TY - JOUR
AU1 - Thompson, D.S.
AB - Abstract This paper examines the rheological properties of the fruit epidermis of tomato (Lycopersicon esculentum L.). This research was conducted because previous work had demonstrated that the rate of tomato fruit growth is determined by the interaction of tissue pressure and epidermal properties. A constant‐load (or ‘creep’) extensiometer was employed in these experiments and the results interpreted using a model which describes creep retardation using a limited number of rheological elements, one of which appears analogous to plant growth and is of similar magnitude to fruit growth rate in vivo. The effects of pH, applied force and boiling upon the individual components of the model have been examined and indicate that several elements are strongly pH‐dependent and that this dependency is eliminated by boiling. These results suggest that enzyme activity (plausibly that of one or more expansins) reduces the viscosity of the cell wall over a wide range of time scales. Further consideration of the creep of tomato epidermis in terms of models developed to describe the behaviour of artificial polymers suggests that the types of molecular event described by each rheological element can tentatively be identified and that pH‐dependent enzyme activity facilitates both conformer rotation and macromolecular movement within the plant cell wall. These interpretations ascribe considerable importance to the time scale over which creep occurs. Tomato, fruit, growth, cell wall, rheology. Introduction It has been argued that the existence of significant tissue tension in fruits such as tomato indicates that the fruit epidermis is of importance in determining the rate of expansion in fruit that exhibit tissue tension (Thompson et al., 1998; Kutschera, 1989). It has also been proposed that the growth rate of plant tissue is determined by the interaction of cell wall stress resulting from tissue turgor pressure and cell wall mechanical properties (Lockhart, 1965). This model of plant growth has been generally accepted (Cosgrove, 1993). The control of cell wall mechanical properties is therefore believed to be a crucial component of growth rate regulation and a key element of the response of growing tissues to environmental changes. Simple assays of the rheological properties of growing plant tissues in vitro can therefore assist plant scientists in detecting and quantifying regulatory events leading to altered growth rates and may allow the biophysical and biochemical basis of responses to be identified. For example, although a number of cell wall enzymes thought to affect cell wall mechanical properties have been identified (Andrews et al., 2000; Fry et al., 1992; Inouhe and Nevins, 1991a, b) exact relationships between most of these enzyme activities and the rheological properties of plant cell walls have not been clarified (the expansin and yieldin groups of enzymes are an exception and were identified by their biomechanical effects; McQueen‐Mason et al., 1992; Okamoto‐Nakazato et al., 2000a, b). This is partially due to the difficulties encountered in measuring and characterizing the physical properties of the plant cell wall. The majority of investigations of cell wall mechanical properties have used an ‘Instron’ style extensiometer to determine stress–strain relationships of plant tissue and attempted to relate these properties to tissue growth rate, especially the degree of irreversible deformation which is used to calculate ‘plastic extensibility’ (Cosgrove, 1993). Good relationships between plastic extensibility of the material tested and growth rate prior to harvest have often been observed (e.g. Van Volkenburgh et al., 1983) but the importance of such relationships has been questioned by a number of workers (Masuda et al., 1974; Cleland, 1984; Hohl and Schopfer, 1992). One additional major shortcoming of the Instron method is that it extends the tissue very rapidly (over several minutes) whereas the same change in length would take several hours in vivo. This investigation has therefore employed a constant load or ‘creep’ extensiometer to observe tissue extension at time scales and stresses similar to growth in vivo. This type of assay involves measurement of the sample extension caused by an applied stress over a period of time, which is often called creep. Creep extensiometer assays have been used to show that cell walls of frozen and thawed oat coleoptiles and cucumber hypocotyls exhibit prolonged extension at pH 4.5 but not at pH 7 (Cleland et al., 1987; Cosgrove, 1989). Such alteration of cell wall mechanical properties at reduced pH has often been observed. Cell wall acidification has frequently been observed during growth promotion and has been proposed as a component of growth regulation (Cleland, 1992), although some workers believe there to be a discrepancy between the cell wall pH in normal plant growth and the pH required to significantly alter wall properties (Kutschera, 1994). In this paper the mechanical properties of the fruit epidermis have been examined in order to understand the factors determining tomato fruit size. Methods of analysis and interpretation of the data obtained using a simple creep assay are proposed which allow detailed quantification of cell wall properties over a wide range of time scales. It is hoped that these analytical methods will contribute to the available methodology for quantitative determination of cell wall properties and improve understanding of the biophysical and biochemical events involved in growth and growth regulation. Rheological theory An important difficulty in characterization of the mechanical properties of plant tissue is that plant cell walls behave viscoelastically, that is they exhibit simultaneous liquid‐like flow and elastic deformation. As a