The biophysics of differential growth

Environmental and Experimental Botany, Vol. 29, No. 1, pp. 7 23, 1989. Printed in Great Britain.

0098~8472/89 $3.00 + 0.00 (C~ 1989. Pergamon Press pie

T H E BIOPHYSICS OF D I F F E R E N T I A L G R O W T H A. DERI T O M O S , MICHAEL MALONE and JEREMY P R I T C H A R D

Adran Biocemeg a Gwyddor Pridd, Coleg Prifysgol Gogledd Cymru, Bangor, Gwynedd LL57 2UW, Wales, U.K.

(Received 23 February 1988; acceptedin revisedform 27 April 1988) TOMOS A. D., MALONE M. and PRITCHARDJ.The biophysics ofdifferentialgrowth. ENVIRONMENTAL AND EXPERIMENTALBOTANY 29, 7--23, 1989. The intrinsic control of uniform and differential growth of plant cells can be traced to a small number of physical parameters. These are cell wall rheology, membrane and tissue hydraulic conductivity, and membrane and tissue solute transport. Water and solute effects are manifested as alterations in turgor pressure. Environmental and biochemical processes always channel their effects through one or more of these parameters. Technical developments such as the pressure probe and Instron tensiometer, together with a reappraisal of older techniques, are beginning to allow assessment of the relative r61es of these factors. Although the importance of cell wall rheology is becoming increasingly apparent, there is still insufficient information to allow generalized conclusions regarding the r61e of turgor pressure in differential growth. This review considers attempts to correlate these parameters with observed anatomical growth patterns.

INTRODUCTION

T o COVER the scope of the title fully in one review would be prohibitive. Therefore, three aspects of the biophysics of d i r e c t i o n a l i t y of cell a n d tissue g r o w t h that have been the subject o f recent work will be considered here. These are cell wall rheology, tissue w a t e r a n d solute relations, a n d tissue heterogeneity. All e n v i r o n m e n t a l a n d biochemical processes channel their effects t h r o u g h these. T h e y are central to o u r u n d e r s t a n d i n g o f growth.

standing o f " d i f f e r e n t i a l g r o w t h " . Let us consider this for a m o m e n t . W i t h the exception, perhaps, of spherical unicellular algae (and their multicellular conglomerates), all p l a n t growth is "differential" in the sense t h a t cell growth differs in rate or direction with time or distance from the meristem. T o illustrate this consider Fig. 1. T w o cells (A and

DIFFERENTIAL G R O W T H

T h e term "differential g r o w t h " is used generally in the sense of g r o w t h that results in curv a t u r e or similar distortion in the outline of a tissue or organ. Since m a n y recent biophysical studies of g r o w t h have been p e r f o r m e d on the linear g r o w t h o f organs, such as oat coleoptiles, pea stems or cereal roots, it m i g h t a p p e a r that such work has little to c o n t r i b u t e to o u r u n d e r -

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Fro. 1. Differential growth of two cells within a tissue. Cell A is growing more rapidly than cell B in the vertical direction in both cases. (a) Differential growth will result in bending of the growth axis. (b) Differential growth will result in continued linear growth.

8

A . D . TOMOS et al.

B) are expanding differentially in each of the two examples (Figs l a and l b). The growth rate of both A and B correspond in the two examples but are different from each other. A is extending in the direction of the axis of the tissue at a faster rate than B. The organ illustrated in Fig. la will curve to the right, while that in Fig. 1b will maintain linear growth. It is only the relative positions of the cells that distinguish the two examples. The parameters controlling growth of cells A and B may well be the same in both cases. These are not imaginary examples: Fig. 1a corresponds to the situation observed in cases such as gravitropically bending shoots, while Fig. lb corresponds to linearly growing shoots or roots.

ORGANIZATION LEVELS OF C O N T R O L

Directionality of growth and development of the characteristic outline of plants have their basis in the duration, speed and direction of vectorial processes at cellular resolution. Changes in growth either in direction or with time must involve different cells in the tissue behaving in different ways. As we shall see, however, this does not necessarily mean that each cell is the master of its fate. At a tissue level, this could be due to individual cells being stimulated to respond differently against a uniform physical background, or it could be due to cells of identical properties responding to physical gradients set up across the tissue. Consider differential turgor pressure as a simple example. A differential in turgor could be set up between two cells as the result of one cell taking up solutes more actively from an apoplast of uniform concentration. The cells are behaving differently. Alternatively, the cells may have identical solute uptake mechanisms, but due to resistance to solute flow from the vascular tissue a gradient of solute concentration is set up. Since solute uptake into the cell may be a function of solute concentration, the cell furthest from the source of solutes will have a different turgor pressure. The first of these scenarios puts the control at the level of the cell, while the second places the emphasis on properties of the tissue as a whole. Examples of possible physical gradients across tissues are those of osmotic pressure (or the con-

centration of a crucial solute) or of water potential. Recently, ToMos and WYN JONES(66) have drawn an analogy between such gradients and those set up in partition chromatography systems with solutes (and water) partitioning between the symplast, apoplast and vacuoles of tissues.

