Reusing and composing models of cell fate regulation of human bone precursor cells

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(1)BioSystems 108 (2012) 63–72. Contents lists available at SciVerse ScienceDirect. BioSystems journal homepage: www.elsevier.com/locate/biosystems. Reusing and composing models of cell fate regulation of human bone precursor cells Rodrigo Assar a,e,∗ , Andrea V. Leisewitz b , Alice Garcia a , Nibaldo C. Inestrosa c , Martín A. Montecino d,e , David J. Sherman a a. INRIA Bordeaux Sud-Ouest, Project-team (EPC) MAGNOME common to INRIA, CNRS, and U. Bordeaux 1, Talence, France Hematology-Oncology Department School of Medicine, Pontificia Universidad Católica de Chile, Santiago, Chile c CRCP, Centro de Regulación Celular y Patología Joaquín V. Luco, Departamento de Biología Celular y Molecular, Pontificia Universidad Católica de Chile, Santiago, Chile d Centro de Investigaciones Biomédicas, Facultad de Ciencias Biológicas and Facultad de Medicina, Universidad Andrés Bello, Santiago, Chile e FONDAP 15090007 Center for Genome Regulation, Santiago, Chile b. a r t i c l e. i n f o. Article history: Received 25 July 2011 Received in revised form 28 December 2011 Accepted 19 January 2012 Keywords: Bone formation Differentiation Wnt pathway. a b s t r a c t In order to treat osteoporosis and other bone mass disorders it is necessary to understand the regulatory processes that control the cell fate decisions responsible for going from bone precursor cells to bone tissue. Many processes interact to regulate cell division, differentiation and apoptosis. There are models for these basic processes, but not for their interactions. In this work we use the theory of switched systems, reuse and composition of validated models to describe the cell fate decisions leading to bone and fat formation. We describe the differentiation of osteo-adipo progenitor cells by composing its model with differentiation stimuli. We use the activation of the Wnt pathway as stimulus to osteoblast lineage, including regulation of cell division and apoptosis. This model is our first step to simulate physiological responses in silico to treatments for bone mass disorders. © 2012 Elsevier Ireland Ltd. All rights reserved.. 1. Introduction A high percentage of the human population suffer diseases such as osteoporosis that affect: one third of women and one twelfth of men over 50 years old. The current treatments for increasing bone mass or reducing resorption have many limitations and side effects (Hoeppner et al., 2009). There is a strong opposition between bone and fat formation. Obesity reduces bone density and is inversely associated with bone formation in osteoporosis (Chen et al., 2010). There is a notorious decrease of the bone/fat formation ratio with the aging (Stenderup et al., 2003; Brockstedt et al., 1992). In this scenario, understanding regulatory signaling pathways that are relevant during control of bone formation (e.g. Wnt-mediated signaling) have emerged as critical components to treat in the future this and other bone disorders (Chen et al., 2010; Krishnan et al., 2006; Shahnazari et al., 2008; Kubota et al., 2009; Issack et al., 2008; Hoeppner et al., 2009). Moreover, it has become necessary to define their contribution within the regulatory processes that control the. ∗ Corresponding author at: FONDAP 15090007 Center for Genome Regulation, 8370415 Santiago, Chile. Tel.: +562 9780584. E-mail addresses: rodrigo.assar@gmail.com (R. Assar), aleisewitz@gmail.com (A.V. Leisewitz), alice.garcia@inria.fr (A. Garcia), ninestrosa@bio.puc.cl (N.C. Inestrosa), mmontecino@unab.cl (M.A. Montecino), david.sherman@inria.fr (D.J. Sherman). 0303-2647/$ – see front matter © 2012 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.biosystems.2012.01.008. cell fate decisions responsible for going from bone precursor cells to bone tissue. In this work, we analyze the process of bone and fat formation at a cellular level. We describe the dynamics of osteoblasts (bone cells), adipocytes (fat cells) and precursors. In such system, many processes interact in order to control the cell division, to regulate apoptosis, and to decide which cell lineages are produced. As proved by Chen et al. (2010), osteoblasts and adipocytes share a common precursor derived from the bone marrow stromal cells. These precursor cells can differentiate into osteoblast or adipocyte lineages depending on regulation signals. The Wnt/␤catenin pathway constitutes a potential target for bone mass disorder treatments such as osteoporosis or to reduce adiposity or fracture risk (Issack et al., 2008; Hoeppner et al., 2009). Its activation promotes osteoblast differentiation, proliferation and mineralization, and blocks apoptosis and osteoclastogenesis (Krishnan et al., 2006). On the other hand, the activation of PPAR (peroxisome proliferator-activated receptor gamma) provokes adipogenesis (Chen et al., 2010). For an approach to this complex system we consider the paradigm of Systems Biology, in which the behaviors emerge from the interaction between different processes (Kitano, 2002). Answers such as a specific increase of osteoblast concentration are provoked by the combined action activating the Wnt/␤-catenin pathway, repressing the expression of PPAR, and repressing the stimuli to osteoblasts apoptosis. Despite the existing models for.

