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Physiology and Biochemistry |
Institut für Biologie II der Universität, Schänzlestrasse 1, D-79114 Freiburg, Germany
Received for publication March 2, 2006. Accepted for publication July 24, 2006.
ABSTRACT
Growth of turgid cells, defined as an irreversible increase in cell volume and surface area, can be regarded as a physical process governed by the mechanical properties of the cell wall and the osmotic properties of the protoplast. Irreversible cell expansion is produced by creating a driving force for water uptake by decreasing the turgor through stress relaxation in the cell wall. This mechano-hydraulic process thus depends on and can be controlled by the mechanical properties of the wall, which in turn are subject to modification by wall loosening and wall stiffening reactions. The biochemical mechanisms of these changes in mechanical wall properties and their regulation by internal signals (e.g., hormones) or external signals (e.g., light, drought stress) are at present incompletely understood and subject to intensive research. These signals act on walls that have the properties of composite materials in which the molecular structure and spatial organization of polymers rather than the distribution of mechanical stresses dictate the allometry of cell and organ growth and thus cell and organ shape. The significance of cell wall architecture for allometric growth can be demonstrated by disturbing the oriented deposition of wall polymers with microtubule-interfering drugs such as colchicine. Elongating organs (e.g., cylindrical stems or coleoptiles) composed of different tissues with different mechanical properties exhibit longitudinal tissue tensions resulting in the transfer of wall stress from inner to peripheral cell layers that adopt control over organ growth. For physically analyzing the growth process leading to seed germination, the same mechanical and hydraulic parameters as in normal growth are principally appropriate. However, for covering the influences of the tissues that restrain embryo expansion (seed coat, endosperm), an additional force and a water permeability term must be considered.
Key Words: cell wall extensibility • cell wall stress relaxation • cellulose microfibril orientation • growth allometry • seed germination • tissue tension • wall loosening • wall stiffening
The development of the multicellular plant is governed by three fundamental processes: growth, differentiation, and morphogenesis. These descriptive terms logically differentiate between becoming bigger, producing structurally and functionally different cells, and creating a specific body form with functionally specialized organs. Evidently, growth can take place without differentiation and morphogenesis, whereas differentiation can normally occur only in the presence of growth, that is also a necessary prerequisite for most other facets of plant development.
The complex entanglement between growth and other developmental changes necessitates a reductionist approach for investigating the mechanical and biochemical mechanisms of growth per se. In experimental terms, this means selecting cells or organs composed of cells that enlarge without changing their differentiation state. Moreover, it is most helpful if these research materials demonstrate growth by diffuse expansion in one dimension (i.e., elongation growth evenly distributed over the extending surface) and respond to externally applied growth factors such as hormones or environmental cues, allowing the experimental manipulation of the growth process. These conditions are best met by excised parts of seedling stems or other cylindrical organs such as grass coleoptiles, which have been used extensively to study the forces and resistances governing cell and organ growth. This review concentrates on the insights into the mechanics—including the hydraulics—of growth, which have been obtained by investigating such simplified experimental systems with biophysical methods during the last 40 years. The great number of relevant papers published during this period necessitates a selective, exemplary treatment of the literature rather than a comprehensive one. The state of this field before that time has been summarized by Lockhart (1965b)
in a seminal book chapter still worth reading.
PRINCIPLES OF CELL EXTENSION
In physical terms, cell growth can be defined as an irreversible increase in cell volume and surface area. It is important to note that animal and plant cells differ fundamentally with respect to their mode of cell enlargement: The typically naked cells in the animal body enlarge basically by an increase in plasma content in an isotonic environment. In contrast, the protoplasts of plant cells are encased in a rigid, elastically expandable cell wall infiltrated with water containing only moderate, osmotically negligible amounts of solutes. This enables the establishment of a large difference in osmotic pressure (
) between protoplastic and apoplastic space (on the order of 0.6–1.0 MPa) which, in the fully turgid state, is compensated by a hydrostatic pressure (turgor, P) of equal magnitude. Thus, plant cells can be conceived as hydraulic systems similar to osmometers that can enlarge by water uptake powered by a difference in water potential (
) between protoplastic and apoplastic space. According to the equation = P – this can be achieved by two means:
produced by an increase of in the protoplast. This hydraulic process can maximally reach the intracellular water volume of the fully turgid state (P = , = 0). Cell enlargement of this type is reversible. It is well known from osmotically regulated motor cells such as guard cells, which perform reversible movements upon uptake of solutes from the apoplastic space. For producing growth, i.e., irreversible increase in cell volume, this mechanism is principally inappropriate. produced by a decrease in P. The only way to achieve this is by lowering the counter pressure exerted by the cell wall on the protoplast, and this in turn can only be achieved if (1) the wall is in a state of tensile stress (= force per cross-sectional area) produced by turgor and (2) this stress is released by some kind of change in the mechanical properties of the wall material: stress relaxation by wall loosening. In this way, continued wall loosening liberates a driving force for water uptake, and water uptake will simultaneously restore the turgor to its (almost) previous level. This mechano-hydraulic process produces irreversible cell enlargement, i.e., growth. Theoretically, this growth slows when P = decreases due to the dilution of the intracellular solute concentration by water uptake. However, growing cells generally maintain a constant by osmoregulatory solute uptake parallel to water uptake and are then capable of steady-state growth for many hours or even days. Similarly, thinning of the cell wall during extension is prevented by apposition of newly synthesized wall layers, although this process generally lags behind cell wall extension.
