Relating the chondrocyte gene network to growth plate morphology: from genes to phenotype.

Abstract

During endochondral ossification, chondrocyte growth and differentiation is controlled by many local signalling pathways. Due to crosstalks and feedback mechanisms, these interwoven pathways display a network like structure. In this study, a large-scale literature based logical model of the growth plate network was developed. The network is able to capture the different states (resting, proliferating and hypertrophic) that chondrocytes go through as they progress within the growth plate. In a first corroboration step, the effect of mutations in various signalling pathways of the growth plate network was investigated.

Full text

Page 1

Relating the Chondrocyte Gene Network to Growth Plate
Morphology: From Genes to Phenotype
Johan Kerkhofs1,2,3, Scott J. Roberts3,4, Frank P. Luyten3,4, Hans Van Oosterwyck2,3, Liesbet Geris1,3*
1Biomechanics Research Unit, University of Lie `ge, Lie `ge, Belgium, 2Biomechanics section, K.U. Leuven, Leuven, Belgium, 3Prometheus, The Leuven R&D division of
skeletal tissue engineering, K.U. Leuven, Leuven, Belgium, 4Rheumatology Department, K.U. Leuven, Leuven, Belgium
Abstract
During endochondral ossification, chondrocyte growth and differentiation is controlled by many local signalling pathways.
Due to crosstalks and feedback mechanisms, these interwoven pathways display a network like structure. In this study, a
large-scale literature based logical model of the growth plate network was developed. The network is able to capture the
different states (resting, proliferating and hypertrophic) that chondrocytes go through as they progress within the growth
plate. In a first corroboration step, the effect of mutations in various signalling pathways of the growth plate network was
investigated.
Citation: Kerkhofs J, Roberts SJ, Luyten FP, Van Oosterwyck H, Geris L (2012) Relating the Chondrocyte Gene Network to Growth Plate Morphology: From Genes
to Phenotype. PLoS ONE 7(4): e34729. doi:10.1371/journal.pone.0034729
Editor: Zhongjun Zhou, The University of Hong Kong, Hong Kong
Received October 5, 2011; Accepted March 8, 2012; Published April 30, 2012
Copyright: ? 2012 Kerkhofs 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.
Funding: This work was supported by the Special Research Fund of the University of Lie `ge (FRS.D-10/20). 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.
* E-mail: liesbet.geris@ulg.ac.be.
Introduction
Recent advances have elucidated the regulatory mechanisms of
endochondral ossification, where bone is formed through a
transient cartilage anlage. During this process cells exhibit distinct
and easily observable differentiation stages, as is readily evidenced
by the morphology of the growth plate [1].
The growth plate is a developmental centre that integrates
many signalling pathways in order to regulate the patterning and
growth of long bones. As the cells progress throughout the growth
plate, going from the long bone’s epiphysis towards the diaphysis,
their shape and function change drastically [2]. At the epiphysis, a
pool of small round chondrocytes makes up the resting zone.
These cells differentiate into more rapidly proliferating flat
chondrocytes, forming proliferative columns. The resting and
proliferating chondrocytes secrete structural proteins, such as
collagen type II, that form a hyaline cartilage matrix. Towards the
diaphysis, chondrocytes differentiate further into prehypertrophic
and thereafter hypertrophic chondrocytes [3]. Hypertrophic
chondrocytes remodel the cartilage matrix into a calcifying matrix
comprising primarily collagen type X. At terminal differentiation,
the hypertrophic cells will induce invasion and resorption of the
mineralized cartilage matrix as well as the start of vascularisation
by secreting a specific set of proteins like MMP13 and VEGF [4].
The growth plate chondrocytes must respond to positional cues,
local agents and hormonal signals to coordinate the formation of
unique skeletal elements [5]. Important local signalling pathways
regulating the endochondral development of bones are the
parathyroid hormone related peptide (PTHrP), Indian hedgehog
(Ihh) [6], bone morphogenic proteins (BMPs) [7], transforming
growth factors b (TGFbs) [8], Wnts [9] and Fibroblast growth
factors (FGFs) [10]. These pathways exert their influence on the
growth plate, at least in part, by regulation of the key transcription
factors Sox9 [11] and Runx2 [12]. The former is crucial for
chondrogenesis, whereas the latter is a central regulator in
chondrocyte hypertrophy.
Ihh and PTHrP form a feedback loop that regulates the length
of the proliferative column. Prehypertrophic chondrocytes exiting
the proliferative pool express Ihh. Through unknown means this
Ihh signals to periarticular chondrocytes to produce PTHrP. This
PTHrP will suppress chondrocyte hypertrophy by binding its
receptor PPR (Parathyroid hormone/PTHrP Receptor) and
prevent Ihh expression until the proliferative chondrocytes leave
the PTHrP signalling range [13].
Several methods to model gene networks are widely used,
ranging from more mechanistic models to entirely empirical
methods. The former include detailed thermodynamic approaches
capable of dealing with limited molecule numbers or the mean-
field approximation of ordinary differential equations based on the
law of mass action or other principles (reviewed in [14]). The latter
include methods such as network inference by correlation,
regression and Bayesian techniques [15]. Given the complexity
and high interdependency of the signalling pathways in endo-
chondral ossification, we set out to take a logical (multi-value
Boolean) approach to model the developmental process. A logical
model is highly practical to structure and research this intricate
system of control mechanisms. This approach has the added
advantage that no exact knowledge of the concentrations and
reaction rates of the factors used by the relevant signalling cascades
is needed, since these data are not readily available in the
literature. For modelling the growth plate, the logical formalism
hence represents a good compromise between the highly detailed
dynamics of mechanistic models and the black box approach of
data-driven phenomenological models [16]. As this work focuses
on the growth plate as an autoregulatory semiautonomous
module, the model includes only autocrine and paracrine
PLoS ONE | www.plosone.org1April 2012 | Volume 7 | Issue 4 | e34729

