On the relation of the microtubule length and dynamics: Boundary effect and properties of an extended radial array

Abstract

In interphase cells, microtubules (MT) are long and form 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 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 MT minus ends are associated with the 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 and the behavior of MT array is quantified using diffusion and drift coefficients (Vorobjev et al., 1997, 1999). We show that establishment of the extended steady-state array could be accomplished solely by the limitation of the MT growth by the cell margin. We determined for the cell radius, tubulin concentration, critical concentration for plus end elongation, and number of nucleation sites the reference point in the parameter space where plus ends of individual MT on average neither elongate nor shorten. In this case average length of MT is equal to the half of cell radius. When any parameter is shifted from its reference value MTs become longer or shorter and consequently acquire positive or negative drift of their ends. In the vicinity of reference point, change in any parameter has major effect on the MT length and rather small effect on the drift. When mean length of the MTs is close to the cell radius the drift of the free plus ends becomes substantial, resulting in processive growth of individual MTs in the internal cytoplasm accompanied by apparent stabilization of the plus ends at the cell margin. Under these conditions small changes in parameters have significant impact on the magnitude of drift. Experimental analysis of the MT plus ends 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.