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BioSystems 217 (2022) 104672
Available online 22 April 2022
0303-2647/© 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Contents lists available at ScienceDirect
BioSystems
journal homepage: www.elsevier.com/locate/biosystems
Modeling the C. elegans germline stem cell genetic network using automated
reasoning
Ani Amar a, E. Jane Albert Hubbard b,∗, Hillel Kuglera,∗
aThe Faculty of Engineering, Bar-Ilan University, Ramat Gan 5290002, Israel
bSkirball Institute of Biomolecular Medicine, Department of Cell Biology, Department of Pathology, NYU Grossman School of Medicine, 540 First Avenue, New
York, NY 10016, United States of America
ARTICLE INFO
Keywords:
Boolean network
C. elegans
Formal reasoning
Gene regulatory network
Germ line
Modeling
Stem cells
ABSTRACT
Computational methods and tools are a powerful complementary approach to experimental work for studying
regulatory interactions in living cells and systems. We demonstrate the use of formal reasoning methods
as applied to the Caenorhabditis elegans germ line, which is an accessible system for stem cell research.
The dynamics of the underlying genetic networks and their potential regulatory interactions are key for
understanding mechanisms that control cellular decision-making between stem cells and differentiation. We
model the ‘‘stem cell fate’’ versus entry into the ‘‘meiotic development’’ pathway decision circuit in the
young adult germ line based on an extensive study of published experimental data and known/hypothesized
genetic interactions. We apply a formal reasoning framework to derive predictive networks for control of
differentiation. Using this approach we simultaneously specify many possible scenarios and experiments
together with potential genetic interactions, and synthesize genetic networks consistent with all encoded
experimental observations. In silico analysis of knock-down and overexpression experiments within our model
recapitulate published phenotypes of mutant animals and can be applied to make predictions on cellular
decision-making. A methodological contribution of this work is demonstrating how to effectively model within
a formal reasoning framework a complex genetic network with a wealth of known experimental data and
constraints. We provide a summary of the steps we have found useful for the development and analysis of
this model and can potentially be applicable to other genetic networks. This work also lays a foundation for
developing realistic whole tissue models of the C. elegans germ line where each cell in the model will execute
a synthesized genetic network.
1. Introduction
Understanding the mechanisms and design principles underlying
the transition of stem cells from self-renewal to differentiation is a
fundamental question in biology. The control of these self-renewal
and differentiation processes is crucial for proper organ formation,
for tissue maintenance and repair, and has important implications in
unraveling the molecular and cellular basis of tumor initiation and
progression (Simons and Clevers,2011;Batlle and Clevers,2017).
The Caenorhabditis elegans germ line provides an accessible system for
studying stem cell decision-making. Over the last decades, a number of
regulatory interactions between core signaling genes governing germ
cell identity have been experimentally determined (see Hubbard and
Schedl,2019 and references within). The current understanding of the
decision of cells to remain stem cells or to differentiate involves the
interaction of multiple pathways that are inhibited by active Notch
pathway signaling. The genetic interactions between these pathways
∗Corresponding authors.
E-mail addresses: ani.amar@biu.ac.il (A. Amar), jane.hubbard@med.nyu.edu (E.J.A. Hubbard), kugler.hillel@biu.ac.il (H. Kugler).
and their components are complex. Computational modeling, especially
cell-based modeling, can play an important role in uncovering proposed
interactions that are inconsistent with available experimental data or
those that may be most informative in clarifying the network structure
and dynamics and therefore deserve more experimental focus.
The adult hermaphrodite gonad is a structure of two U-shaped tube-
like arms that are closed at the distal ends and open to a common
uterus (Fig. 1). At the distal (blind) end of each arm, a somatic cell, the
distal tip cell (DTC), caps the gonad and acts as a signaling center for
the distal-most germ cells. The DTC signals promote stem cell fate by
maintaining the undifferentiated state of stem cells that reside near the
DTC; the DTC therefore acts as a stem cell niche for the germline stem
cells. As germ cells divide and are displaced proximally, they escape the
influence of DTC signaling, exit the mitotic cycle, enter and progress
through meiotic prophase. Finally, they differentiate into functional
https://doi.org/10.1016/j.biosystems.2022.104672
Received 8 August 2021; Received in revised form 31 March 2022; Accepted 4 April 2022
BioSystems 217 (2022) 104672
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A. Amar et al.
Fig. 1. A cartoon of the adult germ line (not to scale, under-represented cell counts) illustrating the computational modeling approach. The DTCs are yellow, proliferating and
meiotic S cells (StemcellFate) are green, meiotic cells (meioticDev) are red. Cells not modeled in this paper are gray: sperm (small circles) oocytes (large circles) with the central
oval representing multiple cells and sheath cells that are omitted. In the model, a Boolean network determines the state of a germ cell, in this figure we present a possible network
for a cell which is close to the DTC and therefore the StemcellFate component is on (represented as bold font in the network) and the MeioticDev component is off (represented
as light font in the network). In a cell that is far away from the DTC the network dynamics will change the value of the components eventually switching MeioticDev component
to on and StemcellFate to off.
gametes. Therefore, the cell fate decision we are modeling (stem cell
versus meiotic entry) is critical for all subsequent aspects of germline
development.
Several computational models for studying network topology (Al-
bert and Othmer,2003), C. elegans vulval precursor cells (VPC) cell
fate specification (Fisher et al.,2007,2005;Kam et al.,2008) and the
C. elegans germ line (Atwell et al.,2015;Setty et al.,2012) (particu-
larly in the context of proliferative germ cell behavior — see Atwell
et al.,2016 and references within) have been developed in the past
years. Albert and Othmer (2003) applied the Boolean network ap-
proach for analyzing and manipulating genetic circuits in Drosophila
melanogaster, focusing on the segment polarity gene network developed
earlier (Von Dassow et al.,2000). To this end, they explored the
possible steady states and their attractors under a wide variety of
conditions such as cell divisions and gene mutations, demonstrating
that the robustness of the network is determined by its topology and
the signature (activation or inhibition) of the interactions. The VPCs are
a classical system in C. elegans that has been widely used to study the
process of cell differentiation in a regulated and robust setting. Fisher
et al. (2005) used the Statecharts formalism (Harel,1987) to create
a dynamic computational model of VPC fate specification. Kam et al.