Page 2

signalling pathways. The purpose of this model is to examine the
individual and combined influence of relevant growth factors and
their subsequent signalling cascades on chondrocyte differentiation
in the growth plate.
Materials and Methods
The network consists of a directed graph where biological
factors and their interactions are represented by nodes and arcs
respectively [17]. Each arc is characterized by a sign, as seen by a
different color and shape in Figure 1. The sign of these arcs
determines an activating (positive) or an inhibitory (negative)
effect. Every arc is furthermore associated with a certain activity
range. This range indicates at which levels of the activating node
the interaction is active. To simulate the dynamics of the model,
every node is associated with a logical function that will set its
value based upon the active interactions. This function associates a
value (called parameter in Chaouiya et al. [18]) with every possible
set of active interactions, hence determining the next value of the
node. A logical function is fully specified by a truth table, an
example of which can be found in Table 1. The left column
specifies which inputs are active, and the right column attributes a
value accordingly. Table 1 contains the truth table of the logical
function specifying regulation of collagen type X (Col-X), as
graphically presented in Figure 1. R-smad, Runx2 and MEF2C
have been shown to stimulate Col-X transcription [19]. PKA on
the other hand inhibits Col-X transcription [20]. The Runx2 and
Col-X nodes can have a level up to two, while the other nodes
have a maximum of one. This use of multi-value logic allows the
model to more accurately capture gradients in the growth plate. In
addition, multi-value logic allows the effects of interactions that
only partly disable (or activate) a node to be included.
Wherever possible the logical function was deduced from
literature. However, deduction of appropriate values is problem-
atic due to the lack of sufficient literature information, especially in
cases where multiple interactions are simultaneously active. In
these circumstances the strength of the different interactions is
taken to be identical, since no data exists on the relative strengths
of gene interactions. Hence the state of a node is determined
somewhat semiquantitatively, and will be active when there are
more stimulatory interactions and inactive in the case of a majority
of inhibitory interactions. This is a weighted sum approach, which
has been applied in systems of ODEs [21], feature extraction [22]
and Boolean networks [23]. In the Boolean formalism, functions of
this type have been termed ‘additive functions’ or ‘majority
functions’ and have been shown to be biologically relevant [22–
24]. In the example of Col-X regulation only when the stimulatory
interactions are all active and the inhibitory interaction is not, the
maximum value is attributed to the Col-X node. If one of the
stimulatory interactions is absent or the inhibitory interaction is
active the node is given a value of one. In all other situations the
node is considered inactive.
Nonetheless information on the nature of the interaction was
frequently available, allowing the values of the logical function to
be further refined. For example, one gene (or rather its protein
product) might activate another through phosphorylation, while
others might increase that genes’ activity through transcriptional
mechanisms. Clearly posttranslational modifications like phos-
phorylation and ubiquitination will only matter if the gene is
transcribed in the first place. In this logic the activity of a gene will
be penalized when it is not activated through phosphorylation or
when it is not effectively transcribed (e.g. a majority of inhibitory
transcription factors is present).
The state of the network is determined by an n-tuple containing
the values of all nodes. The dynamics of the model is simulated
with a dynamical graph. In this graph, nodes represent the state
and the arcs represent spontaneous transitions between the states.
The dynamics of the graph can be either synchronous or
asynchronous. In synchronous dynamics all nodes are updated
at the same time. This means that every interaction is assumed to
have an equal duration, which of course is not realistic in
biological systems. In asynchronous dynamics multiple updating
orders do not occur simultaneously and a criterion is needed to
determine priority. Hence, each interaction is associated with a
certain time delay. When no information on the time delay is
provided, as within this study, all possible transitions are
generated. As a consequence, each state has a number of
successors equal to the number of nodes to be updated at this
state. An example is given in figure 2. Ultimately the gene
regulatory network will reach a steady state which has no successor
distinct from itself. These states are called singleton attractors.
Alternatively, the network can oscillate in a dynamic cycle termed
cyclic attractor, typical for phenomena like circadian rhythms
[25].
Synchronous updating can give rise to modelling artefacts by
creating spurious cyclic attractors [26,27]. By contrast, singleton
attractors are stable regardless of the (discrete) updating mecha-
nism. Given the lack of kinetic information, we use synchronous
updating assumptions. However, as seen in figure 2, an initial state
may flow to a different stable state depending on the updating
mechanism. For this reason, we choose to also investigate the
entire transition graph under asynchronous updating. Further-
more, we only consider singleton attractors to avoid the previously
mentioned modelling artefacts.
Figure 1. Regulation of Col-X. Col-X is regulated by several factors,
each symbolized by a node (yellow square). Arcs represent interactions
of two kinds: an activating interaction is represented by a blue arrow,
whereas an inhibitory one is given by a red line with a dot.
doi:10.1371/journal.pone.0034729.g001
Table 1. Logical function describing the value of node Col-X.
Active interactions Output of logical function
Runx2(2), MEF2C(1)1
Runx2(2), R-smad(1)1
Runx2(2), R-smad(1), PKA(1)0
Runx2(1), MEF2C(1), R-smad(1)1
Runx2(2), MEF2C(1), R-smad(1)2
Runx2(2), MEF2C(1), R-smad(1),
PKA(1)
1
The Runx2(2) interaction is active when Runx2 has a value of 2, while the
Runx2(1) interaction indicates a Runx2 value of 1. The interaction combinations
not shown in the table have a value of zero.
doi:10.1371/journal.pone.0034729.t001
Logical Model of Chondrogenesis in a Growth Plate
PLoS ONE | www.plosone.org2 April 2012 | Volume 7 | Issue 4 | e34729

Page 3

The described approach permits the use of multi-value logic.
This allows modelling several distinct active states so that the levels
can represent different biological effects. All growth factors (with
the exception of TGFb), their receptors and crucial transcription
factors (Runx2, Sox9, b-catenin, Nkx3.2, Smadcomplex) as well as
the output genes Col-X and Col-II were implemented with multi-
value logic. Further details on this logical formalism can be found
in Chaouiya et al. [18]. The formalism is implemented in GINsim
2.3, a java application designed to model and simulate genetic
regulatory networks [28] and the model files are provided as
Material S2.
The knockout of a certain gene is represented by deactivation or
removal of the protein, which is achieved by setting the value of its
node to zero. Constitutive expression of a gene can be represented
by setting the value of the associated node to the highest activation
level (on-state).
Spatial migration through the growth plate cannot be captured
by logical networks but was modelled in this study by altering the
expression level of external ligands (PTHrP, TGFb & some FGFs)
that are expressed locally in the perichondrium surrounding the
growth plate. The presence or absence of these ligands hence
serves as an input. These values are not determined by the
network but influence its outcome.
The logical network presented here is based on an extensive
literature study. The data are mostly taken from studies of the fetal
growth plate in mice and chick models. As the network is cell type-
specific only interactions shown to occur in growth plate
chondrocytes were included, unless no such information was
available, in which case data were taken from related cell types
such as osteoblasts. The network incorporates the effects of the
major paracrine signalling pathways on Sox9/Runx2 activity.
These transcription factors are crucial for early chondrogenesis
and subsequent hypertrophy. Hence we hope to capture the effects
of certain growth factors on these processes by modelling the
factor’s influence on their most crucial mediators. The model
consists of 35 nodes and 111 interactions. For details on the
included signalling pathways and their crosstalks the reader is
referred to the given references and references therein. A list of
interactions and the references from which they were derived is
provided (Material S1).
To assure robustness of our results we also created an ODE
version of our model, an approach similar to that of Mendoza
et al. [29], that allowed us to numerically check whether the
logical stable states where stable if the logical assumptions were
relaxed. Practically, we replaced the logical step functions with
progressively gentler sigmoids (see Material S3 for model
equations and further details). This analysis confirmed the
robustness of our results for the stable states of the wild type
growth plate (see Material S3). Though analytical approaches exist
[30], given the high number of nodes and thresholds in our model,
their application would be cumbersome.
Results
Prediction of Growth Plate Dynamics
The growth plate network is given in Fig. 3. It describes the
influence of important paracrine or autocrine growth factors (blue
nodes) on cell differentiation as represented by the activation of
crucial transcription factors (green nodes). The result of a
synchronous simulation with conditions that match those seen in
the growth plate in vivo is depicted in Figure 4. The stable states
generated by the network results are shown in Table 2. The spatial
configuration of key transcription and growth factors in the growth
plate is shown in Figure 5.
Figure 2. Synchronous versus asynchronous updating strategy.
This example clarifies how the use of different updating strategies can
change the dynamics of the system. Grey and white color indicate the
node has a value of 1 and 0, respectively. Each node is regulated by its
own value and that of the other. Node 1 is governed by an AND gate,
i.e. it is 1 only when both inputs are 1. Node 2 is regulated by an OR
gate, it is 1 when either of its inputs is 1. Under asynchronous updating,
the system will reach a different stable state depending on which node
is updated first. When both nodes are updated synchronously yet
another stable state, unattainable by asynchronous updating, is
reached.
doi:10.1371/journal.pone.0034729.g002
Logical Model of Chondrogenesis in a Growth Plate
PLoS ONE | www.plosone.org3 April 2012 | Volume 7 | Issue 4 | e34729