result of this behaviour, quantitative interpretation of the data is rarely straightforward. In the field of rheology it is common to analyse such results by breaking behaviour down into one or more simple elements with defined mathematical properties and assembling individual equations describing extension or relaxation of each element into an equation capable of describing the behaviour of the material as a whole. This can be extremely useful as the basic elements included in the final model frequently correspond to specific material components or events at a molecular level. Extensiometric data has here been analysed using equations incorporating three types of basic rheological element. A viscous flow element. This describes behaviour of a viscous liquid which flows at a rate proportional to the applied stress and the element viscosity, i.e. for stress σ and viscosity η, dL/dt=σ/η. Cumulative length at time t is given by Lt=σt/η. Although it may seem surprising that plant material can include ‘liquid’ behaviour it should be noted that rheological studies may consider materials to have different properties depending upon the period of the study. Over long enough time scales it becomes appropriate to treat even rock as a liquid. Kelvin elements, also known as Kelvin–Voigt elements, possess both viscosity and elasticity and extend at an exponentially decreasing rate with time. This is often visualized as a spring (the elastic component) and a dashpot (a viscous flow element) arranged in parallel so that stress applied to the element as a whole is divided between the two components. The spring and dashpot are constrained to remain the same length throughout extension. While the spring is not extended all of the stress is exerted upon the dashpot, but as the dashpot and spring both extend, stress is transferred to the spring from the dashpot which extends correspondingly slowly. At time t, the rate of extension of a Kelvin element with viscosity η and retardation time τ subject to stress σ is given by: 1 The retardation time is the time required for dL/dt to decrease by a factor of e. For an element of viscosity η and elastic modulus E, τ=η/E. Integrating equation 1 with respect to time to obtain length at time t gives: 2 Maxwell elements are represented as a spring and a dashpot in series and exhibit exponential reduction in stress at constant length in stress relaxation assays. In practice, a Kelvin element identified in a creep assay will generally correspond to a Maxwell element in an equivalent stress relaxation assay. This reflects the limitations of visualizing such behaviour in terms of springs and dashpots. The third type of component is a log‐time function. Büntemeyer et al. (Büntemeyer et al., 1998) fitted measurements of creep of frozen and thawed Zea mays roots using the log‐time function 3 It was found that treating roots with IAA induced changes in tissue Ncreep which were consistent with growth inhibition in magnitude, threshold IAA concentration and the approximate duration. Provided that (Lt–L0) is small relative to Lt, equation 1 is equivalent to some of the ‘power laws’, often referred to in rheology as Nutting–Scott Blair equations and which have been found to describe the behaviour of many viscoelastic materials exhibiting variable viscosity, including concrete, pitch, flour‐dough, and cheese (Reiner, 1969; Scott Blair, 1969). Rheological models Equation 3 corresponded well to creep of tomato fruit epidermis for up to 30 min after increasing the applied force, but it was apparent that more prolonged extension could not be described by a single simple function, especially in material from rapidly growing fruit. Models used for analysis of the data were obtained by determining the function which corresponded most closely to initial extension and estimating parameter values from as short a period of creep as possible. Creep of this element was then calculated for the entire period of extension and subtracted fom the data. This process was repeated for the remaining data until a value of zero remained for the duration of the experimental period. This process allowed sequential identification of a number of elements describing creep over increasingly prolonged time scales. LVDT data for 240 min following an increase in the force applied to epidermal strips corresponded well to a model based upon a log‐time function element (LTE), two Kelvin elements with different retardation times (KE1 and KE2) and a viscous flow element (VFE). It was not known whether KE1, KE2 and VFE exhibited yield thresholds (i.e. minimum stresses required for extension to occur) and whether the viscosities were independent of stress and rate of extension. Instead, therefore, flow rates (or initial flow rates for KE1 and KE2) were calculated. Detailed information about the distribution of load between the epidermal cell layers and within the cell walls would have been necessary for accurate estimation of σ and use of flow rates in the calculations also eliminated this problem. For each element fn=σ/ηn. f1 and f2 are the initial flow rates of KE1 and KE2, respectively, and f3 the flow rate of VFE. Parameters describing the rheological properties of the sample were determined by fitting length at time t (Lt) using the equation: 4 (The extension rate is given by: dL/dt=Ncreep/t+f1 exp(−t/τ1)+f2 exp(−t/τ2)+f3. Equation 3 can be obtained by integrating this equation with respect to time.) k is required because LTE cannot be extrapolated to zero time (instantaneous tissue elasticity was incorporated into k as the log‐time function cannot be extrapolated to t0). τ1 and τ2 are the retardation times of KE1 and KE2, respectively. τ1 was typically 10–20 min and τ2, 70–120 min (although values outside these ranges were observed). Experimental data and modelled