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Quantifying the effect of experimental perturbations at single-cell resolution


Current methods for comparing single-cell RNA sequencing datasets collected in multiple conditions focus on discrete regions of the transcriptional state space, such as clusters of cells. Here we quantify the effects of perturbations at the single-cell level using a continuous measure of the effect of a perturbation across the transcriptomic space. We describe this space as a manifold and develop a relative likelihood estimate of observing each cell in each of the experimental conditions using graph signal processing. This likelihood estimate can be used to identify cell populations specifically affected by a perturbation. We also develop vertex frequency clustering to extract populations of affected cells at the level of granularity that matches the perturbation response. The accuracy of our algorithm at identifying clusters of cells that are enriched or depleted in each condition is, on average, 57% higher than the next-best-performing algorithm tested. Gene signatures derived from these clusters are more accurate than those of six alternative algorithms in ground truth comparisons.

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Fig. 1: Illustrative description of perturbation analysis using MELD and VFC.
Fig. 2: Vertex frequency analysis using the sample-associated indicator signals and relative likelihood.
Fig. 3: Quantitative comparison of the sample-associated relative likelihood and VFC.
Fig. 4: MELD recovers signature of TCR activation.
Fig. 5: Characterizing chordin Cas9 mutagenesis with MELD.
Fig. 6: MELD characterizes the response to IFN-γ in pancreatic islet cells.

Data availability

Gene expression counts matrices prepared in ref. 13 were accessed from NCBI GEO database accession GSE92872. Gene expression counts matrices prepared in ref. 15 were downloaded from NCBI GEO accession GSE112294. The pancreatic islets datasets are available on NCBI GEO at accession GSE161465.

Code availability

Code for the MELD and VFC algorithms implemented in Python is available as part of the MELD package on GitHub ( and on the Python Package Index. The GitHub repository also contains tutorials, code to reproduce the analysis of the zebrafish dataset and code associated with several of the quantitative comparisons.


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The authors would like to thank C. Vejnar, R. Coifman, J. Noonan, V. Tornini and C. Kontur for fruitful discussions. We would also like to thank G. Wang of the Yale Center for Genome Analysis for help in preparing the pancreatic islet data. This research was supported, in part, by the Eunice Kennedy Shriver National Institute of Child Health & Human Development of the National Institues of Health (NIH) (award no. F31HD097958) (to D.B.); the Gruber Foundation (to S.G.); IVADO Professor startup and operational funds, IVADO Fundamental Research Project grant PRF-2019-3583139727 (to G.W.); NIH grants R01GM135929 and R01GM130847 (to G.W. and S.K.); and Chan-Zuckerberg Initiative grants 182702 and CZF2019-002440 (to S.K.). The content provided here is solely the responsibility of the authors and does not necessarily represent the official views of the funding agencies.

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D.B.B., S.K., G.W., D.v.D. and A.J.G. envisioned the project. D.B.B., J.S., A.T., S.K. and G.W. developed the mathematical formulation of the problem and related numerical analysis. D.B.B., J.S. and S.G. implemented the code. D.B.B. and S.K. performed the analysis of biological and simulated data. A.L.P. and K.C.H. generated and assisted with the analysis of the pancreatic islet dataset. A.J.G. assisted with the analysis of the zebrafish data and related writing. D.B.B., J.S., A.T., S.K. and G.W. wrote the paper. S.G. assisted with the writing.

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Correspondence to David van Dijk or Smita Krishnaswamy.

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The authors declare the following competing interest: S.K. is a paid scientific advisor to AI Therapeutics.

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Supplementary Figs. 1–14, Tables 1 and 2 and Notes 1–3

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Burkhardt, D.B., Stanley, J.S., Tong, A. et al. Quantifying the effect of experimental perturbations at single-cell resolution. Nat Biotechnol (2021).

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