(2008) developed a comprehensive model using a scenario-based ap-
proach (Harel and Marelly,2003) of the VPC dynamics incorporating
mechanistic rules and specifications of experimental observations that
the model needs to recapitulate and demonstrated that the refined
model was indeed capable of reproducing this wide set of biological
observations. In Fisher et al. (2007) an experimentally validated com-
putational model of C. elegans vulval development is presented, where a
key aspect of the model is that it used model checking (Alur et al.,1998;
Clarke et al.,1999) to test a set of interactions based on experimental
observations, including genetic perturbations.
Computational models of germline development have been con-
structed for C. elegans,D. melanogaster and human (see Atwell et al.,
2016 and references therein). In Klein et al. (2010) modeling is used
to study different stem cell-maintenance hypotheses in the context
of mouse spermatogenesis. In Qin et al. (2007), modeling is used to
compare between different competing hypotheses concerning a ge-
netic mutation causative for Apert’s syndrome. Among the first models
exploring C. elegans germ line development (larva) and maintenance
(adult), is the model proposed by Setty et al. (2012). Although the
computational approach made simplifying assumptions regarding the
spatial aspects of the model (assuming a 2D geometry and a discrete
grid in which cells can be positioned), this model nevertheless success-
fully represented germ cell movements inside the gonad, including the
interplay between an individual cell’s cycle control and differentiation
in response to changes in signaling. The limitations in describing spatial
aspects in Setty et al. (2012) were overcome in a mechano-logical
model of the germ line (Atwell et al.,2015), which utilized a more
realistic 3D simulation of germ cell movement and distal tip cell (DTC)
migration. In both models, germ cell behavior was represented by the
statecharts approach (Harel,1987;Harel and Kugler,2004), which
extends classical state machines with orthogonal states, a hierarchy
of states and an executable language enabling efficient code genera-
tion and simulation. Orthogonal states are used for defining various
aspects of cellular behavior (e.g., cell cycle, signaling genes, cell fate
decision), using transitions between states for each component (within
the object), and the conditions required for each transition. There are
some important differences between the two models. First, the Atwell
model (Atwell et al.,2015) has a more realistic representation of cell
spatial location and direction of movement (without the need to be
uniformly spaced on a fixed grid). However, this off-lattice approach
to cell mechanics and special algorithms to efficiently handle cell–cell
neighborhoods increased the computational cost, in comparison to the
lattice-based model of Setty. Second, the Atwell model was applied
to more accurately simulate cell tracking and labeling throughout the
process of gonad development. This is especially useful for studying
the interrelationship between the gonad and the germ line, and be-
tween cells within the germ line over time — a challenging aspect of
experimental approaches.
Here we present a first detailed network model for germline stem
cells, that explores the specification of the cell fate in C. elegans by
means of state-of-the-art formal reasoning synthesis methods, and the
reasoning engine for interaction networks tool (RE:IN) (Dunn et al.,
2014;Goldfeder and Kugler,2019;Yordanov et al.,2016). RE:IN is
a synthesis-based tool, that is now available as an open source data
science framework (the reasoning framework) that supports scalable
formal reasoning procedures combined with a user friendly interface
to specify interaction network models constrained by experimental
results. Synthesis approaches for biological modeling are becoming an
important area of research and applications, see for example (Biane and
Delaplace,2018;Chevalier et al.,2019,2020;Guziolowski et al.,2013;
Koksal,2018;Koksal et al.,2013;Razzaq et al.,2018;Rosenblueth
et al.,2014;Sharan and Karp,2013) and references within. A signif-
icant advantage of synthesis compared to our earlier work on germline
modeling (Atwell et al.,2015;Setty et al.,2012) is the automation and
computational efficiency enabled by the formal reasoning approach,
providing the identification of networks that satisfy a wide set of
biological constraints specified by experimental results. This prevents
the bias introduced by manually searching for one or few networks that
are plausible in a trial and error process. We computationally synthesize
BioSystems 217 (2022) 104672
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A. Amar et al.
networks that capture signaling and genetic interactions within a single
germ cell’s decision-making process, focusing on the transition between
the undifferentiated stem/progenitor fate and differentiation (entry
into the meiotic pathway). Such synthesized networks can ultimately
be incorporated within computational agents representing cells to study
the development of the entire germ line (Atwell et al.,2015;Setty et al.,
2012), resulting in models that can be simulated and compared to in
vivo phenotypes.
Based on published data and known genetic interactions, we con-
structed a genetic network, which represents the ‘‘stem cell fate versus
meiotic development’’ decision circuit in the young adult hermaphrodite
germline stem cell system (Fig. 1) and which extends previous models
in a number of ways. First, our network model is more detailed in terms
of intracellular signaling (number of components and interactions)
and is derived from extensive studies from the literature. Second, we
applied the automated approach for constructing and refining a suitable
model that guarantees satisfying the set of all specified biological
constraints and experiments. Third, the presented approach allows the
synthesis algorithm to find all existing networks (by selecting a subset
of the optional interactions) consistent with encoded experimental
behavior, unlike other approaches that account for one or a limited
set of scenarios.
The model enables us to explore the behavior within an individual
cell, that either resides in a niche in the range of the DTC signal or
just out of range of the DTC signal, or that loses DTC signaling (when
moving proximally away from the DTC). We analyzed the structure and
dynamics of this genetic network, its functional modules and derived
predictive networks for control of self-renewal and differentiation. In
silico analysis of knock-down and overexpression experiments within
our model recapitulate published phenotypes of mutant animals and is
applied to make new predictions on cellular decision making.
Below is a summary of the steps we have found important for the
development and analysis of this model:
1. Extensive study of published experimental data and known /hy-
pothesized genetic interactions in the C. elegans germ line.
2. Preparation of data collection table that determines ‘‘source’’
(starting node) and ‘‘target’’ (ending node) components, the interac-
tions between them and data source (see Table 1 for an example).
3. Development of logical rules leading to an activity of each
component, using the Boolean operators AND, OR, and NOT.
4. Encoding a set of components and interactions in the reasoning
framework.
5. Visualization of the developed network in the reasoning frame-
work and its refinement against data collection table and logical rules.
6. Encoding a set of experimental observations that incorporates all
of the information. The corresponding network model files are provided
in Supplementary data.
7. Selection of analysis options (e.g., experiment length, update
scheme) and running the solver.
8. Assessment of the obtained solutions (if any) vs. expected profiles
of gene activity.
9. Revision of model assumptions (see steps 2, 3 and 6) if no model
solutions exist.
10. Once confirmed to be consistent with experimental data, the
model was extended by adding in silico genetic perturbations (known
phenotypes) to the set of experimental observations.
