Petrungaro Gabriela, Uriu Koichiro, Morelli Luis G
Instituto de Investigación en Biomedicina de Buenos Aires (IBioBA)-CONICET-Partner Institute of the Max Planck Society, Polo Científico Tecnológico, Godoy Cruz 2390, C1425FQD, Buenos Aires, Argentina.
Departamento de Física, FCEyN UBA, Ciudad Universitaria, 1428 Buenos Aires, Argentina.
Phys Rev E. 2019 Jun;99(6-1):062207. doi: 10.1103/PhysRevE.99.062207.
Individual biological oscillators can synchronize to generate a collective rhythm. During vertebrate development, mobile cells exchange signals to synchronize a rhythmic pattern generator that makes the embryonic segments. Previous theoretical works have shown that cell mobility can enhance synchronization of coupled oscillators when signal exchange is instantaneous. However, in vertebrate segmentation, the exchange of signals is thought to comprise delays from signal sending and processing, which could alter the effect of mobility on synchronization. Here, we study synchronization dynamics of mobile phase oscillators in the presence of coupling delays. We find that mobility can speed up synchronization when coupling delays are present. We derive an analytical expression for the characteristic time of synchronization dynamics, which is in very good agreement with numerical simulations. This analytical expression suggests a subdivision of the mobility range into different dynamical regimes and reveals that, with delayed coupling, synchronization is enhanced at a lower mobility rate than with instantaneous coupling. We argue that these results may be relevant to the synchronization of mobile oscillators in vertebrate segmentation.
单个生物振荡器能够同步以产生集体节律。在脊椎动物发育过程中，移动细胞会交换信号，以使生成胚胎节段的节律模式发生器同步。先前的理论研究表明，当信号交换是瞬时的时，细胞移动性可以增强耦合振荡器的同步性。然而，在脊椎动物分节过程中，信号交换被认为包含信号发送和处理的延迟，这可能会改变移动性对同步的影响。在这里，我们研究了存在耦合延迟时移动相位振荡器的同步动力学。我们发现，当存在耦合延迟时，移动性可以加速同步。我们推导出了同步动力学特征时间的解析表达式，该表达式与数值模拟非常吻合。这个解析表达式表明，移动性范围可细分为不同的动力学区域，并揭示出，与瞬时耦合相比，在延迟耦合情况下，较低的移动速率就能增强同步。我们认为这些结果可能与脊椎动物分节过程中移动振荡器的同步有关。
