Increase in lysophosphatidate acyltransferase activity in oilseed rape (Brassica napus) increases seed triacylglycerol content despite its low intrinsic flux control coefficient

Summary Lysophosphatidate acyltransferase (LPAAT) catalyses the second step of the Kennedy pathway for triacylglycerol (TAG) synthesis. In this study we expressed Trapaeolum majus LPAAT in Brassica napus (B. napus) cv 12075 to evaluate the effects on lipid synthesis and estimate the flux control coefficient for LPAAT. We estimated the flux control coefficient of LPAAT in a whole plant context by deriving a relationship between it and overall lipid accumulation, given that this process is a exponential. Increasing LPAAT activity resulted in greater TAG accumulation in seeds of between 25% and 29%; altered fatty acid distributions in seed lipids (particularly those of the Kennedy pathway); and a redistribution of label from 14C‐glycerol between phosphoglycerides. Greater LPAAT activity in seeds led to an increase in TAG content despite its low intrinsic flux control coefficient on account of the exponential nature of lipid accumulation that amplifies the effect of the small flux increment achieved by increasing its activity. We have also developed a novel application of metabolic control analysis likely to have broad application as it determines the in planta flux control that a single component has upon accumulation of storage products.


Supporting Information
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Kinetic equations
If the rate of increase in the amount, , of a substance is proportional to (i.e. first order in M), then: where is the rate constant. (This rate of increase of is also the flux J, which is therefore changing with M, but is proportional to at any specific .) The integrated form of this equation describes an exponential growth process: where ! is the amount at time ! and ! that at a subsequent time ! . The logarithmic form of this equation: (Equation S1 .3) where = ! − ! , shows that a log plot of against will be linear with slope , as frequently used for analysis of microbial growth kinetics.

Analysis of literature data
Published results on the time course of lipid deposition in rape seeds have been noted to show an apparent exponential profile, but this does not seem to have been rigorously scrutinised. Hence graphical data in these papers was digitised using g3data (https://github.com/pn2200/g3data; version 1.5.2) and replotted as log plots (Supporting Information Note S1; Figure 1.1). Though the time scales and final seed weights differed between the studies, all showed an initial lag phase, followed by an exponential phase of variable duration that terminated relatively abruptly at close to the final seed lipid content.
The mean seed lipid content at the start of the exponential phase was 0.03 ± 0.0122 mg.

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A partial time course of the wild type of the plants used in this study confirmed that lipid accumulation was in the exponential phase for at least the period from 20 to 27 DAF (Supporting Information Note S1; Supporting Information Figure S1.2) with a value of the constant within the range seen in the studies shown in Supporting Information Note S1; Supporting Information Figure  b) Slabas et al., (1986); c) Slabas et al., (1987); d) Fawcett et al., (1994); and e) Hellyer et al (1992). The exponential phase of the time course was fitted with LibreOffice Calc.
Supporting Information Note S1; Figure S1.2: Lipid deposition time course for wild-type plants used in this study. Each time point has four measurements.

Control analysis of LPAAT over-expression
Given that seed lipid accumulation is an exponential process, the rate constant (Note 1; Equation S1 .1) describes the flux to lipid, and the control coefficient for LPAAT on this constant can be shown (Fell, 2018) to be identical to the flux control coefficient of LPAAT on the lipid accumulation flux J, as defined in Eqn. (1), main text. The product . can be computed from Note 1; Equation S1 .3, with ! as the measured final weight of TAG per seed (estimated from harvested weight, as discussed in the Main Text) and ! as the mean weight of lipid at the start of the exponential phase as estimated in the previous section from published data, which is assumed to be the same for both the LPAAT over-expressors and their azygote controls. On the assumption that over-expressing a Kennedy pathway enzyme has the potential to change the flux, but that there is no direct mechanism for it to affect , and that a single gene insertion doubling the enzyme content is unlikely to cause other stresses on the cell, we assume that any change in . between the azygotes and the (1) represents) remain constant during the TAG deposition phase. The actual LPAAT activities per embryo will be increasing throughout TAG deposition as the exponential TAG accumulation occurs during exponential growth of the embryos themselves (Murphy and Cummins, 1987). In this case, enzyme activity was approximately doubled by a single gene insertion, suggesting that the activity reflects gene dosage.
However, the flux control coefficient can only be estimated accurately in this way for small changes in enzyme activity, and the increase in LPAAT activity in the transgenics made here is substantial (up to 2-fold), so instead the large change formula (Eqn. (3), Main text, Methods) was applied. This states that the fold-change in flux, f, produced by an r-fold change in activity of an enzyme E with a flux control coefficient of ! ! in the control state is: This equation can be rearranged to give ! ! in terms of the measured values of r (from the LPAAT assays) and f .5), f is obtained as the ratio of the . values obtained from the final lipid masses of the azygotes and the over-expressers according to Eqn. S1.3, modified in the latter case to: with ! the final weight of lipid in the seed of the over-expressers The inevitable outcome of making a large change ΔE in the activity of E is that the control coefficient also alters. However, Equation S1.4 is indifferent whether the change in E is positive or negative, so the altered enzyme activity can be taken as the reference and the values of r and f relating it to the initial control are r'= 1/r and f' = 1/f. Substituting these in Eqn. S1.5 gives the value of the control coefficient !!!" .7)

Justification for applying the large change formula to the LPAAT data
The use of the large change formula depends on the relationship between flux and enzyme activity being approximately hyperbolic. Our results give us three points on this curve: the controls with relative flux 1.0 for relative enzyme activity of 1.0, and the 2A/2B and 3A/3B which is readily derived from Eqn. (S1.3) This is plotted for comparison in (Supporting Information Note S1; Supporting Information Figure S1.4), using the value of 0.14 for the control coefficient of LPAAT and supports the claims made in the Discussion of the main paper.
Supporting Information Note S1; Figure S1.4: Predicted effects of over-expression of LPAAT on relative flux to lipid and on final seed lipid accumulation.
The curves have been calculated using the function in Equations (S1.4) and (S1.6) for a wildtype flux control coefficient of 0.14 in order to extrapolate the curve fitted to our experiments in Fig. S1.3.