Microtubule length and dynamics: Boundary effect and properties of extended radial array

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Abstract

In interphase cells, microtubules (MT) form an extended radial array. The length of individual MTs in living cells exhibits substantial stochastic fluctuations, while the average length distribution in a cell remains nearly constant. We present a quantitative model that describes the relation of the MT length and dynamics in the steady state in the cell using the minimal set of parameters (cell radius, tubulin concentration, critical concentration for plus-end elongation and the number of nucleation sites). The MT array is approximated as a radial system, where minus-ends of MTs are associated with nucleation sites on the centrosome, while plus ends grow and shorten. Dynamic instability of MT plus ends is approximated as a random walk process with boundary conditions; the behavior of an MT array is quantified using diffusion and drift coefficients (Vorobjev et al., 1997; Vorobjev et al., 1999). We show that the establishment of the extended steady-state array could be accomplished solely by the limitation of MT growth by the cell margin. For the cell radius, tubulin concentration, critical concentration for plus-end elongation, and the number of nucleation sites we determined the reference point in the parameter space where plus ends of individual MTs, on average, neither elongate nor shorten. In this case, the average MT length is equal to the half of the cell radius. When any parameter is shifted from its reference value, MTs become longer or shorter and, consequently, acquire a positive or negative drift of their plus ends. In the vicinity of the reference point, a change in any parameter has a major effect on the MT length and a rather small effect on the drift. When the average MT length is close to the cell radius, the drift of free plus ends becomes substantial, resulting in processive growth of individual MTs in the internal cytoplasm, accompanied by the apparent stabilization of plus ends at the cell margin. Under these conditions small changes in parameters have a significant impact on the magnitude of the drift. Experimental analysis of MT plus-end dynamics in different cultured cells shows that, in most cases, plus ends display positive drift, which, in the framework of the presented model, is in agreement with the simultaneous presence of long MTs.

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