Plant-fungus water relations affect carbohydrate transport from pea leaf to powdery mildew (Erysiphe pisi) mycelium

Trans. Br, mycol. Soc. 88 (1), 97-104 (1987)

Printed in Great Britain

PLANT-FUNGUS WATER RELATIONS AFFECT CARBOHYDRATE TRANSPORT FROM PEA LEAF TO POWDERY MILDEW (ERYSIPHE PISI) MYCELIUM By L. E. WYNESS AND P. G. AYRES Department of Biological Sciences, University of Lancaster, Bailrigg, Lancaster LAl 4YQ, U.K. The effects that water relations may have on the net uptake of carbohydrate by powdery mildew mycelium were investigated. Strips of pea leaves infected by the powdery mildew fungus (Erysiphe piSI) were fed [14C]sucrose. Net uptake into leaf (plus haustoria) and mycelial fractions were measured separately. An examination of experimental variables governing uptake showed that total uptake was approximately linear over a 3 h pulse period, about 12 % of the total being in the mycelium. This increased to 26 % during a 3 h chase period on unlabelled medium. Uptake by both leaf and mycelium was generally insensitive to pH in the range 4.8-6.8. Over a range of external sucrose concentrations uptake by both leaf and mycelium was biphasic, the pattern suggesting that uptake to the fungus was predominantly active in the range 0·05-10·0 mmol dm". The fungus apparently had a higher affinity for sucrose, K m 7.65 mmol dm", than did the leaf, K m 23·52 mmol dm", and on a dry-weight basis took up more sucrose than the leaf. Water stress, both of plants from which strips were taken and during incubation, increased the amount of sucrose taken up by the leaf but decreased the percentage of total 14C taken up that was found in the mycelium. In combination, pre-incubation and incubation stress had additive, negative effects on transport to the mycelium. Uptake by leaf and mycelium were stimulated by air movement and the proportion of total uptake in the mycelium rose to 38 % in the most rapidly moving air. It is proposed that air movement stimulated transpiration which, in turn, promoted the development of turgor pressure gradients driving carbon transport by mass flow into the mycelium. Water stress inhibits the development of such turgor pressure gradients and in this way it could exacerbate the stress-induced inhibition of carbohydrate transport to the mycelium that was observed in leaf strips in still air. Powdery mildew fungi are sensitive to the water status of host plants. In barley seedlings infected by Erysiphe graminis DC. f.sp. hordei Marchal and grown in either wet or dry soil, colony extension rate and numbers of mycelial cells (compartments) and conidiophores were all less in stressed than in well-watered plants (Ayres & Woolacott, 1981; Woolacott, 1982). In addition, sporulation was both delayed and reduced in water-stressed plants (Woolacott & Ayres, 1984). In powdery mildew (Erysiphe pisi DC.) of pea, mycelial growth and spore production were increasingly inhibited with decreasing leaf water potential (Ayres, 1977). Powdery mildews are wholly dependent upon their host for a supply of carbon, and this supply may be diminished during water stress because host photosynthesis is limited. It is, however, possible that stress-induced changes in the solute relations of leaf and fungus could affect the transfer of carbohydrate from host to parasite; this possibility was tested in the experiments reported here. 4

Although Spencer-Phillips & Gay (1980) and Manners & Gay (1982b) have studied solute uptake by isolated haustorial complexes and have concluded that environmental water and solute relations may affect transport, there have been no detailed studies of environmental factors affecting carbohydrate transport from leaves to powdery mildew fungi that have utilized intact leaf/fungus systems. Most studies of carbohydrate transport after infection have labelled carbohydrates by feeding 14C0 2 to leaves, i.e. have labelled carbohydrates at their source of origin in chloroplasts (Edwards & Allen, 1966; Edwards, 1971; Manners & Gay, 1978, 1982a; Spencer-Phillips & Gay, 1980). Since rates of CO 2 fixation are low in infected tissue (Ayres, 1976) and are further greatly reduced by water stress, this method could not be used in the present case, where the object was to compare transport of carbohydrate from host to fungus in stressed and control leaves. Instead, infected leaf strips were supplied with labelled MYC 88

