Reusing and composing models of cell fate regulation of human bone precursor cells
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 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/β-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 PPARγ (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/β-catenin pathway, repressing the expression of PPARγ, and repressing the stimuli to osteoblasts apoptosis. Despite the existing models for 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 PPARγ (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/β-catenin pathway (Kim et al., 2007) to stimulate the osteoblast lineage, and with a probabilistic model that describes the activation of the PPARγ 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.
Section snippets
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
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
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.
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
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 PPARγ pathway, the division of
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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