Several important conclusions can be drawn from this concept that was first stated comprehensively by Ray et al. (1972)
: (1) Growth of plant cells is brought about by water uptake (mainly into the vacuole occupying more than 90% of the volume of typical growing cells). (2) The driving force of this water uptake is provided by wall stress relaxation produced by wall loosening in turgid cells. (3) Turgor serves as a necessary condition rather than as a direct driving force for growth. Turgor causes tension, but not extension of the wall. (4) Water uptake during growth leads to a dilution of the cell sap and thus = P decreases in proportion. However, except during extended growth periods, these secondary changes can be ignored in most experimental conditions. In the presence of absorbable solutes, this effect can be offset by osmoregulation allowing steady-state growth at constant turgor. (5) Raising of is normally unsuitable for producing growth. However, under conditions of water deficit (drought stress) an active increase in intracellular (osmotic adaptation) can help to maintain turgor at low external . (6) Even in the presence of wall loosening, the wall of growing cells maintains its mechanical properties as a rigid elastic corset preventing bursting of the cell at high turgor. This concept has been supported during the last years by a large body of experimental evidence (Boyer, 1985
; Cosgrove, 1986
, 1993b
; Tomos et al., 1989
) and is now generally accepted.
MATHEMATICAL FORMULATION OF CELL GROWTH
A theoretically derived set of equations describing growth as a mechano-hydraulic process was developed by Lockhart (1965a)
and further elaborated by Ray et al. (1972)
. First, volume increase during growth (dV/dtV) can be described as a water transport process, driven by the water potential difference between protoplast and apoplast and limited by a water conductance coefficient L:
|
| (1) |
|
| (2) |
Y) is the turgor above a yield threshold Y that must be exceeded for enabling plastic rather than merely elastic wall extension, and 
is an extensibility coefficient representing the time-dependent yielding properties of the cell wall in the direction of growth. It should be mentioned at this point that in this equation P and Y are quantitatively equivalent, easier-to-measure substitutes for corresponding overall wall stresses that actually determine the driving forces for wall extension upon stress relaxation. The wall stress in the direction of growth can deviate in magnitude from turgor (a multidirectional force) depending on cell form (see next section).
Representing the two sides of the same coin, Eqs. 1 and 2 can be combined, yielding the general formula of mechano-hydraulic cell growth (Lockhart equation):
|
| (3) |
+ P – Y) can be substituted by ( – Y). Assuming that (1) the cell behaves as an ideal osmometer and (2) the cell wall behaves as a plastically deformable material, this equation implies that growth can be quantitatively described by four (or five) physically measurable quantities included in a complex growth potential and a complex growth coefficient. Equation 3 can be simplified for two limiting cases: First, if L << , Eq. 3 reduces to Eq. 2, and growth can be treated purely in terms of water transport. Second, if L >> , growth is limited by cell wall extensibility, and Eq. 3 reduces to Eq. 1. This last approximation has proven to be generally applicable to cells or small tissue samples incubated in water (Cosgrove and Cleland, 1983
) and has greatly simplified the analysis of growth responses of tissues such as sections from coleoptiles or seedling stems. However, in the intact plant, the conductivity of the water transport pathway may have profound effects on growth, and Eq. 3 must be employed for avoiding misleading results.
Growth is accompanied by a consumption of water by the expanding cells and can therefore generate water potential gradients between growing and nongrowing regions of a plant, depending on the hydraulic conductance of the water pathway (Boyer, 1988
, 2001
). In an organ such as the stem of pea seedlings, these gradients were found to be small or nonexistent, indicating that the conductance for water is no seriously limiting factor of growth in these materials (Malone and Tomos, 1992
).
