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. 2011 Nov 23;109(2):419–427. doi: 10.1093/aob/mcr296

A mathematical model of mucilage expansion in myxospermous seeds of Capsella bursa-pastoris (shepherd's purse)

Wenni Deng 1,2,3,*, Dong-Sheng Jeng 1, Peter E Toorop 4, Geoffrey R Squire 3, Pietro P M Iannetta 3
PMCID: PMC3268541  PMID: 22112439

Abstract

Background and Aims

Myxospermy is a term which describes the ability of a seed to produce mucilage upon hydration. The mucilage is mainly comprised of plant cell-wall polysaccharides which are deposited during development of those cells that comprise the seed coat (testa). Myxospermy is more prevalent among those plant species adapted to surviving on arid sandy soils, though its significance in determining the ecological fitness of plants is unclear. In this study, the first mathematical model of myxospermous seed mucilage expansion is presented based on seeds of the model plant species Capsella bursa-pastoris (shepherd's purse).

Methods

The structures underpinning the expansion process were described using light, electron and time-lapse confocal micrographs. The data and experimental observations were used to create a mathematical model of myxospermous seed mucilage expansion based on diffusion equations.

Key Results

The mucilage expansion was rapid, taking 5 s, during which the cell mucilage volume increased 75-fold. At the level of the seed, this represented a 6-fold increase in seed volume and a 2·5-fold increase in seed surface area. These increases were shown to be a function of water uptake (16 g water g−1 mucilage dry weight), and relaxation of the polymers which comprised the mucilage. In addition, the osmotic pressure of the seed mucilage, estimated by assessing the mucilage expansion of seeds hydrated in solutions of varying osmotic pressure, was –0·54 MPa (equivalent to 0·11 m or 6·6 g L−1 NaCl).

Conclusions

The results showed that the mucilage may be characterized as hydrogel and seed-mucilage expansion may be modelled using the diffusion equation described. The potential of myxospermous seeds to affect the ecological services provided by soil is discussed briefly.

Keywords: Capsella bursa-pastoris, shepherd's purse, myxospermy, seed mucilage, mathematical model

INTRODUCTION

Plant mucilage is produced by many different species of plant species and in plant parts that include seeds, leaves and roots (van Rheede, van Oudtshoorn and Van Rooyen, 1999). It provides functional advantages such as water storage (especially in succulents; Landrum, 2002), a lubricant for growing roots as they penetrate soil (Guinel and McCully, 1986), and a trap for prey in carnivorous plants (Vintéjoux and Shoar-Ghafari, 2000; Adlassnig et al., 2000). Despite the ecological functions plant mucilage may perform, the underpinning capacity of mucilage to hold water, as by myxospermy, has received most attention (Ryden et al., 2000; Singh et al., 2007; Zimmermann et al., 2007).

Myxospermy is a trait that defines the ability of a seed to become sheathed by a mucilaginous coat upon hydration in water (Frey-Wyssling, 1976; Grubert, 1981). Myxospermy is associated with the seeds of many different plant families and species in different parts of the world. It predominates among members of the Angiospermae, having been reported for seeds of species within phylogenetically diverse, and predominantly dicotyledonous, plant families such as the Brassicaceae, Asteraceae, Cistaceae, Solanaceae, Linaceae and Plantaginaceae (Grubert, 1974, 1981), and especially species that commonly occur as weeds (Young and Evans, 1973). Angiosperms are characterized by their ability to reproduce and persist using seeds, and, while seeds are variable and complex structures, the basic form comprises three main components: embryo, endosperm and seed coat (testa). Seed mucilage is mainly comprised of plant cell-wall polysaccharides (pectin, hemicellulose and cellulose), which are deposited during development within those cells that comprise the seed coat (Western et al., 2000; Windsor et al., 2000), the myxospermous capability becoming apparent when the mucilage within the apoplastic space hydrates.

Despite the broad phylogenetic basis for this trait, myxospermy has been mainly characterized from studies of the model plant species Arabidopsis thaliana (arabidopsis; Western et al., 2000; Willats et al., 2001; Macquet et al., 2007; Arsovski et al., 2009). However, it has also been noted from ecological surveys that a high proportion of those plant species which persist in arid desert environments possess myxospermous seeds or seed-pods (Murbeck, 1919; van Rheede van Oudtshoorn and Van Rooyen, 1999). A selective advantage of myxospermy as an aid to plant fitness in these niches is therefore implicated, possibly through improved germination. For example, the intact achenes of Artemisia sphaerocephala (Asteraceae) which contain mucilage in their pericarp, exhibited a higher germination rate than that of demucilaged achenes (Yang et al., 2010). It has also been proposed that myxospermous seeds improve contact and adhesion to soil particles (Grubert, 1974).

