Growth kinetics of mycelial colonies and aggregates of ascomycetes

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Mycol. Res. 97 (5):513-528 (1993) Printed in Greaf Britain

REVIEW

Growth kinetics of mycelial colonies and aggregates of ascomycetes

J. I. PROSSER Department of Molecular and Cell Biology, University of Aberdeen, Marischal College, Aberdeen, AB9 IAS, Scotland

Many aspects of hyphal extension and branching in fungi are well understood at the cellular level and may be linked to the growth kinetics of individual hyphae and branching mycelia on solid media and in liquid culture. Thus, growth of a typical colony on solid medium may be described and quantified, using concepts such as the peripheral growth zone and hyphal growth unit. These concepts also increase our understanding of growth of dispersed mycelia in liquid culture. 'Atypical' growth, e.g. sector formation, rhythmic growth, pellet formation are less well understood, but provide a link between vegetative mycelial growth and aggregation of hyphae to form more complex differentiation structures. Aggregate formation is frequently associated with alterations in the balance between hyphal extension rate and branch production but temporal and spatial control of these processes is not well understood. This review emphasizes the need for a quantitative approach to studies on aggregate formation, and discusses the application of mathematical models describing differentiation and pattem formation.

Quantitative information regarding growth kinetics and pattem formation during developmental processes in all living organisms is difficult to obtain. Filamentous fungi are no exception. While morphological and biochemical aspects of many differentiation processes can be described in qualitative detail, it is generally impossible to explain and predict in quantitative terms the spatial distribution of structures such as fruiting bodies or the processes involved in initiation and development of their growth. This results in part from practical and technical difficulties but more importantly through the absence of a quantitative and theoretical approach to developmental biology of fungi. Such an approach is necessary if mechanisms which control both spatial and temporal aspects of morphogenesis are to be fully understood. In contrast, many features of growth and branching of vegetative mycelia in liquid culture and on solid medium can be described quantitatively and can be explained well in terms of cellular growth mechanisms. Early colony growth on a Petri dish is obviously easier to follow than complex differentiation processes, but a better description of vegetative growth has resulted from a desire to relate, in a quantitative manner, processes at the cellular level to those at the mycelial or population level. In considering fundamental mechanisms controlling growth, both environmental and cellular aspects must be taken into account. The filamentous growth form has developed in order to solve problems encountered by unicellular organisms. So, for instance, an expanding, branching mycelium, by regulating and controlling the proportions of biomass directed towards hyphal extension and branch formation, can cover solid nutrient medium much more eficiently than a bacterial or 33

yeast colony. Similarly, hyphal extension provides an alternative to motility, for example, between nutrient sources. Another, possibly more important advantage is the ability to segment hyphae, by formation of septa, allowing separate development of different regions of the mycelium and enabling formation of pseudotissues. The environmental and evolutionary pressures which have selected for the growth forms and structures observed must therefore be considered. Attempts must then be made to determine how the organism has reacted to these pressures and this requires study at the cellular, biochemical and genetic levels. Cellular mechanisms may be specific for particular organisms or groups of organisms but environmental pressures are common to all. In this respect, therefore ascomycetes must not be considered in isolation. The growth kinetics and branching patterns during colony development on solid media appear to be common to all mycelial fungi studied and even extend to filamentous prokaryotes, the actinomycetes (Allan & Prosser, 1983, 1985). Cellular mechanisms for growth in fungi and actinomycetes differ fundamentally but quantitative aspects of their growth are similar. This may also apply to developmental processes in these different organisms, and within the fungi. This account will summarize formation of 'typical' colonies on solid media, variation in growth patterns resulting from environmental and genetic factors and growth in liquid medium. The mechanisms controlling growth and branching in these situations will be described and consideration will then be given to the failure, modification or replacement of these mechanisms during differentiation processes. Finally, the potential for quantitative approaches to development and differentiation will be discussed. Although much of the

Growth kinetics of mycelial colonies and aggregates

Distance from colony centre (mm) Fig. 1. Glucose concentration of medium in uninoculated plates (O),and of medium below colonies of Rhizocfonia cerealis on minimal and 6 d Arrows indicate the medium containing (a) 10 mM glucose, (b) 25 mM glucose and (c) 50 mM glucose for 3 d (a),5 d position of the colony margin 3, 5 and 6 d after inoculation. (From Robson ef al., 1987, with permission.)

(a)

relevant work has been camed out using ascomycetes, material from other groups will be introduced where information is sparse or lacking.

COLONY GROWTH AND MORPHOLOGY Although mycelial growth and branching show some interspecies variation, certain basic features are common to all fungi which have been studied. It is therefore possible to describe the development of a 'typical' colony. A summary only will be provided here; reviews by Trinci & Cutter (1986), Trinci (1984), Jennings (1986) and Prosser (1983) provide more detailed accounts and reference lists. A fungal spore inoculated onto agar-solidified nutrient medium and inoculated under suitable conditions will form a germ tube which, for a short period, increases in length exponentially. Subsequently, a constant linear extension rate is achieved and either dichotomous or lateral branches are formed. During early growth, branch hyphae grow in the manner of their parents extending at an initial exponential rate before reaching the constant linear extension rate of the parent hyphae. When measured in terms of total mycelial length, growth is exponential as a result of exponential branch formation. Both total mycelial length and the total number of tips or branches increase exponentially at the same specific rate. This rate is equivalent to the specific growth rate of the organism under the same growth conditions in liquid medium, where biomass may be measured directly as dry weight (Trinci, 1974). The hyphal growth unit (Caldwell & Trinci, 1973) calculated as the ratio of total mycelial length to total number of hyphal tips, soon becomes constant and represents the average hyphal length, or more correctly hyphal volume (Robinson & Smith, 1979), associated with each branch. It is

(v).

therefore a property of the population rather than of an individual hypha and its relationship to other hyphal and colony growth parameters has been extensively analysed by Kotov & Reshetnikov (1990). During this early growth, branches are subtended at an angle of approximately 90' but subsequent extension is negatively autotropic and radially directed, i.e. hyphae tend to avoid neighbouring hyphae and grow away from the centre of the colony. Eventually a circular colony is formed with equally spaced, radially directed, marginal hyphae extending at a constant rate. Natural variability in extension rate appears to allow some branches to catch up with their parent hyphae to maintain hyphal spacing at the colony margin (Hutchinson et al., 1980). In addition, variability in extension rate, interbranch distance and branch angle is sufficient to give rise to circular morphology. Exponential growth cannot proceed indefinitely and growth at the colony centre eventually becomes restricted. This is due to factors such as accumulation of inhibitory metabolic endproducts or staling compounds, unfavourable pH, reduced oxygen supply, space limitation and exhaustion of nutrients. Robson et al. (1987) showed the extent to which nutrients are depleted beneath a developing colony (Fig. I). Rhizoctonia cerealis was grown on medium containing 10, 25 and 50 mM glucose for 3, 5 and 6 d. The shapes of glucose concentration profiles varied little with initial glucose concentration but glucose depletion increased greatly as the colony developed. There was evidence for depletion in advance of the colony margin and at the colony centre glucose became exhausted. Following restriction of growth at the centre of the colony, exponential growth is confined to a ring of marginal mycelium, the peripheral growth zone, whose width (w)remains constant as the colony expands. The rate of colony radial expansion

