2012/10/31 by Björn Zelinski, Nina Müller, Jan Kierfeld · 20 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Biology #Bounded function #Cellular Mechanics and Interactions #Classical mechanics #Dynamics (music) #Mathematical analysis #Mathematics #Mechanics #Microtubule #Microtubule and mitosis dynamics #Microtubule polymerization #Photosynthetic Processes and Mechanisms #Physics #Tubulin #physics.bio-ph #q-bio.SC
paper · pdf · doi:10.1103/physreve.86.041918
published in Physical Review E 86(4), 041918 (American Physical Society)
openalex publication_date 2012/10/31 · arxiv created 2012/12/14 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the microtubule polymerization dynamics with catastrophe and rescue events for three different confinement scenarios, which mimic typical cellular environments: (i) The microtubule is confined by rigid and fixed walls, (ii) it grows under constant force, and (iii) it grows against an elastic obstacle with a linearly increasing force. We use realistic catastrophe models and analyze the microtubule dynamics, the resulting microtubule length distributions, and force generation by stochastic and mean field calculations; in addition, we perform stochastic simulations. Freely growing microtubules exhibit a phase of bounded growth with finite microtubule length and a phase of unbounded growth. The main results for the three confinement scenarios are as follows: (i) In confinement by fixed rigid walls, we find exponentially decreasing or increasing stationary microtubule length distributions instead of bounded or unbounded phases, respectively. We introduce a realistic model for wall-induced catastrophes and investigate the behavior of the average length as a function of microtubule growth parameters. (ii) Under a constant force, the boundary between bounded and unbounded growth is shifted to higher tubulin concentrations and rescue rates. The critical force f(c) for the transition from unbounded to bounded growth increases logarithmically with tubulin concentration and the rescue rate, and it is smaller than the stall force. (iii) For microtubule growth against an elastic obstacle, the microtubule length and polymerization force can be regulated by microtubule growth parameters. For zero rescue rate, we find that the average polymerization force depends logarithmically on the tubulin concentration and is always smaller than the stall force in the absence of catastrophes and rescues. For a nonzero rescue rate, we find a sharply peaked steady-state length distribution, which is tightly controlled by microtubule growth parameters. The corresponding average microtubule length self-organizes such that the average polymerization force equals the critical force f(c) for the transition from unbounded to bounded growth. We also investigate the force dynamics if growth parameters are perturbed in dilution experiments. Finally, we show the robustness of our results against changes of catastrophe models and load distribution factors.