Fig 1.
Schema depicting flow fields of cytoplasmic streaming.
Cell boundaries are shown in black, and flow directions near the cell cortex and at the cell center are shown in blue and red arrows, respectively. (A) Cytoplasmic streaming in the C. elegans embryo. The myosin-II-enriched region is shown in green. (B) Cytoplasmic streaming in the mouse oocyte. The Arp2/3-enriched actin cap is shown in green, and the meiotic spindle is shown in orange. (C) Definitions for source and drain poles used in this study.
Fig 2.
The DA method and a benchmark test.
(A) Overall scheme for estimating the optimum distribution of stress. (B) Scheme used to automatically calculate optimum stress distribution using the DA method developed in this study. We used NSample = ~120,000 patterns of the shear-stress distribution. (C) In the benchmark test, we tested if we could estimate the shear-stress distribution τ(z) = 3 × (1 − z2)0.5 driving streaming in a sphere (black line). Estimation procedures were applied starting from a prior stress distribution (gray line). The result of the estimation is shown in red. The results converged to the correct answer, which is indicated by the black line. Dimensionless units were used for both the position and shear stress.
Fig 3.
Axial symmetry of cytoplasmic streaming in C. elegans embryos.
(A) Scheme of 3D flow in C. elegans embryos. Flow direction near the cell cortex and at the center are shown in blue and red arrows, respectively. (B, C) Flow field on a plane parallel (B) or perpendicular (C) to the AP axis; the field was quantified by PIV analysis carried out using SPIM images. White dotted ellipses approximately indicate the borders of the embryo.
Fig 4.
Estimation of shear-stress distribution in C. elegans embryos.
(A) The shear-stress distribution estimated based on the proposed method. The fitting was performed for six embryos (indicated using distinct colors). The horizontal axis shows the position along the drain (anterior)-source (posterior) axis, with 0 indicating the drain pole. (B) Color map of the flow field measured experimentally for an embryo (left) and that of the simulation performed using the shear-stress distribution estimated using data from the same embryo. The map was normalized relative to maximal velocity. (C, D) Velocity distribution along the central source-drain axis (C) and cell cortex (D) in vivo and in the simulation performed using estimated shear stress. Velocity component and position were projected onto the middle AP axis. In vivo and simulation data represent average values from six embryos and the corresponding six fitted simulations, respectively. Error bars represent one standard deviation (simulation: black; in vivo: gray). Velocities values are positive or negative when directed towards the source and drain poles, respectively. Average differences between in vivo and simulation velocities are indicated by gray triangles. (E) Velocity along the cell cortex in the simulation and in vivo at individual positions along the cell surface, plotted against estimated shear stress at the same position.
Fig 5.
Estimation of shear-stress distribution in mouse oocytes.
Estimated shear-stress distribution (A), velocity distribution (B–D), and stress-velocity relationship for cytoplasmic streaming in mouse oocytes are shown as in Fig 4 for streaming in C. elegans. The fitting was performed for seven mouse oocytes. The horizontal axis in (B–D) shows the position along the drain-source (actin cap) axis, with 0 indicating the drain pole.
Fig 6.
Shear-stress distribution in mouse oocytes contributes to the generation of a pressure gradient that enables the positioning of the meiosis II spindle near the cell surface.
(A) Comparison of shear-stress distributions of the C. elegans embryo and mouse oocyte showing that shear stress is localized closer to the cell periphery in the latter. (B) Pressure when flow is generated using the estimated shear stress plotted against source-drain position. The plot shows that the gradient is steeper when we assume the shear-stress distribution in the mouse oocyte rather than that in the C. elegans embryo in both spherical- and capsule-shaped cells. (C) Comparison of the pressure gradient at the source end in Fig 6B; the pressure gradient is steeper in the mouse oocyte than in the C. elegans embryo. *P < 0.005 (t test, assuming non-equal variance).