CELL E X P A N S I O N AND DIVISION

Although it is possible to envisage the growth of an organ in the absence of cell division, in reality no cells appear capable of indefinite expansion (with the exception of Jack's Beanstalk)J 9/ Cell division is clearly a prerequisite of continued volume growth. However, as cogently argued by GREEN,C18)volume growth occurs only as the result of wall extension. More specifically in the control of differential growth, the responses observed in the various tropisms are often too rapid to be explained by changes in cell division rate; also, they can occur in zones of the organ where no cell division is taking place. Whether cell division rate ever directly limits cell extension rate (or indeed the reverse) is a factor of current interest beyond the scope of this review. Coordination of cell expansion and division has been reviewed by LLOYD and BARLOW.(35) The fundamental basis of uniform or differential growth lies, therefore, in the direction and amount of cell wall extension at the level of the single cell. The plant outline is defined by the sum of the individual cell walls. Relating this behaviour to its foundation in gene expression is one of the great current challenges of plant science.

IRREVERSIBLE CELL E X P A N S I O N

The sequence of events that may lead to irreversible growth of a higher plant cell embedded in a tissue has been usefully summarized by COSGROVE./1°) The wall of the cell contains elastic elements linked in series with elements capable of plastic deformation (Fig. 2). The wall is under tension generated by the cell turgor pressure. This tension is manifested by extension of the elastic elements. To allow growth, a bond in the plastic

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stage these must enter the protoplast via an energy-linked process. T h e nature of the solutes, each with its individual transport properties, could also be crucial. THE U N K N O W N S

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FIG. 2. Mechanical model of the viscoelastic wall elements. (a) Turgor pressure maintains a stress on the elastic elements (E). (b) On scission of a bond within the plastic element (P), that element is stretched due to the stress in the elastic elements. (c) On recovery of turgor pressure, stress returns to the elastic element and the system is ready for another cycle. After COSGROVE.

(10)

element is released and the element extends due to the tension. At this stage there is no extension of the wall as a whole since the extension of the plastic element is taken up exactly by a relaxation in the elastic element. T h e resultant diminution of stress in the wall results in a decrease in both turgor pressure and protoplast water potential; as a consequence, a water potential gradient across the plasmalemma is established. W a t e r flows into the protoplast driven by this water potential gradient. T u r g o r pressure increases and stress is once again introduced into the elastic bonds to renew the cycle of events. In order to maintain the cycle indefinitely, the solute content of the cell requires topping-up to compensate for dilution by cell expansion. This final event provides the t h e r m o d y n a m i c link with biochemical energy derived from cellular metabolism and drives growth. T h e rate of growth and its duration can be modulated at several points in the scheme. Within the wall, these are the rate of breakage within the plastic elements and the degree of relaxation of the elastic elements. Alternatively, the rate of flow of water into the protoplast can be limiting. At steady state, this would depend on the resistance to water flow from the bulk pool (ultimately the soil), while under fluctuating conditions it would also be a function of the various water capacitances of that pathway. (4/ Finally, for sustained growth a supply of solutes is required; at some

Such bold statements of the processes to be considered belie our current level of ignorance. Briefly, we have no idea of the biochemical identity of the plastic and elastic elements in the wall. Likewise, we have uncertainty regarding the passage of water and solutes across tissues, relatively little idea of the control of solute uptake, little information on what determines m a x i m u m cell expansion in any direction and much remains to be discovered regarding the basis of the control of orientation of cell division. What, then, have we discovered regarding the biophysics of uniform and differential growth? Let us look in turn at each of the likely control parameters. T U R G O R PRESSURE

It is important to realize that cell turgor pressure does not constitute a vectorial driving force. To be of use the force must be directed in the same way as steam drives the pistons of a locomotive. However, as proposed by LOCKHARTi36/ and others, growth rate (r) m a y be a function ofturgor pressure (P) as follows: r = q~(P- 11).

(1)

This defines two theological parameters of the cell wall material, namely, yield stress threshold ( and plastic extensibility (or compliance) (~b). We shall return to these below. T w o intrinsic processes are involved in regulating turgor pressure. These involve the solute and the water relations of the growing cells. (Extrinsic processes, such as water or salt stress, will also influence turgor pressure and m a y result in differential growth under stress conditions.)

Maintenance of osmoticpressure balance T h e turgor pressure of an expanding cell is determined by the maintenance of a force to drive water into that cell. W a t e r uptake is generally considered to be passively osmotic (although

10

A . D . TOMOS et al.

active processes involving flux coupling are also possible/65/and have been recently re-assessed by KATOU and FURUMOTO(29'3°)). Alteration of the osmotic pressure of the cell will alter the driving force of water uptake and, other factors being equal, will alter turgor pressure and growth rate. At one extreme, if no solute uptake occurs then cell expansion will dilute the cell contents and osmotic pressure (and with it turgor pressure) will decline; 1362at the other extreme, uptake will exceed growth rate and turgor pressure will rise. To promote the growth rate of cell A in Fig. 1, increased solute uptake by the cell (or indeed hydrolysis of internal polymers) will increase protoplasmic osmotic pressure relative to the immediate water s o u r c e - t h e apoplast. This will increase turgor pressure in two ways. Not only will the increase in intracellular osmotic pressure achieve this, but also, by removing solutes from the apoplast, the osmotic pressure of that compartment will decrease. (Turgor pressure is a function of the differential osmotic pressure across the plasmalemma.) This latter effect is indeed an efficient and sensitive way of modulating turgor pressure with a minimum of solute transport since a flux across the plasmalemma will result in a proportionately larger change in solute concentration in the smaller compartment, the cell wall, than in the larger compartment, the protoplast. For continued growth it is important, therefore, that an adequate supply of solutes be available to the apoplast. Growing tissue, which will generally have a low transpiration rate, is supplied with solutes via the phloem. Phloem unloading, then, becomes a potential point of control in parallel with the solute uptake processes of the expanding cells. Filling the expanding apoplast with solutes which are not taken up by cells would lower turgor pressure, while supplying solutes to cells involved in accelerated uptake would increase turgor pressure. Thus, either intra- or extracellular osmotic gradients could in principle result in differential growth. The solute status of the apoplast of growing tissue is a current point of controversy. Although it is clear that the apoplasts of mature cells can have very high osmotic pressures, in some cases the situation in growing tissue is equivocal) 33'35/ COSGROVE and CLELAND (11) claim values of

approximately 0.2 MPa in expanding coleoptile tissue, while NONAMI and BOYER/44) argue for the absence of osmotically significant solutes in the apoplasts of expanding zones of soybean and pea seedlings. In principle the maintenance of sufficient osmotic pressure in growing cells appears not to pose a problem for plants, except for those growing under saline conditions where cellular osmotic pressure is high and a considerable transport capacity is required to maintain it./~6'23) Maintenance o f a water supply

