IQCELL: A platform for predicting the effect of gene perturbations on developmental trajectories using single-cell RNA-seq data

Abstract

The increasing availability of single-cell RNA-sequencing (scRNA-seq) data from various developmental systems provides the opportunity to infer gene regulatory networks (GRNs) directly from data. Herein we describe IQCELL, a platform to infer, simulate, and study executable logical GRNs directly from scRNA-seq data. Such executable GRNs allow simulation of fundamental hypotheses governing developmental programs and help accelerate the design of strategies to control stem cell fate. We first describe the architecture of IQCELL. Next, we apply IQCELL to scRNA-seq datasets from early mouse T-cell and red blood cell development, and show that the platform can infer overall over 74% of causal gene interactions previously reported from decades of research. We will also show that dynamic simulations of the generated GRN qualitatively recapitulate the effects of known gene perturbations. Finally, we implement an IQCELL gene selection pipeline that allows us to identify candidate genes, without prior knowledge. We demonstrate that GRN simulations based on the inferred set yield results similar to the original curated lists. In summary, the IQCELL platform offers a versatile tool to infer, simulate, and study executable GRNs in dynamic biological systems.

Full text

RESEARCH ARTICLE
IQCELL: A platform for predicting the effect of
gene perturbations on developmental
trajectories using single-cell RNA-seq data
Tiam HeydariID
1,2
, Matthew A. LangleyID
3¤a
, Cynthia L. FisherID
1,2
, Daniel Aguilar-
HidalgoID
1,2
, Shreya ShuklaID
3,4
, Ayako Yachie-KinoshitaID
3¤b
, Michael HughesID
5
,
Kelly M. McNagnyID
1,5
, Peter W. ZandstraID
1,2
*
1School of Biomedical Engineering, University of British Columbia, Vancouver, British Columbia, Canada,
2Michael Smith Laboratories, University of British Columbia, Vancouver, British Columbia, Canada,
3Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, ON, Canada, 4Notch
Therapeutics, Vancouver, British Columbia, Canada, 5Department of Medical Genetics, University of British
Columbia, Vancouver, BC, Canada
¤a Current address: Division of Biology and Bioengineering, California Institute of Technology, Pasadena,
United States of America
¤b Current address: The Systems Biology Institute, Shinagawa, Tokyo, Japan
*peter.zandstra@ubc.ca
Abstract
The increasing availability of single-cell RNA-sequencing (scRNA-seq) data from various
developmental systems provides the opportunity to infer gene regulatory networks (GRNs)
directly from data. Herein we describe IQCELL, a platform to infer, simulate, and study exe-
cutable logical GRNs directly from scRNA-seq data. Such executable GRNs allow simula-
tion of fundamental hypotheses governing developmental programs and help accelerate the
design of strategies to control stem cell fate. We first describe the architecture of IQCELL.
Next, we apply IQCELL to scRNA-seq datasets from early mouse T-cell and red blood cell
development, and show that the platform can infer overall over 74% of causal gene interac-
tions previously reported from decades of research. We will also show that dynamic simula-
tions of the generated GRN qualitatively recapitulate the effects of known gene
perturbations. Finally, we implement an IQCELL gene selection pipeline that allows us to
identify candidate genes, without prior knowledge. We demonstrate that GRN simulations
based on the inferred set yield results similar to the original curated lists. In summary, the
IQCELL platform offers a versatile tool to infer, simulate, and study executable GRNs in
dynamic biological systems.
Author summary
Executable GRNs provide an important strategy to model complex intracellular dynamics
in development and disease. Here we introduce IQCELL, a platform to infer, simulate,
and study executable logical GRNs directly from single cell sequencing data. IQCELL is
an integrative platform that includes modules for gene selection, building logical GRNs,
and simulating developmental trajectories under normal and perturbed conditions. We
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OPEN ACCESS
Citation: Heydari T, A. Langley M, Fisher CL,
Aguilar-Hidalgo D, Shukla S, Yachie-Kinoshita A, et
al. (2022) IQCELL: A platform for predicting the
effect of gene perturbations on developmental
trajectories using single-cell RNA-seq data. PLoS
Comput Biol 18(2): e1009907. https://doi.org/
10.1371/journal.pcbi.1009907
Editor: Qing Nie, University of California Irvine,
UNITED STATES
Received: August 20, 2021
Accepted: February 8, 2022
Published: February 25, 2022
Peer Review History: PLOS recognizes the
benefits of transparency in the peer review
process; therefore, we enable the publication of
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responses alongside final, published articles. The
editorial history of this article is available here:
https://doi.org/10.1371/journal.pcbi.1009907
Copyright: ©2022 Heydari et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: The source code of
IQCELL python package generated during this
study and example notebooks of IQCELL’s

demonstrate the utility of IQCELL by reconstructing GRNs for early mouse T-cell and red
blood cell development. We show that IQCELL can “automatically” infer the vast majority
of gene interactions previously reported from decades of experimental research. IQCELL
also provides users with a platform to simulate the developmental trajectories of cells. We
show that dynamic simulations of the inferred GRNs resemble experimentally observed
gene expression dynamics and capture the effects of genetic perturbation studies. IQCELL
offers a versatile tool to infer and simulate GRNs in dynamic biological systems.
Introduction
Stem cell fate decisions are made via dense arrays of interacting transcription factors (TFs)
forming gene regulatory networks (GRNs) [1]. Information gleaned from GRNs during stem
cell differentiation can lead to more effective design-based cell cultures, applicable to cell thera-
pies [2,3]. As a prominent example, the effect of TFs on GRNs has been widely utilized in the
reprogramming of embryonic and adult somatic cell GRNs for the establishment of a pluripo-
tent state via induction of driver TFs [4]. Stem cell reprogramming and differentiation can be
modeled as executable and logical (Boolean) GRNs undergoing state transition [5–7]. Execut-
able GRNs provide information about both the topology and the regulatory rules of gene inter-
actions that can be simulated as time-evolving (dynamical) systems. However, deriving
informative, executable, and predictive GRNs for stem cell differentiation has proven to be a
challenging task. Specifically, developing executable GRNs by piecing together evidence from
gene perturbation experiments has shown to be an effective strategy [6] but is extremely time-
consuming, labor intensive, and expensive. In a notable advancement, automated formal rea-
soning successfully identified a set of minimal GRNs underlying naive pluripotency in mice.
Gene expression observations across multiple culture conditions were used to logically con-
strain possible GRN configurations, and the resulting set was able to accurately predict the out-
come of 70% of new experiments [8,9]. Yet, these methods are not based on high-throughput
data.
More recently, the emergence of single-cell profiling technologies has provided an unprece-
dented archive of information regarding cells undergoing fate determination and maturation.
Deriving more accurate GRNs based on single-cell data is at the center of many recent efforts
[10–12]. Formal reasoning has been used to infer executable GRNs directly from high
throughput single-cell quantitative PCR (sc qPCR) data [13,14]. However, using single-cell
RNA-sequencing (scRNA-seq) data has many advantages in terms of coverage, availability,
flexibility in gene selection, and accuracy in clustering and pseudo-time inference compared
to sc qPCR. These benefits exist alongside the disadvantage of dropout effects and low sensitiv-
ity in profiling TFs. Despite the availability of this data resource, this emerging field is still
missing an integrated platform to infer, study, and simulate executable GRNs directly from
scRNA-seq.
Herein we report an effective platform (IQCELL), implemented as a Python software pack-
age for reconstructing GRNs directly from scRNA-seq data. Our strategy includes steps for
gene selection, correcting dropout effects, building logical GRNs directly from pseudo-time
with respect to interaction hierarchy and mutual information between gene pairs, and simulat-
ing developmental trajectories under normal and perturbed conditions. We demonstrate the
utility of IQCELL by reconstructing GRNs for early mouse T-cell and red blood cell develop-
ment, well characterized mammalian developmental systems [15,16], using published scRNA-
seq datasets [17,18]. Our resulting GRNs based on a curated set of genes, recover over 74% of
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implementation are available on Gitlab: (https://
gitlab.com/stemcellbioengineering/iqcell). The raw
sequencing data generated in this study have been
submitted to GEO under the accession number
GSE196972.
Funding: TH, MAL, AYK, CLF, DAH, SS, and PWZ
were supported by the Canadian Institutes of
Health Research (CIHR), Foundation Grant FRN
154283, and the Natural Sciences and Engineering
Research Council of Canada (NSERC), Discovery
Grant RGPIN-2020-06496), to PWZ. PWZ is the
Canada Research Chair in Stem Cell Bioengineering
(https://www.chairs-chaires.gc.ca). The funders
had no role in study design, data collection and
analysis, decision to publish, or preparation of the
manuscript.
Competing interests: The authors have declared
that no competing interests exist.