The Lockhart equation has been very useful for determining the physical growth potentials and cell wall extensibility coefficients in a variety of growing tissues. An important result from such measurements is the observation that the turgor remains unchanged, or even decreases, if growth is induced by auxin while cell wall extensibility dramatically changes under these conditions (Green and Cummins, 1974
; Cleland, 1977
; Kutschera and Schopfer, 1986a
; Kutschera, 1991
; Hohl and Schopfer, 1992b
). Corresponding observations have been made when growth was inhibited by abscisic acid. In studies on growth of shoot organs under drought stress conditions, growth rates greatly declined at low water supply even when the turgor was maintained by osmotic adjustment (Matthews et al., 1984
; Westgate and Boyer, 1985
). In wheat roots abscisic acid inhibits growth although it causes an increase of turgor (Jones et al., 1987
). These findings confirm the notion that changes in cell wall extensibility, produced by active cell wall loosening or stiffening, are the basic mediators controlling cell growth.
Although the Lockhart equation has great merits for describing and measuring growth in physical terms, it ignores the vectorial aspects of growth and provides no hints with respect to the molecular changes in the wall properties represented by the parameters and Y. A thermodynamic model of cell wall stretching, which attempts to describe the secretion and interactions of wall polymers and their contribution to Y, was developed by Veytsman and Cosgrove (1998)
. Although the conclusions derived from this model agree with the relevant experimental data, it has not yet led to concrete predictions as to the biochemical mechanism of wall loosening.
MECHANICAL PROPERTIES OF GROWING CELL WALLS
In physical terms, the primary walls in growing tissues are assumed to represent a nonlinear viscoelastic material (Niklas, 1992
) potentially capable of plastic expansion. The mechanical properties of this material can be analyzed by rheological techniques. Two types of mechanical devices have been extensively applied to isolated cell walls: (1) extensiometers measuring the extension kinetics after application of a constant stretching force and (2) Instron-type stress–strain analyzers measuring the kinetics of stress changes during a period of extension with constant rate or after an instantaneous extension to a constant strain (stress relaxation) (Cleland, 1967
; Lockhart et al., 1967; Masuda, 1978
). Qualitatively, all three procedures lead to similar results (Cleland, 1981
). Primary walls behave like viscoelastic composite materials demonstrating a time-dependent extension ("creep") under load and a time-dependent stress relaxation after stretching. Both effects fade with time in an approximately exponential manner due to structural rearrangements in the cell wall or stress hardening. Moreover, also typical for viscoelastic materials, cell walls exhibit a pronounced hysteresis during loading and unloading (Lockhart, 1967
), which has previously often been mixed up with irreversible (plastic) extension (Hohl and Schopfer, 1992c
; Nolte and Schopfer, 1997
). Taking this pitfall into account, there is no unequivocal evidence from rheological measurements that native, untreated cell walls isolated from growing tissues exhibit true plastic extension under load. The increase in apparent plastic extensibility by auxin reported by previous investigators (e.g., Cleland, 1967
; Masuda et al., 1974
; Kutschera and Schopfer, 1986a
) can be traced back to an alteration in the shape of the closed hysteresis loop measured by loading followed by unloading, i.e., to a change in reversible viscoelastic rather than plastic material properties (Hohl and Schopfer, 1992c
).
The deficiency of plastic extensibility in isolated cell walls is understandable if one realizes that the rheological properties of such walls can no longer be expected to exhibit the mechanical changes produced by the chemical wall loosening process before killing the cells. This in vivo process is under direct control by intracellular metabolism, indicated by the fact that growth stops within a few minutes upon inhibition of respiration (Ray, 1961
). Pointed out by Masuda (1978)
, the unwarranted equalization of rheological material properties with in vivo properties represented by the extensibility coefficient in Eq. 1 has caused considerable confusion in the older literature.
Information about the in vivo extensibility properties of cell walls during growth can be obtained by load-enforced extension measurements with living tissue segments (Lockhart et al., 1967
; Kutschera and Schopfer, 1986b
) or stress relaxation measurements by the micropressure probe or psychrometer techniques (Cosgrove et al., 1984
). These methods determine the rate of stress relaxation from the kinetics of the fall in P or in tissue samples after disconnecting them from a water source. In this case, water uptake is prevented, i.e., the cells no longer enlarge, and continued wall loosening causes a time-dependent decrease in wall stress that can be measured either as –dP/dt or –d/dt. After correcting for elastic changes, these kinetics allow the calculation of . This is certainly the most reliable in vivo method for the quantitative determination of cell wall extensibility during growth. Using this technique, Cosgrove (1985)
has shown that auxin increases in pea epicotyl segments from 0.08 to 0.24 MPa–1·h–1. As stress relaxation proceeds, the turgor decays from 0.60 MPa to the threshold Y of 0.29 MPa that is not affected by auxin.
Additional physical techniques for measuring stress relaxation in intact plants have been developed by Cosgrove (1987)
, but not extensively used so far for analyzing mechanical cell wall changes during growth. A comprehensive, critical survey of the methods available for measuring the mechanical properties of growing cell walls in vivo and in vitro can be found in Cosgrove (1993a)
.
