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are determined by the temperature sensitivity of the slowest processes of intracellular assimilation and relative rates of surface exchange (Foy et al., 1976; Konopka and Brock, 1978).

This pattern of behaviour is emphasised in the plot (in Fig. 5.2b) of the species-specific slopes

Surface-to-volume ratio / |xm_1

of temperature sensitivity of replication (p, from Fig. 5.2a) against the corresponding organismic (sv-1) value. p is a significant (p < 0.05) correlative of the surface-to-volume attributes of the eleven algae tested. The regression, p = 3.378 - 2.505 log (sv-1), has a coefficient of correlation of 0.84 and explains 70% of the variability in the data. The open circles entered in Fig 5.3a are not part of the generative dataset but come from a previously untraced paper of Dauta (1982) describing the growth responses of eight microalgae. They have been left as a verification of the predictive value of the regression.

The hypothesis that algal morphology also regulates the temperature sensitivity of the growth rate is not disproved. For the present, p can be invoked to predict the growth rate of an alga of known shape and size at a give temperature, 9, following Eq. (5.6):

logr) = log(r2 0) + P [1000/(273 + 20) - 1000/(273 + 9 )]d-1

5.3.3 Resourcing maximal replication

That the slowest anabolic process should set the fastest rate of growth leads to an important corollary of concern to the ecologist. It is simply that it cannot be obtained without each of its resource requirements being supplied at demand-saturating levels. At steady state, the rate of photosynthesis and the rates of uptake of each of its nutrients match the growth demand. Moreover, as pointed out in Chapters 3 and 4, the pho-tosynthetic and uptake systems carry such excess capacity that they can sustain higher demands than those set by maximum growth rate. This is not to deny that the demands of cell replication might not at times exceed the capacity of the environment to supply them or that growth rate might not, indeed, fall under the control of (become limited by) the supply of a given resource. Following this logic, we can nominate the demand for resources (D) set by the sustainable growth rate and compare this with the abilities of the harvesting mechanisms to perform against diminishing supplies (S).

As a case in point, the Chlorella strain used in the analysis of growth rate (Table 5.1 and Reynolds, 1990) achieved consistently a maximal rate of biomass increase of 1.84 d-1 at 20 °C. Given the size of its spherical cells (d ~4 |im; s ~50 |im2; v ~33 |im3), this is faster than is predicted by the Eq. (5.6) of the regression (Fig. 5.2), which gives r20 = 1.31. Staying with the real data, one biomass doubling (taken as the equivalent of an orthodox cell cycle culminating in a single division) defines the generation time; by rearrangement of Eq. (5.3), tG = 9.05 h. During this period of time, the alga will have taken up, assimilated and deployed 1 g of new carbon for every 1 g of cell carbon existing at the start of the cycle. It is not assumed that the increase in biomass is continuously smooth but the average exponential specific net growth rate over the generation time is (1.84/86 400 s =) 21.3 x 10-6 s-1. This, in turn requires the assimilation of carbon fixed in photosynthesis at an instantaneous rate of 21.3 x 10-6 g C (g cell C)-1 s-1. From the maximum measured photosynthetic rate at ~20 °C [17.15 mg O2 (mg chla)-1 h-1] and, assuming a photosynthetic quotient of 1 mol C : 1 mol O2 (12 g C : 32 g O2) and a C : chla of 50 by weight, Reynolds

(1990) calculated a possible carbon delivery rate of 35.7 x 10-6 g C (g cell C)-1 s-1. This is sufficient to meet the full growth requirement in 19 416 s, or about 5.4 h. Interestingly, it is also possible to deduce, from the number of photosyn-thetic reaction centres represented by 1 g chla (between 2.2 and 3.4 x 1018) (see Section 3.2.1) and their operational frequency at 20 °C (~250 s-1), that photosynthetic electron capture might proceed at between 0.55 and 0.85x1021 (g chla)-1 s-1. The potential fixation yield is thus between 0.07 and 0.11 x 1021 atoms of carbon per second, or between 0.11 and 0.18 x10-3 mols carbon per (g chla)-1 s-1, or again, between 4.9 and 7.6 mg C (mg chla)-1 h-1. Putting C : chla = 50, a carbon delivery rate of between 27 and 42 x 10-6 g C (g cell C)-1 s-1 may be proposed, which, again, is well up to supplying the doubling requirement in something between 4.6 and 7.1 h (Reynolds, 1997a). The calculations suggest that photosynthesis can supply the fixed-carbon requirements of the dividing cell in a little over half of the generation time. However, they make no allowance for respirational or other energetic deficits (see Section 5.4.1 below).

For comparison, the well-resourced Chlorella cell has no problem in gathering the carbon dioxide to meet the photosynthetic requirement. The diffusion rate calculated from Eq. (3.19) in section 3.4.2 indicated that delivery of the entire doubling requirement of carbon in ~2300 s (i.e. just over 38 minutes). In order to maintain steady internal Redfield stoichiometry, the growing cell must absorb 9.43 x 10-3 mol P (mol C incorporated)-1 per generation (i.e. 1 mol/106 mol C). The phosphorus requirement for the doubling of the cell-carbon content of 0.63 x 10-12 mol is 5.9 x 10-15 mol P cell-1, which, at its maximal rate of phosphorus uptake (13.5 x 10-18 mol P cell-1 s-1 (Fig. 4.5), the cell could, in theory, take up in only 0.44 x 103 s, that is, in just 7.3 minutes! Note, too, that an external concentration of 6.3 x 10-9 mol L-1 is sufficient to supply the entire phosphorus requirement over the full generation time of 9.05 h (see Fig. 4.6). Solving Eq. (4.12) for the supply of nitrogen to the same cell of Chlorella, a concentration of 7 |mol DIN L-1 should deliver ~175 x10-18 mol N s-1, sufficient to fulfil the doubling requirement of

(0.151 x 0.63 x 10-12 =) 0.095 x 10-12 mol N in 540 s (9 minutes).

These calculations help us to judge that, for the rate of cell growth to qualify for the description 'limited', whether by light or by the availability of carbon, phosphorus or any other element, then it has to be demonstrable that the generation time between cell replications is prolonged. Moreover, it has to be shown that the additional time corresponds to that taken by the cells of the present generation to acquire sufficient of the 'rate-limiting' resource to complete the G1 stage and thus sustain the next division.

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