Limits...
Equilibria of idealized confined astral microtubules and coupled spindle poles.

Maly IV - PLoS ONE (2012)

Bottom Line: It is found that depending on parameters, the symmetric position of the spindle can be stable or unstable.If they are not, then it is necessary to ask what forces external to the microtubule cytoskeleton counteract the bending effects sufficiently to actively establish symmetry.Conversely, regarding the cases with asymmetry, it is now necessary to investigate whether the cell controls the microtubule parameters so that the bending favors asymmetry apart from any forces that are external to the microtubule cytoskeleton.

View Article: PubMed Central - PubMed

Affiliation: Department of Computational and Systems Biology, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America. ivanvmaly@gmail.com

ABSTRACT
Positioning of the mitotic spindle through the interaction of astral microtubules with the cell boundary often determines whether the cell division will be symmetric or asymmetric. This process plays a crucial role in development. In this paper, a numerical model is presented that deals with the force exerted on the spindle by astral microtubules that are bent by virtue of their confinement within the cell boundary. It is found that depending on parameters, the symmetric position of the spindle can be stable or unstable. Asymmetric stable equilibria also exist, and two or more stable positions can exist simultaneously. The theory poses new types of questions for experimental research. Regarding the cases of symmetric spindle positioning, it is necessary to ask whether the microtubule parameters are controlled by the cell so that the bending mechanics favors symmetry. If they are not, then it is necessary to ask what forces external to the microtubule cytoskeleton counteract the bending effects sufficiently to actively establish symmetry. Conversely, regarding the cases with asymmetry, it is now necessary to investigate whether the cell controls the microtubule parameters so that the bending favors asymmetry apart from any forces that are external to the microtubule cytoskeleton.

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Limiting case of θmax = π, long microtubules.(A) Pole force function. (B) Spindle force function. (C, D) Equilibrium conformations. L = 1.1 R, S = 0.3 R. Plotting conventions as in Fig. 3.
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pone-0038921-g004: Limiting case of θmax = π, long microtubules.(A) Pole force function. (B) Spindle force function. (C, D) Equilibrium conformations. L = 1.1 R, S = 0.3 R. Plotting conventions as in Fig. 3.

Mentions: The positioning of an isolated complete aster with comparatively long microtubules was considered in our interphase model [20]. In this case, considered now in application to the isolated spindle pole, the pole force function has a root at approximately xp = 2(L–R): a more centrally positioned pole is attracted to the cell margin, while a more eccentrically positioned one is repelled. Considering now the spindle with such an aster at each pole, one can observe that the presence of the root does not affect the stability of symmetry. Like in the case of short microtubules (Fig. 3), the pole force function is still monotonically decreasing for xp>0, albeit it now changes sign (Fig. 4A). Thus, the symmetry of the spindle will be stable.


Equilibria of idealized confined astral microtubules and coupled spindle poles.

Maly IV - PLoS ONE (2012)

Limiting case of θmax = π, long microtubules.(A) Pole force function. (B) Spindle force function. (C, D) Equilibrium conformations. L = 1.1 R, S = 0.3 R. Plotting conventions as in Fig. 3.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3375304&req=5

pone-0038921-g004: Limiting case of θmax = π, long microtubules.(A) Pole force function. (B) Spindle force function. (C, D) Equilibrium conformations. L = 1.1 R, S = 0.3 R. Plotting conventions as in Fig. 3.
Mentions: The positioning of an isolated complete aster with comparatively long microtubules was considered in our interphase model [20]. In this case, considered now in application to the isolated spindle pole, the pole force function has a root at approximately xp = 2(L–R): a more centrally positioned pole is attracted to the cell margin, while a more eccentrically positioned one is repelled. Considering now the spindle with such an aster at each pole, one can observe that the presence of the root does not affect the stability of symmetry. Like in the case of short microtubules (Fig. 3), the pole force function is still monotonically decreasing for xp>0, albeit it now changes sign (Fig. 4A). Thus, the symmetry of the spindle will be stable.

Bottom Line: It is found that depending on parameters, the symmetric position of the spindle can be stable or unstable.If they are not, then it is necessary to ask what forces external to the microtubule cytoskeleton counteract the bending effects sufficiently to actively establish symmetry.Conversely, regarding the cases with asymmetry, it is now necessary to investigate whether the cell controls the microtubule parameters so that the bending favors asymmetry apart from any forces that are external to the microtubule cytoskeleton.

View Article: PubMed Central - PubMed

Affiliation: Department of Computational and Systems Biology, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America. ivanvmaly@gmail.com

ABSTRACT
Positioning of the mitotic spindle through the interaction of astral microtubules with the cell boundary often determines whether the cell division will be symmetric or asymmetric. This process plays a crucial role in development. In this paper, a numerical model is presented that deals with the force exerted on the spindle by astral microtubules that are bent by virtue of their confinement within the cell boundary. It is found that depending on parameters, the symmetric position of the spindle can be stable or unstable. Asymmetric stable equilibria also exist, and two or more stable positions can exist simultaneously. The theory poses new types of questions for experimental research. Regarding the cases of symmetric spindle positioning, it is necessary to ask whether the microtubule parameters are controlled by the cell so that the bending mechanics favors symmetry. If they are not, then it is necessary to ask what forces external to the microtubule cytoskeleton counteract the bending effects sufficiently to actively establish symmetry. Conversely, regarding the cases with asymmetry, it is now necessary to investigate whether the cell controls the microtubule parameters so that the bending favors asymmetry apart from any forces that are external to the microtubule cytoskeleton.

Show MeSH