In a first approximation, the cell wall can be regarded as a composite material composed of cellulose microfibrils embedded in an amorphous matrix of hemicelluloses and pectins (Fry, 2004
). Creep, time-dependent stress relaxation, and hysteresis of load-extension curves are characteristic and diagnostic features of the viscoelastic nature of this material. There have been attempts to simulate some of these properties by technical analogous models such as the Voigt or Maxwell models composed of a spring (elastic component) and a dash pot (viscous component) arranged in parallel or in series, respectively (Lockhart, 1965b
; Ferry, 1980
). These models provide simple illustrations of viscoelasticity and formal parameters for measuring stress relaxation with the stress–strain analyzer (Masuda, 1978
). However, models of this type are too crude for helping to understand the mechanical properties of cell walls in more detail. For instance, these models do not account for the fact that the walls of growing cells are composed of layers of different age, greatly differing in the extent of deformation experienced during extension. A corollary of this situation is that the mechanical properties of these walls gradually change from inside to outside and that this gradient depends on the previous history of the cell.
CELL WALL ARCHITECTURE AND THE DIRECTIONALITY OF GROWTH
Turgor pressure exerts a homogeneous, multidirectional force on the elastically stretched cell wall. However, the tensile forces generated in the wall by the turgor and the ability to yield by liberation of these forces can be quite different in different regions of the cell, depending on form and local structure of the wall. Wall form and wall structure are interdependent properties. If surrounded by a structurally homogeneous (isotropic) wall, a cell would expand in the form of a sphere, i.e., at the lowest level of energy. In the wall of a cylindrical cell, the tangential (circumferential) stress produced by turgor in the side walls is given by 
= Pr/d, where r is the radius of the cylinder and d is the thickness of the (uniform) wall. In contrast, the longitudinal stress is given by = Pr/2d, that is numerically half as large as the tangential stress (Castle, 1937
). These geometric constraints predict that the wall must exhibit anisotropic properties in order to maintain the cell shape of a cylinder during growth. Anisotropic mechanical properties are consequences of anisotropic molecular wall structure, determined by the spatial arrangement of the cellulose microfibrils that are generally organized in layers of parallel fibers. Microfibrils convey a relatively high strain resistance (tensile strength) to the wall in the direction in which they are laid down by cellulose-synthase complexes drifting in the plasma membrane. The direction of the drift is thought to be directed by cortical microtubules attached to the inner side of the membrane (microtubule–microfibril paradigm; Giddings and Staehelin, 1991
). In primary walls of elongating cells, the microfibrils are typically oriented perpendicularly to the longitudinal axis, reinforcing the wall in girth similar to the hoops of a barrel. This particular orientation of the microfibrils determines the direction of growth. The wall of a long, cylindrical cell with net orientation of microfibrils in the side walls perpendicular to the long axis will expand preferentially in length even though the wall stress in girth is twice as high as in length and therefore per se favors growth in girth. It follows from these considerations that cell growth is oriented by the specific architecture of the cell wall. This statement can be supported by a multitude of observations. For example, the outer epidermal wall of elongating plant organs shows hoop reinforcement during early growth, followed by a transition to net longitudinal microfibril orientation toward the end of the growth period (Paolillo, 2000
). Extrapolated to the level of the whole plant, the biomechanical concept outlined above implies that the specific form of an organ is modeled during growth by local regulatory changes in the orientation of microfibrils newly deposited at the inner wall surface.
These ideas have been introduced and supported by many ingenious experiments by Paul Green and collaborators (Green, 1980
; Green and Poethig, 1982
). Moreover, Green devised a way for understanding the mechanism of microfibril alignment in growing cells. By applying external mechanical stresses to internodal cells of the macroalga Nitella and recording the induced changes in microfibril orientation, Green (1963
, 1964
) was inspired to postulate the existence of "long ectoplasmic elements akin to spindle fibres" (Green, 1964
, p.124)—later known as microtubules—that direct the orientation of newly deposited microfibrils from the inner side of the plasma membrane. If these structures are destroyed by microtubule-depolymerizing drugs such as colchicine, the subsequently deposited microfibrils assume a random orientation. After some time of extension and thinning of the old wall layers, the cell switches from growth in length to growth in width, finally approaching the shape of a sphere. This concept has proven to be also applicable to multicellular organs of higher plants (Bergfeld et al., 1988
). Figure 1 shows that the coleoptile, mesocotyl, and roots of a maize seedling grown in the presence of colchicine drastically change their direction of growth, approaching a more or less perfect spherical form. Experiments of this type provide strong evidence for a causal relationship between microtubule orientation, microfibril orientation, and directionality of cell and organ growth (Baskin, 2005
). Although the precise mechanism of microtubule orientation has so far resisted elucidation (Baskin, 2001
), there is ample evidence that the microtubules associated with the inner surface of the plasma membrane are highly dynamic structures that can change their orientation in response to internal and external stimuli, for instance, in response to oriented mechanical stresses (Fischer and Schopfer, 1998
).
