Elastic properties of the growth-controlling outer cell walls of maize coleoptile epidermis

Abstract

The effects of tensile stress and temperature on cell wall elasticity have been investigated in the outer cell walls of coleoptile epidermis of 4- and 6-day-old Zea mays L. seedlings. The change in tensile stress from 6 to 40 MPa caused the increase in cell wall elastic modulus from 0.4 to 3 GPa. Lowering the temperature from 30 to 4 °C resulted in instantaneous and reversible cell wall elongation of 0.3–0.5 ‰. At a given temperature and stress level, the wall elastic modulus of 6-day-old seedlings tended to be 30 % higher than that of 4-day-old plants. The relationship between cell wall elasticity and mechanical stress indicated that the stress distribution within the cell wall is highly uneven. The analysis of the effect of temperature on cell wall elastic strain showed that structural differences between crystalline and amorphous load-bearing polymers were not the only cause of the uneven stress distribution. Based on the results obtained by Hejnowicz and Borowska-Wykręt (Planta 220:465–473, 2005), we suggested that the uneven stress distribution is partially related to the stress gradient between inner and outer layers of the cell wall.

Appendices

Appendix 1

Theoretical analysis yields the following relationships between the cell wall elastic modulus (E) and the volumetric modulus (ε) of a spherical cell:

$$\varepsilon = \frac{2Et}{3r},$$

where t is the cell wall thickness and r is the cell radius (Wu et al. 1985).

During the pressure probe experiments t and r could not change significantly, so, in accordance with the above equation, the proportionality between the cell volumetric modulus and turgor pressure implies the proportionality between the elastic modulus of cell walls and tensile stress.

Appendix 2

Thermally induced strain of a polymer material is directly related to the thermal mobility of its constituent macromolecules. In the case of crystalline cellulose, an increase in temperature causes an increase in the length of interatomic bonds but to a lesser extent affects conformation of the polymer chain. Therefore, at about room temperature the crystalline cellulose generally has positive thermal expansion coefficients (Wada 2002). In the case of amorphous polymers the situation is more complicated (Wu and Sharpe 1979). Thermal response of amorphous polysaccharides is not limited to an increase in the lengths of interatomic bonds, but also includes the intensification of bending and rotational motions. Thermal motions cause amorphous macromolecules to be randomly coiled and counteract the stretching of the molecules under an external tensile force. The result is a negative coefficient of thermal expansion in the direction of tensile force. Its magnitude can be derived from the following relation:

$$f = pT\left[ {\left( {\frac{{l^{\text{str}} }}{{l^{\text{rlx}} }}} \right)^{2} - \frac{{l^{\text{rlx}} }}{{l^{\text{str}} }}} \right] $$

(5)

where f is the tensile force, p is the material parameter, T is the Kelvin temperature, and l ^str and l ^rlx is the cell wall length at the temperature T in the stretched and unstretched (relaxed) states, respectively (Wu and Sharpe 1979).

It follows from Eq. (5) that at small strains the decrease in temperature from T ₁ to T ₂ causes the elastic strain to increase proportionally to the change in temperature:

$$\frac{{l_{{T_{1} }}^{\text{str}} - l_{{T_{2} }}^{\text{str}} }}{{l_{{T_{1} }}^{\text{str}} - l_{{T_{1} }}^{\text{rlx}} }} = \frac{{T_{1} - T_{2} }}{{T_{2} }} $$

(6)

The numerator of the left-hand side of Eq. (6) represents the elastic strain caused by temperature change under constant mechanical stress (Fig. 5). The denominator of the left-hand side of Eq. (6) represents the elastic strain caused by mechanical stress at constant temperature (Fig. 4). The ratio of the cell wall strain caused by the decrease in temperature from 30 to 4 °C (Fig. 5) to its strain caused by mechanical stress (Fig. 4) is 0.5–1 %.

According to the Eq. (6), if the elastic elongation of an amorphous polymer material is due to the restriction of thermal motion, the temperature change from 30 to 4 °C (303 to 277 K) leads to the material elongation by (303 − 277)/277 = 9.4 % of the strain caused by mechanical stress. Comparing this value with the above experimentally derived data shows that less than 11 % of the cell wall elastic elongation could be attributed to the mechanism of restriction of polysaccharide thermal motions. Furthermore, the increase in tensile stress from 6 to 38 MPa caused only about 25 % reduction in the thermally induced strain (Fig. 5). Consequently, the sevenfold increase in the cell wall elastic modulus observed with increasing stress (Fig. 3) could not be due only to a decrease in the relative structural role of amorphous polysaccharides.

Appendix 3

Let us consider the load-bearing wall polymers as springs that obey Hooke’s law. In such a case, the cell wall modulus corresponds to the sum of the stiffnesses of wall polymers under tension (∑k ^ten) minus the sum of the stiffnesses of those under compression (∑k ^comp):

$$E = {{\Upsigma}}k^{\text{ten}} - {{\Upsigma}}k^{\text{comp}} $$

(7)

To evaluate changes in the cell wall elasticity caused by a decrease in tensile stress, consider the following situation. Suppose that all cell wall components were initially in tension. In this case the initial cell wall modulus equals:

$$E^{\text{initial}} = \chi k $$

(8)

where χ is the total number of cell wall components and k is their mean stiffnesses. Suppose further that the reduction of stress caused λχ (λ <1) components to be brought under compression and, consequently, (1 − λ)χ components were left under tension. When this occurs, in accordance with the Eq. (7), the new modulus equals:

$$E^{\text{final}} = (1 - \lambda )\chi k - \lambda \chi k = (1 - 2\lambda )\chi k $$

(9)

A comparison of the Eqs. (8) and (9) shows that the new modulus 1–2λ times larger than the initial:

$$\frac{{E^{\text{final}} }}{{E^{\text{initial}} }} = 1 - 2\lambda $$

(10)

It follows from Eq. (10) that to explain the sevenfold decrease in the modulus caused by the decrease in stress (Fig. 3) it is sufficient to assume that 43 % of the initially stretched cell wall components passed into the compressed state.