Data normalization

We considered a core subset of six physiological features from the dataset of ref. [13] for mathematical modelling: mitochondrially encoded ETC mRNA pool size, ETC protein levels, glycolysis mRNA pool size, cell volume, cell proliferation rate (or cell growth rate as termed in ref. [13]) and maximal respiratory capacity. We performed many normalizations to the data, the result of which is shown in Figure 1.

Selected measurements of 143B TK⁻ osteosarcoma cells heteroplasmic in MELAS 3243A>G, from ref. [13]. (A) mRNA levels for 11 mitochondrially encoded ETC subunits (COX3, ND2, ND5, CYTB, ND3, ND6, COX1, ND4, COX2, ND1 and ND4L). (B) Protein levels for complexes I, III and IV. (C) Glycolysis mRNA levels, for genes (PKM2, ENO1, PGAM4, PGK1, GAPDH, ALDOA, PFKP, GPI, HK2 and SLC2A1). All errors in A–C are the standard error of the transformed renormalized mean [see eqn (2)]. (D) Mean cell volume of an asynchronous population of growing cells ± SEM. (E) Growth rate, determined by linear regression. Error is the standard error in the slope from linear regression. (F) Maximum respiratory capacity. Details of the data normalization and regression may be found in Materials and Methods. See ref. [13] for experimental protocols.

OXPHOS, as well as glycolysis, have multiple different mRNAs participating in their respective pathways. To have some measure of the overall expression level of a pathway (E¯), we used the mRNA concentration (in RPMK, reads per kilobase of transcript per million mapped reads), for each gene corresponding to enzymes of the pathway (e_i,k(h), for gene i and technical replicate k at heteroplasmy h) and took a normalized sum as follows:

where n_r = number of technical replicates and N = number of genes in the pathway of interest. This quantity normalizes the expression level of each gene to mean h = 0 levels, to avoid effects from consistently highly expressed genes. The factor of 1/N results in E¯ having the value of 1 at h = 0, so may be interpreted as a fold-change in expression relative to h = 0.

The standard error of E¯ over technical replicates k may be written as follows:

where V_k(x_k) is the sample variance over x_k. Eqns (1) and (2) are applied to glycolysis and ETC mRNAs in our main model, which yield dimensionless, normalized, measures of transcript levels for each biological pathway.

ATP synthase was excluded from both ETC mRNA and protein data, as it is expected to be regulated differently from other ETC proteins. This difference arises because mitochondrial membrane potential is required for cell growth [14], and glycolytic ATP may be used, even in cells without mtDNA, by ATP synthase to maintain membrane potential [15]. Thus, protein levels of ATP synthase may be expected to be regulated quite differently to those of the ETC, and not generally indicative of respiratory activity.

For ETC protein, we simply used the sample mean of complexes I, III and IV, since the data given by Picard et al. [13] are already normalized.