Plant-fungus water relations carbohydrate, [14C]sucrose being chosen because sucrose is the major translocatable photoassimilate within plant tissues (Giaquinta, 1979; Whipps & Lewis, 1980) and is probably taken up intact by powdery mildew haustoria (Manners & Gay, 1982a). Due to the lack of plasmodesmata I connexions between mesophyll and epidermal cells in pea leaves (Bushnell & Gay, 1978), sucrose is likely to be absorbed by infected epidermal cells in vivo directly from the apoplast of the leaf. The haustorial neckband isolating the extrahaustorial membrane from the leaf apoplast ensures that solutes entering the fungus are directed through haustoria via the epidermal cytoplasm (Gil & Gay, 1977). The presence of sucrose in the apoplast may be enhanced in infected leaves by the increased permeability of mesophyll cell membranes (Bushnell & Gay, 1978; Wheeler, 1978). A series of experiments was carried out to define the effect of some experimental variables upon carbohydrate uptake into the leaf and fungus. Using a technique based on these results, effects of plant-fungus water relations were examined.

specific activity 20'42 GBq mmol ? (Amersham Int. PLC) (pulse medium). Leaf strips were rinsed twice in ice-cold distilled water before either transfer to the chase medium (unlabelled, but otherwise identical to pre-incubation medium) or sampling. At each sampling, rinsed strips were blotted gently and placed, mycelium facing down, on to the sticky surface of Sellotape. The leaf strip was then gently separated from the mycelium, both tissues placed in glass vials and stored at - 5°. The samples were then combusted in a Tri-Carb sample oxidizer (Packard) with 'Carbosorb' as the CO 2 absorbant and' Permafluor' as the scintillant (both Packard Chemicals). Radioactivity was counted in a Tri-Carb scintillation counter with appropriate corrections for quenching, oxidizing and counting efficiencies. Dry weights of leaf and mycelium were determined on subsamples after gently brushing the mycelium from infected leaves on to aluminium foil. Leaf minus mycelium, and separated mycelium, were each weighed after oven drying at 60°. Representative values are presented in Table 3.

MA TERIALS AND METHODS

Effects of water stress The effects of two different types of water stress on 14C uptake were examined. Stress of plants during growth (pre-incubation stress) was examined by comparing uptake in strips taken from either well-watered or water-stressed plants (soil water potential -0·8 MPa). Stress during uptake (current stress) was examined by incubating strips in media containing polyethylene glycol 2000, which lowered the osmotic potential of the medium to -0'7 MPa. The two stresses were combined in a 2 x 2 factorial experiment. Each value presented in Table 3 b is the mean of four replicates.

Plant material and inoculation Seeds of Pisum sativum cv. Progress NO.9 were sown in trays containing vermiculite (Vermipeat Ltd) and incubated at 21°C until seedling emergence. Seedlings were transplanted into 11 em diam pots (2 plants per pot) containing peat and coarse sand, 1: 1, and maintained within a growth cabinet at 21 ± 1° (light, 16 h) and 18 ± 1 °C (dark, 8 h). Irradiance of 250±25 ,umol m- 2 S-I PAR was provided by metal halide fluorescent Kolorarc lamps (Thorn EMI). Relative humidity was 62 ± 5 % during the day and 52 ± 5 % at night. Plants were inoculated with conidia of E. pisi shaken from above from heavily infected plants. Experiments were carried out 7 d after inoculation. Uptake of 14C

All experiments were carried out on strips (20 x 5 mm, cut at right angles to the mid-rib of the leaf) held in the dark at 21°. Strips were cut from the fifth leaves of infected plants approximately 1 h before dawn and loose conidia were removed. Prior to radiolabelling, thirty strips were placed in each Petri dish containing 20 em" of solution with either MES (Sigma Chemicals) plus NaOH buffer, or citric acid plus Na 2HP0 4 buffer, both at pH 5.8 (unless stated otherwise) and unlabelled sucrose (pre-incubation medium). After floating for 1 h on the solution, leaf strips were transferred on to an identical solution with 40 mm" [U_14C]sucrose,

Regulation of evapotranspiration To determine whether 14C uptake was affected by the rate of transpiration of leaf and fungus, air was passed over leaf strips at different rates, in order to produce relatively high or low rates of water loss, during incubation on the labelled medium. Each value presented in Table 4 is the mean of four replicates. A perspex block containing six sealed chambers (10 em") each holding two leaf strips (30 x 5 mm) was constructed. After a pre-incubation period of 1 h on unlabelled solutions in Petri dishes as previously described, infected strips were floated on solutions containing 1'5 cm" MES, NaOH buffer (pH 5'8), 0'2 mmol drn " sucrose and 14'8 kBq cm" [U-14C]sucrose for 1 h, during which air at a flow rate of either 1100 ern" min-lor