11. Comparison of the obtained solutions to the results of known
phenotypes.
12. Formulation and evaluation of new predictions that have not yet
been experimentally observed.
2. The reasoning framework
To investigate the dynamics of the germline genetic network and the
underlying regulatory interactions, we used the reasoning framework
(for more information see Yordanov et al.,2016 and the Materials and
Methods section). This approach supports the modeling of gene net-
works via Abstract Boolean Networks (ABN). In this logical modeling
framework, an ABN contains a set of components (e.g., genes/signals
/ transcription factors/proteins) which can be active or inactive (rep-
resented by a Boolean value) and interactions (definite or possible)
which can be either positive (activation) or negative (inhibition). In
addition, a set of (18) regulation conditions allows choice in defining
how interactions are combined to determine the effect of multiple
interactions on a given component. For example, if two components
g1 and g2 regulate component g, the choice of the regulation condition
will determine if both g1 and g2 are required to activate g (AND logical
function) or either g1 or g2 are sufficient to activate g (OR logical func-
tion). In general, the current 18 regulation conditions supported in the
reasoning framework take into account multiple regulators (activators
and inhibitors), and define the activation of a gene as a logical function
depending on the activity state (active/inactive) of these regulating
components (see Yordanov et al.,2016 and Supplementary Material,
Figure S1). The regulation conditions distinguish between a case where
all, some or none of the activators (inhibitors) are active. The regulation
conditions have a property of monotonicity, implying that if a regulated
component is active, and one of its activators switches from inactive to
active, the regulated component will remain active, and similarly if a
regulated component is inactive, and one of its inhibitors switches from
inactive to active, the regulated component will remain inactive. There
are several features of this approach that should be emphasized in terms
of the current genetic network construction:
1. The formal reasoning-based synthesis algorithms are utilized to
efficiently explore the large state space of potential networks and to
find solutions that recapitulate all specified experimental observations.
2. Each consistent network is a concrete Boolean network, which
includes a specific subset of the optional interactions, all the definite
interactions, and one regulation condition for each component. For
example, a target gene may requires the following regulation condition
(regulation condition 5, Supplementary Material, Figure S1):
𝑅(𝑐, 𝑞)=𝐴𝑙𝑙𝐴𝑐𝑡𝑖𝑣𝑎𝑡𝑜𝑟𝑠(𝑐 , 𝑞)∨(𝑁𝑜𝑅𝑒𝑝𝑟𝑒𝑠𝑠𝑜𝑟𝑠(𝑐 , 𝑞)
∧¬𝑁𝑜𝐴𝑐 𝑡𝑖𝑣𝑎𝑡𝑜𝑟𝑠(𝑐, 𝑞)) (1)
where AllActivators(c,q) indicates that all activators of a component
care present in a state q,NoRepressors(c,q) indicates that no repres-
sors of care present in q. And, by negating the function NoActiva-
tors(c,q), we obtain the function (¬NoActivators(c,q)) that indicates that
some activators of care present in state q. In this case, the solver
can select which interaction (one of the redundant genes or all of
them) and corresponding pathway satisfies the encoded experimental
observations.
3. A set of experimental observations (constraints) that a network
must satisfy are encoded as predicates over system states, limiting
the feasible choices of optional interactions and conditions that yield
consistent models. For example, in our network, we formalized an
observation where the DTC signal is considered to be initially active,
but should be inactive at time step 20 (see example in Supplementary
Material, Figure S6), simulating a cell just proximal of the DTC. In this
case, the solver identifies the existing trajectory (if any) that satisfies
the following expression:
(𝑒, 0, 𝑐, ⊤)∧(𝑒, 20, 𝑐 , ⊥)(2)
where eis the experiment label, cdenotes the DTC component, ⊤(true)
and ⊥(false).
4. The solver allows the user to set analysis options (e.g., solu-
tions limit, synchronous /asynchronous updates, experiment length —
number of time steps).
BioSystems 217 (2022) 104672
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A. Amar et al.
5. Once the tool finds consistent networks, these networks can be
utilized to investigate the network under conditions that were not
explicitly specified in the original model-building, and can therefore be
used to predict the outcome of new experiments including simultaneous
mutations.
3. Materials and methods
We briefly summarize the main formal definitions and concepts
underlying the reasoning framework (Paulevé et al.,2020;Shavit et al.,
2016;Yordanov et al.,2016). At the core of the approach are Abstract
Boolean Networks, an extension of Boolean Networks (BNs) (Bartocci
and Lió,2016;Kauffman,1969). BNs are a class of GRN models that are
Boolean abstractions of genetic systems, i.e., every gene is represented
by a Boolean variable specifying whether the gene is active or inactive.
The concept of Abstract Boolean Networks (ABNs) (Dunn et al.,2014)
was introduced to allow the representation of models with network
topologies and dynamics that are initially unknown or uncertain. The
main goal of the framework is to automatically identify a choice of
allowed network topology and dynamics that is consistent with all spec-
ified experimental constraints or to prove that no consistent network
exists.
Let 𝐺be a finite set of genes. Let B= {⊤, ⊥}be the Boolean domain
and let B𝑛be all vectors of 𝑛Booleans. Let 𝐸be a set of directed
signed edges between elements of 𝐺, i.e., 𝐸 ⊆ 𝐺 ×𝐺×B. The sign
of an interaction is either ⊤for positive regulation (activation) or ⊥for
negative regulation (repression). Let 𝑔and 𝑔′be genes from 𝐺. We call
𝑔an activator of 𝑔′iff (𝑔, 𝑔′, ⊤) ∈ 𝐸, and a repressor iff (𝑔 , 𝑔′, ⊥) ∈ 𝐸. We
define the state space of a system as 𝑄=B𝐺. For a given state 𝑞∈𝑄
and a gene 𝑔∈𝐺, we denote by 𝑞(𝑔)the state of 𝑔in 𝑞.
Each gene is associated with an update function 𝑓𝑔with a signature
𝑓𝑔∶𝑄→Bdefining its dynamics. For synchronous updates, the
dynamics of the system are defined in terms of the update functions
of all genes applied at each transition, where, given a current state
𝑞and next state 𝑞′,𝑔∈𝐺𝑞′(𝑔) = 𝑓𝑔(𝑞). In this work we focus on
synchronous semantics, but asynchronous semantics are also supported
by the reasoning framework.