(2) 64. R. Assar et al. / BioSystems 108 (2012) 63–72. each individual process, models for cross-talks and functional interactions between them have not been developed yet. Based on reusing existing models of individual processes, and combining them, we look for describing the process of bone and fat formation to analyze it in silico. The development of an accurate combined model will allows us to analyze in silico the physiological responses to treatments of bone mass disorders based on the Wnt signaling pathway, and to explore the efficiency of new medical strategies before testing them in animal models. At the current phase, our model predicts expected qualitative behaviors: activation or repression of each cell lineage. Motivated by the recent model proposed by Schittler et al. (2010) and the results of Chen et al. (2010), we defined the expression of RUNX2 (runt-related transcription factor 2) as associated with the osteogenic differentiation (Krishnan et al., 2006; Lian et al., 2003), while PPAR (peroxisome proliferator-activated receptor gamma) as associated with adipogenesis (Chen et al., 2010). Both transcription factors are mutually exclusive and auto regulated. This inter-regulated system is modeled by our main osteo-adipo switch model. We describe the differentiation from osteo-adipo progenitor cells into osteoblasts and adipocytes by associating the main osteo-adipo switch model with a well-described model of the Wnt/␤-catenin pathway (Kim et al., 2007) to stimulate the osteoblast lineage, and with a probabilistic model that describes the activation of the PPAR pathway during stimulation of the adipocyte differentiation (Krishnan et al., 2006; Chen et al., 2010). To accomplish this, we consider stimuli coefficients of the main osteo-adipo switch model as functions of the pathways activation. Finally, we include one good established and validated model (Kim et al., 2006) that reflects how apoptosis is controlled. We call such a combined model the cell fate decisions model. The paper is structured as follows: Section 2 describes the material and methods used here: the biological system, the use of Systems Biology to consider emerging behaviors, the reused models and the implementation using BioRica; Section 3 presents the theoretical elements considered here: Gene Regulatory Networks and Switched Systems, combination of models; Section 4 present our models: the osteo-adipo switch model that introduces the Wnt pathway as bone formation stimulus, and the combined model for describing cell fate decisions for osteo-adipo differentiation; Section 5 shows and compares the simulation results of the combined models; Section 6 concludes and discusses the scopes and future improvements of our work. 2. Materials and methods 2.1. The biological systems: from progenitor cells to osteoblasts and adipocytes In this paper we describe the dynamics for formation of osteoblasts and adipocytes from a common precursor derived from the bone marrow stromal cells. We model this system by using the Systems Biology paradigm (Kitano, 2002, Section 2.3). The differentiation of precursor cells into osteoblast and adipocyte lineage depends on many regulation processes as we describe here. In multi-cellular organisms, inter and intra-cellular processes control the metabolism (Greenwald, 1998; Bukauskas, 1991). The basic function of a cell can be explained by four essential processes: growth, division, differentiation and apoptosis (Alberts et al., 2002). These processes are responsible for going from a unique cell to several specialized cell lineages. The cell decision between self-renewal, differentiation and apoptosis defines the cell fate (Wagers et al., 2002). The cell cycle is comprised of several events that lead to cell division itself (mitosis and cytokinesis). It is regulated by several proteins named cyclins and cyclin dependent kinases (Alberts et al., 2002). The process through which an undifferentiated cell acquires specialized functions is called differentiation. During this process the undifferentiated precursor cell, called progenitor, can differentiate into different specific lineages. Thus, hematopoietic (blood) cells differentiate from a common progenitor into red blood cells, to transport oxygen, or into white blood cells that have defensive functions in the organism (Huang et al., 2007). Osteoblasts (bone cells) and adipocytes (fat cells) share a common precursor derived from the bone marrow stromal cells (Chen et al., 2010). The Wnt/␤-catenin pathway plays an important role in the stimulation of bone formation (Krishnan et al., 2006). It promotes osteoblat differentiation, proliferation. and mineralization, and blocks apoptosis and osteoclastogenesis. Consequently, it is fundamental during bone remodeling and repair, constituting a potential target for the treatment of bone mass disorders such as osteoporosis or to reduce adiposity or fracture risk (Issack et al., 2008; Hoeppner et al., 2009). As example, it has been shown that loss of function of LRP4 and LRP5 (Wnt receptors, Krishnan et al., 2006) is associated with osteoporosis (Kumar et al., 2011). The presence of some Wnt ligands activates the canonical Wnt pathway and induces the accumulation of ␤-catenin in the nucleus of the cell, which interacts with a TCF/LEF transcription factor to activate the expression of the so-called Wnt target genes (Hodar et al., 2010). Some proteins that stimulate bone formation, such as RUNX2 considered here, are Wnt targets (Krishnan et al., 2006). Apoptosis, programmed cell death, can occur during cell-cycle or during the differentiation. It is controlled by a diverse range of cell signals, which may originate after either intrinsic or extrinsic inducers. Intracellular apoptosis begins in response to a stress such as heat, radiation, nutrient deprivation, viral infection, or membrane damage (Hunziker et al., 2010). Extracellular lethal signals include toxins, hormones, growth factors, nitric oxide or cytokines. In the case of bone cells, it has been shown that homocysteine induces strongly apoptosis in bone precursors and osteoblasts via the mitochondria pathway (Kim et al., 2006). The mechanisms here considered are shown in Fig. 1(A). 2.2. Reused models To describe cell differentiation we reuse the osteo-chondro switch model proposed by Schittler et al. (2010) (Fig. 2), but replacing chondrocyte lineage variable by adipocyte lineage (see Section 4.1). The model corresponds to a description by differential equations of a Gene Regulatory Network (see Section 3.1), implemented here. We validated our implementation by comparing our results on the osteochondro switch model with the published results. The parameters of this model were adjusted a posteriori to human behaviors according to the results by De Ugarte et al. (2003), Schmidmaier et al. (2006), Manolagas (2000) and Arner et al. (2010). More details in Section 4.4. About the stimulus models, we considered models for human cells built a priori. To simulate the induction of differentiation, we combined this model with other specific models that describe an engagement to the osteoblast lineage (by activation of the Wnt/ˇ catenin pathway) or to the adipocyte lineage (by activation of the PPAR/ pathway). Hence, we call the main osteo-adipo switch model the differentiation model before specifying the stimulus models, and the osteo-adipo switch model the model that includes the specific inductions to osteoblast and adipocyte lineages. To simulate the activation of the Wnt/␤-catenin pathway, we reuse the model by Kim et al. (2007) (specified in SBML) performing the analyses under both control conditions and considering the activation of the Wnt pathway for a period of 500–1000 min. On the other hand, the activation of the PPAR-pathway is stochastically simulated. With regard to apoptosis, we reuse the model proposed by Kim et al. (2006) that explains how homocysteine (Hcy) induces strongly the apoptosis of bone precursors and osteoblasts in a mitochondria-mediated manner. According to the results obtained in HS-5 osteoblastic lineage and primary human bone marrow stromal cells (both lines from ATCC, Manasas, VA, USA), when the concentration of Hcy is 10 ␮M the apoptosis rates of osteoblasts and precursors are increased to 47% and 41% respectively. We implemented directly this effect as an external factor on the differentiation process (see Section 4.3). We include as part of our combined model a component computing the period between cell divisions. Due to the complexity of the cell cycle of human cells, currently we consider this period as a parameter of the model. While minimal models such as Tyson (1991) and Goldbeter (1991) are valid for simple organisms like yeasts, for human colon carcinomas cells are considered models such as presented by Haberichter et al. (2007). 2.3. Our goal and the need for combining models Our main goal of this work is to build a model capable of predicting bone or fat formation considering a scenario near in vitro or in vivo conditions. As we explained in the previous section, there are many factors affecting bone formation in human body. The differentiation process, responsible for producing osteoblasts and adipocytes from precursor cells, depends on multiple regulation mechanisms. So, for modeling the dynamics of such cell lineages it is necessary to consider the dynamics of those mechanisms. It is incorrect to describe the osteoblast formation by considering just a model validated on specific conditions of regulation mechanisms here considered. The activation or inhibition of the Wnt signaling pathway, the PPAR expression, the division of progenitor cells, and the apoptosis of progenitor or osteoblast cells, work as a whole to generate osteoblasts and adipocytes from precursor cells. By using the Systems Biology paradigm (Kitano, 2002), we consider each mechanism separately and define the interaction between their models. The bone formation is considered an emerging property of the interacting processes. We mathematically describe each control mechanism effect, such as the activation of the Wnt pathway, by considering a specific coefficient of the differentiation model to be controlled by such mechanism. Reusing regulation mechanism validated models assure their accuracy and the construction of good combined models focus on the accurate inclusion of interactions..