The ultimate aim of this study is to empower theoretical investigations of myxospermous seed–soil interactions using a mathematical model of myxospermous seed mucilage expansion, which is to be developed in two stages. The first stage, presented here, is based on experimental data of mucilage expansion for the myxospermous seeds of a model weed species (Capsella bursa-pastoris; shepherd's purse), hydrating in simple environments (seeds immersed in solutions of increasing osmotic pressure). The data are used to create the initial mathematical model of myxospermous seed mucilage expansion, capable of predicting features such as the rate of water ingress, the rate of mucilage expansion and the volume and density of mucilage. In the second phase, the model will be developed and applied iteratively to more complex and variable environments.

Shepherd's purse, is a widespread and abundant arable weed (Hawes et al., 2005; Iannetta et al., 2007; Begg et al., 2011), and is presented as a model plant species for studies of plant adaptation and persistence in arable fields (Iannetta, 2011). The composition and stages of mucilage expansion for shepherd's purse have been characterized. The general structure and composition are similar to that described for the genetically syntenous species arabidopsis (Iannetta, 2011). There are important differences, however, between arabidopsis and shepherd's purse. Notably, shepherd's purse seeds are heteromorphic, occurring in myxospermous and non-myxospermous forms. Seed heteromorphism is proposed as a bet-hedging strategy while the absence of the myxospermous capability is correlated with reduced seed dormancy (Toorop et al., 2012). Furthermore, shepherd's purse is among the most commonly occurring in-field, broadleaf weed species.

From assessment of the water-holding capacity of polysaccharides (Guinel and McCully, 1986; Sealey et al., 1995; McCully and Sealey, 1996; McCully and Boyer, 1997), seed mucilage may be characterized as a ‘gel’ (Tibbits et al., 1998; Zwieniecki et al., 2001) – a three-dimensional, cross-linked, hydrophilic polymer that exhibits the properties of both solid and liquid states. Numerous theoretical models have been proposed to simulate gel expansion under different environmental conditions, which include temperature, pressure, pH and ionic strength (Tanaka and Fillmore, 1979; Peters and Candau, 1988; Birgersson et al., 2008; Hong et al., 2008; Wallmersperger, 2009; Lai and Li, 2010). Among those of greatest potential utility are models based upon the conservation of energy, mass and momentum. For example, Flory (1953) established a thermodynamic theory from energy conservation laws to define ‘equilibrium volume transitions’, i.e. those environmental thresholds at which gel properties alter from one condition to another (such as solid- to liquid-type changes). While this approach provides the equilibrium volume transition of gels, the parameters for these models are difficult to obtain as they are assumed to be based upon molecular interactions. In contrast, the transient volume changes of gels may be captured by diffusion equations based on the theories of mass conservation (Thomas and Windle, 1982; De Kee et al., 2005). In diffusion models, the osmotic pressure of the solute is the driving-force for changes in gel volume.

Accordingly, a first mathematical model of myxospermous seed mucilage expansion based on equations of water diffusion is presented here. Micrographs of hydrated seeds were used to parameterize the timing of expansion, and the dimensions of those cells that contain the polysaccharide before (dry) and after expansion (hydrated). The proposed mathematical model is compared with data generated from mucilage expansion of seeds imbibed in solutions of different osmotic pressure.