Page 4

In the network, the prehypertrophic zone does not normally
form a stable state. In early hypertrophy, Wnt and FGF have a
synergistic effect and upregulate each other’s ligands. This leads to
further upregulation of Runx2 and fastens hypertrophy. When
BMP signalling is sufficiently hampered by FGF activity, the
expression of Ihh, typical for the prehypertrophic zone, will be
lowered. Hence every chondrocyte undergoing hypertrophy will
highly express Ihh for a limited amount of time, between the onset
of Runx2 expression and the decrease in canonical BMP
signalling. However, the discrete time step of the logical model
does not directly correspond a real time step. For this reason, we
cannot estimate how long this expression would persist nor how
dependent this state is on the actual speed of interactions. In order
to correctly model expression in the resting zone, the induction of
PTHrP by Ihh was assumed to be indirect (see discussion for more
detail).
Simulation of Mutant Cases
The network can be validated by and used to investigate certain
knockouts or activating mutations of key players of growth plate
dynamics. We have carried out simulations of mutants in each of
the 5 major pathways included: the Ihh/PTHrP feedback loop,
FGF, BMP, Wnt and TGFb signalling. In the case of the Ihh/
PTHrP feedback loop, the outcome of a disabled and constitu-
tively active PTHrP pathway is examined. In the PTHrP null
network, the situation within the resting zone is the same as in wild
type mice except for a lack of PTHrP production. The relevant
stable states are shown in Table 3. Since PPR is not expressed in
this zone the network behaviour is unchanged. When in the
proliferating zone external Ihh induces BMP expression, the
network will enter a hypertrophic state as a consequence of absent
PTHrP signalling. The network hence predicts that chondrocytes
will undergo hypertrophy faster, as the stable state characterizing a
proliferative chondrocyte is skipped. By calculating the transition
ERK1/2
extlhh
extlhh
Lef/Tcf
MEF2C
Col-ll
Runx2
HDAC4
Col-X
Col-XSTAT1
PTHrPNkx3.2
Sox9
CCND1
lhh
lhh
Dsh
Wnt3a
Rsmad
Smad
complex
Smad7
Smad3
BMPR
Gli2
Gli2
BMP
STAT1
FGFR3
FGFR1
FGF
extFGF
extPTHrP
PPR
PKA
MMP13
TGFβ
NFKβ
Smad3/Lef
Smad/Dlx5
β-catenin
Major hub gene
Growth factor
Gene product
Boundary condition
Other
Inhibition
Activation
Continuous source
Figure 3. The growth plate chondrocyte gene regulatory network. Every node in the gene network is represented as a square, the
interactions are represented by arrows between squares. The network as shown here was coarse grained, i.e. nodes not influenced by multiple
reactions were omitted. Therefore linear signalling cascades are not represented here.
doi:10.1371/journal.pone.0034729.g003
Logical Model of Chondrogenesis in a Growth Plate
PLoS ONE | www.plosone.org4 April 2012 | Volume 7 | Issue 4 | e34729

Page 5

graph it becomes clear that under asynchronous updating these
stimuli can induce either a Sox9 positive state or the aforemen-
tioned state of hypertrophy. Which state will be reached in vivo is
determined by the unknown pace of the interactions represented
by the network arcs. More specifically, in the real biological
network every interaction has a certain rate, which can be related
to how fast a reaction should be updated. The state that is
achieved by first updating nodes that are under control of faster
interactions, such as phosphorylation, is more likely to be
biologically relevant.
In the model with a constitutively activated PPR expression
(identical to ectopic expression of PTHrP) the situation in the
Figure 4. Representation of growth plate dynamics. The expression values of each node as the network progresses from one stable state
(framed columns) to the next by changing the inputs (indicated by a red circle). White, grey and black respectively indicate values of 0, 1 and 2. The
resting (green), proliferating (dark green) and hypertrophic (red) stable states are indicated. As noted, the prehypertrophic state (yellow rectangles) is
not stable but is a transient state between the proliferating and hypertrophic states. It is characterised by simultaneous expression of Runx2 and Sox9
and increased Ihh expression.
doi:10.1371/journal.pone.0034729.g004
Table 2. Stable states of the wild type network.
Growth factorsTranscription factors
Zone BMPWntTGFb
FGFIhhPTHrPSox9Runx2Gli2
Resting zone01110 2(+ext)100
Proliferative zone1111 1(ext)1(ext)201
Prehypertrophic zone1111 2(+ext)
1(+ext)
0110
Hypertrophic zone2101 (+ext)0021
The values of nodes representing growth factors and transcription factors are tabled for every zone in the growth plate. As the Ihh/PTHrP feedback loop involves
diffusion of ligands from the prehypertrophic zone into the resting zone and vice versa, the nodes in the network indicate the presence of diffused Ihh and PTHrP
respectively. Furthermore, FGF18 diffuses from the perichondrium to bind FGFR3 in proliferating chondrocytes [9]. The presence of paracrine signalling is indicated in
the table (ext or +ext if auto- and paracrine signalling are mixed).
doi:10.1371/journal.pone.0034729.t002
Logical Model of Chondrogenesis in a Growth Plate
PLoS ONE | www.plosone.org5April 2012 | Volume 7 | Issue 4 | e34729