(3) R. Assar et al. / BioSystems 108 (2012) 63–72. 65. Fig. 1. Cell fate decisions: from progenitor cells to osteoblasts and adipocytes. The symbol → denotes stimulus effects,  inhibition. Hexagonal boxes represent cellular phenotypes, ellipses and rounded rectangles regulation processes. (A) A progenitor cell can divide into new progenitor cells, or can die (apoptosis), also can differentiate into more specific lineages. Each one of these possibilities is controlled by a regulatory system. Apoptosis is stimulated by increases of Hcy protein. Division is induced if the cell carries a sufficiently high level of maturation. Differentiation is stimulated by the inhibition of the progenitor maintenance role, after which that the cell decides its lineage. Each specific lineage is stimulated by signals: the activation of the canonical Wnt pathway (model in Kim et al., 2007) stimulates osteoblast lineage, and the expression of PPAR the adipocyte lineage. (B) The combined model of the system. At the center the model that describes the osteo-adipo differentiation (osteo-adipo switch model), and around it the models affecting it..

(4) 66. R. Assar et al. / BioSystems 108 (2012) 63–72. Fig. 2. The osteo-chondro switch differentiation model by Schittler et al. (2010). Rounded rectangles in yellow denote the cell and its nucleus, rounded white rectangles correspond to external stimuli modeled by stochastic switches, green boxes denote genes and proteins, and arrows correspond to expression (→) and inhibitions (). The expression of RUNX2 and SOX9 is associated with the bone and cartilage formation, respectively. The gene TWEAK is the bio-marker for the progenitor state. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.). It is possible to improve the combined model following the same idea: adding new control mechanisms affecting the differentiation process, by defining its model and the effect on the coefficients of the differentiation model. With the inclusion of sufficient regulation mechanisms we want to be able to accurately predict the bone/fat formation process from osteo-adipo precursor cells. The final goal is to have an in silico way for testing medical treatments of bone mass disorders in order to regenerate bone tissues. 2.4. Implementing combined models with BioRica We implemented our model by using the BioRica framework BioRica: a high-level modeling framework that integrates discrete, continuous, stochastic, non-deterministic and timed behaviors in a non-ambiguous way allowing multi-scale dynamics, composition of models, translation from SBML models, and hierarchical relations. BioRica extends the ideas of AltaRica (Arnold et al., 1994, 1999) to biological systems, allowing one to solve differential equations and simulating stochastic and non-deterministic behaviors, together with reusing and combining the existing models. Models are represented by nodes, which can be combined by using input–output relations, and event synchronizations (Section 3.2) to implement combined models. The BioRica framework allows us to control the consistency of combined models, local clocks and solvers allow us to manipulate diverse types of dynamics, different timescales and complexity levels. Given a composed (combined) node (model) and a variable that is used by many sub-nodes, one controls how the changes on this variable are perceived by the sub-nodes associating to that variable a flow variable, and imposing assertions of equality between the versions of that flow variable on different nodes (Soueidan et al., 2007). The BioRica compiler reads a specification of the hierarchical model and compiles it into an executable simulator. The compiled code uses the Python runtime environment and can be run stand-alone on most systems. The co-existence of multiple dynamics is assured by a pre-computation of each specified sub-model. Once computed, each part acts as a component that can be queried, but also modified by trajectory modifications induced by discrete parts of the model. More details in Assar (2011).. molecules and proteins are represented by the same variables, and post-transcriptional regulations (common in eukaryotes) are not included. Nevertheless, this approach allows the study a wide range of systems and also to integrate microarray results. Promotion and inhibition functions are described by Hill functions (Hill, 1910), sigmoidal curves used to describe influences between elements of a system. They measure the influence of an element on a target, depending on the concentration of the affecting element x, an exponent m to control the curve steepness, and on the mean point of influence  (h+ (x, , m) = xm /(xm +  m ) for activation and h− (x, , m) = 1 − h+ (x, , m) for inhibition). Although Hill functions have their origin in biochemistry to describe the cooperative binding of oxygen to hemoglobin (Hill, 1910), they have applications in diverse areas such as pharmacology (Goutelle et al., 2008) or thermodynamics (Langmuir, 1916). Currently the metabolic control of gene regulatory networks is being considered as a way to obtain indirect interaction between genes, to obtain better descriptions of the underlying behaviors. In Baldazzi et al. (2010), it is divided between fast processes, such as enzymatic actions and complex formations, and slow processes such as proteins synthesis and degradation. So, the effect of metabolic processes is included within the gene regulatory networks by implicit functions that describe the fast dynamics of the metabolites and enzymes. In the theory, this idea works fine, but in the practice one can obtain only boolean answers: at each time genes are expressing or not. Our approach, here explained, could allow us to connect the activation of metabolic pathways with gene regulatory networks to obtain continuous models of the genes activity. To connect the activation of the pathways with the regulatory model, we consider stimulus coefficients that change their values to stimulate the expression of specific target genes as answer to the activation of the associated pathway. We describe regulatory systems by combining continuous models, given by ordinary differential equations, with discrete models that control instantaneous coefficients changes. That is to say, we use Switched systems (Branicky, 1994; Shorten et al., 2005; Tavernini, 1987) which includes possible stochastic or nondeterministic changes in the differential equations and allow the interaction between the different regulatory systems. The stimulus processes generate changes on other model by changing coefficients associated with the so-called mode variables into the continuous models. The dependent variables of the model are called state variables, while continuous and discrete factors are considered controllers. These systems are described using a mixture of continuous, discrete dynamics and logical relations to allow multiple interacting components. In switched systems, the continuous dynamics are described by ordinary differential equations whose solution over time depends on the initial conditions. The discrete dynamics are given by the evolution of the mode variables (Assar, 2011). 