data generally correlated with r2>0.9995. As τ=η/E, element elastic modulus (E) of KE1 and KE2 can also be determined. For periods of extension which were too short for separation of KE2 and f3, extension of the strips was approximated by the following equation: 5f2 and f3 are combined as flow rate f(2+3). Correlation between up to 60 min of experimental data and modelled data generally correlated with r2>0.999. Figure 1 shows sample time‐courses of creep of epidermal strips incubated in buffers of differing pH during a series of step increases in applied force. Figure 2a is an example of the observed creep of an epidermal strip after the force applied to a strip bathed in buffer at pH 5.0 was increased from 0.392 N to 0.490 N, together with the behaviour fitted using equation 4. Figure 2b shows the same creep data together with the individual behaviour of each of the elements of the model. LTE and KE1 dominate the early creep behaviour (especially the first 30 min), while the effects of KE2 and f3 become more prominent over longer periods of extension. Examination of extremely long time‐courses (>12 h) suggested that f3 also decayed to some extent. This may indicate the existence of a third KE (and perhaps an additional non‐decaying flow rate, f4), but it is also possible that decay of f2 was slightly non‐exponential or exhibited a distribution of retardation times rather than a single discrete retardation time. Unfortunately, the method of data analysis employed was unable to obtain the parameters of expanded versions of equation 4 including common models of the behaviour of substances exhibiting a spectrum of multiple retardation times. f2 and f3 determine the behaviour of the strips over time scales analogous to growth and may arise from similar polymer interactions to those involved in growth. f3 at pH 5.0 was generally slightly greater than the fruit RER prior to harvest. In this paper, unloading of strips has not been examined but a preliminary experiment is illustrated in Fig. 3. The tissue strips exhibited a considerable degree of hysteresis (as described by Hohl and Schopfer; 1992) but some deformation remained even after the tissue had been completely unloaded for 12 h (this was the case even if the LVDT cores had been lifted off the cantilever arms so that the strips became slack). Permanent deformation equalled or exceeded that predicted assuming that only f3 was irreversible. In the example illustrated, permanent deformation exceeded the combined predicted extension of KE1, KE2 and VFE. It is therefore clear that although hysteresis is likely to be an important consideration in short‐term experiments, it is not an adequate explanation for long‐term behaviour. Fig. 1. Open in new tabDownload slide Time‐course of creep of epidermal strips incubated in buffers of different pH during a series of step increases in applied force. The force was increased by 0.098 N at intervals of 2 h. The buffers were pH 4.5 (○), pH 5.0 (•), pH 5.5 (□), and pH 6.0 (▪). Lines connect all data points but symbols representing only every twelfth data point were plotted. Fig. 2. Open in new tabDownload slide Example of creep of tomato epidermal strip in pH 5.0 buffer after the applied force was increased from 0.392 N to 0.490 N (○). Graph (a) also shows an equivalent series of values calculated using parameters obtained by fitting equation 4 to the data (white line). The inset graph shows the relationship between experimental data and modelled values. Graph (b) shows the data together with the behaviour of each element of the rheological model, i.e. the log time function (□), KE1 (▾), KE2 (▵), and viscous flow f3 (▴). Lines connect all data points, but symbols representing only every twelfth data point were plotted. Fig. 3. Open in new tabDownload slide Illustration of strip elongation including unloading to show permanent deformation (•). At arrows 1 to 5 the applied force was increased in stepwise increments to 0.490 N. The applied force was removed at arrow 6. At arrow 7 the LVDT core was removed for approximately 27 h so that the strip became slack. The LVDT core was replaced at arrow 8 (no data could be recorded between arrows 7 and 8). Calculated cumulative length increase due to f3 (○), KE2+f3 (□) and KE1+KE2+f3 (▵) are also shown (f3 for step increases to 0.392 N was estimated from the average ratio of f(2+3) to f3). Materials and methods Plant material Tomato plants (cv. Counter, donated by De Ruiter Seeds, Bergschenhoek, Netherlands) were grown in compost (Levington M3, Levington Horticulture Ltd., Ipswich, UK) in a greenhouse as described previously (Thompson et al., 1998). Flowers were pollinated by hand and trusses pruned to four fruit. Fruit 31–37 mm diameter (20–26 d post anthesis) were picked early in the morning. RER of the fruit prior to harvest averaged 0.040±0.005 by diameter or 0.075±0.009 by surface area. Slices 2 mm wide were cut into the fruit using two razor blades mounted on a block and strips of fruit epidermis were peeled from the slices using a new hand‐held razor blade. Unless otherwise stated the strips were immediately placed in 1.5 ml microfuge vials, which were then closed and dropped into liquid nitrogen for 5–10 min in order to kill the tissue cells. Seasonal changes in epidermal properties were observed, but all experiments were conducted using equivalent control tissue (in most cases strips prepared from the same fruit) and are internally consistent. Extensiometry Vials containing strips were removed from liquid nitrogen. The strips were thawed by pipetting 1 ml of room temperature 10 mol m−3 MES buffer (containing 5 mol m−3 KCl and 0.1 mol m−3 CaCl2, titrated to the experimental pH with 1 kmol m−3 NaOH) into each vial. Once thawed, one end of each strip was clamped to the bottom of a tube containing the same buffer