Nédélec F (2002), Computer simulations reveal motor properties ge...

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J Cell Biol 2002 Sep 16;1586:1005-15. doi: 10.1083/jcb.200202051.

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Computer simulations reveal motor properties generating stable antiparallel microtubule interactions.

Nédélec F .

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An aster of microtubules is a set of flexible polar filaments with dynamic plus ends that irradiate from a common location at which the minus ends of the filaments are found. Processive soluble oligomeric motor complexes can bind simultaneously to two microtubules, and thus exert forces between two asters. Using computer simulations, I have explored systematically the possible steady-state regimes reached by two asters under the action of various kinds of oligomeric motors. As expected, motor complexes can induce the asters to fuse, for example when the complexes consist only of minus end-directed motors, or to fully separate, when the motors are plus end directed. More surprisingly, complexes made of two motors of opposite directionalities can also lead to antiparallel interactions between overlapping microtubules that are stable and sustained, like those seen in mitotic spindle structures. This suggests that such heterocomplexes could have a significant biological role, if they exist in the cell.

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Species referenced: Xenopus
Genes referenced: fubp1

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	Figure 1. Summary of the screens. Screen 1 was performed with two kinds of homocomplexes, with all sorts of configurations of minus or plus end–directed motors. It produced fusion of the asters or their full separation. Screen 2 is inspired by the putative configuration of the biological motors involved in the spindle. Screen 3a was performed with one kind of heterocomplex. It produced fusion, full separation, oscillations, and one type of nonfused stable interaction, solution S1. To achieve S1, the speeds of the motors u and v need to satisfy u + v < 0 and u × v < 0, as depicted in the diagram. Screen 3b is a variation in which the motors could hold on to the microtubule ends. Four solutions are found, as discussed in the text.
	Figure 4. Symmetry arguments. (A) Two asters can have antiparallel overlaps, but also parallel ones, when they are close. (B) On an antiparallel overlap, heterocomplexes of speeds u and v produce attractive force if u + v < 0, or repulsive force if u + v > 0. Both possible motor configurations produce forces in the same direction. (C) On a parallel overlap, if u ≠ v, the two configurations result in opposite forces. If they are equally probable, these forces cancel each other. A homocomplex (u = v) does not produce any force on parallel microtubules and stabilizes the overlap.
	Figure 2. Examples of stable interactions between dynamic asters with heterocomplexes. (Top) Solutions of type S1. The speeds (μm/s) of the two motors forming the complex are as follows: left, 0.35 and -0.91; middle, 0.31 and −0.73; and right, 0.6 and −0.83. (Bottom) Example of solution S2 speeds are as follows: left, 0.95 and −0.45; middle, 0.47 and −0.45; and right, 0.89 and −0.64. Below each example is plotted the distance between the two asters (μm) as a function of time (s). It is not possible to distinguish from these views the different solutions. See animations at (http://www.embl-heidelberg.de/ExternalInfo/nedelec/asters).
	Figure 6. Probing the constraints on the speeds. Each symbol represents one simulation and is plotted here as a function of the unloaded speeds (Vmax) of the two motors in the complex. Dots, S1 produced in screen 3a; circles, S2 produced in screen 3b, in which the motor could stay attached only to growing microtubules; pluses, S2 produced in screen 3c when the motor could stay attached also to shrinking ends.
	Figure 3. The balance of forces in the solutions. Schematic asters in 1D only have two opposing microtubules radiating from a common center represented by a black diamond. All solutions are built from one kind of heterocomplex with two speeds u and v, which must satisfy the conditions specified here. Solution S1 is found even when motors immediately detach from the end of the microtubules, whereas the others are obtained when the motors can stay at the end (in this situation, u or v is replaced by e). Pushing or pulling is schematically represented here by the tilt of the complex, which is a consequence of the relative movement of both motors. The attractive or repulsive nature of the forces can be deducted by mentally trying to restore the complexes in a vertical position.
	Figure 5. Reliability of a solution S1. Figures produced by 49 simulations, all performed with the same parameter set, but with different initial configurations and random number sequences. The figures are all similar, showing the reliability in which the parameter set determines the evolution of the system toward a unique interaction configuration. Each picture covers 30 × 30 μm.
	Figure 7. The zipper effect. Schematically, the action of homocomplexes on two microtubules produces parallel microtubule overlap, whereas heterocomplexes produce antiparallel overlaps.

References [+] :

Bayley, A simple formulation of microtubule dynamics: quantitative implications of the dynamic instability of microtubule populations in vivo and in vitro. 1989, Pubmed