experimentally validated causal gene-gene interactions spanning years of research. Dynamic
simulations of the inferred GRN resemble experimentally observed gene expression dynamics
and capture the effects of knocking out or forcibly expressing various genes. Next, we use
IQCELL’s TF selection pipeline to automatically infer a set of genes to construct a GRN. We
show that the pipeline selects many previously known TFs that are important for T-cell and
red blood cell development, without prior knowledge. Finally, we show that perturbation out-
comes from the unbiased GRN are highly concordant with the perturbation outcomes from
the GRN made based on the curated gene lists. Our platform is applicable to scRNA-seq data
derived from dynamic developmental systems and should serve as a useful resource for many
applications.
Results
An integrated platform for predicting the qualitative effects of gene
perturbations on developmental trajectories (IQCELL)
IQCELL infers logical regulatory networks directly from existing information in the scRNA-
seq data of cells during development and uses these regulatory networks to simulate and pre-
dict the behavior of developing cells under perturbed conditions (Fig 1). IQCELL works with
quality controlled and pre-processed scRNA-seq gene expression data [19,20]. The second
input of the IQCELL platform is the inferred pseudo-time ordering of cells based on scRNA-
seq data (Fig 1). The temporal dynamics of genes helps with the inference of causal gene inter-
actions. Pseudo-time ordering of cells using scRNA-seq data has been shown to be informative
for capturing temporal and developmental dynamics [21,22].
IQCELL has a customized gene selection pipeline based on the pySCENIC platform [23]. In
this pipeline (S1A Fig), the TFs are selected based on the highly active and dynamic regulons
(see Methods). Since gene dropout is common among many scRNA-seq datasets, particularly
for TFs with low mRNA copy numbers, IQCELL employs a recently developed graph-based
Fig 1. Overview of IQCELL. IQCELL infers logical GRNs directly from sc-RNA seq data and allows the simulation
and analysis of in silico developmental trajectories in normal and perturbed conditions. The typical inputs of IQCELL
are sc-RNA seq expression data along with the pseudo-time ordering of the cells. After correction of dropout effects
and gene selection steps, gene-gene interactions are calculated and weighted based on mutual information. Binarized
gene expression values are used to constrain possible gene-gene interactions and obtain a functional GRN for the data.
IQCELL can be used to analyze the GRN and simulate possible developmental trajectories under normal and
perturbed conditions.
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algorithm (MAGIC) to recover gene expression [24], (S1B Fig). Next, IQCELL generates a set
of possible interactions between genes. Information-based metrics such as mutual information
are well suited for quantifying relationships between genes [25]. IQCELL scores gene-gene
interactions according to the mutual information between gene pairs [26] and assigns a regula-
tory sign (activation or repression) to each interaction based on the significance and sign of
their correlation (S1C Fig). These steps result in a dense weighted network of gene-gene inter-
actions that needs to be filtered into a functional GRN. In a functional GRN, interactions are
not necessarily biophysically direct but capture the consequence of regulatory relations.
To reduce the number of possible gene interactions, IQCELL forms a gene interaction hier-
archy in which higher ranked genes influence lower ranked ones. To form this hierarchy,
IQCELL binarizes the gene expression counts by clustering them into expressed and non-
expressed states [27]. The binarization process divides the pseudo-time axis into regions with
compact and sparse expression densities for the genes, reflecting the pseudo-time domains
where a gene is expressed at a higher or lower level (S1D Fig). Next, the platform identifies the
transition points between expression regions for all genes and uses the order of transitions to
form a gene interaction hierarchy, with highly ranked genes (with earlier transition points)
having greater potential to influence those downstream. This acts as an additional filter on
gene-gene interactions along with the mutual information (S1E Fig). The resulting directional
network serves as the foundation for inferring executable GRNs.
To obtain an executable GRN model, IQCELL models interactions between genes as Bool-
ean logic functions [7]. IQCELL uses a satisfiability modulo theory engine (Z3) (S1F Fig), [28]
to identify logic functions that are compatible with the pseudo-time dynamics of binarized
gene expression states [13]. Finally, it selects the GRN with the highest average mutual infor-
mation as the most probable constrained model. The result is a functional and executable
GRN that optimally fits the input scRNA-seq data. IQCELL has built-in capabilities to simulate
GRN dynamics via random asynchronous Boolean simulation [7] and compare the results
with experimental data under normal and perturbed conditions. In summary, IQCELL pro-
cesses scRNA-seq data inputs to infer an executable logical GRN that best fits the data.
IQCELL sorts genes based on transition points and places them in a
biologically relevant order
To assess the functional capabilities of IQCELL, we evaluated its performance using a well
characterized mammalian developmental system: mouse early T-cell development [29,30].
The T-cell developmental program takes place in the thymus, where pre-thymic progenitors
differentiated within the bone marrow progress toward T lineage commitment, involving a
dense network of genes [31]. Sustained exposure to Notch signaling drives early thymic pro-
genitors (ETP) to the CD4/8 double-negative 2a (DN2A) and 2b (DN2B) stages, where upregu-
lation of T-cell lineage-specific genes and progressive loss of potential for other blood cell fates
occurs. Once committed to the T-cell fate, the double-negative 3 (DN3) T-cell progenitors
begin recombining the β-chain of the pre-T-cell receptor (TCR). Cells are selected for func-
tional β-chain rearrangements through pre-TCR signaling and proceed toward CD4/8 double
positive state (DP) (Fig 2A). We used a publicly available scRNA-seq dataset [18], where the
authors used fluorescence-activated cell sorting to capture mouse thymocytes at ETP-DN2
and DN3 stages based on cell surface markers. After processing the data in a manner consis-
tent with the original publication (S4 Fig and S2 Table), the gene expression profiles and the
pseudo-time orders were used as inputs to IQCELL.
After expression recovery, selecting a curated list of genes that are known to be important
during early T-cell development (S1 Table and Fig 2B, see METHODS), and finding possible
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gene-gene interactions, IQCELL binarized gene expression values and calculated the expres-
sion density over pseudo-time (Fig 2C) (see Methods). Sorting the genes based on their transi-
tion points placed Notch1 and Hes1 at the top of the gene interaction hierarchy (since their
expression level stayed relatively high consistently) followed by Lmo2,Tcf7,Myb, and Runx1
which agrees with their position in the regulatory hierarchy during T-cell lineage establish-
ment [30]; whereas DN3 associated genes such as Cd3e,Lef1, and Ptcra [32,33] appeared at the
bottom of the hierarchy (Fig 2C).
Next, IQCELL used this order of genes (Fig 2C) as a hierarchical filter of possible interac-
tions, with the genes at the top having the most regulatory potential in terms of number of
genes they can regulate. The combination of the regulatory potential of individual genes, the
mutual information between gene pairs, and interaction signs, led to a directed gene interac-
tion network comprising the set of possible interactions (Fig 2D). This network then consti-
tutes a foundation for further constraints and analyses at next steps.
IQCELL is highly predictive for functional regulatory interactions
Following our in silico analysis, we compared predictions from our initial inferred interaction
network to validated regulatory interactions in mouse T-cell development. The initial interac-
tion network (Fig 2D) was simplified with additional constraints. These constraints enforce
the gene interactions to follow the expression patterns throughout the pseudo-time axis (Fig
2B) when executed as a logical network. This resulted in a set of possible update logical rules
for each gene, selecting the most probable interactions as scored by mutual information lead-
ing to a provisional executable GRN for early T-cell development (Fig 3A and S1 Table).
To benchmark this GRN, we compared our predicted directional interactions with a recent
comprehensive GRN model of mouse T-cell development based on experimentally validated
gene interactions [16]. This network consists of 38 reported interactions between the genes of
Fig 2. IQCELL initial processing of early T-cell development sc-RNA seq data. (A) Summary of the scope of the sc-
RNA seq data used as an input to IQCELL [18]. ETPs originated from pre-thymic progenitors progress toward DN2A,
DN2B (coincides with upregulation of Bcl11b and lineage commitment), DN3 stages and eventually lead to DP cells
(not covered here). (B) Log transformed expression matrix for selected genes from sc-RNA data along the pseudo-time
axis. Gene expression is corrected for dropout effects using MAGIC [24]. Red indicates high expression, blue indicates
low expression. (C) Smoothed binarized gene expression matrix (expression density). Gene expression values were
binarized by clustering, averaged over a pseudo-time window, then sorted based on transition points from early to late.
Red indicates high expression, blue indicates low expression. (D) The set of all possible gene-gene interactions, filtered
by interaction hierarchy and mutual information. Positive and negative interactions are represented by blue and red
edges, respectively. Edge width represents the relative amount of mutual information of the interaction.
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interest, of which 29 (over 75%) are de novo captured directly by our simulated functional reg-
ulatory network (Fig 3B and 3C). For example, it is well known that Bcl11b, the gene that
marks T lineage commitment, is activated by Notch signaling, Gata3,Tcf7, and Runx1 [34].
