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. 2008 Jul;147(3):935–938. doi: 10.1104/pp.108.121178

Is the Loss of Stability Theory a Realistic Concept for Stress Relaxation-Mediated Cell Wall Expansion during Plant Growth?

Peter Schopfer 1
PMCID: PMC2442521  PMID: 18612070

Plant cells grow by irreversible expansion of their walls accompanied by a corresponding increase in water volume. There is general agreement that irreversible (plastic) wall expansion in turgid cells is brought about by stress relaxation of the wall kept under tensional stress by turgor pressure (Ray et al., 1972). Based on physical considerations and supported by a large body of experimental evidence, stress relaxation can be attributed to chemorheological changes in the load-bearing polymer network, enabling a plastic deformation of wall dimensions. In other words, growth of turgid cells is initiated and maintained by chemical modifications of the wall (wall loosening) followed by mechanical stress relaxation generating a driving force for osmotic water uptake through the water-permeable plasma membrane (Cosgrove, 1993; Schopfer, 2006).

This traditional concept, designated as chemical wall loosening (CWL) in the following, has been challenged in a recent contribution to this journal (Wei and Lintilhac, 2007). Extending a previous publication (Wei and Lintilhac, 2003), these authors presented an alternative concept for explaining wall stress relaxation during cell growth that is founded on the theory of loss of stability (LOS) adopted from material sciences. The basic idea of this theory is that solid bodies, or closed pressure vessels, placed under gradually increasing stress will respond with abruptly facilitated deformation once a critical level of stress is reached. Wei and Lintilhac (2003) propose “that the walls of a growing plant cell behave similarly; with turgor pressure rising smoothly to a critical point determined by material properties and cell geometry, followed by a loss of stability that manifests itself as wall extension and growth” (p. 306).

Applying the LOS theory to plant cells, Wei and Lintilhac (2003, 2007) fail to appreciate that plant cells behave as hydraulic systems modeled by osmometers, the mechanical properties of which are governed by osmotic water relations rather than by physical mechanics of closed pressure vessels. Growth of a turgid cell, defined as irreversible volume increase by water uptake, can only be brought about by lowering the water potential of the cell content (Ψi) below that of the outer medium (Ψo), creating a driving force ΔΨ = Ψo − Ψi for water influx. Dictated by the fundamental equation Ψ = P − Δπ, ΔΨ can theoretically be produced either by a decrease in turgor pressure (P) or an increase in osmotic pressure (Δπ) of the cell contents. Based on extensive experimental evidence, cell growth can take place in the absence of uptake or intracellular liberation of solutes (Cosgrove, 1993; Schopfer, 2006). Therefore, Δπ can be ignored in the present context, leaving P as the critical parameter governing the water relations of growing cells. P contributes positively to Ψi, and thus an increase in P will elevate Ψi over Ψo, producing an outwardly directed Ψ gradient. If, in a turgid cell (ΔΨ = 0), the turgor could be raised by some mysterious water pump, this would create a driving force for the extrusion of water, i.e. cell shrinkage followed by a readjustment of turgor to the previous level. The only condition for creating a ΔΨ for driving water influx is a decrease in turgor resulting from a decrease in wall stress due to wall loosening. This is just the opposite of the prediction of the LOS theory that stress relaxation leading to growth occurs when the turgor increases to the critical point. The basic problem resulting from applying the LOS theory to plant cells becomes apparent when we consider the causal chain implied by this theory. Wei and Lintilhac (2003) correctly state that, because water is an incompressible fluid, turgor increase can be produced only by water influx into the cell. However, they go on to conclude the following: “As water enters a cell, turgor pressure increases; once turgor pressure reaches its critical value, the wall loses stability, with wall stress relaxation and cell enlargement resulting” (p. 309). This obviously inverts cause and effect with respect to stress relaxation and water uptake leading to growth.

It should be noted that the CWL and LOS concepts differ with respect to the points of control offered for affecting growth by the turgid cell. For accomplishing the transition from the nongrowing to the growing state, CWL can be initiated by the activation of chemical loosening reactions in the cell wall. In contrast, LOS suggests a lowering of the critical wall stress from a nonpermissive level to the level determined by the actual turgor. It can be predicted that in this unstable situation even a small reduction in turgor, for instance, experimentally produced by applying an external osmoticum, will cause growth to cease immediately (Wei and Lintilhac, 2007). However, the experimental evidence obtained with numerous growing tissues demonstrate that, generally, the growth rate is a continuous function of turgor (in excess of a yield threshold), in agreement with the CWL concept (Hohl and Schopfer, 1992).