MATERIALS AND METHODS

Microscopy

Ultra-structural measurements were made from light micrographs of hydrated myxospermous seed of Capsella bursa-pastoris (L.) Medik., sectioned after embedding in either Tissue-Tek™ (frozen) or wax (at room temperature). For cryo-sections, seeds were hydrated in deionized water for 1 h before immersion in phosphate-buffered saline (0·1 m, pH 7) containing 30 % (w/v) sucrose, incubated overnight at –4 °C, then embedded for sectioning in Tissue-Tek™ (#R1180; Agar Scientific) and frozen using liquid nitrogen. Cryosections (8 µm thick) were cut in a cryotome (Cryostat Leica CM3050 S) and placed on SuperFrost™ plus slides (#631–0108; VWR International). Sections were stained with 0·2 % (w/v) Toluidine Blue (#T3260; Sigma-Aldrich, Poole, UK) for 10 min, rinsed three times (using running tap water) and dried (5 min) on a slide heater. The sections were observed using a stereomicroscope (Leica MZFLIII attached to Leica DC500 camera). For sectioning of wax-embedded samples, seeds hydrated in water were embedded directly in molten paraffin wax (VWR International, Poole, UK) within a metal cradle and sectioned using a Leica Microtome (RM2125RT; Wetzlar, Germany).

Observations and measurements of seed surfaces were made from cryo-SEM and time lapse confocal images. For cryo-SEM, seeds were rapidly frozen in liquid nitrogen within the freezing-chamber of an Oxford Instruments Alto 2500 cryo-preparation system. The samples were then transferred under vacuum to the cryo-stage where they were warmed to –95 °C for 5 min to sublime surface water. After sublimation the samples were cooled to –115 °C prior to coating with 5 µm gold/palladium. Specimens were examined using a Philips XL30 SEM operating at a voltage of 15 kV. Micrographs were taken with a focused ion beam-scanning electron microscope (FIB-SEM) from samples that were plunge-frozen in liquid nitrogen slush at −210 °C and transferred under vacuum using a Quorum Technologies PP2000T cryo transfer system (Quorum Tech. Inc., Guelph, Canada) to the cryo-preparation chamber of an FEI Quanta200 3D DualBeam FIB-SEM (FEI Europe, Eindhoven, The Netherlands). The sample temperature was raised to –95 °C to sublime condensed surface ice and the sample sputter coated with platinum. The sample was passed through the transfer lock to the FIB-SEM cryo-stage, which was held at −145 °C and imaging performed using an accelerating voltage of 10 kV. For confocal microscopy, seeds were hydrated in water with 0·2 % (w/v) calcofluor (#F3543; Sigma-Aldrich) for 30 min. A small volume of solution was pipetted into the gap between a slide and raised cover-slip to allow visualization without the seed being compressed by the cover-slip. Calcofluor-treated samples were visualized using a UV light source. The seeds were observed with an inverted Nikon Ti-Eclipse or Leica SP2 confocal microscope using a blue diode (405nm) laser (Nikon Instruments Europe BV, Kingston, UK).

Weight of shepherd's purse seed

For each of three replicates, 1000 shepherd's purse seeds were weighed to four decimal places. These seeds were placed into a cylindrical column (2 cm diameter, 1 cm height) cut from a long white plastic pipe, and onto which a disc of plastic mesh (0·2 mm) was glued. Columns were placed in a shallow trough of water (2 mm depth) to allow hydration from the base of the column. Then the column was removed from the water and excess water was removed by filter paper before weighing. The weight of hydrated seeds was measured every hour until a plateau was reached.

The relative weight of the soluble and non-soluble components of shepherd's purse seed mucilage was estimated by weight comparison after seed treatment by cell-wall degrading enzymes (water as a control). Mucilage removal was possible after incubation in Cellic™ CTec (density 1·15 g mL−1; Novozymes A/S, Denmark) at pH 5·5. The degradation of the cellulosic component appeared to facilitate complete removal of the innermost component, which was difficult to remove normally (i.e. with aqueous solutions). Two groups of shepherd's purse seeds (each group had six replicates of 5 g) were mixed with distilled water (1 : 10, w/v). One group of seeds was shaken for 48 h at 50 °C, while the other group was treated with Cellic™ CTec [12 % (w/w) of seed weight] and shaken for 48 h at 50 °C. The seeds of each group were washed (three times) before centrifugation (3000 g, 20 min). The supernatants from both extractions were collected and freeze-dried for 5 d. The remaining seeds were dried at room temperature for 5 d, before being weighed to record their relative mucilage loss: the weight decline being expressed as a percentage of the original pre-treatment seed weights.

