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Swire et al. The cellular geometry of growth drives the amino acid economy of
Caenorhabditis elegans
SUPPORTING INFORMATION
I. Evidence for the weakness of a pure ageing effect.
We have shown that amino acid usage is driven by geometry rather than
age per se: when we controlled for the effects of age-response we found that
the correlation between the change in amino acid usage observed between
cytoplasmic and membrane proteins and the change between early and late
proteins was maintained (r2age controlled = 0.88, p = 1.6 x10-10). By contrast, when
we controlled for the effects of compartment this correlation collapsed
(r2compartment controlled = 0.19, p = 0.021) (Figures 2c, d). In order to examine the
robustness of these results we resampled our dataset 100,000 times. When we
resample rcompartment controlled we find the median correlation coefficient is 0.32 (p =
0.056, one-tailed Spearman’s rank correlation; the original unresampled
correlation was 0.43) with widely separated 5th and 95th percentiles of -0.02
and 0.59. Conversely, when we resample rage controlled the median correlation
coefficient is 0.92 (p = 1.9 x 10-9, original correlation 0.94) with tight 5th and
95th percentiles of 0.87 and 0.96. In other words it is not simply that after
controlling for compartment the average differences between late and early
proteins are small and only weakly similar (as in Figure 2d); it is also the case
that individual early proteins differ greatly in composition from one another and
individual late proteins differ greatly in composition from one another. This
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explains the very broad distribution of correlations in Figure S1, blue bars. Any
pure ageing effect must, therefore, be weak and barely visible against the
backdrop of other effects. Conversely, after controlling for protein age we see
not only that the average differences between cytoplasmic and membrane
proteins are large and strongly similar (as in Figure 2c), but also that individual
cytoplasmic proteins are relatively similar in composition to one another and
individual membrane proteins are relative similar to one another (Figure S1, red
bars). We conclude that ageing, in so far as it affects amino acid composition,
is largely a by-product of shifting geometry.
Figure S1. Distributions following resampling of the Pearson’s correlation coefficients presented
in Figures 2c and d. 99 genes were drawn randomly without replacement in each of the
categories early-membrane, late-membrane, early-cytoplasm, late-cytoplasm. n=100,000.
II. Results of the four regression models for the metabolome correlations.
When we estimate the rate of change in the relative prevalence of an
amino acid in the metabolome we are forced to model the relationship with time.
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As in the case of the transcriptomic data, we used four models (see Materials
and Methods); here we present the results for all four (Table S1). We prefer the
linear model (Figure 4), both because it is the most intuitive and because it
presented the best fit for more amino acids than did any of the other models
(Table S1, column 2). Note that the power and exponential models give
stronger results (with respect to our hypotheses) than does the linear.
model
nbest r2age
p, age
r2geometry p, geometry
linear
5
0.39
0.0087, 0.0061
0.41
0.0067, 0.00092
log
4
0.35
0.014, 0.019
0.38
0.0096, 0.0044
power
3
0.39
0.012, 0.0052
0.54
0.0021, 0.00056
exponential
2
0.49
0.0040, 0.0044
0.63
0.00060, 0.00042
TABLE S1. Results of four models for the relation between amino acid metabolome levels and
time. nbest gives the number of the 14 amino acids for which the particular model gives the best
fit in Figure 3. r2age gives the correlation coefficient between (i) the slope between amino acid
pool sizes and time (according to the particular time model) and (ii) the log(late/early)
transcriptomic vector. In the case of the linear model, this was presented as Figure 4a. r2geometry
gives the correlation coefficient with the log(cytoplasmic/membrane) transcriptomic vector (i.e.
Figure 4b). p values are one-tailed Pearson correlations followed by one-tailed Spearman Rank
correlations.
III. Predicting the transcriptome is more reliable than predicting the
metabolome.
It appears that the geometric hypothesis explains less of the variation in
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pools of free amino acids (Figure 4b) than it does variation in the amino acid
proportions of mRNAs (Figure 2b). To a certain extent we expect this: after all,
free pools of amino acids will not solely be used for protein synthesis.
Moreover, protein expression levels vary over five orders of magnitude, so a
relatively small group of highly-expressed proteins will be responsible for most
of the demand for free amino acids. However, our cytoplasm/membrane and
late/early measures necessarily treat each protein as making an equal
contribution, and thus fail to recognise any distinctive contribution from highlyexpressed proteins. Given this, it is remarkable that the correlations in Figure 4
are as high as they are, and this suggests that the idiosyncratic requirements of
a few highly-expressed proteins do not swamp the average changes captured
in our ratios. In any case, we should be careful not to overemphasise the
distinction in correlations, for there are two sources of noise that will diminish
the correlations in Figure 4 compared to that in Figure 2b. First, the Y-axis in
Figure 4 involves the estimate of a slope on the basis of five time point
readings, and this will be inherently less accurate than the amino acid usage
proportions, averaged over thousands of proteins, which form the Y-axis in
Figure 2b. Second, when estimating the Y-axis values in Figure 4, we must
measure slopes; this entails choosing one model, and the linear model that we
have chosen is best for only 5/14 amino acids (Table S1) which means that the
Y-axis estimates for the other 9 will be especially noisy. By contrast the Y-axis
values in Figure 2b are based on the consensus of four models, as we do not
have to use measurements of slopes directly, but rather can take the
consensus of four models as to the direction (+/-) of slopes to divide the data
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into the two classes of late/early genes.
IV. Selection for metabolic efficiency does not explain the change in
amino acid usage during worm ontogeny
Our hypothesis is that the ontogeny of amino acid usage is driven by
changing cellular geometry. An alternative hypothesis is that it is driven by the
changing energy requirements of the worm. If energy becomes more or less of
a constraint on the worm as it grows, then the power of cost selection on its
amino acid usage will wax or wane. If this is so, then amino acid synthesis
costs should predict the change in amino acid usage with age (i.e. ageresponse — log (late/early). And indeed they do: r = -0.59, p = 0.0058 (twotailed).
However, cellular geometry (aka compartment) has far greater
explanatory power than synthesis cost, since in a multiple correlation analysis in
which age-response is the dependent, and synthesis cost and compartment –
log (cytoplasmic/membrane) – are independent variables, synthesis cost is no
longer significant (two-tailed partial regression p values: compartment, p =
0.00010, cost p = 0.57, interaction p = 0.36; and without interaction,
compartment p = 0.000029, cost p = 0.73). Thus, there is no evidence for a
cost effect independent of cellular geometry.