Water entry into the expanding cells is a function not only of osmotic pressure gradients, but also of the relevant resistances to water flow and its coupling to osmotic gradients. LOCKHART (36) indicated that the hydraulic conductivity (Lp) of the cell wall and plasmalemma will limit the growth rate of isolated cells since r = L p ( A P - aAl-I)

(2)

(AP and All are the hydrostatic and osmotic pressure gradients across the pathway, and a is the reflection coefficient that relates the actual driving force due to the osmotic gradient to the magnitude of that gradient. A value of 1 for a signifies that the membrane is ideally semi-permeable.) Under some circumstances, Lp could become significantly growth limiting, i.e. if the wall were capable of expanding at a rate faster than the required volume of water could be supplied to it (see also ret~ 8 and 51). While for isolated single cells the resistance to water flow would be relatively low, for higher plant cells in a tissue it is the resistance of the entire pathway from expanding cell to xylem (or indeed the soil) that needs to be considered as this may be of large magnitude. To play a r61e in differential growth, the pathway of water flow to cell A (Fig. l) must have a significantly higher conductivity than that to cell B. How large are such resistances, and might they play a r61e in differential growth? Current thinking regarding this is exemplified by two recent, and in this context conflicting, reviews. (4'9) There is general agreement that gradients in water potential (~) occur between the xylem and the expanding cells in tissues. The act of wall loosening itself will lower ~O as noted above. The

BIOPHYSICS OF DIFFERENTIAL GROWTH "bone of contention" is whether at dynamic equilibrium the bulk of the water potential gradient across the tissue to the expanding zone is due to the wall loosening and a high resistance to water flow [thus influencing the AP component of Equation (2) ], or whether it owes its value to a gradient of osmotic solutes in the apoplast across the tissue from the walls of the expanding cells [thus influencing the AII component of Equation (2)]./93°/ I f the apoplast has (as might be expected) a very low reflection coefficient (a), a gradient of osmotic potential in the cell walls will be ineffective in driving water flow across the apoplast./62/ (As can be seen from Equation (2), when the value of a is low a large osmotic gradient is required to drive water flow.) In COSaROVE'S/9~ description, the small hydrostatic pressure component of the water potential gradient indicates a relatively low resistance to water flow; it is thus unlikely to be growth limiting and hence of much significance in differential growth. BOYER'S(4) model envisages a larger resistance that could limit growth. The argument currently centres around the value of the apoplast osmotic pressure discussed above. The resolution of the argument appears to require the simultaneous measurement of turgor pressure and osmotic pressure in the expanding cells of non-transpiring plants./65/ This would allow the definition of the relative importance of the two components of water potential in the ceils. The cell sampling technique reported by SHACKEL/6°) may allow this to be done in the near future. Not only is measuring the hydraulic conductivity of the tissue difficult but also the relative importance of three possible pathways of flow is unknown. Water may cross tissues via a symplastic, an apoplastic, or a "vacuole-to-vacuole" pathway. (66) If water flow follows either the symplastic or the vacuole-to-vacuole pathway the reflection coefficient would be determined by membranes and therefore have a value close to unity. Various combinations of these pathways could be envisaged as the basis for differential growth under some circumstances. Several attempts have been made to estimate the relative importance of the pathways across tissues. In his review of the field, BoYEl~{4/ concluded that the apoplast does not appear to be

ll

the dominant path. In some cases, however, tissue conductivity is remarkably high. For example, JoNEs et al. 1281have recently re-assessed the model for water flow across the root cortex and find whole root radial resistances which are barely higher than the absolute minimum for a nonapoplastic flow when single cell Lp values are compared with those obtained for osmotically induced flow across the entire root. Suggestions that hydraulic conductivity is one of the potential controlling sites for differential growth (e.g. ref. 1) are largely based on reports of hormonal control of tissue conductivity (see ref. 1 for reports relating to auxin, and ref. 15 for ABA). The cellular basis of these responses in higher plants is still unclear. Using the pressure probe, EAMUS and TOMOS/~5/ detected a small increase in mean single cell Lp in Rhoeo leaf epidermal cells on application of abscisic acid (ABA), while JONES/27) could find no change in the Lp of a single mature wheat root cell measured before and after application of ABA. M E A S U R E M E N T OF T U R G O R PRESSURE IN DIFFERENTIALLY GROWING SYSTEMS

The potential r61es of solute or water transport in differential growth are conveniently testable by measuring their manifestation in differential turgot pressureJ TM With the advent of the pressure probe/~6/such measurements are now possible at the required cellular level of resolution. Extrinsic influences (such as water stress) that vary turgor pressure do indeed vary growth rate according to Equation (1). This was clearly demonstrated for the giant-celled alga Nitella. '~71 By measuring growth rate and cell turgor pressure simultaneously in cells bathed in various strengths ofosmoticum, values for Y and 4) were obtained. Rapid changes in extracellular osmotic pressure led to rapid changes in turgor pressure as the cells relaxed elastically to the new water potential equilibrium. Growth rate changed as predicted from Equation (1). However, over a period of some minutes the initial growth rate was recovered despite no recovery of the initial turgor pressure. (Clearly, this cannot be reconciled with Equation (1); either Y or 4) is under biochemical control.) From the behaviour of the cell following its replacement in the original bathing solution it

12

A . D . TOMOS et al.

