Hydrodynamics for Simple Fluid Quantitatively Describes the Flow Dynamics in C. Elegans One-Cell Stage Embryo

Abstract

Cytoplasmic streaming refers to hydrodynamic flow inside the cell. The rheological property of the cytoplasm has been an important subject in biophysics. Here, we show the rheology for simple fluid is sufficient to describe the dynamics of cytoplasmic streaming in the Caenorhabditis elegans one-cell stage embryo. Near the cell surface, the streaming transports materials into anterior direction (cortical flow), whereas in the central region of the cell, the streaming transports materials into posterior direction (cytoplasmic flow). Both flows depend on myosin. Myosin meshwork on the cell surface migrates into the anterior direction and generates cortical flow. We assumed that the migration of myosin on the cell surface is driving cytoplasmic flow through the hydrodynamic property of the cytoplasm. On that assumption, we tested if the rheology for simple fluid is sufficient or not, for describing flow dynamics. We conducted live-cell imaging and fluid dynamics simulation for simple fluid. The flow of GFP-labeled yolk granules were imaged with confocal microscopy. The flow velocity distribution was quantified with the image processing method, particle image velocimetry (PIV). The quantified in vivo velocity distribution was compared with that in simulation of Newtonian fluid dynamics. For simulation method, moving particle semi-implicit (MPS) method was chosen, since it enables us to simulate flow in deforming cell easily. We found qualitative and quantitative agreement of flow dynamics in experiment with that in simulation. Furthermore, in simulation, we also recapitulated flow caused by pronuclear-movements in vivo. Collectively, our results indicate that hydrodynamics for simple fluid is a prominent coarse-graining model for describing cytoplasmic streaming (Niwayama et al., 2011, PNAS, 108: 11900-11905). Using this model and Bayesian statistical technique, we are currently trying to estimate the distribution of the forces which generate cytoplasmic streaming.