3.2. Combining models by composition. 3. Theory and calculation 3.1. Gene Regulatory Networks and Switched Systems In the Gene Regulatory Networks approach, for a given gene, we associate logic relations to define what other genes promote its expression and which additional genes inhibit it. These modulations depend on the expression of all of these genes: if the expression of a gene is sufficiently high (the gene is active) it promotes (or inhibits) the expression of its target gene (Gebert et al., 2007; De Jong, 2002). Here, we use ordinary differential equations to model Gene Regulatory Networks (Gebert et al., 2007; De Jong, 2002). Many approximations are needed to use this type of model: mRNA. To model this system we consider the Systems Biology point of view (Kitano, 2002). With this approach, to perceive behaviors that emerge from the interaction of many individual biological processes, complex behaviors, it is necessary to combine all these different processes within a model that describes the complete system. We can consider two possibilities: building a new model, or combining the individual models of each process. We opt for the second option, in which we reuse the knowledge accumulated in previous research. The combination of validated models allows us to be confident about the accuracy of individual models, also gives us a task to establish the interactions correctly. The process of combining models is difficult. It is necessary to have a common vocabulary for the models, after that one needs.

(5) R. Assar et al. / BioSystems 108 (2012) 63–72. to define the relations between them, then finally the combined model is built. The first step is approached by Sabetzadeh et al. (2007); with which one can merge different models but the automatic detection of relations is not considered yet. In our case, the modeler can consider two types of relations between models: input–output connections, and synchronizations. The notion that allows us to combine different models is the so called Composition (Maus et al., 2008). As a result, we can describe systems with hierarchical relations and different control levels, considering models with different complexities and timescales. The input–output connections are flow assertions and allow us to build consistent models; if two sub-models share a state variable, we impose that such a variable has the same value in both models (see Section 2.4). The synchronization relation allows us to connect behaviors in any hierarchy level for controlling interactions between processes. Synchronizing two changes, we associate different processes by imposing that the occurrence of a specific change in one process coincides with the occurrence of another change in the other one. In our case, the activation of a stimulatory process (e.g. the Wnt pathway) provokes a change in the affected process (the differentiation into osteoblasts). Input–output relations allow us to transmit signals from one process to other (e.g. Wnt pathway active transmitted to the process of differentiation into osteoblasts). As was explained before, we opt for reusing validated models (Assar, 2011). Moreover, we reuse models without rewriting them. The rewriting of models consumes time, increases the possibility of mistakes and is not practical. If we do not have access to one model but to the state variables values computed (e.g.: executing software) rewriting is not possible. An important question arises at this point, what about the internal values of the individual model? We understand the modeling process as composed by different hierarchical steps. The first step consists in the selection of the system to study, the factors and the conditions. Our system is composed by osteoblasts, adipocytes and precursor cells. We study its temporal behavior (its dynamics), which is affected by regulation mechanisms such as the activation of the Wnt pathway or the expression of PPAR. About the conditions, for the final model we consider adult human cells, specific dynamical parameters of differentiation to be adjusted and initial conditions for each lineage. At the second step we take the individual validated models. The internal parameters of each model are chosen in function of the global conditions. In our case, to describe human cells we need models parameterized for human cells. At the third step we describe the interactions between the models: activations and repressions of different lineages.. Fig. 3. Osteo-adipo switch differentiation model. The expressions of two mutually inhibiting genes (RUNX2 and PPAR) are associated to the osteoblast and adipocyte lineage decision respectively, and a third bio-marker (OCT4 or SOX2) detects osteoadipo progenitor cells. Rounded rectangles in yellow denote the cell and its nucleus, green boxes denote genes and proteins, and arrows correspond to expression (→) and inhibitions (). If the canonical Wnt pathway is active (stimulated by lithium in pink box), the ␤-catenin complex goes to the nucleus to promote the expression of RUNX2, cooperating with TCF and other transcription factors (white boxes). The activation of the PPAR stimulates the formation of adipocytes (gray box). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.). bio-markers (e.g. OCT4, SOX2 or both, MacArthur et al., 2008) is associated with maintenance in the uncommitted state that prevents the expression of RUNX2 and PPAR. The concentration of mRNA associated with the progenitor state is denoted xP , the mRNA concentration of the osteogenic state is denoted xO and that associated with the adipogenic differentiation is denoted xA . To incorporate the extracellular pro-differentiation, proosteogenic and pro-adipogenic stimuli, we considered three inputs: zD , zO and zA with positive value. The effects that promote or inhibit expressions of regulated genes are incorporated by using variants of the common Hill functions. The model is represented by Eqs. (1)–(3). We have not considered the white noise introduced in the osteo-chondro switch model reported by Schittler et al. (2010).. ẋP (t) =. ẋO (t) = 4. Our models Our approach is based on reusing and composing validated models of cell division, differentiation and apoptosis to build a consolidated model that explains the interactions that lead to bone and fat formation. As shown in Fig. 1, the models explained in Section 2.2 are connected by input–output relations that allow us to incorporate activation effects and repression effects. 