Page 6

resting zone is unchanged as PPR is not expressed here (Table 3).
The proliferative stable state is unaffected as well, however this is
under the assumption that Ihh is present. With constitutively
activated PPR the chondrocytes cannot leave the proliferative
pool, even when TGFb signalling, also inhibiting hypertrophy, is
assumed to be absent. However, an alternative stable state with
moderate Runx2 activity is possible if PTHrP expression is not
maximal. This can be observed experimentally in mice expressing
PTHrP under the control of a Col-II promoter (Table 3). In these
mice PTHrP expression mirrors Col-II which is expressed to a
lesser extent in some areas, notably on the fringes of the long bone
[31].
For the FGF pathway, we simulated an overactivation of the
fibroblast growth factor receptor 3 (FGFR3) (Table 4). Achondro-
plasia can be simulated by forcing the FGFR3 node to be
maximally activated. The FGFR3ACHmutant does not change
chondrocyte behaviour in the resting zone, the increased FGF
signalling has little effect here as there is no BMP and wild type
chondrocytes do not proliferate in this zone. The more activated
ERK pathway might stimulate Runx2 activity, but the activation
of the ERK node is insufficient to change Runx2 expression. In the
proliferating zone BMP ligands allow for more active Sox9.
However, due to dominant FGF signalling Sox9 is less activated in
the FGFR3ACHproliferating chondrocytes. Furthermore, the
CCND1 gene, which is associated with an increased proliferation
rate [32], is not expressed (not shown). When perichondrial TGFb
signalling diminishes, the chondrocytes will undergo hypertrophy.
The way this hypertrophy is achieved is different than in the case
of the normal network, where MEF2C, a transcription factor
regulating hypertrophy [33], will be expressed before Runx2. In
Figure 5. Predicted versus observed expression patterns in the growth plate. The literature derived (light) and predicted (black) expression
patterns in 4 growth plate zones. BMP ligands become more abundant as chondrocytes mature [66] as is also the case in the modelled gene network.
The expression pattern of Wnt4a [46] is shown here to represent the canonical Wnts, this pattern also closely resembles that of active b-catenin which
is the canonical Wnt signal transducer [67]. TGFb is expressed throughout the growth plate, except in the hypertrophic zone [8]. FGFs are excreted in
increasing amounts in more mature cells under influence of Runx2 [68,69] PTHrP and Ihh are expressed by resting zone and prehypertrophic
chondrocytes respectively [5]. Runx2 expression increases as chondrocytes hypertrophy [70], while Sox9 activity reaches its peak in proliferative
chondrocytes [71–73]. Gli2 is also continuously expressed in the growth plate, but its expression tapers off in hypertrophic cartilage [74].
doi:10.1371/journal.pone.0034729.g005
Table 3. Stable states of the PTHrP mutant networks.
Growth factorsTranscription factors
PTHrP-BMPWntTGFb
FGFIhhPTHrPSox9Runx2Gli2
Resting zone01(ext)1(ext)100100
Hypertrophy
(synchronous)
211110021
Sox9 positive
(asynchronous)
111110101
PTHrP+ + (PPR+ +)BMPWntTGFb
FGFIhhPTHrPSox9Runx2Gli2
Resting zone011002100
Proliferative11101(ext)2201
11021(ext)2201
Hypertrophy110111011
The values of nodes representing growth factors and transcription factors are tabled for the relevant stable states in the mutant growth plate. The presence of paracrine
signalling is indicated in the table (ext). For the PTHrP null network, the resting zone situation is unchanged, save for PTHrP secretion. However, a stable proliferative
state is nonexistent and a state of hypertrophy is reached instead. By calculating the state transition graph a Sox9 positive state can be detected. In a network with
constitutively active PPR (PTHrP+/PPR+), the resting zone is identical to the wild type situation. The proliferative zone is also unaffected. However, no hypertrophy is
reached as the PTHrP pathway remains active and hence blocks chondrocyte differentiation. Hypertrophy might be reached if PTHrP signalling is diminished.
doi:10.1371/journal.pone.0034729.t003
Logical Model of Chondrogenesis in a Growth Plate
PLoS ONE | www.plosone.org6April 2012 | Volume 7 | Issue 4 | e34729

Page 7

the mutant network this sequence is reversed. Additionally, due to
the absence of the Smad complex, a lower amount of Ihh secretion
is predicted. The stable states of the FGFR3 mutant are shown in
Table 4.
The BMP pathway is tested by simulation of a Receptor-
regulated Smad (R-Smad), the canonical effectors of BMP
signalling [7], knockout. The resting zone is unaffected, as BMP
ligands are not present there (Table 4). However, the situation of
proliferating zone chondrocytes will not differ much from those of
the resting zone. PPR is not activated in the mutant network,
which results in a reduced proliferation rate and a lowered Sox9
expression. This state is similar to the resting zone state. If
perichondrial signalling alters to promote hypertrophy, i.e. no
expression of TGFb and increased FGF expression, the cells will
not enter a hypertrophic phase but they will lose Sox9 expression.
By calculating the transition graph, it is observed that two possible
stable states can be attained. One state is the same as the one
reached by synchronous updating, the other is a state of
hypertrophy with production of Ihh. The results for the Smad
mutant are listed in Table 4.
Discussion
The network constructed in our study qualitatively captures the
behaviour of growth plate chondrocytes in response to the
modelled signalling pathways. The network is able to capture
the different stable states (resting, proliferating and hypertrophic)
that the chondrocytes transcend as they progress through the
growth plate [3,4]. The prehypertrophic state was predicted to be
an unstable state at the transition between proliferation and
hypertrophy.
It is unknown whether Ihh regulates PTHrP expression in the
periarticular chondrocytes in a direct or indirect fashion. In the
model presented in this paper, the induction of perichondrial
PTHrP by Ihh was assumed to be indirect since the network
perspective of the growth plate presented in this paper speaks
against direct control of PTHrP by Ihh. Firstly, Ihh target gene
Ptch1 expression is strongest in the domain adjacent to the Ihh
domain, fading away towards the articular surface [6,34]. This
shows that the concentration of Ihh in the periarticular region will
be minimal, if any. Secondly, Ihh has been shown to induce BMP
in chondrocytes, while BMP is not expressed in the resting zone
[35,36]. Hence the assumption of secondary signals prevents the
prediction of non-physiological BMP expression in periarticular
chondrocytes and consequently a lower Sox9 activity in the resting
zone. The absence of BMP molecules in the resting zone can
alternatively be explained by assuming that Ihh-dependent BMP
production only takes place once a certain threshold concentration
of Ihh is reached. This would mean that Ihh can stimulate PTHrP
production at much lower concentrations then required for BMP
expression. However, no such dependency has been reported.
Therefore we have assumed Ihh signals to the resting zone by a
secondary factor, more specifically by ligands excreted in the
proliferating zone perichondrium. Signals from perichondrial cells
themselves might be responsible rather than diffused Ihh ligands
since Ptch1 expression can be detected in these cells, indicating
that Ihh indeed exerts an influence upon perichondrial cells [37].
Perichondrial cells excrete TGFb and Wnt ligands which could in
turn diffuse to periarticular chondrocytes to induce PTHrP ligand
secretion [38,39]. TGFb signalling (in the perichondrium) may
mediate the Ihh/PTHrP feedback loop by acting upstream of
PTHrP but downstream of Ihh [39]. Decapentaplegic (Dpp,
analogue of TGFb) mediates Hh signalling in Drosophila although
TGFb is certainly not a universal target of the pathway [40] but
microarray data indicates Gli can upregulate TGFb in chondro-
cytes [35]. All TGFbs stimulate PTHrP expression in chondro-
cytes, presumably through Smad-dependent mechanisms. These
data indicate that TGFb is a plausible messenger downstream of
Ihh. Of note, only less differentiated cells can express PTHrP [41].
However, the ensemble of factors responsible for this difference
requires clarification.
PTHrP expression might additionally be regulated by BMP
since in osteoblasts BMPs can inhibit PTHrP expression.
Accordingly BMPs may play a similar role in proliferating
chondrocytes [42]. Interestingly, in Ptch1-/-mouse where Hh
signalling activity is always at maximum the PTHrP expression
pattern does not change, indicating some other factor, indepen-
dent of Ihh, must be responsible for this localization [43]. This
discussion shows that while the Ihh/PTHrP feedback loop has
been extensively studied, the exact mechanisms through which Ihh
controls PTHrP require further investigation.
Although we opted not to include noncanonical Wnt signalling,
a clear cut distinction between both types is hard to make as a
marked delineation between canonical and noncanonical Wnts
might be idiosyncratic and could easily be blurred by varying
Table 4. Stable states of the FGFR3 mutant network.
Growth factorsTranscription factors
FGFR3+ +
BMPWntTGFb
FGFR3 IhhPTHrPSox9Runx2Gli2
resting zone011202(+ext)100
proliferative11121(ext)1(ext)101
hypertrophy210210021
Smad KORSmad Wnt TGFb
FGFIhh PTHrPSox9Runx2 Gli2
resting zone011102100
apoptosis01021(ext)0000
hypertrophy010210020
The values of nodes representing growth factors and transcription factors are tabled for the relevant stable states in the R-Smad and FGFR3 mutant growth plate. The
presence of paracrine signalling is indicated in the table (ext). The situation in the resting zone is virtually unchanged. However, the activity of Sox9 in the proliferation
zone is hampered. The stable state representing hypertrophy is also unaffected. For the Smad mutant the proliferative zone is more severely impacted and no
expression of Sox9 is predicted. The hypertrophic state can be reached under certain asynchronous updating assumptions, as is apparent from the state transition
graph.
Logical Model of Chondrogenesis in a Growth Plate
PLoS ONE | www.plosone.org7 April 2012 | Volume 7 | Issue 4 | e34729