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FIG. 3. Growth rate as a function of turgor pressure in epidermal and cortical cells of hydroponically grown wheat roots following short-term (1-15 min) immersion in various mannitol concentrations. The two lines represent data with (0) or without (O) 10 mol m -3 KC1. Lines are fitted by linear regression. The pattern appears to follow the behaviour predicted from Equation (1) (see text). Potassium appears to influence Y while leaving ~b relatively unchanged. was apparent that the cell was regulating Y in order to preserve ( P - Y ) at a constant value. The decrease in Y appears to be under metabolic control, while the corresponding increase following an increase in turgor pressure seems to be a non-metabolic strain-hardening process. (22) A recent example of cellular behaviour that parallels Equation (1) in higher plants is the correlation between growth rate and the reduction of turgor induced by transpiration in sycamore leaves. (63) Similarly, a reduction in growth rate has been correlated with the rapid reduction of turgor pressure in wheat roots following a rapid increase in the external osmotic pressure (Fig. 3; PRITCHARD, unpublished). As with NiteUa, however, the osmotic stress initiated secondary responses. The wheat roots immediately began to adjust osmotically: both turgot pressure and growth rate were regulated back to their prestress levels with Y and ~b apparently remaining unchanged. In contrast to the observations with

sycamore, TAYLOR and DAVIES(6s) in a similar experiment with birch leaves found that the leaf cells recovered growth rates at the lowered turgor pressure by altering ~b. While growth rate may indeed be subject to an extrinsic water stress that influences turgor pressure, if one generalizes from the small number of examples studied to date, then growth rate does not appear to be widely modulated by turgor pressure as an intrinsic control parameter. (1°) This is perhaps surprising in view of the r61e played by differential turgor pressure in the reversible mechanical movements of stomata, etc. To illustrate this, using the pressure probe, PRITCnARD (unpublished) measured single cell turgor pressure (Fig. 4) in ranks of epidermal and cortical cells of growing intact wheat roots away from the tip (corresponding to cells in Fig. l b). Mature cells immediately proximal to the expanding zone had identical turgor pressures to those in the expanding zone itself. Cessation of

BIOPHYSICS OF DIFFERENTIAL GROWTH

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FIG. 4. Distribution of turgor pressures within the core of a 4-day-old hydroponically grown wheat root. Each point represents a measurement from a single cell. (a) Turgot pressure as a function of distance from the tip (arrow indicates position of transect for b). (b) Turgor pressure along the radius of a root 3--4 mm from cap apex. cell expansion on approaching maturity is clearly not related to decreased turgor pressure. Similarly, when growth rate was modulated by the addition of osmotically insignificant amounts o f K + ions, growth rate was again independent of turgot pressure. I47) RXCHand ToMos (Ssl looked at a phototropically reacting material using the pressure probe. In the blue-light-induced phototropic bending of Sinapis alba the shaded side accelerates, and the illuminated side decelerates, its growth rate c54) (cf. Fig. 1a). Measurement of epidermal and cortical cell turgor pressure at either face of the responding zone showed no change during either the lag or the main bending phase. However, in the geometrically similar gravitropic response of maize coleoptiles, R. D. FInN and colleagues (unpublished) have been unable to detect changes in rheological properties measured with the Instron technique (discussed below) associated with the upper (non-growing) part of the negatively gravitropically responding organ. By a process of elimination this would suggest a r61e for turgor pressure in this response. Clearly it is imperative for turgor and rheological measurements to be performed on the same system. In contrast to the lack ofturgor changes found in Sinapis alba stems, a recent report claims that periodic turgor pressure changes are responsible

for circumnutation in stems ofPhaseolus vulgaris. (~) This report is difficult to evaluate as the reported turgor pressure data are derived from plasmolytically determined osmotic pressure (I-I) values that apparently have not been corrected for cell wall elasticity. On the one hand, the differential values ofl-I at either surface of the growing zone may merely represent differential elasticity, with cells of low elastic modulus (5) contracting (and concentrating their cytoplasmic contents) more than those with higher values of 5. On the other hand, the observation that the concave tissue contracts during the process tends to suggest that turgor pressure changes may well be involved. Confirmation of this by use of a pressure probe is called for. Another report that suggests turgor pressure gradients is that of MUELLER et al. (42) who found a change in tissue compression measured with an in situ strain gauge during a restrained gravitropic response ofRicinus communis stems. However, preliminary pressure probe measurements have failed to detect differential turgor pressures of individual cells of the upper and lower faces of such stems (A. D. TOMOS and F. B. SALISBURY, unpublished). Turgor pressure has also been claimed as a controlling factor in the dimorphism of the water plant CaUitriche heterophylla 113) where submerged

14

A . D . TOMOS et al.

and aerial leaves have different shapes. The cellular biophysical basis of this finding is unknown. In conclusion, the constancy of turgor pressure between cells of different growth rates, in some tissues at least, indicates that the supply of osmotic solutes and water to the cells is not limiting. In these cases, differential growth is not due to differential turgor pressure. Clearly, however, more work needs to be performed in this area. A LINK BETWEEN SOLUTE T R A N S P O R T AND G R O W T H RATE