J. I. Prosser

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(&)is determined solely by growth in the peripheral growth zone and is related to the specific growth rate in liquid culture (p) by the equation & = pw (Trinci, 1971). The peripheral growth zone surrounds an expanding, circular region where growth ceases or occurs at a reduced rate, dependent largely on translocation of nutrients from other regions and on turnover of existing biomass. In this region, branches are narrower, hyphal growth in less well directed and fusion of vegetative hyphae is common. Branching patterns may be quantified by classifying branches as primary, secondary, tertiary, etc. Primary branches subtend no branches, secondary branches subtend primary branches and tertiary branches subtend secondary branches. A wide range of fungi and other biological and non-biological branching systems show an inverse logarithmic relationship between the number of branches belonging to a particular order and order number. This relationship represents the situation where maximum surface area may be colonised while minimizing the total length of filament required. Environmental factors therefore lead to development of mechanisms for generation of this pattern, allowing optimal efficiency by fungal colonies in accessing nutrients while minimizing the amount of biomass synthesized. The relationship between the mean length of branches of a particular order and branch order is more complex. Park ( 1 9 8 5 ~ )suggested that during unrestricted growth, as exhibited by young colonies, the mean length of branches will increase arithmetically with order number. A logarithmic relationship may be expected when hyphal extension rates decrease, for example due to space or nutrient limitation or production of staling compounds. The latter relationship was also found in a colonial mutant of Neurospora crassa which forms self-limiting, discrete colonies (see below). In a survey of 183 colonies of 14 fungal species (Park, 1985 b), the majority showed an inverse logarithmic relationships between branch number per order and branch order. A minority showed proportionality between the logarithm of mean branch length and order number, a greater proportion showed an arithmetic relationship and in the greatest proportion mean branch length was related to the logarithm of branch order. Park also found significant variability in slopes of regression lines for branch number with further variation during colony development. This is thought to be related to mycelial differentiation which is discussed further below. -

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CELLULAR MECHANISMS OF GROWTH A N D BRANCHING Two major processes give rise to the growth and pattern exhibited by a typical mycelial colony: hyphal extension and branch formation. For each of these processes both the rate or kinetics and positional or directional information must be considered.

The rate of hyphal extension Extension of vegetative hyphae on solid medium occurs by tip growth. Material required for wall and membrane expansion is synthesized in distal hyphal regions and is transported to

the tip in membrane-bounded vesicles (Gooday, 1983; Wessels, 1986). Hyphal extension occurs through fusion of vesicles with the tip in a tapered apical zone, the extension zone. During normal growth the extension zone has constant length, diameter and shape. The rate of tip extension is therefore determined by the area over which material may be added and the flux of material to the tip. The former is related to the size of the extension zone and the latter depends on the specific growth rate, which determines the rate of synthesis of material, and the length, or more correctly, the volume of hypha supplying material to the tip. Extension rate therefore depends on the hyphal diameter and on the volume of the peripheral growth zone. At the mycelial level, the peripheral growth zone width is the marginal mycelial ring giving rise to colony expansion; whereas, at the level of the individual hypha, it corresponds to the volume of hypha contributing to tip growth. The peripheral growth zone is therefore the maximum volume of hypha associated with each tip while the hyphal growth unit is the mean volume.

The direction of hyphal extension Little is known of the factors affecting directional growth of hyphae on solid media. Chemotropism towards amino acids has been demonstrated in the oomycetes Achlya (Musgrave ef al., 1977; Manavathu & Thomas, 1985) and Saprolegnia (Robinson & Bolton, 1984). In the latter study, the closest distance of approach of two hyphae decreased, from 28 to 0 pm, with the logarithm of the total amino acid concentration in the range of 0 - 0 2 5 4 4 7 g I-'. A similar relationship was found at different concentrations of malt extract. The frequency of negative autotropic responses increased with increasing numbers of amino acids and was also dependent on amino acid composition, increasing with the inclusion of aromatic amino acids. Amino acids will be depleted around a growing hypha and negative autotropism appears to result from positive chemotropic growth towards a higher concentration of amino acids. Tropism towards nutrients, however, appears to be rare in fungi and a more general explanation for negative autotropism is the establishment of gradients in oxygen concentration immediately surrounding hyphae (Robinson, 1973a, b). A hyphal tip approaching a growing hypha will turn in response to reducing oxygen concentration when this concentration is sufficiently low to reduce the hyphal extension rate. Branch initiation is similarly influenced and, in Geotrichum candidum, branches originate from sides of hyphae facing the higher oxygen concentration. These effects are less noticeable in older regions of the mycelium where hyphal growth lacks direction and hyphal fusions are common. Trinci ef al. (1979) observed negative autotropic responses when the mean distance of approach of two hyphae was 30, 27 and 24 vm for N. crassa, Aspergillus nidulans and Mucor hiemalis. Similar data were obtained by Hutchinson ef al. (1980) who concluded that the orientation of hyphae in colonies of Mucor mucedo was not due to avoidance responses of individual hyphae. Although hyphae brought into close proximity did turn to avoid each other, the maximum range of such reactions was generally 10-20 pm, and the majority of hyphae in the colony were spaced further apart than this. In