A set of 18 biologically plausible update function templates, called
regulation conditions are used to determine the dynamics of a gene
(see Supplementary Material, Figure S1). Introducing these function
‘templates’ aims to reduce the number of Boolean functions that need
to be considered (thus simplifying analysis) while still maintaining and
emphasizing biological and experimental plausibility.
To capture possible uncertainty and partial knowledge of the pre-
cise network topology, we allow some interactions to be marked as
optional (denoted by the set 𝐸?), each of which could be included
in a synthesized concrete model. Thus, in terms of network topology,
this means a set of 2𝐸?concrete models, each of which corresponds
to a unique selection of possible interactions. Additionally, a choice
of several possible regulation conditions for each gene is taken into
consideration, leading to the following definition:
An abstract Boolean network is a tuple 𝐺, 𝐸, 𝐸 ?, 𝑅, where 𝐺is a
finite set of genes, 𝐸 ⊆ 𝐺 ×𝐺×Bis a set of definite (positive or negative)
and directed interactions between them, 𝐸?∶𝐺×𝐺×Bis a set of
optional interactions and 𝑅= {𝑅𝑔∣ ∀𝑔∈𝐺}, where 𝑅𝑔specifies a
(non-empty) set of admissible regulation conditions for gene 𝑔(Dunn
et al.,2014;Yordanov et al.,2016;Shavit et al.,2016).
An ABN is transformed into a concrete Boolean network by selecting
a subset of the possible interactions to be included and assigning a
specific regulation condition to each gene. The semantics of such a
concrete model is defined in terms of a transition system = (𝑄, 𝑇 ),
where 𝑄=B𝐺is the state space and 𝑇is a transition relation defined
in terms of the predicate 𝑇∶𝑄×𝑄→B. The semantics of the
synchronous transition system is then given by
∀𝑞, 𝑞′∈𝑄.𝑇(𝑞, 𝑞′)↔
𝑔∈𝐺
𝑞′(𝑔) = 𝑅𝑔(𝑞)(3)
A finite trajectory of length 𝑘is defined as a sequence of states
𝑞0,𝑞1,…,𝑞𝑘−1 where 0<𝑖<𝑘 . 𝑞𝑖∈𝑄∧𝑇(𝑞𝑖−1, 𝑞𝑖).
A set of experimental observations that a BN must be able to satisfy
are encoded as predicates over system states, which limits the feasi-
ble choices of possible interactions and regulation conditions yielding
consistent models. The approach developed and described in Dunn
et al. (2014) and Yordanov et al. (2016) allows GRN synthesis: given
an ABN and a set of experiments, find a choice of interactions and
regulation conditions that guarantees that the resulting concrete BN is
consistent with all experimental observations. The synthesis algorithm
constructs concrete, consistent models if they exist, or formally proves
no solution exists. The reasoning framework is publicly available at
(https://github.com/fsprojects/ReasoningEngine).
4. Results
4.1. Construction of the model
To construct a genetic regulatory network, we collected litera-
ture data about known interactions between the core Notch pathway
genes and their downstream effectors regulating stem cell fate ver-
sus meiotic development decision in the young adult hermaphrodite
germline stem cell system (see Hubbard and Schedl,2019 and refer-
ences within). Genes were selected for implementation of the circuit
as a Boolean model within the reasoning framework (Yordanov et al.,
2016). The proposed genetic network includes twenty-four (24) compo-
nents (genes/gene products) and forty (40) interactions (Fig. 2) with a
large state space of possible combinations (224 =16,777,216 states).
We defined the network model to be updated under a synchronous
update scheme (i.e., the states of all components are updated simul-
taneously at each step). Interactions that are well characterized and
have strong experimental support were denoted as definite interactions
(represented as solid edges), while interactions that are hypothesized
but their current experimental support is weaker or that may be re-
dundant, were denoted as optional interactions. To reproduce expected
profiles of the core gene activity (the attributes of gene function that
are inferred from genetic manipulation, but that can be the result of
changes in levels or function of the resultant mRNA or protein), a set
of experimental observations was encoded, which contain input state
(constraints on the initial state) as well as output state (constraints
on the resulting steady state) of certain genes involved in a particular
experiment. Furthermore, functional effects of the selected genes were
included by encoding knock-out and/or overexpression experimental
observations based on known phenotypes (Table 2). To simulate ge-
netic perturbations, a gene was defined as knocked out (KO), or as
constitutively active/ ‘‘overexpressed’’ (FE =forced expression) along
with corresponding experimental constraint (e.g., ‘KO(g) =1’ if gene
g is knocked out, or ‘FE(g) =1’ if gene g is over expressed) (for an
example of encoding such constraints see Supplementary Files). Once
the set of interactions and observations were encoded and the analysis
started, the solver searched for all existing networks (if any) that were
consistent with all encoded experimental observations. Each network is
visualized by presenting the topology of a single specific solution out
of many possible solutions (see example in Supplementary Material,
Figure S2) and a table representing a simulation of each experiment
showing Boolean values of each gene in this solution (see Section 4.3).
4.2. Functional modules
First, we identified the functional modules (genetic pathways) in
the network (Fig. 2), associated with specific processes: genes that act
downstream of GLP-1 signaling (LST-1, SYGL-1 and FBF-1); the GLD-1,
GLD-2 and SCFPROM-1 meiotic entry pathways; the GLD-1 accumulation
module. It is assumed that the initiation of network interactions occurs
due to contact between undifferentiated GLP-1-expressing germ cells
BioSystems 217 (2022) 104672
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A. Amar et al.
Fig. 2. A genetic network model of stem cell fate versus meiotic development derived
from extensive studies from the literature. Definite interactions are denoted as solid
lines, optional interactions as dashed lines, arrowhead line corresponds to activation
and T-shaped line corresponds to inhibition.
and the distal tip cell (DTC), allowing GLP-1 on the surface of the
germ cells to bind the membrane-bound ligands LAG-2 and/or APX-1
and to start downstream signaling (for details, see Fig. 2 and Table 1).
Consequently, DTC — germ cell signaling promotes the stem cell fate by
inhibiting the meiotic entry pathways (GLD-1, GLD-2, and SCFPROM-1).
Next, we analyzed the kinetics of regulatory module downstream of
GLP-1 signaling (LST-1, SYGL-1 and FBF- 1). LST-1 and SYGL-1 proteins
are direct transcriptional targets of GLP-1 signaling, that function at
least in part with FBF-1 in repressing GLD-1 levels (Chen et al.,2020).