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Fig. 1. Uptake of [14C]sucrose by mycelium (solid line) and leaf (broken line) during continuous radioactive labelling for 3 h, followed by incubation on unlabelled media from 3 to 6 h. Bar above abscissa indicates unlabelled period. Incubation solution consisted of 0'05 mmol dm-' MES at pH 5·8 with 0'2 mmol dm-' sucrose and 14.8 kBq [U_14C]sucrose. Bars indicate least significant differences (P = 0'05).

80 em" min " was passed over the surface ofthe leaf strips. Control of soil water deficits A standard curve was constructed relating soil water potential to soil water content (Rawlins, 1979). When plants were to be stressed, watering was stopped for 5 d until daily samples of soil fresh weight indicated, according to the curve, a bulk soil water potential of -0·8 MPa. In order to maintain this potential, daily watering recommenced but only further losses of water were replaced. Statistics Analyses of variance were applied to all sets of data, percentages being transformed to arcsine derivatives prior to computation (Snedecor & Cochran, 1 97 8). RESUL TS

Infected leaf strips were incubated on 0'2 mmol dm" sucrose in MESjNaOH buffer, pH 5'8. This made 1'37 mg sucrose available to the

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Fig. 2. Uptake of [14C]sucrose, flg mg " weight, by mycelium (square symbols) and leaf (triangular symbols) on MES buffer (closed symbols) and citric acid buffer (open symbols). Incubation solution contained 5 mmol drrr? sucrose with 14'8 kBq [U_14C]sucrose. Bars indicate least significant differences (P = 0'05)·

30 leaf strips in each dish (one treatment replicate). The net total amount absorbed by 30 infected strips over 3 h was approximately 26'9 pg sucrose. Mycelium of E. pisi accumulated more l4C than leaf tissue on a dry-weight basis throughout both 3 h pulse and 3 h chase periods (Fig. 1). The average distribution of the net total label absorbed by both tissues during pulse was 12 % in the mycelium in 88 % in the leaf. During the subsequent chase period the percentage in the mycelium increased from 14 % after 1 h to 26 % after 3 h (7 h since pre-incubation began). During the chase period the mycelium absorbed a net total equivalent to 26 ng of sucrose per strip whilst the leaf lost 87 ng sucrose per strip. A 3 h pulse, with or without chase, was used in subsequent experiments. Buffer and pH Net uptake of l4C into both leaf and mycelium was higher in MES-NaOH buffer than in citratephosphate buffer (Fig. 2). The proportion of the net total 14C absorbed by both tissues that was within the mycelium was not affected by buffer species (Table 1). Partitioning to the fungus showed a clear optimum at pH 5·8 on MES buffer, but on citrate-phosphate buffer there was no significant difference between partitioning at pHs 5'8 and 6·8 (Table 1).

Plant-fungus water relations

100

Table 1. Distribution of radioactivity (Ue ) between leaf and mycelium of Erysiphe pisi after 3 h incubation ofinf ected leafstrips on differently buffered media containing [uCJsucrose Vo /S

Activity in mycelium (% arcsine transformed) pH

Citric acid

MES

4 °8 5°8 6°8

23°63 30 °93 32 °86

28 °86 3 2°82 27°31

Least significant difference between buffers (P = 0 °05) = 5°370

50

Table 2. Effect of sucrose concentration on the net uptake of carbon by infected leaf strips and the contribution of the active component to total net uptake

100

150

( In cubat ion medium contained MES buffer, pH 5'8) Conen in external solution (mmol dm" ) 0°05 0.1 1 5 10 50 LoS.Do

Net uptake of carbon Cpg sucrose

mg ? n.w.)