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Growth kinetics of mycelial colonies and aggregates addition, the direction of growth of most hyphae was unaffected when colonising agar from which growing hyphae had been removed or by the proximity of dead hyphae. They discounted the hypothesis that avoidance resulted from nutrient depletion or metabolite production around a growing hypha, unless such a metabolite was volatile or unstable. These data are not inconsistent with oxygen gradients influencing negative autotropism. The cellular mechanisms determining the direction of hyphal growth are unclear but must reside in the tip, as the extension zone has been demonstrated as the region giving rise to tropic responses (Trinci & Halford, 1975). Robinson (1973 b) suggested that a gradient of respiratory activity across a hyphal tip could lead to increased production and concentration of vesicles at the side of the hypha subjected to a higher oxygen concentration. Chemotropism towards oxygen could therefore result in increased extensibility of the wall in this region, leading to bulging and consequent extension towards the higher oxygen concentration. Jennings (1986) also discussed localized changes in tip wall extensibility but resulting from extrusion of water and increased, localized, hydration of wall material or from localised changes in pH. Wall hydration was suggested as a mechanism for tropisms generated by osmotic gradients and also for hyphal fusions. The latter could occur through wall exudations by an approaching hyphal tip increasing wall hydration, releasing lytic enzymes and enabling fusion of the two hyphae. Localized pH changes were invoked to explain chemotropism towards amino acids in Achlya. In this organism, protons are taken up by the hyphal tip in symport with amino acids and are involved in generation of hyphal currents (see below). One mechanism for chemotropic growth is a reduction in activity of electrogenic pumps on the side of the wall experiencing the higher amino acid concentration as a result of transinhibition of the symport. Alternatively, increased removal of protons from the wall by increased activity of the symport could cause a localised increased in pH which might decrease wall elasticity. Both of these mechanisms involve rigidification of the wall on the side to which the hypha subsequently bends while Robinson (1973 b) suggests an increase in elasticity leading to bulging in the direction of subsequent growth. Cytological and biochemical events at the hyphal tip, and their interaction with biophysical forces associated with turgor pressure and wall elasticity, are crucial to our understanding of tropisms and further research is required in this area.

material synthesized within the peripheral growth zone cannot be incorporated at the hyphal apex. This interrelationship between extension rate, branch formation and specific growth rate provides an explanation for qualitative and quantitative variation in branching patterns and is discussed further below.

Positioning of branches

The site of branch production is less easily explained. Branch formation and septation are integral features of the duplication cycle which has been characterized in a number of fungi (Trinci, 1979). In some fungi, e.g. Geofrichurn candidurn, there is a close relationship between both processes and branches are formed a fixed time after septation and are positioned immediately behind septa. In others, particularly those such as Aspergillus nidulans which possess septa with a central unplugged pore, the relationship is less close and branch position within intercalary compartments is more variable. The coupling of branch position and septa, along with evidence from electron microscopy and analysis of septation mutants, have led to the hypothesis that branch initiation occurs at the site of accumulation of vesicles, whose translocation to the tip is prevented by a septum. Vesicle accumulation must occur before establishment of a new tip but this may not be the initial event in branch formation. In addition, branches are formed in aseptate hyphae, although this may also result from vesicle accumulation for different reasons associated with loss of apical polarity. At the biochemical level, there is strong evidence for internal regulation of branching by Ca2+and cyclic nucleotides. Ca2+ has been shown to affect hyphal extension rate and branch formation in N. crassa (Reissig & Kinney, 1983; McGillivray & Gow, 1987; Schmid & Harold, 1988; Dicker & Turian, 1990; Robson ef al., 1991a) and in Achlya bisexualis (Harold & Harold, 1986). Schmid & Harold (1988) found that low levels of Ca2+ reduce hyphal extension rate, had less effect on biomass production, but significantly altered hyphal morphology. Treatment with a calcium ionophore resulted in loss of calcium from the hyphae and increased branching and they suggested that a cytoplasmic Ca2+gradient was required for apical dominance but not for polarised growth. Dicker & Turian (1990) observed low extension rates and induction of 'frost' and 'spray' branching pattems following treatment of N.crassa with the calcium channel blocker verapamil. Similar branching pattems in 'frost' and 'spray' mutants reverted to normal morphology in the presence of high levels of exogenous calcium. Deficiencies in calcium uptake may Kinetics of branch formation therefore give rise to increased branching in these and other At the population level, the timing of branch formation may morphological mutants. Robson ef al. (1991a) suggested that be considered with respect to the hyphal growth unit, which the effect of calcium is mediated through calmodulin dependent is approximately constant in a young colony and in the protein kinases. Antagonists of calmodulin decreased experipheral growth zone of a mature colony. Thus, when the tension rate and increased branching in Fusariurn graminearurn ratio of total mycelial length to branch number exceeds this with no effect on specific growth rate. Control of branching by CAMPhas also been suggested by value, a branch must be formed somewhere in the colony to several workers (Mishra, 1976; Terenzi et al., 1976; Pall & maintain the hyphal growth unit. At the level of the individual hypha, a branch is formed due to the inability of a hypha Robertson, 1986). Recently Robson et al. (1991b) found that extending at a linear rate to accommodate biomass synthesized treatment of mycelia of F. graminearurn with exogenous CAMP at an exponential rate. A branch is therefore formed when decreased extension rate and increased branching, while

J. I. Prosser

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Mycelial development The description above is for 'typical' mycelial growth but even within the peripheral growth zone, there is evidence of changes during colony development. The best characterised system, within the ascomycetes, is that of mycelial differentiation in N. crassa. In young mycelia of this fungus, all hyphae are similar in terms of hyphal diameter, extension zone length and hyphal extension rate and all branches are subtended at an angle of 90" from the parent hypha. At approximately 22 h several dramatic changes occur (McLean & Prosser, 1987). Branch angle decreases from 90 to 63' (Fig. 2a), hyphal extension rates and diameters increase (Fig. 2b, c) and a hierarchy is established in which parental hyphae are wider and extend faster than branches which they subtend. After approximately 10h, constant extension rates and diameters are reached. The ratio between diameters of leading hyphae, primary branches and secondary branches is 100 :66 :42 and for extension rates is 100:62:26. Similar ratios are obtained for other strains of Neurospora and for other fungi (Prosser, 1983). The most likely explanation for this behaviour is the production at the colony centre, where growth is reduced, of a secondary metabolite or staling compound which diffuses to the colony margin. This compound, or group of compounds, simultaneously reduces the rate of branch initiation, increases extension rate and results in negative chemotropism such that branches are directed away from the colony centre. It appears, therefore, that staling compounds may be involved in chemotropic responses, although Pall & Robertson (1986) suggested a role for CAMP in internal control of the hierarchical patterns in hyphal diameter and extension rate. Zhu & Gooday (1992) also found differences in the susceptibility of undifferentiated and differentiated hyphae of Botytis cinerea and Mucor rouxii to antibiotics affecting wall synthesis. In both organisms, hyphal diameter increased with age, and in B. cinerea hyphal extension rate was directly proportional to the square of hyphal diameter. This suggests a correlation between extension rate and cross-sectional area, 1000 but a similar relationship was not found in M. rouxii. Hyphal E tips of differentiated mycelia of B. cinerea and M. rouxii were 3 ; 800 both more susceptible than hyphae in young colonies to u E treatment with nikkomycin, an inhibitor of chitin synthesis. .-5 600 Hyphae in differentiated mycelia of M. romii were also more E sensitive to treatment with echinocandin, which inhibits 400 glucan synthesis. Differential effects on the two fungi may be explained by differences in wall structure, B. cinerea containing 200 both chitin and glucans, while hyphal walls of M. rouxii possess both chitin and chitosan, in addition to glucans. The 0 I I I I 20 25 30 35 40 45 50 reasons for greater sensitivity of wider, faster growing hyphae Time (h) is not clear but may result from the larger surface area of Fig. 2. Changes in (a) branch angle (b) hyphal diameter, and (c) extensible material, providing a greater target for attack. hyphal extension rates in colonies of Neurospora crassa. 0, Leading hyphae; 0 , primary branches; 0, secondary branches).