Our model predicted four activators for Bcl11b:Notch1 (as a Notch signaling mediator [35]
and target gene [36] functionally represents the presence of Notch signaling), Gata3,Tcf7, and
Runx1. The presence of Runx1 in our model is a notable result. Runx1 is present in developing
Fig 3. The provisional GRN for mouse early T-cell development inferred by IQCELL captures essential gene interactions and accurately simulates T-
cell developmental trajectories. (A) The provisional GRN for early mouse T-cell development. The GRN is obtained by constraining the possible
interactions to both follow the in vitro data progression when executed as a logical network and maximize mutual information between gene pairs. Positive
and negative interactions are represented by blue and red edges, respectively. (B) Out of 38 experimentally reported gene interactions of early mouse T-cell
development [16], 29 of them are captured by the functional GRN model proposed by IQCELL. (C) Detailed representation of the proposed interactions by
IQCELL and experimentally reported ones. Rows and columns represent regulators and effector genes, respectively. Blue indicates that the interaction is
captured by the model directly (dark blue) or indirectly (light blue); in the latter case, the numbers indicate the number of intermediate genes. Dark gray
indicates that the interaction is only proposed by IQCELL. The red color indicates the experimentally validated interaction is not present in the model. Light
gray cells indicate no interaction. Genes downstream of Spi1 comprise 50% of the experimentally-reported interactions not captured by IQCELL. (D) The
PCA plot of the binarized scRNA-seq data color-coded with the pseudo-time values attributed to each cell. The binarization is performed by clustering the
scRNA-seq expressions into expressed or not expressed levels. On top of that, the binarized expressions of CLP, ETP, DN2A, DN2B, and DN3A cells have
been calculated from the Immgen microarray data [38] and overlaid on RNA-seq data. (E) The four initial states that have been used in simulations. Three
variations of the state representing ETP are due to the noisy expressions of Notch1 and Hes1 genes in recovered sc-RNA seq data with early pseudo-time.
Genes that are expressed (1) and not expressed (0) are represented with blue and grey circles, respectively. (F) The PCA plot of the simulated developmental
trajectories are overlaid on the binarized scRNA-seq. The two detected attractors are colored red, and the attractor that matches the DN3A state is marked
by star (). The simulated data is color coded by the value of average simulation step (average distance to the attractor of simulation). (G) Average gene
expression at each simulation step. All simulations started from the same initial condition (ETP) and move toward the same attractor (). (H) Expression
states of the GRN model steady state attractors. Genes that are expressed (1) and not expressed (0) are represented with blue and grey squares, respectively.
(I) Percentage of similarity between the two attractors (vertical axis) and binarized microarray expression profiles of CLP, ETP, DN2A, DN2B, and DN3A
cells (horizontal axis) [38]. The average agreement between two random states is 50%.
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cells, however it only gains access to the Bcl11b locus after chromatin restructuring during the
DN2A stage [37]. Notably, more than half of the interactions that were not captured by our
model are related to the Spi1 gene which is a T-cell lineage suppressor [30].
To test the performance of IQCELL with another source of data on T-cell development
under different conditions, we performed scRNA-seq analysis of in vitro differentiation of fetal
liver hematopoietic progenitor cells toward the T-cell lineage. Application of IQCELL to this
second scRNA-seq data set provided further validation of its ability to predict gene-gene inter-
actions (S3 Fig).
One advantage of logical GRN models is that they can not only provide information about
gene interactions, but can also be simulated to predict how the system evolves in time. To dem-
onstrate this capability, we simulated our inferred logical GRN model and compared its output
to experimental observations of mouse T-cell development. The scRNA-seq expression data
[18] was binarized by grouping the gene expression count into on and off states. This data was
then used in principle component analysis (Fig 3D) and the simulated trajectories overlaid on
top of the binarized scRNA-seq gene expression data (Fig 3F). As the initial states of the simu-
lations (representing the starting expression state of simulations), we used the binarized repre-
sentation of cells at the beginning of the pseudo-time trajectory. These cells resemble the
known expression state of ETP cells [30]. However, given the noisy expression of Notch1 and
Hes1 at the earlier pseudo-time points (Fig 2C), we considered the expression states of these
two genes to be random which results in four distinct initial states in total (Fig 3E). Two steady
states have been obtained for the given initial cell states (Fig 3F), with one of them matching
the DN3A cell profile (noted by star in Fig 3). The simulated gene expression dynamics from
ETP state towards this steady state shows a similar trajectory compared to the one observed
from scRNA-seq data (Fig 3G,compare with Fig 2C). The other steady state shares similarities
with common lymphoid progenitors (CLP) and ETP cells (Fig 3H and 3I). Overall, this analy-
sis demonstrates that our GRN model is informative about both gene interactions and the
behavior of genes at the system level. Such a model has the potential to predict the effect on
gene perturbations at the system level as well.
IQCELL predicts the effect of gene perturbations on developmental
trajectories
Next, we tested the effect of gene perturbations on simulated developmental trajectories (Fig
4A). Specifically, we tested the effect of gene perturbations known to result in halting or pro-
moting T-cell development during the ETP-DN3 stages (reviewed in [30]).
Notch1, a cell surface receptor that mediates Notch signaling, is known to play an essential
role in early T-cell development. Notch1 deficiency leads to blocked T-cell development and
accumulation of other hematopoietic lineages [35]. Using our inferred executable network, we
simulated the developmental trajectory of ETP cells in the absence of Notch1. Simulations pre-
dicted the presence of two possible steady state attractors, localized near the earlier section of
the pseudo-time domain (Fig 4B). Comparing the expression states of the simulation attrac-
tors (Fig 4C) with the binarized expression of known cell states extracted from microarray
data [38], we found that the attractor states are more similar to ETP or CLP, and none show
significant similarities to later stages of T-cell development (Fig 4D). This agrees with previous
reports [35] that lack of Notch1 blocks T-cell development.
Tcf7 is a crucial TF for T-cell specification and differentiation that is upregulated by Notch
signaling. Lack of Tcf7 results in premature arrest of T-cell development before the DN2 stage
[39]. Our model predicts a single attractor state in the absence of Tcf7 (Fig 4B). This attractor
precedes the DN2 stage and does not express Gata3,Bcl11b,Ets1,Cd3e, or Cd3g (Fig 4C), in
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agreement with experimentally reported analysis of Tcf7-/- lymphoid-primed multipotent pro-
genitors cultured in vitro (on OP9-DL4) at day 4 [39]. The simulated Tcf7 knockout (KO)
steady state attractor shows more similarity to microarray profiles for ETP cells than either
DN2 and DN3 cells (Fig 4D), which is in agreement with previous reports [39].
Next, we investigated the effect of simulated KO of Bcl11b, a crucial gene for T-cell commit-
ment [40]. It has been shown experimentally that Bcl11b deficient cells cannot proceed beyond
the DN2 stage [41]. Our in silico results predict one attractor in the absence of Bcl11b (Fig 4B).
This attractor resembles the DN2A cell state (Fig 4D) which recapitulates the aforementioned
experimental result of Bcl11b KO [41].
We also simulated the effects of perturbing Runx1,Tcf12 and Myb. KO of Runx1 stops T-
cell development before the DN3 stage [42]; KO of Tcf12 results in developmental blockage
before DP stage [43], whereas Tcf12 overexpression (OE) enhances T-cell development[44];
KO of Myb causes multiple blocks during T-cell development [45]. We have simulated these
gene perturbations, and found qualitative agreement with the experimentally reported results
(Fig 4B,4C and 4D).
Next, we tested our model for a simultaneous perturbation of two genes. Interestingly,
while the absence of Notch signaling results in loss of T-cell development, forced expression of
Tcf7 can partially rescue T-cell development in the absence of Notch [39]. To test our model
against this observation, we simulated shutting off the expression of Notch1 and forcing
Fig 4. Testing the known effect of eight gene perturbations on in silico developmental trajectories. (A) Schematic
of performed gene perturbations. In OE, the gene is always expressed (represented with 1) and in KO the gene is
always silent (represented with 0). (B) PCA plot of the simulated developmental trajectories under perturbed
conditions are overlaid on the binarized scRNA-seq. The perturbations include KOof Notch1, KO of Tcf7, KO of
Bcl11b, KO of Runx1, KO of Tcf12, KO of Myb, OE of Tcf12 and the double perturbation, OE of Tcf7 and KO of
Notch1 at the same time. (C) Expression states of the model attractors under perturbations. Genes that are expressed
(1) and not expressed (0) are represented with blue and grey squares, respectively. (D) Percentage of similarity between
the model attractors under perturbations (vertical axis) and the binarized expressions of CLP, ETP, DN2A, DN2B, and
DN3A cells (horizontal axis) [38] (left). Description of known effect of the gene perturbation on T-cell development
(right).
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expression of Tcf7 to the ‘on’ state simultaneously. This resulted in two attractors (Fig 4B), one
of them localized at earlier stages, and one of them close to the DN2 stage, which reflects the
limited but not complete development of T-cells when compared with the KO of Notch1 (Fig
4C and 4D).