Page 8

circumstances such as tissue type, differentiation state of cells, the
availability of receptors on the cell surface and the presence of
other factors in the cell lumen [44]. The focus of research efforts in
chondrocytes thus far has been more on b-catenin/TCF
signalling, providing a relative abundance of information on
canonical signalling when compared to knowledge on the
mechanisms referred to as noncanonical signals. Be that as it
may, some workers have concluded that noncanonical Wnt5a and
Wnt5b cooperate to antagonize hypertrophic differentiation and
hence b-catenin/TCF signalling, although which exact signalling
pathways are employed remains to be elucidated [9,45]. Hence an
important caveat on the results presented here is that the
incorporation of Wnt signalling in the presented network is
incomplete and might lead to faulty conclusions.
In a first corroboration step the in vivo expression patterns of
genes featuring in the network are compared to the activity of their
logical counterparts. Fig. 5 evaluates the expression patterns
observed in the growth plate and the modelling results. The
predictions and observations match well, taking into account the
discretization innate to the logical framework. Some mismatches
can be found, however, such as the presence of Wnt in the resting
zone. This is due to the assumption that Wnt is downstream of
Ihh. The expression pattern can be rectified by presuming TGFb
to be the only Ihh messenger molecule, notwithstanding that the
molecular mechanisms utilised to transcribe perichondrial PTHrP
remain elusive. There is also evidence that Wnt ligands and
consecutive signals are regulated by insulin-like growth factor
1(IGF-1), which was not included in the model [46].
Another discrepancy is the appearance of Gli2 in hypertrophic
chondrocytes, an error that is corrected by allowing FGF signalling
to inhibit Hh signalling, as was described previously [47,48], or by
letting Ptch1 expression decrease as a result of Sox9 absence
[49,50]. However, since the detailed mechanisms of these
interactions remain obscure they were not included in the current
model.
The mutant results can be compared to murine models as a
further step towards model corroboration. Mice with a homozy-
gous deletion of PTHrP show no abnormalities in early
development, but show defects later during endochondral bone
development and die shortly after birth [51]. In these PTHrP null
mice the transition of chondrocytes from the proliferative to the
hypertrophic phase is accelerated, resulting in advanced and
premature ossification [52]. Additionally, the mice appear to be
smaller at birth in comparison to their wild type relatives. This
dwarfism is likely due to proliferating chondrocytes that divide less
before undergoing hypertrophy. A similar phenotype is found in
mice lacking PPR. Hence these mouse models corroborate the
results reached by the growth plate network for the case of PTHrP
deactivation. However, it remains to be seen whether chondro-
cytes are capable of reaching a state similar to the Sox9 positive
state predicted by asynchronous updating. An activating mutation
in the PPR gene has been found to cause Jansen’s metaphyseal
chondrodysplasia, a disease characterized by dwarfism of the limbs
and hypercalcemia [53]. A mouse model where PTHrP is
overexpressed in cartilage by a Col-II promoter reveals a similar
phenotype [31]. The mice exhibit a short-limbed dwarfism and are
born with a cartilaginous skeleton, indicating that hypertrophy did
not occur, in accordance with the model results. After about seven
weeks the skeleton will have mineralized starting at the periphery
of the bones, inverting the process of endochondral ossification
where the bone is mineralized inside out [31]. This means that at
the periphery of the bone PTHrP expression might be lower, and
hypertrophy could occur here. The chondrocytes would then
reach the state of hypertrophy predicted by the model in the case
of lower PTHrP expression. The model was able to successfully
predict the changes in the growth plate structure for the mutated
PTHrP signalling.
FGFR3 is the most common aetiological factor of human
dwarfism or achondroplasia (ACH). A mutation in the gene causes
it to become more active. The effect of this mutation is relatively
minor, since more powerful activating mutations have a lethal
phenotype, such as in thanatophoric dysplasia [54]. FGFR3ACH
mice have been created by using regulatory elements from the
collagen-II gene to transcribe an activated form of FGFR3 in the
cartilage growth plate. Hence the situation in these mice is similar
to the conditions simulated to corroborate the behaviour of the
FGF pathway. These transgenic mice exhibit appendicular skeletal
hypoplasia alongside other bone defects. Their skeletal underde-
velopment seems to originate from a reduced chondrocyte
proliferation combined with a slower differentiation [48]. This is
also shown in the model where CCND1, an important gene in the
cell cycle, is no longer expressed. The model also predicts the
hypertrophic differentiation of the chondrocytes is hampered given
the absence of MEF2C and Dlx5, both hypertrophy-promoting
transcription factors.
In the case of a conditional knock out (CKO) of the R-Smads (1
and 5) in chondrocytes growth plate morphology is dramatically
disrupted. R-Smad CKO mice exhibited an increased area with
occurrence of apoptosis but a total absence of a hypertrophic zone.
Furthermore, these mutants show a decreased expression of Col-II
and decreased levels of Sox9 in the mutant cartilage, indicating
that the chondrocytes might not be fully differentiated [55].
Accordingly, the model predicts absence of Sox9 expression at this
stage. This may be linked with the increased apoptosis, as Sox9 is
required for chondrocyte survival [56]. In an asynchronous
updating regime the network can reach a hypertrophic state.
However, the R-Smad CKO growth plate shows no apparent
hypertrophic zone. Nonetheless, a low level Runx2 expression was
detected by RT-PCR demonstrating a patched expression of the
transcription factor in the disorganised mutant growth plate [55].
Hence a limited number of cells might reach this stable state. The
other major pathways were tested in a similar way providing
further corroboration (see Material S4). Together these mutant
cases suggest the major pathways and their function in the growth
plate can indeed be simulated adequately by the presented logical
model.
It should be noted that many signalling pathways have been
simplified to a generic signalling molecule representing many
ligand/receptor combinations. For example, the network does not
differentiate between BMP2, -4, -6 or -7, which are differentially
expressed in the growth plate [5]. Neither was a distinction
between BMPR1A and -1B included. The reason for this is
twofold. Firstly, very few data are available on the differences
between these BMP ligands, let al.one on their mutual interactions
and combinations with different receptor types. Hence inclusion of
these data paints an incomplete picture of BMP ligand control
resulting in very erratic expression patterns, whereas their
combination in a generic signal results in robust behaviour.
Secondly, the dissimilarities between these interactions are often
quantitative in nature, which is hard to reconcile with a logical
model, which is inherently qualitative. For the purposes of
qualitative predicting cell behaviour, there was consequently no
impetus to include the individual ligands.
This model has several limitations. For instance, from the
behaviour of the chondrocyte network it is apparent that the
presence of the perichondrium is necessary to form an autoreg-
ulatory unit. Therefore a more comprehensive model could be
constructed which includes differentiation of mesenchymal cells to
Logical Model of Chondrogenesis in a Growth Plate
PLoS ONE | www.plosone.org8April 2012 | Volume 7 | Issue 4 | e34729