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cGMP had the reverse effect. cGMP also decreased branching in highly branched, colonial mutants of F, gramineamrn but CAMP had no effect. As with Ca2+,they suggest that cyclic nucleotides may exert effects on tip growth and branch formation through phosphorylation of specific proteins.

ENVIRONMENTAL AND GENETIC CONTROL OF BRANCHING PATTERNS During the process of mycelial development a reduction in branching is correlated with an increase in hyphal extension rate. Many effects of environmental factors and paramorphogens on mycelial growth and branching can also be explained

Growth kinetics of mycelial colonies and aggregates by the intimate relationship between hyphal extension rate, branch initiation and specific growth rate. Thus, if specific growth rate is unaltered and extension rate decreased, newly synthesized biomass must be redirected towards increased branch formation. Similarly, an increase in specific growth rate which does not affect extension rate will also increase branching. The relationship may be expressed in the equation E = pG, where E is the mean extension rate and G is the hyphal growth unit length, which decreases as branch formation increases. This relationship is discussed by Bull & Trinci (1977) and Prosser (1983) and will be illustrated here by one example only. L-sorboseinduces formation in N. crassa of discrete, densely branched, self-limiting colonies distinct from the diffuse spreading colonies observed during normal growth. Sorbose does not affect specific growth rate but results in increased branch formation (reduced hyphal growth unit length) and reduced hyphal extension rate. At a concentration of 20 g I-', hyphal growth unit length is decreased from 323 to 40 pm while colony radial growth rate decreased from 1001 to 100 pm h-I (Trinci & Collinge, 1973). Increased hyphal density increases substrate utilization and/or production of inhibitory staling compounds to such an extent that the hyphal extension rate is insufficient to allow growth into areas of fresh substrate. A similar situation is normal for yeast and bacterial colony formation and is an example where alteration in the regulation of branch formation, relative to extension rate, reduces the efficiency with which solid medium may be colonized and nutrients utilized. This alteration could, however, be an advantage in the formation of differentiation structures which involve hyphal aggregation; induction of a factor reducing extension rate could be the initial event in such a process. The primary effect of sorbose in N.crassa may be inhibition of wall synthesizing enzymes leading to reduction in extension rate, with increased branch formation a secondary effect. Similar effects are also found in mutants in which hyphal growth and branching have been altered. For example, colonial mutants of N. crassa show the colonial morphology described above. Again this is due to an increase in branching frequency but with specific growth rate equal to that of the wild-type strain (Trinci, 1973). A wide range of colony morphology is exhibited by mutants of N. crassa resulting from variation in hyphal extension rate, specific growth rate and branching frequency and Scott (1976) and Mishra (1977) discuss the role of mutants in elucidation of mechanisms controlling these processes. In glucose limited chemostat cultures of F. graminearurn, colonial mutants are selected with morphologies ranging from sparsely branched mycelia, with hyphal growth units approximately 75 % of the wild type, to . very densely branched mycelia (Wiebe ef al., 1 9 9 2 ~ )Hyphal growth units in the latter are less than 10% of the wild type. Selection and dominance by colonial mutants is determined by the nature of the mutant, the nature of the limiting nutrient and the dilution rate. The mutation may affect maximum specific growth rate, the affinity for the limiting substrate and, in one strain, activity of phosphoketopentaepimerase has been implicated through observation of competition under different forms of carbon limitation (Wiebe ef al., 1992 b). Genetic recombination also gives rise to different patterns

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100

200

300

400

500

Fig. 3. Profiles of electrical current flow around hyphae of (a)

Neurospora aassa and (b) Aspergillus nidulans. (From Gow, 1984, with permission.)

of growth within a single colony. The familiar phenomenon of sectoring was described by Pontecorvo & Gemmell (1944). Sectors arise through a spontaneous occurrence of areas of mycelium with either different hyphal extension rates, different specific growth rates or where relative specific growth rate changes during colony development. In all of these cases, observed patterns may be explained in terms of the interrelationship between specific growth rate, hyphal extension rate and branch initiation.

The role of electrical currents in growth and branching During the last 10 yr, the role of electrical currents in hyphal growth has attracted increased interest. Electrical current is generated within the hypha by flow into the tip of positive ions and their expulsion in distal regions. Initial studies were carried out on Achlya (Kropf et al., 1983, 1984; Gow, Kropf & Harold, 1984; Kropf, 1986) but the generation of transh~phal ion currents now appears to be a universal characteristic of hyphal growth. Gow (1984) has demonstrated such currents in representatives of the major fungal groups and current patterns for N.c r a m and A. nidulans are illustrated in Fig. 3. In the majority of cases, positive current enters apically, leaves distally and is absent from non-growing hyphae. The situation is reversed in Allomyces macrogynw, in which current flows outwards from hyphal tips but enter rhizoids. In Achlya the current is mediated by protons which flow into the tip by symport with amino acids and are expelled

J. I. Prosser Tip

Branch

Fig. 4. The generation of transcellular ion currents by Achlya bisexualis. (From Kropf et al., 1984, with permission.)

