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First published online November 8, 2006
doi: 10.1242/10.1242/jcs.03240

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Insights into cytoskeletal behavior from computational modeling of dynamic microtubules in a cell-like environment

¹ Interdisciplinary Center for the Study of Biocomplexity, University of Notre Dame, Notre Dame, IN 46556 USA
² Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, IN 46556 USA
³ Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556 USA

View larger version (40K): [in a new window]   Fig. 1. Recapitulating dynamic instability. (A) Snapshots of the simulation at different time steps (T). The MTs grow from seeds at left towards the `cell' edge (right). The colors describe the state (red, GTP; green, GDP) of each subunit. At early times, when free tubulin is near the initial value, MTs grow persistently. As the polymer fraction increases and the concentration of free tubulin drops, catastrophe becomes more frequent. Eventually the steady-state is reached, and the system behavior exhibits behavior very similar to experimentally observed dynamic instability (see Movie 1, supplementary material). (B,C) Comparison between life history plots obtained experimentally in vitro (B) and with our model (C). Experimental data were adapted from Fygenson et al. (Fygenson et al., 1994). C shows three adjacent steady-state MTs from the simulation shown in (A). In this simulation, parameters were chosen arbitrarily; all other simulations reported in this manuscript are correlated to physiological concentrations and dimensions as described in Materials and Methods.

View larger version (23K): [in a new window]   Fig. 2. Relationship between the concentration of total tubulin ([Tu]total), the number of MTs and the behavior of MTs in a spatially constrained environment. (A-D) Life history plots of representative MTs in simulations run under the indicated conditions. (E,F) Distribution of MT lengths taken from a series of simulations conducted under the indicated conditions.

View larger version (13K): [in a new window]   Fig. 3. Relationships between total tubulin and soluble tubulin ([Tu]soluble) at steady-state. (A) Classically expected behavior. Note that little polymer is seen until the critical concentration (Cc) is achieved. At total tubulin concentrations above Cc, all additional tubulin is incorporated into polymer, and the concentration of unpolymerized tubulin remains at Cc. See Materials and Methods for the equations used to plot these curves. (B) Relationship observed in our simulations. Solid red line: system without spatial confinement. Dashed red line: system with spatial confinement. The dotted grey line gives Cc (i.e. [Tu]soluble) that is asymptotically approached as [Tu]total increases. Notice that, in confined systems there is no easily observed Cc. Instead, the concentration of free tubulin continues to rise as total tubulin rises, at first slowly, and then more steeply. The curves in B are not fits to an equation but are provided to guide the eye as it follows the progression of the data.

View larger version (18K): [in a new window]   Fig. 4. Dependence of MT behavior on the concentration of soluble tubulin ([Tu]sol) available at steady-state. (A) Life-history plots of individual MTs at different values of [Tu]soluble. * and **, average length of MTs at steady-state in 4.1 µM and 4.7 µM free tubulin, respectively. At 6.4 µM free tubulin, there is no steady-state length – the mass of polymer increases with time (MT growth is `unbound'; see also supplementary material Fig. S1); (B) relationship between [Tu]soluble and the mean MT length at steady-state. (C) Relationship between persistent growth and [Tu]soluble. The data plotted on the y-axis give average rates of increase in polymer length as a function of [Tu]soluble. The concentration of free tubulin required for the transition to persistent growth is indicated by the x-axis intercept of the dashed line. In B and C, error bars give the standard deviation of values observed from 50 different simulations at the indicated [Tu]soluble. Notice that, in all three panels, the MTs do not compete with each other for free tubulin (because free tubulin is held constant at the indicated value), and the cell size is made so large so that no MTs interact with the edge during the course of the simulation. This is similar to an experimental situation in vitro in which the pool of free tubulin is not depleted during the time course of the experiment.

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