A Molecule Based Reaction-Transportation Model Explains the Oscillatory Migration of Zyxin-Depleted Human Fibrosarcoma Cells

Abstract

Cell migration is essential in biology, and it is closely related to biological functions such as wound healing, immune responses and cancer cell metastases. Without chemical or physical gradients, cells migrate randomly. Recently, the Wirtz lab discovered the large scale periodic cell migration of Zyxin-depleted human fibrosarcoma cells with period longer than 2 hours. These cells exhibit distinct regular oscillatory migration patterns in three-dimensional ECM and along one-dimensional chambers. Here, we present a reaction-transportation model based on a coarse-grained molecular picture of the process. Migrating cells have well-defined polarity and microtubules are known to play important roles. By explicitly incorporating k, we successfully reproduced the experimentally observed periodic migrating patterns. Our results suggest that, although diffusion and motor-based active material transportation (convection) both exist in cell, the periodic switching of cell's polarity is mainly due to the motor-based convection. Surprisingly, we discovered two distinct oscillatory phases: in the first phase, the polarization factors undergo simple and fast end-to-end oscillation, which would not lead to the observed large scale periodic migration; whereas in the second phase, the polarization factors not only oscillate between two cell ends but also generate vortex-like local patterns at either ends. These vortex-like patterns greatly elongate the period of the oscillation, which effectively stabilizes the migration in either direction, leading to the large scale oscillatory migration. Based on our model, the cell length dependences of various oscillatory characteristics have been predicted for future experimental verification. The identified two oscillatory phases may provide useful insights to the general picture of how cells alter direction during rather persistent migration, and the developed reaction-transportation model provides a general framework for studying the long-range cytoplasmic translation dynamics of any molecules.