distally by a proton translocating ATPase (Fig. 4). Initially a causal relationship was sought between electrical currents and apical growth and polarity and, in Achlya, there was evidence that reversal of current preceded and predicted branch formation (Fig. 4). Subsequent observations indicate links between apical polarity and current generation to be incidental. For example, the polarity of current can reverse without effects on tip extension and polarity, normal currents can be generated by non-growing hyphae and inward current and branch formation are not always correlated (McGillivray & Gow, 1987; Schreurs & Harold, 1988; Takeuchi ef al., 1988; Cho, Harold & Schreurs, 1991). It now seems likely that electrical currents indicate regions of localized nutrient

transport. This is best illustrated with reference to A. rnacrogynus, where inwardly directed current is found in rhizoids, the site of nutrient uptake, but not in hyphae (de Silva et al., 1992). External electrical fields do, however, influence hyphal growth and morphogenesis. McGillivray & Gow (1986) investigated the effect of applied electrical fields on germ tube emergence, the site of branch formation and the direction of hyphal extension in several fungi. Effects varied between different organisms, but will be illustrated with respect to N. crassa. Both conidiospores and young colonies were exposed to electrical fields of varying strength. Germ tubes emerged on the side of the anode and this polarization increased with increasing field strength. At low-field strength, germ tube hyphae grew towards the anode and hyphae which had formed in the absence of a field re-orientated to grow towards the anode when a field was applied. At high field strength, growth became perpendicular to the direction of the field. Applied fields also increased the rate of branch formation and -branches were formed on the side directed towards the anode. This resulted in the formation of spindle shaped colonies (Fig. 5). Growth towards the anode may occur through electrophoresis of morphogenetic membrane proteins or through the influence of ion uptake on the cytoskeleton at the hyphal tip. Perpendicular orientation in strong fields was thought to

Fig. 5. Colonies of Neurospora crassa exposed to exogenous electrical field of 30 V cm-' for 24 h (from McGillivray & Gow, 1986, with

permission).

Growth kinetics of mycelial colonies and aggregates

520 Light-sensitive fungi

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Fig. 6.Spiral growth of leading hyphae of (a)Neurospora crassa (scale bar, I mm) and (b) Aspergillus nidulans, (scale bar, I mm) 30 and 36 h, respectively after inoculation. (From Trinci et a]., 1979, with permission.)

relieve inhibition of extension resulting from perturbations of the membrane potential at the tip. Orientation of newly formed branches and increased branch frequency may also result from electrophoresis of morphogenetic proteins and/or from disruption of the vesicle transport system giving rise to local accumulation of vesicles. While the fields applied in the studies were greater than those experienced during normal growth, ion currents may play a significant role in the timing and positioning of branch formation, and will certainly prove a useful tool in the elucidation of mechanisms for hyphal extension and branching.

SPIRAL GROWTH Sprial growth is frequently observed in fungal colonies (Ritchie, 1960) and is illustrated in Fig. 6 for Neurospora crassa. Madelin, Toomer & Ryan (1978) examined 157 fungal isolates of which 21 and 39 showed pronounced and weak spiralling respectively. The process involves bending or coiling of hyphae and occurs on the surface of solid media but not in liquid medium, in aerial hyphae or in hyphae penetrating agar. It is thought to result from rotation of the hyphal tip causing it to roll over the surface. The cellular mechanism of tip rotation is poorly understood but may involve stretching of spiral structures in the wall of the extension zone, under the influence of turgor pressure. Beever (1980) isolated mutants of N.crassa which exhibited more pronounced spiral growth and he suggested that the mutation was in a gene controlling the

Fig. 7. Schematic representation of development of mycelial bands in Petri dish cultures due to an endogenous rhythm (clock-mutant) and light dependent gowth rhythm. (From Lysek, 1984, with permission.)

orientation of spiral structures in the wall, or in one reflecting the effect of turgor pressure on the extension rate. Tip rotation has never been directly observed in vegetative hyphae but occurs in sporangiophores of Phycomyces blakesleeanus and M. mucedo, and conidiophores of Aspergillus giganteus (see Gooday & Trinci, 1980). In Phycomyces sporangiophores, the tip rotates in either a clockwise or counter-clockwisedirection depending on the phase of growth, and in some regions the rate of spiralling is related to the hyphal extension rate. The proportion of hyphae spiralling is dependent on the hardness of the agar (Trinci ef al., 1979) and is best observed in young or sparse colonies and on weak nutrient media. In older, dense colonies negative autotropic hyphal interactions obscure spiral g o w t h behaviour.

RHYTHMIC GROWTH

A final example of 'atypical; growth on solid medium is rhythmic growth or banding which may be induced by a variety of genetic and environmental factors (Lysek, 1984). The process results from the relationship between hyphal extension rate, branch formation and specific growth rate and is illustrated by Fig. 7. In the case of the Podospora nnserina clock-mutant, hyphae growing on the agar surface increase

J. I. Prosser branching, and growth of the surface mycelium becomes self limiting due to staling. Submerged hyphae do not increase branching, continue to extend and reach the surface some distance beyond the staled mycelial front. This prevents further growth of the latter and the process is then repeated giving rise to regions, or bands of alternatively dense and sparse mycelium. The differences in branching frequency between surface and submerged hyphae appear to be due to differences in oxygen availability. When rhythmic growth is induced by light-dark cycles, extension of surface hyphae is reduced by exposure to light, while submerged hyphae are protected and are again able to extend beyond the margin of the surface mycelium. In both cases variation in extension rates and branching is associated with gradients in oxygen concentration and reduced extension rates and increased branching are accompanied by increased oxygen uptake. Lysek (1984) lists factors which induce rhythmic growth and suggests alteration of membrane structure and/or permeability as a common mechanism, with consequent changes in the flux of ions and molecules. Increased oxygen uptake is believed to be due to increased permeability of the membrane to protons, increased turnover of ATPase to maintain proton gradients and consequent accumulation of potassium ions within the hyphae. Increased permeability may also allow leakage of potassium ions throughout the hypha rather than at the tip only, as occurs normally. This may lead to a loss of apical polarity and reduction and cessationof hyphal extension. As pointed out by Lysek, rhythmic growth represents a form of differentiation and provides a mechanism for the spatial and temporal distribution of mycelia with different functions and properties. Thus, elongating hyphae, seeking out new sources of nutrients, are separated spatially from staling hyphae which may differentiate into sporing and resting structures. There are many examples throughout the fungal kingdom of rhythms and banding in the formation of such structures. Mycelial growth rhythms therefore provide a link between the relatively well understood and characterized processes of vegetative growth and branching and the formation of more complex structures and pseudotissues, and point to ways in which the former may increase our understanding of initial events in differentiation.

