# Essay 14.3 Biophysical Coordination of Water Uptake and Cell Wall Enlargement

Water uptake in all plant cells is a passive process. There are no active water pumps; instead the growing cell uses the trick of wall stress relaxation to lower the water potential inside the cell so that water is taken up spontaneously in response to a water potential difference, without direct energy expenditure.

To put this in physical terms, we begin by defining the water potential difference, Δ*ψ*_{w} (expressed in megapascals, MPa), as the water potential outside the cell (*ψ*_{o}) minus the water potential inside (*ψ*_{i}) (see Chapters 3 and 4). The rate of uptake depends on Δ*ψ*_{w} times the surface area of the cell (*A*, in square meters) times the permeability of the plasma membrane to water (*Lp*, in meters per second per MPa). Membrane *Lp* is a measure of how readily water crosses the membrane, and it is a function of the physical structure of the membrane and the activity of aquaporins (see Chapter 3). The rate of water uptake is defined as Δ*V*/Δ*t*, expressed in volume per second. Assuming that a growing cell is in contact with pure water (with zero water potential), then we have:

Rate of water uptake = Δ

V/Δt=A×Lp(ψ_{o}–ψ_{i}) =A×Lp(0 –ψ_{i}) = –A×Lp(ψ_{p}+ψ_{s})

(Equation 1)

This equation states that the rate of water uptake depends only on the cell area, membrane permeability to water, cell turgor (*ψ*_{p}), and cell osmotic potential (*ψ*_{s}).

Equation 1 is valid for both growing and nongrowing cells in pure water. But how can we account for the fact that growing cells can continue to take up water for a long time, whereas nongrowing cells soon cease water uptake?

In a nongrowing cell, water absorption would increase cell volume, causing the protoplast to push harder against the cell wall, thereby increasing cell turgor pressure, *ψ*_{p}. This increase in *ψ*_{p} would increase cell water potential, *ψ*_{w}, quickly bringing Δ*ψ*_{w} to zero. Water uptake would then cease.

In a growing cell, Δ*ψ*_{w} is prevented from reaching zero because the cell wall is “loosened”: it yields irreversibly to the forces generated by turgor and thereby reduces simultaneously the wall stress and the cell turgor. This process is called **stress relaxation**, and it is the crucial physical difference between growing and nongrowing cells.

Stress relaxation can be understood as follows. In a turgid cell, the cell contents push against the wall, causing the wall to stretch elastically (i.e., reversibly) and giving rise to a counterforce, wall stress. In a growing cell, biochemical loosening enables the wall to yield inelastically (irreversibly) to the wall stress. Because water is nearly incompressible, only an infinitesimal expansion of the wall is needed to reduce cell turgor pressure and, simultaneously, wall stress. Thus, stress relaxation is a decrease in wall stress with essentially no change in wall dimensions.

As a consequence of wall stress relaxation, the cell water potential is reduced and water flows into the cell, extending the cell wall and increasing cell surface area and volume. Sustained growth of plant cells entails simultaneous stress relaxation of the wall (which tends to reduce turgor pressure) and water absorption (which tends to increase turgor pressure).

Many studies have shown that wall relaxation and expansion depend on turgor pressure. As turgor is reduced, wall relaxation and growth slow down. Growth usually ceases before turgor reaches zero. The turgor value at which growth ceases is called the **yield threshold** (usually represented by the symbol *Y*). This dependence of cell wall expansion on turgor pressure is expressed in the following equation:

GR= ΔV/Δt=m(ψ_{p}–Y)

(Equation 2)

where *GR* is the cell growth rate, and *m* is the coefficient that relates growth rate to the turgor in excess of the yield threshold. The coefficient *m* is usually called **wall extensibility**. Mathematically, it is defined as the slope of the line relating growth rate to turgor pressure.

Under conditions of steady-state growth, *GR* in Equation 2 is the same as the rate of water uptake in Equation 1. The two equations are plotted in Figure 1. Note that the two processes of wall expansion and water uptake show opposing reactions to a change in turgor. For example, an increase in turgor increases wall extension but reduces water uptake. Under normal conditions, turgor is dynamically balanced in a growing cell exactly at the point where the two lines intersect. At this point both equations are satisfied, and water uptake is exactly matched by enlargement of the wall chamber.

**Figure 1 **Graphic representation of the two equations that relate water uptake and cell expansion to cell turgor pressure and cell water potential. The values for the rates of cell expansion and water uptake are arbitrary. Steady-state growth is attained only at the point where the two equations intersect. Any imbalance between water uptake and wall expansion results in changes in cell turgor and brings the cell back to this stable point of intersection between the two processes.

This intersection point in Figure 1 is the steady-state condition, and any deviations from this point will cause transient imbalances between the processes of water uptake and wall expansion. The result of these imbalances is that turgor will return to the point of intersection, the point of dynamic steady state for the growing cell.

The regulation of cell growth—for example, by hormones or by light—typically is accomplished by regulation of the biochemical processes that regulate wall loosening and stress relaxation. Such changes can be measured as a change in *m* or in *Y*.

The water uptake that is induced by wall stress relaxation enlarges the cell and tends to restore wall stress and turgor pressure to their equilibrium values, as we have shown. However, if growing cells are physically prevented from taking up water, wall stress relaxation progressively reduces cell turgor. This situation may be detected, for example, by turgor measurements with a pressure probe or by water potential measurements with a psychrometer or a pressure chamber (see Web Topic 3.6). Figure 2 shows the results of such an experiment.

**Figure 2 **Reduction of cell turgor pressure (water potential) by stress relaxation. In this experiment, the excised stem segments from growing pea seedlings were incubated in solution with or without auxin, then blotted dry and sealed in a humid chamber. Cell turgor pressure (*P*) was measured at various time points. The segments treated with auxin rapidly reduced their turgor to the yield threshold (*Y*), as a result of rapid wall relaxation. The segments without auxin showed a slower rate of relaxation. The control segments were treated the same as the group treated with auxin, except that they remained in contact with a drop of water, which prevented wall relaxation. (After Cosgrove 1985.)