4.1. The osteo-adipo switch model Based on the osteo-chondro differentiation model by Schittler et al. (2010) (Fig. 2) and the results described in Chen et al. (2010), we developed the osteo-adipo switch model shown in Fig. 3. Progenitor cells differentiate into osteoblasts (bone cells) or adipocytes (fat cells). We associate two mutually exclusive genes (RUNX2) and (PPAR) with engagement to the osteogenic or the adipogenic differentiation, respectively. Expression of progenitor. 67. ẋA (t) =. aP · xPn + bP. mP + zD + cPP · xPn. − kP · xP ,. n +b +z aO · xO O O. n +c n n mO + cOO · xO OA · xA + cOP · xP. aA · xAn + bA + zA. n +c n mA + cAA · xAn + cAO · xO AP · xP. (1). − kO · xO ,. (2). − kA · xA ,. (3). With n = 2, aP = 0.2, bP = 0.5, mP = 10, cPP = 0.1, kP = 0.1, aO = aA = 0.1, bO = bA = 1, mO = mA = 1, cOO = cAA = cOA = cAO = 0.1, cOP = cAP = 0.5, kO = kA = 0.1 known parameters. As explained in Schittler et al. (2010), n = 2 is the lowest Hill coefficient producing a sigmoidal shape of the activation term; aP , aO and aA are the rate of autoactivation in formation of promoters, osteoblasts and adipocytes respectively; bP , bO and bA correspond to basal activity in such formations; mP , mO , and mA are related to the inflection points of each dynamics; kP , kO and kA are the decay rates per unity of concentration; and finally the coefficients cPP , cOO , cAA , cOA , cAO , cOP , cAP denote, depending on the sub-indexes, self-inhibition strengths or mutual inhibition strengths between the different differentiation states..

(6) 68. R. Assar et al. / BioSystems 108 (2012) 63–72. 4.2. The osteo-adipo switch model: including the Wnt pathway as a stimulus for bone cell differentiation The activation of the Wnt/␤-catenin pathway stimulates the expression of RUNX2 (Krishnan et al., 2006) and therefore, bone cell differentiation (Krishnan et al., 2006; Lian et al., 2003). We introduced to the main osteo-adipo switch model (Eqs. (1)–(3)) the activation of the canonical Wnt pathway as positive stimulus for bone formation (Fig. 2) and the activation of the PPAR pathway that favors the adipocyte lineage. We build a composed model in which the coefficient zO represents the activated state (it takes value 1) when the concentration of ␤-catenin is sufficiently high, and zA represents the activated state when the PPAR pathway is turned on. As shown in Fig. 3, the Wnt pathway can be externally activated by incubation of cells with lithium as well as by other treatments (Cai et al., 2010; Hoeppner et al., 2009; Arrázola et al., 2009). The differentiation stimuli into specific lineages are separately modeled and connected with the main osteo-adipo switch model by considering stimuli coefficients of the main differentiation model as functions of the activation of the pathways. We build the osteo-adipo switch model connecting by composition the canonical Wnt pathway model and a probabilistic model for the PPAR-pathway with the main osteo-adipo switch model, hence simulating in the system the presence of a biological stimulus that produces either bone or fat cells (Fig. 3). We considered that the concentration of the ␤-catenin/TCF complex is sufficiently high to promote osteoblast lineage when it reaches 1.1 times its normal value (8.81 nM). That is to say, we assume that the concentration in the inactive state has a deviation of 0.1 times the mean, and we say that the pathway is active (rejecting the null hypothesis) if the concentration overcomes that threshold. So, if the pathway is active, we impose zO = 0.8 in the main differentiation model. 4.3. The cell fate decisions model Finally, we propose a consolidated model that describes cell fate decisions of bone precursor cells by considering division, differentiation and apoptosis models. We designate this as the cell fate decisions model (Fig. 1(B)). It connects the dynamic models of division and differentiation described here, with lineage-stimuli and apoptosis models. We consider as apoptosis stimulus the increase of homocysteine (Hcy) that leads to apoptosis of progenitors and osteoblasts (Kim et al., 2006). According to results obtained in HS5 osteoblastic lineage and primary human bone marrow stromal cells (both lines from ATCC, Manasas, VA, USA), when the concentration of Hcy is 10 ␮M the apoptosis rates of osteoblasts (kO ) and precursors (kP ) are increased in 47% and 41% respectively on the osteo-adipo switch model (Eqs. (1)–(3)). Therefore, our model for osteo-adipo progenitor cell differentiation is the result of the interaction of multiple regulatory models. The DIFFERENTIATION node defines the dynamics in the concentrations of progenitor xP , osteoblast xO , and adipocytes xA by a system of ordinary differential equations. The STIMULI node defines the switches of the differentiation model by giving the values of the input parameters to DIFFERENTIATION (codes for Fig. 4, in Supplementary material). Transitions in the STIMULI node are controlled by the different models that regulate cell division, apoptosis and differentiation considered here. Each one of these regulatory models describes the dynamics of the signals that trigger these decisions. First, the cell division rate of progenitor cells aP (input of the main osteo-adipo differentiation model) depends on the period between divisions and is considered a parameter. Apoptosis of osteo-adipo progenitor cells and osteoblasts are stimulated by increasing Hcy (homocysteine) that promotes apoptosis of osteoblasts by switching kO to 1.47 · kO , and of progenitor cells by. switching kP to 1.41 · kP . Differentiation begins after an exponential time with mean of 100 min (zD is switched to 1). The activation of the canonical Wnt pathway stimulates osteoblast lineage in the period of 500–1000 min after the process is initiated (zO is switched to 0.8), and the activation of the pathway of PPAR (exponential distribution with mean 1333 min) stimulates the adipocyte lineage (zA switched to 0.8). 4.4. Adjusting the model to human cells Using our cell fate decisions schema (Fig. 1(B)), we adjusted parameters (of differentiation and division period) to represent the behavior of adult human bone precursor cells by assuming conditions according to the literature: the doubling time of precursor cells is 86 h (De Ugarte et al., 2003), for osteoblasts is 72 h (observed in HS-5 cells, Schmidmaier et al., 2006) and for adipocytes is 78 h (observed in liposuctioned adipose tissue, De Ugarte et al., 2003). For adjusting the apoptosis coefficients, we considered that precursor cells have a lifespan between 6 and 9 months, osteoblasts have lifespan of 3 months (Manolagas, 2000) and the relative rate of adipocytes death is 10% per year (mean age of 10 years, Arner et al., 2010). 