Estimating the osmotic pressure of the shepherd's purse seed mucilage

Approximately 40 shepherd's purse seeds were immersed in 2·5 mL of PEG (polyethylene glycol) 6000 solutions containing 0·02.% (w/v) Toluidine Blue for 20 min. The PEG concentrations ranged from 0 % to 30.% (w/v) with sterile distilled water. The corresponding osmotic pressure of PEG solutions was calculated according to Michel (1983). Seed mucilage size after expansion was measured from digital images taken using a microscope (Leica MZFLIII with Leica DC 500) under illumination with white light. Images were analysed using ImageJ software (http://rsbweb.nih.gov/ij/). The shape of shepherd's purse seed is assumed to be ellipsoid (prolate spheroid), with sizes a = b < c, where a, b and c are the seed width, thickness and length, respectively. Thus, the seed volume and surface area are assessed using 4/3πabc and 2π(a2 + c2α/tan α), respectively, in which α = arccos(a/c). Three replicates of 40 seeds were used to estimate mucilage expansion in each PEG solution.

MODELLING SEED MUCILAGE EXPANSION

Shepherd's purse seed mucilage expansion: process description

The testa of shepherd's purse seeds is composed of a layer of hexagonal cells within which the mucilage is synthesized and deposited during seed development (Fig. 1A). The individual testa cells are shown under increasing magnification (Fig. 1B–D), and key features, such as the central columella (Fig. 1D), are shown relative to the size of the subtending periclinal cell walls (Fig. 1E). This structure is represented schematically in Fig. 2A. The inner-most periclinal wall (closest to the endosperm and embryo) and short side walls appear as thickened secondary cell walls. The outer periclinal wall is a flexible primary cell wall that appears to be anchored at the top of each short wall that borders each testa cell, and seems also attached to the central columella. The shepherd's purse seed mucilage is mainly comprised of pectin which is embedded in a matrix of cellulose fibres (P. P. M. Iannetta, unpubl. res.). During hydration, the outer periclinal cell wall is raised at the radial cell walls, and is subsequently ruptured by the expanding pectin and unfurling cellulose fibres to form a ‘boundary layer’ which marks the outermost limit of the cellulose network. The pectinaceous component of the mucilage extends beyond the boundary layer to form an outer sheath. An equivalent process, taking up to 20 s, has been reported in arabidopsis seed mucilage expansion (Arsovski et al., 2009). Also, it was reported that the outer layer of mucilage appeared soluble, while the inner layer of mucilage was strongly attached. The inner and outer layers possessed different chemical compositions that affected hydration speed differentially: the inner mucilage hydrated more slowly than the rapidly expanding soluble outer mucilage, which is mainly comprised of unbranched rhamnogalacturonan I. However, the whole process can be simulated as water movement through the periclinal cell wall and the resultant expansion of the contained mucilage.

Fig. 1.

Fig. 1.

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Capsella bursa-pastoris seed coat structure shown using scanning electron (A–D) and light (E) micrographs. (A) A whole shepherd's purse seed. (B–D) the testa cells that form the surface of shepherd's purse seed under increasing magnification. The central columella is identified by an asterisk in (B) and (C) while (D) shows the columnella under highest magnification. (E) Section taken from a paraffin wax-embedded seed, showing a sectional view of the columella (*) which is an outgrowth of the testa [thickened secondary seed coat cell walls (cw)]. This micrograph also shows a gap (g), which is an artefact caused by the embryo dissociating from the seed coat and subtending endosperm cells (e; the lumen of an endosperm cell). There is no physical connection between the embryo and endosperm. The endosperm consists of a single cell layer (also with thickened walls), which lies beneath the cell layer which comprises the seed coat. Scale bars: (A) = 100 µm; (B, E) = 40 µm; (C, D) = 10 µm.

Fig. 2.

Fig. 2.

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Schematic representations of seed mucilage expansion in Capsella bursa-pastoris. (A) The testa cells and internal dry mucilage in a dry state (I), and a fully hydrated state (II). For I and II, light-grey shading denotes the pectinaceous component, and hatching the orientation of cellulose fibres (P. P. M. Iannetta et al., unpubl. res.). The thick black lines show the periclinal secondary thickened cell walls at the base and sides of each cell. The uppermost diagonal black line at the top of each cell denotes the uppermost (primary) periclinal cell wall. The central columella has internal diagonal hatching and a dark-grey infill. (B) The dimensions of the mucilage-filled void situated between the columella and the outer wall are shown, simplified as a rectangle and shown in sectional half-cell view. The large arrow shows the direction and face through which water ingress occurs. The numbers 1–4 relate to each of the four cell-walls (boundary conditions) used for the half cell which is modelled, each boundary being attributed relative characteristics for the simulation of water ingress. Respectively, these relate to columella, innermost surface, uppermost surface and thickened vertical wall. The other parameters used for mathematic modelling are given in Table 1.