as had been used to thaw the strip. The other end of the strip was clamped to one end of a cantilever so that 10–12 mm of the strip was exposed between the clips. Strips were completely immersed in buffer. The clamps were constructed of nylon rod of 10 mm diameter with a central machined slot 3 mm wide. The epidermal strip was placed into the slot and ‘sandwiched’ against its side with a 1.5 mm wide piece of epoxy‐glass board, which was then clamped against the strip by advancing a stainless steel screw through the nylon rod so that pressure was applied to the epoxy‐glass board. The pressure was sufficient to leave an impression upon the remaining pericarp material. The impression always remained at the edge of the clip at the end of the experimental period, demonstrating that the strips did not slip. The initial strip length was measured using a magnifying eyepiece with a graticule. Damage to strips during preparation or clamping resulted in exponentially increasing creep rates leading to failure allowing easy identification of such material. The cantilever was arranged so that the arm to which the strip had been fixed was one‐third of the length of the opposite arm in order to amplify strip extension mechanically. The maximum deviation of the cantilever from horizontal was ±0.06 radians, and so no mathematical or mechanical correction for rotation of the cantilever was implemented. An LVDT core (Schlumberger DFG 2.5 from RS Components Ltd., Corby, Northants, UK) was balanced on the end of the longer cantilever arm. The cantilever was counterweighted so that at minimum load the force applied to the strip was 0.004 N (counterweighting included the LVDT core weight and the weight and buoyancy of the upper clip). If the LVDT core was removed from the cantilever arm, the strip became slack. Output from the LVDT was recorded by a personal computer via a Bede PC‐ADH24 analogue input card (Bede Technology, Jarrow Tyne & Wear, UK; computer program written by the author). Every 35 s the LVDT core position was determined 1000 times and the average recorded. Resolution of the LVDT position was±0.2 μm. Six arrangements of tube, clips, cantilever, and LVDT were mounted on a weighted steel base‐plate. The base‐plate rested on tennis balls to dampen vibration and was placed inside a temperature controlled cabinet (construction described in Thompson et al., 1999). Experiments were carried out at 25 °C. Force was applied to the strips by sliding brass weights along the cantilever arms. In most experiments force was increased by 0.098 N increments every 2 h to a maximum of 0.49 N. The strips were allowed to extend at the maximum force for at least 4 h. Strip lengths were calculated relative to their length before the force applied to the strip was increased. Force was generally applied in a series of steps (rather than a single step) in order to allow analysis of the linearity of the relationship between applied force and rheological behaviour and to increase the resolution of LVDT position attainable (improved resolution could be achieved by limiting the range of input voltage). It was unfortunate that extended immersion of the strips in buffer was required, but separation of f2 and f3 required a data series covering a period of at least 2τ2 (determined empirically from analysis of data generated using equation 4). In rheological analysis of non‐biological material, molecular events only observable late in a time‐course can be determined earlier at elevated temperatures but this option is not readily available to researchers examining biological material. In order to minimize effects of immersion in buffer, MES was used even though some of the pH values required lay at the limits of its buffering capacity (pH of solutions were checked at the end of the time‐course). Also potassium and calcium were added to the experimental solutions in order to minimize the effects of loss of ions from the cell wall material. It remains possible that at least part of the decrease in extension rate over long incubation periods was due to enzyme inactivation (and would be likely to exhibit similar behaviour to a Kelvin element). However, extension of boiled strips in which high extension rates have been induced by treatment with calcium chelators is consistent with equation 4 and so this appears unlikely. Selection of experimental force Tissue pressure of fruit of equivalent age was determined using a procedure suggested by Dr M Malone (personal communication). The turgor pressures of fruit were determined using a pressure probe as described earlier (Thompson et al., 1998). A small piece of pericarp was then rapidly excised from the fruit using a new double‐edged razor blade, covered with a light coat of petroleum jelly and fixed in an enclosed optical methacrylate cuvette through which humidified air was passed. Water was also added to the bottom of the cuvette but it was ensured that no water came into direct contact with the pericarp tissue. Water droplets condensed on the side of the cuvette so it was assumed that relative humidity within the cuvette was very close to 100%. The new turgor pressure of the pericarp cells was then determined by inserting the pressure probe through a small window into the cuvette (the window was covered when the pressure probe was not in use). Pericarp turgor pressures were measured at intervals of 15 min for 2 h after the tissue was excised. The excised pericarp turgor pressure immediately fell to approximately 25% of the turgor pressure prior to excision. As no further decrease in turgor pressure was observed, it was assumed that the initial decrease was due to tissue relaxation, and that the difference between initial and final pericarp turgor pressure equalled tissue pressure in the intact fruit (detailed analysis in preparation). This