|
For the sake of simplicity, cell growth has so far been regarded mainly as a one-dimensional process, i.e., cell elongation. This is of course a simplification that in pure form is rarely realized in nature. Cells growing in the absence of differentiation normally expand simultaneously in three dimensions whereby the rates of expansion in different directions may differ but are related by constant proportions such that cell shape changes smoothly according to simple mathematical rules. For example, a cylindrical cell expanding in length by 1%/h and in diameter by 0.5%/h will become relatively thin with time in a quantitatively predictable manner. This phenomenon, termed "allometric growth," can be observed in cells such as the internodal cell of Nitella (Green, 1964
) or in multicellular organs such as fern prothallia (May, 1964
) or squash fruits (Sinnott, 1960
). It provides perhaps the simplest demonstration of how growth can change cell shape and affect morphogenesis. Another example for allometric growth is shown in Figs. 2 and 3 illustrating the dramatic changes in growth proportions elicited by disturbing the microfibril-orienting function of microtubules with colchicine (see Fig. 1). Figure 2 demonstrates that it takes c. 24 h until the altered allometric ratio is fully established. This agrees with the prediction that a mechanically significant part of the existing (ordered) wall must be replaced by newly deposited (non-ordered) wall before this change is manifested.
|
|
|
| (4) |
The developmental mechanisms controlling and executing these rules as well as their genetic background are still completely unknown.
BIOCHEMICAL MECHANISMS OF WALL LOOSENING
This controversially debated topic can only be touched upon in the present context. It is clear from the preceding that in a cylindrical cell with transverse microfibrils the longitudinal stress is borne mainly by the network of matrix polymers rather than by the microfibril hoops. Moreover, for irreversible deformation of the cell wall to occur, metabolism is directly required and some kind of chemical cross-links between load-bearing wall elements must be broken. Candidate mechanisms for this task have been investigated mostly for auxin-mediated growth responses. Treating water-incubated stem or coleoptile segments with auxin results in elongation growth elicited by an increase in wall extensibility and simultaneous wall relaxation (Cosgrove, 1985
). In addition, "memorizing" the growing state, the wall exhibits an increase in viscoelasticity, which can be measured by rheological techniques with the isolated wall material but, as discussed before, provides little information about the mechanism of plastic deformation during growth. An operational criterion for identifying a mediator of plastic cell wall extension in vivo is that it must become active when auxin-induced growth starts (approximately 15 min after hormone application) and inactive when growth ceases (approximately 30 min after hormone removal) (Bergfeld et al., 1988
). The extensive search for polysaccharide-hydrolyzing or -transglycosylating enzymes in the wall that (1) loosen walls in vitro and (2) obey these temporal conditions in vivo has altogether failed. A hypothesis potentially consistent with these criteria proposes that proteins called "expansins" are involved in wall loosening (Cosgrove, 2000
). This name has been given to a group of wall proteins that have been discovered owing to their ability to induce expansion of stretched cell walls—or filter paper—by catalyzing the disruption of hydrogen bonds between cellulose molecules, or cellulose microfibrils and associated hemicellulose molecules, in an acidified wall (McQueen-Mason, 1995
; Cosgrove, 2000
). Because auxin reversibly induces proton secretion into the apoplast and acid buffers can reversibly induce cell extension, the basic players of auxin-mediated cell wall loosening seem to be assembled. However, the so-called "acid growth hypothesis" (Cleland, 1977
, 1981
) fails to explain several critical experiments at the quantitative level (Schopfer, 1993
; Kutschera, 1994
). Moreover, the action displayed by expansins in vitro is difficult to reconcile with the geometric constraints given by the cell wall architecture. In the wall of a cylindrical cell, the transverse stress is a priori twice as high as the longitudinal stress, theoretically favoring growth in width over growth in length (Castle, 1937
). It is the strong reinforcement by transverse microfibrils that counteracts this tendency and allows preferential cell expansion in length during elongation growth. However, as illustrated in Fig. 4, disruption of hydrogen bonds within microfibrils, or between microfibrils and matrix polymers, would facilitate the slippage of microfibrils along each other and therefore expansion in width, supported by the twofold stronger stress in that direction. This is just the opposite of what can be observed during elongation growth. Turning this argument around, we can conclude that any wall-loosening mechanism producing elongation in hoop-reinforced cells must leave the microfibrils and their anchorage untouched but can become effective by selectively attacking load-bearing bonds of matrix polymers between microfibrils. However, according to present knowledge, this is not the way expansins affect the bonding between cell wall polymers (McQueen-Mason, 1995
; Cosgrove, 2000
).
