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

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

Estimation of shear-stress distribution in <i>C</i>. <i>elegans</i> embryos.

<p>(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.</p

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

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.

<p>(A) Comparison of shear-stress distributions of the <i>C</i>. <i>elegans</i> 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 <i>C</i>. <i>elegans</i> 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 <i>C</i>. <i>elegans</i> embryo. *P < 0.005 (t test, assuming non-equal variance).</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

Schema depicting flow fields of cytoplasmic streaming.

<p>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 <i>C</i>. <i>elegans</i> 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.</p

PLK1 is required for chromosome segregation, first polar body extrusion, and maintenance of the condensed state of chromosomes.

<p>(A) Experimental scheme. Oocytes were cultured for 6 hours in control medium, and then MG132 was added. The oocytes were incubated for 4 hours to arrest oocytes at the late metaphase I. After release from MG132, 100 nM BI2536 was added and oocytes were imaged. (B) Anaphase phenotypes after MG132 release in control and BI2536-treated oocytes. PB = the first polar body. (C) Imaging of securin-EGFP (green) and H2B-mCherry (red) after DMSO (control, top) or 100 nM BI2536 (lower panels) was added at the time of the MG132 washout. Each phenotype from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0116783#pone.0116783.g006" target="_blank">Fig. 6B</a> is shown on a representative image sequence. Arrows indicate lagging chromosomes. Note that none of the BI2536-treated oocytes undergoing abnormal chromosome segregation extruded the first polar body. Time after MG132 washout (h:mm). Scale bar = 30 μm. Also see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0116783#pone.0116783.s014" target="_blank">S7 Movie</a>. (D) Quantification of securin-EGFP destruction. Values were normalized to 1 when the imaging was started. Time relative to MG132 washout (h). The ‘BI2536 with anaphase’ curve represents BI2536-treated oocytes that underwent abnormal chromosome segregation either with or without DNA decondensation (3^rd and 4^th rows in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0116783#pone.0116783.g007" target="_blank">Fig. 7C</a>). The ‘BI2536 w/o anaphase’ curve represents BI2536-treated oocytes that did not undergo chromosome segregation (2^nd row in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0116783#pone.0116783.g007" target="_blank">Fig. 7C</a>). Average and s.d. are shown (n = 23, 40). (E) Degradation rate of securin-EGFP calculated from (D). Average and s.d. are shown. ***p < 0.001.</p

PLK1 is required for chromosome alignment.

<p>(A) Imaging of meiosis I in oocytes expressing EGFP-CENP-C (kinetochores, green) and H2B-mCherry (chromosomes, red) in the presence of DMSO (control) or 100 nM BI2536. Maximum intensity z-projection images are shown. White lines indicate kinetochore tracks over 5 timepoints. Time after NEBD (h:mm). Scale bar = 10 μm. Also see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0116783#pone.0116783.s011" target="_blank">S4 Movie</a>. (B) Kinetochore positions were determined from (A) and shown in the 3D plot as green spheres. Red bars connect homologous kinetochores. The view along the chromosome distribution equator (side view) is shown. Black arrowheads indicate misaligned chromosomes. Time after prometaphase belt formation (h:mm). The unit of the grid is 5 μm. (C) Chromosome positions along the estimated spindle axis were plotted for all twenty chromosomes of a single oocyte cultured in the presence of DMSO (control, black) or 100 nM BI2536 (red). (D) Distances between chromosomes and the equator at 0 and 2 hours after the prometaphase belt formation were potted. The box indicates 10–90 percentile (n = 60, 60, 60, 60 from three oocytes for each condition). ***p < 0.0001. (E) Oocytes 4 hours after NEBD were briefly treated with a cold buffer and fixed for immunostaining of microtubules (blue) and kinetochores (red). 100 nM BI2536 was added at 2 hours after NEBD. DNA was stained with Hoechst33342 (blue). Insets show magnified images of kinetochore-microtubule attachments. Scale bar = 10 μm. Average and s.d. of the population of unattached kinetochores are shown (n = 5, 5. **p < 0.01).</p

PLK1 localizes to MTOCs and kinetochores and becomes activated around NEBD.

<p>(A) Imaging of meiosis I in oocytes expressing EGFP-PLK1 (green) and 3mCherry-CENP-C (kinetochores, red). Maximum intensity z-projection images are shown. At 7:50, the saturated signal locates at the spindle midzone, as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0116783#pone.0116783.s001" target="_blank">S1A Fig.</a> Time after induction of meiotic resumption (h:mm). Scale bar = 10 μm. Insets show magnified images on kinetochores. Also see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0116783#pone.0116783.s008" target="_blank">S1 Movie</a>. (B) Immunostaining of active PLK1 phosphorylated on T210 (pPLK1) during meiosis I. Pictures represent single selected confocal sections through MTOCs for pPLK1 (fire-pseudocolored or green) and pericentrin (MTOCs, red) and maximum intensity z-projection for DAPI (DNA, blue). Arrowheads indicate pPLK1 signals on MTOCs. Time after induction of meiotic resumption (h:mm). Quantification of MTOC-associated pPLK1 signals (n = 11, 5, 7, 5, 5, 9, 17 oocytes). Averages with the 95% confidence intervals are shown. Scale bar = 20 μm. Insets show magnified images on MTOCs. (C) Localization of pPLK1 on kinetochores in metaphase I oocytes. Oocytes stained for pPLK1 (green), kinetochores (CREST, red), acetylated α-tubulin, and DAPI (DNA). Scale bar = 10 μm.</p