In an attempt to support LOS, Wei and Lintilhac (2007) cite a textbook (Burgess, 1985) referring to elongating oat coleoptiles as follows: “Burgess observed that if the bathing medium contained mannitol at a concentration just sufficient to lower cell turgor slightly without inducing plasmolysis, growth stopped, whereas when auxin was added to the medium resulting in a change in the elastic properties of the wall, the growth rate increased without any corresponding increase in turgor pressure” (p. 770). Burgess (1985) wrote: “Growth is dependent upon the turgor pressure within cells; if the bathing medium contains mannitol at a concentration just insufficient to cause plasmolysis, growth ceases. Applied auxin causes an increase in growth rate after a lag period of a few minutes. This increase is known to be due to a change in the plasticity of the wall, and not, for example, to an increase in the turgor pressure within the cells. If auxin is added to the mannitol-containing medium which inhibits growth, then the change in the properties of the cell wall still takes place, although no growth results, since it cannot in the absence of turgor pressure” (pp. 75–76). This represents a perfect description of the basic tenets of CWL.

References

  1. Burgess J (1985) An Introduction to Plant Cell Development. Cambridge University Press, Cambridge, UK
  2. Cosgrove DJ (1993) Water uptake by growing cells: an assessment of the controlling roles of wall relaxation, solute uptake, and hydraulic conductance. Int J Plant Sci 154 10–21 [DOI] [PubMed] [Google Scholar]
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  4. Ray PM, Green PB, Cleland R (1972) Role of turgor in plant cell growth. Nature 239 163–164 [Google Scholar]
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Plant Physiol. 2008 Jul;147(3):935–938.

Response to Schopfer Letter

Chunfang Wei 1,*, Philip M Lintilhac 1

Schopfer's comments on our recent articles begin with the assertion that we are challenging the “traditional concept, designated as chemical wall loosening (CWL)”; and, furthermore, that by “Applying the LOS theory to plant cells, Wei and Lintilhac (2003, 2007) fail to appreciate that plant cells behave as hydraulic systems modeled by osmometers, the mechanical properties of which are governed by osmotic water relations rather than by physical mechanics of closed pressure vessels.”

But the loss of stability (LOS) theory does not in any way challenge either the principles of osmotic water relations or the notion of biochemically mediated wall loosening. On the contrary, in our series of articles on the theory of LOS (Wei and Lintilhac, 2003, 2006, 2007), we have repeatedly addressed the importance of these factors in regulating plant cell growth. In the first of the series, for instance, under the subheading “The Regulation of Turgor Pressure,” we state: “For a growing cell, the water potential gradient across the cell membrane, which is largely due to an osmotic potential gradient, provides the driving force for water movement” (Wei and Lintilhac, 2003, p. 309). Clearly, plant cells are both osmometers and pressure vessels and any meaningful model has to be able to accommodate both perspectives. Furthermore, the notion of “chemical wall loosening” (Schopfer's CWL) is fundamental to the cell's ability to precisely manipulate PCR at the local level, thereby enabling the fine-tuning of the underlying biophysical control circuitry at the biochemical level. From the same article, we note “it is likely that PCR values for growing primary cell walls are continuously modifiable by metabolic or biochemical means” (p. 309).

Regarding the water relations of growing cells, we do not agree that water potential difference (ΔΨ = Ψo − Ψi) of a growing cell can be treated as zero. Schopfer correctly states that ΔΨ is the driving force for water influx into growing cells. But he then seems to assert that the ΔΨ of a “turgid” cell must be zero, which requires him to postulate a “mysterious pump” if pressures are to rise even further to drive LOS behavior. This leads to the conclusion that the “mysterious pump,” raising the internal pressure even further, “would create a driving force for the extrusion of water.” Simply put, if the ΔΨ of a turgid cell equals zero, then how can cells continue to uptake water and grow? But biophysically speaking, the walls of a growing turgid cell constitute an elastic system; therefore, Schopfer's idea that any turgor increase in an already turgid cell will lead to immediate water extrusion without further wall extension is without merit.