We choose the model proposed by Brenner and Schedl (Brenner and
Schedl,2016), where LST-1 acts in both the same pathway and in
parallel to FBF-1, while SYGL-1 acts in the same pathway as FBF-
1 to repress base GLD-1 levels (Fig. 3A). In addition, we modeled
functional redundancy of LST-1 and SYGL-1 that has been experimen-
tally observed in C. elegans (Kershner et al.,2014).
For the GLD-2 pathway, which includes GLD-2 and GLD-3, we
constructed the module such that the dynamic behavior of FBF-1 can
be further investigated. FBF- 1 was found to inhibit the GLD-2 pathway
through repression of GLD-3 accumulation (Eckmann et al.,2004).
Conversely, FBF-1 appears to promote meiotic development through
binding to the GLD2/GLD3 complex in the absence of LST-1 and SYGL-1
partners (Hansen and Schedl,2006;Shin et al.,2017). This leads to the
model suggesting that FBF-1 function in this module may switch in a
partner-dependent manner (Hubbard and Schedl,2019).
We represent this complex partner-dependent behavior using a two-
state (bound–unbound) model, where FBF-1 function is controlled by
attachment and detachment of SYGL-1 or LST-1 (based on Shin et al.,
2017). We assume two molecular states, which are required to char-
acterize FBF-1 function with respect to SYGL-1/LST-1: a state where
FBF-1 is bound to SYGL-1 or LST-1 in a molecular complex inhibiting
the expression of the GLD2/GLD3 (FBF1B), and an unbound state where
FBF-1 acts as a promoter of GLD-2/GLD-3 activities (FBF1U) (Fig. 3B).
The GLD-1 accumulation pattern involves a number of genes
(Fig. 3C): (1) NOS-3, which functions upstream of GLD-1, promoting its
accumulation (Hansen et al.,2004b) and (2) the GLD2/GLD3 complex,
which promotes the accumulation of GLD-1 only in the absence of
FBF1B, SYGL-1 and LST-1 (Brenner and Schedl,2016). Our model
includes the redundancy of NOS-3 vs GLD2/GLD3 complex as positive
regulators of GLD-1 accumulation. This provides a functional module,
where GLD-1 accumulation will be inhibited, as is observed in the distal
end of gonad arm, unless LST-1, SYGL-1 and FBF-1 no longer repress
GLD-1 levels in the absence of GLP-1 Notch activation (in the proximal
part of the germ line).
The results of a recent study suggest that SCFPROM-1 meiotic entry
pathway acts redundantly with and in parallel to the GLD-1 and/or
GLD-2 pathways, and downstream of GLP-1 Notch signaling (Moham-
mad et al.,2018). However, the genes that control the SCFPROM-1
activity are unknown. Hence, one possible simplified model to describe
the interactions of these genes is that the GLP-1 signaling inhibits
the meiosis-promoting activities of SCFPROM-1 through FBF-1. We used
the same model (inhibition through FBF-1 or FBF-2) to describe the
repression of meiotic chromosome axis and SC proteins, which act as
additional regulators of meiotic development (Merritt and Seydoux,
2010).
4.3. The regulatory network reproduces expected profiles of gene activity
The model explores the effects of Notch signaling on the GLD-
1, GLD-2 and SCFPROM-1 pathways that dictate the switch from stem
cell fate to meiotic development. The simulated gene profiles were
compared to the results of known phenotypes based on extensive
experimental studies (see Table 2).
In Fig. 4 the simulation results (the table of Boolean values of each
gene) of a single specific network solution (see example in Supplemen-
tary Material, Figure S2) are presented. Since this is a synchronous
Boolean network, if the state of all components repeats itself in two
consecutive time steps, the system will remain in this state indefinitely.
The simulations describe gene expression dynamics in an a priori stem
cell that is experiencing Notch signaling activity by virtue of its distal
position in the germ line. Hence, the DTC signal was modeled as
constitutively active (by means of self-activating signal (S0), causing
the core genes to be active over the course of the simulation. The
expected outcome in this example after 20 steps is StemcellFate.
Next, we analyzed the architecture and the order of gene activity in
two different setups (see Supplementary Material, Figure S3 and S6).
One setup allows to simulate a stem cell that loses DTC signaling as
it moves from the distal-most end of the germ line further proximally.
Another setup represents a cell further from the DTC in the proliferative
zone by reducing but not eliminating the DTC signal duration (setting
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A. Amar et al.
Fig. 3. Functional modules in the gene regulatory network (A) Module A — SYGL-1 and LST-1 model. (B) Module B — two-state model of FBF-1. (C) Module C — GLD-1
accumulation model.
Table 1
Regulations of genes as depicted in Fig. 2 and their literature references.
Source Regulates Target Reference
DTC act APX1 Nadarajan et al. (2009)
DTC act LAG2 Henderson et al. (1994)
LAG2 act GLP1 Henderson et al. (1994)
APX1 act GLP1 Nadarajan et al. (2009)
GLP1 act GLP1ICD Greenwald and Kovall
(2018)
GLP1ICD act SEL8 Petcherski and Kimble
(2000)
GLP1ICD act LAG1 Petcherski and Kimble
(2000)
SEL8 act LAG1 Petcherski and Kimble
(2000)
GLP1 act HOP1 Agarwal et al. (2018)
HOP1 act GLP1ICD Agarwal et al. (2018)
GLP1 act SEL12 Levitan and Greenwald
(1995)
SEL12 act GLP1ICD Levitan and Greenwald
(1995)
SEL10 rep GLP1ICD Hubbard et al. (1997)
SEL10 rep SEL12 Wu et al. (1998)
LAG1 act LST1 Kershner et al. (2014)
LAG1 act SYGL1 Kershner et al. (2014)
LST1 rep GLD1 Brenner and Schedl (2016)
LST1 rep FBF1 Brenner and Schedl (2016)
FBF1 rep GLD1 Brenner and Schedl (2016)
SYGL1 rep FBF1 Brenner and Schedl (2016)
LAG1 act FBF2 Lamont et al. (2004)
FBF2 rep GLD1 Brenner and Schedl (2016)
FBF act GLD3 Hansen and Schedl (2006),
Shin et al. (2017)
FBF1 and FBF2 rep GLD3 Eckmann et al. (2004)
GLD3 act GLD2 Eckmann et al. (2004)
NOS3 act GLD1 Hansen et al. (2004b)
GLD2 act GLD1 Hansen et al. (2004b)
FBF1 rep SCFPROM-1 Jantsch et al. (2007)
FBF1 and FBF2 rep AxisandSCprotein Merritt and Seydoux
(2010)
SCFPROM-1 rep CYE1/CDK2 Fox et al. (2011)
‘‘act’’ for activate; ‘‘rep’’ for repress
DTC =1 at t=0 only). Once we confirmed that the literature-derived
regulatory network reproduces the expected gene expression profiles of
young adult hermaphrodite germline stem cell system, we proceeded to
conduct in silico perturbations.
