Mathematical treatment of water movement in plant cells and tissue: a review

Abstract. Over the past three decades, many contributions have been made to the development of a mathematical basis for describing water transport in plant cells and tissue. This review paper attempts to summarize the more significant contributions and to outline the concepts upon which the various mathematical analyses are founded.
The paper itself is divided into three major sections. Section I deals with the quantitative water relations of single plant cells. Basic equations are developed which describe the water statics and water dynamics of such cells. Included is a discussion of the theory and methods for measuring the various parameters (permeabilities, cell wall elastic moduli, etc.) which enter into the development. The section closes with a presentation of circuit analog models for single plant cells.
Section II is devoted to a review and development of the water relations of plant tissues which contain numerous cells in series. Following a historical overview, various existing models are derived and physical tissue properties which enter the derivation are identified. The concept of 'local equilibrium' is discussed and circuit analog models for single cells are generalized and applied to several cells in series.
The final section contains two example applications of water transport theory as it applies to plant tissue. One application involves radial water movement in a soybean hypocotyl while the other deals with water transport in a growing root tip. A summary at the end of the section is largely devoted to a discussion of the limitations of mathematical models dial are presently available.