Physical Forces Determining the Persistency and Centering Precision of Microtubule Asters

Abstract

In early embryos, microtubules form star-shaped aster structures that can measure up to hundreds of micrometres, and move at high speeds to find the geometrical centre of the cell. This process, known as aster centration, is essential for the fidelity of cell division and development, but how cells succeed in moving these large structures through their crowded and fluctuating cytoplasm remains unclear. Here, we demonstrate that the positional fluctuations of migrating sea urchin sperm asters are small, anisotropic, and associated with the stochasticity of dynein-dependent forces moving the aster. Using in vivo magnetic tweezers to directly measure aster forces inside cells, we derive a linear aster force-velocity relationship and provide evidence for a spring-like active mechanism stabilizing the transverse position of the asters. The large frictional coefficient and spring constant quantitatively account for the amplitude and growth characteristics of athermal positional fluctuations, demonstrating that aster mechanics ensure noise suppression to promote persistent and precise centration. These findings define generic biophysical regimes of active cytoskeletal mechanics underlying the accuracy of cell division and early embryonic development.

Fig. 1. Fluctuation analysis of centering microtubule asters.

(a and b) High-resolution tracking of sperm microtubule asters during the constant speed centration phase. The representative 3 min trajectory corresponds to 3600 time points. Aster XY position was defined using X as the centering axis. (c) PDFs of residual displacements along X and Y for different δt. Bold lines are best-fit Gaussian distributions. (d) X and Y MSrDs for control and Ciliobrevin D-treated samples plotted as a function of δt in log scale. The broken line indicates a slope of 1. Inset: Transverse MSrD (blue curve) of controls superimposed with a fit of the model from Eq. 1 (broken line), plotted on a linear scale. The absolute magnitude of the residual error between the fit and the data is also depicted (green curve). (e) Contributions of cytoskeletal components to aster positional fluctuations. The fluctuation amplitude was characterized by computing the MSrD at δt=5 sec. Error bars represent standard deviations.

Fig. 2. Force-velocity relationships of microtubule asters.

(a) Aggregates of injected magnetic beads were targeted to the aster center to directly apply magnetic forces to centering asters. (b-g) External magnetic forces were applied to asters either against (b-d) or along (e-g) the centering direction. The 1D kymographs (c and f) and time-evolution of aster XY positions (d and g) show how applied forces consistently change aster longitudinal speed. (h) Aster longitudinal speed V_x plotted as a function of external force amplitude. N=71 measurements from 22 cells. The red broken line indicates a linear fit.

Fig. 3. Direct demonstration of a transverse feedback stabilizing asters along their centering direction.

(a and b) External forces were applied orthogonally to the centering direction along the Y-axis for 140 sec. The applied force causes a drift towards the magnet tip. (c) Aster Y saturation (shown in b) plotted as a function of external force amplitude. N=10 measurements from 10 cells. The spring constant κ=59 pN/μm was determined from the slope of the linear fit (red broken line). (d) Recovery dynamics of aster Y position. Aster Y position after force cessation was plotted as a function of time. N=10 measurements from 10 cells. Solid lines indicate best fits with exponential function (eq. S6), yielding a mean recovery timescale τ_r = 72 +/- 18 sec. Inset: Recovery timescale plotted as a function of Y saturation. The correlation analysis indicates that there is no correlation between the two variables.

Fig. 4. Aster mechanics ensure fast, persistent and precise aster centration.

The large frictional coefficient of asters suppresses active fluctuations along the longitudinal axis. This process was analyzed using a simple Poisson model, in which a single dynein-force generation event causes an aster step motion (see main and supplementary text). Given this large drag, asters must exert large net endogenous forces to move at high speed in the cytoplasm. Along the transverse axis, fluctuations are further suppressed by a dynein-dependent feedback mechanism, which stabilizes the centering direction with respect to cell geometry.