THE BALANCE OF FORCES GENERATED BY THE WATER POTENTIAL IN THE CELL‐WALL‐MATRIX—A MODEL

A cell in contact with air is considered. The nature of the water within a cell wall is assumed (with citations in support) to be that of free water and essentially free of diffusible solutes, so that the air-water interface generates negative pressures (Pf) (at all relative humidities less than 100o), equal to the overall cell-water-potential. At the inner wall-surface, the turgor pressure (Pr) is balanced by the sum of Pf and a pressure resisting collapse of the wall matrix (P51); at the outer wall-surface, Pf is balanced only by a similar pressure (P,0). Under all circumstances, Psi = Pt Pf, and the osmotic term of the internal cell-water-potential (Pim) = -P,i. At full turgor, Pso is zero, and it rises as water is lost, equalling Psi when Pt is zero (Psi = -Pf. In cells in contact with solutions of solutes which penetrate the wall, Pf and P,0 are zero and Psi follows Pt. In either case, the hoop stress, tending to enlarge the cell surface, is proportional to Pt, but the cell-in-contact-with-air has radial stresses not found in submerged cells. The nature of the forces resisting radial compression of the wall is discussed, and thought to be a combination of mechanical elastic forces and osmotic forces due to non-diffusible polysaccharides of the wall. THE HOFLER DIAGRAM, describing the changes in the components of the water potential as a cell varies in water content (relative volume) has long been a part of standard treatments of plant water relations. However, such treatments describe only the vacuole and cytoplasm; the cell wall is treated as an externality, providing only a greater or lesser degree of elasticity to the cell volume. Likewise, treatments of the mechanical properties of the wall, in relation to elastic and plastic expansion, have only dealt with turgor pressure among the forces applied (Nobel, 1974). In addition, it can be shown (Passioura, 1980), although perhaps it is not generally recognized, that the water potential of a tissue cannot be segmented into osmotic, pressure, and matric terms as is sometimes stated. But the "matric potential" of the cell wall by itself ought to be worthy of special treatment. It is the purpose of this report to describe the variation of the forces imposing the water potential within a plant cell wall, in just the same fashion as the Hofler diagram describes the forces imposing the water potential within the vacuole and cytoplasm combined. Inasmuch as these forces are different, in cells submerged in solutions of solutes that 1 Received for publication 22 August 1980; revision accepted 24 March 1981. I am indebted to anonymous reviewers for critical comments, and to Professor Donald N. Pierce, Department of Engineering Mechanics, University of Nebraska-Lincoln, for assistance. penetrate the wall, from those in cells in contact with air, both situations will be described, with emphasis on the complications of the latter. Also, to avoid undue complexity, the walls will be treated as perfectly elastic bodies, ignoring any irreversible deformations, and as at equilibrium. THE AMOUNT AND STATE OF WATER IN THE CELL WALL-Although it is customary to refer to the extensive literature on water in soils, when discussing the matrix potential (Passioura, 1980), the cell wall substance is not homologous with soil, nor even analogous, since the cell wall matrix is a continuous phase, unlike clay. Like clay, it resists compression, but unlike clay it has a limited volume in expansion. Water in cell walls has long been of concern in wood and paper technology and its physical chemistry has been described in much detail (Skaar, 1972). T-hus, the amount and state of water in wood should suit as an example of the more general case. However, it must be noted (Stamm, 1971) that most of the study of water in wood has dealt with wood that has had part of its volume irreversibly collapsed by drying, with major consequences between relative humidities (RH) of 100 and 80%. This is the region of interest in live cells, since the relative humidity is related to the water potential by P = RT ln RH , and 99% V 100' RH corresponds to -1.4 MPa (14 bars).