procedure suggested tissue pressure in the experimental fruit to be approximately 0.17 MPa. Identical uni‐directional and multi‐dimensional stresses do not have the same effect because lateral contraction allows greater extension in the direction of the applied stress. The uni‐directional stress equivalent to a given multi‐dimensional stress can be calculated if the ratio of relative lateral contraction to relative longitudinal extension is known (Hejnowicz and Sievers, 1995a, b, 1996). This is known as the Poisson's ratio (ν). Poisson's ratios of the strips were determined by measurement of photographs of the strips taken using a Vivitar 100 mm f3.5 Macro 1:2×lens fitted with a matched 1:1×adapter (Vivitar UK Service, Westmead, Swindon, UK). Strip length was measured on the photographs using a ruler and strip width using an ocular graticule (Ernst Leitz Wetzlar Gmbh, D‐35578 Wetzlar, Germany). Photographs were taken immediately prior to each step increase in epidermal stress and at the end of the experiment. Assuming that the pericarp occupies approximately 50% of the cross‐sectional area, the epidermis of the experimental fruit was expected to experience a force of approximately 0.75 N mm−1in vivo. If it is assumed that v is the same laterally and longitudinally, then from Hejnowicz and Sievers (Hejnowicz and Sievers 1995a, b, 1996) the uni‐directional stress σu equivalent to a known multi‐dimensional stress σm is given by: 6 From the average Poisson ratio (0.72±0.05), a one‐dimensional force of approximately 0.42 N applied to a strip 2 mm wide should be equivalent to the two‐dimensional stress experienced by the epidermis in vivo (Hejnowicz and Sievers, 1995a, b, 1996). (If the thickness of the strips decreased by more than a marginal amount (3%), such a high value would probably indicate that water was forced out of the tissue during lateral contraction.) The maximum applied force (0.49 N) was selected in order to approximate this value. Analysis Models were fitted to time series of 60 min or 240 min of experimental data in Sigmaplot by minimizing squares of residuals. The effectiveness of models in describing experimental data was determined by calculating predicted results for time series equivalent to the experimental data using fitted model parameters and determining correlation with the experimental data using Excel. The efficacy of models in predicting extension of strips for time series longer than those used for curve fitting was also considered in assessing models. Results Interaction of applied force and pH Figure 4 shows the parameters obtained by fitting equation 4 to creep of strips after the applied force was increased from 0.392 N to 0.490 N. The strips were incubated in buffers of pH 4.5, 5.0, 5.5, and 6.0. f1, f2 and f3 were all considerably reduced at high pH. It has been suggested that the apoplast pH of many growing plant tissues falls between pH 5.0 and pH 6.0 (Schopfer, 1993) and so, although the apoplast pH of growing tomato fruit has yet to be investigated, it is interesting that pH affects these cell wall properties to such a degree within this relatively narrow range. Ncreep and τ1 were largely unaffected by pH, while τ2 appeared slightly reduced at high pH. The flow rates and retardation times of KE1 and KE2 suggest that the element elastic moduli were also considerably increased at high pH, especially KE2 (Table 1). The creep of strips incubated in buffers of pH 5.0, pH 5.5 and pH 6.0, and which experienced a series of short 0.098 N step increases in stress to a maximum of 0.490 N were analysed employing equation 5. The parameters obtained are presented in Fig. 5. The results were consistent with the analysis of longer term creep using equation 4. f1 and f(2+3) were reduced at high pH and this effect appeared more pronounced at higher stresses. Ncreep and τ1 were largely unaffected by pH. If 0.490 N was applied to the strips in a single step, Ncreep, f1 and f2 were approximately equal to the sum of values calculated for the incremental step increases while f3, τ1 and τ2 were approximately equal to the values at the maximum applied stress (results not presented). The effect of pH upon elements of the creep behaviour of the tomato epidermis suggests that in the growing fruit tested and at the experimental stresses employed, a significant component of epidermal behaviour was determined by cell wall and not cuticular properties. The force applied was also considerably greater than the fracture force of isolated tomato fruit epidermal cuticle (Petracek and Bukovac, 1995). This may not be the case throughout fruit development and it should be noted that the effect of pH was less marked when the applied force was small. Fig. 4. Open in new tabDownload slide The effect of pH on model parameters for an increase in the applied force from 0.392 N to 0.490 N. Mean values (±s.e.) obtained by fitting data to equation 4 are plotted (pH 4.5 n=20, pH 5.0 n=22, pH 5.5 n=19, pH 6.0 n=15). Fig. 5. Open in new tabDownload slide The effect of pH on model parameters for a series of step increases in the applied force by 0.098 N to a maximum of 0.490 N: pH 5.0 (•); pH 5.5 (▪); pH 6.0 (▴). Mean values (±s.e.) obtained by fitting data to equation 5 are plotted (pH 5.0 n=10, pH 5.5 n=7, pH 6.0 n=8). Table 1. Treatment effects on the relative elastic moduli of KE1 (E1) and KE2 (E2) Treatment E1 (N strip−1) E2 (N strip−1) pH 4.5 20.3 3.2 pH 5.0 26.8 4.5 pH 5.5 29.5 9.0 pH 6.0 39.9 19.1 pH 5.0 control 17.5 5.4 pH 5.0 boiled 28.3 7.6 pH 6.0 control 29.5 15.7 pH 6.0 boiled 24.3 10.6 Treatment E1 (N strip−1) E2 (N strip−1) pH 4.5 20.3 3.2 pH 5.0 26.8 4.5 pH 5.5 29.5 9.0 pH 6.0 39.9 19.1 pH 5.0 control 17.5 5.4 pH 5.0 boiled 28.3 7.6 pH 6.0 control 29.5 15.7 pH 6.0 boiled 24.3 10.6 Open in new tab Table 1. Treatment effects on the