Differential expression (DE) analysis

Differential expression (DE) analysis compares protein or peptide abundance between experimental conditions. In msmu, mm.tl.run_de() performs DE analysis and returns a DeaResult.

For a worked example using processed protein data, see the DE tutorial.

Input and comparison

Select the modality and the .obs column containing the condition labels with modality and category. The analysis reads .X, or .layers[layer] when a layer is specified. For a simple two-group comparison, ctrl and expr define the reference and experimental groups; a positive log2fc means higher abundance in expr.

For example, compare G2 against G1 using the condition labels in mdata["protein"].obs:

de_res = mm.tl.run_de(
    mdata,
    modality="protein",
    category="factor value[condition]",
    ctrl="G1",
    expr="G2",
    min_pct=0.5,          # require observations in at least 50% of each group
    stat_method="limma",  # "limma", "welch", "student", or "wilcoxon"
    p_adjust="auto",      # multiple-testing correction; see options below
)

Missing values and test eligibility

min_pct sets the minimum observed fraction required in every compared group or design cell. A value of 0.5 requires observations in at least 50% of samples in each group. The default, 0.0, still requires enough observations for the selected test.

run_de() does not impute missing values. Returned results retain untestable features with NaN in p_value and q_value.

Statistical methods

The default, stat_method="limma", moderates per-feature variance estimates using information across features, as described by Smyth (2004) and Ritchie et al. (2015). msmu uses inmoose, described by Colange et al. (2025), for this analysis.

`stat_method`	Test
`"limma"`	Empirical-Bayes moderated-t
`"welch"`	Label permutation of Welch's t
`"student"`	Label permutation of Student's t
`"wilcoxon"`	Label permutation of the Wilcoxon rank-sum statistic

The permutation methods compare the observed statistic with a null distribution obtained by rearranging group labels. n_resamples sets the requested number of label permutations. For small groups, the number of possible label permutations is limited, so increasing n_resamples may not add new information.

Multiple testing and correction

p_adjust selects how the multiple-testing result in q_value is calculated. It leaves the test statistic, log2fc, and unadjusted p_value unchanged.

`p_adjust`	Method
`"auto"`	Default: `"bh"` for limma; `"empirical"` for permutation methods
`"empirical"`	Permutation-based FDR estimate
`"bh"`	Benjamini–Hochberg
`"by"`	Benjamini–Yekutieli
`"bonferroni"`	Bonferroni
`"holm"`	Holm–Bonferroni
`"hochberg"`	Hochberg
`"hommel"`	Hommel

FDR concerns the expected fraction of false discoveries among selected features. Family-wise error concerns the probability of at least one false discovery across the tested features. All methods write to q_value; for family-wise methods, this column contains adjusted p-values rather than FDR-based q-values. The standard correction methods are also described in the R p.adjust documentation.

The standard corrections are applied to the non-missing p-values within the current comparison; untestable features retain NaN. To inspect uncorrected significance, use p_value. There is no p_adjust="none" option. See the run_de() API reference for parameter details.

Empirical FDR estimation

With p_adjust="empirical", msmu estimates FDR from the label-permutation null, following the framework discussed by Xie et al. (2005) and Storey and Tibshirani (2003):

estimated FDR ≈ pi0 * mean null exceedances / observed discoveries

pi0 is the estimated proportion of features with no true difference. Null exceedances and observed discoveries are counted at the same absolute test-statistic cutoff; observed discoveries include both true and false positives. Each q_value is the minimum estimated FDR over cutoffs that include that feature.

Interactions and covariates

Limma also supports more complex designs. Set interaction to a second .obs factor and interaction_levels to two levels to compare the expr - ctrl effect between them. The contrast subtracts the effect at the second listed level from the effect at the first. Use covariates to adjust for additional .obs variables, such as batch; these change the reported model contrast from a raw group difference.

Limma requires an explicit expr group. For comparison against all groups other than ctrl, the permutation methods support expr=None. Design arguments and examples are in the run_de() API reference.

For a dataset with condition, genotype, and batch columns in the protein modality's .obs:

# Two-group moderated-t
de_res = mm.tl.run_de(
    mdata,
    modality="protein",
    category="condition",
    ctrl="control",
    expr="treated",
    stat_method="limma",
)

# Interaction: does the treated-vs-control effect differ between genotypes,
# adjusting for batch?
de_res = mm.tl.run_de(
    mdata,
    modality="protein",
    category="condition",
    ctrl="control",
    expr="treated",
    stat_method="limma",
    interaction="genotype",
    interaction_levels=["wild_type", "knockout"],
    covariates=["batch"],
)

de_res.to_df()  # get results as a pandas DataFrame

Results

Use de_res.to_df() to obtain a pandas DataFrame:

Column	Interpretation
`features`	Protein or peptide identifier
`repr_ctrl`, `repr_expr`	Group means, or medians for `wilcoxon`, on the input scale
`pct_ctrl`, `pct_expr`	Percentage of samples with an observed value in each group
`log2fc`	Log2 fold change; `expr - ctrl` for a simple two-group comparison of log2 data
`statistic`	Test statistic for the selected method
`p_value`	Unadjusted p-value
`q_value`	Multiple-testing result using the selected `p_adjust` method

Interpret effect size together with the adjusted result and observed coverage. A missing p-value or q-value indicates that significance could not be estimated for that feature.

References

Colange, M., Appé, G., Meunier, L., Weill, S., Johnson, W. E., Nordor, A., and Behdenna, A. Bridging the gap between R and Python in bulk transcriptomic data analysis with InMoose. Scientific Reports 15, 18104 (2025). https://doi.org/10.1038/s41598-025-03376-y.

Smyth, G. K. Linear models and empirical Bayes methods for assessing differential expression in microarray experiments. Statistical Applications in Genetics and Molecular Biology 3(1), 1–25 (2004). https://doi.org/10.2202/1544-6115.1027.

Ritchie, M. E., Phipson, B., Wu, D., Hu, Y., Law, C. W., Shi, W., and Smyth, G. K. limma powers differential expression analyses for RNA-sequencing and microarray studies. Nucleic Acids Research 43(7), e47 (2015). https://doi.org/10.1093/nar/gkv007.

Xie, Y., Pan, W., and Khodursky, A. B. A note on using permutation-based false discovery rate estimates to compare different analysis methods for microarray data. Bioinformatics 21(23), 4280–4288 (2005). https://doi.org/10.1093/bioinformatics/bti685.

Storey, J. D. and Tibshirani, R. Statistical significance for genomewide studies. Proceedings of the National Academy of Sciences 100(16), 9440–9445 (2003). https://doi.org/10.1073/pnas.1530509100.