GROWTH OF HYPHAL AGGREGATES In liquid culture filamentous fungi grow as dispersed mycelia or as pellets. Growth and branching of dispersed mycelia are in many respects similar to unrestricted growth of young colonies on solid medium. The major difference is the absence of significant gradients in substrate and product concentrations which, coupled with physical forces in stirred cultures, usually prevents differentiation. Growth kinetics are similar to those for unicellular organisms but deviations may result from the filamentous growth fonn. Van Suijdam & Metz (1981) provide a review of growth of dispersed mycelia, and stress the effects of the filamentous growth form in increasing medium viscosity and reducing mass transport of nutrients, oxygen and heat. The latter leads to some heterogeneity within mycelia but this is not sufficient to give rise to differentiation. This can,

Fig. 8. Cross-section of a pellet of Penicillium chysogenum stained with cresyl violet. See text for description of layers LI-L4. (From Wittler et al., 1986, with permission.)

however, occur at the air-water interface of unstirred cultures and conidiation may occur in both batch and continuous cultures under conditions of nutrient exhaustion or limitation. Van Suijdam & Metz (1981) present a mathematical model based on extension rates and branching, breakage or fragmentation of hyphal and hyphal tensile strength, and which considers the effect of growth rate and shear stresses on morphology resulting from stirring. The model provides good qualitative predictions but was rejected because of poor quantitative fit between experimental and theoretical results. The authors suggest that this lack of fit was due to variation in hyphal tensile strength with both age and specific growth rate. While many studies into growth in liquid culture are directed towards industrial fermentations and product formation, experiments with liquid cultures, particularly continuous cultures, have provided important information regarding mechanisms of growth and branching in colonies growing on solid medium. Two examples are Trinci's work on colonial mutants of Neurospora crassa, discussed above, and work by Robinson & Smith (1976, 1979, 1980) and Smith & Robinson (1980), which elucidated the effects of glucose concentration and specific growth rate on growth and branching in G. candidurn both in liquid and on solid medium. Pellets are mycelial aggregates which result from either aggregation of spores, entrapment of spores by young germtubes or, less commonly, aggregation of young mycelia. The properties of pellets and factors affecting their production have been reviewed by Whittaker & Long (1973) and Metz & Kossen (1977).They vary in shape from sphericalto ellipsoidal, may have a smooth or rough surface and aggregates may be loose/fluffy or compact, the latter reducing diffusion of substrates from surrounding medium into the pellet. Wittler ef al. (1986) stained pellet sections with cresyl-violet and described four distinct layers (Fig. 8). The outer layer (Ll) was heavily stained, contained growing hyphae and surrounded a second layer (L2) which was less easily stained and showed

522

Growth kinetics of mycelial colonies and aggregates signs of autolysis. The third layer (L3) contained cytoplasm, as indicated by staining, and was only observed in hollow pellets with irregular wall structure. The centre of the pellet (L4) was hollow, contained no hyphae but sometimes contained precipitates from the nutrient medium. The thickness of the four layers varied both during fermentation and with different fermentation conditions. A theoretical consideration of the growth kinetics of pellets was first provided by Pirt (1966). Pellet radius was considered to increase at a constant rate and after initial exponential growth throughout the pellet, growth at the centre became limited by diffusion of oxygen and subsequent exponential growth was restricted to an outer layer of constant width. This model predicted cube root kinetics for increase in pellet biomass which has been observed experimentally. Subsequent models have incorporated factors such as hyphal fragmentation, death, autolysis, substrate and oxygen utilization, transport of nutrients and oxygen by diffusion and convective flow and pellet size distribution (Metz & Kossen, 1977; Van Suijdam, Hols & Kossen, 1982; Edelstein & Hadar, 1983; Wittler ef al., 1986). Wittler ef al. (1986) used a microprobe to measure dissolved oxygen tension within pellets of Penicillium chysogenum and compared experimental data with predictions of the theoretical model. The data indicate, however, that any description is complicated by the distribution of mycelial biomass within the pellet, its oxygen requirements and the dynamics of flow and diffusion within the pellet. Their microscopic data showed hyphae in the outer layer directed radially away from the centre of the pellet. Aggregation of the hyphae within pellets results mainly from physical factors and is not a true differentiation process. Such processes are most readily observed on solid media and have already been introduced in considering colonial mutants of Neurospora crassa and rhythmic growth. More complex examples are the formation of fruiting bodies, sclerotia and mycelial cords or rhizomorphs, (Watkinson, 1979; Cooke, 1983). Formation of these structures involves aggregation of hyphae and to an extent can be explained by the interrelationship between hyphal extension rate and branching. For example, sclerotium formation is associated with an increase in branching and a decrease in hyphal extension rate while formation of mycelial cords involves suppression of lateral branch formation and reinforcement of apical dominance to maintain extension rate. Initiation of fruiting bodies also involves increased branching and the similarities between sclerotium and fruiting-body initiation has been discussed by Cooke (1983). A further major feature in these processes is the loss, or masking of negative autotropism and the occurrence of hyphal fusions. Such processes are observed in old regions of typical colonies on solid medium and are features of staling. Cooke (1983) and Watkinson (1979) describe factors which stimulate initiation of secondary growth structures, many of which are associated with staling. As pointed out by both authors, however, our knowledge of both the factors which initiate formation of secondary structures and the physiology of their growth is poor and the environmental and endogenous factors involved are varied and numerous. In addition, there is little information on the spatial organization and separation of

such structures within a developing colony. In the next section, a possible basis for such studies into these aspects will be discussed.

Theoretical models There have been several attempts to describe aspects of fungal g o w t h in terms of mathematical models (for review see Prosser, 1982, 1983). Most models operate at a particular level, e.g. cellular, biochemical, mycelial, population, but attempts have been made to relate growth at different levels. Here I will describe three models which have been constructed specifically for fungal colony q o w t h and a fourth approach which may have potential for mycelial fungi. Prosser & Trinci (1979) constructed a model for early mycelial colony growth based on cellular mechanisms for hyphal growth and branching. Vesicles were produced at a constant rate in distal hyphal regions and were transported to the tip at a constant rate, where they accumulated and fused with existing wall and membrane to give hyphal extension. The duplication cycle concept was introduced by considering septation in apical compartments. Accumulation of vesicles behind septa resulted in formation of lateral branches which extended in the manner of the parent hyphae. The model generated re dictions at the m~celiallevel regarding changes in total mycelial length, number of branches and interbranch distances. These re dictions compared favourably with experimental data on growth of Aspergillus nidulans and Geofrichum lacfis. Although it was not attempted, the model has potential for investigation of the effects of environmental factors on vesicle production and transport and consequent effects on mycelial growth and branching. This would be a necessary preliminary to its use in predicting formation of hyphal aggregates. The model of Edelstein (1982) and Edelstein & Segel(1983) effectively incorporates and substantially extends the model of Prosser & Trinci (1979). While the latter predicted features of colony growth from the properties and behaviour of many hyphae considered individually, the formers workers considered average properties of hyphae and emphasized the crucial role of the hyphal tip in controlling and regulating mycelial growth. They were also the first to seriously consider hyphal death, hyphal fusion and differences resulting from different forms of branching. Growth was described in terms of two basic properties, hyphal density (p: hyphal length per unit area) and a new variable, tip density (n: the number of tips per unit area). The basic model therefore consists of two ~artialdifferential equations describing changes in these two variables. 6p/6f = nu -d(p), 6n/6t = 6nv/6x o(p, n).