4.4. Comparing knock-out and overexpression simulations to experimental
data
To test our model’s behavior under in silico perturbations we chose
to simulate a number of conditions with known effects on the stem cell
fate or meiotic development (see Table 2). The encoded experimental
Table 2
In silico knock-out (KO) and ‘‘overexpression’’ (FE) experiments.
Experiment Comments Ref
GLP-1 Meiotic entry pathway Austin and Kimble (1987)
LST-1 No effect on stem cell
fate
Kershner et al. (2014)
KO SYGL-1 No effect on stem cell
fate
Kershner et al. (2014)
LST-1 and SYGL-1 Meiotic entry pathway Kershner et al. (2014)
GLD-1 and GLD-2 Failure to enter meiosis Kadyk and Kimble (1998)
GLP-1 Failure to enter meiosis Berry et al. (1997)
FE LST-1 Failure to enter meiosis Shin et al. (2017)
SYGL-1 Failure to enter meiosis Shin et al. (2017)
observations can be found in Supplementary Files. The following sim-
ulations demonstrate how a cell residing adjacent to the DTC niche
responds to mutations. As mentioned, the DTC functions to promote
the stem cell fate/inhibit meiotic development through GLP- 1 Notch
signaling. Loss of GLP-1 signaling activity causes all previously estab-
lished stem cells to eventually undergo meiotic entry. GLP-1 activity
can be removed during the adult stage using a conditional reduction-
of-function allele of glp-1. When this mutant is reared at the restrictive
temperature, the phenotype is indistinguishable from the glp-1(null)
loss-of-function (Austin and Kimble,1987). Therefore, we can define
the GLP-1 gene as knocked out in the reasoning framework, simulating
loss of GLP-1 activity (starting at time step t=0) in the young adult
germ line (Supplementary File — Experiment Five). The simulations
show that in the absence of GLP-1 at step t=0, even though DTC
is constitutively active, none of the core Notch pathway genes within
the scope of the model are activated, while the meiotic entry pathways
(the GLD-1, GLD-2 and SCFPROM-1) promote meiotic entry (Fig. 5A).
Furthermore, the absence of GLP-1 has the same effect on the cell fate
decision in the case of degrading DTC signaling (not shown). The results
of the model simulations are consistent with experiments in the glp-
1mutant, where following loss of GLP-1 signaling activity all germ
cells that would normally divide mitotically in the presence of GLP-1
signaling, enter meiosis (Austin and Kimble,1987).
Next, we simulated constitutive activity of GLP-1 Notch signaling
by defining the glp-1 gene as constitutively active in the reasoning
framework (Supplementary File — Experiment Ten). It is known that
constitutive activity of GLP-1 prevents entry into meiosis (Austin and
Kimble,1987). In all the solutions, meiotic development is not attained
upon constitutive GLP-1 signaling, in line with investigations by Berry
et al. (1997), as indicated by the constant activation of the core Notch
pathway genes (Fig. 5B).
The effector genes lst-1 and sygl-1 function redundantly to pro-
mote the stem cell fate downstream of GLP-1 activity. Experiments
demonstrate that either an lst-1 or sygl-1 single deletion mutation does
not interfere with the germline stem cell fate, indicating that each
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A. Amar et al.
Fig. 4. The table of Boolean values of each gene of a specific network solution. Each column corresponds to a specific gene activity (sorted by order of activation, StemcellFate
appears adjacent to the DTC for convenience) throughout the simulation. Each row corresponds to the state of the genes at a different time step, with a green rectangle indicating
that a gene is active, and a red rectangle indicating that a gene is inactive. The DTC signal is modeled as constitutively active, promoting the stem cell fate.
is sufficient for maintaining stem cell fate (Kershner et al.,2014). In
our model simulations, knock-out of either gene alone (Supplementary
File — Experiment Eight and Nine) results in normal stem cell fate
retention (see LST-1 knock-out example in Fig. 6A) as compared to the
nonperturbed network (Fig. 4). In contrast, performing the lst-1 sygl-1
double mutant (Supplementary File — Experiment Six) in the presented
regulatory network model exhibited meiotic entry (Fig. 6B) similar to
the complete loss of GLP-1 Notch signaling (Fig. 5A) and in accordance
with the in vivo results (Kershner et al.,2014).
In the setup with constitutive activity of either LST-1 or SYGL-1
(Supplementary File — Experiment Eleven and Twelve), the model
exhibited failure to enter meiosis as the outcome of the simulations
(not shown). In vivo, overexpression of LST-1 or SYGL-1 proteins in the
presence of FBF-1 (a key partner of mRNA repression in stem cells)
generates an overproliferation phenotype and leads to germline tumor
formation (Shin et al.,2017).
The GLD-1 and GLD-2 pathways have been demonstrated to pro-
mote meiotic development together with the SCFPROM-1 pathway. As
shown in Kadyk and Kimble (1998), the germline phenotype of gld-
2(0) gld-1(0) double mutants is a meiotic entry defect. That is, the
mutant germ line is mitotic throughout, forming meiotic entry-defective
tumors. The knock-out simulation of gld-1 gld-2 combination (Supple-
mentary File — Experiment Seven) in the presented genetic regulatory
network model shows a failure to enter meiosis (Fig. 7).
In the setup with degrading DTC signaling, the results of in silico
perturbations described in this section were similar to that obtained
with the constitutively active DTC (not shown). In summary, in each
case, the simulations recapitulated the in vivo observations.
4.5. Testing the null hypothesis for a range of genetic perturbations
Our reasoning framework enables exploration of the new behavior
of the presented network and finding new patterns, if any, that have not
yet been experimentally observed. The solver can search for solutions
that satisfy the set of defined experimental constraints based on the
network topology even if they contradict experimentally observed be-
havior. This type of test is termed here the null hypothesis (the opposite
of the accepted hypothesis).