5. Results We analyze the results of our osteo-adipo switch model and cell fate model explained previously. All the BioRica codes were included in Supplementary material. The osteo-chondro switch and the osteo-adipo switch models (Fig. 4(A) and (B)) were implemented by defining a BioRica node to describe the differential model (DIFF) and another one to describe the stimuli (STIMULUS) by computing the values of the parameters z. The node MAIN describes the input–output connections between both nodes. By comparing the results for each model, we show the new elements sequentially included (see Section 5.4). We go from the osteochondro switch model to our osteo-adipo switch model; and from this one to our cell fate decisions model in which we included all the stimulus here considered. The results for the osteo-chondro switch model by Schittler et al. (2010) are used as validation (Fig. 4(A)). In the case of the final consolidated model, the parameters are adjusted and apoptotic signals are incorporated by external changes in the differentiation model (see Fig. 4 and Supplementary material). We finish by comparing the results, showing how our model allows us to incorporate each new regulation mechanism here considered, discussing the advantages and difficulties of our approach (Section 5.4), and biological insights we gained (Section 5.5). 5.1. Osteo-chondro switch model For the scenarios analyzed in the osteo-chondro switch model described in Schittler et al. (2010) (Fig. 2), we obtained similar results, but our representation provides flexibility to the model. For example, in Fig. 4(A) we consider another scenario, where pro-differentiation, pro-osteogenic and pro-chondrogenic stimuli occur with exponential probabilities over time (Poisson process, Wilkinson, 2006). This corresponds to a switched system, in which delay times have random behaviors. We considered three possible switches: the system can be stimulated to favor the differentiation of progenitor cells, and to decide one or another lineage specification. Near 100 min after initiated the process differentiation is activated. The concentration of progenitor cells decreases and the concentrations of osteoblasts and chondrocytes increase. At approximately 250 min the formation of chondrocytes is stimulated, the concentration of SOX9 (xC ) strongly increases, the concentration of osteoblasts (xO ) decreases and becomes.

(7) R. Assar et al. / BioSystems 108 (2012) 63–72. 69. Fig. 4. Simulation results. D.xp denotes the concentration of progenitors, D.xo osteoblasts, D.xc chondrocytes, D.xa adipocytes. (A) Osteo-chondro switch differentiation model in Schittler et al. (2010). Stimuli included by a probabilistic scenario. (B) Osteo-adipo switch model: including the activation of the canonical Wnt pathway as stimulus to the osteoblast lineage, and activation of the PPAR to stimulate the adipocyte lineage. (C) Cell fate decisions model: apoptosis stimuli are added to (B).. stable. After approximately 1000 min the formation of osteoblasts is stimulated, its concentration increases and decreases the concentration of chondrocytes. After these transitions, the concentrations became stable. 5.2. Osteo-adipo switch model We incorporate into the osteo-adipo switch model, with Eqs. (1)–(3), the activation of the Wnt pathway as stimulus to bone. formation (Fig. 3, results in Fig. 4(B)). We automatically translate the SBML model by Kim et al. (2007) (BioRica node WNT) to use the activation of the canonical Wnt pathway as stimulus to express RUNX2 to favor differentiation into osteoblasts. We detect its activation by measuring the concentration of nuclear ␤-catenin/TCF. We consider that the pathway is active if it is sufficiently high (1.1 times its normal value in state inactive). The activation of the PPARpathway is simulated by a Poisson process (Wilkinson, 2006) with mean 1000 min..

(8) 70. R. Assar et al. / BioSystems 108 (2012) 63–72. As shown in Fig. 4(B), the system responds to the differentiation stimuli by changing its behavior. Initially, the expression patterns of progenitor-, osteoblast- and adipocyte-state bio-markers increase (variables xP , xO , xA ). After near 100 minutes the differentiation is stimulated: xP decreases until becoming stable while xO and xA increase with the same rate. After that (near 500 min) the Wnt signal (␤-catenin/TCF complex sufficiently high) is received to stimulate the bone formation: xO increases its growth while xA decreases. Finally, near 700 min the PPAR-pathway is activated: xA increases while xO decreases until both concentration becoming stable. 5.3. Consolidated model: the cell fate decisions model Next, we estimated the dynamics of osteo-adipo progenitor cells, osteoblasts and adipocytes, in response to division stimuli, favoring each lineage specification (bone or fat formation), as well as to apoptosis stimuli. We show percentages of osteoblasts, adipocytes and progenitors relatives to the initial quantity of progenitors (Fig. 4(C)). It was considered that initially there is a high presence of progenitors and absence of adipocytes and osteoblasts. As shown in Fig. 4(C), the decrease of progenitor cells due to the differentiation stimulus is favored, arriving to the end, by the apoptotic action of Hcy. Adipocytes exhibit higher growth rates than osteoblasts, but bone formation is favored by the activation of the Wnt pathway near 500 min. The formation of fat is stimulated following around 600 min of the PPAR pathway activity. Dynamical parameters of differentiation were adjusted to conditions as explained in Section 4.4. 5.4. Advantages and limitations Each model here described reflects a different level of complexity. The original osteo-chondro switch model, allows us to describe the differentiation system from osteo-chondro precursor cells into osteoblasts and chondrocytes as a switched system depending on the values of the pro-differentiation, pro-osteogenic and prochondrogenic coefficients, but it does not incorporate a description of the dynamics of such stimuli. Thus, our first approach, the osteoadipo switch model, includes a stochastic description of these stimuli, but this description is yet too distant to the reality. The inclusion of a model describing the activation of the Wnt pathway (Kim et al., 2007) into the osteo-adipo switch model, and the inclusion of an apoptotic stimulus model (Kim et al., 2006) into the final cell fate decisions model allows us to incorporate real biological stimuli that affect our system. While in Fig. 4(A), with the osteo-chondro switch model, we observed the effect of the stimuli to differentiation and each differentiated state, with the osteo-adipo switch model (Fig. 4(B)) we incorporate how biologically to control the differentiation stimuli. In particular, we describe the way by activating the osteogenic stimulus by the Wnt pathway. The cell fate decisions model allows us to incorporate the biological effect of apoptotic signals (model by Kim et al. (2006)), on progenitors and osteoblasts, into the differentiation models. With these considerations, we advance to obtain an integrated model of the differentiation process that considers the factors affecting its dynamics. With our