+

According to equation (I), hyphal density will increase as a result of tip growth at a rate equal to the product of tip density and tip extension rate (v), which is assumed constant. This product, nu, is equivalent to tip flux. Hyphal density will decrease through hyphal death (4 which is described as a function of r and a rate constant for autolysis (y,). Changes in tip density will depend on flux within a specific

J. I. Prosser

Distance from centre of colony (cm) Fig. 9. Experimentally observed hyphal density distribution for colonies of Sclerofium rolfsii grown on media containing (a) 0.05 % glucose and (b) 2% glucose after 52 h (-), 76 h (----), 94 h (----) and 1113 h (.-.-.-) growth. Horizontal lines indicate the sizes of weighed samples. (From Edelstein et al., 1983, with permission.)

region [the first term in equation (2)] and will increase due to branching and/or decrease due to tip death or anastomoses, all of which are represented by o. Substitution for o by suitable functions describes dichotomous and lateral branching, tip to hypha and tip to tip anastomoses and tip death due to atrophy or overcrowding. For example, dichotomous branching is represented by o = o,,n, where o, is the product of the rate of branching and the number of daughters produced per tip. Lateral branching is represented by o = o, where o, is the number of branches produced per unit length of hypha per unit time. The basic model was extended to consider uptake of a growth limiting substrate from the medium and its redistribution within the mycelium. Distribution of substrate within the medium was described by simple diffusion and uptake by Michaelis-Menten kinetics. Changes within the mycelium were dependent on uptake, diffusive and convective flux and consumption for growth and maintenance. A major advantage of the basic model was the ability to apply phase plane analysis, in which two dependent variables are plotted against each other for a number of time dependent solutions, to determine the ability of mycelial colonies to propagate under different branching conditions. For example, hyphae which formed dichotomous branches and tip to tip anastomoses developed colonies which grew locally, with growth occurring throughout the colony and hyphal density increasing significantly at the centre. With tip to hypha anastomoses, tip density maintained a maximum immediately behind the colony margin and spreading colonies were formed with uniform hyphal density. Although the former case is atypical for growth on agar, it may be better adapted to growth on small, concentrated nutrient sources and also provides the localized increase in hyphal and tip density necessary for formation of fruiting bodies and other secondary structures.

Throughout their analysis, rate constants were assumed to have constant values. This may not be the case in natural situations; indeed, a regulated change in, for example, a branching rate constant may initiate a differentiation process. The model is capable of predicting the outcome of such behaviour but the increase in complexity prevents use of phase plane analysis and relies on simulation of differential equations by numerical methods. The same applies to the extended model, in which substrate uptake and utilization are considered. The latter provided predictions for depletion of nutrients below a developing colony which appear qualitatively similar to those obtained by Robson et al. (1987) (see Fig. 9). The mode1 also suggests a mechanism for rhythmic mycelial growth. To achieve this, assumptions are made regarding the effect of intracellular metabolite concentration on extension rate and branching frequency. Below a concentration c, hyphae do not extend and at c, reach their maximum extension rate. Branching frequency switches from a basal level, below concentration c,, to a higher maximum level above concentration c,. With careful choice of rate constants, this model predicts the regular occurrence of regions of high hyphal and tip density and the authors discuss factors which control its periodicity. Thus, although the model is sensitive to values chosen, it does allow for the existence of such bands. The basic model of Edelstein (1982) has been tested by comparison with experimental data on colony growth of Sclerotitrm rolfsii (Edelstein et al., 1983). Hyphal density was determined in colonies growing on solid medium containing 0.5 and 2 % glucose by weighing portions of mycelium removed from growing colonies (Fig. 9). At both glucose concentrations hyphal density near the colony centre was low, but density near the margin increased during growth. At 0.5 % glucose, hyphal density decreased, in particular at the colony

524

Growth kinetics of mycelial colonies and aggregates

developing colony but additionally predicts the effect of nutrient concentration and agar depth on the yield of conidia obtained. It therefore provides a basis for experimental work in this area.

Reaction-diffusion models

10

20

30

10

20

30

Distance from centre of colony Fig. 10. Predicted changes in (a, b) hyphal density and (c, A) tip

density from simulation of the model of Edelstein ef al. (1983).For two sets of parameters (a, band c, A). (From Edelstein ef al., 1983, with permission.)

centre, but this did not occur at 2 % glucose. These experimental data agree qualitatively with predictions of a model which assumed lateral branching, tip to hypha anastomosis and hyphal autolysis (Fig. 10). The model predictions also imply that the hyphal growth unit is constant within the peripheral growth zone. This approach provides a fuller description of colony growth than had previously been obtained and is a basis for consideration of differentiation processes. Description of substrate uptake and utilization provides a useful mechanistic basis to the model but necessarily increases complexity. Its probable function is in predicting what is possible qualitatively. AS with many of its predecessors, the major problem in quantitative prediction lies in the inability to measure reliably rate constants and other parameters required for simulation. Georgiou & Shuler (1986) also presented a model in which the fungal biomass is considered as a whole, rather than as individual hyphae. and used this to predict growth and conidiation on solid medium. Four components of biomass were considered, vegetative biomass, competent biomass (capable of differentiation) conidiophore biomass and conidial biomass. The basic model consisted of seven differential equations describing rates of change of these four biomass components, the increase in colony radius and changes in concentrations of glucose and nitrate. Additional equations were included for diffusion of substrate within the agar. Prediction of the effect of glucose concentration on extension rate agreed favourably with published data. Other predictions, particularly those regarding conidiation, were impossible to test due to a lack of experimental data. This model, like the one previously described, predicts nutrient depletion below a

Finally, a more general approach to differentiation and pattern formation will be considered, which has yet to be applied to fungal systems. This is the reaction-diffusion model of Gierer & Meinhardt, comprehensively described by Meinhardt (1982). Possibly the most attractive feature of this theory is its simplicity. It proposes that pattern is generated by two factors or compounds. One is an activator, an autocatalyst stimulating its own production, and the other inhibits production of the activator. Both diffuse from the area of production but the inhibitor diffuses more rapidly and consequently prevents activator production in the surrounding regions but cannot prevent autocatalysis at the original site of production. There is, therefore, long range inhibition and short range activation. Eventually, increase in the activator comes to rest due to some limiting factor (e.g. diffusion of the activator) and stable activator and inhibitior concentration profiles are obtained. Variability in the type, periodicity, stability and other properties of the pattern result from differences in diffusion coefficients, rates and decay and other features of model parameters. As pattern depends on just two compounds, the basic model consists of two equations describing changes in concentration of activator (a) and inhibitor (h). Each varies with both position ( x ) and time (f),necessitating description by partial differential equations [equations (3 and (4)].