Mathematic model

Governing equation

The mass transfer of water into a testa cell is governed by a diffusion model:

graphic file with name mcr296eqn1.jpg (1)

where C is water content of mucilage, t is time, D is a diffusion coefficient and ∇ denotes the vector differential operator.

Boundary and initial conditions

Figure 2B shows a diagrammatic representation of the testa cells and mucilage expansion. The flux at boundary 3 (uppermost wall; Fig. 2B) is determined by:

graphic file with name mcr296eqn2.jpg (2)

where n is the outward unit normal vector on the boundary and km is the mass transfer coefficient (m s−1). Ceq, the water holding capacity or equilibrium water content, is a function of the osmotic pressure of the external solute and it is obtained from the experimental data of PEG solution given by:

graphic file with name mcr296eqn3.jpg (3)

where p is osmotic pressure of PEG solution (MPa).

For boundary 1 (the columella, Fig. 2B), the axial symmetry boundary condition is applied

graphic file with name mcr296eqn4.jpg (4)

The other two boundaries (2 and 4, lowermost wall and right-hand side wall; Fig. 2B) are insulating boundaries, i.e. no water transfers through them:

graphic file with name mcr296eqn5.jpg (5)

Then the initial condition is given:

graphic file with name mcr296eqn6.jpg (6)

The measurement of mucilage expansion

The volume of mucilage after expansion is given by:

graphic file with name mcr296eqn7.jpg (7)

where V is the total volume after expansion, V0 is the initial volume of mucilage and Vw is the volume of water, the sum of water moving through the boundary. The coefficient α is used to describe the effect of polymer chain change during mucilage expansion, α ≥ 1. If α = 1, there is no change, and the volume of water absorption is equal to the volume increase. The experimental measurements and calculations (below) showed that mucilage volume changed in relation to the amount of water absorbed and that expansion was due to a combination of water uptake and polymer-chain relaxation. Of the total expansion (×75) on a per testa cell basis the contribution is apportioned as 1 : 3·7, respectively. α is therefore attributed a value of 4·7. The degree of mucilage expansion is characterized by Q, which is formed as:

graphic file with name mcr296eqn8.jpg (8)

The absorption of water will reach equilibrium when the expansion pressure reaches zero, and the equilibrium depends on the interaction of osmotic pressures of mucilage and water. The expansion degree at equilibrium is noted as Qeq.

Model parameters

The parameters of transport are dominant in this model. The diffusion coefficient has the most important effect on the volume change of mucilage. The diffusion of water into mucilage may be influenced by the composition and microstructures of the cell wall. For simple molecules in plant tissue, the order of the diffusion coefficient is 10−10 m2 s−1. In this paper, the coefficient of water diffusion through an apple slice from Hough et al. (1993) was applied as 1·9 × 10−10 m2 s−1, which was determined by the best fit of their model. For a dry seed, the initial water content of mucilage is very low. In this model, C0 is assumed to be 0·1 g g−1, and is assumed to be close to the water content of seeds stored at room temperature and room humidity (ISTA, 1996).

The cell walls comprising the shepherd's purse seed testa form a structure consisting of hexagonal units that collectively are similar in appearance to the structure of bee honey-comb (Fig. 1). Here, the mathematic geometry of each testa cell is simplified in two dimensions as two cylinders; the inner and outer cylinders represent the columella and cell walls, respectively. The mucilage is situated in the void between the two cylinders. Due to the symmetry of the cylindrical geometry, the void (and expansion processes therein), is modelled in two dimensions as a ‘half-cell’ (Fig. 2B). The convection and diffusion equations with boundary and initial conditions were solved using the software Multiphysics COMSOL (http://www.comsol.com), using the parameters and expressions defined in Table 1.

Table 1.