|
). Because of their short life of a few nanoseconds, hydroxyl radicals perform this reaction only close to the site of their generation. It has recently been shown that (1) hydroxyl radicals, experimentally produced in the cell wall, degrade polysaccharides and cause the wall to extend under stress in vitro and in vivo; (2) cell wall peroxidase can generate hydroxyl radicals if supplied with the precursors superoxide and hydrogen peroxide, which are products of NAD(P)H oxidase activity localized in the plasma membrane; (3) cell growth can be inhibited by hydroxyl radical scavengers and peroxidase inhibitors; and (4) hydroxyl radical production can be promoted by auxin (Chen and Schopfer, 1999
; Frahry and Schopfer, 2001
; Schopfer, 2001
; Schopfer et al., 2002
; Schweikert et al., 2002
). An Arabidopsis mutant with impaired root and root hair growth has recently been shown to be also deficient in hydroxyl and superoxide radical production due to the mutation of a plasma membrane NAD(P)H oxidase gene (Foreman et al., 2003
; Renew et al., 2005
). Although these results satisfy the "hydroxyl radical hypothesis" of growth in qualitative terms, further work is needed to test it at the quantitative level. GROWTH CONTROL BY WALL STIFFENING AND CONTRACTION
In the long run, wall loosening must be accompanied by wall reinforcement in order to maintain the strength of the expanding wall for sustaining the forces generated by turgor pressure. This requirement is generally satisfied by the synthesis of cellulose and other polysaccharides and their apposition to the inner surface of the wall. However, the incorporation of new materials in the growing wall can also downregulate growth by increasing wall stiffness. An example studied in some depth is the inhibition of mesocotyl elongation in maize seedlings by light (Schopfer et al., 2001a
). In the dark-grown seedling, this internodal organ rapidly elongates at c. 2 mm·h–1 in a small growth zone below the cotyledonary node. After transfer to the light, elongation stops within less than 1 h. This effect can be reversed slowly, but only if the seedlings are returned to darkness within a few hours. After 12 h in the light, the cessation of growth is no longer reversible. These growth changes are accompanied by striking changes in the mechanical cell wall properties in the growth zone. Light induces a rapid increase in cell wall stiffness, measured as an increase of the elastic modulus, as well as an increase in lignin content in the walls of the growth zone. Both effects are reversed when growth resumes in darkness after short light treatments. It can be concluded from this example that active, metabolically controlled cell wall stiffening can be used for effecting a controlled cessation of growth responses, whereby oxidative cross-linking of phenolic materials serves as a biochemical mechanism (Schopfer, 1996
). Placed into wider context, these results support the general concept that cell extension depends on a balance of antagonizing wall-loosening and wall-stiffening processes that can be independently regulated by different growth factors such as hormones and light. This does not exclude other causes for changes in cell wall extensibility, for example, a simple cessation of the wall-loosening process as a rapid response to growth-inhibiting light treatments (Cosgrove, 1988
). The capacity for cell wall stiffening during wall-loosening-mediated growth has been demonstrated in coleoptiles in which stress relaxation was interrupted by applying external osmotic pressure (Hohl and Schopfer, 1992b
; Hohl et al., 1995
).
Attenuating growth by wall stiffening seems to be widespread in plants, especially when they are subjected to environmental stresses. For example, treatment with the stress hormone abscisic acid elicits a decrease in cell wall viscoelasticity of shoot organs leading to a reduction in growth rate at unchanged turgor (Kutschera and Schopfer, 1986a
). Drought stress inhibits growth of shoot organs even at high turgor (osmotic adaptation) by lowering cell wall extensibility (Chazen and Neumann, 1994
). Roots respond under these conditions by increased wall extensibility, allowing the maintenance of growth even at low water potential in the soil (Westgate and Boyer, 1985
; Itoh et al., 1987
). The adaptive value of these opposite regulatory changes in mechanical cell wall properties is obvious.
A rather exotic growth response, called "negative growth," can be added at this point. Gardeners are familiar with the phenomenon that the bulbs or corms of tulip, hyacinth, daylily, etc. are drawn to deeper positions in the soil by contracting roots that develop pulling forces up to 1.5 N and rates up to 1 cm·mo–1 (Pütz, 1991
). The mechanics of this active organ-shortening process have not yet been elucidated in detail. Because the outer cell layers of such roots form folds like a concertina, the motor tissue seems to be located in the inner regions of the organ. Histological investigations have revealed that cells in the cortex expand radially and shorten before they collapse (Pütz and Froebe, 1995
).
