Supplementary material for SINCERITIES: Inferring gene regulatory network from time-stamped cross-sectional single cell transcriptional expression data Nan Papili Gao 1,2 , S.M. Minhaz Ud-Dean 3 and Rudiyanto Gunawan 1,2 1 Institute for Chemical and Bioengineering, ETH Zurich, Zurich, Switzerland 2 Swiss Institute of Bioinformatics, Lausanne, Switzerland 3 Werner Siemens Imaging Center, Department of Preclinical Imaging and Radiopharmacy, Eberhard Karls University Tuebingen, Tuebingen, Germany Distribution distances In addition to the Kolmogorov-Smirnov distance, we also evaluated the use of the Cramér–von Mises (CM) criterion [1] as the DD metric. The CM criterion is given by: CM j,Δt l = ∫ −∞ ∞ ( F t l+1 ( E j ) −F t l ( E j ) ) 2 dF t l ( E j ) (S1) where CM j,Δt l denotes the CM criterion of gene j in the time window Δt l , and F t l ( E j ) denotes the cumulative distribution function of gene j expression (E j ) at time point t l (l = 1, 2, …, n−1). In addition to the CM criterion, we also tested the Anderson-Darling (AD) criterion [2], which is given by:
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ethz.ch · Web viewIn addition to the Kolmogorov-Smirnov distance, we also evaluated the use of the Cramér–von Mises (CM) criterion [1] as the DD metric. The CM criterion is given
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Supplementary material for
SINCERITIES: Inferring gene regulatory network from
time-stamped cross-sectional single cell transcriptional expression data
Nan Papili Gao1,2, S.M. Minhaz Ud-Dean3 and Rudiyanto Gunawan1,2
1 Institute for Chemical and Bioengineering, ETH Zurich, Zurich, Switzerland2 Swiss Institute of Bioinformatics, Lausanne, Switzerland3 Werner Siemens Imaging Center, Department of Preclinical Imaging and Radiopharmacy, Eberhard
Karls University Tuebingen, Tuebingen, Germany
Distribution distances In addition to the Kolmogorov-Smirnov distance, we also evaluated the use of the Cramér–von Mises
(CM) criterion [1] as the DD metric. The CM criterion is given by:
CM j , Δ tl=∫
−∞
∞
(F tl+1( E j )−Ft l
( E j ))2d Ft l( E j ) (S1)
where CM j , Δ tl denotes the CM criterion of gene j in the time window Δtl, and F tl
( E j ) denotes the
cumulative distribution function of gene j expression (Ej) at time point tl (l = 1, 2, …, n−1). In addition
to the CM criterion, we also tested the Anderson-Darling (AD) criterion [2], which is given by:
AD j , Δ tl=∫
−∞
∞ ( F tl+1( E j )−F tl
( E j ))2
F t l( E j )(1−F tl
( E j ))d F tl
( E j ) (S2)
The CM and AD criteria provide more sensitive measures of the global change in the distribution than
the KS distance [3]. In contrast, the KS distance better reflects the shift of the center of the distribution.
We evaluated the performance of SINCERITIES using the CM criterion using the in silico single cell
dataset (see Methods). Table S2 below report the AUROCs and AUPRs for the CM and AD criteria,
showing that these criteria could provide a comparable performance to the KS distance. However, for
the THP-1 differentiation dataset, both CM and AD criteria gave much poorer AUROC and AUPR
values than the KS distance (AUROC: 0.54 for CM, 0.56 for AD vs. 0.70 for KS, AUPR: 0.20 for CM,
0.22 for AD vs. 0.33 for KS). The reason for the poor performance of AD and CM might have to do
with the reference TF network of THP-1, which came from population-average transcriptional data of
RNAi experiments. Since the KS is a more sensitive metric of the mean-shift than AD and CM, the
GRN prediction from SINCERITIES using KS agreed better with the RNAi experiments.
Table S2 Performance comparison for SINCERITIES with KS, AD or CM distance on in silico data.AUROC AUPR AUROC AUPR