The parameter values (definitions and sources) that were used and applied to the proposed mathematical model for myxospermous seed mucilage expansion

Parameter Values Description Reference
r0 20 µm Radius of single testa cell Measured
z0 10 µm Initial mucilage (or testa cell) height Measured
D 1·9 × 10−10 m2 s−1 Diffusion coefficient of water Hough et al., 1993
µw 10−3 Pa s−1 Viscosity of water Crowe et al., 2001
C0 0. 1 g g−1 Initial water content Assumed
km 2·3 × 10−5 m s−1 Mass transfer coefficient Spiazzi and Mascheroni, 1997
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RESULTS AND DISCUSSION

Seed size and weight change during mucilage hydration and expansion

Mucilage expansion may take place through the uptake of water and increased polymer chain relaxation. Therefore, to assess the contribution of these two processes, mucilage volume changes were assessed as a result of hydration in water and in relation to the weight or volume of water absorbed. If the proportional volume change was similar to weight gain, then expansion was predicted to be only a function of water uptake. However, if the proportional volume change was greater than that predicted by weight gain, then polysaccharide relaxation had also occurred. Furthermore, the weight of mucilage contained in each seed was measured relative to the mucilage dry weight to assess the hydrogel capacity of the mucilage.

Towards this end, measurements from light micrographs showed that the average size of a dry shepherd's purse seed was 0·92 ± 0·07 × 0·51 ± 0·05 mm (length × width, respectively; n = 40), the volume 0·134 ± 0·005 mm3 and the weight 114 ± 3 µg (n = 500). After hydration in water, the length increased by 0·52 ± 0·01 mm, the width by 0·60 ± 0·01 mm and the volume to 0·93 ± 0·03 mm3, which was an approx. 6-fold increase over that of the dry seed. The average weight of a single seed after hydration was 573 ± 20 µg, an increase of 460 µg or 4-fold. The quantity of mucilage (as a proportion of the dry seed weight) was estimated by extraction, and the extraction distinguished the relative contribution (by weight) of the two mucilage layers. Specifically, the soluble outer layer of mucilage accounted for 3·7 ± 0·2.% of seed weight, while the enzyme extraction process, which removed all the seed mucilage, accounted for 25·2 ± 0·5 % of seed weight (approx. 28·7 µg). The inner layer mucilage weight therefore accounted for 21·5 ± 0·1 % of the dry seed weight. Consequently, after hydration and on the per seed basis, the mucilage increased its weight by approx. 16-fold. For the volume increase, only the inner layer mucilage was considered, as the outer layer was diffused and the volume was difficult to measure. The initial inner layer mucilage volume was calculated by measuring the epidermal cells and the volume increase was estimated to be 75-fold. The volume increase was therefore greater than the weight increase, which indicated that mucilage expansion was not only due to water uptake but also the polymer-chain relaxation. Also, the scale of increase (16-fold) indicated that the shepherd's purse seed mucilage may be characterized as a ‘superabsorbent hydrogel’ (that is capable of absorbing water in the range 10–1000 g g−1 dry mucilage; cf. Zohuriaan-Mehr and Kabiri, 2008).

Mucilage expansion kinetics at different PEG concentrations

For the purposes of modelling the mucilage expansion process, it was important to know the osmotic pressure of the seed mucilage. Mucilage expansion was found to decrease as the osmotic pressure of the hydration solution increased (Fig. 3A–C). The volume and surface area of hydrated seeds were also measured to find out their relationship with the osmotic pressure of the hydration medium (Fig. 3D, E). Seed mucilage volume decreased from 0·93 ± 0·03 mm3 in water to a recordable minimum of 0·134 ± 0·022 mm3 at –1·15 MPa (representing a decline in seed surface area from 4·635 ± 0·093 to 1·35 ± 0·043 mm2, respectively). Both the volume and surface area of hydrated seeds were expressed as exponential functions of osmotic pressure (Fig. 3D, E). Seed plus mucilage volume and surface area did not change significantly in solutions of osmotic pressures lower than –0·54 MPa. To give this data an environmental context, specifically an indication of the ability of the mucilage to compete for soil moisture, the osmotic pressure of the mucilage (–0·54 MPa) was equivalent to a salt (sodium chloride) concentration of 0·11 m (6·6 g L−1; cf. Van't Hoff, 1887). In germination studies of arabidopsis at the same PEG concentration (20 % (w/v) PEG, or –0·54 MPa), wild-type seed germination was 30 % of total germination in water, whereas seed mucilage-deficient MYB61 mutants failed to germinate (Penfield et al., 2001). Similarly, seed of A. sphaerocephala failed to germinate when imbibed in aqueous solutions at –0·87 MPa (equivalent to 0·2 m NaCl) or lower (Yang et al., 2010). Myxospermous seeds may therefore benefit from the capacity of the mucilage to compete effectively for water within the soil environment, and enhance seed germination and plant establishment.

