposite apical end

was registered at a capture rate of 100 steps per second.

RESULTS AND DISCUSSION Figures 2c,d and 3c,d show the results obtained after the simulated bending of the model. The

distribution of stresses in a transverse section of the model, superimposed with a transverse cut of the

hypocotyl at the 6 vascular stands region, are shown in Fig. 2c,d. Stress fields inside the hypocotyl,

sequentially distributed during two stages of bending are shown in Fig. 3c,d. It can be seen that the position and the pattern of maximum stress values are always

significantly higher near the vascular tissue (Fig. 2c,d). This is a consequence of the proximity of the

fiber strands, which have the highest Young’s modulus (Fs: E= 9.9 MN), to xylem and phloem.

Moreover, the sequential results of the dynamic simulation (Fig. 3c,d) show that at the

beginning of the simulation, highest stress values are observed near the shoot apical meristem (noted

as Top in Fig. 3c). Then stresses are propagated basipetally (Fig. 3d) as a consequence of the inequity

in the number of vascular traces along the hypocotyl (Fig. 2b).

There is experimental evidence that higher plants have evolved a mechanism that allows the

selective translocation of long-distance signaling molecules by the phloem, for delivery to distant organs of the plant (Ruiz-Medrano et al., 1999).

Calcium-dependent protein kinases act as major mediators in Ca2+ signaling in plants through

the direct interaction of Ca2+ with the calmodulin-like regulation domain (White and Broadley, 2003).

Phloem sap contains a wide variety of proteins (Barnes et al., 2004) and some of these proteins that

move in the translocation stream could act in signal transduction cascades involved in the integration

of developmental and physiological processes occurring within distantly located organs (Jaffe et al., 2002). The phloem translocation stream could then serve as a conduit for the long-distance delivery of

proteins and ribonucleoprotein complexes and could be the way in which higher plants integrate

developmental and physiological processes at the whole-plant level.

The model described in this paper, a theoretical representation of a melon’s hypocotyl, its

constitutive tissues and their biomechanical properties, is able to predict stress distribution patterns

inside the structure. The proximity of stressed cells to the phloem and xylem elements support the

hypothesis that mechanical stimulus cannot only act at the stem surface but could also increase the

transport transfer of the mechanical stimulus at the vascular tissue level.

ACKNOWLEDGEMENTS

This work is supported by the Secretaría Gral. de Ciencia y Tecnología (SeGCyT) UNS, the

Comisión de Investigaciones Científicas (CIC-PBA), La Plata and the Argentine Sunflower

Association (ASAGIR). Authors want to thank Ms. A. Flemmer for histological processing, Mr. S. D.

Aman for collaborating in the assembly of the MT device and Mrs. L. I. Lindström and Dr. D. Ball

(Oregon State Univ.) for their valuable comments on the manuscript.

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Figures

Fig. 1. a) Brusher designed according to Björkman (1999) for applying pretransplant brushing to

melon seedlings (From Ayastuy, 2004). WF: wooden frame with height regulation; FRP:

foam rubber plate. b) Experimental apparatus to measure the force imposed by the foam rubber plate (FRP) on a whole individual melon seedling during brushing. The seedling

root system (SRS) was enclosed in a plastic bag to keep optimum water status and

mounted on an electronic digital scale in a horizontal position, fixed at the hypocotyl with a metal clamp. A 10 cm length piece of the rubber foam was displaced at a speed of 10

cm.sec-1 in vertical direction using a micrometer powered by an electric engine (EE).

Displacements (Displac.) and mechanical loads were recorded on a PC.

WF

FRP

a

b

Digital scale

Computer

EE

FRP

SRS

Displac.

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Fig. 2. a) Histological components of the hypocotyl at the region of 6 vascular strands (Vs). Ep:

epidermis; Col: colenchyma; Cp: cortex parenchyma; Mp: medullar parenchyma; Ph: phloem;

Xy: xylem; Fs: Fiber strand (From Ayastuy, 2004). b) Meshed model in a transverse cut. The

3-D model was constructed as an uniaxial projection of the transverse cut meshed model,

considering two sections with vascular tissue composed by 4 strands in the lower hypocotyl (0 to 4 cm) and 6 strands in its topmost section (4 to 10 cm) (See Fig. 3b). Scale bar identify the

5 material groups in the model. Arrows indicate the directions of applied forces in separated

simulations. c) Stress distribution at a 6-strand level of the modeled hypocotyl when force was oriented as in F1, superimposed with its correspondent schematic histological arrangement of

Fig 2a.d) Similar to c, but the force was applied as in F2. Note that in both cases (c and d) the

higher stress values (VonMises; N.m-2) correspond to the sites where the phloem an xylem are

located. Scale bars indicates gradient areas (from maximum, lighter, to minimum, darker) of

VonMises stresses in the simulation. Bar: 100 µm

b

Ph

a Ep Col

Cp

Mp

Xy Fs

F1

F2

Fs

Cp

Mp

Xy

Ep + Col

F1

c

F2

d

Vs

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Fig. 3. a) Curve of force vs. time resulting from the procedures described in Fig. 1b. For

each point n=15. b) Schematic representation of the FE model at the beginning (T0

secs) and at the end (T1.2 secs) of the simulation. Vertical legends in the model show

the relative position of 4 and 6 vascular strands. c-d). Calculated stresses

sequentially depicted at two moments, since the beginning of the bending simulation

(T0.1 secs ; A) to the end (T1.2 secs ; B). Note that during bending the stress pattern is

basipetally displaced, following the alternate arrangement of the tissues that conform

the model (Fig. 2b). Scale bars as in Fig. 2c-d.

4 s

tra

nd

s

(fro

m 0

- 4

cm

) 6 s

tran

ds

(fro

m 4

-10 c

m)

b Top at T0

secs Top at T1.2

secs

d

c

Top

Bottom

F1

T0.1 secs

Top

Bottom

F1

T1.2 secs

T1.2 secs

T0 secs

a

Bottom