In equation (3), the first term represents production of a, which is proportional to a2 (representing autocatalysis) and inversely proportional to inhibitor concentration (rate constant c). The second term represents decay, with first order rate constant, p. The third term describes changes due to diffusion, with diffusion coefficient D,. Production of inhibitor [equation (4)] also depends on activator concentration, but is not inhibited, also decays, with rate constant u, and diffuses with a diffusion coefficient D,. This mechanism leads, for instance in an array of cells which have an extension comparable to the range of the activator, to a peak of activator concentration at one end of the array and no activator at the other end, that is, to a polar concentration profile. Two applications of this model will be described which have relevance to fungal growth. The first is the formation of net-like structures (Meinhardt, 1976), specifically production of veins in leaves, and has relevance to branch formation and anastomosis. The second is formation of periodic patterns, with applications to the formation of fruiting bodies and other secondary structures in fungal colonies. Formation of net-like structures begins with a field of undifferentiated cells from which a branching filament of differentiated cells will develop. The model is expanded to

J. I. Prosser

525

Activator (a)

A

A

@' Inhibitor (h)

Depleted substance ( s )

Differentiation (y)

Time -t Fig. 11. Formation of a filament and branches of differentiated cells from a field of undifferentiated cells over a series of time intervals a-h. Activator (a), inhibitor (h) and substrate (s) concentrations are represented on the z axis. Achievement of a critical activator concentration increases concentration of the differentiation factor y. (From Meinhardt, 1982, with permission.)

Activator (a)

L&& Depleted substance (sf

Differentiation (y)

0 0 (a)

(b)

Time + Fig. 12. Formation of a dichotomously branching structure over a series of time intervals a-e. Differentiation (y) results from achievement of critical concentrations of activator (a) with inhibition by depletion of substrate (s). (From Meinhardt, 1982 with permission.)

include substrate concentration (s) and a substance whose concentration, y, is high in the differentiated state. Four equations are therefore required to describe this system. The first two are equivalent to equations (3) and (4) above, but modified such that activator and inhibitor production depend on substrate concentration, and there is a constant basal rate of production of both. The third and fourth equations describe

changes in s and y. The former is produced at a constant rate by each cell, decays with first-order rate kinetics, is removed by differentiated cells and is subject to diffusion. The concentration of y increases in proportion to activator concentration, decays and also undergoes positive feedback, such that following production of a certain concentration of y by a, further production is independent of a.

Growth kinetics of mycelial colonies and aggregates

Fig. 13. Formation of a periodic pattem in a non-growing field. Activator concentrations are shown over a series of time intervals a-d.

(From Meinhardt, 1982, with permission.)

Changes in the concentration of all four substances within a growing field are illustrated in Fig. 11 over a series of time intervals. In Fig. 11 (intervals a, b) activator and inhibitor concentrations combine to give a localized increase in activator, leading to formation of the first differentiated cell of the filament. Activator production by this cell is reduced by depletion of a but increases in neighbouring cells, one of which subsequently develops a new activator maximum and a new differentiated cell is formed. Repetition of this process leads to development of a filament of differentiated cells (Fig. 11, intervals c-f). Inhibitor production is dependent on activator concentration and the high activator concentration at the growing tip results in high inhibitor concentrations. This provides a mechanism for apical dominance which, along with substrate depletion by the differentiated cells, prevents activator maxima developing within the filament. Eventually (Fig. 11, interval g) inhibitor diffusion from the tip can no longer prevent accumulation of activator by the basal rate of production. New maxima are then formed within and then to one side of the filament, where s is high, and a lateral branch is formed. Repetition results in formation of further lateral branches. Conditions are described for both s-dependent and s-independent branching density and growth of filaments is directed towards regions of high s concentration. This results in negative autotropic effects due to strong repulsion by inhibitor produced by growing tips and weaker repulsion due to reduced substrate concentration along the filament. The model also predicts tip to filament anastomosis, but not tip to tip fusion. Further modification, in fact simplification, of the model predicts dichotomous branching which occurs when inhibition of activator autocatalysis results from depletion of substrate. The system can therefore be modelled by just three equations, for a, s and y, and changes in these three substances are illustrated in Fig. 12. The model as originally constructed considers differentiation of existing undifferentiated cells and for this and other reasons would require modification before application to fungal growth and branching. The predictions regarding several important features of mycelial growth do, however, indicate that such application would increase our understanding of mycelial growth and branching. Formation of periodic structures is based on the work of Turing (1952) and occurs in a field which is large with respect to the range of the inhibitor. Activator peaks can therefore develop when the distance from existing peaks exceeds a critical value. This produces an irregular pattem but one in which maximum and minimum distances between centres are

maintained (Fig. 13). Expansion of the field, through growth, will cause centres to move apart allowing creation of new activator maxima and maintenance of distances between centres. This model has been used to explain the formation of stomata on leaves, cilia on the surface of a Xenopus embryo and distribution of hairs and bristles on insects. Again, modification would be required, but the approach has potential in describing the spacing of fruiting bodies and other structures in a developing colony.

CONCLUSION During the last 25 yr, an extensive range of studies has provided a good understanding of branching of filamentous fungi and the cellular mechanisms involved. This has necessitated a quantitative approach and the introduction of concepts such as the peripheral growth zone and the hyphal growth unit which have directed experimental work. Questions still remain, particularly with regard to orientation of hyphal growth, the positioning of new branches and the mechanism of vesciular transport. Both the experimental work and the quantitative approach provide a basis for understanding the initial events in formation of secondary structures, but we are largely ignorant of the factors involved in formation of mycelial aggregates and their distribution and spacing within a colony. The theoretical modelling approach may not necessarily provide a ready made solution to every problem in ascomycete developmental biology. Meinhardt's work provides a mechanism for generation of spatial and positional information but the complete analysis requires knowledge of the factors affecting hyphal extension and branching. Such factors are many and varied and differentiation may result from production of several factors (compounds) or the combined effect of many. In addition, technical advances are required to ~ r o v i d eexperimental data to test model predictions. The role of theoretical models, therefore, lies in directing such experimental work by defining key questions to be answered, preventing development and use of techniques which cannot answer such questions and discouraging a merely descriptive approach to developmental biology. I would like to thank Dr Neil Gow for helpful discussions regarding electrical currents.

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(Accepted 18 October 1992)

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