Page 9

form the surrounding perichondrium (an osteogenic lineage). A
further limitation of the model is the inability to simulate the
terminal differentiation phase, which would require inclusion of
survival-related pathways responsible for apoptosis. A crucial
consideration is that the growth plate network combines informa-
tion from multiple species. While the majority of interactions were
confirmed in mouse models, 18% was not. We assumed these
interactions to be evolutionary conserved across vertebrates,
though this remains unconfirmed. More information on the
models from which interactions were derived can be found in
Material S1. Moreover, the results of the model are dependent on
the weighted sum approach. Using another principle such as
dominant inhibition would significantly alter the results. We
selected the weighted sum approach because it seemed to comply
best with the kind of data available for interactions and their effect
on gene expression.
Additionally, the many simplifications of logical networks have
some drawbacks. Sometimes an all-or-nothing response is
insufficient to describe wide range of continuous concentrations
a certain protein may have. This is increasingly problematic in
hub genes, where many pathways converge with often contradic-
tory effects. This problem is partially mediated by the use of multi-
value logic, as was done in this study. Furthermore, a logical
network does not have any spatial or realistic temporal resolution.
The dynamics of the networks are hence only roughly approxi-
mated. More specifically, caution is warranted concerning the
appearance of a transitory prehypertrophic state, which may be
depended on the time scale at which interactions take place. The
model could be further improved by associating a time delay with
every interaction, thereby enhancing time resolution [57].
However, since we lack kinetic information and a random
approach is not computationally feasible due to the amount of
possible time delays and combinations thereof we have limited our
simulations to two cases. The first case is that of synchronous
dynamics where all interactions are equally fast and in the second
case we consider all the possible dynamics when each gene is
updated randomly, which is equivalent to calculating the transition
graph. Furthermore, the logical formalism did not allow direct
incorporation of diffusion and interaction of growth factors with
extracellular matrix proteins. Previous models of signalling in the
growth plate have explicitly modelled diffusion, whereas in the
current work diffusion is modelled implicitly by changing the value
of nodes representing diffusion [58–62].
In this work we have aimed to simulate the gene network that
drives chondrocyte differentiation in the fetal growth plate. This
model shows how genes interact to regulate and modify the
differentiation state of a cell. Despite hiatuses in our current
understanding of growth plate regulation the model provides a
feasible representation of the governing regulatory apparatus. The
rigid description of gene interactions allows testing the plausibility
of hypotheses on gene interactions in silico. Hence a modelling
approach helps in the formulation and subsequently rejection or
corroboration of putative gene interactions in the context of an
elaborate gene network, which in its intricacy is capable of defying
human intuition.
The model introduced has further practical uses in the context
of tissue engineering (TE). Currently, TE of bones uses a poorly
characterized process in which the quantity and quality of the
produced bone are low [63]. An alternative would be to use a
biomimetic process growing bones via endochondral ossification,
the natural route for long bone development. The developmental
process is robust and behaves as an autoregulatory module. In
accordance with the novel paradigm of ‘‘developmental engineer-
ing’’ these characteristics are highly desirable in an in vitro tissue
engineering process [64]. The logical model can be instructive to
design such a process, both in improving process robustness,
observability and controllability and can hence assist in overcom-
ing regulatory hurdles [65].
Supporting Information
Material S1
interactions in the logical model with indication of the (animal)
model species used.
(PDF)
Complete list of references for the different
Material S2
(ZIP)
Model files used to generate the results
Material S3
stability of the logical model
(PDF)
Set-up and details of the ODE system used to assess
Material S4
TGFb pathway and for the case where the perichondrium was
removed.
(PDF)
Results for conditional knock-outs in the Wnt and
Acknowledgments
Johan Kerkhofs is a PhD fellow of the research Foundation Flanders
(FWO-Vlaanderen). This work is part of Prometheus, the Leuven Research
& Development Division of Skeletal Tissue Engineering of the Katholieke
Universiteit Leuven: www.kuleuven.be/prometheus.
Author Contributions
Conceived and designed the experiments: JK SR LG. Performed the
experiments: JK. Analyzed the data: JK SR LG FL HVO. Wrote the
paper: JK SR LG FL HVO.
References
1.Wuelling M, Vortkamp A (2010) Transcriptional networks controlling
chondrocyte proliferation and differentiation during endochondral ossification.
Pediatric Nephrology 25: 625–631.
Kronenberg HM (2006) PTHrP and Skeletal Development. Annals of the New
York Academy of Sciences 1068: 1–13. 10.1196/annals.1346.002.
Solomon LA, Be ´rube ´ NG, Beier F (2008) Transcriptional regulators of
chondrocyte hypertrophy. Birth Defects Research Part C: Embryo Today:
Reviews 84: 123–130. 10.1002/bdrc.20124.
Burdan F, Szumilo J, Korobowicz A, Farooquee R, Patel S, et al. (2009)
Morphology and physiology of the epiphyseal growth plate. Folia Histochemica
et Cytobiologica 47: 5–16. 10.2478/v10042-009-0007-1.
Kronenberg HM (2003) Developmental regulation of the growth plate. Nature
423: 332–336. 10.1038/nature01657.
Kobayashi T, Chung Ui, Schipani E, Starbuck M, Karsenty G, et al. (2002)
PTHrP and Indian hedgehog control differentiation of growth plate chondro-
cytes at multiple steps. Development 129: 2977–2986.
2.
3.
4.
5.
6.
7.Pogue R, Lyons K (2006) BMP Signalling in the Cartilage Growth Plate. In:
Gerald PS, ed. Current Topics in Developmental Biology Academic Press. pp
1–48.
Li TF, O’Keefe RJ, Chen D (2005) TGF-beta signalling in chondrocytes. Front
Biosci 10: 681–8. pp 681–688.
Hartmann C, Tabin CJ (2000) Dual roles of Wnt signalling during
chondrogenesis in the chicken limb. Development 127: 3141–3159.
10. Ornitz DM, Marie PJ (2002) FGF signalling pathways in endochondral and
intramembranous bone development and human genetic disease. Genes &
Development 16: 1446–1465.
11. Akiyama H (2008) Control of chondrogenesis by the transcription factor Sox9.
Modern Rheumatology 18: 213–219.
12. Komori T (2003) Requisite roles of Runx2 and Cbfb in skeletal development.
Journal of Bone and Mineral Metabolism 21: 193–197.
8.
9.
Logical Model of Chondrogenesis in a Growth Plate
PLoS ONE | www.plosone.org9April 2012 | Volume 7 | Issue 4 | e34729