relative elastic moduli of KE1 (E1) and KE2 (E2) Treatment E1 (N strip−1) E2 (N strip−1) pH 4.5 20.3 3.2 pH 5.0 26.8 4.5 pH 5.5 29.5 9.0 pH 6.0 39.9 19.1 pH 5.0 control 17.5 5.4 pH 5.0 boiled 28.3 7.6 pH 6.0 control 29.5 15.7 pH 6.0 boiled 24.3 10.6 Treatment E1 (N strip−1) E2 (N strip−1) pH 4.5 20.3 3.2 pH 5.0 26.8 4.5 pH 5.5 29.5 9.0 pH 6.0 39.9 19.1 pH 5.0 control 17.5 5.4 pH 5.0 boiled 28.3 7.6 pH 6.0 control 29.5 15.7 pH 6.0 boiled 24.3 10.6 Open in new tab Creep of boiled strips In these experiments strips were immersed in boiling water for 45 s before immersion in liquid nitrogen for 5–10 min. The strips were thawed in buffers of pH 5.0 or 6.0 and fixed for extensiometric assay. Force was applied to the strips in 0.098 N increments to a maximum of 0.490 N. Creep of the strips after the force was increased from 0.392 N to 0.490 N was analysed using equation 4 to give the results shown in Fig. 6. The effect of boiling upon Ncreep and f3 of strips incubated at pH 6.0 (and to a lesser extent the effect on Ncreep of strips incubated at pH 5.0 and τ2 of strips incubated at pH 6.0) appear to indicate that the cell wall structure was affected by boiling. It was assumed that boiling would inactivate many cell wall enzymes, but these effects can most plausibly be attributed to denaturing of structural proteins and perhaps some solubilization of pectins. f1, f2 and f3 of boiled strips incubated at pH 5.0 were all reduced to the flow rates observed in unboiled strips incubated at pH 6.0. This suggests that the effect of pH on each of the flow rates is dependent upon enzyme activity. The effects of pH and boiling upon f1, f2 and f3 are similar to their effect upon expansins and so these rheological elements plausibly reflect activity of expansins or similar proteins (McQueen‐Mason, 1995). It is interesting that none of the separate viscous flows were completely eliminated by boiling or at increased pH. The increase in f3 in boiled strips incubated at pH 6.0 is puzzling, but may correspond with the similar increase in Ncreep. It is possible that an effect of boiling upon f3 of strips incubated at pH 5.0 was hidden by the effect of enzyme inactivation. Although the increase in τ2 at pH 6.0 demonstrates a decrease in E2, the apparently similar effect on τ2 at pH 5.0 is more than off‐set by the decrease in f2, so that an increase in E2 results (see Table 1). This further suggests that boiling results in ‘stiffer’ cell walls at pH 5.0 and ‘looser’ cell walls at pH 6.0. Analysis of creep of boiled strips after the step increases in applied force using equation 5 exhibited a similar pattern of behaviour to long‐term creep at the maximum applied force. Fig. 6. Open in new tabDownload slide Effect of boiling on model parameters of epidermal strips incubated at pH 5.0 and pH 6.0 for a step increase in force from 0.392 N to 0.490 N. Values are ratios of means of parameters obtained by fitting creep of boiled and control strips to equation 4 (pH 5.0, filled columns; pH 6.0, unfilled columns; n=6 for all values). Comparison with artificial polymer creep compliance Many artificial polymers share characteristic patterns of stress relaxation and creep compliance with time. Such patterns are often summarized as ‘master curves’ using logarithmic scales (Ward and Hadley, 1993; especially Fig. 6.7–6.10). A plot of relative length against time using logarithmic scales (Fig. 7) appears to share many characteristics with parts of such polymer creep compliance master curves. Such curves generally consist of three or more approximately straight lines separated by transition periods. The straighter sections of the curve approximate log‐time functions of the type proposed earlier (Büntemeyer et al., 1998) and are each thought to correspond with a predominance of particular types of molecular movement (Matsuoka, 1992). In the initial period ‘glassy’ behaviour is observed and creep is largely due to intramolecular movement. There follows a transition to a second phase of ‘viscoelastic’ behaviour believed to result from movement of molecules relative to one another. In this period polymer molecular weight affects creep to a large degree and so transglycosylases and glycanases might be expected to alter cell wall behaviour. Interpretation of Fig. 7 in this context suggests that in epidermis from growing fruit incubated at pH 5.0, creep events prior to approximately e2.5 (12 min) are primarily due to intramolecular events, presumably conformer rotation. The duration of this period indicates that intermolecular cooperativity is necessary for such rotation to occur. This is consistent with the limited mobility of xyloglucan and cellulose polymers observed in cucumber cell walls using C13 NMR spectroscopy (Fenwick et al., 1999). Similarly events after e4.5 (90 min) are likely to be largely due to the movement of cell wall polymers relative to one another. It is interesting that although such a transition from glassy to viscoelastic behaviour was observed in epidermis of growing fruit at pH 6.0 and epidermis of mature fruit which had ceased to grow at pH 5.0, the transition was much less pronounced. Preliminary examination of cell walls from growing and mature leaves suggests that the magnitude of this transition from glassy to viscoelastic behaviour is a general and perhaps defining property of tissues capable of growth. Over longer time periods a third stage of ‘rubbery’ behaviour thought to be due to movement of cross linked or ‘tangled’ matrices becomes apparent in artificial polymers, but this has not been observed in the experiments reported. Fig. 7. Open in new tabDownload slide Plot of log‐relative length of epidermal strips of growing fruit incubated at pH 5.0 (○), strips of growing fruit incubated at pH 6.0 (□) and strips of non‐growing mature fruit incubated at pH 5.0 (▵) against log‐time after a step increase in applied force from 0.392 N to 0.490 N. Discussion The model It may appear that the model corresponding to equation 4 is excessively complex. It should, however, be noted that the components of the model fall into two clear groups. As may be seen from Fig 2b, LTE and KE1 describe short‐term creep and KE2 and VFE medium to long‐term behaviour. Medium to long‐term behaviour must include both decaying and non‐decaying components and this could not be accomplished with fewer parameters than the three required by KE2 and VFE. On the other hand, LTE and KE1 correspond closely in the time scale of their extension. Although models including only LTE or KE1 did not exactly reproduce the shape of curves representing experimental data, these simpler models were only marginally less effective than equation 4 and may be preferable on the grounds of parsimony. Both elements were retained because both pH and boiling affected LTE and KE1 differently. It seems likely that LTE and KE1 correspond to similar molecular events or to different components of the same events but it was felt that the presence of separate elements corresponding to pH dependent and independent behaviour is likely to be of mechanistic importance. Retention of both elements is therefore probably unnecessary in the analysis of experiments conducted for purely physiological reasons. Alternative models A number of rheological elements more complex than Kelvin elements have been described. ‘Burgers’ and ‘Jeffreys’ bodies include a viscous flow element in series with a Kelvin element so that viscous flow is added to the behaviour of the Kelvin element (a Burgers body additionally includes an instantaneous elastic element). Long‐term creep of the epidermal strips (>1 h) can be described by a Jeffreys body (i.e. KE2 and VFE together constitute a Jeffreys body). Overall, however, replacing components with a Jeffreys or Burgers body did not modify or simplify the model behaviour (instantaneous elasticity included in k could be incorporated into a Burgers body). ‘Poynting and Thomson’ and ‘Lethersich’ bodies are similar to Kelvin elements but each include an extra component. A Poynting and Thomson body has an elastic element and a viscous flow element parallel to an elastic element, while a Lethersich body has an elastic element and a viscous flow element parallel to a viscous flow element. Extension of these bodies is indistinguishable from a Kelvin element (or a Kelvin element in series with an elastic element for a Poynting and Thomson body) but exhibit different behaviour during unloading. Data such as that presented in Fig. 3 suggests that KE1 and KE2 may be Lethersich bodies which (unlike Kelvin elements) retain some irreversible deformation after stress is removed. Other models such as the ‘Schofield and Scott Blair’ body include a viscous flow element exhibiting a yield threshold. This type of behaviour did not affect formulation of the model because flow rates were used rather than viscosities but the data presented in Fig. 5 suggests that there is probably a low yield threshold. The similarity of f(2+3) at pH 5.0 and pH 6.0 at low loads also indicates that enzyme mediated creep may require a rather higher minimum stress. Another important group of models are those which describe rheological elements with a range of retardation times. Such retardation time spectra often correspond to populations of polymers of a range of molecular weights (Matsuoka, 1992) and so it is regrettable that the curve‐fitting procedures employed could not reliably utilize equations derived from these models. It seems likely that KE1 and KE2 (and perhaps also LTE) approximate this type of behaviour. Physiological importance of the rheological parameters The relationship between cell wall stress, tissue mechanical properties and growth rate in vivo has often been considered in terms of the ‘Lockhart equation’ (Lockhart, 1965). 7r is the growth rate, ϕ is generally referred to as extensibility, P is the tissue turgor pressure (i.e. the source of cell wall stress), and Y the yield threshold (i.e. the minimum turgor pressure required for growth). The model presented suggests an in vitro parameter equivalent to ϕ. ϕ appears to be the inverse of the viscosity of a rheological element and VFE specifically appears analogous to plant growth at steady turgor as considered by Lockhart. It can therefore be suggested that f3/σ (or 1/η3) is plausibly equivalent to in vivo tissue extensibility. This is consistent with the similar magnitude of f3 and the fruit growth rate prior to harvest. The Lockhart equation would describe tissue behaviour accurately if η3 behaved in a Newtonian fashion (i.e. viscosity was unaffected by flow rate). This appeared to be largely true. A yield threshold would arise if work was required to deform the wall permanently in addition to frictional energy losses (Veytsman and Cosgrove, 1998). The biochemical implications of the rheological parameters The viscosities of KE1, KE2 and f3 were decreased at low pH but this effect was abolished by boiling, suggesting that each of the flow rates was increased by enzyme activity. Expansins were initially detected as a conrsequence of their effects on creep of boiled cell walls at low pH (McQueen‐Mason et al., 1992). It therefore seems likely that expansins are a component of enzyme promotion of viscous flow in this system. Interestingly, the elastic moduli of KE1 and KE2 were also considerably reduced at low pH. This effect was reduced in boiled strips. This observation suggests that both the viscosity and elasticity of the polymers and polymer composites with which expansins interact are affected by expansin activity. Taken together these observations suggest that expansins may be involved in mediating different