In addition to these perturbations, we have performed full systematic GRN perturbations
for one and two gene perturbations (S2A Fig and S3 and S4 Tables) and sensitivity analysis of
gene interactions (S2B Fig and S3 and S4 Tables). Taken together, we showed that our model
can predict the effect of single and double gene perturbations on the developmental trajectory
of early T-cell development.
An automated TF selection module can replace the need for a curated gene
list
In many biological systems, validated lists of curated relevant genes are not known a priori. To
enable the unbiased construction of predictive executable GRN, we developed a customized
pipeline that automatically selects a set of TFs directly from scRNA-seq data (Fig 5A). This
pipeline starts by identifying a set of 2000 highly variable genes (HVGs) from the data. Next, it
leverages the pySCENIC platform [23] to select more than 200 TFs that are components of
core regulons during the differentiation process. As a final step, the module selects a subset of
these genes based on their gene dynamics score (GDS), (S5A Fig), (see METHODS for more
details).
We applied this pipeline to the previously utilized scRNA-seq dataset [18] and selected the
top 14 genes based on GDS. Our analysis automatically captured many biologically important
Fig 5. Constructing mouse early T-cell GRN based on automated TF selection pipeline. (A) Overview of TF
selection procedure. After selecting HVGs, IQCELL uses pySCENIC to select active regulons (TFs and their effectors),
and finally IQCELL uses GDS to rank and select TFs for the final list. We have added Notch1 for its known biological
importance and Rag1 and Cd3g as biological markers of DN3 stage to the list. (B) Comparison of automated vs curated
TF selection show that the TF selection pipeline captures 8 of 14 genes in the curated gene list. (C) The PCA plot of the
binarized scRNA-seq data color-coded with the pseudo-time values attributed to each cell. The binarization is
performed by clustering the scRNA-seq expressions into expressed or not expressed levels. (D) The PCA plot of the
simulated developmental trajectories are overlaid on the binarized scRNA-seq. The detected attractor is colored red
and marked by star (). The simulated data is color coded by the value of average simulation step (average distance to
the attractor of simulation). (E) Expression states of the GRN model steady state attractor. Genes that are expressed (1)
and not expressed (0) are represented with blue and grey squares, respectively. (F) Percentage of similarity between the
attractor (vertical axis) and binarized microarray expression profiles of CLP, ETP, DN2A, DN2B, and DN3A cells
(horizontal axis) [38]. The average agreement between two random states is 50%. (G) Comparison of gene
perturbations between automated and curated GRNs show 17 matches of the predicted sates out of 18 perturbations.
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TFs involved in mouse T-cell development including Tcf7,Gata3,Runx1,Bcl11b, and Tcf12.
As discussed before, a known factor in T-cell development is Notch signaling (represented by
Notch1), we added this gene along with two DN3 stage markers (Cd3g and Rag1) to the gene
set to create the final gene list (Fig 5A). Comparing the automated TF selection with the
curated gene list shows that 8 out of 14 TFs that are selected via the pipeline are in common
with the curated gene list (Fig 5B).
Next, we followed IQCELL’s GRN inference pipeline to obtain a functional GRN for the
system (S5A–S5E Fig). The dynamic simulation of the GRN matches the scRNA-seq data (Fig
5C and 5D) and the attractor state matches the DN3 stage (Fig 5E and 5F).
Next, we performed systematic KO and OE simulations on genes of the GRN (S5F and S5G
Fig), including the 8 TFs and Notch1 which are in common with the curated gene list. Com-
paring the predictions of two GRNs on these 9 genes showed that the resulting state of 17 out
of 18 perturbations agreed. The only difference is the outcome of OE of Spi1gene (DN2A vs
DN2B).
To conclude we have shown that the IQCELL TFs selection pipeline is able to capture bio-
logically important genes and the predicted effects of gene perturbations are robust against the
selected gene set.
Testing IQCELL performance in red blood cell development
To test IQCELL platform on an additional data set, we evaluated its performance in the context
of erythropoiesis, the development of red blood cells. Erythroid progenitors (ErP) arise from
megakaryocyte/erythroid progenitors (MEPs) via a lineage bifurcation process [46] (Fig 6A).
IQCELL performance in this context was evaluated using a publicly available dataset of mouse
hematopoietic stem and progenitor cell differentiation [17]. This dataset is an atlas of single-
cell HSPC expression and the differentiation of these cells into multiple lineages. Building on a
recent analysis of this dataset [47], we isolated the MEPs and ErP subclusters from the dataset,
and constructed a pseudo-time ordering of the cells connecting MEPs to ErPs. Initially we
used a curated list of erythropoiesis—associated genes and a well characterized interaction net-
work [15] including Gata1,Gata2,Klf1,Fli1,Spi1,Zfpm1, and Zbtb71 (Fig 6B).
Following the previously described IQCELL GRN inference pipeline we calculated the
expression density over pseudo-time after the expression recovery step for the curated gene list
(S6A Fig) and constructed the initial interaction network (S6B Fig). This resulted in an exe-
cutable GRN model (Fig 6C), which includes 11 interactions among 7 genes. Notably, IQCELL
correctly predicted the target genes of Gata1 including Zfpm1 (known as FOG-1), Spi1,Klf1
and Gata2 (the detailed interaction rules can be found in S5 Table). Comparing the known
gene-gene interactions in erythropoiesis [15] with the inferred GRN, demonstrated that out of
16 known interactions, 11 were captured by IQCELL (over 68%), (Fig 6D). Among the 5
uncaptured interactions, 3 of them are related to two genes, Fli1 and Spi1 which are known to
be activated in the megakaryocyte lineage [15], and thus their effects may be masked in eryth-
ropoiesis. To initiate the simulated dynamics of the GRN, we programmed the initial state to
resemble the binarized gene expression of MEPs (S6A Fig). Simulation results show that the
dynamics matches the progression of scRNA-seq data (Figs 6E and S6C and S6D) and the cor-
responding attractor state matches the ErP stage (S6E Fig).
Next, we tested the effect of gene perturbations on simulated developmental trajectories
(Fig 6F). The TF Gata1 plays an important role in erythropoiesis as it regulates multiple down-
stream genes in erythroid cell development [15]. In vitro and in vivo studies of hematopoietic
cells that lack the normal expression level of Gata1, show that the lack of Gata1 halts erythroid
differentiation [48,49]. Our model also predicts a block of erythroid differentiation in the
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absence of Gata1 with a single attractor state resembling the MEPs (Fig 6F). Notably, while
IQCELL predicts that OE of Gata1 leads to the ErP cell state, in vitro assays show that OE of
Gata1 causes apoptosis [50]. Zfpm1 (FOG-1) is a Gata1 transcriptional cofactor, it has been
shown that the lack of Zfpm1 leads to arrested development in erythropoiesis at a stage similar
to Gata1 KO cells [51]. Our model also predicts that Zfpm1 KO cells fail at an early stage (Figs
6F and S6F and S6G). The OE of Zfpm1 looks to have no significant effect in erythropoiesis
[52] which is consistent with our in silico result (Fig 6F). The deficiency of Spi1 in erythroid
progenitors leads to cell differentiation which is consistent with IQCELL KO simulation result
(Fig 6F), but also it has been reported that because of immature differentiation, the cells
undergo proliferation arrest [53]. On the other hand, the IQCELL model predicts that OE of
Spi1 stops erythroid differentiation at an early stage (Figs 6F and S6G), it has been reported
that the OE of Spi1 leads to blockage of erythroid differentiation in vitro [54]. We have also
simulated the KO effect of Fli, which leads to increased erythroid output [55], the OE effect of
Fli, which suppresses the erythroid differentiation [56], KO effect of Klf1, which causes defects
in erythroid differentiation [46], and the OE effect of Klf1, which blocks megakaryocyte
Fig 6. Constructing mouse erythropoiesis GRN. (A) Summary of the scope of the sc-RNA seq data used as an input
to IQCELL [17]. Erythroid progenitors (ErP) arise from megakaryocyte/erythroid progenitors (MEPs). (B) Log
transformed expression matrix for selected genes from sc-RNA data along the pseudo-time axis. (C) The constructed
GRN for mouse erythropoiesis. The GRN is obtained by constraining the possible interactions to both follow the in
vitro data progression when executed as a logical network and maximize mutual information between gene pairs.
Positive and negative interactions are represented by blue and red edges, respectively. (D) Out of 16 known
interactions [15], 11 were captured by IQCELL (top). Detailed representation of the proposed interactions by IQCELL
and experimentally reported ones. Rows and columns represent regulators and effector genes, respectively. Blue
indicates that the interaction is captured by the model directly (dark blue) or indirectly (light blue); in the latter case,
the numbers indicate the number of intermediate genes. Dark gray indicates that the interaction is only proposed by
IQCELL. The red color indicates the experimentally validated interaction is not present in the model. Light gray cells
indicate no interaction (bottom). (E) The PCA plot of the simulated developmental trajectories are overlaid on the
binarized scRNA-seq (the curated genes). The detected attractor is colored red and is marked by star (). The arrow
(blue-red) represent the direction of inferred pseudo-time. (F) Percentage of similarity between the model attractors
under perturbations (vertical axis) and binarized expression of MEPs and ErPs (horizontal axis) (left). Description of
known effect of the gene perturbation (right). (G) Comparison of automated vs curated TF selection show that the TF
selection pipeline captures 5 of 7 genes in the curated gene list. (H) The PCA plot of the simulated developmental
trajectories are overlaid on the binarized scRNA-seq (the genes resulting from automated TF selection). The detected
attractor is colored red and is marked by star (). The arrow (blue-red) represent the direction of inferred pseudo-time.