The constancy of turgor, moreover, has a further implication. Growing cells appear to be capable of homeostatic turgor adjustment. I f solute inflow into the cell were constant, decreased growth rate would be expected to result in an increased turgor pressure. In cases such as the long-term depression of growth in maize roots by low temperature (PRITCHARB, unpublished) this has been observed (although the observed pressure increase is far less than that expected if solute accumulation continued unabated at the very low growth rates observed). In other examples such as the phototropically responding stem of Sinapis alba, (53) turgor pressure remains as constant as can be measured. Solute transport must, therefore, be regulated precisely in step with extension--even during differential growth. The level of p~ecision of the turgor pressure measurements (in this case ___0.02 MPa) suggests that if turgor pressure reduction is the signal for osmotic adjustment, then the sensor is very sensitive indeed. Several turgor pressure sensitive transport processes have been reported for plant tissues (see ref. 65), although whether these could provide such precision is yet to be shown. CELL WALL RHEOLOGICAL PROPERTIES

I f evidence for a r61e of turgor pressure in the control of differential growth is difficult to come by, that for a r61e of wall rheological properties is not so scarce. However, information regarding its r61e in tropic and other deformation processes is almost totally missing. Two types of experimental approach have been used to study tissue and cell rheology. The first (of which R. E. CLELAND and Y. MASUDA are amongst the major proponents) involves the study

of the rheological properties of cells or tissue segments (generally killed by boiling in alcohol) analysed in a tensiometer. Several techniques are used, such as the Instron method, which measure the rate of stress increase as the result of a linear application of increasing strain. The data most easily interpreted here refer to work performed on the giant cells of the alga Nitella. This work also permits the analysis of the anisotropy of the growth of single cells--essential for differential growth--to be detailed, at least in this model system. For such cylindrical cells it can be shown that the tangential wall stress will be twice that experienced longitudinally at any specific turgor pressure./39/ Despite this, these cells, after an initial multiaxial expansion phase, expand exclusively in the longitudinal direction. Clearly, an anisotropy of extensibility and/or yield stress threshold must occur. Indeed, 25 years ago PROBINE and PRESTON/49~were able to demonstrate this for both the elastic and plastic extensibility properties of isolated wall material by measuring these parameters in longitudinal strips and transversely cut hoops. The corresponding ratio of elastic extensibility was about 5:1 for growing cells, and diminished to 2 : 1 tbr mature ceils (although any relationship between elastic, rather than plastic, properties and growth remains obscure). Longitudinal plastic creep at constant stress correlated well with growth rate, whereas the rate of transverse creep was too low to be detected. Subsequently, using a similar analysis of longitudinal strips and transverse hoops, M~TRAUX and TAIZ/39) demonstrated that both the yield stress threshold and plastic extensibility are indeed anisotropic with the value of the former in the transverse direction being twice that in the longitudinal and that the ratio of transverse to longitudinal viscoelastic extensibility decreased from 4 : 1 in the growing cell to about 2 : 1 as the cells matured. Again, longitudinal plasticity correlated well with measured longitudinal growth rate. However, the relationship in the transverse extensibility was not so unequivocal since constant transverse extensibility was not accompanied by constant transverse growth rate. Although measured orthogonally, these measurements remain uniaxial. Under these conditions CLELAND (6) has pointed out that elastic

BIOPHYSICS OF DIFFERENTIAL GROWTH extensibility can be 10 times that estimated in vivo. MI~TRAUXet al. (38) and RICHMONDet al. 155) applied a multiaxial stress by inflating isolated Nitella cell walls with mercury and monitoring their subsequent extension. Several observations were made. (1) Most significant is that the plastic anisotropy is essentially infinite, i.e. negligible transverse extension is observed. (2) As expected, on initial inflation to pressures observed in vivo, cell volume returned to that of the living cell. However, this involved a plastic component indicating a plastic contraction of the tissue on initial excision. A rough correlation was observed between this latter component and in vivo growth rate in slow-growing mature cells, but no correlation was observed for young rapidly growing cells. The creep rate observed, in addition to the "instantaneous" extension, also differed between old and young tissue. However, the rates were considered too low to have significance. In response to criticism that the extensibility value of oat (Arena sativa) coleoptile tissue does not correspond quantitatively to growth rates, CLELAND (6'7) has suggested a modification of the interpretation of stress/strain data: it may reflect the growth rate over a period of time prior to tissue excision rather than the current or future rate. He argues that during growth, bonds oriented in all directions are broken, but that only those in the direction of growth are pulled apart. The remainder reform after a lifetime of an hour or so. The non-physiological uniaxial stress of the Instron device is thought to extend these remaining loosened bonds. Convincing evidence for the hypothesis, at least for the case of oat coleoptiles is presented by CLELAND. (7) MI~TRAUXet al., 138'39~ however, have argued against this for the isolated walls of Nitella, pointing out that "acid" and "base" bands have different growth rate histories, but similar mechanical properties. Sadly, data derived by these techniques cannot be used to insert values for the rheological parameters of Equation (1) for the growth of cells in vivo. Cells and tissues do not grow in response to a uniaxial stress of the type used in the majority of stress/strain analyses, but from a multiaxial stress derived from the hydrostatic pressure (turgor) inside the cell. The resultant growth may be multiaxial or apparently linear. (We say "apparently", since even the uniaxial growth of cyl-

