Najafi J et al. (2023), Size- and position-dependent cytoplasm viscoela...

ECB-ART-51609

Proc Natl Acad Sci U S A 2023 Feb 28;1209:e2216839120. doi: 10.1073/pnas.2216839120.

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Size- and position-dependent cytoplasm viscoelasticity through hydrodynamic interactions with the cell surface.

Najafi J , Dmitrieff S , Minc N .

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Many studies of cytoplasm rheology have focused on small components in the submicrometer scale. However, the cytoplasm also baths large organelles like nuclei, microtubule asters, or spindles that often take significant portions of cells and move across the cytoplasm to regulate cell division or polarization. Here, we translated passive components of sizes ranging from few up to ~50 percents of the cell diameter, through the vast cytoplasm of live sea urchin eggs, with calibrated magnetic forces. Creep and relaxation responses indicate that for objects larger than the micron size, the cytoplasm behaves as a Jeffreys material, viscoelastic at short timescales, and fluidizing at longer times. However, as component size approached that of cells, cytoplasm viscoelastic resistance increased in a nonmonotonic manner. Flow analysis and simulations suggest that this size-dependent viscoelasticity emerges from hydrodynamic interactions between the moving object and the static cell surface. This effect also yields to position-dependent viscoelasticity with objects initially closer to the cell surface being harder to displace. These findings suggest that the cytoplasm hydrodynamically couples large organelles to the cell surface to restrain their motion, with important implications for cell shape sensing and cellular organization.

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	Fig. 1. Probing cytoplasm rheology at large length-scales. (A) Sea urchin unfertilized eggs injected with single 1-µm diameter beads, beads aggregate with diameters ranging from ~4 to 12 µm and large oil droplets containing hydrophobic beads. Calibrated magnetic forces were applied to translate these magnetized objects in the cytoplasm. The trajectories of the objects tracked at 1 Hz during force application (green) and force release (red) are overlaid on the cells, and also represented in time color coded graphs at the bottom of cells. (B) Representative displacement curves scaled by forces plotted as a function of time for beads, aggregates and magnetized oil droplets. Jeffreys viscoelastic model is depicted as an Inset in the graph for single beads, with representative constants overlaid on the curve. Solid lines are fits of Jeffreys model. (C) Normalized recoiling displacements plotted as a function of time for the same objects as in B. Note that the recoil of small beads toward their initial position is nondirectional due to intrinsic cytoplasm noise. (D–G) Cytoplasm viscoelastic parameters for objects of variant sizes computed by fitting creep and relaxation curves with Jeffreys model (n = 21, 15 and 18, respectively): viscous drags (D), restoring stiffness (E), viscoelastic timescale during the rising phase (F) and in the releasing phase (G). Error bars correspond to +/− SD. (Scale bars, 5 µm.)
	Fig. 2. Viscoelastic properties depend on cytoplasm crowding and bulk cytoskeleton networks. (A) Schematic of experiments in which cytoplasm crowding is modified by placing cells in hypoosmotic or hyperosmotic ASW. (B) Displacement curves scaled by forces during pulling phases, and normalized relaxation curves after force retraction for control (n = 18), hypoosmotic (n = 26), and hyperosmotic (n = 13) conditions for oil droplets. (C) Viscous drag, restoring stiffness, and viscoelastic timescale in the rising phase at different osmotic conditions. (D) Schematic of experiments in which F-actin or microtubule were depolymerized using Latrunculin B or Nocodazole, respectfully. (E) Viscoelastic drag, restoring stiffness, and viscoelastic timescale in the rising phase for controls (n = 18) and for eggs treated with Latrunculin B (n = 11) and Nocodazole (n = 19). Shaded areas represent +/− SEM and error bars correspond to +/− SD.
	Fig. 3. Experimental and theoretical mapping of cytoplasm flows created by the translation of large objects inside cells. (A) Schematic of a moving oil droplet and consequent viscoelastic flows. (B) Vector fields of cytoplasm flows obtained by PIV around a moving oil droplet at the beginning of the pulling phase, end of pulling, and beginning of the release phase overlaid on DIC images. (C) Scaled displacement curve of the pulling phase and normalized curve of the release phase for the same experiment as in B. Time points of temporal snapshots of the vector fields are indicated by color-coded circular markers on the curves. (D) Experimental streamlines and speed heat maps of cytoplasm flow for the same snapshots as in B. (E) Scaled displacement curve of the pulling phase and normalized release phase obtained from 3D finite-element simulations with input parameters taken from experimental measurements. (F) Numerical streamlines and speed heat maps of the same time points as in D in the mid-plane parallel to the pulling direction. Arrowheads in the simulations are proportional to the speed. (G) Profile of the cytoplasm velocity along the force x-axis for the experiment and simulation averaged along stripes passing through the oil droplet center as indicated in the flow maps in D and F. (Scale bar, 30 µm.)
	Fig. 4. Cell confinement enhances cytoplasm viscoelastic resistance in a nonlinear manner. (A) Viscous drag and restoring stiffness increase with the object size in a nonlinear manner, and deviate from linear Stokes’ law for confinement ratios larger than ~0.1. The red curve represents the analytical prediction for a confined Newtonian fluid, the blue line is the Stoke’s law with no confinement, gray solid circles are 3D simulations, and solid colored symbols are average values for beads (n = 21), aggregates (n = 15), and oil droplets (n = 18). Deviations from experimental data to the linear Stokes’ model are significantly larger (R2 = −1.86 and RAE = 1.018) than deviations to the nonlinear model including the confinement correction (R2 = 0.37 and RAE = 0.53). (B and C) Individual viscous drags (B) and restoring stiffness (C) computed from experiments and simulations for individual droplets of various sizes in the cytoplasm. Hollow circles indicate the linear Stokes’ model predictions for the oil droplets of various sizes in the experiments. Dashed lines in B and C guide the eyes for a perfect match between experiment and models.
	Fig. 5. Impact of slip or stick boundary conditions for the influence of cell confinement on large object mobility. (A–C) Simulated streamlines and flow patterns of the cytoplasm for various boundary conditions on the oil droplet and cell surfaces. (D) Slippage over the boundaries increases the flow speed for all confinement ratios. The magnitude and direction of the pulling force are set to be the same for all spheres of different sizes. (E and F) Viscous drag and restoring stiffness grow in a nonlinear manner for all types of boundary conditions, but the values of viscoelastic parameters are smaller when the fluid can slip over surfaces. Arrowheads in the simulations are proportional to the speed. (Scale bar, 30 µm.)
	Fig. 6. Cytoplasm viscoelastic properties are heterogeneous and anisotropic depending on object position. (A) Simulation of viscous drags experienced along the pulling force axis (x-axis) for objects positioned with offsets along the force axis or orthogonal to this axis (Z-axis). (B) Simulations of viscous drags experienced by objects of bigger or smaller sizes. (C) Simulation of fluid hydrodynamics interaction with the cell surface as the sphere is pulled toward or away from the surface. (D) Measured viscous drags and restoring stiffness for oil droplets pulled along the x-axis starting from different initial positions (n = 47 pulls, from four cells). The values of viscoelastic parameters have been renormalized to the values in the cell center, and experimental results are binned and overlaid with simulation results. Error bars correspond to the SD of data. (Scale bar, 30 µm.)

References [+] :

Al Jord, Cytoplasmic forces functionally reorganize nuclear condensates in oocytes. 2022, Pubmed