Centrosome centering and decentering by microtubule network rearrangement

Abstract

The centrosome is positioned at the cell center by pushing and pulling forces transmitted by microtubules (MTs). Centrosome decentering is often considered to result from asymmetric, cortical pulling forces exerted in particular by molecular motors on MTs and controlled by external cues affecting the cell cortex locally. Here we used numerical simulations to investigate the possibility that it could equally result from the redistribution of pushing forces due to a reorientation of MTs. We first showed that MT gliding along cell edges and pivoting around the centrosome regulate MT rearrangement and thereby direct the spatial distribution of pushing forces, whereas the number, dynamics, and stiffness of MTs determine the magnitude of these forces. By modulating these parameters, we identified different regimes, involving both pushing and pulling forces, characterized by robust centrosome centering, robust off-centering, or "reactive" positioning. In the last-named conditions, weak asymmetric cues can induce a misbalance of pushing and pulling forces, resulting in an abrupt transition from a centered to an off-centered position. Taken together, these results point to the central role played by the configuration of the MTs on the distribution of pushing forces that position the centrosome. We suggest that asymmetric external cues should not be seen as direct driver of centrosome decentering and cell polarization but instead as inducers of an effective reorganization of the MT network, fostering centrosome motion to the cell periphery.

FIGURE 1:

Centrosome centering by pulling forces. (A) Simulation in which the motors are distributed in the cell. (B) Simulation in which the motors are distributed only on the edge the cell. Dynein motors are shown in green and MTs in black. Right, centrosome positions, indicated by colored points, from blue (0 s) to red (400 s). Left, centrosome trajectories. The gray area is the area filled by motors. (C) Variation of the number of motors for both cytoplasmic and cortical motor distribution. Fifteen trajectories are shown on each plot, in which the number of simulated dyneins is increased from 0 to 7000 with a step of 500. The initial position of the centrosomes was set on an arc axis to make them all visible on a single plot. This should not affect the outcome of the simulation, since the system has rotational symmetry. In all cases, the centrosomes are initially placed at a distance from the center corresponding to half the cell radius. Right, maximal speed reached by the centrosome during each simulation as a function of the number of dyneins for both cortical and cytoplasmic distributions. Each symbol is the result of one simulation, and the lines are guides for the eye.

FIGURE 2:

Centrosome positioning by pulling forces. (A, B) Top, snapshot after 400 s of a centrosome simulated in different geometries: ellipse, rectangle, equilateral triangle, acute isosceles triangles, and isosceles triangle whose base is the longest side. Dyneins are shown in green, MTs in black, and the centrosome in gray. Motors are distributed (A) cytoplasmically or (B) cortically. Bottom, trajectories of centrosomes in 15 simulations for each geometry. Centrosome position is indicated by colored points, from blue (0 s) to red (400 s), in the trajectory plots. The gray area is the area covered by motors. Black dot indicates the center of gravity of the shape. (C) Left, box plot of the distance of the centrosome to the center of gravity after 400 s for each geometry for cytoplasmic and cortical distributions (full and empty boxes, respectively). Right, strip chart of the final speed of the centrosome in the simulations for all geometries for cytoplasmic and cortical distributions (full and empty triangles, respectively).

FIGURE 3:

MT network rearrangement in the presence of pushing forces. (A) Left, schematic representation of a MT plus end gliding at the cortex and a MT pivoting around its anchor point in the centrosome. MTs and centrosomal complex are in green, actin cortex in red. Right, snapshots of simulations (400 s) covering all the possibilities when pivoting and gliding are independently allowed or not. (B) Trajectories of centrosomes in 15 simulations in which the centrosome was initially positioned at different distances from the cell center and for each of the pivoting/gliding conditions. The center of each disk is marked with a black point. (C) Left, trajectories of centrosomes in simulations with varied pivoting stiffness when gliding is not allowed. Pivoting stiffness is varied geometrically from 0 to 150 pN/μm from left to right along the arc. Right, centrosome positioning as a function of pivoting stiffness, measured by the distance to the cell center. The dashed line indicates the initial centrosome–center distance. (D) Left, trajectories of the centrosome in simulations with varying gliding stiffness when pivoting is not allowed. Gliding stiffness is varied geometrically from 0 to 15.5 pN/μm from left to right along the arc. Right, centrosome positioning as a function of gliding stiffness, measured by the distance to the cell center. The dotted line indicates the initial centrosome–center distance. In all of the plots, the color of the centrosome trajectories indicates time, from blue (0 s) to red (400 s).

FIGURE 4:

Efficiency of pushing forces with pivoting and gliding allowed. (A–C) Simulations in which one parameter was geometrically varied: MT rigidity, from 1 to 300 pN/μm²; MT unloaded catastrophe rate, from 0.01 to 0.06 s⁻¹; and number of MTs in the aster, from 15 to 350. Left, two exemplary simulations (400 s) obtained by varying one parameter in each case. Middle, trajectories of centrosomes obtained by varying one parameter, displayed along an arc, with increasing values from left to right. For each trajectory, time is indicated by the color, from blue (0 s) to red (400 s). The center of each disk is marked with a black dot. Right, centrosome positioning as a function of various parameters, measured by the distance to the cell center. The dotted lines represent the initial centrosome–center distance (half of the confinement radius).

FIGURE 5:

Transitions between centering and decentering regimes. (A–E) Simulations in which one parameter was geometrically varied: MT rigidity, from 1 to 260 pN/μm²; MT unloaded catastrophe rate, from 0.01–0.06 s⁻¹; number of MTs, from 15 to 350; MT gliding stiffness while pivoting is not allowed, from 0 to 10 pN/μm; and MT pivoting stiffness when gliding is not allowed, from 0 to 110 pN/μm. In each case, 100 cytoplasmic dynein motors were randomly positioned in the cell and one parameter of the system was varied systematically. Cell radius is 10 μm in A and 7 μm in B–E. Left, exemplary simulations for two different outcomes observed while varying a parameter. Middle, trajectories of simulations obtained while varying a parameter, displayed along an arc, with values increasing from left to right. For each trajectory, time is indicated by the color, from blue (0 s) to red (400 s). The center of each disk is marked with a black dot. Right, centrosome positioning as a function of various parameters, measured by the distance to the cell center. The dotted line represents the initial centrosome–center distance (half of the confinement radius). In A–C, MTs were allowed to pivot and glide.

FIGURE 6:

Sensitivity of centrosome positioning to external cues, modulated by internal properties. (A, B) The centrosome is initially placed in the center of the cell and is decentered. The cell has a radius of 10 μm and contains 300 randomly positioned cytoplasmic dyneins. MT rigidity is set to 15 pN/μm². (A) Simulations in which MT pivoting and gliding are not allowed (top) and MT pivoting and gliding are allowed (bottom). Left, simulations (400 s) in which different numbers (5, 130, 400, and 800) of cortical dynein have been added on a 60° crescent at the bottom part of the cell. Right, trajectories of centrosomes, in a color representing the number of dyneins in the cell from 0 (green) to 1000 (red). The position of the cortical crescent was shifted to make it possible to distinguish the different trajectories on a single plot. (B) Left, schematic representation of MT network configuration when MT pivoting and gliding are not allowed (blue) and when both are allowed (purple). Cortical dynein molecules are represented in black. Right, final distance of centrosome to cell center according to the number of cortical dyneins placed on the crescent when gliding and pivoting are not allowed (blue) and allowed (purple). The black horizontal dashed line indicates the threshold above which we considered the centrosome to be off center. Colored vertical dashed lines represent threshold number of motors necessary to be decentered in each case.