types of polymer interaction and movement within the cell wall. This may shed light upon the exact role of expansins in vivo. Ncreep, however, was largely unaffected by pH and was increased by boiling and therefore appears to be independent of expansin activity. Time scales of creep retardation Interpretation of the creep of tomato fruit epidermal strips in the light of creep compliance behaviour of artificial polymers provides another powerful tool for examining the nature of plant growth responses (even though such an interpretation also suggests that the classical rheological models employed in equations 4 and 5 are probably somewhat simplified, and that τ1 and τ2 are more likely to be ‘characteristic retardation times’ of retardation time distributions than unique values). Placing equation 4 and 5 parameters in a temporal context from the time scales in which they exert greatest influence upon overall behaviour allows characterization of the nature of the biophysical events likely to be described by the parameters. The log‐time function and KE1 dominate the early creep of the strips and are, therefore, probably due to intramolecular movement (conformer rotation), while f3 dominates later creep behaviour and reflects movement of polymers relative to one another. KE2 is most important during the transition between these two periods and is more likely to involve conformer rotation, either of a different population of polymers or as a part of a prolonged retardation spectrum. pH and boiling affect behaviour of KE1, KE2 and f3 suggesting that expansins are capable of catalysing several different types of molecular movement. Transitions from glassy to viscoelastic behaviour can also result from temperature increases. This is thought to be due to an increase in the free space within the polymer matrix. Likewise intramolecular movements in the glassy state are thought to be considerably affected by the degree to which conformer rotation is constrained by adjacent conformers (and therefore conformer density). As expansins appear to affect both these processes, it can be argued that a component of expansin action may involve creation of free space within the polymer matrix. This would be consistent with the high levels of expansin gene transcription observed in ripening fruit, which are generally not growing, but where cell wall swelling is often observed (Rose and Bennett, 1999). The strong effects of pH upon f1, f2 and f3 could be interpreted as evidence for the acid growth theory, but it should be noted (Büntemeyer et al., 1998) that IAA‐treatment was found to cause a rapid change in Ncreep. Ncreep does not appear to involve expansin activity and so some components of auxin action are likely to be independent of expansins and pH. Extensiometric methodology It has already been proposed that f3 provides the best in vitro measure of interaction between tissue growth and cell wall properties, however f(2+3) from equation 5 is easier to obtain (requiring a much shorter period of tissue creep) and shares enough properties with f3 to suggest some common biochemical mechanisms. Consequently, for many experimental purposes use of equation 4 to analyse relatively short time‐courses may be preferable. It should also be noted that KE1 constitutes a relatively minor component of strip behaviour and is difficult to resolve, and could be omitted under many circumstances. Another useful assay method may be to measure the approximate gradients of the glassy and viscoelastic extension periods of log‐time against log‐length plots such as Fig. 7. The glassy gradient is essentially identical to the log‐time function suggested previously (Büntemeyer et al., 1998) and probably reflects polymer conformer rotation, while the viscoelastic gradient is likely to indicate polymer flow and long‐term extensibility. Summary Although it has long been known that plant cell wall mechanical properties affect plant growth rates to a large degree, simple and unambiguous assay of these properties in vitro has proven problematic. Technically, the simplest assay method is the creep extensiometer and in this paper a rheological model of creep of tomato epidermis is suggested which appears to contain elements analogous to plant growth in vivo. Furthermore, these results can be interpreted in the light of research into rheology of artificial polymers to create a powerful framework for analysis of the biomechanics of tomato fruit epidermis. 1 Fax: +44 20 7911 5087. E‐mail: thompss@wmin.ac.uk Philip Smith constructed the extensiometer and other equipment. I also wish to thank Dr Harry Pinkerton for advice on rheology, Dr Mike Malone for suggesting the tissue pressure assay and Professor Bill Davies and Dr Jane Taylor for their comments upon the manuscript. Seed was kindly donated by De Ruiter seeds. The work was funded by MAFF. References Andrews J, Malone M, Thompson DS, Ho LC, Burton KS. 2000 . Peroxidase isozyme patterns in the skin of maturing tomato fruit. Plant, Cell and Environment 23, 415 –422. Google Scholar Crossref Search ADS Büntemeyer K, Lüthen H, Böttger M. 1998 . Auxin‐induced changes in cell wall extensibility of maize roots. Planta 204, 515 –519. Google Scholar Crossref Search ADS Cleland RE. 1984 . The Instron technique as a measure of immediate‐past wall extensibility. Planta 160, 514 –520. Google Scholar Crossref Search ADS Cleland RE. 1992 . 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TI - Extensiometric determination of the rheological properties of the epidermis of growing tomato fruit
JF - Journal of Experimental Botany
DO - 10.1093/jexbot/52.359.1291
DA - 2001-06-01
UR - https://www.deepdyve.com/lp/oxford-university-press/extensiometric-determination-of-the-rheological-properties-of-the-5F0yPXpolA
SP - 1291
EP - 1301
VL - 52
IS - 359
DP - DeepDyve
ER -