15

indrical tissues involves re-orientation of components in all directions within the wall.) Use of mercury-filled cells overcomes this, but clearly these can only approximate the living system. The second approach to the study of cell wall rheology is to use Equation (1) directly. By measuring growth rates at a series of turgor pressures, values of Y and ~b can be determined. A considerable body of information regarding tissue/organ expansion properties has been obtained in this way from the relation between tissue-averaged growth rate and turgor pressure (whether measured with the probe or averaged for a tissue). In reviewing the literature, VAN VOLKENBUROH a n d CLELAND (67) referred to work indicating that growth rate can be a function of changing rheology. In the expansion of bean leaves on exposure to white light (1~'25'4°'5°/ growth promotion is accompanied by an increase in ~b, while the decrease in growth rate in water-stressed sunflower leaves is accompanied by changes in both Y and ~b./37) TAYLOR and DAVIES(63) have described similar observations in a clear ecological context by comparing the growth control parameters of shade-intolerant (birch) and shade-tolerant (sycamore) trees. For both, Y remains constant under shaded and non-shaded conditions. No changes were found in values of q~ for sycamore and growth rate was governed by transpirationinduced changes in turgor pressure as noted above. In birch, however, ~b increased three-fold on illumination allowing rapid growth to continue at the lowered turgor pressures. Control of cereal root growth--a case study A combination of several methods has recently been applied to growing cereal (wheat, maize) roots in order to assess the importance of turgor pressure and rheological adjustment on their extension growth. This system might be expected to correspond to that illustrated in Fig. 1b. These include measurement of in vivo turgor pressure through the expanding zone, qualitative correlation of this with relative elemental growth rates, and measurement of Instron plasticity and elasticity at low (5 mm) resolution increments from the tip. (48) Growth rate was modulated by the presence of K + ions, C47/ excision t48) and by low temperature (PRITCHARD,BARLOW, ADAM

16

A . D . TOMOS et al.

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FIG. 5. Elemental linear growth rates (G) along a wheat root as a function of distance from the base of the root cap. Growth rate changes do not correspond to any changes in cellular turgor pressure (see Fig. 4). and ToMos, submitted). Measurement of shortterm growth rate after rapid manipulation ofturgor pressure by immersion in an impermeant solute (mannitol) allowed Y and ~b to be estimated in an analogous fashion to that used by GR~E~ 1~7~ for Nitella (PRn'CI-IARD,unpublished). This could also be achieved by monitoring growth rate during osmotic (and turgor) adjustment. The presence of constant turgor pressure (Fig. 4), despite large changes in growth rate through the expanding zone (Fig. 5), indicates that control of growth is not modulated by turgor adjustment. Preliminary observations of growth rate diminution by K + (see Fig. 3) suggest a correlation with changes in Y without significant changes in ~. Instron plastic extensibility decreases away from the expanding zone as would be predicted if growth rate were determined by wall rheology (Fig. 6). In a related observation from pea roots, microfibril orientation in the cell wall appeared to correlate with the local rates of growth. (24) In both these examples the observed changes in wall properties continue into zones of the root where cell expansion has ceased.

In a final example, recovery of growth rate following the release from low temperature stress was accompanied by a reduction in the turgor pressure within the cortical cells of the growing zone of maize roots. This could be due either to a growth-induced decrease in water potential, or a re-coupling of solute transport to a steady growth rate. At the time of writing, the corresponding behaviour of osmotic pressure of this tissue has not been characterized and thus no conclusion can be drawn as to the r61e of tissue water potential gradients in the response. Considering the data as a whole, we believe it seems likely that expansion growth in cereal roots is regulated by wall rheology, at least as far as the cessation of growth at the distal end of the expansion zone is concerned. SUB-CELLULAR DIFFERENTIAL GROWTH

While a full understanding of growth processes as envisaged in Fig. 1 requires information at cellular resolution, it must not be forgotten that in some cases considerable variation in growth

17

BIOPHYSICS OF DIFFERENTIAL GROWTH

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FIG. 6. Decline in the tissue elastic (O) and plastic ( • ) extensibility of methanol-killed sections of 4-day-old wheat roots (grown in 0.5 mol m -3 CaC12) with increasing distance from the tip. Sections, 5 mm long, were tested and values plotted against their mean distance from the tip. Note that extensibility continues to decline well after growth has stopped (cf. Fig. 5). rate along a specific axis can occur within an individual cell. For example, in NiteUa acid- and alkali-secreting bands of the wall have different growth rates, growth being largely restricted to the acid areas. 1381 In higher plants, examples are found in the growth of expanding root cells where elegant microscopical work by SINNOTT and BLOCH(61)demonstrated that a wave of elongation begins at the proximal end of the cells before it propagates to the distal ends (the same work also indicated that cells do not slide past each other during growth). Also, in cotton hairs, pollen tubes and root hairs, expansion is restricted to a zone at or immediately below the tip. (3) Even with cells that appear to be expanding uniformly over their entire surface, such as the expanding epidermal cells of oat coleoptiles, (5) it

has been suggested that evidence of surface growth microheterogeneity may be observed under the electron microscope. (57) Since turgor pressure cannot vary at sub-cellular resolution, such heterogeneity of growth can only be due to differential rheological properties of the walls. ORGANIZATION

AT TISSUE LEVEL

So far, we have been largely concerned with the growth of cells in isolation; their growth as affected by the presence of surrounding cells has been mentioned only in the context of solute and water supply. In higher plants, however, analogies with single cells are rarely obtained since their tissues are not merely conglomerates of expanding Nitella-like cells. The mechanical influ-

