Bayesian Inference of Forces Causing Cytoplasmic Streaming in <i>Caenorhabditis elegans</i> Embryos and Mouse Oocytes

<div><p>Cellular structures are hydrodynamically interconnected, such that force generation in one location can move distal structures. One example of this phenomenon is cytoplasmic streaming, whereby active forces at the cell cortex induce streaming of the entire cytoplasm. However, it is not known how the spatial distribution and magnitude of these forces move distant objects within the cell. To address this issue, we developed a computational method that used cytoplasm hydrodynamics to infer the spatial distribution of shear stress at the cell cortex induced by active force generators from experimentally obtained flow field of cytoplasmic streaming. By applying this method, we determined the shear-stress distribution that quantitatively reproduces in vivo flow fields in <i>Caenorhabditis elegans</i> embryos and mouse oocytes during meiosis II. Shear stress in mouse oocytes were predicted to localize to a narrower cortical region than that with a high cortical flow velocity and corresponded with the localization of the cortical actin cap. The predicted patterns of pressure gradient in both species were consistent with species-specific cytoplasmic streaming functions. The shear-stress distribution inferred by our method can contribute to the characterization of active force generation driving biological streaming.</p></div

Estimation of shear-stress distribution in mouse oocytes.

<p>Estimated shear-stress distribution (A), velocity distribution (B–D), and stress-velocity relationship for cytoplasmic streaming in mouse oocytes are shown as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159917#pone.0159917.g004" target="_blank">Fig 4</a> for streaming in <i>C</i>. <i>elegans</i>. 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.</p

Axial symmetry of cytoplasmic streaming in <i>C</i>. <i>elegans</i> embryos.

<p>(A) Scheme of 3D flow in <i>C</i>. <i>elegans</i> 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.</p

The DA method and a benchmark test.

<p>(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 <i>N</i>_{<i>Sample</i>} = ~120,000 patterns of the shear-stress distribution. (C) In the benchmark test, we tested if we could estimate the shear-stress distribution <i>τ</i>(<i>z</i>) = 3 × (1 − <i>z</i>²)^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.</p