Tumor Biology Department, SRB3, Moffitt Cancer Center and Research Institute, 12902 Magnolia Drive, Tampa, FL, 33612, USA.
Oncology and Cancer Biology PhD Program, University of South Florida, Tampa, FL, USA.
Sci Rep. 2021 Mar 15;11(1):6055. doi: 10.1038/s41598-021-84888-1.
Bone-forming osteoblasts and -resorbing osteoclasts control bone injury repair, and myeloid-derived cells such as monocytes and macrophages are known to influence their behavior. However, precisely how these multiple cell types coordinate and regulate each other over time within the bone marrow to restore bone is difficult to dissect using biological approaches. Conversely, mathematical modeling lends itself well to this challenge. Therefore, we generated an ordinary differential equation (ODE) model powered by experimental data (osteoblast, osteoclast, bone volume, pro- and anti-inflammatory myeloid cells) obtained from intra-tibially injured mice. Initial ODE results using only osteoblast/osteoclast populations demonstrated that bone homeostasis could not be recovered after injury, but this issue was resolved upon integration of pro- and anti-inflammatory myeloid population dynamics. Surprisingly, the ODE revealed temporal disconnects between the peak of total bone mineralization/resorption, and osteoblast/osteoclast numbers. Specifically, the model indicated that osteoclast activity must vary greatly (> 17-fold) to return the bone volume to baseline after injury and suggest that osteoblast/osteoclast number alone is insufficient to predict bone the trajectory of bone repair. Importantly, the values of osteoclast activity fall within those published previously. These data underscore the value of mathematical modeling approaches to understand and reveal new insights into complex biological processes.
成骨细胞和破骨细胞控制着骨骼损伤的修复,而髓系细胞(如单核细胞和巨噬细胞)已知会影响它们的行为。然而,使用生物学方法很难解析这些多种细胞类型如何在骨髓中随时间协调和调节彼此,以恢复骨骼。相反,数学模型非常适合应对这一挑战。因此,我们使用从胫骨内损伤的小鼠中获得的实验数据(成骨细胞、破骨细胞、骨量、促炎和抗炎髓系细胞)生成了一个常微分方程(ODE)模型。仅使用成骨细胞/破骨细胞群体的初始 ODE 结果表明,损伤后骨稳态无法恢复,但在整合促炎和抗炎髓系细胞群体动力学后,该问题得到解决。令人惊讶的是,ODE 揭示了总骨矿化/吸收峰值与成骨细胞/破骨细胞数量之间的时间不连续。具体来说,该模型表明,破骨细胞活性必须有很大的变化(>17 倍)才能在损伤后使骨量恢复到基线,这表明仅成骨细胞/破骨细胞数量不足以预测骨修复的轨迹。重要的是,破骨细胞活性的值落在之前发表的值范围内。这些数据强调了数学建模方法在理解和揭示复杂生物学过程中的新见解的价值。