Theoretical Biology Laboratory, RIKEN Advanced Science Institute, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan.
Phys Biol. 2012 Jun;9(3):036006. doi: 10.1088/1478-3975/9/3/036006. Epub 2012 May 4.
Cell movement and intercellular signaling occur simultaneously during the development of tissues, but little is known about how movement affects signaling. Previous theoretical studies have shown that faster moving cells favor synchronization across a population of locally coupled genetic oscillators. An important assumption in these studies is that cells can immediately interact with their new neighbors after arriving at a new location. However, intercellular interactions in cellular systems may need some time to become fully established. How movement affects synchronization in this situation has not been examined. Here, we develop a coupled phase oscillator model in which we consider cell movement and the gradual recovery of intercellular coupling experienced by a cell after movement, characterized by a moving rate and a coupling recovery rate, respectively. We find (1) an optimal moving rate for synchronization and (2) a critical moving rate above which achieving synchronization is not possible. These results indicate that the extent to which movement enhances synchrony is limited by a gradual recovery of coupling. These findings suggest that the ratio of time scales of movement and signaling recovery is critical for information transfer between moving cells.
细胞运动和细胞间信号传递在组织发育过程中同时发生，但对于运动如何影响信号传递知之甚少。先前的理论研究表明，运动速度较快的细胞有利于在局部耦合遗传振荡器的种群中实现同步。这些研究中的一个重要假设是，细胞在到达新位置后可以立即与其新邻居进行相互作用。然而，细胞系统中的细胞间相互作用可能需要一些时间才能完全建立起来。在这种情况下，运动如何影响同步尚未得到检验。在这里，我们开发了一个耦合相振子模型，其中我们考虑了细胞运动以及细胞在运动后经历的细胞间耦合的逐渐恢复，分别用移动速率和耦合恢复速率来描述。我们发现（1）存在一个最佳的同步移动速率，以及（2）一个临界移动速率，超过这个速率就不可能实现同步。这些结果表明，运动增强同步的程度受到耦合逐渐恢复的限制。这些发现表明，运动和信号恢复时间尺度之比对于运动细胞之间的信息传递至关重要。
