No abstract

( 1) where V is the volume of the cell wall chamber, 9 is the extensibility of the cell wall, and P is the turgor pressure. It is noted that this equation is analogous to the constitutive relationship (between the strain rate and the stress) for a Newtonian fluid: e = a/i (2) where e is the strain rate (for elongation only, e = dl/(ldt)), a is the stress, and u is the dynamic viscosity. Now assuming that a is directly proportional to P, and substituting, P for a, 9 for l/,u, and, v for e, Eq 1 is obtained from Eq 2. Another constitutive relationship is obtained in the case where the stress must exceed some minimum value, ao, (yield stress) before irreversible strain occurs: e = (a -ao)/4 (3) Now making the previously mentioned assumptions and substitutions, we can obtain the following: v = 0(P -PO) (4) where P, is the critical turgor pressure, and corresponds to the yield stress, ao. This is the equation for irreversible cell wall extension which was first derived for elongation only by Lockhart (5) and subsequently derived for volumetric expansion by Ray et aL (7).At this point, it is important to remember that the force, and thus the stress and turgor pressure, was assumed to be constant (dF/dt = da/dt = dP/dt = 0). Furthermore, it is important to recognize that because of this assumption the elastic component ofthe total cell wall extension or expansion was eliminated from the constitutive equations (Eq 1-4

The pressure probe was used to conduct in vivo creep and in vivo stress relaxation experiments on the sporangiophores of Phycomyces blakesleeanus. The in vivo creep and in vivo stress relaxation methods are compared with respect to their utility for determining the irreversible wall extensibility and the yield threshold. The results of the in vivo stress relaxation experiments demonstrate that the growth usually does not cease when the external water supply is removed, and the turgor pressure does not decay for hours afterwards. A successful stress relaxation experiment requires that the cell enlargement rate (growth rate) be zero during the turgor pressure decay. In a few experiments, the growth rate was zero during the turgor pressure decay. However, in general only the yield threshold could be determined.In vivo creep experiments proved to be easier to conduct and more useful in determining values for both the irreversible wall extensibility and the yield threshold. The results of the in vivo creep experiments demonstrate that small steps-up in turgor pressure, generally <0.02 MPa, elicit increases in growth rate as predicted by the growth equations and the augmented growth equations. The irreversible wall extensibility and the yield threshold were determined from these results. The results also demonstrate that steps-up in turgor pressure larger than 0.02 MPa, produce a different response; a decrease in growth rate. The decreased growth rate behavior is related to the magnitude of the step-up, and in general, larger steps-up in turgor pressure produce larger decreases in growth rate and longer periods of decreased growth rate. Qualitatively, this growth behavior is very similar to the "stretch response" previously reported by Dennison and Roth (1967).

Plants change size by deforming reversibly (elastically) whenever turgor pressure changes, and by growing. The elastic deformation is independent of growth because it occurs in nongrowing cells. Its occurrence with growth has prevented growth from being observed alone. We investigated whether the two processes could be separated in internode cells of Chara corallina Klien ex Willd., em R.D.W. by injecting or removing cell solution with a pressure probe to change turgor while the cell length was continuously measured. Cell size changed immediately when turgor changed, and growth rates appeared to be altered. Low temperature eliminated growth but did not alter the elastic effects. This allowed elastic deformation measured at low temperature to be subtracted from elongation at warm temperature in the same cell. After the subtraction, growth alone could be observed for the first time. Alterations in turgor caused growth to change rapidly to a new, steady rate with no evidence of rapid adjustments in wall properties. This turgor response, together with the marked sensitivity of growth to temperature, suggested that the growth rate was not controlled by inert polymer extension but rather by biochemical reactions that include a turgor-sensitive step.This study was undertaken to determine whether growth can be distinguished from elastic deformation when plants enlarge. Both processes are present in plants, but they occur together and are superimposed on each other when a plant becomes larger. Nevertheless, they are fundamentally different because growth results from irreversible enlargement, whereas elastic enlargement is not permanent and reverses when the deforming force is removed. At the cell level growth extends the wall permanently, whereas elastic wall deformation is reversible. Both involve water uptake because growth is associated mostly with increased cell water content, whereas elastic deformation is caused mostly by changes in P that result from changes in water content. These similar origins make the two phenomena hard to separate but, without separation, it is not possible to accurately study the growth process.Some efforts to separate growth from elastic deformation involved plasmolyzing or freezing and thawing excised tissues to remove elastic effects of P (Ursprung and Blum,

The yielding properties of the cell wall, irreversible wall extensibility (m) and yield threshold (Y), are determined for stage I sporangiophores of Phycomyces blakesleeanus from in-vivo creep experiments, and compared to the values of m and Y previously determined for stage IVb sporangiophores using the same pressureprobe method (Ortega et al., 1989, Biophys. J. 56, 465). In either stage the sporangiophore enlarges (grows) predominately in length, in a specific region termed the "growing zone", but the growth rates of stage I (5-20 urn · min(-1)) are smaller than those of stage IVb (30-70 μm · min(-1)). The results demonstrate that this difference in growth rate is the consequence of a smaller magnitude of m for stage I sporangiophores; the obtained values of P (turgor pressure), Y, and P-Y (effective turgor for irreversible wall extension) for stage I sporangiophores are slightly larger than those of stage IVb sporangiophores. Also, it is shown that the magnitude of m for the stage I sporangiophore is regulated by altering the length of the growing zone, Lg. A relationship between m and Lg is obtained which can account for the difference between values of m determined for stage I and stage IVb sporangiophores. Finally, it is shown that similar changes in the magnitude of m and ϕ (which have been used interchangeably in the literature as a measure of irreversible wall extensibility) may not always represent the same changes in the cell-wall properties.