Contribution (%)

Leaf

Mycelium

Leaf

Mycelium

0 °06 0 '13 1°21 4 °46 9 °10 36 °99 1064

0'26 0 °61 4°82 15°78 25°25 137°95 4 °97

42 46 42 22 23 6

46 54 42 11 0

0

(P = 0 °05)

MES buffer, pH S08, was used in subsequent experiments. Sucrose concentration Net uptake by both leaf and mildew increased in response to increasing external concentrations of sucrose (Table 2) in media containing MES buffer at pH S·8. Sucrose concentration had no significant effect on the proportional distribution of label between leaf and mycelium. Since uptake was possibly biphasic for both leaf and mildew comprising an initial saturable phase between OoOS and 10 mmol drn" external concentration and a subsequent non-saturable linear phase between 10 and SO mmol drn " , the data in Table 2 were transformed to an Eadie-Scatchard plot (F ig, 3). This showed significant deviations from linearity and may be interpreted as indicating the presence of two separate transport components, a vertical

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phase between o-oj and 10 mmol dm'? external sucrose probably representing an active component and a horizontal phase, between external sucrose concentrations of 10 and So mmol dm " , probably representing a passive component (F ischer & Luttge, 1980; Maynard & Lucas, 1982). To determine the relative contribution of each of these phases to total uptake , the slope of uptake values for both leaf and mycelium between 10 and So mmol dm- a was multiplied by the external sucrose concentration at each point. Subtracting this value from total net influx gives the rates for the active component. Table 3 presents the possible contribution of an active phase. Replotting the data in Table 2 for values between o'OS and 10 mmol dm " external sucrose concentrations,

L. E. Wyness and P . G. Ayres 28

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Effects of transpiration rate

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Net uptake by both leaf and fungus, and the proportion of total net uptake (leaf plus fungus) found in the mycelium was greater in the high than in the low transpiration treatment (T able 4)·

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the dr y weight of leaf or mycelium (T able 3 a). Apart from the effect of pre-incubation stress on the mycelium after 3 h, both pre-incubation stress and current stress increased the amount of net sucrose taken up after both 1 and 3 h of a pulse period (T able 3b ). Although the amounts taken up by the mycelium were not significantly reduced by the separate str esses, the proportion of net total uptake (leaf plu s fungus ) in the fungus after 3 h pulse was significantly reduced by pre-incubation stress. In combination, the two stresses reduced both net uptake by the fungus and the proportion of total radioactivity found in the fungus.

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Fig. 4. Eadie-Hofsteeplots from data presented in Table 2 using points between 0 '05 and 10 mml dm '? external sucrose concentrations. (a) Displays mycelial and (b) leaf parameters. V, the rate of net sucrose absorption, is plotted against V I I S), the net rate divided by the external sucrose concentration. K m is derived from the slope of the points fittedby linearregression. Vrn a x is the intercept with the ordinate at V I[Sj = o. Correlation coefficients for (a) = - 0'949 (95% significant) and (b) = -0·866 (95 '/0 significant).

parameters characterizing the uptake process, Vm ax the maximum rate of absorption and K m the external concentration in the bathing medium at ~ Vm ax ' can be determined . As shown, the K m for net uptake by the mildew, 7'65 mmol dm", exceeds that of the leaf, 23'52 mmol dm", indicating that the fungus has the higher affinity for sucrose (Fig. 4). An external concentration of 0 '2 mmol dm" sucrose was used in subsequent experiments. Pre-incubation stress had no significant effect on

The object of this investigation was to determine the effect that plant water relations may have on the uptake of carbohydrate by powdery mildew mycelium, so a ready-synthesized (and labelled) carbohydrate was fed to leaves in order that the fungus would have approximately equal amounts of carbon available to it in control and stressed plants. Sucrose was supplied because available evidence suggests that this is the form of carbohydrate taken up by mildew haustoria (H ewitt & Ayres, 1976; Manners & Gay , 1982). Whether or not sucrose is transferred intact, radio label in the mycelium will reside in compounds other than sucrose. Amounts of radiolabelled compounds are , however, expressed as sucr ose equivalents in order to facilitate comparisons between uptake into the leaf and uptake int o the fungus, and also to indicate better the total amount of sucrose removed from the external medium. In a healthy leaf transport of carbohydrate from the site of CO 2 fixation to epidermal cells will be subject to a number of controlling factors and the complexity of the transport system will probably increa se after mildew infection. The method adopted here by-passed many of those factors by supplying carbohydrate directly to the apoplast of the leaf from which epidermal cells, because of their lack of plasmodesmatal connexions with underlying mesophyll cells, normally take up carbohydrate. Studies of carbohydrate movement in the apoplast ofhealthy leaves (M aynard & Lucas, 1982) sugge st that in the pre sent experiments the concentration in the apoplast of leaf slices would have