approach, the system behaviors emerge from the interaction of all the processes (Systems Biology, Kitano, 2002). We described the system by modeling each individual process, reusing models, and describing the interactions between them given by activations and repressions (Section 3.2). The activation or inhibition of the Wnt signaling pathway, the PPAR expression, the division of progenitor cells, and the apoptosis of progenitor or osteoblast cells, work as a whole to generate osteoblasts and adipocytes from precursor cells.. There are many complicated points in our approach. To incorporate stimulus factors, we need a priori knowledge about relevant differentiation factors, their models or biological insights about them, and the effect on the differentiation process. That is to say, we need to build models (not necessarily deterministic) and describe the interactions between them. A favorable point is that most of important biological processes are described in the well known SBML format, but interactions between models are not documented and finding them is the key. In our particular application, the situation is better than general case. Some relevant factors of the osteo-adipo differentiation process are documented in literature, and SBML specifications here were reused. We are finding specifications of other differentiation factors, and their effects on the process. Another potential complicated point is the consideration of chaotic models: parameter changes can provoke uncontrolled changes on the dynamics. To avoid this problem, we considered changes in specific coefficients. In Schittler et al. (2010) was done an analysis of specificity, and they determined how to incorporate changes in differentiation conditions by specific changes in pro-differentiation and pro-differentiated states coefficients. Such changes provoke controlled changes in the dynamics for arriving to specified stationary states: progenitor state, one cell lineage (osteoblasts), the other cell lineage (adipocytes in our case). One of the most difficult points is the biological validation. In this paper we adjusted the model by considering the literature information about differentiation, division and apoptosis, as explained in Section 4.4. However, the accuracy of such biological validation is not sufficiently strong due to the diversity of cultures. We consider that it is necessary to re-adjust the parameters with stricter accuracy to allow the interacting models effectively describe the system behavior. With future experiments we want to adjust the normal proportion of cells that differentiate into osteoblasts respecting to adipocytes and the ability of the Wnt pathway to selectively stimulate the expression of RUNX2, and by taking advantage of reagents like RGZ (rosiglitazone) that have been shown to activate the PPAR pathway and induce adipocyte formation (Wei et al., 2010), it will be possible cross-link the effects generated by the activation of both signaling pathways. 5.5. Biological insights In previous sections we discussed how the combination of models allows us to represent the complexity of the differentiation process, but what about the biological insights that we obtained here? Well, we summarize in three gained points: a strategy for including different factors affecting the osteo-adipo differentiation process, the observation in silico of the effect well known in vivo and in vitro of the activation of the Wnt pathway, PPAR pathway, and apoptosis regulation on this differentiation process, and the analysis of the combined effect of all these regulation mechanisms. We described a strategy for including different types of factors relevant in the osteo-adipo differentiation process. The approach here presented is adapted to the Systems Biology paradigm, it allows to combine different types of regulation mechanism by means of reusing their models and describing their effects on the osteo-adipo differentiation process. As explained in Section 5.4 this approach can be used to improve our model by including new relevant factors. The use of the BioRica framework (Section 2.4) allows us to simulate the dynamic of the process, and it adapts to our requirements. The second gained point is more related with the application of this strategy, and with our final objective: building a model capable of predicting how to regenerate bone tissues. We were capable of describing in this in silico description biological facts about the important role of the Wnt pathway in osteoblastogenesis,.

(9) R. Assar et al. / BioSystems 108 (2012) 63–72. and other relevant factors in osteo-adipo differentiation which are described in literature, tested in vitro and in vivo. The integration of all these mechanisms allows us to go beyond. With our approach it is possible to analyze the combined action of all these mechanisms relevant for regulating differentiation, looking for new treatments for bone mass disorders. We consider that this approach is our first step to predict in silico the formation of osteoblasts starting from osteo-adipo precursor cells by modulating the Wnt pathway, and regulating cell division, death rates and other relevant factors. The next challenge is major: accurately adjusting the parameters and including models of other not controlled differentiation factors. By considering the same approach, combining validated models, is possible to incorporate such stimulus models. In vivo or in vitro activations of the Wnt pathway, and controlling the other relevant factors, make possible to study the feasibility of this way of treatment for the bone formation stimulation.. 6. Conclusion and discussions We have modeled the dynamics of cell fate decisions when going from osteo-adipo progenitor cells to bone (osteoblasts) and fat (adipocytes) cells. Bone and fat formation are controlled by many connected processes. Progenitor cells divide, differentiate into osteoblasts or adipocytes, or die, depending on regulatory processes. With the models here presented we can predict the changes in bone and fat formation by stimulating (or inhibiting) the Wnt pathway, the PPAR pathway, the division of progenitor cells, and the apoptosis of progenitor or osteoblast cells. This model is our first phase to simulate physiological responses to treatments for bone mass disorders in silico, and to explore the efficiency of new medical strategies before testing them in mice or other animals in vitro or in vivo. In this first phase we validated our model by observing some qualitative results that agree with the expected behaviors. The activation of the Wnt pathway provokes the differentiation to the osteoblast lineage, while the activation of the PPAR- pathway provokes the selection of the adipocyte lineage. Apoptosis of bone precursor cells or osteoblasts also have the expected effects. We adjusted parameter values for adult human cells according to data in the