Schopfer claims, “The only condition for creating a ΔΨ for driving water influx is a decrease in turgor resulting from a decrease in wall stress due to wall loosening.” This implies a stepwise increase in the turgor pressure of any growing cell, with wall loosening preceding turgor loss and subsequent water uptake. Again, his statement results from his incorrect assumption that the ΔΨ of a turgid cell must be zero and from his notion of singular causality, whereby only biochemical wall loosening can lead to stress relaxation and turgor loss. We note, however, that because of structural inhomogeneities, stress relaxation is not an event that will occur at the same instant over the entire wall body (which would indeed lead to a stepwise increase in turgor pressure). Instead, relaxation consists of a multitude of local events that happen frequently at different sites during growth, with each event finding the location where PCR is at its lowest value at that moment (we call this local LOS; Wei and Lintilhac, 2003). Thus, we see LOS events “flickering” over the surface of the cell during growth. New wall synthesis can thus have two different results. If synthesis is homogeneous and rapid, it will thicken the cell wall uniformly, thereby resulting in a higher value for PCR and allowing turgor pressure to increase accordingly. If new synthesis is patchy, it will shift LOS behavior to other parts of the wall that remain at a lower PCR value. Of course, new synthesis can also affect LOS behavior by modifying the modulus of elasticity or geometry of the wall.

It is difficult to evaluate Schopfer's comment citing historical studies that relate growth rate to turgor pressure without being able to examine them in detail. Different experimental approaches and materials highlight different aspects of growth dynamics and make direct comparison difficult. For instance, he asserts “the experimental evidence obtained with numerous growing tissues demonstrate that, generally, the growth rate is a continuous function of turgor …,” and offers Hohl and Schopfer (1992) as an example. But this article refers to a multicellular system, where the growth dynamics of the individual cells are likely masked in the aggregate. We can offer a counter-example, titled “Enlargement in Chara studied with a turgor clamp: Growth rate is not determined by turgor” (Zhu and Boyer, 1992). Clearly, there are many difficulties to be overcome before we will be able to generalize from our unicellular model to a rigorous multicellular model.

Schopfer fails to understand what it is that LOS theory is challenging, which is the thought process that grew out of the traditional viscoelastic/creep-based mechanism for wall stress relaxation. Both LOS and viscoelastic/creep theories were developed to provide a context for modeling the physical (not chemical!) mechanism for wall stress relaxation. The use of pressure vessels as models for growing plant cells is not new (Métraux and Taiz, 1978; Steudle et al, 1982; Sellen, 1983). Any article that has used the two conventional equations σh = PR/t and σL = PR/2t (where P, R, and t represent the internal pressure, cell radius, and wall thickness, respectively) to describe the hoop and longitudinal stresses in a cylindrical cell is actually using a cylindrical pressure vessel model. In reality, this has been a remarkably fruitful model. Our own development of LOS theory invokes both spherical and cylindrical pressure vessels as models for cell growth, enabling us to extend Euler and Panovko's notion of LOS to the stress-strain analysis of plant cell walls. Without biophysical models, biochemical process would be hard pressed to reveal the significance of stress-strain relationships, geometrical inputs, and complex anisotropies, or indeed to offer reasonably predictive details of any sort.

Schopfer's criticism that the perception that plant cell growth involves turgor-induced physical stress relaxation in the walls “obviously inverts cause and effect with respect to stress relaxation and water uptake leading to growth” is also not new and is reminiscent of the now-discredited views expressed by Burström, who noted in his 1971 article that “the rigidity of the walls preventing the entry of water is the cause of the turgor pressure, which arises as a consequence of the resistance of the wall to an expansion. How then can the turgor pressure cause expansion?” Burström thus concluded: “The literature on plant cell growth would certainly improve if the notion of turgor expanding the cell was abandoned and replaced by accepted equations for water balance or fluxes” (Burström, 1971, p. 488). In response, Ray et al. (1972) observed: “Burström failed to come to grips with the principle that irreversible increase in plant cell volume involves simultaneous water uptake (driven by a water potential difference) and cell wall yielding that depends on turgor stress …” (p. 163).

The problem of plant cell volume growth lying as it does at the intersection of pure biophysics, cellular biochemistry, and the new realities of nanostructural composite materials is inherently difficult to circumscribe within a single theoretical framework. The goal is to articulate a biophysical framework that rests on accepted mechanical principles but that is robust enough to admit other perspectives. We believe that the LOS theory has the ability to do this, although its application to many of the details of growth may be beyond our grasp at present.

References

  1. Burström (1971) Wishful thinking of turgor. Nature 234 488 [Google Scholar]
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  3. Métraux JP, Taiz L (1978) Transverse viscoelastic extension in Nitella. Plant Physiol 61 135–138 [DOI] [PMC free article] [PubMed] [Google Scholar]
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  8. Wei C, Lintilhac PM (2006) Loss of stability, pH, and the anisotropic extensibility of Chara cell walls. Planta 223 1058–1067 [DOI] [PubMed] [Google Scholar]
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  10. Zhu GL, Boyer JS (1992) Enlargement in Chara studied with a turgor clamp: Growth rate is not determined by turgor. Plant Physiol 100 2071–2080 [DOI] [PMC free article] [PubMed] [Google Scholar]

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