Page 10

13. Segre G, Lee K, Lanske B, Kronenberg H (1997) Parathyroid hormone-related
protein and Indian hedgehog regulate the pace of cartilage differentiation.
Journal of Bone and Mineral Metabolism 15: 109–114.
14. Hasty J, McMillen D, Isaacs F, Collins JJ (2001) Computational studies of gene
regulatory networks: in numero molecular biology. Nat Rev Genet 2: 268–279.
10.1038/35066056.
15. Christensen C, Thakar J, Albert R (2007) Systems-level insights into cellular
regulation: inferring, analysing, and modelling intracellular networks. Systems
Biology, IET 1: 61–77.
16. Morris MK, Saez-Rodriguez J, Sorger PK, Lauffenburger DA (2010) Logic-
based models for the analysis of cell signalling networks. Biochemistry 49:
3216–3224.
17. Schlitt T, Brazma A (2007) Current approaches to gene regulatory network
modelling. BMC Bioinformatics 8: S9. 10.1186/1471-2105-8-S6-S9.
18. Chaouiya C, Remy E, Mosse ´ B, Thieffry D (2003) Qualitative Analysis of
Regulatory Graphs: A Computational Tool Based on a Discrete Formal
Framework Positive Systems. In: Benvenuti L, De Santis A, Farina L, eds.
Springer Berlin/Heidelberg. pp 830–832.
19. Kozhemyakina E, Cohen T, Yao TP, Lassar AB (2009) Parathyroid hormone-
related peptide represses chondrocyte hypertrophy through a protein phospha-
tase 2A/histone deacetylase 4/MEF2 pathway. Mol Cell Biol 29: 5751–5762.
20. Riemer S, Gebhard S, Beier F, Po ¨schl E, von der Mark K (2002) Role of c-fos in
the regulation of type X collagen gene expression by PTH and PTHrP:
Localization of a PTH/PTHrP-responsive region in the human COL10A1
enhancer. J Cell Biochem 86: 688–699. 10.1002/jcb.10260.
21. Wessels LF, van Someren EP, Reinders MJ (2001) A comparison of genetic
network models. Pac Symp Biocomput 508–519.
22. Ouyang Z, Zhou Q, Wong WH (2009) ChIP-Seq of transcription factors
predicts absolute and differential gene expression in embryonic stem cells.
Proceedings of the National Academy of Sciences 106: 21521–21526.
23. Darabos C, Di Cunto F, Tomassini M, Moore JH, Provero P, et al. (2011)
Additive Functions in Boolean Models of Gene Regulatory Network Modules.
PLoS ONE 6: e25110. doi:10.1371/journal.pone.0025110.
24. Seshadhri C, Vorobeychik Y, Mayo JR, Armstrong RC, Ruthruff JR (2011)
Influence and Dynamic Behavior in Random Boolean Networks. Physical
Review Letters 107: 108701.
25. Verdicchio MP, Kim S (2011) Identifying targets for intervention by analyzing
basins of attraction. Pac Symp Biocomput 350–361.
26. Huberman BA, Glance NS (1993) Evolutionary games and computer
simulations. Proceedings of the National Academy of Sciences 90: 7716–7718.
27. Klemm K, Bornholdt S (2005) Stable and unstable attractors in Boolean
networks. Physical Review E 72: 055101.
28. Naldi A, Berenguier D, Faure ´ A, Lopez F, Thieffry D, et al. (2009) Logical
modelling of regulatory networks with GINsim 2.3. Biosystems 97: 134–139. doi:
10.1016/j.biosystems.2009.04.008.
29. Mendoza L, Xenarios I (2006) A method for the generation of standardized
qualitative dynamical systems of regulatory networks. Theoretical Biology and
Medical Modelling 3: 13. 10.1186/1742-4682-3-13.
30. Plahte E, Mestl T, Omholt SW (1998) A methodological basis for description
and analysis of systems with complex switch-like interactions. J Math Biol 36:
321–348.
31. Weir EC, Philbrick WM, Amling M, Neff LA, Baron R, et al. (1996) Targeted
overexpression of parathyroid hormone-related peptide in chondrocytes causes
chondrodysplasia and delayed endochondral bone formation. Proceedings of the
National Academy of Sciences 93: 10240–10245.
32. Hyman JM, Firestone AJ, Heine VM, Zhao Y, Ocasio CA, et al. (2009) Small-
molecule inhibitors reveal multiple strategies for Hedgehog pathway blockade.
Proceedings of the National Academy of Sciences 106: 14132–14137.
33. Arnold MA, Kim Y, Czubryt MP, Phan D, McAnally J, et al. (2007) MEF2C
Transcription Factor Controls Chondrocyte Hypertrophy and Bone Develop-
ment. Developmental Cell 12: 377–389. doi: 10.1016/j.devcel.2007.02.004.
34. Zou H, Wieser R, Massague ´ J, Niswander L (1997) Distinct roles of type I bone
morphogenetic protein receptors in the formation and differentiation of
cartilage. Genes & Development 11: 2191–2203.
35. Eichberger T, Sander V, Schnidar H, Regl G, Kasper M, et al. (2006)
Overlapping and distinct transcriptional regulator properties of the GLI1 and
GLI2 oncogenes. Genomics 87: 616–632. doi: 10.1016/j.ygeno.2005.12.003.
36. Adams SL, Cohen AJ, Lassova ´ L (2007) Integration of signalling pathways
regulating chondrocyte differentiation during endochondral bone formation.
J Cell Physiol 213: 635–641. 10.1002/jcp.21262.
37. Liu Z, Xu J, Colvin JS, Ornitz DM (2002) Coordination of chondrogenesis and
osteogenesis by fibroblast growth factor 18. Genes & Development 16: 859–869.
38. Mak KK, Kronenberg HM, Chuang PT, Mackem S, Yang Y (2008) Indian
hedgehog signals independently of PTHrP to promote chondrocyte hypertro-
phy. Development 135: 1947–1956.
39. Alvarez J, Sohn P, Zeng X, Doetschman T, Robbins DJ, et al. (2002) TGFß2
mediates the effects of Hedgehog on hypertrophic differentiation and PTHrP
expression. Development 129: 1913–1924.
40. Chen Y, Struhl G (1996) Dual Roles for Patched in Sequestering and
Transducing Hedgehog. Cell 87: 553–563. doi: 10.1016/S0092-8674(00)81374-
4.
41. Koziel L, Wuelling M, Schneider S, Vortkamp A (2005) Gli3 acts as a repressor
downstream of Ihh in regulating two distinct steps of chondrocyte differentiation.
Development 132: 5249–5260.
42. Susperregui ARG, Vin ˜als F, Ho PWM, Gillespie MT, Martin TJ, et al. (2008)
BMP-2 regulation of PTHrP and osteoclastogenic factors during osteoblast
differentiation of C2C12 cells. J Cell Physiol 216: 144–152. 10.1002/jcp.21389.
43. Goodrich LV, Milenkovic L, Higgins KM, Scott MP (1997) Altered Neural Cell
Fates and Medulloblastoma in Mouse patched Mutants. Science 277:
1109–1113.
44. van Amerongen R, Nusse R (2009) Towards an integrated view of Wnt
signalling in development. Development 136: 3205–3214.
45. Gao B, Song H, Bishop K, Elliot G, Garrett L, et al. (2011) Wnt Signalling
Gradients Establish Planar Cell Polarity by Inducing Vangl2 Phosphorylation
through Ror2. Developmental Cell 20: 163–176. doi: 10.1016/j.dev-
cel.2011.01.001.
46. Wang L, Shao YY, Ballock RT (2010) Thyroid hormone-mediated growth and
differentiation of growth plate chondrocytes involves IGF-1 modulation of
betacatenin signalling. J Bone Miner Res 25: 1138–1146. 10.1002/jbmr.5.
47. Ogawa T, Shimokawa H, Fukada K, Suzuki S, Shibata S, et al. (2003)
Localization and inhibitory effect of basic fibroblast growth factor on
chondrogenesis in cultured mouse mandibular condyle. Journal of Bone and
Mineral Metabolism 21: 145–153.
48. Naski MC, Colvin JS, Coffin JD, Ornitz DM (1998) Repression of hedgehog
signalling and BMP4 expression in growth plate cartilage by fibroblast growth
factor receptor 3. Development 125: 4977–4988.
49. Vortkamp A, Pathi S, Peretti GM, Caruso EM, Zaleske DJ, et al. (1998)
Recapitulation of signals regulating embryonic bone formation during postnatal
growth and in fracture repair. Mechanisms of Development 71: 65–76. doi:
10.1016/S0925-4773(97)00203-7.
50. Oh CD, Maity SN, Lu JF, Zhang J, Liang S, et al. (2010) Identification of SOX9
Interaction Sites in the Genome of Chondrocytes. PLoS ONE 5: e10113.
51. Lanske B, Karaplis AC, Lee K, Luz A, Vortkamp A, et al. (1996) PTH/PTHrP
receptor in early development and Indian hedgehog-regulated bone growth.
Science 273: 663–666.
52. Vortkamp A, Lee K, Lanske B, Segre GV, Kronenberg HM, et al. (1996)
Regulation of rate of cartilage differentiation by Indian hedgehog and PTH-
related protein. Science 273: 613–622.
53. Schipani E, Langman CB, Parfitt AM, Jensen GS, Kikuchi S, et al. (1996)
Constitutively Activated Receptors for Parathyroid Hormone and Parathyroid
Hormone–Related Peptide in Jansen’s Metaphyseal Chondrodysplasia. New
England Journal of Medicine 335: 708–714. doi: 10.1056/
NEJM199609053351004.
54. Naski MC, Wang Q, Xu J, Ornitz DM (1996) Graded activation of fibroblast
growth factor receptor 3 by mutations causing achondroplasia and thanatopho-
ric dysplasia. Nat Genet 13: 233–237.
55. Retting KN, Song B, Yoon BS, Lyons KM (2009) BMP canonical Smad
signalling through Smad1 and Smad5 is required for endochondral bone
formation. Development 136: 1093–1104.
56. Bi W, Deng JM, Zhang Z, Behringer RR, de CB (1999) Sox9 is required for
cartilage formation. Nat Genet 22: 85–89.
57. Schlatter R, Schmich K, Avalos Vizcarra I, Scheurich P, Sauter T, et al. (2009)
ON/OFF and Beyond - A Boolean Model of Apoptosis. PLoS Comput Biol 5:
e1000595. doi:10.1371/journal.pcbi.1000595.
58. van Donkelaar CC, Huiskes R (2007) The PTHrP-Ihh feedback loop in the
embryonic growth plate allows PTHrP to control hypertrophy and Ihh to
regulate proliferation. Biomech Model Mechanobiol 6: 55–62.
59. Brouwers JEM, van Donkelaar CC, Sengers BG, Huiskes R (2006) Can the
growth factors PTHrP, Ihh and VEGF, together regulate the development of a
long bone? Journal of Biomechanics 39: 2774–2782. doi: 10.1016/j.jbio-
mech.2005.10.004.
60. Fasano A, Herrero MA, Lo ´pez JM, Medina E (2010) On the dynamics of the
growth plate in primary ossification. Journal of Theoretical Biology 265:
543–553. doi: 10.1016/j.jtbi.2010.05.030.
61. Garzo `n-Alvarado D, Garcı ´a-Aznar J, Doblare ´ M (2009) A reaction-diffusion
model for long bones growth. Biomechanics and Modeling in Mechanobiology
8: 381–395.
62. Garzo `n-Alvarado DA, Garcı ´a-Aznar JM, Doblare ´ M (2009) Appearance and
location of secondary ossification centres may be explained by a reaction-
diffusion mechanism. Computers in Biology and Medicine 39: 554–561. doi:
10.1016/j.compbiomed.2009.03.012.
63. Oliveira SM, Mijares DQ, Turner G, Amaral IF, Barbosa MA, et al. (2009)
Engineering endochondral bone: in vivo studies. Tissue Eng Part A 15: 635–643.
64. Lenas P, Moos M, Luyten FP (2009) Developmental Engineering: A New
Paradigm for the Design and Manufacturing of Cell-Based Products. Part I:
From Three-Dimensional Cell Growth to Biomimetics of In Vivo Development.
Tissue Engineering Part B: Reviews 15: 381–394. doi: 10.1089/ten.-
teb.2008.0575.
65. Lenas P, Moos M, Luyten FP (2009) Developmental Engineering: A New
Paradigm for the Design and Manufacturing of Cell-Based Products. Part II.
From Genes to Networks: Tissue Engineering from the Viewpoint of Systems
Biology and Network Science. Tissue Engineering Part B: Reviews 15: 395–422.
doi: 10.1089/ten.teb.2009.0461.
66. Nilsson O, Parker EA, Hegde A, Chau M, Barnes KM, et al. (2007) Gradients in
bone morphogenetic protein-related gene expression across the growth plate.
Journal of Endocrinology 193: 75–84.
67. Enomoto-Iwamoto M, Kitagaki J, Koyama E, Tamamura Y, Wu C, et al. (2002)
The Wnt Antagonist Frzb-1 Regulates Chondrocyte Maturation and Long Bone
Logical Model of Chondrogenesis in a Growth Plate
PLoS ONE | www.plosone.org10 April 2012 | Volume 7 | Issue 4 | e34729