A related case of "negative growth" has been observed during drought acclimation in wilting leaves. For example, isolated, moderately wilted cabbage leaves incubated in a moist atmosphere became turgid again despite slowly decreasing further in water content (Levitt, 1986
). This remarkable case of turgor recovery in the absence of water uptake is accompanied by a decrease in leaf volume and an increased resistance to water uptake during subsequent rehydration. The only plausible explanation for these findings is that at least some cell walls in the leaf are capable of active contraction.
These few examples indicate that plant growth involves phenomena that have not yet been adequately explained at the mechanical level.
THE ROLE OF TISSUE TENSIONS IN ORGAN GROWTH
In contrast to the mechanical situation of a cell exposed to the surrounding medium such as the Nitella internodal cell, a cell embedded in a tissue is affected by the mechanical properties of neighboring cells. In a morphologically uniform tissue in equilibrium, however, forces between cells cancel out leaving alone the forces at the surface. In the essential absence of mechanical and hydraulic gradients, the principles valid for single cells can be applied also to such tissues with good approximation. This situation no longer holds in organs composed of different tissues with different physical properties. This applies for example to seedling stem segments, minimally composed of a central stele of vascular, partly lignified tissues surrounded by a parenchymatous cortex covered at the surface by an epidermal cell layer. A striking consequence of tissue heterogeneity in such organs is the occurrence of tissue tensions (Kutschera, 1989
, 1992
). This phenomenon has been noticed and mechanically interpreted already by Sachs (1865
, referring also to earlier work of Hofmeister) and subjected to quantitative modelling by Hejnowicz and Sievers (1995a
, b
, 1996
). It represents an effective stability-generating principle known as "pre-stressing" in material sciences. For example, this principle contributes as much as 50% to overall flexural stiffness of the tulip flower stem (Niklas and Paolillo, 1997
).
Longitudinal tissue tension can be strikingly demonstrated with axial seedling organs. If a stem or coleoptile segment is split lengthwise and placed in water, the split-halves spontaneously bend outward due to the relaxation of longitudinal tension between the outer and the inner tissues. The inner tissues take up water and expand elastically while the outer tissues lose elastic tension and shrink. Similar conclusions can be drawn from peeling experiments: stem or coleoptile segments from which the epidermal cell layer has been carefully removed expand spontaneously in water while the peeled epidermis contracts (Kutschera et al., 1987
). These changes indicate that in the intact, turgid organ the walls of the inner tissues are kept in a state of submaximal tension, limited by the higher tension in the outer tissue that compensates part of the turgor prevailing in the inner tissues. In other words, the inner tissues are kept in a state of compression and the outer tissues in a state of quantitatively equivalent tension compared to the states these tissues would assume if isolated in contact with water. In extreme cases such as the tube-shaped coleoptile of maize seedlings, the mechanical role of the outer tissue is taken over almost exclusively by the thick, sturdy outer epidermal wall, that counteracts the net expansive force generated by parenchyma, vascular bundles, and inner epidermis together (Kutschera et al., 1987
). The transfer of cell wall tension from these tissues to the outer epidermal wall is close to 90%, i.e., the inner tissues are kept at very low wall stress during growth (Hohl and Schopfer, 1992a
; Kutschera and Köhler, 1992
). Obviously, the stress component generated by turgor in the epidermal cells is insufficient for driving well expansion. Growth of these cells is primarily powered by forces created in the inner tissues that also transmit their anisotropic stress pattern to the epidermis. This explains the observation that the inner tissue walls of elongating organs such as coleoptiles generally demonstrate strict hoop reinforcement (Bergfeld et al., 1988
), whereas the thick, sturdy outer epidermal wall is composed of layers of mixed microfibril orientation (polylamellate wall, often with a rhythmic succession of fibril angles; Roland et al., 1982
; Satiat-Jeunemaitre, 1984
). Hence, growth anisotropy is dictated in this case by the inner tissues, while the more or less isotropic outer epidermal wall provides the major resistance to expansion without affecting the directions of growth (Baskin, 2005
).
It follows from these considerations that, in mechanical terms, the inner and outer tissues of elongating organs fulfill specific functions and that the outer epidermal wall represents a growth-limiting organ wall covering an anisotropically pretensioned body of parenchyma cells. Another important consequence is that it is sufficient for growth-inducing agents such as auxin to induce wall loosening in the outer epidermis only, provided that tissue tension is maintained. This prediction has been confirmed experimentally. First, auxin causes split stem or coleoptile segments to reverse the spontaneous outward bending by a time-dependent inward bending through a selective promotion of extension at the outer epidermal side. This growth response is dependent on auxin concentration and can thus be used as a biotest for auxin (Went and Thimann, 1937
). Second, thoroughly peeled segments can no longer be induced to expand by auxin (van Overbeek and Went, 1937
; Kutschera et al., 1987
) or to suspend expansion in the presence of abscisic acid (Wakabayashi et al., 1989
). The basic experiments by van Overbeek and Went (1937)
have since been reproduced, with a single exception (Cleland, 1992
), in numerous laboratories. Possible reasons for inconsistent results are that different incubation conditions, growth period, and peeling efficiencies can have variable effects in these investigations.
