It is worth noting the high fit of the model (r¼0.89) and that
the main contribution (higher regression coefficient) to PolB
comes from the third component, the main component (PC1,
repair system as a whole) has a statistically significant influence on
PolB (p<0.0001) but its contribution to the PolB value (0.33) is
lower than the PC3 contribution (0.42). PC2 instead has a negli-
gible influence on PoLB determination. The fit of the equation
does not reach the complete deterministic reconstruction of PolB
(r¼1.00) because we use only the first three components, that in
any case are the relevant ones, being the component from fourth
onward only modeling noise (experimental error). The above equa-
tion returns a clear quantitative estimation of the relevant para-
meters of the system at hand: the PolB expression dynamics is
modeled in terms of relative contributions of mutually independent
“fluxes of variation.” Correspondent to general ‘repair activity’
(PC1) and ‘specific repair mode’ (PC3).
The same procedure is applied to MLH1 obtaining a very high
fit as well (r¼0.90,p<0.0001).
This allows us to concentrate on the “pure PC3 driven” corre-
lation between the two enzymes; this can be done by subtracting
the actual expression values of the two genes by their estimation
based upon PC1 and PC2, i.e.,
MLH1 (pc3specific)¼MLH1 – MLH1 est (PC1, PC2)
PolB (pc3 specific)¼PolB – PolB est (PC1, PC2)Where MLH1 and PolB are the raw (observed) variables, while
MLH1 est (PC1, PC2) and PolB est (PC1, PC2) are the least
squares estimation of MLH1 and PolB respectively, by means of
PC1 and PC2 scores namely MLH1 est ¼ 19.31 + 0.485
(PC1) + 0.644 (PC2), Pearsonr ¼0.65 (p <0.0001); Polβ
est ¼18.60 + 0.326(PC1) + 0.092(PC2), Pearson r ¼ 0.56
(p<0.002).
Given the components are independent of each other by con-
struction, the subtraction of the PC1, PC2 contribution from
MLH1 and PolB actual values only keeps alive the PC3 (signal)
and noise (minor components) contributions. This allows checking
for the statistical significance of the hypothesized inverse correla-
tion of MMR (marked by MLH1) and BER (marked by PolB); this
corresponds to asking for a statistically significant correlation hold-
ing between MLH1(pc3specific) and PolB(pc3specific). This was
actually the case (r ¼0.61p< 0.001) demonstrating noise
(minor components) still allows recognizing the PC3 pathway
influence on the two gene expression causing their negative corre-
lation (mutual balance).
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