Page 11

Development during Limb Skeletogenesis. Developmental Biology 251:
142–156. doi: 10.1006/dbio.2002.0802.
68. Shum L, Nuckolls G (2002) The life cycle of chondrocytes in the developing
skeleton. Arthritis Res 4: 94–106. 10.1186/ar396.
69. Jonason JH, Xiao G, Zhang M, Xing L, Chen D (2009) Post-translational
Regulation of Runx2 in Bone and Cartilage. Journal of Dental Research 88:
693–703.
70. Hecht J, Seitz V, Urban M, Wagner F, Robinson PN, et al. (2007) Detection of
novel skeletogenesis target genes by comprehensive analysis of a Runx2-/-
mouse model. Gene Expression Patterns 7: 102–112. doi: 10.1016/j.mod-
gep.2006.05.014.
71. Lefebvre V, Smits P (2005) Transcriptional control of chondrocyte fate and
differentiation. Birth Defects Research Part C: Embryo Today: Reviews 75:
200–212. 10.1002/bdrc.20048.
72. Hattori T, Mu ¨ller C, Gebhard S, Bauer E, Pausch F, et al. (2010) SOX9 is a
major negative regulator of cartilage vascularization, bone marrow formation
and endochondral ossification. Development 137: 901–911.
73. Goldring MB, Tsuchimochi K, Ijiri K (2006) The control of chondrogenesis.
J Cell Biochem 97: 33–44. 10.1002/jcb.20652.
74. Mau E, Whetstone H, Yu C, Hopyan S, Wunder JS, et al. (2007) PTHrP
regulates growth plate chondrocyte differentiation and proliferation in a Gli3
dependent manner utilizing hedgehog ligand dependent and independent
mechanisms. Developmental Biology 305: 28–39. doi: 10.1016/j.yd-
bio.2007.01.031.
Logical Model of Chondrogenesis in a Growth Plate
PLoS ONE | www.plosone.org11 April 2012 | Volume 7 | Issue 4 | e34729