(I) Comparison of gene perturbations between automated and curated GRNs show 8 matches of the predicted states
out of 10 perturbations.
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differentiation and increases the erythroid differentiation output [57]. These in silico results
show consistency with experimental evidence (Figs 6F, more details at S6F).
Testing IQCELL performance via automated TF selection in erythropoiesis
We also tested IQCELL when candidate GRN TFs were selected algorithmically from scRNA-
seq data (S7A Fig). Given the GDS, we selected the top 18 TFs to be included in the model
(S7B Fig). The gene list produced by the TF selection algorithm captured 5 out of 7 TFs that
were included in the curated model (Gata1,Gata2,Spi1,Fli1, and Klf1), (Fig 6G). Next, we
applied IQCELL’s GRN inference pipeline to construct a functional GRN for the system (S7C–
S7F Fig). The result of the dynamic simulation of the GRN matched the observed dynamics in
scRNA-seq data (Figs 6H and S7G and S7H) with the attractor state matching the ErP state
(S7I Fig).
After performing systematic KO and OE simulations on the GRN (S7J and S7K Fig), we
compared IQCELL’s predictions on gene perturbations between the GRN that is made via
curated gene list and automated TF selection (Fig 6I). Comparing the predictions of two
GRNs shows that out of 10 common perturbations, the results agreed between 8 of them. The
only differences are the outcome of OE of Spi1and Fli1 (Fig 6I).
Finally, we compared IQCELL’s performance with other state of the art GRN inference
methods [12] using both the T-cell and erythropoiesis datasets. Our results show that IQCELL
outperformed the other methods, with a higher area under the precision-recall curve
(AUPRC) for both datasets (S9 Fig).
Discussion
There is an increasing availability of scRNA-seq datasets for different developmental systems.
To date, the inference, analysis, and simulation of logical GRNs directly from scRNA-seq data
have not been integrated together. Here we present IQCELL, an integrated platform imple-
mented as a Python package to infer, analyze, and simulate GRNs directly from scRNA-seq
data and pseudo-time order of the cells.
IQCELL is able to capture, directly from scRNA-seq data, over 74% (38 out of 54) of the
reported gene interactions in early T-cell development and erythropoiesis [15,16]. These inter-
actions were obtained and characterized by decades of research and experiments [30]. For
example, regulators of Bcl11b, an essential gene for T lineage commitment, were successfully
identified by IQCELL. More than half of the interactions that were not captured in T-cell
development by IQCELL were Spi1 effector genes, which is a Notch signaling antagonist [58].
However, Notch signaling contains Spi1 inhibitory effect on T-cell regulators [58] and poten-
tially masks Spi1 negative regulatory roles in early T-cell development.
We also tested the dynamics of the obtained GRNs. For example, in early T-cell develop-
ment, we showed that when the logical GRN is simulated from the ETP cell state, its dynamics
evolves to the cell state associated with the DN3 stage, in agreement with experimental obser-
vations. Importantly, we showed that our platform can produce GRN models with high predic-
tive power for the effect of genetic perturbations. For example, simulated KO of Bcl11b caused
the developmental trajectory to halt at the DN2 stage, in agreement with experimental studies
in early T-cell development. We identified eight gene perturbations that halt T-cell develop-
ment at different points between the ETP and DN3 stages, and IQCELL showed satisfactory
agreement for all perturbations with experimental studies (Fig 4C). We have also tested
IQCELL against gene perturbations with known effects in erythropoiesis with satisfactory
agreement (Fig 6F).
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In many biological systems, curated and validated lists of important genes are not a priori
known. IQCELL’s customized pipeline for TFs selection was used to independently create a
new set of TFs for mouse T-cell development and erythropoiesis. We show that this inference
module successfully captured many of the known important TFs in both systems (Figs 5B and
6G). We used this set of genes to create new GRNs and test the robustness of IQCELL’s predic-
tion against gene perturbations. For example, in early T-cell development, we showed that out
of 18 perturbations that were in common between the two GRNs (automated and curated),
IQCELL predictions were similar in 17 cases. This validation encourages future investigations
into systematic gene perturbation outcomes of this GRN.
These results show that the multi-step strategy implemented in IQCELL is effective for
reconstructing functional GRNs from existing information in scRNA-seq data. Because its
methodology is not specific to a single developmental system, IQCELL may be broadly useful
in understanding how GRNs contribute to cell development in a variety of developmental con-
texts. IQCELL results may help uncover functional relations between genes and thereby help
design more effective gene manipulation strategies to drive cell differentiation cultures in vitro
toward fates of interest. Synthetic gene interactions can be added to the GRNs outputted by
IQCELL to predict the effect of novel synthetic gene circuits on native cell GRNs. A major goal
in systems biology is the creation of multi-scale models that connect the decisions of individual
cells within a multicellular system to emergent properties of the whole tissue [59,60]. IQCELL
can fill an important layer in such multi-scale models. By exposing the intracellular decision-
making machinery of single cells, IQCELL could interface with other methods that connects
these cellular decisions to tissue-level dynamics.
To date, there have been many methods introduced for reconstructing GRNs from single-
cell data [12] and many of them focus on finding some type of correlation between genes. In
one case, binarized sc qPCR data was used to decode logical GRNs for embryonic blood devel-
opment [14]. In another recent study, sc qPCR data and its pseudo-time order was used to
decode GRNs of blood stem cells [13]. However, to the best of our knowledge, prior to
IQCELL there has not been any existing method or platform to infer executable and logical
GRNs from scRNA-seq data, nor have previous methods dealt with the associated challenges
of lower sensitivity and dropout effects.
Although the IQCELL framework allowed us to effectively model regulatory modules as
logical (Boolean) gates where no extra parameters are required, logical models are limited in
some respects. Firstly, logical modeling cannot effectively capture dose-dependency in gene
interactions; for example, it is known that the downstream responses to Gata3 are dose-depen-
dent [61]. We suggest in future that this aspect be captured by multilevel models [62]. Multi-
level modeling requires more sensitive measurements of TF expression levels, which may
become feasible with emerging TF profiling methods [63]. Secondly, capturing biophysical
timescales in the logical framework is not trivial; one solution would be assigning a weighted
time scale [64] to each simulation update step of the logical model. This can potentially help to
include some time-scale sensitive events in cell GRN dynamics, such as stochastic chromatin
restructuring events [37].
Here we have tested IQCELL’s performance in single developmental trajectories. However,
IQCELL could be used to infer GRNs from multiple developmental trajectories (e.g. trajecto-
ries with bifurcations) by inferring candidate GRNs for each trajectory. Since IQCELL pro-
vides users with a flexible framework, future studies could integrate other sources of
information such as binding of TFs to DNA via ChIP-seq [65] and CRISPR screening on the
effect of gene perturbations on developmental trajectories [66] to potentially improve GRN
reconstruction. In a recent study, the combination of scATAC-seq and scRNA-seq with
machine learning methods have been used to infer a set of informative TFs during
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differentiation [67]. In addition, new opportunities are arising to investigate the decision mak-
ing machinery of the cells in their native environment (via in situ cell profiling) [68]. The com-
bination of these methods, prior knowledge of cell-cell interactions [69,70], and emerging
theoretical knowledge and computational technologies for capturing and quantifying spatio-
temporal information content of cell signaling [71–74] can be used as invaluable resources for
the next generation of GRN inference methods. These next-generation methods would ideally
integrate cell signaling [75] with GRNs directly from multi-omics single-cell data. In conclu-
sion, the results presented here suggest that IQCELL will be a broadly useful tool to study cellu-
lar decision making in a variety of developmental systems.
Methods
Selecting a suitable scRNA-seq dataset as IQCELL’s input
There is a direct relationship between the quality of the scRNA-seq data (and the inferred
pseudo-time) with the quality of the inferred GRN. A suitable dataset for IQCELL captures the
cells in transient states (i.e., along developmental trajectories or other interesting biological
transitions) so IQCELL can correctly infer the dynamics of the fate changes. For example,
some in vitro differentiation processes can take several days to happen, and having samples
from intermediate days will potentially capture the transient cells. Also, more depth in
sequencing will give more confidence in counting TFs, and potentially better performance of
IQCELL as the accuracy of calculating mutual information and update rules will increase.