For example, we previously tested whether gld-1 gld-2 double knock-
out leads to failure to enter meiosis (Fig. 7). We also tested the null
hypothesis — that the same knockout condition might result in meiotic
entry. For this purpose, we use the same experimental constraint for
the initial state and an opposite constraint for the final state of the
simulation (see Supplementary File). The results of this simulation
clearly showed that for the GLD-1 GLD-2 double knock-out the null
hypothesis is satisfiable. Therefore, it was concluded that some models
predict that the GLD-1 GLD-2 double knock-out will lead to failure to
enter meiosis, while others predict that this knock-out might not lead to
failure to enter meiosis. In this particular case, the result that meiotic
entry occurs in the GLD-1 GLD-2 double KO is possible in the model
due to activity from the remaining SCFPROM-1 pathway and meiotic
chromosome axis and SC protein that continue to promote meiotic
entry in the absence of both GLD-1 and GLD-2 (Fig. 8).
Next, we tested the null hypothesis for all the previously mentioned
knockout and ‘‘overexpression’’ conditions (per Table 2). We found that
for all the existing models the null hypothesis is unsatisfiable, which is
consistent with in vivo studies.
5. Discussion
In this study, we present a new computational model represent-
ing the genetic regulatory network that controls the stem cell fate
versus meiotic development decision in the young adult C. elegans
hermaphrodite germ line. This model allowed us to describe how the
on/off states of gene activity (as gleaned from both genetic and bio-
chemical experiments reported in the experimental literature) and their
interactions lead to a cell fate choice (either an undifferentiated state
— ‘‘stem cell fate’’ or to enter into a differentiated state — ‘‘meiotic
development’’) and are consistent with experimental evidence.
5.1. The network model describes germline stem cell decision
We show that simulations of the current model reproduce the over-
all sequence of gene states over the course of decision-making steps.
As discussed below, the predictive power of our model was tested by
comparing the simulated order of the gene activation/repression with
previously published experimental data.
The process of developing this regulatory network highlighted pos-
sible gaps in our knowledge. For example, when we simulated a stem
cell in the proliferative zone responding to reduced level of the DTC
signal, only some of the simulations resulted in a meiotic development
decision, implying that some other component promotes specification
of the stem cell fate. This modeling result led to the identification of
the need to impose regulation of the CYE1/CDK2 complex in promoting
the proliferative fate; the activity of this complex was not initially
regulated in our model. Indeed, when we reduce CYE1/CDK2 activity,
together with a low DTC signaling activity, the network attains meiotic
development decision. We modeled this by introducing an external self-
degrading signal that controls CYE1/CDK2 activity from initiation of
the simulation.
This example illustrates how the combination of experimental
knowledge and computational model can give important clues about
the role of CYE1/CDK2 in proliferative fate specification or can reveal
missing regulatory interactions that control its expression. Although
CYE1 and CDK2 are known as regulators of G1/S cell cycle phases, their
expression in stem cells is phase-independent (Fox et al.,2011;White
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A. Amar et al.
Fig. 5. In silico genetic perturbations. KO and constitutive activity of GLP-1. Black rectangles correspond to certain components involved in a particular experiment. (A) If GLP-1
Notch signaling is knocked out, even though DTC is constitutively active, none of the core Notch pathway genes are activated. (B) Upon GLP-1 Notch constitutive signaling, the
core Notch pathway genes are active throughout the simulation.
and Dalton,2005), and CDK2 levels are controlled transcriptionally
by glycogen synthase kinase GSK-3 through inhibition of transcription
factor DPL-1 (Furuta et al.,2018).
We further simulated a range of genetic perturbations (KO and
FE) and compared the results with known abnormal phenotypes from
several experimental studies. The order of gene activity matches ex-
pectations of intermediate gene profiles and ends in cell fate choice
of observed phenotypes (Austin and Kimble,1987;Berry et al.,1997;
Kadyk and Kimble,1998;Kershner et al.,2014;Shin et al.,2017).
For example, constitutive activity of GLP-1 signaling activity leads to
failure to enter meiosis. This simulation result is consistent with the
DTC ablation in glp-1(oz112) animals, where germ cells never leave the
mitotic cell cycle (Berry et al.,1997).
5.2. Formulating model predictions
To determine whether a genetic perturbation can result in a bio-
logical behavior that has yet to be experimentally observed, we tested
the null hypothesis for each case. This analysis investigated whether
some, all or none of the models contradict expected behavior and what
is a mechanism through which this behavior is achieved. The results
of these simulations show that for all the existing models, except the
GLD-1 GLD-2 double KO model, the null hypothesis is unsatisfiable. This
means that all these models predict the behavior, which is consistent
with in vivo studies. The GLD-1 GLD-2 KO hypothesis states that gld-1
gld-2 combination knock-out leads to failure to enter meiosis (Kadyk
and Kimble,1998). For the GLD-1 GLD-2 KO model, we found that
both the KO and the null hypothesis are satisfiable independently. Do
germ cells enter meiotic prophase normally despite the knock-out of
two out of three meiotic entry pathways? This scenario was ruled
out by several experimental studies (Hansen et al.,2004a;Kadyk and
Kimble,1998;Mohammad et al.,2018). Moreover, several studies
suggest that the relative strength of each pathway is different (Hansen
et al.,2004a,b;Mohammad et al.,2018;Wang et al.,2002). In our com-
putational model, the outcome of this simulation is possible because
the solver gives equal weight to each of these components (GLD-1,
GLD-2, SCFPROM-1 and meiotic chromosome axis and SC protein). This
simulation is an example of how the capability of the solver to make
predictions of multiple biological behaviors is limited by the absence
of quantitative information, which is essential for understanding of
many genetic regulatory mechanisms on the molecular level. On the
other hand, a contradictory result can alert investigators to areas where
quantitative information will be most valuable.
5.3. Suitability of the network model to simulate various biological phenom-
ena
Our network model demonstrates various important phenomena
that take place in biological systems: (1) gene redundancy, (2) bound
and unbound motifs, (3) dynamic behavior of extracellular/intracellular
input signals, and (4) various regulatory mechanisms for individual
network components. In vivo, the robustness of cell fate choice in the
C. elegans germ line is partially attributed to the redundancy of gene
activities. The effect of inactivating one gene can often be hidden by
sufficient activity of its redundant partners. Examples of apparently
redundant gene activities in our model include hop-1 and sel-12,lst-1 and
sygl-1, and nos-3 vs gld-2 and gld-3 (when acting as activators of GLD-1
accumulation). In these cases, in the current model we assume that the
redundant genes are equally effective, and that each is sufficient for
the normal pattern of germline development. For example, we tested
whether either lst-1 or sygl-1 knock-out can affect germline stem cell
fate based on experimental observations of Kershner et al. (2014).