Fig. 3.

Fig. 3.

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(A–C) The expansion of Capsella bursa-pastoris seed-coat mucilage, as assessed with light microscopy, in solutions of PEP 6000 with increasing osmotic pressure: (A) seeds hydrated in water; (B) and (C) seeds immersed in PEG 6000 at 15 % and 30 % (w/v) solutions (representing osmotic pressures of –0·32 and –1·15 MPa, respectively). Abbreviations: s, seeds; *, seed mucilage. Scale bars = 1 mm. (D, E) Changes in physical parameters of shepherd's purse whole seeds (seed plus mucilage) are also shown as they responded to hydration in different osmotic pressure (PEG 6000) environments: (D) volume responses; (E) surface area responses. The responses are fitted to exponential decay models (continuous lines), where volume = 0·9749e2·9574p (R2 = 0·9821) and surface area = 4·6847e1·7757p, R2 = 0·9594, for (D) and (E), respectively. Seed-only volume and surface area changes are shown with a dotted line.

Model simulations of mucilage expansion

Using those parameters determined in the previous sections, or gathered from the literature, simulations were run on mucilage expansion at equilibrium Qeq, in response to different osmotic pressures (Fig. 4A). Qeq data generated from model simulations (closed circles, Fig. 4A), compared favourably with the experimental measures. The Qeq decreased as the osmotic pressure increased and the theoretical findings were therefore in close agreement with the observed data. Shepherd's purse mucilage expansion was halted at –1·15 MPa, and above this value mucilage volume increased greatly (75-fold) as already demonstrated (Fig. 4A).

Fig. 4.

Fig. 4.

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Mucilage expansion from mathematical model simulations in response to PEG concentration [% (w/v)]: (A) the model-generated and observed experimental data, as indicated; (B) changes in relation to expansion time, with osmotic pressures of 0, –0·15, –0·54 and –0·81 MPa, as indicated; (C) mucilage depth (z; see Fig. 2B), with mucilage depths of 10, 15, 20 and 25 µm, as indicated.

Other simulations were also carried out which simulated the values for Q over time in response to four different aqueous environments of increasing osmotic pressure (Fig. 4B), and different mucilage depths (Fig. 4C). These indicated that mucilage expansion required more time to reach equilibrium in water (5 s; and in agreement with experimental observations), than in a solution of lower osmotic pressure (e.g. 2·2 s in –0·54 MPa PEG; Fig. 4B). In addition, while mucilage depth (or cell height) did not alter Qeq, expansion time to reach Qeq, increased as mucilage depth increased (Fig. 4C). At a depth of 10 µm (as measured in dry seeds) the time for expansion to Step II was about 5 s, similar to that estimated from confocal time-lapse microscopy (P. P. M. Iannetta et al., unpubl. res.), while at double this depth expansion time had increased to 12 s.

Conclusions

Myxospermous seed mucilage expansion in shepherd's purse occurs as a function of water uptake and polymer-chain relaxation. The mucilage has a low osmotic pressure (to –0·54 MPa), and may be described as superabsorbent hydrogel capable of absorbing 16 g water per gram dry mucilage. Experimental observations of mucilage expansion were used to provide theoretical and empirical data which enabled the creation of a mathematical model that uses diffusion equations to predict seed mucilage expansion in relation to varying biological and environmental conditions. The mathematical model takes into account the contribution of polymer relaxation and is the first mathematical model to simulate the expansion of myxospermous seed mucilage. The model will be developed to assess interactions between myxospermous seed mucilage and soil. For example, myxospermous seeds within the soil seed bank will expand upon hydration and thereby possibly affect soil stability and hydraulic conductivity via a reduction in pore space. Such effects of myxospermous seeds may be related to soil type, and simulations could identify those parameters for seed–soil combinations which optimize both stability and water retention.

ACKNOWLEDGEMENTS

P.P.M.I. and G.R.S. are funded by the Scottish Government and W.D. by the CECHR (www.dundee.ac.uk/centres/cechr).

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