Bone remodeling in tissue engineering is a long-term physiological process that dynamically balances osteogenesis and bone resorption and re-distributes bone mass to match the external mechanical changes [1
]. This complex biological event involves intracellular signaling, stem cell driven lineage developing, and intercellular communications among various cellular phenotypes. A variety of systematic and local factors play important roles in such multi-scale signaling [4
]. Bone remodeling is especially critical to the success of tissue-engineered bone grafts. Failure to accumulate bone mass according to the physiological needs of mechanical strength will cause post-implantation bone fractures and poor outcomes. Personalized tuning of bone remodeling process is another challenge. For example, osteoporosis patients are often victims of bone fractures, and in their bone scaffolds the osteogenesis should be enhanced to overcome the patient hormone and cytokine environments that promote bone resorption. A flexible and tunable infrastructure which allows fine tuning of the bone remodeling process is required to meet the clinical needs.
This challenge can be potentially addressed by cytokine combination therapy which encapsulates multiple cytokines (or growth factors) into polymer nanospheres, expected to produce a better effect than the single factor. Recently our group [5
] and others [9
] have shown the capabilities of accurately and independently controlling drug release rates of individual growth factors and cytokines from the delayed slow-release hydrogels embedded in artificial bone scaffolds. Hydrogels are highly absorbent natural (e.g. hyaluronic acid) or synthetic polymers (e.g. polyvinyl alcohol, sodium polyacrylate, and acrylate polymers) that may possess a degree of flexibility very similar to normal tissue because of their considerable water. When used as scaffolds for bone tissue regeneration, hydrogels often contain human primary cells (e.g. osteocytes and endothelial cells) and growth factors or cytokines to repair bone tissue. Cytokines (e.g. BMP2, TGFβ and Wnt ligands) play an important role in osteogenic differentiation of MSC and bone remolding. Ideally key cytokines can be programmatically released into the micro-environments of the bone graft and guide desired bone remodeling [12
]. This study addresses the effects of optimally-combined cytokines after released from hydrogels on bone regeneration.
Osteoblast and osteoclast lineages are responsible for two competing but coordinated processes, bone formation and resorption, respectively, and thus profile the dynamic of bone remodeling. These two processes occur in a structure called basic multi-cellular units (BMU) [14
] at multiple sites in the skeleton as well as artificial scaffolds [1
]. Bone marrow mesenchymal stem cells (MSC) differentiate to pre-osteoblast, then osteogenic lineages, which are responsible for bone formation; while hematopoietic stem cells (HSC) differentiate to the pre-osteoclasts, and then osteoclasts, which govern bone resorption.
A number of mathematical models have been developed to describe the bone remodeling in recent years. Komarova et al. [15
] constructed a mathematical model to calculate cell population dynamics and changes in bone mass at a discrete site of bone remodeling, considering the autocrine and paracrine interactions among osteoblasts and osteoclasts. Lemaire et al. [16
] proposed another cell population model to explain the interactions between osteoblasts and osteoclasts by estabishing the intercellular signaling pathway RANK-RANKL-OPG. Then Pivonka et al. [17
] extended this pathway to study and theoretically explore the functional implications of particular RANK/OPG expression profiles on bone mass. Furthermore, Pivonka et al. [17
] used such models to investigate the possible therapeutic intervention to restore bone mass due to the imbalance of RANK-RANKL-OPG regulation [18
However, previous studies have often lacked an intracellular signaling and fell short on representing the intracellular molecular mechanism. Several molecular signals and mechanisms involved in the bone healing or remodeling have been revealed from in vitro
and/or in vivo
experiments. The osteoblast commitment, differentiation and functions are controlled by several transcription factors resulting in the expression of genes responsible for the osteoblastic lineage from MSC to pre-osteoblasts and then to active osteoblasts [19
], as described in
. Runt-related transcription factor 2 (Runx2) and Osterix (Osx) have been generally demonstrated to be two crucial transcription factors in osteogenic differentiation [19
]. Various cytokines, such as BMP2, TGFβ and Wnt ligands, can stimulate the expression of Runx2 and Osx through a variety of pathways [19
]. After the pathway is activated, Runx2 and Osx play different particular roles in different stages of osteoblastic lineage. Both Runx2 and Osx can promote the differentiation of MSC into pre-osteoblasts [19
], whereas Runx2 can inhibit the differentiation of pre-osteoblasts into active osteoclasts [19
Schematic illustration of intracellular and intercellular signaling and cellular dynamics in bone healing and bone remodeling
Moreover, only a few mathematical models have been developed to investigate the effect of cytokine therapy, especially cytokine combination therapy, for bone healing. Particularly, we are concerned with the following questions in the bone healing therapy. First, are the effects of cytokine combination better than those of single cytokine? Second, how do we evaluate the synergism of the cytokine combination therapies? Third, what are the most efficient dose and ratio of specific cytokine combination to achieve expected bone remodeling goals? To answer these questions, numerous candidate conditions should be examined for this complex system of multiple cell type, various cytokine candidates, and multiple time scales. Traditional biological experiments are expensive and time-consuming. Therefore, a systems biological model is required to best utilize our current knowledge of the bone remodeling process to explore in silico candidate conditions, screen out critical factors and key cytokines of the system, and guide the biological experiments.
This work was designed to build up a computational systematic model to study the combination effects of cytokines released from hydrogels including Wnt, BMP2, and TGFβ for controlling the balance of bone formation and resorption of implanted bone scaffolds based on the intracellular signaling pathway. We firstly developed a systematic model composed of a system of ordinary differential equations (ODEs) to describe the intracellular signaling pathway to regulate osteogenic differentiation. And then, we combined the intracellular signaling pathway with intercellular signaling pathway to control osteoclast differentiation. Next, we integrated the intracellular and intercellular signaling pathways into the cellular population dynamics described by a set of stochastic differential equations (SDEs) to simulate bone healing and remodeling. The unknown coefficients in the intracellular signaling pathway were estimated by fitting them to the dynamic experimental data [21
] using optimization algorithm. Finally, we investigated the response of cellular population dynamics to therapies of single or combined cytokines as well as quantitatively evaluated the combination effect of cytokines by Loewe and Bliss indexes.