Gene expression recovery
scRNA-seq data is usually affected by dropouts, which is a technical term that is used to
describe the false-negative reads of mRNAs. Dropout effects cause the expression profile of
genes to be underrepresented. Usually, genes with low copy numbers (e.g TFs) are more
impacted by this effect. IQCELL applies a recent method (MAGIC) that uses a graph-based
imputation method to infer the expression of dropouts [24] (S1B Fig). The MAGIC algorithm
was selected based on a recent benchmarking paper [76] as it outperforms other methods. This
imputation is important as dropouts can affect the inference of gene relations (S1B Fig). In
summary, MAGIC calculates the affinities between neighboring cells in high dimensional data
and uses this information to recover the undercounted values of gene expression of individual
genes (dropouts) from the neighboring cells. This process leads to the imputation of gene
expression [24].
Selecting a curated gene list for early T-cell differentiation
Selecting a small subset of genes to include in a functional GRN from the entire set of genes
detected by scRNA-seq is, in general, a challenging task. Fortunately in mouse T-cell develop-
ment, many relevant genes are known. We have curated a list of genes based on literature
[16,31,37], and limited ourselves to genes that are included in to HVGs. Below, we describe a
possible general approach for a selecting smaller subset of genes from a large set.
Selecting relevant genes for a functional/causal GRNs is generally a multilayered process
(S1A Fig) which ideally combines multiple sources of information. One possible source is
prior knowledge of important genes in the process, which can be obtained through literature
review or systematic gene perturbation experiments (such as genome-wide CRISPR screen-
ing). Alternatively, genes of interest can be selected directly from scRNA-seq data via various
information theory metrics [77]. Many scRNA-seq data analysis packages set an initial filter to
only select HVGs for downstream analysis. HVGs are genes whose mean-scaled variance
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exceeds an automatic threshold. Although this is generally a useful filter, it does not necessarily
select for genes whose expression levels vary significantly across pseudo-time. Therefore,
IQCELL has a built-in function to visualize expression dynamics along pseudo-time and calcu-
late the degree of variation, which can be used as an additional input for gene selection.
Besides these, there are other network-based approaches to select informative genes. These
methods typically prioritize genes with connections to many other genes (high degree). Finally,
enrichment analysis and ChIP-seq data can be another source of gene selection; however,
these methods are generally low-throughput, noisy, and prone to false positives and negatives.
For this study, we manually curated a list of genes based on biological significance [16] and
dynamics along the pseudo-time (S1A Fig and S1 Table).
Creating an initial list of TFs in automated gene selection
The IQCELL gene selection pipeline starts with a set of HVGs. Next, it uses the pySCENIC
platform [23], which was chosen as it is the only platform to our knowledge that effectively
combines binding motifs and expression enrichment [78]. We select TFs that are components
of core regulons during the differentiation process to calculate their GDS.
Gene dynamics score
The GDS measures the variability of genes along the pseudo-time. The method implemented
in IQCELL for this purpose is based on the mean value. The normalized gene expression along
the pseudo-time is assigned to a number of bins (5 as default).
For each gene (g), the mean of each bin is calculated (MBg
i), and the matrix of mean dis-
tances (MMD) are formed:
MMDg
i;j¼ jMBg
ij
The GDS for each gene is calculated as the maximum of arguments of MMD matrix:
GDSg¼argmaxðMMDg
i;jÞ
Establishing the initial gene-gene interaction network
To form the initial gene-gene interaction network from scRNA-seq data (S1C Fig), IQCELL
first forms a list of all possible pairwise gene-gene interactions. This list does not include auto-
regulation by default (optional) except in some cases (see Implementing the Z3 reasoning
engine to infer logical GRNs). Next, it uses a recent method (DREMI) to calculate the resam-
pled and conditional mutual information between gene pairs [26] (S1C Fig). In general, the
mutual information (I) between a pair of variables X and Y (where X and Y represent two
genes) is calculated as below:
IðX;YÞ ¼ HðYÞ  HðYjXÞ
where H(X) is called the entropy of distribution X and P(X) is the probability density of the
variable X:
HðXÞ ¼ XPðXÞlog PðXÞ
The mutual information score is symmetric and unsigned. Next, IQCELL applies the Pear-
son correlation coefficient to assign a sign (+/- which represents activation/repression) to the
interactions, based on the sign of the correlation between two genes (S1C Fig):
cðX;YÞ  0! þ
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cðX;YÞ<0! 
Where c(X,Y) is the Pearson correlation coefficient of the pair of gene X and Y:
c X;Yð Þ ¼ EðXYÞ  EðXÞEðYÞ
sXsY
E(X) is the expected value and σ
X
is the standard deviation of X. Finally, IQCELL eliminates
interactions that are difficult to assign a sign (+/-) to them (their absolute correlation values are
smaller than a threshold). The default threshold is permissive so that many interactions can pass
and will be signed (for example see S1C Fig). If an update rule is found for a particular gene, lower-
ing the threshold will only increase the search-time, because it is likely that the link will be selected
(due to higher correlation). This threshold allows us to assign a sign (positive or negative) to interac-
tions, its initial purpose is not to cut interactions, but to eliminate interactions with sign ambiguity.
Binarization of gene expressions
IQCELL binarizes the expression (S4F Fig) for each gene individually. To do this, it can apply
two possible methods that can be chosen by the user (S1D Fig). The first method finds the
mean of expression and assigns ‘off’ (0) to the genes (for each cells) with the expressed num-
bers of mRNAs that are smaller than the prefixed threshold and ‘on’ (1) if they are larger. The
second method (the default method) binarizes the expression based on the cut-off identified
by k-means clustering (k = 2) method (S1D Fig) [27]. In general, we group the expression of
each gene in each cell g
i
(i2N
cells
) into two possible groups S
i
= {S
off
, S
on
} by finding:
arg minSX
i2off ;on X
g2Sijjgmijj
In which μ
i
(centroids) is the mean of expression values in ‘on’ or ‘off’ cluster. The threshold
(τ) is obtained as the average of two centroids:
t¼ ðmoff þmon Þ=2
The binarized gene expression value (G
i
) is obtained similar to the mean method:
ifðgitÞ ! Gi¼0
ifðgi>tÞ ! Gi¼1
Establishing the gene hierarchy via pseudo-time
After binarization of expression levels, IQCELL calculates an interaction hierarchy to further
filter gene-gene interactions, thereby eliminating interactions that are less likely to be causal.
First, it averages the binarized expression values in a sliding window over pseudo-time (S1E
Fig). To do this, IQCELL first sorts the cells based on their pseudo-time values c
i
(i2N
cells
).
Next, it averages the values of binarized gene expressions over an averaging window (with the
default length of L = N
cells
/N
genes
). This results in a density representation of the binarized
gene expression values along pseudo-time (t) (S1E Fig):
DðtÞ ¼ X
i2ðtL=2;tþL=2Þ
Gi=L
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Next, it calculates transition points between low-to-high or high-to-low density regions for all
genes (S1E Fig) and sorts genes based on their transition points (S1E Fig). Finally, IQCELL
includes autoregulation (autoactivation) as a possible self-interaction for genes with less than two
possible activators. This step is optional and is used in the current study, leading to inclusion of
autoactivation interactions for Hes1,Notch1,Lmo2, and Spi1 in the final interaction network.
Implementing the Z3 reasoning engine to infer logical GRNs
To generate functional GRNs, IQCELL implements a modified network inference strategy in
the Z3 engine [13]. This method effectively finds optional logical rules for each gene based on
the possible list of interactions obtained from previous steps. The optimal rules are those that
when executed as logical gates for each gene (given the state updates of other genes along the
pseudo-time as an input), follow the experimental data. This is quantified with the percentage
of similarity (based on Hamming distance) between the two (S1F Fig). Similar to [13], we
allow up to four possible activators and up to two repressors for each gene. In contrast to [13]
and similar to [8], for gene activation, we assume that all the activators are necessary (which is
implemented with the ‘and’ logic gate), but only one repressor is enough for repression (which
is implemented with the ‘or’ logic gate). In summary, the most general logical rule for the regu-
lation of a gene (g
j
) by (the maximum number of) six regulators including (maximum) four
activators (A
1
, A
2
, A
3
, A
4
) and (maximum) two repressors (R
1
, R
2
) is:
gj¼ ðA1and A2and A3and A4Þand not ðR1or R2Þ
Which indicates that all activators and none of the repressor should be expressed for the
gene to be expressed. The assumption of having ‘and’ between activators and ‘or’ between
repressors is a strict assumption. IQCELL has the option to relax this assumption to include
both ‘and’ and ‘or’ in all rules with the cost of more computational time. We suggest that users
first use the default configurations, and in the case of not finding any satisfying rule, then try
the relaxed assumptions.