Plant-fungus water relations

102

T able 3. Effect of a soil-water deficit prior to incubation on dry weight per unit area of leaf and mycelium, and of current stress on net uptake of [14C]sucrose by leaf and mycelium (a)

Dry wt (mg em : ")

Stressed Well watered

1

Preincubation stress

Current stress

+ +

+ +

L.S oDo (P = 0°05)

Leaf

Mycelium

2 °40 2 °31

0 °10 4 0°108

(b) Uptake Net uptake of carbon (pg sucrose rng ? dry wt) h pulse 3 h pulse

Mycelium

Leaf

% of total in mycelium

Mycelium

Leaf

% of total in mycelium

0 °957 1°147 1"46 3 0 °588 0°395

0°184 0°281 0 °2 33 0°316 0°095

29 °2 25°1 3 2 °6 16°8 7°2

1°351 1°154 13°99 0°588 0°395

0°356 0°569 0"49 6 0°802 0°095

22 °8 12 °3 21 °2 10 °5 7°2

Table 4. Effect ofair movement on [14C)sucrose uptake by strips of pea leaf and mildew myc elium Net uptake of carbon

(pg mg- I dry wt ) after 1 h

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0°65

% in mycelium (arcsine Mycelium transformed) 5°83

33°0

reached equilibrium with that in the external solution within 1 h of any change of external concentration. The route of carbohydrate transport from apoplast into the fungus would have been, as it is in vivo (Gay, 1984), through the epidermal cytoplasm and across the haustorial membranes ° Preliminary studies of dye movement showed no evidence of solute transport from the bathing medium directly into the mycelium. The distribution of radioactivity between mycelium and leaf that was observed here , i.e. ranging from 12 % in the mycelium during a 3 h pulse period in still air to 37 % in a 1 h pulse period in rapidly moving air, corresponds welI with the values of 18 % for mycelium of E. pisi isolated from leaves (M anners & Gay, 1982a ) and 32 % for intact mycelium of E. graminis f.sp. hordei (Edwards & Allen, 1966), both after feeding 14C0 2 to infected leaves in the light . Small discrepancies can be expected between reports because of the different

experimental procedures, for example in the present case radioactivity in haustoria was included in the 'leaf' fraction, but generally the method adopted here seems appropriate for studying carbohydrate transport into mildew mycelium. Amounts of carbon taken up by leaf and fungus during both pulse and chase periods are net amounts, since they are the result of gross influx minus efflux and also minus any respiratory losses , Efflux from leaf strips to the incubation medium would probably have been large, but efflux from the fungus to the leaf would probably have been small since, although Manners & Gay ( 19 80) demonstrated ('4C]ethirimol effluxed from isolated haustoria I complexes, the conversion of sucrose to mannitol and other fungal storage carbohydrates, as well as translocation from the haustorium int o the mycelium, would have reduced the concentration of carbohydrate inside the haustorial plasma membrane. Attempts were made, using Gilson respirometers or Cartesian divers, to quantify respiratory losses in the fungus, but these were unsuccessful because of technical problems associated with the intimacy of the tissues . Unless, however, respiration in host and /or fungus is affected markedly by water stress the failure to account for respiration does not invalidate the treatment effects noted here . Net uptake of carbon by the fungus, rather than gross uptake, will be important for its development. Uptake by both fungus and leaf was less in citrate-phosphate buffer than in MES buffer. Possibly, citrate ions competed, or somehow interfered, with sucrose uptake ° Alternatively, since phosphate has a regulatory role in sucrose