18

A . D . TOMOS et al.

ence of the surrounding cells upon each other needs to be considered. KUTSCnERA et al. 13~1have strongly criticized the "Nitella-composite" approach by reiterating the many observations (dating from the initial observation of SACHS/Ss/) of the phenomenon of tissue tension. In 1939 DIErtL et al. 1~4) working on Helianthus hypocotyls related their observations on differential expansion primarily to the modulation of the mechanical properties of the outer epidermal wall. The many subsequent reaffirmations of the structural heterogeneity of these organs are listed by KUTSCI~ERAet al. (3~1 Continuing this approach using maize coleoptiles, KUTSCrtERA et al. (311 have provided strong evidence to demonstrate that in this tissue the driving force of growth is provided not by each cell acting independently but by the pressure of the cortical cells as a whole being restrained by the outer epidermal wall. They thus envisage coleoptile growth not as that of a collection of isolated cells but as that in which the outer epidermal wall acts analogously to the cell wall of Nitella to limit growth, and the cortical cells as a whole act like the osmotically-pressurized protoplast of Nitella to drive growth. (BERGFELD et al. 12) refer to the outer wall structure of the coleoptile as a "wall sheath".) This provides a very different basis of differential growth from that envisaged in Fig. 1 since the point of interest now moves to the anisotropy of the wall sheath. KUTSCHERA and BRIGGS(32) have shown that a similar situation pertains to pea internodes. On removal of the epidermis the tissue swells independently of the presence or absence of indole acetic acid (IAA). The stripped epidermis, on the other hand, contracts by some 10% . This contraction is also independent of IAA. However, whereas the plastic extensibility of the cortex, as measured by the Instron technique, is unaffected by IAA, that of the epidermis is increased by an amount that correlates with the growth rate of the intact plant. Such observations indicate that the various tissues of an organ are not homogeneous with respect to their rheological properties. Figure 7 illustrates three conceivable configurations of cells within the differentially growing organ. A "NiteUa-composite", shown in Fig. 7a, represents the situation illustrated in Fig. la. Here, cells are shown growing independently of

each other. It is such a model that has been the basis of much of the discussion on the previous pages. Evidence of rheological inhomogeneity and the r61e of the outer epidermal wall in regulating growth, however, leads to the configurations illustrated in Figs 7b and 7c. In Fig. 7c both the longitudinal and transverse stress of the tissue is borne by the outer epidermal wall sheath. Here the whole organ is behaving like a single Nitella cell, with the wall sheath playing the r61e of the Nitella cell wall (the limiting tissue). Differential growth under these circumstances must be due to differential rheological properties of the opposite elements of the growth limiting tissue (e.g. the opposite surfaces of the wall sheath). We shall consider below the equivalent situation in roots. In this configuration, transverse elasticity of internal cell walls must be higher (i.e. they have a lower elastic modulus) than that of the tissue sheath. Turgor pressure will therefore be uniform throughout the driving tissue (including the epidermal cells, since it appears that it is only the outer epidermal wall that is limiting) since any release of external force on a cell due to a decrease in turgor pressure ofa neighbouring cell will result in the expansion of that cell towards the neighbour until the opposite forces on the common wall are equal. Since the walls of the limiting tissue take the stress of the driving cell turgor pressure, the stress within the walls of the driving tissue will be less than that within the growth-limiting element. To allow growth to occur uniformly through the tissue, plastic extensibility (~b) must be the same for each wall (cortex and epidermis). Since the driving cell wall is under less stress, however, its stress yield threshold must be lower. On the other hand, its strain yield threshold must be at least as high as that of the growth limiting tissue (otherwise problems will occur following elastic stretching of the growth-limiting tissue). The stress and strain thresholds can have different values in the tissue due to different values of the volumetric elastic moduli (e) of the driving and limiting cells. If the two were the same then the cells would be totally mechanically independent of each other (i.e. as in Fig. 7a). In rheological terms, the volumetric elastic modulus (e) of the organ as a whole will be greater

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FI~. 7. Diagram of possible configurations of tissue bending due to differential growth along the major axis of an organ. The driving force in each case is the turgor pressure of all the ceils (four cells are illustrated). The elements responsible for limiting growth in the longitudinal (1--vertical arrows) and tranverse (t--horizontal arrows) directions vary between the configurations. (a) Growth both in the 1 and t directions is limited by the wails of each cell individually (Nitella-composite). (b) An outer wall-sheath limits extension in the 1 direction, expansion in the t direction is limited by each cell individually (partial NiteUa-composite). (c) Growth in both the 1 and t directions is limited by the outer wall-sheath only. than that of the individual cells. A similar situation in a non-growing tissue has been described by PALTA et al. ~45)for the sugarbeet tap root. Here, the value of e of cells in excised tissues measured with a pressure probe appeared to be an order of magnitude lower than that of the organ as a whole. In the study ofBERGFELD et al. I2) it is noted that whereas the outer epidermal wall has a robust and complex structure of cellulose microfibril orientation, in the inner, more delicate epidermal and cortical walls the microfibrils are perfectly transversely oriented, suggesting that the inner walls may also be elastically and plastically anisotropic. This opens the possibility of a configuration resembling that in Fig. 7b. This is intermediate between the "Nitella-composite" of Fig. 7a and the full "wall sheath" of Fig. 7c. In this case, the inner cell walls bear the transverse stress while the wall sheath bears the longitudinal stress. Consequently, turgor pressure gradients across the tissues are possible and could result in differential growth, as mentioned earlier. However, as noted above, no unequivocal examples of such turgor pressure gradients have been shown. Indeed, their absence across growing tissues has been demonstrated for several tissues using the pressure probe: these are the growing pea stem/H) the phototropically-responding mustard stem ~53/