The maximum number of 6 regulators in total is selected due to the computational cost of
searching the state-space of possible interactions (S8A Fig). In summary, the process of find-
ing the rules is costly, since for each possible rule, we calculate the agreement score for thou-
sands of cells along the pseudo-time. Having up to 4 activators and up to 2 repressors, gives
rise to up to nRules, where this is defined by (S8A Fig):
nRules ¼N
1
 þN
2
 þN
3
 þN
4
  M
0
 þM
1
 þM
2
  
Where N and M are the numbers of all possible activators/repressors in the initial interac-
tion network respectively. Increasing the possible value of activators/repressors will increase
nRules
T
and computational cost. As a reference, we have included the distribution of edge
degree for all genes of the final Boolean GRN in this study (S8B Fig).
Next, for each gene, the rule with the highest average mutual information for interactions is
selected by IQCELL for the final GRN (S1 Table). Inclusion of self-activation in the final Bool-
ean GRN model selection will be costly for the update rule since we have set the mutual infor-
mation of self-activation interaction to ‘0’. This reduces the average mutual information
weight of terms that have self-activation. This decision is made because self-activation cannot
be weighted effectively by mutual information value against other genes (mutual information
is the final criteria used in IQCELL to select the final GRN). However, including self-activation
in a Boolean update rule can help the rule to make the cutoff of Z3 step. This ensures that the
self-activation is only included if necessary.
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Asynchronous simulator of GRN under normal and perturbed condition
To analyze the system level behavior of the obtained GRN models and predict the effect of
gene perturbations on developmental trajectories, IQCELL uses asynchronous Boolean simu-
lations. Boolean GRNs contain a set of genes G¼ fG1;G2;. . . GNgenes gand their update func-
tion which encodes the gene regulatory details (one update function per gene). The update
function of a gene (FGi) implies what will be the activity state of that gene (on or off) at the next
discrete time point G
i
(t+1) given the state of all the genes at the current discrete time point
fG1ðtÞ;G2ðtÞ;...GNgenes ðtÞg:
Giðtþ1Þ ¼ FGiðG1ðtÞ;G2ðtÞ;. . . GNgenes ðtÞÞ
IQCELL uses the asynchronous update strategy [7]. In this strategy, at each discrete time
step, only one random gene is selected and updated. This results in stochastic dynamics. This
lets us average the expression states (average_exp) at each discrete time point (j) over the
ensemble of stochastic states that started from the same initial point and are now at that partic-
ular time point (EX(j)) (Fig 3G):
average expj¼X
S2EXðjÞ
S=jjEXðjÞjj
Where S = {0,1} therefore:
0avrage expj1
To calculate the average step of each simulation data point (e.g. Fig 3F), we first find the
attractor of interest (the attractor marked by ), then for each simulation data point (p), we
find where that particular point is (XP
T) for each possible trajectory, then we normalize this
value to the length of the trajectory (L
T
):
xP
T¼XP
T=LT
Where xP
Tis the scaled place of the point P in trajectory T. Finally for each point, we average
over all trajectories:
aspP¼<xP
T>T
which gives us the average simulation step (asp
P
) for each point.
IQCELL also has a built-in function to perturb the GRNs in two ways. It has the capability
to perform KO (setting the gene to be always ‘off’) and OE (setting the gene to be always ‘on’)
experiments simultaneously for one or multiple genes systematically. Also it can perturb the
gene-gene interactions systematically (S2 Fig).
Software architecture of IQCELL
IQCELL is implemented as a Python package. It is modular and scalable, to help researchers to
expand, optimize, and customize it for their future studies. Also, it has a minimal Python inter-
face, which allows the users with minimal computational skills to use it, and implement it in
their system of interest.
Pre-processing the scRNA-seq data
To dissect the developmental trajectory of T-cell development (from ETP to DN3 stages), we
used an existing scRNA-seq dataset [18], and analysis pipeline [79]. After the quality control
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and normalizing expression values, single-cell transcriptional states were visualized in reduced
dimensional space using UMAP (S4A Fig). To understand the underlying structure of data we
performed clustering based on the Louvain method (S4B Fig) which yields 14 sub-clusters.
Next, we evaluated the expression pattern of developmentally important genes in blood and
particularly T-cell development. ETP associated genes (Flt3,Lmo2,Mef2c) are all expressed in
the cell clusters in the left side (S4C Fig). DN2A stage is marked by Il2ra, this gene along with
the gene associated with committed DN2 cells (Bcl11b) and DN3 associated genes (Cd3e and
Rag1) expression are localized on the right side (S4C Fig). Altogether we conclude that cluster
0 includes many of the cells at the ETP stage and the developmental progression is toward clus-
ters 9 and 11 as the endpoints (S4C Fig).
Using a previously reported approach [18], we performed pseudo-time ordering on the
subset of genes that are known to be developmentally important in T-cell development or are
alternate lineage markers. The selected genes were similar to [18] and DDRtree pseudo-time
ordering was performed on the data [22]. As established in the cluster analysis, step cluster
number 0 is the best candidate as the cluster with the earliest developmental stage and is used
as the root for the algorithm. The result shows a single trajectory starting at cluster 0 and pro-
gressing toward later stages (S4D Fig). Pseudo-time ordering shows the dynamics of genes as a
function of differentiation (S4E Fig).
We processed the erythroid differentiation dataset the same way as in the original publica-
tion [17] to better support our comparisons; specifically we used the Slingshot method to infer
the developmental trajectory [80].
Calculating area under the precision-recall curve (AUPRC) for IQCELL
outputs
To calculate the area under the AUPRC, we followed Pratapa et al., 2020. For each dataset, we
first weighted the gene interactions based on the average mutual information of the rule that
the interaction is located in. For duplicated interactions that are present in two or more rules,
we picked the highest rank. Next, we weighted the interactions based on their position in the
raking and used the Beeline software [12] to calculate AUPRC for IQCELL and other the
methods (S9 Fig).
Sample preparation and single-cell RNA-sequencing of in vitro T-cell
differentiation
Isolated fetal liver cells from decapitated E13.5 CD1 mouse embryos were subjected to TER-
119 depletion by EasySep magnetic sorting (STEMCELL Technologies). Next, sorted HSPCs
(Sca-1+ cKit+) cultured at 3.1 x10E3 HSPCs/cm2 (corresponding to 1000 cells/well) in DL4
(10 μg/mL) and VCAM-1 (2.32 μg/mL) coated 96-well plates [81]. 10X Chromium was used to
prepare single-cell cDNA libraries, and Illumina Nextseq was used to 3’ sequence the samples.
Gene-barcode expression matrices were calculated from the raw data via CellRanger (10X
Genomics).
Supporting information
S1 Fig. Overview of IQCELL parts and algorithms. (A) Overview of gene selection criteria
(left). IQCELL’s gene selection pipeline (right). After selecting HVGs, IQCELL uses pySCE-
NIC to select active regulons (TFs and their effectors), and finally IQCELL uses GDS to rank
and select TFs for the final list. (B) Overview of gene expression recovery step. The scRNA-seq
data is corrected for dropout effect via a borrowed library ‘MAGIC’ from literature (left). Raw
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(grey) and recovered (blue) expression of Bcl11b vs Gata3 (right). (C) Overview of generating
the initial interaction network. The steps toward obtaining the directional and signed interac-
tion network from an initial list of genes (left column). The histogram of mutual information
between gene pairs, the histogram of Pearson correlation between gene pairs (the correlation
value of 1 is for the correlation of genes with themselves, marked by red), and mutual informa-
tion vs. correlation values (right column). In the histogram of Pearson correlation values, the
interactions that end up in the final model are marked by short red lines and the vertical green
line shows the sign cutoff (which its value has been chosen to be permissive); results are for the
T-cell dataset. (D) Overview of expression binarization step. There are two implemented
binarization methods in IQCELL. K-means clustering (default) and binarization based on the
mean value of expression of the gene between all the cells (left). Example of binarization of
genes and their expression along the pseudo time (right). (E) Overview of generating the gene
hierarchy step from the binarized gene expressions. First, the expression levels are averaged
with a sliding window along the pseudo-time. This results in the density profile of binarized
genes along the pseudo-time (left). Next, based on clustering the density, the transition point
(from high to low or low to high) are captured (center). Finally, genes are sorted based on tran-
sition points. Genes can interact with genes with a lower rank (right). (F) Overview of imple-
menting the Z3 reasoning engine. At this step, the filtered set of interactions are used to make
provisional update rules for each gene.
(PDF)
S2 Fig. GRN perturbations via IQCELL. (A) Systematic gene perturbations. The expression
states of the model attractor (left). The percentage of similarity between the attractors (vertical
axis) and the binarized expressions of CLP, ETP, DN2A, DN2B, and DN3A cells (horizontal
axis) [38] (right) for systematically perturbed GRN with single gene KO and OE. (B) System-
atic gene-gene interaction perturbations. Overview of GRN link perturbation (top). The per-
centage of similarity between the attractors (vertical axis) and the binarized expressions of
CLP, ETP, DN2A, DN2B, and DN3A cells (horizontal axis) [38] (bottom) for systematically
perturbed GRNs.