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A. Amar et al.
Fig. 6. Knock out of LST-1 and LST-1 SYGL-1 double knockout. (A) When setting LST-1 as knocked out, the network remains unperturbed. (B) Simulation of lst-1 sygl-1 double
knockout combination. As a result, the network demonstrates abolished self-renewal (‘‘stem cell fate’’).
Fig. 7. Knock out of both GLD1 and GLD2. GLD1 GLD2 double knockout combination in the presented network exhibits failure to enter meiosis.
We showed that both lst-1 or sygl-1 knock-out simulations exhibited
profiles of gene activity comparable to non-perturbed signaling, which
suggests that gene redundancy can be accurately reproduced with the
presented network model. Moreover, using the reasoning framework
it is possible to specify more than two redundant genes per function.
Future extensions of this tool will be to permit simulations of more
expressive functional effects between redundant genes.
Protein–protein interactions correspond to binding and dissociation
mechanisms, which depends on the number of binding sites, the bind-
ing affinity, the structural and functional properties of protein–protein
complex, etc. The same protein can have multiple functions in the
same biological system depending on its binding partners. Our model
simulates this complex behavior using a two-state model. An example
is FBF-1. By including bound and unbound states of FBF-1 (FBF-1B and
FBF-1U) as distinct components of the network, we could describe a
partner-switching behavior (from interacting with LST-1 and SYGL-1 in
repression of the meiotic entry pathways to promotion of GLD-2/GLD-3
activities, resulting in activation of meiotic entry). A similar approach
using the reasoning framework could be applied to study more complex
pathways by considering several possible states of protein, transitions
between them and temporal information regarding these transitions.
Using the reasoning framework, we study three possible states of
the single cell: within the range of the DTC signal, out of range of
the DTC signal or losing the DTC signal. These model state setups
differ in the strength (duration of activation) of signaling from the DTC
(by employing a constant external signal S0, without it or with three
external signals S1, S2, S3). The use of ‘‘external signals’’ allows us
to reproduce the profiles of gene activity similar to in vivo responses
BioSystems 217 (2022) 104672
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A. Amar et al.
Fig. 8. Null hypothesis for knock out of both GLD1 and GLD2. The Gld1 Gld2 double knockout might not lead to failure to enter meiosis due to SCFPROM-1 pathway and meiotic
chromosome axis and SC protein that continue to promote meiotic entry.
of Notch signaling. Depending on the specific research question or
hypothesis, we can use the reasoning framework to model input sig-
nals with various dynamic behavior. For example, when simulating
sustained expression of a gene, the input signal should be specified as
sustained (active) throughout the experiment. Another example is loss
of signaling activity, which can be modeled with a self-degrading signal
(that is specified to become active for a single time step). An additional
possible case is when genes show an oscillating expression pattern due
to alternating protein levels or crosstalk with other pathways.
Changes of external or internal cell conditions often induce associ-
ated changes in the expression of underlying genes. Since our model is
represented as a Boolean network, the state of each component (either
on or off) is calculated from the state of adjacent components. The
synchronous updates are used in order to avoid scenarios in which
not all genes are updated throughout the experiment or certain genes
are repeatedly updated, but not others. Investigating an asynchronous
update scheme for this model is a topic for future work with more
constrained and complex networks.
The reasoning framework uses a set of regulation rules where none,
some or all component regulators (activators/repressors) are present,
considering two regulators of each type. For modeling gene redun-
dancy, the downstream components can use conditions where only one
of two regulators (activators or repressors) is present. The result from
applying these regulation conditions in our model is a reliable and
robust demonstration of a biological function of components in the
genetic network, using few activators and/or repressors as happens in
vivo.
5.4. Future extensions
We used a Boolean representation which supports efficient reason-
ing over a large set of possible networks and is a well-established ap-
proach in computational modeling. However, in the Boolean formalism
quantitative gene regulation information (i.e., the rate of production
of a component or gene expression levels) is neglected and partial
knockouts are not supported. Future research can build upon the results
presented here to construct quantitative models and thus expand the
phenomena that can be studied.
In addition to the possible extensions of the reasoning framework
mentioned above, our network model could be extended and refined
in different ways. For example, currently the model describes the
dynamics of the network that controls cell fate decisions at a single
cell level. The next step towards further development of the model is to
extend it to a population of cells. The combination of a detailed descrip-
tion of the interactions within the cell, the interplay between cells in
population and their communication with the DTC niche could provide
new insights into the regulation of stem cell systems. Furthermore, a
detailed in silico implementation of a single cell provides the possibility
to capture more realistic whole tissue simulations. This will open up
the possibility to computationally test the relative contribution of in-
teractions within the cell that are usually overlooked in experimentally
measured phenotypes of the entire germ line.
Finally, the extended model could be used to explore motif-based
design patterns and their role in controlling cellular behaviors. Simple
regulatory motifs have been identified as the basic building blocks of
many biological networks (Milo et al.,2002) where their structure may
determine a broad range of functions (e.g., sign-sensitive delay, pulse
generation). By employing formal methods for identification of these
motifs and their effect on the cellular functions, one can ensure that a
comprehensive analysis was done for the network of interest (Kugler
et al.,2018).
CRediT authorship contribution statement
Ani Amar: Conceptualization of this study, model coding and
development, analysis and interpretation of data, and preparing the
manuscript. E. Jane Albert Hubbard: Conceptualization of this study,
analysis and interpretation of data, and preparing the manuscript.
Hillel Kugler: Conceptualization of this study, model development,
analysis and interpretation of data, and preparing the manuscript.
Declaration of competing interest
The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared to
influence the work reported in this paper.
Data availability
Supplementary Files related to this article can be found at https:
//github.com/kuglerh/Germline. The Reasoning Engine framework is
available on GitHub (https://github.com/fsprojects/ReasoningEngine).
Acknowledgments
This work was supported by the Horizon 2020 research and innova-
tion programme for the Bio4Comp project under grant agreement No.
732482 and by the ISRAEL SCIENCE FOUNDATION (grant No. 190/19)
to HK.
Appendix A. Supplementary data
Supplementary material related to this article can be found online
at https://doi.org/10.1016/j.biosystems.2022.104672.
BioSystems 217 (2022) 104672
11
A. Amar et al.
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