and the extension zone of the wheat root apex (see Fig. 4). The configuration shown in Fig. 7b would confer advantages in addition to allowing the existence of turgor pressure gradients. The general orientation of growth along the axis would be determined by the individual cells. On the other hand, the rate of growth and "fine tuning" of the direction of growth would be due to the differential rheological properties of the epidermal wall sheath. The implications of the "wall sheath" concept to any rrle of hydraulic conductivity or solute transport in control are clearly dependent on the partial "NiteUa-type" configuration (Fig. 7b). On the other hand, in the context of tissue heterogeneity, the interpretation of rheological data gained by the Instron technique remains valid, but clearly would only apply to the structures that limit longitudinal growth. An analogous situation may pertain in roots, where the outer tissues of the stele (e.g. endodermis) may play the rrle given to the outer epidermal wall above (CLELAND, personal communication). In this case, the cortex (and/or possibly the stele) cells would provide the driving force for growth. The cortical cells would clearly have to be individually supported transversely in a situation analogous to Fig. 7b.

20

A . D . TOMOS et al. O R I E N T A T I O N OF WALL POLYMERS

It has been accepted for some time that the anisotropy of cell wall rheology is in some way related to the orientation of the cellulose microfibrils within the wall./j9'461 Following application ofisopropyl N-phenyl carbamate (IPC) to cells of NiteUa, RICHMOND et alJ TM identified the orientation of the cellulose microfibrils in the most recently laid down inner 25% of the wall as being the site of the mechanical anisotropy. IPC disrupted the ordered orientation of the freshly laid down microfibrils and was accompanied by both isotropic growth in intact cells and by isotropic rheological properties of isolated wails. The orientation of the microfibrils, in turn, is thought to be linked in some way to the orientation ofmicrotubules within the protoplast. The evidence for this has been presented in several chapters in LLOYD. (34) In several reviews GREEN/19 2~/ has emphasized the control ofmicrofibrillar reinforcement during differential growth. The crux of GREEN'S argument is that once established in a nascent cell, the microfibrillar orientation is maintained until the next cell division, at which point the new orientation is determined by two factors. It (a) tends to be parallel to the new cell plate, and (b) will include the smallest pair of faces of the cell. In general these two orientations will coincide. However, GREEN outlines the conditions necessary to enable microfibril orientation, and hence growth direction, to rotate through 90 ° when a new direction of growth, rather than a bending, is initiated. I f the inner portion of the wall is involved in determining the direction of cell expansion, the r61e and fate of the outer layers remains rather obscure. After several decades of useful prominence, the multinet growth hypothesis of ROELOFSEN and HOUWINK(56) appears to be being replaced by other ideas. A detailed critique of this field has recently appeared in a monograph by BOYDJ3/ In a potentially highly significant development, improved techniques of electron microscopy appear to be extending rapidly the list of cell walls that exhibit helicoidal-textured structure. (431 O f particular relevance is its occurrence in the walls o f Nitella (57) (upon which so much basic work on wall rheology has been performed),

in mung bean hypocotyls (56) and in the epidermal wails of expanding maize coleoptiles. (59) In the last-mentioned system, the helicoidal structure is restricted to the external epidermal wall which, as we have seen, is considered to be the growth limiting component. It is absent from both inner epidermal and cortical walls. The relationship of helicoidal growth to the data of RICHMOND et al.(55) on the importance of the microfibrillar orientation of the inner 25% of the wall awaits explanation. Finally, REIs et al. (52~ have introduced a r61e for turgor pressure into the organization of these helicoidally (or twisted) textured cell walls. Osmotically-induced plasmolysis causes a disorientation in the fibrils that are subsequently laid down. About 1 h after the recovery of turgor pressure, ordered deposition of fibrils resumes and the helicoidal structure continues. CONCLUSIONS

In conclusion, it must be stressed that we still have far too little data to draw general conclusions regarding the control of differential growth. The absence of turgor pressure changes on initiation of such growth patterns would point strongly to changes in cell wall rheology as being of importance. Direct measurement ofrheological wall properties would tend to confirm this in a number of cases. A considerable degree of caution, however, needs to be applied in this case since results obtained with the Instron and similar techniques do not always correlate, even qualitatively, with growth rate. In those examples where rheological changes do seem to be important, both yield strain threshold (Y) and wall volumetric extensibility (~b) can be implicated as the basis for growth modulation. At a biochemical level, the basis of these changes is unknown. Although rheological changes reside at this level, the traditional biochemical techniques that search for specific bonds may not be sufficient to provide explanations if the changes involved are those of polymer orientation. Here much needs to be learned regarding phenomena such as the helicoidal growth patterns of growth-limiting structures. Finally, the equivocal evidence for changes in turgor pressure (either as the result of modulation

BIOPHYSICS OF D I F F E R E N T I A L G R O W T H o f solute content or in w a t e r relations) c a n n o t be ignored. I t is i m p e r a t i v e for precise, unequivocal measurements of t u r g o r pressure to be performed on tissues in which t u r g o r pressure changes are suspected as being the cause o f differential growth. T h e pressure p r o b e technique w o u l d a p p e a r to be ideally suited for this. Acknowledgements--We are grateful to Mr Gwynfor Williams for technical assistance and Mr Alan Thomas and Dr John Gorham for stimulating discussions. We are grateful to the AFRC and the SERC for financial support to M.M. and J.P., respectively.

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21

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