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Lavery (1990)

mycelial organisms which show apical growth also grow exponentially. Plomley (1959) was the first to suggest that filamentous fungi have a 'growth unit' which is replicated at a constant rate and is composed of the apex of the hypha and a short length of supporting hypha. Trinci (1974) demonstrated that the total hyphal length of a mycelium and the number of tips increased exponentially at approximately the same rate. Thus, when the volume of the hyphal growth unit exceeds a critical volume a new branch, and hence, a new growing point, is initiated. This is equivalent to the division of a single cell when the cell reaches a critical volume. Hence, the rate of increase in hyphal mass, total length and number of tips is dictated by the specific growth rate and:

where H is total hyphal length and A is the number of growing tips.

In submerged culture (shake flask or fermenter) a mycelial organism may grow as dispersed hyphal fragments or as pellets (see also Chapters 6 and 9). The growth of pellets will be exponential until the density of the pellet results in diffusion limitation. Under such limitation the central biomass of the pellet will not receive a supply of nutrients, nor will potentially toxic products diffuse out. Thus, the growth of the pellet proceeds from the outer shell of biomass which is the actively growing zone and was described by Pirt (1975) as:

where M0 and M are the mycelium mass at time 0 and t, respectively. Thus, a plot of the cube root of mycelial mass against time will give a straight line, the slope of which equals k.

It is possible for new pellets to be generated by the fragmentation of old pellets and, thus, the behaviour of a pelleted culture may be intermediate between exponential and cube root growth.

Whether the organism is unicellular or mycelial the foregoing equations predict that growth will continue indefinitely. However, growth results in the consumption of nutrients and the excretion of microbial products; events which influence the growth of the organism. Thus, after a certain time the growth rate of the culture decreases until growth ceases. The cessation of growth may be due to the depletion of some essential nutrient in the medium (substrate limitation), the accumulation of some autotoxic product of the organism in the medium (toxin limitation) or a combination of the two.

The nature of the limitation of growth may be explored by growing the organism in the presence of a range of substrate concentrations and plotting the biomass concentration at stationary phase against the initial substrate concentration, as shown in Fig. 2.2. From Fig. 2.2 it may be seen that over the zone A to B an increase in initial substrate concentration gives a proportional increase in the biomass produced at stationary phase. The situation may be described by the equation:

where * is the concentration of biomass produced, Y is the yield factor (g biomass produced g~'

substrate consumed), SR is the initial substrate concentration, and 5 is the residual substrate concentration.

Over the zone A to B in Fig. 2.2, s equals zero at the point of cessation of growth. Thus, equation (2.4) may be used to predict the biomass which may be produced

Fig. 2.2. The effect of initial substrate concentration on the biomass concentration at the onset of stationary phase, in batch culture.

. a-rtain amount of substrate. Over the zone C to lri'm a LL • the initial substrate concentration p -m increase in noA'ive a proportional increase in biomass. This V- (|uc to either the exhaustion of another subs-"!":_ yr'the accumulation of toxic products. Over the ^ B to C the utilization of the substrate is deleten-ously affected by cither the accumulating toxins or the availability of another substrate.

The yield factor ( Y ) is a measure of the efficiency of conversion of any one substrate into biomass and it can be used to predict the substrate concentration required to produce a certain biomass concentration. However, it is important to appreciate that Y is not a constantit will vary according to growth rate, pH, temperature, the limiting substrate and the concentration of the substrates in excess.

The decrease in growth rate and the cessation of growth, due to the depletion of substrate, may be described by the relationship between ¡j, and the residual growth-limiting substrate, represented in equation (2.5) and in Fig. 2.3 (Monod, 1942):

where s K

is the residual substrate concentration, is the substrate utilization constant, numerically equal to substrate concentration when fi is half /umax and is a measure of the affinity of the organism for its substrate.

The zone A to B in Fig. 2.3 is equivalent to the exponential phase in batch culture where substrate concentration is in excess and growth is at (imax. The zone C to A in Fig. 2.3 is equivalent to the deceleration phase of batch culture where the growth of the organism has resulted in the depletion of substrate to a growth-limiting concentration which will not support /xnv<x. If the organism has a very high affinity for the limiting substrate (a low Ks value) the growth rate will not be affected until the substrate concentration has declined to a very low level. Thus, the deceleration phase for such a culture would be short. However, if the organism has a low affinity for the substrate (a high Ks value) the growth rate will be deleteriously affected at a relatively high substrate concentration. Thus, the deceleration phase for such a culture would be relatively long. Typical values of Ks for a range of organisms and substrates are shown in Table 2.2, from which it may be seen that such values are usually very small and the affinity for substrate is high. It will be appreciated that the biomass concentration at the end of the exponential phase is at its highest and, thus, the decline in substrate concentration will be very rapid so that the time period during which the substrate concentration is close to Ks is very short.

The stationary phase in batch culture is that point where the growth rate has declined to zero. However, as Bull (1974) pointed out, the stationary phase is a misnomer in terms of the physiology of the organism, as the population is still metabolically active during this phase and may produce products called secondary metabolites, which are not produced during the exponential phase. Bull suggested that this phase be termed the maximum population phase. The metabolic activity of the stationary phase has been recognized in the physiological descriptions of microbial growth presented by Borrow et al. (1961) and Bu'Lock et al. (1965). Borrow et al. investigated the biosynthesis of gibberellic acid by Gibberella fujikuroi and divided the growth of the organism into several phases:

Maximum Specific Growth Rate Umax

Residual limiting substrate concentration

Fig. 2.3. The effect of residual limiting substrate concentration on the specific growth rate of a hypothetical bacterium.

(i) The balanced phase; equivalent to the early to middle exponential phase.

(ii) The storage phase; equivalent to the late exponential phase where the increase in mass is due to the accumulation of lipid and carbohydrate.

Table 2.2. Some representative values of Ks for a range of micro-organisms and substrates

Organism Substrate iCs(mgdm~3) References

Escherichia coli Glucose

Residual limiting substrate concentration

Fig. 2.3. The effect of residual limiting substrate concentration on the specific growth rate of a hypothetical bacterium.

6.8 X 10""2 Shehata and Marr (1971)

Saccharomyces Glucose 25.0 Pirt and cerevisiae Kurowski (1970)

Pseudomonas sp. Methanol 0.7 Harrison

(iii) The maintenance phase; equivalent to the stationary phase.

Gibberellic acid (a secondary metabolite) was synthesized only towards the end of the storage phase and during the maintenance phase. As discussed in Chapter 1, Bu'Lock et al. (1965) coined the terms trophophase, to refer to the exponential phase, and idiophase to refer to the stationary phase where secondary metabolites are produced. The idiophase was depicted as the period subsequent to the exponential phase in which secondary metabolites were synthesized. However, it is now obvious that the culture conditions may be manipulated to induce secondary metabolism during logarithmic growth, for example by the use of carbon sources which support a reduced maximum growth rate (see Chapter 4).

Pirt (1975) has discussed the kinetics of product formation by microbial cultures in terms of growth-linked products and non-growth-linked products. Growth-linked may be considered equivalent to primary metabolites which are synthesized by growing cells and non-growth-linked may be considered equivalent to secondary metabolites. The formation of a growth-linked product may be described by the equation:

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