(PDF)
S3 Fig. Implementation of IQCELL with another early T-cell development scRNA-seq data
set. (A) To demonstrate the universality of IQCELL, we have tested this platform with another
in-house scRNA-seq data. The IQCELL tutorial in the IQCELL website is based on this dataset.
We used 10X scRNAseq by performing whole-genome transcriptional analysis. These experi-
ments are performed with the mouse T-cell progenitor populations from fetal liver (FL)
hematopoietic stem and progenitor cells (HSPCs) differentiated in vitro using the DL4
+VCAM platform [81]. FL HSPCs were seeded on DL4+VCAM coated plates and cultured for
4 or 7 days prior to analysis, or immediately sorted and captured for library preparation. Pool-
ing cells from multiple differentiation time points enabled sampling of cells from the entire T-
cell lineage progression, rather than just endpoint transcriptional states. Here we have selected
a small set of 6 genes that are important in the early T-cell development (from ETP to DN2
stages). The heat map shows the expression matrix of smoothed binarized expressions along
the pseudo-time. (B) The set of all possible gene-gene interactions, filtered by interaction hier-
archy and mutual information cut-off (the thickness of lines represents the mutual informa-
tion between genes), and signed by correlation. (C) Provisional GRN for early mouse T-cell
development. (D) Detailed representation of the proposed interactions provided by IQCELL
and experimentally reported ones. (E) PCA plot of the binarized scRNA-seq data color coded
with the pseudo-time values attributed to each cell. The binarization is performed by clustering
the scRNA-seq expressions into expressed or not expressed levels. On top of that, the binarized
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expressions of CLP, ETP, DN2A, DN2B, cells have been calculated from the Immgen microar-
ray data [38] and overlaid on RNA-seq data. (F) PCA plot of the simulated developmental tra-
jectories are overlaid on the binarized scRNA-seq. (G) Expression states of the model
attractors (top). The percentage of similarity between attractor and known cell states [38]. (H)
Averaged gene expression of the simulated data at each simulation step. All simulations started
from the same initial condition.
(PDF)
S4 Fig. The overall workflow of preprocessing the scRNA-seq data. (A) UMAP representa-
tion of data overlaid with sample ID, number of genes per cell, and density plot. (B) Clustering
of scRNA-seq data. (C) Gene expression of stage-specific gene overlaid on top of UMAP. (D)
The pseudo-time trajectory of the data inferred by Monocle platform. (E) Example expression
of genes along the pseudo-time trajectory. (F) The normalized and scaled to 1 expression of
some example genes.
(PDF)
S5 Fig. The GRN created based on the gene selection pipeline for T-cell development. (A)
The GDS of genes, the top 14 genes have been selected (left). Log transformed expression
matrix for selected genes from sc-RNA data along the pseudo-time axis. Gene expression is
corrected for dropout effects using MAGIC. Red indicates high expression, blue indicates low
expression (right). (B) Smoothed binarized gene expression matrix (expression density). Gene
expression values were binarized by clustering, averaged over a pseudo-time window, then
sorted based on transition points from early to late. Red indicates high expression, blue indi-
cates low expression. (C) The set of all possible gene-gene interactions, filtered by interaction
hierarchy and mutual information. (D) The provisional GRN for early mouse T-cell develop-
ment. (E) Average gene expression at each simulation step. All simulations started from the
same initial condition (ETP) and move toward the same attractor (). (F) Systematic KO: The
percentage of similarity between the attractors (vertical axis) and the binarized expressions of
CLP, ETP, DN2A, DN2B, and DN3A cells (horizontal axis). (G) Systematic OE: The percent-
age of similarity between the attractors (vertical axis) and the binarized expressions of CLP,
ETP, DN2A, DN2B, and DN3A cells (horizontal axis)
(PDF)
S6 Fig. GRN created based on the red blood cell development dataset. (A) Average gene
expression at each simulation step. All simulations started from the same initial condition
(MEPs) and move toward the same attractor (). (B) The set of all possible gene-gene interac-
tions, filtered by interaction hierarchy and mutual information (and signed by correlation.
Positive and negative interactions are represented by blue and red edges, respectively. Edge
width represents the relative amount of mutual information of the interaction. Nodes colored
red have higher out-degrees. (C) The PCA plot of the binarized scRNA-seq data color coded
with the pseudo-time values attributed to each cell. The binarization is performed by clustering
the scRNA-seq expressions into expressed or not expressed levels. (D) Average gene expres-
sion at each simulation step. All simulations started from the same initial condition (MEPs)
and move toward the same attractor (). (E) Expression states of the GRN model steady state
attractors. Genes that are expressed (1) and not expressed (0) are represented with blue and
grey squares, respectively (left). Percentage of similarity between the model attractors under
perturbations (vertical axis) and binarized expression of MEPs and ErPs (horizontal axis)
(right). (F) Systematic gene perturbations. The expression states of the model attractor (left).
The percentage of similarity between the attractors (vertical axis) and the binarized expres-
sions. (G) The PCA plot of the simulated (perturbed) developmental trajectories are overlaid
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on the binarized scRNA-seq. The simulated data is color coded by the value of average simula-
tion step (average distance to the attractor of simulation).
(PDF)
S7 Fig. The GRN created based on the gene selection pipeline for red blood cell develop-
ment. (A) Overview of gene selection procedure for erythropoiesis data. (B) The GDS of
genes, the top 14 genes have been selected. (C) Log transformed expression matrix for selected
genes from sc-RNA data along the pseudo-time axis. Gene expression is corrected for dropout
effects using MAGIC. Red indicates high expression, blue indicates low expression. (D)
Smoothed binarized gene expression matrix (expression density). Gene expression values were
binarized by clustering, averaged over a pseudo-time window, then sorted based on transition
points from early to late. Red indicates high expression, blue indicates low expression. (E) The
set of all possible gene-gene interactions, filtered by interaction hierarchy and mutual informa-
tion. (F) The provisional Boolean GRN for early mouse T-cell development. (G) The PCA plot
of the binarized scRNA-seq data color-coded with the pseudo-time values attributed to each
cell. The binarization is performed by clustering the scRNA-seq expressions into expressed or
not expressed levels. (H) Average gene expression at each simulation step. All simulations
started from the same initial condition (MEPs) and move toward the same attractor (). (I)
Expression states of the GRN model steady state attractors. Genes that are expressed (1) and
not expressed (0) are represented with blue and grey squares, respectively (top). Percentage of
similarity between the model attractors under perturbations (vertical axis) and binarized
expression of MEPs and ErPs (horizontal axis) (bottom). (J) Systematic KO: The percentage of
similarity between the attractors (vertical axis) and the binarized expressions of MEPs and
ErPs (horizontal axis). (K) Systematic OE: The percentage of similarity between the attractors
(vertical axis) and the binarized expressions of MEPs and ErPs (horizontal axis).
(PDF)
S8 Fig. Possible update rules for each gene. (A) Calculating the number of possible rules for
the update function of a gene. (B) Histogram of number of activator/repressors of all genes.
(PDF)
S9 Fig. Comparing IQCELL performance with other methods. Comparison of the area
under the precision-recall curve of IQCELL with other standard GRN inference methods (Pra-
tapa et al., 2020). IQCELL shows improved performance over other methods for both the T-
cell and the erythropoiesis datasets.
(TIF)
S1 Table. The final gene list and provisional logical GRN for early T-cell development. The
rules are picked from possible rules in Z3 step based on maximizing the average mutual infor-
mation per gene.
(PDF)
S2 Table. Genes used for supervised trajectory inference.
(PDF)
S3 Table. Comparison of attractors of perturbed GRN with the known cell states from
microarray data.
(CSV)
S4 Table. The attractor states of perturbed GRN.
(CSV)
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S5 Table. The final gene list and provisional logical GRN for erythropoiesis.
(PDF)
Acknowledgments
We thank Sara-Jane Dunn, Boyan Yordanov, and Ellen V. Rothenberg for our fruitful discus-
sions and Yale S. Michaels and John M. Edgar for critically reading the manuscript. We also
thank Microsoft Research (Cambridge, UK) and Sara-Jane Dunn for facilitating the opportu-
nity for the author to deepen his understanding of the Z3 reasoning engine. We thank Ellen V.
Rothenberg, and Bertie Gottgens for generating publicly available high-quality scRNA-seq
data sets that have been used in this study.
Author Contributions
Conceptualization: Tiam Heydari, Peter W. Zandstra.
Investigation: Matthew A. Langley, Cynthia L. Fisher, Shreya Shukla, Michael Hughes.
Methodology: Tiam Heydari.
Resources: Kelly M. McNagny.
Software: Tiam Heydari, Matthew A. Langley, Ayako Yachie-Kinoshita.
Supervision: Peter W. Zandstra.
Writing – original draft: Tiam Heydari, Daniel Aguilar-Hidalgo, Peter W. Zandstra.
Writing – review & editing: Tiam Heydari, Matthew A. Langley, Cynthia L. Fisher, Daniel
Aguilar-Hidalgo, Kelly M. McNagny, Peter W. Zandstra.
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