Taken together, these results paradigmatically demonstrate that organ growth represents a system's property of the whole rather than a summation of growth responses of individual cells.
BIOPHYSICS OF SEED GERMINATION
Although the germination of seeds and other plant propagules is an all-or-none event, it can be treated, looked at more closely, as a growth process that can be described by Lockhart's growth equation. A quiescent seed imbibed in water rapidly expands by osmotic water uptake and activates metabolism initially in a fully reversible ("elastic") manner. After a resting period in the turgid state, growth starts in the embryo axis, further stretching the covering layers (seed coat, endosperm) until they rupture, and the protruding radicle continues to grow unrestricted by external forces. This visible event is generally designated as "germination," although it is in fact a snapshot during a continuous growth process.
In terms of the general Lockhart equation (Eq. 3) the driving force leading to seed coat rupturing can be described by a "germination potential," given by the difference between the potential of embryo expansion ( – Y) and seed coat constraint that formally can be included in the yield threshold Y. Germination requires this complex potential to be positive in the presence of an intact seed coat. A negative germination potential signifies dormancy, i.e., the imbibed seed remains in the ungerminated state until the germination potential is raised at a positive level by some environmental "dormancy-breaking" stimulus. The rate of expansion, and thus the time when germination happens at a given germination potential, can be described by a complex "growth coefficient" determined by cell wall extensibility and water conductance of the seed. Thus, for physically analyzing the growth process leading to germination, the same mechanical and hydraulic parameters as in normal cell growth can be used, except that an additional force term and a water permeability term that cover the influences of the tissues restraining embryo expansion must be included. This similarity is indeed not superficial. In simple, small seeds ( << L) basically consisting of an embryo within a dead seed coat (testa), germination can be controlled by changes in cell wall parameters that are expressed by and/or Y in Eq. 1. For example, in rape seeds germination is accompanied by an increase of and a drop of Y in the embryo. Both changes are reversibly inhibited by abscisic acid concentrations that inhibit germination (Schopfer and Plachy, 1985
). In radish seeds the inhibition of germination by light (phytochrome) can be traced back to a low growth potential due to the maintenance of a height Y in the embryo to which the seed coat adds a constant amount (Schopfer and Plachy, 1993
). Gibberellic acid promotes germination in light-inhibited radish seeds by raising the germination potential again to a positive level (Schopfer et al., 2001b
).
In seeds containing a mechanically significant endosperm, the situation is more complicated because the mechanical properties of this living tissue surrounding the embryo can also serve as targets for regulating influences controlling germination. In tomato seeds, for example, the decisive mechanical change leading to gibberellin-induced germination is the weakening of the endosperm tissue at the site of prospective radicle emergence. These mechanical changes can be physically measured by determining the puncture force necessary to rupture the isolated endosperm (Groot and Karssen, 1987
). Abscisic acid inhibits the development of growth potential in the embryo as well as endosperm weakening in coffee seeds (da Silva et al., 2004
). A similar situation exists in cress seeds, where puncture force measurements with the endosperm revealed that the weakening of the endosperm at the radicle pole is initiated by a signal from the embryo that can be substituted experimentally by gibberellin, whereas abscisic acid inhibits this process (Müller et al., 2006
).
Insofar as seed germination occurs in the soil, the emerging seedling experiences external forces potentially restricting growth until the shoot reaches the soil surface. For the root, this situation remains a permanent burden. Organs adapted to such mechanical constraints are often spear-shaped, like the grass coleoptile, and capable of avoiding hard barriers by oriented, force-induced growth responses. Evidently, they dispose of sensory mechanisms for measuring the magnitude and direction of external forces. This is the field of thigmomorphogenesis (Jaffe et al., 2002
). Mediators of imposed static forces of this type may be the cortical microtubules associated with the inner surface of the plasma membrane. It has recently been shown that in the epidermis of the maize coleoptile microtubules are able to reorient in response to bending forces (Zandomeni and Schopfer, 1994
; Fischer and Schopfer, 1998
). Under the assumption that the microtubule–microfibril paradigm also holds in this case, these findings offer a first glimpse into the signal transduction chain operating in thigmomorphogenesis.
FOOTNOTES
1 The author thanks Dr. G. Leubner for critically reading this manuscript. 
2 Peter.Schopfer{at}biologie.uni-freiburg.de
101 The author thanks Dr. G. Leubner for critically reading the manuscript.
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