J.R. Cooke, R. Rand, J.G. de Baerdemaeker, H.A. Mang:
"A Finite Element Shell Analysis of Guard Cell Deformations";
Transactions of the American Society of Agricultural Engineers, 19 (1976), 1107 - 1121.
In this paper the width of the stomatal aperture, as postulated by von Mohl in 1856, is shown to be a function of the hydrostatic (turgor) pressure in the guard cells, P_g, and the pressure, P_s, of the immediately surrounding epidermal cells, which will be referred to as the subsidiary cells in this paper. The aperature does not depend solely upon the pressure difference (P_g - P_s) as believed by Ursprung and Blum (1924) and Stalfelt (1966). Instead, aperture width is shown to be a simple multilinear relationship (i.e., a linear combination) of P_g and P_s. The recent research by Glinka (1971) and Edwards, Meidner and Sheriff (1976), showing the relative contributions of the opposing pressures P_g and P_s, is, thus, given a
The analysis of a guard cell as an elliptical torus shows that a stomate could function without either of the two conditions clasically believed to be essential (Meyer et al. 1960, p.84, Meidner and Mansfield 1968, pp. 14-17, Bidwell 1974, p.298). The "thickened wall" (ventral wall) of the guard cell facing the aperture need not necessarily be stiffer than the dorsal wall common to the adjacent epidermal cell for the proper functioning of a stomate. The radially oriented cellulose microfibrils in the guard cel wall are not vital but are important for quite differetnt reasons than claimed by Aylor et al. (1973). Consideration of the radial stiffening by means of the introduction of a mechanically equivalent orthogonally anisotropic (i.e., orthotropic) material causes the aperture width to be more sensitive to a unit increment in P_s than to a unit increment in P_g (for parameters of physical interest). The guard cell volume, however, is smaller than the adjacent cell volume and P_g is believed to be larger thatn P_s, in general. We conjecture that this increased sensitivity for the subsidiary cell (i.e., closing) pressure is important for the functioning of the feedback control loops regulating the aperture width. We define an antagonism ratio to characterize this property. The pore length in the model is shown to be surprisingly constant during opening, as is reported for many species (Meidner and Mansfield 1968, p. 12).
The guard cell is generally believed to bulge into the neighboring epidermal cell upon opening (Meidner and Mansfield 1968, p.15). However, the shell model suggests that the outermost prtion of the guard cell at the widest point (and not visible in an in vivo situation) actually moves away from the neighboring cell. The approximate point at which the exposed surface of the epidermal cell joins the guard cell exhibits only limited motion. Note that there are especially thin regions here in the epidermal cell thought to behave as hinges (Hautgelenke). Even when the extreme, unphysiological case of a fixed aperture length is imposed, the outermost perimeter moves from the adjacent cell. If the epidermis is opaque, the view from outside the leaf suggests that the guard cell "bulges" into the neighboring cell, as claimed in the classical hypothesis, provided the stiffening effect of the micellae is sufficiently prominent an dprovided the guard cell pressure is significantly larger than the epidermal cell pressure.
The opposin influence of the turgor pressure in the guard cells and in the adjacent epiedermal cells is shown to be an inherent part of the stomatal mechanism (von Mohl 1856). Pressure influence coefficients for the guard cell are defined and related to parameter changes, e.g., material and thickness.
The multilinear relationship of aperture width to the opposing turgor pressures was found and revealed that pore width does not depend solely on the pressure difference between the guard cell and the adjacent epidermal cell. Finally, the theory developed is shown to embrace and to clarify the experimental results of Glinka'a plasmolytic study (1971) and the direct method of Edwards et al. (1976).