literature (Manolagas, 2000; De Ugarte et al., 2003; Schmidmaier et al., 2006; Arner et al., 2010), but for specific culture conditions of osteo-adipo progenitor cells, it may be necessary to re-adjust these parameters with stricter accuracy to allow the interacting models effectively describe its behavior. We may have to adjust the normal proportion of cells that differentiate into osteoblasts with regard to adipocytes and the ability of the Wnt pathway to selectively stimulate the expression of RUNX2. Also, by taking advantage of reagents like RGZ (text itrosiglitazone) that have been shown to activate the PPAR pathway and induce adipocyte formation (Wei et al., 2010), it will be possible cross-link the effects generated by the activation of both signaling pathways. In the future, we will continue with this quantitative validation. With regard to the theoretical basis, we used validated models of individual processes based on regulatory networks, switched systems to include stimuli effects, and composition between components to describe the interactions between the regulatory processes. We code, simulate and compose models using the BioRica framework (BioRica). BioRica allows us to describe switched systems, to reuse models described by the popular SBML format (Hucka et al., 2010) providing higher flexibility to make future improvements and to reuse models. Two important limitations of our approach are the modeling difficulties for the merging process, and the potential apparition of chaotic behaviors. Fortunately, both elements here were avoided. We supported the combination process of models by the biological knowledge about important. 71. factors in osteo-adipo differentiation, and the specific effects on the osteo-adipo switch model (Section 3.2). The coefficient changes we introduced in such differentiation model, affecting pro-differentiation and pro-states coefficients and rates, have controlled effects on the dynamics (Section 5.4). To begin with cell differentiation, we have proposed the osteo-adipo switch model. Here, we consider the gene RUNX2 as bio-marker for the osteoblast lineage and PPAR for the adipocyte lineage (Fig. 3). Moreover, we introduced the canonical Wnt pathway to externally simulate a stimulus to the osteoblast lineage commitment, while the adipocyte lineage was stochastically simulated. As a result, we obtained a way to estimate the stimulatory effect of Wnt/␤-catenin and PPAR on bone and fat formation in silico. By means of these stimuli, we can switch the differentiation process to favor bone or fat formation and to analyze treatments developed to prevent or reduce bone mass disorders such as osteoporosis. Finally, we have considered a more complete description of the process of bone formation: the cell fate decisions model. We propose (Fig. 1) a composed model that includes four essential cell processes: cell growth, cell division, cell differentiation and apoptosis. Our consolidated model, the cell fate decisions model (Sections 4.3 and 5.3), integrates the Wnt pathway-mediated (Kim et al., 2007) stimulation of the osteoblast lineage commitment, programmed cell death (Kim et al., 2006), and stochastic models to stimulate generic differentiation of the adipocyte lineage. Importantly, we can adjust this model to simulate the effect for combining these regulation mechanisms and including other factors, such as aging, on the differentiation process. While children show high tendency to regenerate bone, this process is slower in adults, who in turn form fat tissue with higher facility (Brockstedt et al., 1992; Stenderup et al., 2003). Therefore, this paradox could be assessed by incorporating the aging factor in the control functions z of our main osteo-adipo switch model. As a primary step, in this paper we have initially considered only a limited set of regulatory events during cell fate commitment but the process is more complex. There are many other factors that affect life and death of bone cells (Manolagas, 2000; Bilezikian et al., 2002). Also, in the case of apoptosis, it is well known that factors such as the protein sclerostin (a bone morphogenetic protein that functions as a BMP antagonist) produce marked increase in caspase activity and apoptosis of human mesenchymal stem cells (Sutherland et al., 2004). The tumor suppressor protein p53 is involved in apoptosis too. MacArthur et al. (2008) have presented an alternative model to explain differentiation towards osteoblasts, chondrocytes and adipocytes. They define a pluripotency circuit (provided by OCT4, SOX2 and NANOG) to regulate precursor cells, which interacts with a mutually inhibiting network (provided by RUNX2, SOX9 and PPAR) to regulate each lineage. In that case, stimuli are simulated by switching coefficients of the model and it is possible the same inclusion of stimuli models performed here. There are other bone formation phases to model too. We do not consider in our simulations the process of bone remodeling. Osteoclasts, in contrast to osteoblasts, are responsible of bone resorption. Osteoblasts form bone by differentiating into osteocytes or lining cells (Manolagas, 2000). As reported earlier (Krishnan et al., 2006) the canonical Wnt pathway has also a regulatory role in all these aspects of bone remodeling. The bone tissue formation is consequence of all these phases. Acknowledgments RA was supported by the INRIA on a CORDI-S fellowship. RA thanks Daniella Schittler at Institute for Systems Theory and Automatic Control of the University of Stuttgart for sharing ideas that motivated this work..

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Figure

Fig. 1. Cell fate decisions: from progenitor cells to osteoblasts and adipocytes. The symbol → denotes stimulus effects,  inhibition
Fig. 1. Cell fate decisions: from progenitor cells to osteoblasts and adipocytes. The symbol → denotes stimulus effects,  inhibition p.3
Fig. 2. The osteo-chondro switch differentiation model by Schittler et al. (2010).
Fig. 2. The osteo-chondro switch differentiation model by Schittler et al. (2010). p.4
Fig. 3. Osteo-adipo switch differentiation model. The expressions of two mutually inhibiting genes (RUNX2 and PPAR) are associated to the osteoblast and adipocyte lineage decision respectively, and a third bio-marker (OCT4 or SOX2) detects  osteo-adipo pr
Fig. 3. Osteo-adipo switch differentiation model. The expressions of two mutually inhibiting genes (RUNX2 and PPAR) are associated to the osteoblast and adipocyte lineage decision respectively, and a third bio-marker (OCT4 or SOX2) detects osteo-adipo pr p.5
Fig. 4. Simulation results. D.xp denotes the concentration of progenitors, D.xo osteoblasts, D.xc chondrocytes, D.xa adipocytes
Fig. 4. Simulation results. D.xp denotes the concentration of progenitors, D.xo osteoblasts, D.xc chondrocytes, D.xa adipocytes p.7

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