Adaptive Mitochondrial Thresholds Across Cell Types

Why a Single Mitochondrial Cutoff Can Mislead

A mitochondrial RNA fraction is useful for identifying cell barcodes whose expression profiles may reflect damaged or stressed cells. But the fraction is not a universal measure of quality: cell types can have different baseline mitochondrial expression, and samples can differ in their distributions. A single fixed cutoff is easy to apply, yet it can exclude a biologically plausible population simply because that population tends to have higher fractions.

The goal of an adaptive threshold is not to make every group retain the same proportion of cells, nor to guarantee that all retained cells are valid. It is to compare cells with an appropriate reference distribution while keeping the biological meaning of the groups in view. The threshold is a screening decision that should be documented and checked, not a direct measurement of cell viability.

The denominator must be defined consistently across cells and samples. For example, if \(T_i\) is the total gene-associated count in the count matrix, then \(f_i\) is the share of those counts assigned to mitochondrial genes. A threshold stated as 0.10 is equivalent to 10%. The fraction is compositional: it can rise because mitochondrial counts increase, because other counts decrease, or both. Thus, a high fraction alone does not identify its cause.

Fixed and Adaptive Rules

A fixed rule has the form \(f_i>c\), where \(c\) is chosen in advance, for example \(c=0.10\). Its strengths are transparency, simplicity, and comparability when the same rule is appropriate across the data being compared. Its weakness is that it assumes the same fraction has the same QC meaning in every relevant sample and cell group. That assumption may be unreasonable when baseline distributions differ.

An adaptive rule first defines a reference group and then estimates a cutoff from the fractions in that group. Possible reference groups include all cells in one sample or cells assigned to a cell group within that sample. The grouping decision matters: a threshold calculated from all cells can be dominated by abundant cell types, while a threshold calculated within a tiny group can be unstable. If cell-group labels are not available independently, grouping by labels inferred from the same data may also create circularity: the cutoff can depend on a classification that is itself affected by QC.

The factor 1.4826 makes the MAD a scale estimate comparable to the standard deviation under a normal distribution. This does not make the fractions normally distributed, nor does it make the resulting cutoff a universal statistical test. The multiplier \(k\), the reference group, and the use of a one-sided upper rule are choices that require justification in context.

An alternative adaptive rule is a group-specific empirical quantile, such as flagging fractions above the 99th percentile. This controls the fraction of reference observations above the empirical cutoff approximately by construction, but it does not ensure that the flagged cells are poor quality. With few cells, quantiles are coarse and sensitive to individual observations. Robust location-and-scale rules and empirical quantiles answer different questions: the former scales a cutoff to estimated spread, while the latter sets a rank-based upper tail boundary.

Why the Robust Cutoff Has This Form

The normal-consistency factor can be justified directly. If observations come from a normal distribution with median \(\mu\) and standard deviation \(\sigma\), then the population median absolute deviation is the value \(d\) satisfying \(P(|X-\mu|\le d)=0.5\). Standardizing \(Z=(X-\mu)/\sigma\), this becomes \(P(|Z|\le d/\sigma)=0.5\). By symmetry, each tail has probability 0.25, so \(d/\sigma=\Phi^{-1}(0.75)\approx0.67449\). Therefore \(\mathrm{MAD}\approx0.67449\sigma\), and \(\mathrm{MAD}/0.67449\approx1.4826\,\mathrm{MAD}\) estimates \(\sigma\) under that model.

Consequently, \(m+k(1.4826\,\mathrm{MAD})\) is a robust, distribution-scaled upper boundary. It is not automatically a calibrated false-positive threshold. For example, interpreting a particular \(k\) as having a specified tail probability would require a distributional model and a suitable calibration. Mitochondrial fractions are bounded between 0 and 1 and may be skewed or multimodal, so that interpretation should not be assumed.

Worked Thresholds Within a Sample

Choosing a Reference Group and Checking the Result

An adaptive threshold depends as much on the reference group as on the formula. Sample-specific thresholds can accommodate sample-to-sample shifts, but pooling cell types within a sample may conceal distinct baseline distributions. Cell-group-specific thresholds address that issue when group labels are credible and groups have enough observations. In practice, a reasonable choice follows the known design and biology rather than a search for a rule that retains a desired number of cells.

Before applying a rule, inspect the distribution within each proposed reference group. Check its center, spread, shape, and sample size, and look for multimodality or a long upper tail. A single median-and-MAD summary may be uninformative for a mixture of subpopulations. Also verify that fractions were computed from the intended genes and denominator, and that zero-denominator cells were handled explicitly rather than assigned an artificial fraction.

After applying a threshold, report how many cells are flagged overall and in each sample and cell group. Examine whether an entire group is being removed, whether the cutoff is determined by only a few observations, and whether cells just above and below the boundary look meaningfully different. The boundary is a practical decision point, not evidence of a sharp biological transition.

Common Mistakes and Limitations

• Using one cutoff because it is familiar. A conventional fixed limit may be convenient but still be inappropriate for a population with a naturally higher fraction. Compare the observed distributions and biological context before applying it.
• Assuming an adaptive rule is automatically superior. Group-specific cutoffs can be noisy, especially for small groups, and can normalize away a genuine quality problem shared by an entire group.
• Calling every flagged cell damaged. The rule identifies a high fraction relative to a chosen boundary; it does not establish why the fraction is high or prove that the cell is unusable.
• Choosing groups after seeing which rule preserves the desired cells. This makes the result difficult to interpret. Define groups and cutoff procedures using defensible biological or design information, and document the choices.
• Treating the robust cutoff as a formal outlier test. Median plus a multiple of scaled MAD is a descriptive screening rule unless a probabilistic model and calibration justify a formal error interpretation.

Fixed cutoffs remain a reasonable alternative when a common criterion is justified and comparability across samples is the priority. Quantile-based rules are useful when the aim is to flag a chosen upper tail, but their flagged proportion is partly determined by the chosen quantile. Robust median-and-MAD rules are less sensitive to extreme observations, but can struggle with very small, highly skewed, or multimodal groups. No single method resolves the central limitation: mitochondrial fraction is only one aspect of a cell's observed profile, and its interpretation requires biological and technical context.