L. E. Wyness and P. G. Ayres transport and metabolism (Whipps & Lewis, 1981), the phosphate ions could have inhibited uptake processes. Uptake by the leaf appeared to be less sensitive to pH than did uptake by the fungus. Lemoine, Debrot & Auger (1984) also noted that sucrose uptake by leaf discs of Vicia faba was relatively insensitive to external pH when tissues were freshly excised. The biphasic response by both host and mycelium to increasing sucrose concentrations strongly suggests that active or carrier-mediated uptake mechanisms were operative. Although active phloem loading in leaf tissue is widely accepted and probably involves proton-sucrose co-transport (Baker, 1978; Giaquinta, 1979; Lichtner & Spanswick, 1981; Maynard & Lucas, 1982), with the kinetics of uptake str ongly resembling those seen here in mildewed pea, there is no general agreement that such active uptake occurs in biotrophic fungi. Proton-dependent sugar co-transport has been observed in Neurospora crassa Shear & Dodge (Slayman & Slayman, 1974) and such phenomena have been widely demonstrated in other fungi . Spencer-Phillips & Gay (1981), using cytochemical techniques, demonstrated significant ATPase and p -glycerophosphatase activity within distinct domains of haustorial and parietal epidermal cell membranes ofthe E. pisi/pea complex. Manners & Ga y (1982 a) suggested that some form of active or facilitated transport would account for the concentration of sucrose being higher in haustoria than in pea leaf tissue. The K m for fungal uptake determined in the present work for mycelium was lower than that for uptake by the leaf (plus haustoria), suggesting that the fungus probably has the higher affinity for sucrose. The K m for leaf uptake was similar to that previously found for healthy Vicia faba under approximately the same conditions of pH and age (Lemoine et al. , 1984). Active uptake into the mycelium occurred in the dark in a still atmosphere approximately saturated with water vapour, i.e, under conditions where transpiration was minimal. A rapid flow of air across the leaf surface stimulated uptake of sucrose and its transference to the mycelium. It was not possible to measure the water relations of the micro-environment at the leaf surface but it seems probable that, because the leaf surface is covered by the dense and raised mycelium, the rapidly moving air would sweep away water vapour more effectively from around the mycelium than from the leaf surface . Thus the gradient of water potential, !'J.ljJ w' the driving force for water movement, would tend to increase between leaf and mycelium, the tendency being opposed to greater or lesser extent by an increased flux of water

1°3

from leaf to haustoria. This flux could itself have promoted carbohydrate uptake by the fungus. However, if !'J.ljJ w were to increase there would be a short-term increase in the turgor gradient between hau storia and mycelium and a mass flow of cytoplasm and solutes into the mycelium and probably into maturing conidia, since all septal pores between conidiophore and conidia are open (Martin & Gay, 1983), and uptake into haustoria might be facilitated. Such gradients of turgor pressure have been shown to drive solute translocation in mycelial strands and rhizomorphs and, probably, also drive translocation in unorganized mycelium (see Eamus & Jennings, 1986, for references). There was 4 % less mycelium present on the surface of stressed leaves than on the surface of unstressed leaves (dry weight per unit area), but stress , whether before or during incubation or at both times, reduced solute transport into the mycelium in spite of increasing uptake into the leaf. It is possible that a stress -induced plant metabolite, e.g. abscis ic acid, specifically inhibited transport to the fungus; however, it seems more likely that transport was reduced because of direct osmotic effects associated with stress. The growth of an haustorium depends on its having a turgor pressure greater than that of the epidermal cell of the host; a stress-induced reduction in fungal turgor may have inhibited haustorial growth and reduced the surface area available for nutrient transport - it may even have caused the shrinkage of existing structures. Woolacott (1982) reported that the volume and surface area of haustoria of E . graminis f.sp. hordei were reduced by water stress of the barley host. Over periods of several days the fungus can only maintain turgor and mycelial growth if it has an osmotic potential lower than that of the host, which in stress conditions is progressively declining, i.e. the fungus must maintain some water uptake and turgor. There is limited evidence, from measurements on conidia, that powdery mildews can adjust their osmotic potential in this way (Woolacott , 1982). Since osmoregulation and growth compete for energy and raw materials it is suggested that it is this competition which causes the reduced uptake of carbohydrate in stres sed mycelium seen here and, ultimately, the reduction of mycelial growth and sporulation in water- and salt-stressed plants reported previously (Ayres, 1977). Transpiration from the mycelium, with its associated throughput of water, probably helps to support high rates of carbohydrate transport into the mycelium when plants are well watered, and in the short term increased transpiration might even lead initially to increased carbohydrate uptake by the fungus in

Plant-fungus water relations

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plants subjected to evapotranspirational stress, but in longer periods of stress the ensuing loss of turgor would only further depress turgor and growth rates.

L. E. Wyness gratefully acknowledges the support of a S.E.R.C. studentship during the course of this work. We thank Dr J. F . Farrar for helpful comments on an earlier draft of this paper. REFERENCES

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(R eceived for publication 8 November 1985)